5.0 The NMR Experiment

Nuclear Properties

We are used to thinking of chemical properties in terms of elements (atomic number).

For nuclear properties we have to think in terms of isotopes (mass number) - different isotopes of the same element have different nuclear properties. The main nuclear property we are interested in connection with NMR is the nuclear angular momentum spin quantum number I, the "spin" of the nucleus.

I = 0 no spin, the nucleus has no magnetic moment and no NMR properties

I > 0 the nucleus has spin (I = 1/2, 1, 3/2, 2, etc) and a magnetic dipole μ, and thus may be suitable for NMR observation.

Nuclei with I = 1/2 have especially advantageous NMR properties, and the vast majority of all NMR experiments are done with such isotopes.

Nuclei with I > 0 have angular momentum P (spinning mass) whose direction is the spin axis. The angular momentum is quantized, and can only have one value:

Nuclei with I > 0 also have a magnetic dipole μ (spinning charge). For the NMR experiment it is the ratio of μ to P that matters (much in the way that m/e is what matters in mass spectrometry). We define γ, the gyromagnetic ratio:

Interaction of Nuclei with a Magnetic Field

When we place a nucleus with spin in a magnetic field the nuclei tend to align with the field. The observable component of the angular momentum Pz is also quantized, and can only have the following values:

Quantum restrictions prevent the nuclei from aligning exactly with Bo, since both the angular momentum (P) and the observable component (Pz) are quantized. For spin ½ nuclei there is a tip angle of 54.7°.

The nuclei precess around the direction of Bo, with a frequency νo (Larmor precession frequency). The frequency is a function of the magnetic field strength (Bo), the angular momentum and the magnetic dipole (Gyromagnetic ratio γ).

Interaction with Radiofrequency

A radiofrequency (at the Larmor precession frequency ν0) applied in the x-direction causes transitions between the spin states if νRF = νo. These transitions are detected by the spectrometer and plotted as an NMR spectrum.

The NMR Spectrometer

An NMR spectrometer consists of a powerful magnet, and the associated electronics to

control the properties of the magnet and create and detect radiofrequency signals. In the first spectrometers (up to 60 MHz proton frequency) permanent magnets were used, then electromagnets (to 100 MHz), and now most spectrometers use superconducting magnets to achieve field strengths which give proton resonances from 200 to as high as

900 MHz. The magnetic field must be very stable over a period of hours and very homogeneous over the sample volume (better than 1 part in 109). A complex array of tuning coils is mounted in the magnet and probe to correct for magnetic field inhomogeneities. The radiofrequency generators (at least two are required) must also be very stable, and capable of providing frequencies accurate to 1 part in 109, and with

short (microsecond range) very accurately timed pulses. All of these very stringent requirements, together with the inherent insensitivity of the NMR experiment, mean that NMR spectrometers have very complex electronics and are hence the most expensive of all common analytic devices used by chemists, running from $100K to $3M (physicists,

of course, use analytic devices that cost billions of dollars).

At the heart of an NMR spectrometer is the probe, which is a removable cylinder inserted into the center of the magnet. The probe contains: the sample tube holder and air spinner outlets; the radiofrequency coils for signal detection, decoupler irradiation,

and locking of the magnetic field; the electronics, dewar, gas inlets and outlets for cooling and heating of the sample; the tuning coils for fine adjustments of the magnetic

field, as well as (in advanced probes) coils for producing precise field gradients. The very

latest probes have the electronics for signal detection cooled to liquid helium temperatures (cryoprobes) to provide substantially improved sensitivity (at a factor of 10 increase in cost). Just an ordinary probe can cost more than a low-end IR or UV spectrometer, and a cryoprobe alone can cost as much as an entire mass spectrometer

or X-ray diffraction instrument.

Detection of NMR Signals

The first generation of NMR spectrometers detected the NMR signals in much the same way as was done for the earlier spectroscopic methods such as IR and UV/VIS - the instrument scans through the frequency region of interest (or keeps the frequency constant and scans the magnetic field, a technically easier pocess used in the first spectrometers). When there is a frequency match (resonance: νRF = νo) the transitions

are detected by the spectrometer, and, after signal processing, are plotted as an NMR spectrum.

Advances in microwave electronics made possible a much more efficient way of

detecting NMR signals in which frequencies are not scanned, but instead a very short powerful pulse is applied to the sample. The pulse is short enough that its frequency is not well defined to within a few thousand Hertz, so it interacts with all of the nuclei of one isotope in the sample. The pulse duration is accurately specified so that the

precession of the nuclei around the axis of the pulse corresponds to a well defined angle (say 90 degrees).

The pulse rotates the excess magnetization (resulting from the higher population of magnetic nuclei in the more stable orientation aligned with the magnetic field Bo) from the z-direction to the x-y plane. This magnetization vector rotates around the x-y plane at the Larmor precession frequency. The fluctuating magnetic field produced by these nuclei is detected by the spectrometer. Each set of nuclei with a distinct chemical shift in the sample has its own precession frequency (the chemical shift), and the spectrometer detects the sum of all of these oscillations (the Free Induction Decay, or FID). The FID is then mathematically manipulated (Fourier transformation) to detect the individual frequencies, which are plotted as a spectrum.

Chemical Shift

Circulation of electrons around the nucleus creates local magnetic fields which shield the nucleus from the external field Bo. The extent of shielding depends on the local chemical environment. Thus NMR signals show a chemical shift. The first NMR spectrometers used continuous wave detection, initially by using a magnetic field sweep to scan through the spectrum, later frequency sweep electronics were developed. All modern spectrometers use pulse techniques to detect NMR spectra.

The Larmour precession frequency νo depends on the magnetic field strength. Thus at a magnet strength of 1.41 Tesla protons resonate at a frequency of 60 MHz, at 2.35 Tesla at 100 MHz, and so on. Although Hz are the fundamental energy unit of NMR

spectroscopy, the use of Hz has the disadvantage that the position of a peak is dependent on the magnetic field strength. This point is illustrated by the spectra of 2-methyl-2-butanol shown below at several different field strengths, plotted at a constant Hz scale.

For this reason, the distance between the reference signal (Me4Si) and the position of a specific peak in the spectrum (the chemical shift) is not reported in Hz, but rather in dimensionless units of δ, which is the same on all spectrometers. Note that in the above spectra the multiplet separations (doublet, quartet) are the same at all fields, whereas in

the spectra below the chemical seperations are equal

Coupling

Neighboring magnetic nuclei can also perturb the local magnetic field, so we observe J-coupling, which causes multiplet structure for NMR signals. J coupling is mutual (JAX = JXA). Coupling constants are independent of the magnetic field, and thus should

always be reported in Hz.

Multiplet structure resulting from several couplings to a given nucleus, however, often depends strongly on the chemical shifts between the nuclei, with larger chemical shifts usually leading to simpler spectra. Since chemical shifts (in energy units like Hz)

increase with magnetic field strength, higher field magnets typically give much simpler and more easily interpreted NMR spectra. AB,AB2, ABX, ABX3, AA'BB'

Sensitivity

The population difference between the spin states is small (ca 10-5), so NMR signals are inherently weak.

The energy separation between the two spin states of a spin ½ nucleus is directly proportional to the strength of the magnetic field (ΔE = μBo). This in turns affects the Boltzmann population differences of the α and β spin states. Thus stronger magnetic fields result in large increases in the strength of the NMR signal.

Relaxation

Relaxation of spin for I = 1/2 nuclei is slow (T1 = 0.1 to 100 sec). This may further weaken NMR signals when the RF field is applied repeatedly (as it usually is), since the population of the spin states can become equalized if nuclei cannot fully relax back to their normal populations between pulses (saturation). See Section 8-TECH-1.

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5.1 Integration of Proton NMR Spectra

© Copyright Hans J. Reich 2012

All Rights Reserved University of Wisconsin

NMR is unique among common spectroscopic methods in that signal intensities are directly proportional to the number of nuclei causing the signal (provided certain conditions are met). In other words, all absorption coefficients for a given nucleus are

identical. This is why proton NMR spectra are routinely integrated, whereas IR and UV spectra are not. A typical integrated spectrum is shown below, together with an analysis.

The vertical displacement of the integral gives the relative number of protons It is not possible to determine the absolute numbers without additional information (such as a molecular formula). In the example above, if we add up all of the integrals, we get 74.3. Dividing each integral by the smallest one (15.2) gives a ratio of 2.38/1.0/1.50 for the three signals. Multiplying by two gives 4.76/2.0/3.03, which is close to the integral numbers (5/2/3) expected for a pure compound. However, there is nothing in the spectrum that rules out 10/4/6 or higher multiples. If we have a molecular formula (in this case C8H10O2S), dividing by the number of hydrogens gives 7.4 mm per H. We can then determine the number of protons corresponding to each multiplet by rounding to the nearest integer. It is generally possible to reliably distinguish signals with intensities of 1 to 10 or so, but it becomes progressively harder to make a correct assignment as

the number of protons in a multiplet increases beyond 10, because of the inherent

inaccuracies in the method.

The two parts of aromatic proton integral at δ 7.6 and 7.9 can be separately measured as a 2:3 ratio of ortho to meta+para protons.

If given the molecular formula (C8H10O2S), we know there are 10H in molecule

Total area: 36.2 + 15.2 + 22.8 = 74.2 mm

Thus 7.4 mm per H

36.2 / 7.4 = 4.89 i.e. 5H

15.2 / 7.4 = 2.05 i.e. 2H 22.8 / 7.4 = 3.08 i.e. 3H

Accuracy of Proton NMR Integrations

The integration of NMR spectra can be carried out with high accuracy, but this is only possible if a number of sources of error are properly handled. On a modern spectrometer accuracy of ±5% can be achieved easily if relaxation issues are handled properly. To get errors of <1% a number of factors have to be considered and optimized.

1. Signal to Noise. The spectrum must have adequate signal to noise to support the level of accuracy required for the experiment.

2. Saturation Effects. NMR spectroscopy has a feature unique among spectroscopic methods, that relaxation processes are relatively slow (on the order of seconds or tenths of seconds), compared to milli, micro, and pico seconds for IR and UV. In other words, once the spectrometer has perturbed the equilibrium population of nuclei by scanning over the resonance frequency or pulsing the nuclei, it takes from 0.1 to 100s of seconds (typically several seconds) for them to return to their original populations (T1 thespin-lattice relaxation time). If power settings are too high (for CW spectra) or pulse angle and repetition rates too high (for FT spectra) then spectra can become saturated, and integrations less accurate, because the relaxation rates of various protons in the sample are different. Saturation effects are particularly severe for small molecules in mobile solvents, because these typically have the longest T1 relaxation times.

To get reliable integrations the NMR spectrum must be acquired in a way that

saturation is avoided. It is not possible to tell whether a spectrum was run appropriately simply by inspection, it is up to the operator to take suitable precautions (such as putting in a 5-10 second pulse delay between scans) if optimal integrations are needed. Fortunately, even a proton spectrum taken without pulse delays will usually give reasonably good integrations (say within 10%). It is important to recognize that integration errors caused by saturation effects will depend on the relative relaxation rates of various protons in a molecule. Errors will be larger when different kinds of protons are being compared (such as aromatic CH to a methyl group), than when the protons are similar or identical in type (e.g. two methyl groups).

3. Line Shape Considerations. NMR signals in an ideally tuned instrument are Lorenzian in shape, so the intensity extends for some distance on both sides of the center of the peak. Integrations must be carried out over a sufficiently wide frequency range to capture enough of the peak for the desired level of accuracy. Thus, if the peak width at half height is 1 Hz, then an integration of ±2.3 Hz from the center of the peak is required to capture 90% of the area, ±5.5 Hz for 95%, ±11 Hz for 98% and ±18Hz for

>99% of the area. This means that peaks that are closely spaced cannot be accurately

integrated by the usual method, but may require line-shape simulations with a program like NUTS or WINDNMR to accurately measure relative peak areas.

4. Digital Resolution. A peak must be defined by an adequate number of points if an

accurate integration is to be obtained. The errors introduced are surprisingly small, and reach 1% if a line with a width at half height of 1 Hz is sampled every 0.5 Hz.

5. Isotopic Satellites. All C-H signals have 13C satellites located ±JC-H/2 from the

center of the peak (JC-H is typically 115-135 Hz, although numbers over 250 Hz are known) Together these satellites make up 1.1% of the area of the central peak (0.55% each). They must be accounted for if integration at the >99% level of accuracy is desired. Larger errors are introduced if the satellites from a nearby very intense peak fall under the signal being integrated. The simplest method to correct this problem is by 13C

decoupling, which compresses the satellites into the central peak. A number of other elements have significant fractions of spin ½ nuclei at natural abundance, and these will also create satellites large enough to interfere with integrations. Most notable are 117/119Sn, 29Si,77Se, 125Te, 199Hg. For more on satellites, see Section 7, Multinuclear

NMR.

There is a bright side to 13C satellites: they can be used as internal standards for the quantitation of very small amounts of isomers or contaminants, since their size relative to the central peak is accurately known.

6. Spinning Sidebands. These can appear at ± the spinning speed in Hz in spectra run on poorly tuned spectrometers and/or with samples in low-quality tubes. They draw intensity from the central peak. SSBs are rarely significant on modern spectrometers.

7. Baseline Slant and Curvature. Under some conditions spectra can show significant distortions of the baseline, which can interfere with obtaining high-quality integrations. Standard NMR work-up programs (like NUTS) have routines for baseline adjustment.

8. Decoupling. When decoupling is being used, as is routinely done for 13C NMR spectra and occasionally for 1H NMR spectra, peak intensities are distorted by Nuclear Overhauser Effects (NOE, see Sect. 8). Integrations of such spectra will not give accurate ratios of peak areas.

Peak Intensities. Under certain conditions, peak heights can also be a quite accurate method of quantitation. For example, if several singlets are being compared, and they all have identical line widths, and the spectra were measured such that there aresufficient data points to define the lineshape of each singlet, then peak heights may be useful, and under ideal conditions more accurate than integrations.

Determining Absolute Amounts by NMR Integration. Although NMR spectra in principle follow Beer's law, it is difficult (although not impossible) to make effective use of the absolute intensities of NMR spectra for quantitation (as is routinely done for UV, and sometimes IR). NMR integrations are always relative. Thus an internal standard must be used to determine reaction yields by NMR integration. A commonly used internal standard for proton NMR spectra is pentachloroethane -- it is a liquid, not

too volatile, and appears in a region of the NMR spectrum (δ 6.11) where there are few signals. It is strongly recommended to avoid using volatile materials like CH2Cl2, CHCl3, C6H6 and others, since it is very difficult to avoid some losses during the transfer process, leading to incorrect (high) concentrations of the substrate.

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5.2 Chemical Shift

© Copyright Hans J. Reich 2012

All Rights Reserved

University of Wisconsin

Fortunately for the chemist, all proton resonances do not occur at the same position. The Larmor precession frequency (νo) varies because the actual magnetic field B at the nucleus is always less than the external field Bo. The origin of this effect is the "superconducting" circulation of electrons in the molecule, which occurs in such a way that a local magnetic field Be is created, which opposes Bo (Be is proportional to Bo). Thus B = Bo - Be. We therefore say that the nucleus is shielded from the external magnetic field. The extent of shielding is influenced by many structural features within the molecule, hence the name chemical shift. Since the extent of shielding is proportional to the external magnetic field Bo, we use field independent units for chemical shifts: δ values, whose units are ppm. Spin-spin splitting is not dependent on the external field, so we use energy units for coupling constants: Hz, or cycles per second (in mathematical formulas radians per second are the natural frequency units for both chemical shifts and couplings).

The Proton Chemical Shift Scale

Experimentally measured proton chemical shifts are referenced to the 1H signal of

tetramethylsilane (Me4Si). For NMR studies in aqueous solution, where Me4Si is not sufficiently soluble, the reference signal usually used is DSS (Me3Si-CH2CH2-SO3

-Na+, Tiers, J. Org. Chem. 1961, 26, 2097). For aqueous solution of cationic substrates (e.g., amino acids) where there may be interactions between the anionic reference compound

and the substrates, an alternatice reference standard, DSA (Me3Si-CH2CH2-NH3+ CF3CO2

-, Nowick Org. Lett. 2003, 5, 3511) has been suggested.

Proton chemical shifts cover a range of over 30 ppm, but the vast majority appear in the region δ 0-10 ppm, where the origin is the chemical shift of tetramethylsilane.

In the original continuous wave (CW) method of measuring NMR spectra, the magnetic field was scanned from left to right, from low to high values. We thus refer to signals on the right as upfield or shielded and signals to the left as downfield or deshielded. Later spectrometers gained the capability of scanning frequency, which then had to decrease from left to right during the scan, hence the "backwards" nature of NMR scales. δ units are defined as follows:

Chemical shifts of all nuclei should be reported using δ values, with frequency and δ

increasing from right to left. Many early papers on proton and multinuclear NMR used the opposite convention (not to mention other references) - in particular the τ scale was used in the early days: δ = 10 - τ. Coupling constants are field independent, and should always be specified in Hz. IUPAC Recommendations.

The chemical shifts of protons on carbon in organic molecules fall in several distinct regions, depending on the nature of adjacent carbon atoms, and the substituents on those carbons. The scale below should be used only as a rough guideline, since there are many examples that fall outside of the indicated ranges. To a first approximation,

protons attached to sp3 and sp carbons appear at 0-5 ppm, whereas those on sp2 carbons appear at 5-10 ppm.

Within these ranges, for a given type of C-H bond (sp3, sp2 or sp) the chemical shift is strongly affected by the presence of electronegative substituents as can be seen in the

methyl shifts summarized below, which range from δ -2 for MeLi to δ 4 for MeF.

The 1H chemical shifts of protons attached to heteroatoms (H-X) show a very wide chemical shift range, with no obvious correlation to the electronegativity of X or the acidity of HX.

Calculation of Proton Chemical Shifts

Parameters for the calculation of proton chemical shifts for many kinds of molecules have been tabulated (see Section 9, Proton NMR Data). All of these work in the same way. We establish the base chemical shift for a reference substance (e.g., ethylene for olefins, benzene for substituted aromatic compounds, methane for alkanes) and tabulate Substituent Chemical Shift values (Δδ) for the introduction of substituents into the reference molecules. Thus for a vinyl proton (C=C-H) there will be parameters for the introduction of substituents cis, trans, or gem to the hydrogen we are calculating, and this leads to reasonable estimations for most molecules, as in the example below (parameters from Section 9-HDATA-6.1). However, when there are strong resonance or other electronic interactions between substituents (as in the β-aminoenone below), or strong conformational effects then the predictions made by these calculations will be less accurate. NOTE: the chemical shifts increments were determined in weakly interacting solvents like CCl4 and CDCl3. They will work poorly for spectra taken in aromatic solvents like benzene or pyridine (see later section on aromatic solvent shifts).

For aliphatic (sp3) C-H proton chemical shifts we can use the Curphy-Morrison table

(Section 9-HDATA-5.1). In this system there are base shifts for CH3 (0.9), CH2 (1.2) and C-H (1.55) protons, and then corrections are applied for all α and β substituents. The corrections for CH3, CH3 and CH protons are slightly different, and no corrections are applied for alkyl groups.

Accuracy of Chemical Shift Calculations

Calculations using simple parameter lists such as in Section 9-HDATA-5.1 and Section 9-HDATA-6.1 will typically give results accurate to within 0.5 ppm, but there are exceptions:

Multiple Substituents: The more parameters you are adding together, and the larger they are, the less accurate the calculation is likely to be. This is especially true for

electronegative substituents like O, N and Cl if they are applied several times to the same proton as the examples below. This is perfectly reasonable, since electron withdrawal from the C-H group becames progressively more difficult as the C-H group becomes more electron deficient.

Cyclic Systems: Calculations are usually poor for cyclic systems, or otherwise

conformationally constrained compounds. The base shift for a CH2 group in an alkane is 1.2 ppm, and this would be the calculated value of any methylene group in a cycloalkane. The actual shift for methylenes in cycloalkanes varies by 1.7 ppm, from δ 0.2 for cyclopropane to δ 1.9 for cyclobutane, although if you ignore cyclopropane and

cyclobutane, the range is only 0.5 ppm. One of the reasons is that in cyclic compounds conformational mobility is greatly restricted, so that less rotational averaging of various chemical shift anisotropic effects occurs. At low temperatures the axial and equatorial hydrogens of cyclohexane differ by 0.5 ppm, the average shift at room temperature is 1.44, close to the standard value of 1.2. Note especially that the protons

on 3-membered rings of all kinds are strongly shifted to lower frequency from the acyclic value.

Even more dramatic chemical shift effects are seen in polycyclic compounds. The Curphy-Morrison calculated values for all of the compunds below would be δ 1.55 (the base value for a methyne group), yet the actual values vary by several ppm.

Cubane and dodecahedrane are especially far from the typical values.

Reproducibility of Proton Chemical Shifts

It is important to understand that the chemical shift of a given proton is not an

invariant property of a molecule (like a melting point or boiling point), but will change depending on the molecular environment. The variability is especially large for NH and OH protons (several ppm), but even for CH protons reported shifts vary by a few tenths of a ppm. This is in part due to changes in measurement conditions, but additional

variability in chemical shift is present in old NMR data (CW spectra) since spectrometer calibrations and spectrum referencing were not nearly as accurate as they are today. Nevertheless, if conditions are rigorously controlled, very high reproducibility of chemical shifts can be achieved. Databases of precise chemical shifts for many biomolecules have been created which facilitate simultaneous detection by NMR in aqueous solution.

Solvent effects. The aromatic solvents benzene and pyridine cause changes in chemical shifts as large as 0.5 to 0.8 ppm compared to less magnetically active solvents like chloroform or acetone. Since the standard solvent for chemical shift parameters like

the Curphy-Morrison ones is CCl4 or CDCl3, expect less accurate calculations for spectra taken in aromatic solvents.

Concentration dependence. Chemical shifts of C-H protons can vary with

concentration, especially if intermolecular hydrogen bonding can occur, as for many amines, alcohols and carboxylic acids. The chemical shifts of protons on oxygen (OH) and nitrogen (NH), which are often directly involved in hydrogen bonding are especially

strongly dependent (several ppm) on concentration, solvent and temperature. Aromatic

molecules can also show significant concentration dependence because of the aromatic solvent effect mentioned above.

Temperature dependence. For molecules that are conformationally flexible, the

populations of conformations change with temperature. Since the chemical shifts of various conformations are different, the chemical shifts will vary with temperature (the observed chemical shift is the weighted average of the shifts of the individual conformations). Temperature will also affect the degree of intermolecular hydrogen

bonding or other types of aggregation, and this provides an additional source of shift changes.

Paramagnetic impurities (unpaired electrons, transition metals with unpaired spins) can cause very large shifts (tens and hundreds of ppm) as well as large amounts of line

broadening. Must avoid these alltogether if you want to get high quality NMR spectra.

Proton Chemical Shift Effects

1. Electronegativity. Proton shifts move downfield when electronegative substituents are attached to the same or an adjacent carbon (see Curphy-Morrison chemical shift table). Alkyl groups behave as if they were weakly electron withdrawing, although this is probably an anisotropy effect.

The chemical shifts of protons attached to sp2 hybridized carbons also reflect charges within the π system (approximately 10 ppm/unit negative or positive charge).

Even without formal charges, resonance interactions can lead to substantial chemical shift changes due to π polarization.

This is especially useful in the interpretation of the NMR chemical shift of protons in

aromatic systems. The protons ortho and para to electron donating and electron withdrawing substituents show distinct upfield and downfield shifts.

2. Lone Pair Interactions. When lone pairs on nitrogen or oxygen are anti to a C-H bond, the proton is shifted upfield (n --> σ* interactions). There is thus a strong conformational dependence of chemical shifts of protons α to heteroatoms. This interaction is one of the reasons that Curphy-Morrison chemical shift calculations work poorly when multiple O or N substituents are attached to one carbon. This effect is also

present in 13C chemical shifts. C-H bonds anti to lone pairs also show Bohlmann bands in the IR spectra, as a result of weakening of the C-H bond by hyperconjugation. For example, the Θ = 180 ° compound shows IR absorption at 2450 cm-1, as well as at 2690-2800 cm-1.

3. Steric Compression. When molecular features cause a proton to be forced close to other protons, or to various functional groups, the proton will in general be deshielded (dispersion interactions). Shifts of this type are hard to distinguish from magnetic

anisotropy interactions.

These shifts are especially large in highly compressed compounds like the "birdcage" molecules. The inside proton in the "out" alcoholA at δ 4.48 is downfield by 0.96 ppm from the model B. Even more striking are the shifts in the "in" alcohol C, where the proton jammed into the OH group at δ 3.55 is downfield by 2.3 ppm from the model D, and the gem partner at δ 0.88 is actually upfield by 0.5 ppm from its position in D,

suggesting a migration of electron density from the sterically compressed inside H to the outside H.

4. Magnetic Anisotropy. Whereas the local circulation of electrons around HA is a

shielding effect (i.e., to the right in the NMR spectrum, -δ), there can be both shielding and deshielding effects on HA from electron motion in other parts of the molecule. We refer to such interactions as magnetic anisotropy effects, since they are caused by anisotropic electron circulation (i.e., the electron circulation is stronger in some

orientations of the molecule in the magnetic field than in others).

The most dramatic examples of anisotropy effects are seen with benzene and other aromatic rings, which cause very large shielding(-δ) effects for protons placed above the

ring, and smaller deshielding (+δ) effects for protons to the side of it. These chemical shift effects occur because electron circulation is stronger when the plane of the benzene ring is perpendicular to the magnetic field than when it is parallel to it

The consequence of magnetic anisotropy effects is to provide a stereochemical component to the chemical shift of a nucleus: the chemical shift changes depending on the spacial relationship between a proton and nearby functional groups. Such effects can be valuable for making stereochemical assignments. Some proposed magnetic anisotropy shielding/deshielding cones are shown below:

1. H. C. Brown, A. Suzuki J. Am. Chem. Soc. 1967, 89, 1933. L. A. Paquette, G. Kretschmer, J. Am. Chem. Soc. 1979, 101,

4655. 2. C. D. Poulter et al. J. Am. Chem. Soc. 1972, 94, 2291.

3. The Thiosulfinyl Group Serves as a Stereogenic Center and Shows Diamagnetic Anisotropy Similar to That of the Sulfinyl

Group: Tanaka, S.; Sugihara, Y.; Sakamoto, A.; Ishii, A.; Nakayama, J.; J. Am. Chem. Soc., 2003, 125, 9024.

4. Magnetic Anisotropy of the Nitro Group by NMR I. Yamaguchi, Mol. Phys. 1963 , 6, 103

Aromatic Chemical Shifts. The ring current in Huckel aromatic systems, i.e., those with 4n + 2 π electrons (2, 6, 10, 14, 18 ...) causes downfield shifts in the plane of

aromatic ring.

When protons are above or below the plane (or in the middle) of the aromatic ring then upfield shift effects are observed.

When a cyclic conjugated system is planar and antiaromatic, i.e., 4n π electrons (4, 8, 12, 16 ... ) then chemical shift effects are in the opposite direction: downfield over the ring, and upfield in the ring plane. This is seen in the Staley 10 and 12-electron methano

annulene cation and anion above, as well as in the 14-electron dihydropyrene below. The normal chemical shift effects are seen in the 10 and 14π-electron systems. In the 12 and 16 π-electron anions the methylene bridge and propyl groups over the ring show very large downfield shifts as a result of the antiaromatic ring current. The paramagnetic ring currents are a consequence of the small HOMO-LUMO separation that is characteristic of

4n π (antiaromatic) systems.

In the [16]-annulene the neutral compound has antiaromatic character. The shifts were measured at low temperature, where conformational averaging has stopped. In the 18π-electron dianion, large aromatic shifts are reported.

Chemical Shift Effects of Phenyl Groups. The effects of a phenyl substituent are highly dependent on conformation. For example, for styrenes the chemical shift effect of the phenyl is downfield when the phenyl is in the plane of the double bond, but upfield when the rotamer with the phenyl group perpendicular is the more stable one:

The large differences in chemical shifts of the butadienes below can also be used to

assign stereochemistry, based on the effect of the "rotated" bezene ring when it is cis to the other vinyl group.

If steric effects force a phenyl to adopt a face-on conformation (as in the lactone example below) then a cis CH3 group will be shifted upfield compared to a trans group.

Determination of Enantiomer Ratios and Absolute Configuration with Mosher

Esters. Esters of 2-phenyl-2-methoxy-3,3,3-trifluoropropionic acid (Mosher esters, or MTPA esters) with secondary alcohol show characteristic chemical shift effects in the alcohol portion which can be used to assign the absolute configuration of the alcohol. Is is necessary to assign key protons unambiguously, and to make both the R- and S-

Mosher ester to arrive at an unambiguous determination (Dale, J. S.; Mosher, H. S. J. Am. Chem. Soc., 1973, 95, 512; Ohtani, I.; Kusumi, T.; Kashman, Y.; Kakisawa, H. J. Am. Chem. Soc., 1991, 113, 4092).

This method works because the principal conformation of MTPA esters is the extended

one shown. The anisotropy of the phenyl group then causes upfield shifts of the protons behind the plane of the paper, downfield shifts for those in front. A typical procedure is to do a complete analysis of all assignable protons of the R and S esters, and calculate the difference between the chemical shifts of the two diastereomers. Note that the t-Bu

group is upfield in the R,S ddistaereomer, whereas the Me group is upfield in the R, R isomer.

For a related method using 1-phenyltrifluoroethanol, see Org. Lett. 2003, 5, 1745.

"Chiral Reagents for the Determination of Enantiomeric Excess and Absolute Configuration Using NMR Spectroscopy." Wenzel, T. J.; Wilcox, J. D. Chirality 2003, 15,

256-70. " The Assignment of Absolute Configuration by NMR," Seco, J. M.; Quinoa, R.; Ricardo, R.Chem. Rev. 2004, 104, 17. "NMR Determination of Enatiomeric Purity" Chem. Rev. 1991, 91, 1441

Aromatic Solvent Induced Shifts (ASIS). Polar molecules have substantially

different chemical shifts in aromatic solvents (benzene, pyridine, C6F6) than in less magnetically interactive solvents like CCl4, CDCl3, acetone-d6 and CD3CN. A typical result of going from CDCl3 to benzene is ahown in the spectra of butyrophenone below. The shifts are large enough that chemical shift calculations can be seriously in error when

applied to moleculea whose spectra were taken in benzene (P. Laszlo Progr. NMR Spectrosc. 1967, 3, 231).

The origin of these chemical shift effects is believed to be a partial orientation of the solvent by the dipole moment of the solute. For benzene, the shifts can be rationalized on the basis of a weak and transient complexation of the electron-rich π-cloud of the aromatic ring with the positive end of the molecular dipole, such that the protons spend additional time in the shielding (-δ) region above and below the benzene ring. There is a strong correlation between the dipole moment and the size of the solvent shift. With occasional exceptions, the benzene shifts are upfield (-δ).

Effect of benzene to simplify a strongly coupled NMR spectrum.

Anisotropy of Double Bonds. The magnetic anisotropy of C-C double bonds has generally been assumed to be similar to that of aromatic rings, with a deshielding region

in the plane of double bond. This explains both the downfield shifts of vinyl protons, and the larger downfield shifts of the internal (which are affected by the anisotropy of both π systems) versus the terminal protons in conjugated dienes. It also explains the downfield shifts of allylic protons.

The shielding region above and below the plane of the double bond is more controversial. A number of examples show the expected upfield shifts of protons above double bonds.

There is, however, one major exception. In norbornene itself, the proton shifts are in the opposite direction than seen in the 7-substituted norbornenes above (J. Am. Chem. Soc. 1968, 90, 3721). Both the proton assignment and the absence of a -δ region above the double bond are supported by high level ab initio MO chemical shift calculations (J.

Am. Chem. Soc. 1998, 120, 11510). Thus the deshielding region above double bonds shown in the figure must be viewed with some skepticism.

For this reason, assignment of stereochemistry in cyclopentanes based on an assumed anisotropy of double bonds, as in the examples below, should be used with caution. Possibly the shifts are the result of C-C single bond anisotropy of the C-vinyl bond.

Anisotropy of Carbonyl Groups. The magnetic anisotropy of C=O has a strongly deshielding (+δ) region in the plane of carbonyl group. This accounts for numerous chemical shift effects in aryl ketones, α,β-unsaturated carbonyl compounds, and conformationally rigid ketones, and is reliable enough to be used for structure

assignments.

The effect is seen both when the proton is β to the carbonyl group, as in the enones

and acetophenones below, or when there is a γ-relationship.

In the compounds below, the proton is γ to the carbonyl and close to same plane, leading to quite large downfield shifts:

In the stereoisomer A below, one of the aromatic protons is close to the carbonyl, and is shifted downfield by 1.3 ppm, whereas in isomer B the carbonyl is remote, and the chemical shift is normal.

These α,β-unsaturated esters show a shift range of 1.7 ppm resulting from the various β- and γ-carbonyl interactions. In the most upfield shift (δ 6.50 for the E,Z-isomer) there

are no close interactions, whereas the most downfield proton (δ 8.20 for the same isomer) has a β-interaction with one carboxylate function, and a γ-interaction with the other:

Amides also show these chemical shift effects. Thus for the two rotamers of the formamide below the α-N proton is 0.9 ppm downfield in the isomer with this proton close to the formyl oxygen (Buchi, G.; Gould, S. J.; Naf, F. J. Am. Chem. Soc. 1971, 93,

2492 DOI)

There is some evidence that there is a shielding (-δ) region above the plane of the

carbonyl group:

Anisotropy of Nitro groups. The NO2 group may have a a small anisotropic effect

similar to that of C=O groups, with a deshielding (+δ) region in the plane of carbonyl group. The ortho protons of nitrobenzenes are strongly downfield, in part due to this interaction. For example the proton Ha between the NO2 and Br groups (the small downfield doublet) has a very similar electronic environment in the two compounds

whose spectra are shown below. The upper one has this proton upfield in part because the ortho-methyl group turns the nitro group out of the plane. Of course, turning the nitro group also causes reduced resonance interactions, which causes a shift in the same direction, as seen from the change in the proton ortho to the Me group (Hb).

A similar chemical shift effect in a naphthalene is illustrated below:

Anisotropy of Acetylenes. The magnetic anisotropy of C≡C bonds seems to be well-defined. Both the unusual upfield shift of C≡C-H signals, and the downfield shifts of protons situated next to a triple bond as in the examples below support a strong diamagnetic affect of electron circulation around the triple bond π system. .

Anisotropy of Nitriles. The cyano group presumably has the same anisotropy as the alkynyl group, as shown by the examples below.

Anisotropy of Halogens. Protons positioned near lone-pair bearing atoms such as the halogens generally show downfield shifts, as in the phenanthrene examples below. Interpretation of these Δδ values is complicated by the close approach of the X and H atoms, which can cause geometry and orbital distortions and affect the chemical shifts.

Single Bond Anisotropy. Because of the many single bonds in typical organic molecules, each with local anisotropic effects, it has been hard to define single bond

chemical shift effects. Nevertheless, useful stereochemical effects have been identified in several situations, loosely based on a magnetic anisotropy of C-C single bonds in which flanking hydrogens are shifted upfield, end-on hydrogens downfield.

Axial and Equatorial Cyclohexane Shifts. In cyclohexane itself, as well as in most substituted and heterocyclic 6-membered rings the axial protons are upfield of the

equatorial ones. Unfortunately, there are a few exceptions, and so this chemical shift

effect must be used with caution. Below some δe-δa values:

One explanation for this shift effect is based on the anisotropy cones shown in the

figure, where the equatorial protons reside in the deshielding (+-δ) region of the C-C anisotropy, and the axial in the -δ region. An alternative explanation, or additional contributing effect, is based on the supposition that a C-H bond is a stronger σ donor than a C-C bond, which leads to increased electron density in the axial protons (anti to

two C-H bonds), hence -δ. The variation in 1JCH has also been interpreted in these terms.

A more complicated bicyclic ring system shows several exceptions to the chemical shift effects of δeq > δax:

Substituent effects on cyclohexanes (Anteunis Tetrahedron Lett. 1975, 687):

Assignment of syn and anti Aldol Adducts. A similar type of single bond anisotropy has been used to rationalize the empirical observation of a systematic variation in the chemical shift of the CHOH proton in syn and anti isomers of aldol products (δsyn > δanti) that can be used to assign configuration, although such assignments should be viewed is

less definitive than other methods, because of the usual problem with interpreting small chemical shift differences (Kalaitzakis, D.; Smonou, I.; J. Org. Chem. 2008, 73, 3919-

3921). The argument is that in the favored conformation of the hydrogen bonded anti

isomer the carbinol proton is in a pseudo-axial orientation subject to similar anisotropy effects as an axial cyclohexane proton, whereas in the syn isomer the proton is pseudo-equatorial.

Cis-Substituent effect in Rigid Rings." Chemical shifts in rigid bicyclic or polycyclic systems can provide some insights into general chemical shift effects, although care must be utilized because there are typically a number of effects operating

simultaneously. One example is the tendency for eclipsed or nearly-eclipsed cis-vicinal substituents to cause upfield shifts relative to the trans proton (and also relative to the compound with hydrogen replacing the substituent). In the dibenzobicyclo[2.2.2]octadiene system A the proton which is eclipsed (or nearly so) with the R substituent is always upfield of the one trans to it, and upfield of the unsubstituted compound as well. For the hexachloro bicyclo[2.2.2]heptane B this is also seen, although here the inherent shift difference is not known since the compound with R = H has not been reported.

The upfield shift of cis substituents is also seen in a series of succinic anhydrides:

Stereochemical Relations in Cyclopentanes. Because coupling constants are not very

reliable for determining stereochemical relationships in 5-membered rings, chemical shift effects such as the one discussed above have been utilized more extensively than in cyclohexanes. It has been observed that in cyclopentanes, γ-butyrolactones (Ollis JCS-PT1 1975, 1480) and tetrahydrofurans the diasterotopic chemical shift effect of a

CH2 group is consistently larger when flanking substituents are cis to each other (when the anisotropic effects of the C-C or C-O bonds are additive) compared to when they are trans. More specifically, protons with cis-vicinal substituents are generally shifted to lower δ values (upfield) than those with cis hydrogens.

Similarly, the chemical shift of a proton will be a function of the number of cis-alkyl substituents on the ring. To use such chemical shifts it is necessary to have several members of a series for comparison.

5. Hydrogen Bonding Effects on Chemical Shifts - OH, NH and SH Protons. The chemical shifts of OH and NH protons vary over a wide range depending on details of sample preparation and substrate structure. The shifts are very strongly affected by

hydrogen bonding, with large downfield shifts of H-bonded groups compared to free OH or NH groups. Thus OH signals tend to move downfield at higher substrate concentration because of increased hydrogen bonding. Both OH and NH signals move downfield in H-bonding solvents like DMSO or acetone.

There is a general tendency for the more acidic OH and NH protons to move further downfield. This effect is in part a consequence of the stronger H-bonding propensity of acidic protons, and in part an inherent chemical shift effect. Thus carboxylic amides and sulfonamides NH protons are shifted well downfield of related amines, and OH groups of

phenols and carboxylic acids are dowfield of alcohols.

Recognizing Exchangeable Protons. In many samples NH and OH protons can be recognized from their characteristic chemical shifts or broadened appearance. When this

fails, the labile protons can be identified by shaking the sample with a drop of D2O, which results in disappearance of all OH and NH signals. This works best if the solvent is water immiscible and more dense than water (CDCl3, CD2Cl2, CCl4) since the formed DOH is in the drop of water floating at the top of the sample where it is not detected. In water miscible solvents (acetone, DMSO, acetonitrile, pyridine, THF) the OH and NH signals are

largely converted to OD and ND, but the DOH formed remains in solution and will be detected in the water region.

Hydroxyl OH Protons. In dilute solution of alcohols in non hydrogen-bonding solvents

(CCl4, CDCl3, C6D5) the OH signal generally appears at δ 1-2 At higher concentrations the signal moves downfield, e.g. the OH signal of ethanol comes at δ 1.0 in a 0.5% solution in CCl4, and at δ 5.13 in the pure liquid (from Bovey).

Dynamic Exchange. Under ideal conditions OH groups of alcohols can show sharp signals with full coupling to neighboring protons even at room temperature, as in the spectrum of neat ethanol above, and in the spectrum of 1-phenyl-4,4-dimethyl-1-pentyn-3-ol below.

More typically, signals for OH protons are subject to intermolecular exchange processes, which may result in broadening or complete loss of coupling to neighboring protons. Such exchange can also broaden or average the signals of multiple OH, NH or

SH groups in the sample, if more than one is present. The rates of exchange are a

complex function of temperature, solvent, concentration and the presence of acidic and basic impurities. In CDCl3 the presence of acidic impurities resulting from solvent decomposition often leads to rapid acid catalyzed exchange between OH groups. In contrast, solvents like DMSO and acetone form strong hydrogen bonds to the OH group.

This has the effect of slowing down the intermolecular proton exchanges, usually leading to discrete OH signals with observable coupling to nearby protons. Note the triplet and doublet for the HOCH2 group in the spectrum below taken in DMSO.

In the remarkable NMR spectrum of the OH region o sucrose below (Adams, Lerner J. Am. Chem. Soc. 1992, 114, 4828) all of the OH signals and their coupling are resolved in aqueous acetone solvent.

Phenols. The OH signals of phenols are generally well downfield of those of alcohols, appearing at δ 5-7 in CDCl3, and δ 9-11 in DMSO. The higher acidity of phenols results in faster exchange rates, so that polyphenolic compounds will usually show only one OH signal.

In DMSO solution, even the exchange between carboxylic acid protons and other OH groups can be slowed enough to allow individual observation, as in the spectrum of 2-hydroxycinnamic acid below.

β-Dicarbonyl Compounds. Especially dramatic shifts are observed for the strongly intramolecularly H-bonded enol forms of β-dicarbonyl compounds, o-ketophenols and related structures.

Carboxylic Acids. Most carboxylic acids are strongly hydrogen bonded in non-polar solvents, and the OH protons are correspondingly downfield shifted. Acetic acid dimer in

Freon solvent (CDClF2/CDF3) at 128 K appears at δ 13.04, and the OH signals of acetic acid hydrogen bonded to a protected adenosine under conditions of slow exchange appear at even lower field (Basilio, E. M.; Limbach, H. H.; Weisz, K. J. Am. Chem. Soc. 2004, 126, 2135).

Amine and Amide N-H Protons. NH2 protons of primary alkyl amines typically appear

as a somewhat broadened signal at δ 1-2 in CDCl3. The broadening has several sources: partially averaged coupling to neighboring protons, intermolecular exchange with other NH or OH protons, and partially coalesced coupling to the quadrupolar 14N nucleus (I = 1), which usually has a short T1. In the example below, the CH2 group bonded to amino (δ 2.82) shows little indication of coupling to the NH2 protons, so NH exchange must be

rapid on the NMR time scale. The amide proton at δ 7.1 is broadened by residual

coupling to 14N, not by exchange, since the N-CH2 signals are a sharp quartet from

accidental equivalance of the vicinal HN-CH2 and CH2-CH2 couplings..

The N-H signals of ammonium salts are strongly downfield shifted, typically appearing at δ 4-7 in CDCl3 and δ 8-9 in DMSO. If spectra are taken in strongly acidic solvents (e.g. trifluoroacetic acid), where intermolecular exchange is slowed, the signals are

sometimes very broad, and can show poorly resolved 1H-14N J coupling (1:1:1 triplet, JHN ≈ 70 Hz).

Aniline NH Protons. The NH protons of anilines are typically at δ 3.5-4.5 in CDCl3 solution, moving downfield by 1-2 ppm in DMSO solution. o-Nitroanilines (ca δ 5-6) and heterocyclic amines such 2-aminopyridines (δ 4.5) have signals downfield of this range.

Amide NH Protons. Amide NH signals typically appear around δ 7, as in the example of N-acetylethylenediamine above. They are generally in slow exchange with other NH and OH signals. Thus, neighboring protons will show coupling to the NH proton, as in the example, where the CH2 bonded to the amide nitrogen is a quartet. The amide N-H

protons are typically broad from poorly resolved coupling to 14N, so the coupling to

neighboring protons is often not resolved in the NH signal.

Thiol S-H Protons. S-H protons of alkyl thiols typically appear between δ 1.2 and 2.0 in CDCl3. The position is not strongly affected by hydrogen bonding solvents like acetone

or DMSO, since SH protons are only weakly hydrogen bonded. Coupling to nearby protons is usually seen, although broadened or fully averaged signals are not uncommon, especially in molecules containing OH protons.

Aryl thiol S-H signals are further downfield, typically δ 3.5-4.5, as a result of normal ring-currrent effects, and the greater electron withdrawing effect of aryl vs alkyl groups.

Selenol and tellurol protons (SeH and TeH) behave like thiol protons, but appear

somewhat further upfield (around δ 0 for SeH and δ -3 to -5 for TeH.

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5.3 Spin-Spin Splitting: J-Coupling

© Copyright Hans J. Reich 2012

All Rights Reserved University of Wisconsin

There are two distinct types of magnetic interaction (coupling) between nuclei (A and X) with a non-zero spin - the direct interaction (dipole-dipole coupling: D) and the indirect or scalar coupling (spin-spin splitting: J). The direct interaction is about 1000 times as large as the scalar coupling (e.g. at 2 Å distance H-H dipolar coupling is ca

30,000 Hz). These direct couplings make the observation of high-resolution NMR spectra in solids and very viscous liquids difficult, and make NMR spectra in liquid crystals (where molecules are partially oriented, and the dipolar coupling is only partially averaged) very complex. In mobile isotropic liquids the random motion of molecules

completely averages the dipolar coupling, so no direct effects are seen. There are however, indirect effects, such as the Nuclear Overhauser Effect (NOE) which have important consequences for NMR spectroscopy (see Sect. 8). In the following sections we will be concerned only with J coupling.

The scalar coupling J is a through-bond interaction, in which the spin of one nucleus perturbs (polarizes) the spins of the intervening electrons, and the energy levels of neighboring magnetic nuclei are in turn perturbed by the polarized electrons. This leads to a lowering of the energy of the neighboring nucleus when the perturbing nucleus has

one spin, and a raising of the energy whenwhen it has the other spin. The J coupling (always reported in Hz) is field-independent (i.e. J is constant at different external magnetic field strength), and is mutual (i.e. JAX = JXA). Because the effect is usually transmitted through the bonding electrons, the magnitude of Jfalls off rapidly as the number of intervening bonds increases. Coupling over one (1J), two (2J) and three (3J) bonds usually dominates the fine structure of NMR spectra, but coupling across four (4J) and five (5J) bonds is often seen, especially through π bonds (double and triple bonds, aromatic carbons).

Sign of Coupling Constants

Coupling constants can be either positive or negative, defined as follows: coupling constants are positive if the energy of A is lower when X has the opposite spin as A (αβ

or βα), and negative if the energy of A is lower when X has the same spin as A (αα or ββ).

Mechanism of spin polarization: It is known from spectroscpoy of the hydrogen radical (H·) that the more stable orientation has the angular momentum vectors of the nucleus and the electron antiparallel. Since the gyromagnetic ratio of the nucleus is positive, and that of the electron is negative, this means that the magnetic vectors are parallel.

For the Fermi contact mechanism of spin-spin coupling (there are other mechanisms), the bonding electrons for a H-13C fragment will become polarized as shown, so that the more stable orientation of the 13C-nucleus will be down, when the proton is up. This corresponds to a positive one-bond C-H coupling.

If we continue down the bond sequence, the polarization of the C-H electrons will cause polarization of the C-C electron pair. Again, parallel spins are the more stable orientation

(triplets are more stable than singlets -- Hund's rule). Thus the two-bond coupling (2J) is

predicted to be negative, and the three-bond coupling (3J) positive. This alternation of signs is often (but by no means always) seen.

A depiction of the perturbation of energy levels of a nucleus A by a

neighboring magnetic nucleus X is shown below (spin-spin splitting). The principal magnetic nuclei are other protons, the 100% abundant spin ½ nuclei 19F and 31P, and some spin 1 or greater (quadrupolar) nuclei such as 14N, 2H, 11B, and 12B. Although Br, Cl, and I all have isotopes with spin >½, coupling is not seen because of relaxation

effects. This will be discussed in more detail in Section 7.

Two Different Couplings to one Proton

Consider the NMR spectrum of 3,4-dichlorobenzoyl chloride below.

The proton-proton couplings in benzene are typically 7-9 Hz for Jortho, 2-3 Hz for Jmeta and <1 Hz for Jpara. The substitution pattern can be derived from examination of each of the three aromatic protons. For example, the doublet at δ 8.2 with J = 2.5 Hz is interpreted as follows: this proton has no protons ortho to it, and only one proton meta to it. Structure A summarizes the information. For the doublet of doublets at δ 7.95 (J = 8.5, 2.3 Hz), formed by coupling of one proton to both an ortho and a meta proton, the

two structures B and C are possible. The doublet at δ 7.6 (J = 8.5 Hz) defines the substitution pattern of structure D. In each case the position marked by ? is undefined since the para coupling is usually too small to resolve.

A slightly more complicated case is 1,1,2-trichloropropane. A simulated spectrum is shown below.

The C-2 proton is coupled to one proton at C-1 and three protons of the methyl group at C-3. Naively, one might expect a pentet(p), as shown in the left spectrum below. Although pentets are, in fact, often observed in such situations, this occurs only if J1-

2 andJ2-3 are identical. When they are not (as is actually the case in this example), then we get a quartet of doublets (qd). It is customary to quote the larger coupling first (q) and then the smaller coupling (d). A proper text description of the multiplet is: δ 4.30, 1H, qd, J = 6.6, 3.8 Hz.

First Order Coupling Rules

1. Nuclei must be chemical shift nonequivalent to show obvious coupling to each other.

Thus the protons of CH2Cl2, Si(CH3)4, Cl-CH2-CH2-Cl, H2C=CH2 and benzene are all singlets. Equivalent protons are still coupled to each other, but the spectra do not show it. There are important exceptions to this rule: the coupling between shift equivalent but magnetically inequivalent nuclei can have profound effects on NMR

spectra - see Sect. 5.7

2. J coupling is mutual, i.e. JAB = JBA always. Thus there is never just one nucleus which shows J splitting - there must be two, and they must have the same splitting constant J. However, both nuclei need not be protons - fluorine (19F) and phosphorus (31P) are two other common nuclei that have spin ½ and 100% abundance, so they will couple to all nearby protons (the other 100% spin 1/2 nuclei are 89Y, 103Rh and 169Tm). If these nuclei are present in a molecule, there are likely to be splittings which are present in only one proton multiplet (i.e. not shared by two multiplets).

3. Two closely spaced lines can be either chemically shifted or coupled. It is not always possible to distinguish J from δ by the appearance of the spectrum (see Item 4 below). For tough cases (e.g. two closely spaced singlets in the methyl region) there are several posibilities: · decouple the spectrum · obtain it at a different field strength (measured in Hz, coupling constants are field independent, chemical shifts are proportional to the magnetic field) · measure the spectrum a different solvent (chemical shifts are usually more solvent

dependent than coupling constants, benzene and chloroform are a good pair of solvents).

For multiplets with more than two lines, areas, intensities, symmetry of the pattern and

spacing of the lines generally make it easy to distinguish chemical shift from coupling.

For a simple example see the spectrum of 3-acetoxy-2-butanone below. Here it is pretty easy to identify one of the doublets as the 4-methyl group, the other "doublet" (with a

separation of 9 Hz, which could easily be a coupling) actually corresponds to the two CH3C(=O) groups.

4. Chemical shifts are usually reported in δ (units: ppm) so that the numeric values will not depend on the spectrometer frequency (field-independent units), coupling constants are always reported in Hz (cycles per second). Chemical shifts are caused by the magnetic field, couplings are field-independent, the coupling is inherent in the magnetic properties of the molecule. However, all calculations on NMR spectra are done using Hz (or, more precisely, in radians per sec).

5. Protons two (2J, geminal) or three bonds (3J, vicinal) apart are usually coupled to each other, more remote protons (4J, 5J) maybe if geometry is right, or if π-systems (multiple bonds) intervene. Long range couplings (4J or greater) are usually small, typically <0.5 Hz, but up to 3 Hz in some cases where there are intervening π bonds.

6. Multiplicity for first order patterns follows the "doubling rule". If all couplings to a particular proton are the same there will be 2nI+1 lines, where I is the spin and n is the number of neighboring nuclei (n + 1 for 1H I = 1/2). The intensities will follow Pascal's triangle.

7. If all couplings are different, then the number of peaks is 2n for 1H, and the intensities are 1:1:1: . . .. Thus a proton coupled to two others by different couplings gives a dd (doublet of doublets, see Figure). This pattern is never called a quartet. As the number of couplings gets larger, accidental superpositions of lines will sometimes occur, so that the 1:1:1... intensity ratio no longer applies. The intensities are also often distorted by leaning effects (see AB/AX patterns), as seen in several examples below.

8. More typically, some of the couplings are the same, others different, so get a variety of patterns. In favorable cases, these patterns can be analyzed and all couplings extracted. The number and size of couplings (J-values) provide important structural information.

Second Order Effects

Protons or groups of protons form simple multiplets only if the chemical shift differences between the protons (Δν) are large compared to the coupling constants between them (J). If Δν /J (all in Hz) is <5 then second order effects appear (see 5-HMR-9) which complicate the analysis.

Rules for Analyzing First Order Multiplets

A first order multiplet can be expected when both of the following criteria are met:

First, the chemical shift of the observed proton must be far away from any of the protons it is coupled to (far away means Δν >>J). In practice, multiplets can be treated in a first order fashion if Δν > 3J, although the substantial leaning distortions can

complicate analysis. The leaning will have almost completely disappeared by the time Δν = 10J.

Second, if more than one proton is coupled to the observed one, then these protons

must not be "strongly coupled." In other words, if they are coupled to each other and very close in chemical shift then the observed proton multiplet may not yield true coupling constants on analysis, even though it looks first order. See the section on Virtual Coupling.

Structure of First Order Multiplets. The fundamental rule governing multiplet intensities for spin 1/2 nuclei with all couplings identical is Pascal's triangle (n = number of equivalent couplings). A very characteristic and diagnostic intensity relationship is that beteen the first and second lines - the intensity ratio is 1/n, where n is number of

equivalent coupling partners.

A first order multiplet consists of the product (not the sum) of several such multiplets. In other words, a single line will first be split into one of the symmetrical multiplets (1:1 d, 1:2:1 t, 1:3:3:1 q, etc), then each line of this multiplet will be again split into d, t, q, or higher multiplet.

Recognizing a First Order Multiplet.

1. All truly first order multiplets are centrosymmetric - there is a mirror plane in the middle (in real spectra, this is usually not strictly true because of leaning and other distortions). However, the reverse is not true: not all symmetrical multiplets are first order.

2. If the small outermost peaks are assigned intensity 1, then all other peaks must be an integral multiple intensity of this one (1x, 2x, 3x, 4x in height), and the total intensity of all peaks must be a power of 2 (2, 4, 8, 16, 32, etc). The intensity of each of the two outermost lines is 1/2n of the total multiplet intensity, where n is the number of protons which are coupled with the proton signal being analyzed. There can be no lines smaller than the outermost one. Note, however, that if n is large, the outermost peaks may not be distinguishable from noise. Intensity assignments and determination of n cannot be easily made for such multiplets

3. There is a strict regularity of spacing in a first order multiplet: if you have correctly identified a coupling constant J, then everypeak in the multiplet must have a

partner J Hz away to the left or to the right of it.

4. Most first order multiplets integrate to a single proton, a few may be 2 or 3 protons in area. It is rare to have more than 3 protons, unless there is symmetry in the molecule (e.g., (CH3)2CH- gives a 6-proton doublet for the methyl groups). Thus a 4-proton

symmetrical multiplet is usually not a first-order pattern (it is more likely to be the very common AA'BB' pattern).

5. The symmetry and intensities of an otherwise first-order multiplet can be distorted by leaning effects (see Section 5-HMR-9). Many such multiplets can still be correctly analyzed by first-order techniques, but you have to mentally correct for the intensity distortions. However, the coupling constants extracted may not be perfectly accurate.

Analyzing a First Order Multiplet. First order multiplets are analyzed by constructing a reverse coupling tree, by "removing" each of the couplings in turn, starting with the smallest.

1. "Take out" the smallest couplings first. The separation between the two lines at the edge of the multiplet is the smallest coupling. Each time you remove a coupling you

generate a new, simpler multiplet, which can then be analyzed in turn. Remember

that each line of the multiplet participates in each coupling.

2. Watch line intensities (i.e., peak areas or peak heights) carefully--when you "take out" a coupling, the intensities of the newly created lines should be appropriate (i.e.,

each time you "take out" a coupling, also "take out" the proper intensity). When a coupling has been taken out completely, all intensity should be accounted for. Keep track of your analysis by using a "coupling tree".

3. The couplings may be removed one at a time as doublets, or as triplets, quartets and higher multiplets. The intensity ratio of the first two lines signals the number of protons involved in the coupling: 1:1 means there is only one proton, 1:2 means that there is a triplet splitting (2 protons), etc. Be especially careful to keep track of intensities when you "take out" triplets (1:2:1) or quartets (1:3:3:1). Each time you

completely remove a coupling you generate a new simpler multiplet which follows first order rules, and can be analyzed in turn.

When you have finished your analysis, all peaks in the multiplet must be accounted for.

You can check the analysis as follows: the separation of the two outermost peaks of the multiplet is the sum of all the J's (i.e., for a dt, J = 8, 3 Hz the outermost lines are separated by 8 + 3 + 3 = 14 Hz).

Reporting a First Order Multiplet. Multiplets are reported starting with the largest coupling, and the symbols must be in the order of the reported numbers: δ 2.10, 1H, qt, J = 10, 6 Hz means: a single proton q of 10 Hz, t of 6 Hz with a chemical shifts of 2.10 ppm.

Quartets. Keep clear in your mind the distinction between a simple q (one proton equally coupled to 3 others, with an intensity 1:3:3:1), an ABq (2 protons coupled to each other, see Section 5-HMR-10), and the quartet formed by coupling with a spin 3/2 nucleus (e.g., 7Li, intensity 1:1:1:1, see Sect 7-MULTI-2). Only the first of these should

be referred to by just a "q" symbol. The early NMR literature (and even modern novices) sometimes call doublets of doublets "quartets" (there are four lines, after all).

Practice Multiplets

First Order Analysis

Simple Multiplets

Exercise: Assign the protons where structure and chemical shift scale are given

Note the leaning, indicating that the coupled partner is close by.

Symmetrical Multiplets which are NOT First Order

Exercise: Only ONE of the multiplets below is first order, find it. A second one is almost first order, but ultimately can be shown to ruled out because of a very subtle line position inconsistency.

Some criteria to use: · Pattern must be centrosymmetric (true of all of these) · Intensity of lines - patterns must be repeated, especially examine outer lines

· Be wary if #H > 1, especially if 4H · Consider size of possible couplings

5-HMR-3.14 Measurement of Coupling Constants

The accurate measurement of J coupling constants requires that the multiplets be correctly analyzed. In the following pages are described techniques for performing such analyses. The procedures are summarized below.

For first order multiplets a simple "coupling tree" analysis as described in Section 5-HMR-3.9 can directly yield coupling constants within the accuracy of the digital resolution

of the spectrum. This includes AB spectra, where JAB can be measured directly.

SeeSection 5-HMR-7 for a description of the ABC... (Pople) nomenclature for spin systems.

For AB2 spectra both the coupling constant JAB and the chemical shifts can be obtained

by simple arithmetic manipulations, provided that line assignments can be made correctly. For ABX spectra JAB is accurately measureable by inspection. An approximate analysis, which treats the peaks as AMX, will give values for JAX and JBX that will be in error by varying amounts, depending on the relative size of JAB and νAB (the smaller

νAB the larger the error), and the relative size of JAX and JBX. To get accurate values for theJAX and JBX coupling constants a proper ABX analysis as described in Section 5-HMR-12 is required.

For many simple compounds the symmetry is such that protons are homotopic or

enantiotopic, and no coupling constants can be measured directly (e.g., the 2J coupling in methane or dichloromethane; the ortho, meta, and para couplings in benzene; the cis, trans and gem couplings in ethylene, etc). For such compounds the following techniques are used to measure JHH:

Analysis of Complex Spin Systems. In molecules where the chemical shift-equivalent protons are of the AA' type (part of anAA'XX', AA'X3X3' or similar system), complete analysis of the coupling system can, in favorable circumstances, give the value of JAA'. An example is 1,3-butadiene, an AA'BB'CC' system in which all protons are

compled to all other ones. Analysis of the complex NMR spectrum gave, among numerous others, values for the following couplings between chemical shift equivalent nuclei: 3JAA',

5JBB' and5JCC' (Hobgood, R. T., Jr.; Goldstein, J. H. J. Mol. Spectr. 1964, 12, 76).

Isotopic Substitution. Replacing one of the protons by deuterium (or even tritium) breaks the symmetry of the coupled system and allows measurement of JHD (or JHT). The value of JHH can then be calculated from the gyromagnetic ratios. In the example below, the 60 MHz NMR spectrum of a mixture of undeuterated (s), monodeuterated (1:1:1 triplet, the spin of D is 1, see Sect. 7-MULTI-2) and dideuterated (1:2:3:2:1 quintet) acetonitrile is shown. Note the isotopic shifts (Grant, D. M.; Barfield, M. JACS 1961, 83, 4727)

Analysis of 13C Satellite Spectra. Vicinal couplings between homotopic or

enantiotopic protons 3JHH can often be obtained by analysis of the 13C satellites. The 1H NMR signal for the vinyl protons of dimethyl maleate is a singlet. However, the 13C satellites are doublets, with a splitting that is equal to 3JHH. In effect, the A2 spin system of the 12C isotopomer has become an ABX pattern in the mono-13C labelled compound, where X is the 13C nucleus, and A and B are the two vinyl protons, one on 13C and the

other on 12C.

Below is an example of the measurement of a 4JHH in a symmetric tricyclic system using the 13C satellite method (Masamune, S. J. Am. Chem. Soc. 1964, 86, 735)

For systems of the X-CH2-CH2-X type, the mono-13C isotopomer is an AA'BB'X pattern, which can be solved to obtain JAA' (= JBB') as well as JAB and JAB'. Note that when both protons are on the same carbon the value 2J cannot be determined by this method. Thus

for the O-CH2-O signal, the 13C satellites are singlets.

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5.4 Geminal Proton-Proton Couplings (2JH-H)

© Copyright Hans J. Reich 2012

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Two-bond H-H couplings vary in a complicated way with structure, and they can only be understood if both magnitude and sign is taken into account. Some extreme examples are given below.

Most 2J couplings fall into two well-defined groups. For unstrained sp3 CH2 protons with innocuous substituents, the coupling is typically around -12 Hz, whereas the 2-bond coupling of sp2 (vinyl) protons is much smaller, typically 2 Hz. The molecular orbital perturbation theory of Pople and Bothner-By (J. Chem. Phys. 1965, 42, 1339) predicts

the electronic effects of substituents on these coupling constants based on the interaction between filled and empty orbitals of the CH2 fragment. Excitation between

orbitals of the same symmetry has a negative effect on J, between orbitals of opposite

symmetry has a positive effect. The 1/E term is largest for the HOMO-LUMO transition, so coupling effects are dominated by the ψ2 ψ3 transition. Substituents which reduce the energy gap between ψ2 and ψ3 (i.e. raise ψ2 or lower ψ3) will increase the size of 1/E and thus have a (+) effect on the coupling, whereas those which increase the energy

gap (i.e. lower ψ2 or raise ψ3) will have a (-) effect. There are also changes in the orbital coefficients which affect the magnitude of the coupling.

σ-Acceptor substituents (electronegative atoms like F, O, N) interact mainly with ψ3 and ψ1 because of symmetry restrictions. The most important effect is to lowerr ψ3, and thus have a (+) effect on the coupling, whereas σ-donor substituents like Si or other metals will raise ψ3 and thus have a (-) effect.

Remarkably, π-donors and acceptors have the opposite effect -- symmetry requires that these will interact mainly with ψ2. Thus π-donor substituents (directly attached atoms with lone pairs, or adjacent electron rich bonds) will raise ψ2, and result in a (+) effect, and π-acceptor substituents (carbonyl groups and related functions, or adjacent electron poor bonds) will lower ψ2 and have a (-) effect.

Gem coupling in Saturated Carbons (sp3): In acyclic and unstrained ring systems the gem coupling is typically from -10 to -13 Hz. Substituents will change these

couplings as described above: when the CH2 group is substituted with a π-acceptor like a

carbonyl or cyano group, the coupling becomes more negative, i.e larger in magnitude, ranging from -16 to -25 Hz. This is a reliable and important effect which can help with structure assignments.

Conjugating aryl, alkene and alkyne substituents also make the coupling more

negative.

Substituents like the halogens, alkoxy and amino groups are both σ-acceptors and π-donors. Both are (+) effects, so the couplings become more positive (i.e. smaller numbers), in some cases they are close to zero.

Ring strain has a (+) effect on gem coupling. Thus in cyclopropane the coupling has increased from -12 to -4 Hz. The additional (+) effects of oxygen bring the coupling to +5.5 in ethylene oxide

Gem coupling in Unsaturated Carbons (sp2): The gem coupling in ethylene itself is +2.5 Hz, and most terminal alkenes have small couplings in the range of 1-3 Hz. Electronegative substituents (F, O) on the double bond behave as π-acceptors, with a (-) effect on the coupling, which can become close to zero for weakly accepting substituents (as in methyl vinyl sulfide). Electropositive substituents on the neighboring carbon (Si, Li) behave as π-donors with a (+) effect on the coupling. For α-trimethylsilylvinyllithium both substituents have a (+) effect, and result in an exceptionally large coupling, whereas in α-ethoxyvinyllithium the two substituents have opposite effects, and the

coupling was too small to observe.

The large positive coupling in formaldehyde, and large negative coupling in ketene can be understood in these terms as well. For formaldehyde the oxygen substituent behaves

as a strong σ-acceptor as well as a strong π-donor from the π-lone pair, both (+) effects, rendered especially large because of the short bond distance. Imines also show large positive 2J.

In a similar vein, for ketene the carbonyl substituent behaves as a strong π-acceptor, giving an usually large negative coupling.

Geminal Proton-Proton Couplings Summary (2JH-H)

Geminal couplings between protons vary widely in sign and magnitude. There are both positive and negative substituent effects on the coupling, as summarized below. The remarkable feature is that σ and π acceptors have opposite effects on the coupling, as do

σ and π donors.

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5.5 Vicinal Proton-Proton Coupling 3JHH

© Copyright Hans J. Reich 2012

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The single most useful H-H coupling relationship is that between vicinal protons. The

size of 3JH-H is predictable and provides detailed information about the spacial orientation between the two protons. Almost all 3JHH values are positive (a rare exception is the -2 Hz 3JH-H in cis-1,2-difluoroethylene), but their magnitude varies widely (from close to 0 Hz up to 25 Hz) depending on structural and conformational details.

Three-Bond Coupling across Single Bonds. In acyclic systems with small conformational preferences, vicinal couplings are generally in the range 6-8 Hz, with electronegative substituents causing smaller J values. Note in particular the

reduced 3J for protons on carbons bearing oxygen substituents, which is seen for all types of 3-bond couplings.

The Karplus relationship gives us approximate values for 3JHH as a function of dihedral angle between the protons. It should be remembered, however, that this relationship strictly applies only in unstrained hydrocarbon systems, and that electronegative substituents and ring constraints may cause substantial perturbations (in both positive and negative directions) to the values predicted by this equation. Nevertheless, the Karplus curve, and its more complicated variants, is the mainstay of conformational analysis for all ring systems, and has generally proved reliable if care is taken. The constants Jo and K are used to correct for substituent effects in more sophisticated uses of the Karplus equation, different Jo values are also used for the 0 to 90° and the 90 to

180° sections of the curve.

The Bothner-By equation provides an empirical "Karplus" curve that does not require different J0 values for the 0-90 vs 90-180° sections:

A convenient graphical form of the Karplus relationship is given in Figure 5.5.1 below. Here two curves, separated by 120°, represent the predicted coupling constants for a proton H1 coupled to an adjacent methylene group (Hcis and Htrans), as a function of the dihedral angle.

Figure 5.5.1. Double Karplus Curve for Vicinal coupling in Cycloalkanes.

5.5.3 Determination of Stereochemistry in Cyclic Compounds Using 3JHH

Cyclohexanes. It is often straightforward to establish stereochemical relationships among substituents, provided that the spectrum can be analyzed. In chair cyclohexanes, the relationship among vicinal protons is restricted to the narrow regions for Θ1-c = 40-

60 onFigure 5.5.1 (i.e. to the left of the H1-eq crossing point at 60°, and to the right of the H1-ax point). These regions correspond to flattening of the cyclohexane, which is energetically easy. The opposite distortion (Θ1-c = 60-85 ) cannot occur to any significant extent. Jaa is usually much larger (9-12 Hz) than Jee or Jea (each usually 3-4 Hz).

Below is reproduced the 100 MHz NMR signal of the H1 proton of iodocyclohexane at -80°C (from F. R. Jensen, C. H. Bushweller, Beck JACS 1969 91, 344, 3223). Under these conditions the ring inversion is slow on the NMR time scale, and separate signals are seen for the two conformational isomers. The couplings are not always this well

resolved, but the axial proton multiplet will almost invariably be much wider than the equatorial one (remember that the separation of the outer two lines of a first order multiplet is the sum of all the coupling constants). At room temperature, the ring inversion will be fast on the NMR time scale, so an average spectrum will be observed. It will look much like that of the axial proton, since the equatorial isomer is the major one.

The coupling constants in cyclohexane itself were determined by analysis of the AA'BB' pattern of 1,1,2,2,3,3,4,4-octadeuteriocyclohexane at -103 °C (Garbisch, J. Am. Chem. Soc. 1968, 90, 6543). The top spectrum (deuterium decoupled) is the experimental one, the bottom one is a simulation with the parameters listed.

The spectra of iodocyclohexane and cyclohexane itself also illustrate another feature common to many axial and equatorial cyclohexane protons: the chemical shift of the axial proton is usually upfield of the equatorial one, in the case of cyclohexane by 0.5 ppm.

The near identity of the magnitudes of the gem (2JAB = -13.05 Hz) and axial-axial (3JAA' = 13.12 Hz) couplings seen in cyclohexane is a common feature of substituted chair cyclohexanes and half-chair cyclohexenes. In molecules with electronegative substituents (e.g. pyranose sugars) the vic ax-ax couplings are smaller than these, with typical values between 8 and 11 Hz.

In an idealized cyclohexane, Jee and Jae would be identical, since each corresponds to a dihedral angle of 60°. However, cyclohexanes are typically slightly flattened, presumably

due to axial-axial repulsions. This moves the dihdral angle for Jee to slightly higher than 60°, hence smaller coupling, and that of Jae to slightly below 60°, resulting in larger coupling (see the shaded areas in Figure 5.5.2). The dihedral angle in cyclohexane itself is 57°, and this leads to the slightly smaller value for Jee (JBB' = 2.96) compared to Jae (JAB' = 3.65). Similar effects are also commonly seen in substituted cyclohexanes which are conformationally homogeneous, especially if there are axial substituents of any size. If the flattening is substantial, Jee can become too small to detect (as is the case for some bicyclo[3.3.1]nonanes with Θ1-t = 90°), and Jae can become substantially larger than the normal values of 3-4 Hz, reaching valuesof 5 or even 6 Hz. Thus you cannot always rely on getting an exact count of vicinal neighbors to a proton from its multiplicity.

Figure 5.5.2. Karplus Curve (using the Bothner-By equation: 3J = 7 -cos Θ + 5·cos 2Θ) for vicinal coupling in cycloalkanes. The shaded area represents the conformational

space of chair cyclohexanes, showing ring flattening.

The near identity of Jee and Jea has the unfortunate consequence that the couplings to an equatorial proton do not provide information about the stereochemistry of

neighboring protons (i.e. whether they are axial or equatorial) although they will usually provide a count of the vicinal neighbors.

Exercise: Analyze the NMR spectrum of the mixture of 3,5-

diphenylbromocyclohexanes below (assign signals):

Exercise: Examine the 220 MHz spectrum of proto-quercitol reproduced below, and analyze the couplings and chemical shifts (McCasland, G. E.; Naumann, M. O.; Durham, L. J., J. Org. Chem. 1968, 33, 4220).

The pyranose forms of pentose and hexose sugars provide many examples where vicinal proton coupling constants allow complete assignment of stereochemistry. Analyze the 1H NMR spectrum of glucose pentaacetate reproduced below, assuming that you

don't know the stereochemistry. Analysis of this type always begin with the specific assignment of one or more of the protons, either from chemical shift information or the number of couplings. In this example, the best place to start is H1, which can be recognized both from its chemical shift (at δ 6.6), as well as from the fact this it will be the only proton in the molecule coupled to just one other proton.

Exercise: Examine the 300 MHz spectrum of glucose pentaacetate reproduced below. Assume you don't know the stereochemistry and use the spectrum to assign it at each carbons.

Boat Conformations. In boat and twist-boat cyclohexanes there are multiple conformations, each of which have available several C-C-C-C dihedral angles. In an idealized twist-boat there are four kinds of hydrogens, with eight dihedral angle relationships (ca 30, 30, 50, 50, 70, 90,150, 170 degrees). In addition, there are six

different twist boats possible for a multiply-substituted cyclohexane so stereochemical assignments are very difficult. Twist-boat cyclohexane is ca 5 kcal higher in energy than the chair form, so they are quite rare, being commonly seen only in bicyclic structures, or in 6-membered rings with multiple heteroatoms or those containing multiple sp2 carbons. Even cyclohexanes with a tert-butyl groups forced to be axial can adopt

modestly distorted chair conformation.

Cyclopentanes. The conformational analysis of substituted cyclopentanes is much more complicated than that of cyclohexanes. The energy differences between various envelope and twist conformations in five-membered rings are generally small, and there are as many as ten different envelope and ten different twist conformations, and each

conformation has multiple dihedral angle relationships. Several of the 20 possible

conformations may be populated in an individual structure. Thus the vicinal couplings in 5-membered rings are highly variable. For cyclopentanes in envelope conformations Jcis > Jtrans in the flat part part of the envelope, whereas in twist conformations the tendency is for Jtrans > Jcis. In general, no firm assignments of

stereochemistry can be made using the size of couplings alone unless a specific substitution pattern or heterocyclic system has been carefully investigated, or if substitution patterns allow prediction of the conformation.

Inspection of the double Karplus curves indicates a significant difference between the typical behavior of adjacent CH2 groups in cyclohexanes and cyclopentanes. In a chair cyclohexane only one of the four vicinal couplings can be large (> 7 Hz), whereas in a

cyclopentane it is common for 2 or even 3 of the 3J couplings to be large.

In most cyclopentanes, the C-C-C-C dihedral angles are significantly smaller than the 60° found in cyclohexanes. Cis protons will tend to have H-C-C-H dihedral angles close to 0°, and trans near 120°. The cis couplings (8-10 Hz) are usually larger than trans (2-9 Hz). However the Karplus curves for cyclopentane have a region where the cis and trans lines cross (Figure above, at ca 20° dihedral angle), so there are cases

where cis and trans couplings are identical (see below, where the allylic proton is a

quartet of doublets, arising from accidental equivalence of three vicinal couplings), as well as a smaller region where Jtrans > Jcis .

If the ring puckering is strong enough, then Jtrans > Jcis. In bicyclo[2.2.1]heptanes the

endo-endo and exo-exo 3J are always greater than endo-exo couplings. Thus stereochemical relations among vicinal protons in 5-membered rings cannot be reliably determined by simply measuring coupling constants, except in cases where the substitution pattern of the specific ring system has been carefully investigated. For

example, in the benzodihydrofurans below, changing the size of the substituent R causes a reversal in the size of Jcis and Jtrans.

Cyclobutanes. Cyclobutanes are even flatter than cyclopentanes, so that cis couplings are almost always larger (6-9 Hz) than trans (2-8). However, if structural features which promote strong puckering of the ring such as a trans ring fusion, large or electronegative substituents are present, then trans couplings can become larger than cis, as shown for 1,3-dibromocyclobutane and cyclobutanol below.

Cyclopropanes. Dihedral angles in cyclopropanes are rigidly fixed by the geometry of

the ring system. We therefore find that Jcis(7-10 Hz) is always larger than Jtrans (2-6 Hz), and this can be reliably used for structure assignment. The same relationship holds for the 3-membered ring heterocycles, although the range of observed couplings is wider.

Summary: On the double Karplus curve below are indicated the dihedral angles and hence the cis and trans 3-bond couplings that can be observed for various rings. Chair cyclohexanes are conformationally well defined, with a relatively small range of 3J couplings possible (Jeq-eq and Jeq-ax typically 3-4 Hz, and Jax-ax typically 8-13 Hz). With 5 and 4 membered rings a wider range of couplings are seen depending on the extent and type of puckering present. Cis couplings will typically be larger than trans couplings. Unfortunately for both cyclopentanes and (less commonly) cyclobutanes, Jtrans can occasionally be larger than Jcis for pseudoaxial protons, if the conformation places the dihedral angle to the left of the crossing point at ca 20°. For such systems both Jtrans and Jcis will be relatively large (8-10 Hz). Cyclopropanes are rigid, and Jcis (eclipsed, Θ = 0°) is always greater than Jtrans (Θ = 120°). With this in mind, the appearance of only well defined large (ca 10 Hz) and small (ca 3 Hz) in a CH

coupled vicinally to one or more CH2 groups is quite characteristic of cyclohexanes. Cyclopentanes and cyclobutanes, on the other hand, tend to more frequently have intermediate size couplings (5-9 Hz), and often nearly equal and large coupling to cis and trans vicinal neighbors..

5.5.10 Acyclic Stereochemistry using 3JHH

The use of 3J for conformational analysis in acyclic systems can be more difficult than within rings because of the larger number of conformations typically possible. Basically, a single coupling constant cannot usually distinguish which of two diastereomers might be present since there are 3 possible staggered conformations for each diastereomer, two of which will typically have very similar predicted coupling constants for a pair of vicinal protons. Assignments become possible only when one can make some reliable predictions on which conformation predominates. One such situation is encountered with the diastereomeric products of an aldol condensation, as shown below:

In non-polar media, a hydrogen bond between OH and the carbonyl group is expected. Since in the syn isomer both hydrogen bonded conformations have a gauche relationship between HA and HB, we expect a smaller 3J for the syn isomer than for the anti, where one of the H-bonded conformations has an anti relationship between HA and HB (Stiles-House rule: Stiles J. Am. Chem. Soc.1964, 86, 3337; House J. Am. Chem. Soc. 1973, 95, 3310; Heathcock, JOC, 1980, 45, 1066; Mukaiyama JACS, 1974 96,

7503).

This method will only work if the intramolecular hydrogen bonded conformations are the principal ones for both diastereomers. Thus it sometimes fails in situations where the α and/or β-substituent is large, as in the α-t-Bu aldols below. Here gauche interactions destabilize the hydrogen bonded six-membered ring of the syn isomer, leading to a large coupling because of a high population of the non-hydrogen-bonded conformation with t-Bu and Ph anti periplanar in the syn isomer (Heng, Simpson, Smith J. Org.

Chem. 1981,46, 2932). Similarly, in more complicated systems additional conformational constraints can overwhelm the hydrogen bond effect. For example a 3-alkyl substituent in a cyclohexanone aldol has Jsyn > Janti (Kitamura, Nakano, Miki, Okada, Noyori J. Am. Chem. Soc.2001, 123, 8939).

For use of 13C shifts to assign stereochemistry see: Heathcock, J. Org. Chem., 1979, 4294.

Conformations of CH2 Chains. Adjacent CH2 groups in acyclic molecules (X-CH2-CH2-

Y) typically show apparent triplets, or higher multiplets if X and/or Y contain vicinal protons coupled to the CH2 groups. These are actually AA'BB' or AA'XX' systems, and thus are inherently non-first order. It turns out that if X and Y are sterically small, then the gauche conformation is sufficiently populated (anti/gauche ca 3:1) that nearly equal JAX and JAX' are seen, leading to the apparent triplets. If X and/or Y is sterically

large, then more complicated patterns are seen. See Sect. 5.15.

5-HMR-5.12 Allylic 3J

Couplings of vinyl hydrogens to vicinal protons across single bonds follow Karplus relationships similar to those of other vicinal couplings. The size of J is maximal at dihedral angles of 180° and 0°, and minimal when the C-H bonds are perpendicular (Θ = 90°), although the coupling does not go to 0.

In acyclic systems without strong conformational restrictions, rotational averaging produces couplings of 5-8 Hz, very similar to those observed in aliphatic chains.

For cyclic olefins, the 3J coupling decreases as the ring size gets smaller. In

cyclohexenes the couplings of an adjacent CH2 group to the vinyl hydrogens are typically

4-5 Hz for the equatorial H, and 1-3 Hz for the axial H, as shown in the figure above. In

cyclohexene itself the average of these is observed.

Dienes: The central 3J coupling in acyclic dienes is typically 10 Hz, very similar to the 3Jcis across double bonds, provided that steric effects do not prevent the diene from achieving a near planar conformation. The coupling is again reduced in cyclic dienes, both because the dihedral angle is now 0° instead of 180°, and because of inherent reduction in the coupling because of angle distortions.

Aldehydes: In unconjugated aldehydes the 3J coupling is typically small (1-3 Hz). The coupling becomes considerably larger in conjugated aldehydes like acrolein, where the dihedral angle will be either 0° or 180° to maximize overlap of the π systems.

5-HMR-5.13 Olefinic 3J

The cis and trans couplings across a double bond are very reliable indicators of stereochemistry. With virtually no exceptions, 3Jtrans> 3Jcis, typical vaues are 17 and 10 Hz. However, the ranges do overlap for very strong electron donating (J increases) and withdrawing groups (J decreases).

The coupling varies with bond order. Thus the cis coupling in benzene and other

aromatic six and larger membered rings is typically below 10 Hz (one empirical equation is: 3J = 8.65·(π bond order) + 1.66):

The tropone shows larger bond-alternation effects than the aromatic tropylium ion or the azulene.

Cycloalkenes smaller than cyclohexene show substantially reduced 3J values (Chem. Rev. 1977, 77, 599). Thus cyclopentenes can be easily distinguished from cyclohexenes and larger rings if this coupling can be identified.

Heterocycles also generally have smaller 3J values than hydrocarbon systems.

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5.6 Long-Range (4J and higher) Proton-Proton Couplings

© Copyright Hans J. Reich 2012

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Proton-proton couplings over more than three bonds are usually too small to detect easily (< 1 Hz). However, there are a number of important environments where such couplings are present, and can provide useful structural information. Coupling across π-systems are the most frequently encountered 4J couplings: the meta-coupling in

aromatic compounds, and the 4-bond allylic, propargylic and allenic couplings. 4-Bond couplings across saturated carbons (sp3) or heteroatoms are rarer, and are usually seen only cyclic compounds when there is a favorable geometric alignment along the H-C-C-C-H chain ("W-Coupling"). Longer range couplings (5J and higher) are also observed, particularly in acetylenes and allenes (Chem. Rev. 1977, 77, 599).

W-Coupling in Saturated Systems. Normally long-range couplings across saturated carbons (or O and N) are too small to detect easily (<1 Hz). However, if there is proper

orbital alignment between C-H bonds and the intervening C-C bonds then 4-bond and higher couplings can be observed. The most favorable alignment is the W arrangement of the connecting bonds ("W-coupling"), in which the H-C-C and C-C-H fragments are close to coplanar in an anti-arrangement. Thus coupling between 1,3-equatorial protons in cyclohexanes is frequently seen. However, couplings across U-shaped HCCCH

fragments can also sometimes be detected. Long-range couplings can become quite large in rigid strained bicyclic ring systems and/or when there are multiple coupling pathways available.

Cyclobutanes generally show substantial cross-ring 4J couplings, with 4Jcis, which has the proper orientation for a W-coupling, greater than 4Jtrans. In fact, Jcis > 0 and Jtrans < 0 in almost all cases (A. Gamba, R. Mondelli Tetrahedron Lett. 1971, 2133), so this coupling can be used to assign stereochemistry in cyclobutanes. The figure below illustrates the effect of the long range couplings in a cyclobutanone (a simple AB quartet would be expected if there were no long-range couplings - top simulation). An AA'BB' simulation gives the parameters shown on the figure. The pattern is not completely centrosymmetric because there is a small long-range coupling from the side-chain

CH2 (δ 1.75) to one of the cyclobutane protons.

Stereochemistry of cis/trans Decalins. A useful application of long range couplings for the assignment of ring-fusion stereochemistry in decalin ring system bearing an

angular methyl group has been developed (Williamson, K. L.; Howell, T.; Spencer, T. A. J. Am. Chem. Soc. 1966, 88, 325). In the trans-decalins, there are usually several ideal W-pathways for long range coupling between the methyl group and axial protons. In cis-decalins, there are fewer or no such pathways. Thus in a pair of cis/trans isomers, the methyl group in the trans isomer will usually be broader (or will actually show

splitting), whereas the cis isomer will have a sharper (unsplit) methyl group.

W-Coupling Across Heteroatoms. In conformationally well-defined systems significant 4J couplings can be seen to OH and other XH protons. In the example below, the long-range W-coupling between the OH proton and the axial proton at C6 was used

to assign configuration to the major isomer formed in the reaction. In the minor isomer the OH proton was not detectably coupled. The well-defined cyclohexane 3Jax-ax and 3Jax-

eq at C2 in both isomers shows that the ring-flip isomer shown predominates (Bueno, A. B.; Carreno, M. C.; Ruano, J. L. G Tetrahedron Lett. 1995, 36, 3737).

In a related system, the observation of an unusually large 4J across the sulfone sulfur was interpreted in terms of the conformation shown, in which the methyl group is over

the ring, rather than alternative conformations in which the sulfone oxygen is over the ring (Kaloustian, M. K.; Dennis, N.; Mager, S.; Evans, S. A.; Alcudia, F. Eliel, E. L. J. Am. Chem. Soc. 1976, 98, 956-965).

Allylic Coupling. 4-Bond coupling of vinyl to allylic hydrogens is usually easily observable. We can think of the coupling as having two components, the usual W-coupling transmitted through the σ-system, which is positive and is maximized for the

trans proton when the allylic C-H bond is in the plane of the vinyl C-H group ( Θ = 0

°, J > 0), and a π-component, which is negative, and whose magnitude is maximized when the allylic C-H bond is perpendicular to the double bond (Θ = 90 °, J < 0) (Garbisch, J. Am. Chem. Soc.1964, 86, 5561). The positive σ-contribution added to the larger negative π-contribution normally results in a numerically slightly smaller

(negative) coupling to the trans vinyl proton, but the effect is small, and not reliable enough for the unambiguous determination of double bond stereochemistry (note the marked entry below in which Jtrans > Jcis) (Barfield, M.; Chakrabarti, B. Chem. Rev. 1969, 69, 757).

Benzylic Coupling. Coupling between benzyl protons and ortho hydrogens on aromatic rings are typically <1 Hz, and thus often not resolved, but almost always cause significant broadening of both the aromatic and benzyl protons. This can be clearly seen

in the spectrum of p-methylacetophenone below, where the Ar-CH3 is noticeably shorter (and wider) than the C(=O)-CH3, and the protons ortho the CH3 are broader than those ortho to the acetyl group. The coupling is related to π-bond order, so it is usually smaller than allylic coupling.

Homoallylic Coupling. Couplings across 5 bonds are unusual, but can be seen under favorable circumstances. Optimum coupling is seen when both C-H bonds are aligned with the π-orbital of an intervening double bond (perpendicular to the plane of the double bond). Especially large long-range couplings are seen for 1,4-cyclohexadienes

and related structures where there are two paths for the coupling.

Long range Couplings in Acetylenes and Allenes. No special structural features are required to observe 4- and 5-bond couplings across acetylenes and allenes - such

couplings are usually present. Even couplings across 5, 6, and more bonds are detected across polyacetylene or cumulene chains

Long range couplings like this are also observed across nitrogen as in the nitrilium ion below:

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5.7 Pople Nomenclature for Coupled Spin Systems

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The analysis of complex NMR patterns is assisted by a general labelling method for spin systems introduced by Pople. Each set of chemically equivalent protons (or other nuclei)

is designated by a letter of the alphabet. Nuclei are labeled AX or AMX if their chemical shift differences are large compared to the coupling between them (Δδ >> 5J). Nuclei are labeled with adjacent letters of the alphabet (AB, ABC or XYZ) if they are close in chemical shift compared to the coupling between them (i.e. if they are strongly coupled).

If groups of nuclei are magnetically equivalent, they are labeled AnBn, etc. Thus CH3 groups are A3, or X3. A group of magnetically equivalent nuclei must have identical chemical shifts, and all members of the group must be coupled equally to nuclei outside the group. If nuclei are chemical shift equivalent but not magnetically equivalent, then

they are labeled AA', BB'B'' or XX'. Thus in anA2X2 system the A nucleus must have identical couplings to the two X nuclei. In an AA'XX' system, on the other hand, JAX ≠ JAX'. There are usually profound differences in the appearance of A2X2 compared to AA'XX' patterns.

Two-Spin Systems

AX

First order. Significant parameters: JAX. A and X are each doublets.

AB

J is directly measurable, νA and νB must be calculated. Intensities are distorted: the doublets are not 1:1; the inner lines are larger, the outer lines smaller.

Three Spin Systems

AX2

First order. Significant parameters: JAX. A is a triplet, X is a doublet.

AB2

Second order. Both JAB and νAB must be calculated - neither can be directly measured from the spectrum. Significant parameters:JAB, νAB.

AMX

First order. Significant parameters: JAM, JAX, JMX. A, M and X are each doublet of doublets.

ABX

Second order. This is a very common pattern. JAB is directly measurable, JAX, JBX as well

as νA and νB can be calculated from the line positions of the spectrum once it has been properly analyzed.

ABC

Second order. This pattern can only be accurately solved using computer simulation methods. Manual analysis as a distorted ABX or even AMX pattern will lead to approximate values of coupling constants, which in severe cases can be drastically wrong.

Four Spin Systems

AX3

First order. Significant parameters: JAX. Commonly seen in CH3CHXY groups.

AB3

Second order. Computer simulation required to solve.

A2X2

First order. This is a very rare pattern. A and X are each triplets.

A2B2

Second Order. Rare.

AA'XX'

Second order. Common pattern. Can be solved by hand, but there are several ambiguities. For example, one cannot distinguish JAA'from JXX'. Significant parameters: JAA', JXX', JAX, JAX'. The AA' and XX' patterns are each centrosymmetric, and

they are identical to each other.

AA'BB'

Second order. This is a common pattern. Requires computer simulation to solve. Seen in X-CH2CH2-Y groups where X and Y have similar shift effects. The entire multiplet is centrosymmetric (i.e., the AA' part is a mirror image of the BB' part).

Five Spin Systems

A2X3

First order. Very common pattern (ethyl groups: CH3CH2-X where X is an electronegative atom)

A2B3

Second order. Seen in ethyl groups CH3CH2-X where X is a metal: e.g. CH3CH2-SiR3.

ABX3

Second order, but soluble by hand. Commonly seen in ethyl groups in chiral molecules where the CH2 protons are diastereotopic.

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5.8 Symmetry in NMR Spectra

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Protons and other nuclei in NMR spectra can be classified as heterotopic, diastereotopic, enantiotopic and homotopic. Heterotopic and diastereotopic protons will

have different chemical shifts and couplings to neighboring magnetic nuclei, enantiotopic and homotopic protons will have identical chemical shifts. They may or may not have identical couplings to other nuclei. Distinction can be made by the substitution test.

The Substitution Test for Equivalance of Protons

For a pair of protons to be tested, replace one and then the other with another group (one not present in the molecule). Compare the two structures formed. If they are identical, the protons are homotopic, if they are enantiomers, the protons are

enantiotopic, if they are diastereomers then the protons are diastereotopic, if they are structural isomers, the protons are heterotopic.

Homotopic Protons:

Enantiotopic Protons:

Enantiotopic protons normally have identical chemical shifts. However, when the

molecule is placed in a chiral environment (say with an optically active solvent, cosolvent or Lewis acid) then the protons can become diastereotopic. This is in contrast to homotopic protons, which are always identical.

Diastereotopic Protons:

The concept of diastereotopicity was first introduced during the early days of NMR spectroscopy, when certain kinds of molecules gave unexpectedly complex NMR spectra, leading to some confusion about the orgins of this hitherto undetected phenomenon (Nair, P. M.; Roberts, J. D. J. Am. Chem. Soc., 1957, 79, 4565). A typical situation

where diastereotopic protons are seen is a CH2 group in a chiral molecule (one with an asymmetric center, or other types of asymmetry).

A more subtle form of diastereotopism is demonstrated in the classical example of diethyl acetal below. Even though diethyl acetal has no asymmetric centers, the CH2 group is diastereotopic. This can be shown by applying the substitution test, which creates a pair of diastereomers G and H. Thus the ethyl group forms an ABX3 pattern

(see Section 5-HMR-13). The key to understanding this type of diastereotopicity is that the molecule has a plane of symmetry (hence is achiral). However, there is no plane of symmetry that bisects the CH2 protons, so they are nonequivalent.

The dibromocyclopropane spectrum illustrates this effect in a different context - the protons of the CH2Cl group are diastereotopic. However, the protons of the cyclopropane CH2 group are not, since they are related by a plane of symmetry.

Not all CH2 groups in chiral molecules are diastereotopic - in the following chiral molecules the CH2 is on a C2 axis of symmetry, and the protons are homotopic. In general, CH2 groups (or other similar groups like CHMe2, CHF2, etc) will be diastereotopic when part of a chiral molecules unless the CH2 group is on a C2 rotation axis (as in the molecules below).

Heterotopic Protons:

Magnetic Equivalence

There is an additional element of symmetry which is important for NMR spectroscopy, the magnetic equivalence or inequivalence of nuclei. Protons that are enantiotopic or homotopic will have the same chemical shift, but they will not necessarily be magnetically equivalent. For two protons to be magnetically equivalent they not only have to have the same chemical shift, but they must also each have the same J coupling to other magnetic nuclei in the molecule. This is easiest to see from some specific examples. The two vinyl and two allylic protons in cyclopropene are each magnetically equivalent because each of the A protons is equally coupled to the two X protons. The spectrum

consists of two identical triplets (A2X2 system).

On the other hand, the two pairs of equivalent protons in trans-dichlorocyclopropane are NOT magnetically equivalent, because each of the A protons is coupled differently to the two X protons (one is a trans coupling, the other a cis). In the Pople nomenclature, such magnetically inequivalent nuclei are given an AA' designation. Thus the dichlorocyclopropane is referred to as an AA'XX' system, where A and A' refer to protons that are symmetry equivalent but not magnetically equivalent. The spectrum will be much more complicated than two triplets. Two more examples are 1,1-difluoroallene, which is an A2X2 system, and 1,1-difluoroethylene, which is an AA'XX' system (see 5-HMR-14.2 for a spectrum).

In general any system which contains chemical shift equivalent but magnetically inequivalent nuclei of the AA' type will not give first order splitting patterns, although sometimes the spectra may appear to be first order ("deceptively simple" spectra). For example, X-CH2-CH2-Y systems are of the AA'XX' type, but the coupling constants JAX and JAX' are often close enough in size that apparent triplets are seen for

each CH2 group. See Section 5-HMR-14 for examples.

Two important generalizations:

Coupling between symmetry equivalent but magnetically inequivalent nuclei typically will affect the appearance of the NMR spectrum. In fact, it is the coupling between the equivalent nuclei that is responsible for the complexity of spectra of the AA'BB'X.. type.

Coupling between magnetically equivalent nuclei does not affect NMR spectra, cannot be detected, and thus can be ignored.

The NMR Time Scale

It is important to recognize that diastereotopic and magnetic equivalence effects are subject to the time scale of the NMR experiment, which is on the order of tenths of a second (see Sect 8-TECH-3). Flexible molecules will often have several conformations, some of which may have lower symmetry than others. However, since these conformations are typically interconverting rapidly, the observed symmetry in the NMR spectrum will be that of the most symmetric conformation reachable. Thus cyclohexane is a sharp singlet at room temperature, whereas at -100 °C the ring inversion is slow on the NMR time scale, and a much more complex spectrum results (see Sect 5-HMR-5.3).

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5.9 Second Order Effects in Coupled Systems

For first order systems J and δ values are directly measurable from line positions. However protons or groups of protons form first order multiplets only if the chemical shift differences between the protons (Δν) are large compared to the coupling constants between them (J), i.e. if Δν /J (all in Hz) is < 5 then second order effects appear.

When Δν /J < 1 then second order effects become very pronounced, often preventing detailed manual interpretation of multiplets, or giving incorrect coupling constants if first order behavior is assumed.

There are a number of changes that occur in NMR spectra which are the result of degenerate or near-degenerate energy levels in strongly coupled systems i.e. when Δ /J becomes small (in English: whenever the coupling constant between two nuclei is similar in magnitude to the chemical shift between them, the spectra get complicated). If the spectrum is measured at higher spectrometer frequency the chemical shifts (in Hz)

become larger, whereas the coupling constants stay the same, so the spectrum usually gets simpler. Exceptions are the AA'XX' type of systems, which are field independent, and usually cannot be completely solved from line positions and intensities alone.

The effects of spectrometer field strength on the ability to resolve NMR coupling information is illustrated in this set of spectra of ethylbenzene, plotted at a constant Hz scale. The aromatic signals go from nearly a singlet at 60 MHz to a reasonably resolved set of peaks at 600 MHz (spectra courtesy of Kris Kolonko). This increase in information content and increased ease of interpretation of NMR spectra at higher magentic field

strength is the main justification for the additional expense of more powerful magnets.

We can define a hierarchy of coupling patterns which show increasingly larger number of second-order effects:

AX and all other first order systems (AX2, AMX, A3X2, etc.) AB (line intensities start to lean, J can be measured, δ has to be calculated) AB2 (extra lines, both J and δ have to be calculated) ABX, ABX2, ABX3, JAB can be measured, others require a simple calculation ABC (both J and δ can only be obtained by computer simulation) AA'XX' (these do not become first order even at higher fields) AA'BB' AA'BB'X (etc)

1. A universally observed effect is that as chemical shifts become comparable to

couplings, line intensities are no longer integral ratios (AB and higher). The lines away from the chemical shift of the other proton (outer lines) become smaller and lines closer (inner lines) become larger (see the triplets below) - the multiplets "lean" towards each other. The leaning becomes more pronounced as the chemical shift difference between

the coupled multiplets becomes smaller.

2. Line positions are no longer symmetrically related to chemical shift positions (AB), eventually calculations may have to be carried out to obtain δ and J (ABX and higher).

3. Some or all of the coupling constants can no longer be obtained from line separations (AB2 and higher).

4. The signs of coupling constants affect line positions and intensities (ABX and higher).

5. Additional lines over that predicted by simple coupling rules appear. First, lines which formally have intensities of 2 or more split into the component lines. Eventually combination lines, which no longer can be assigned to any one nucleus appear (AB2 and higher). A nice example is provided by the compound below. For the BrCH2CH2O group

the two methylenes at δ 3.48 and δ 3.81 have a relatively large chemical shift separation, and they form recognizable triplets, although with a little leaning. For the MeOCH2CH2O group the chemical shift between the CH2 groups is small, and the signals are a complicated multiplet with only a vague resemblance to a triplet. There is likely an

additional complication from variability in the size of the two different vicinal couplings in the two patterns (see Section 5-HMR-15 for more on this). The additional lines can lead to "Virtual coupling" effects: apparent coupling to protons that are actually not coupled. See Section 5-HMR-16)

6. Coupling between equivalent nuclei (e.g., JAA' or JXX') affects line count and positions. Second order effects will appear even if Δν /J is large when groups of magnetically non-equivalent protons with identical chemical shifts are coupled to each other (seeSection 5.8). Thus Me3Si-CH2-CH2-Cl (an AA'XX' system, see Section 5-HMR-14) is not just two triplets. These patterns do not get simpler at higher field strengths.

7. Computer analysis becomes mandatory to extract accurate J and δ values (ABC and higher). A typical example is the spectrum below, where a near coincidence of H2 and

H3 leads to a complex spectrum.

8. Ultimately spectra become so complex that the only useful information is integration,

chemical shift and general appearance.

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5.10 AX and AB Spectra

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The simplest molecules that show J coupling contain two spin 1/2 nuclei separated by 1, 2, 3 (occasionally 4 and 5) bonds from each other. If the chemical shift between the protons HA and HX is large compared to the coupling between them (νAX >> JAX), we

label them as AX. If the chemical shift is comparable to the coupling between the protons (νAB < 5 JAX),we have an AB system. Some molecules that give AB/AX patterns are shown below (spectra are all at 300 MHz):

· Disubstituted alkenes

· 1,2,3,4- and 1,2,3,5-tetrasubstituted benzenes; polysubstituted furans, pyridines, and other aromatic systems

· Isolated diastereotopic CH2 groups. Exercise: Assign the protons in this spectrum.

· Benzyl, methoxymethyl and related protecting groups in chiral molecules. Exercise: Assign the protons in this spectrum.

Energy Levels of AX and AB Spectra

The energy levels for an AX system are given in a very straightforward by the equation:

E = -(mAνA + mXνX) + mAmXJAX

There are four states: αα, αβ, βα, ββ. We will use the convention: αα is the lowest energy state (α is aligned with the field, m = +½) and ββ is the highest energy state (β

is aligned against the field, m = -½). The first term in the equation is the chemical shift part, the second term the coupling part. If the coupling is a small perturbation, then the energy is simply the sum of the two parts. In energy level terms, this means that the energy separation of the αβ and βα states is large compared to J.

AB Spectra

When the energies of the αβ and βα states approach each other, they begin to mix, the

αβ state develops some βα character and vice versa (the mixing parameter Q specifies the degree of mixing). The energy of the βα state, instead of ½ (νA-νB), then becomes ½ [(νA-νB)

2 + J2]½ (here defined as D)

In addition to these perturbations in energy levels, the probability of the transitions (i.e. line intensities) also varies - the A1 and B2transitions become weaker and eventually disappear (i.e. they become forbidden), leaving only the A2 and B1 lines, which appear exactly at the chemical shifts of A and B when Δν becomes 0.

Solving an AB pattern:

Graphical method for determining the position of a leaning coupled partner. The point Q is the horizontal projection of the line 2 on the position of line 1, and

point P is the projection of the line 1 on the position of line 2. The line through P and Q intersects the baseline at the midpoint between the chemical shifts of A and B (point C) (http://www.ebyte.it/library/docs/kts/KTS isoABGeometry.html). You can use this method to quickly estimate where a leaning doublet's coupling partner should be, if other peaks obscure the region of interest, or to determine whether you are

looking at a leaning doublet, or two unrelated peaks.

How to report an AB quartet.

Journals require that NMR spectra be reported in text format. There are several ways

an AB quartet could be reported:

1. Treat the pattern as first order (i.e., as two doublets). This is OK for AB quartets with a large νAB / JAB ratio, say > 4, where the error in chemical shifts caused by simply

taking the middle of each doublet is small:

3.68 (d, 1H, J = 10.3 Hz), 3.79 (d, 1H, J = 10.3 Hz)

2. For closely spaced AB quartets (νAB / JAB < 4) the AB character should be explicitly shown, to indicate that the pattern was recognized, and the shifts were calculated

correctly. One way is to report the chemical shift of the center of the AB quartet, and

ΔδAB and JAB.

2.66 (ABq, 2H, ΔδAB = 0.05, JAB = 12.2 Hz)

A second way is to report the two chemical shifts, and the coupling.

2.63, 2.69 (ABq, 2H, JAB = 12.2 Hz)

Note that the latter two formats not only use less journal space but also contain more information than the "first order" format (1). There is nothing in the first description that specifies that the two doublets are coupled to each other, yet that would be obvious from observing the spectrum.

Shown above is the 60 MHz spectrum of Abel's ketone in CDCl3 solution. There are three sets of protons that one would expect to form AB quartets. Identify them on the

structure.

The AB quartet at 3.7 δ can be analyzed as follows:

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5.11 The AX2 and AB2 Patterns

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Some examples of molecules containing three spin systems in which two of the nuclei are magnetically equivalent are shown below. Perhaps the most common type is 1,2,3-

trisubstituted benzenes in which the 1 and 3 substituents are identical.

AX2 and AB2 patterns are not as common as AMX, ABX and ABC, but there is an

important reason for examining them in some detail. The transition of an AX2 to an AB2 spin system provides additional insight into the appearance of second order effects. In the AB pattern there are two effects of this type:

• The line intensities no longer follow simple rules

• The arithmetic average of line positions no longer gives true chemical shifts, although the coupling constant JAB can still be directly measured from the spectrum.

In AB2 spectra a third and fourth effects appear: none of the line separations correspond to JAB, and additional lines appear which are not predicted by simple multiplet rules. The additional lines arise from splitting of double-intensity lines, as well as from the appearance of new transitions.

The AB2 spectra illustrate this process. In the top spectrum we have Δν/J >> 5, and the system is effectively AX2, it consists of an A triplet and a B doublet. As Δν/J becomes smaller, the double-intensity middle line of A and both B lines split into two lines. An

additional line which is not a direct descendant of any of the AX2 lines appears (a combination line: αβα → βαβ). Since it is essentially a forbidden transition it is usually quite weak, but can sometimes be observed. In the bottom spectrum (Δν/J = 0.7) the intensity of line 9 is 0.4% of the most intense line (line 5).

When Δν/J < 1 the spectrum takes on the appearance of a triplet, with a very intense and broadened central line. Finally, as Δν/Japproached 0 (νA = νB) the outer lines disappear completely, and we are left with a singlet.

Solving an AB2 Pattern

To analyze an AB2 pattern, we number the lines as shown, the four A lines ν1- ν4, the four B lines ν5- ν8, and the very weak combination line ν9. The arithmetic is simple:

Some points to remember about AB2 patterns:

1. The spectrum depends only on the ratio Δν/J. 2. Note that lines 1-4 must correspond to the one-proton part, lines 5-8 to the two-proton part. Thus, if the pattern is A2B then the numbering proceeds in the reverse direction. Distinguish the one and two proton parts by integration. 3. Line ν5 is the most intense line. The lines ν5 and ν6 often do not split up.

4. When Δν/J is much less than 1 the spectra appear nearly symmetrical since ν1, ν2 and ν8 become very weak. The spectrum then has the appearance of a distorted triplet with a 1:10:1 area ratio (the peak heights will not be in this ratio since the center line consists of several closely spaced ones.

5. Neither JBB nor the sign of JAB affect the appearance of the spectrum.

Spectrum is A2B, so ν1 = 0.0 . . . ν8 = 40.7

νB = ν3 = 9.0 Hz

νA = (ν5 + ν7)/2 = (31.9 + 39.1)/2 = 35.5 Hz |JAB| = |(ν1 - ν4 + ν6 - ν8)/3| = |(0 - 15.6 + 32.5 - 40.7)| / 3 = 7.9 Hz δB = (9 + 400)/60 = 6.82; δA = (35.5 + 400)/60 = 7.26

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5.12 ABX Pattern

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AMX, ABX and ABC patterns, and various related spin systems are very common in

organic molecules. Below some of the structural types which give ABX patterns.

AMX Patterns. Three nuclei coupled to each other and separated by a large chemical shifts compared to the coupling between them can be analyzed in first order fashion (Sect. 5-HMR-3): the A, M and X signals are each a doublet of doublets, and the couplings can be extracted by inspection. Exercise: How can the assignments for the A and M protons be done in the example below (see Sect. 5.5?

ABX Patterns. When two of the protons of an AMX pattern approach each other to form an ABX pattern, the characteristic changes in intensities of a strongly coupled

system (leaning) are seen, and, as the size of J approaches the value of νAB more

complicated changes arise, so that the pattern can no longer be analyzed correctly by first order methods. A typical ABX spectrum is shown below:

For this spectrum νAB is less than twice J, and a first order (AMX-type) interpretation

starts to become imprecise, although, in this particular case, it is unlikely to lead to a substantial misinterpretation. On the other hand, for the spectrum below (which is actually an ABMX3, where X = 19F), the second order effects are so large than a first order interpretation may lead to grossly inaccurate couplings, both in magnitude and sign, and a possible misassignment of the structure.

Figure 5-12.2. A borderline ABX pattern (actually an ABMX3 pattern, since the M proton is coupled to the three fluorines. First order analysis of this one is problematic.

Even more likely to mislead is the ABX pattern below, for which any form of first order analysis could lead to wildly incorrect structure interpretations, or even a "false negative" during synthesis of a molecule (i.e., your reaction was actually successful, but

you conclude that if failed because the NMR spectrum does not appear to fit the expected structure).

Figure 5-12.4. A deceptive ABX pattern, in which one of the ab sub-quartets has collapsed to a singlet. No first-order analysis possible.

For these reasons, we will examine ABX patterns in some detail. In the progression

from first-order NMR patterns to incomprehensible jungles of peaks, they represent the last stopping point where a complete analysis (by hand or hand calculator) is still possible, and where insights into the problems that arise in the analysis of more complex systems can be achieved. Specifically, ABX patterns are the simplest systems which show the phenomenon sometimes referred to as "virtual coupling" (see Sect. 5-HMR-16)

and they are the simplest systems in which both the magnitude and the sign of J coupling constants is significant. Furthermore, as illustrated above, there are several pathological forms of ABX patterns which are sufficiently nonintuitive that the unwary spectroscopist can mis-assign coupling constants and even structures.

Development of an ABX Pattern. Consider the stick diagram below which represents an ABX pattern in which we sequentially turn on first the A-X and then the B-X coupling:

One of the two lines in the A-pattern arises from those molecules with the spin of the

X-nucleus aligned against the field (β) and the other from those which have the X-spin aligned with the field (α). Similarly for the B-pattern. Note, however, that the line assignments of the pattern with both JAX and JBX nonzero will be different depending on the relative sign of JAX and JBX, as illustrated in the Figure. Up to this point the line

positions are identical.

The key to understanding ABX patterns is to realize that the A and B nuclei with X = α and those with X = β are actually on different molecules, and cannot interact with each

other. Thus, when we finally turn on JAB, it will be the X = α line of A and the X = α line of B that will couple to form an AB-quartet. Similarly, the two X = β lines will form a second AB-quartet. Since the line intensities and line positions of an AB quartet depend on the "chemical shift" between the nuclei, it is clear that the different relative signs of JAX and JBX will result in different spectra. The ABX pattern is thus the simplest spin

system for which the discerning spectroscopist can identify the relative signs of coupling constants by analysis of the pattern. The figure below shows the final AB part of the ABX pattern for the two cases.

Solving ABX Patterns

Recognizing an ABX Pattern. A typical ABX spectrum consists of an unsymmetrical 8-line pattern integrating to two protons which has 4 doublets with the same separation JAB (each doublet shows strong "leaning"). This is the AB part. The X part is a symmetric 6-line pattern, integrating to one proton, with four lines dominant (often

looking like a dd). The 5th and 6th lines are usually small, and not often seen. JAB and νX are directly measureable, the other parameters (JAX, JBX, νA, νB) must be calculated.

The AB part consists of two superimposed ab quartets (8 lines) which have normal intensities and line separations, both of which have identical JAB values, but can have

very different νab values. We will use "a" and "b" for the AB-subquartets of the AB part of an ABX pattern Occasionally one of the ab1 quartets has νab = 0, and appears as a singlet. Such systems appear as a five line pattern, with one ab quartet and a singlet (see Fig. 5-12.4 for an example). There are also several other deceptive forms with one

or more lines superimposed.

The X part usually consists of an apparent doublet of doublets, although apparent triplets are not uncommon. There are two other lines which are often too weak to be detected (total of 6 lines). They become large when JAB > νAB.

First Order "AMX" Type Solution. Many ABX patterns are sufficiently close to AMX (i.e., νAB>>JAB) that a first-order solution has an excellent chance of being correct. We identify the distorted doublet of doublets (JAB, JAX) which make up the A portion, as well

as the dd (JAB, JBX) for B, and begin the analysis by first removing the JAX and JBX couplings, respectively. This leaves us with an AB pattern, which we can solve in the usual way. Since this is a first-order analysis there is no information about the relative signs ofJAB and JBX.

For ABX patterns which are of the "Solution 1" type (see below) this analysis will lead

to J and δ values that are quite close to correct. The errors become larger when JAX and JBX are very different in size (especially if they are different in sign) and, of course, when νAB is small compared to JAB. However, such an analysis, carelessly applied, can be completely wrong if the system is of the "Solution 2" type.

Correct Analysis of ABX Patterns. In order to correctly analyze an ABX pattern of arbitrary complexity we have to reverse the order of extraction of coupling constants compared to the AMX solution above. We have to first solve for JAB, and then

for JAX andJBX. Proceed in the following order:

1. Identify the two ab quartets. These can usually be recognized by the characteristic line separations and "leaning." We will use the notation ab+ and ab- for the two quartets (+ identifies the one with the larger νab). Number one ab quartet 2,4,6,8 and the other

1,3,5,7 (NOTE: these line numbers will not typically be in sequence in the spectrum). Check to make sure that Jab+ = Jab-, and that the ab quartet with the taller middle lines has the shorter outer lines. Note that ABX patterns are not affected by the sign of JAB.

If the ABX pattern verges on AMX (νAB/JAB >> 2), then line intensity patterns will not allow unambiguous choice of ab subquartets. Such systems can normally be analyzed as an AMX pattern, but with the limitation that the relative sign of JAX and JBX is indeterminate. If you complete the full ABX treatment with the wrong assignment of quartets, the signs of JAX and JBX will be wrong, and there will be small errors in their

magnitude. This could ultimately lead to a wrong Solution 1/2 assignment (see below) if you use the signs of couplings to make the distinction.

Another situation in which the choice of ab subquartets can be difficult is in systems

verging on ABC, where all of the line intensities are distorted. This is where computer simulations might become necessary.

2. Solve the two ab quartets. Treat the ab subquartets as normal AB patterns, and obtain the four "chemical shifts," νa+, νb+ and νa-, νb-.

3. Identify the correct solution. At this point in the analysis we encounter an ambiguity. We know that each of the ab quartets consists of two a and two b lines, but we do not know which half is a and which is b. There are thus two solutions to all ABX patterns which have two ab quartets. (The only exceptions are those ABX patterns in which one of the ab quartets has collapsed to a singlet. For these there is only one solution.) The two

solutions are obtained by pairing up one each of a δ+ and a δ- line (i.e. in the stick spectra shown, pair up one bold and one light line - solution 1 corresponds to pairing up the nearest neighbors, solution 2 to the remote ones). The analysis is completed as below:

As part of the solution we obtain the relative signs of JAX and JBX. In the example above, this means that for Solution 1 the couplings are either both positive or both negative, and for Solution 2 one is positive and one negative.

The relative signs of JAX and JBX are determined by the way in which the ab quartets

overlap. For the statements below, "lines" refers to the νa and νb line positions obtained by solving the ab- and ab+ quartets. Solution 1 is defined as the one with the larger difference between νA and νB. Thus Solution 1 always has the least distorted X-part. The vectors are drawn from a- to a+ and from b- to b+ (bold to thin) in each case.

Distinguishing Between Solutions 1 and 2. Which solution is the correct one? Several criteria can be used to make the assignment:

1. Magnitude of the couplings. Sometimes one of the solutions gives unreasonable couplings. In the example above, if we are dealing with proton-proton couplings,

Solution 2 looks dubious because one of the couplings, JBX at 27.6 Hz, is larger than usually observed for JHH. A coupling this large is not impossible for a proton spectrum, but rather unlikely.

2. Signs of coupling constants. Sometimes the sign of the coupling constants is definitive. If the structure fragment is known, the signs can sometimes be predicted, and may rule out one solution. For example, all vicinal 3JHCCH couplings are positive, geminal 2JHCHcouplings at sp3 carbons are usually negative. A common structure fragment which gives ABX patterns is CHX-CHAHB. Here both JAXand JBX must have the

same sign. On the other hand, if the pattern is CHA-CHBHX (a much less common situation) then the signs must be different. Note, however, that if you misidentified the ab subquartets, then the signs of the coupling constants you calculated may be wrong.

3. Analysis of the X-Part. It is important to note that all lines have identical positions in both Solutions 1 and 2. The intensities of the AB part are also identical for both solutions. However, the intensities of the lines in the X-part are always different, and this is the most reliable and general way to identify the correct solution.

For the vast majority of ABX patterns encountered in organic molecules, Solution 1 is correct. Solution 2 spectra are found when A and B are close in chemical shift and the size of JAX and JBX are very different, and especially when they have different signs.

Checking your solution arithmetic. There are a couple of checks you can run to make sure that there has not been a calculation error:

1. The difference in the centers of the two ab quartets should be half the average of JAX and JBX:

| c+ - c- | = 1/2[JAX + JBX]

2. The average of the two centers should be equal to the average of the two chemical

shifts:

1/2 | c+ + c- | = 1/2 | νA + νB |

Analysis of the X-Part of ABX Patterns. The X part of an ABX pattern is maximally a centrosymmetric 6-line pattern. However, in many cases it closely resembles a doublet of doublets, and it is often treated as such. However, the couplings obtained are only approximate. The errors become larger when JAX and JBX differ greatly in size, and

especially if they have different signs. The sum ofJAX + JBX will be correct, but the individual values will be incorrect, with the errors becoming increasingly larger as νAB becomes smaller. The values of JAX and JBX will be completely wrong if we are dealing with a Solution 2 pattern.

The X-part consists of 6 lines, of which only four are usually visible. The two additional lines are often weak, but can be seen in Solution 2 patterns for which νA and νB are close together, and the X-part is consequently significantly distorted. The lines are numbered as follows: the two most intense are 9 and 12, they are separated by JAX + JBX. The inner

pair of the remaining lines are 10 and 11, their separation is 2D+ - 2D-. The outer lines (often invisible) are 14 and 15, separated by 2D+ + 2D-. Line 13 has intensity of zero. These line assignments are not always straightforward: sometimes lines 10 and 11 are on top of each other, resulting in a triplet-like pattern, sometimes 10 and 11 are very close to 9 and 12, leaving just a doublet.

To carry out an intensity calculation we define lines 9 and 12 to have intensity 1 (i 9 = i12 = 1.0), and proceed as outlined below:

On the following two pages is another complete worked example of an ABX pattern solution. The "eyeball method" is the one described in the previous pages, the "formula

method" is the one commonly presented in NMR books. We recommend the "eyeball" method" because it follows the actual coupling tree in a systematic manner, whereas the "formula method" extracts the information in a mathematically correct but non-intuitive fashion. Both will give identical answers.

5. Analyzing the X Part

Solution 1 and Solution 2 are defined such that Solution 1 has the larger νA - νB value (i.e. the larger chemical shift difference between the A and B nuclei). Hence Solution 1 always corresponds to the one with the least distorted X part. To properly identify the

correct solution in ambiguous cases it is necessary to do an intensity calculation. The six X lines are numbered as follows: the two most intense are 9 and 12, they are separated by JAX + JBX. The inner pair of lines are 10 and 11, their separation is 2D+ - 2D-. The outer pair of lines (often invisible) are 14 and 15, separated by 2D+ + 2D-. Line 13 has

intensity 0.

Define the intensity of lines 9 and 12 = 1.0, and calculate the relative intensity of lines 10 and 14. For this example Solution 1 has a fairly normal appearance close to a dd, whereas Solution 2 has all 6 lines clearly visible.

A Simple ABX Pattern as νAB is Changed

Effect of Relative Sign of JAX and JBX on ABX pattern

ABX with Accidental Coincidences

ABX with Accidental Coincidences

ABX of the Vinyl Type

ABX Going to ABC

ABX Going to A2X

ABXmYnZo Patterns

In real molecules there appear frequently AB patterns that are coupled to more than

just one X proton, there may be several X protons (ABX2, ABX3) or there may be two or more different protons coupled to the AB part (ABXY, ABXYZ). Some part structures illustrate these common types:

Most such spectra can be at least approximately analyzed in a straightforward fashion using an AMX-type approach, by treating the two A lines of the parent AB quartet as each being split into a dd, ddd, dddd, dt, etc. Similar for the two lines of the B part. Fortunately, except in very unusual cases, there is no Solution 1/Solution 2 ambiguity, since the A lines and B lines can be distinguished because each shares common couplings.

Examples of ABXmYnZo Patterns

Sample ABX Spectra

Sample ABX Spectra

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5.13 ABX3 Spectra

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ABX3 patterns are very common in organic molecules: most ethyl groups in chiral molecule will have diastereotopic CH2 protons, and thus form an ABX3 system. The

partial 1H NMR spectrum of 2-ethoxycyclohexanone below illustrates a typical pattern. The A and B signals are well separated, and can be readily understood and solved as a first order "AMX3" pattern.

Just as for ABX systems, there is an exact solution, in which one first solves the four AB quartets, which are present in a 1:3:3:1 ratio (i.e., they represent the subspectra

resulting from the four combinations of X spins: ααα; ααβ/αβα/βαα; αββ/βαβ/ββα; βββ). The solutions to these AB quartets give a 1:3:3:1 quartet for the A proton, and another for the B. These can then be solved as first order patterns.

Fortunately, it is rarely necessary to do an exact solution. If JAX = JBX (or very nearly so), which is usually the case, then a first order treatment of the pattern as an "AMX3" type is quite accurate. What is done here is to treat the pattern as an AB quartet of 1:3:3:1 quartets. In other words, we view the pattern as an AB quartet, each line of which is split by the X3 protons into a 1:3:3:1 quartet. The four 1:3:3:1 quartets will

have the normal intensity ratios of an AB quartet. To solve, identify the AB-quartet of q and then remove the X coupling. What remains is an AB quartet which can be solved in the usual way. Note that this corresponds exactly to the "AMX" solution for ABX patterns (see 5-HMR-12.3), in which we treat the pattern as an AB quartet, each half of which is split into a doublet by the X nucleus.

The simulated spectra shown mimic ABX3 patterns (AB part) of OCH2CH3 groups in chiral molecules. In these spectra all 16 of the lines are resolved, and recognition of the pattern is relatively easy. In real molecules it is common for several of the lines to be

superimposed (especially since JAB is often nearly twice as large as JAX), making recognition of this pattern more difficult. In situations where the distereotopic shift is small, the pattern can be mistaken for a quartets of doublets (see the νAB = 6 Hz spectrum).

It is not necessary for a molecule to have a center of chirality to show diastereoptopic CH2 groups. Molecules with two ethyl groups attached to a prochiral center can also have ABX3 patterns, as illustrated in the spectra of the diethoxysilanes below. The left structure has enantiotopic CH2 protons, the right has diastereotopic ones (see Section 5-

HMR-8 for the substitution test).

The spectrum of diethyl sulfite below is of historical interest - this type of diastereotopicity was first recognized for this molecule (Finegold, H. Proc. Chem.

Soc., 1960, 283), with the correct explanation and analysis described in a classic paper (Kaplan, F.; Roberts, J. D. J. Am. Chem. Soc. 1961, 83, 4666), which also reported the first recognition that 2J and 3J at sp3 carbons have different signs. Diethyl acetals of aldehydes or diethyl ketals of unsymmetrical ketones also form ABX3 patterns.

Sample ABX3 Spectra

The spectra below provide some details of a typical fully developed ABX3 system. If the CH3 group is decoupled, then we are left with a simple AB quartet, exactly analogous to AMX3 solution described above.

The spectra of dichloroacetaldehyde diethyl acetal illustrate that a molecule which contains diastereotopic protons can give decidedly simpler NMR spectra at low field than at high field. The CH2 group appears as a simple quartet at 90 MHz: the outer lines of the ABX3 pattern are too small to see, and the splitting of the inner lines is too small to resolve. At 300 MHz, on the other hand, the CH2 group is much more complex since HA and HB of the ethoxy are now far enough apart to give a well-developed ABX3 pattern,

ABMX3 Patterns

Patterns of the ABMX3 type, such as the one below, can also be readily understood and

analyzed by a simple extension of the ABX3analysis. The CH2 of the ethyl group is an AB quartet, each line of which is split into a doublet of quartets from coupling to the M and X3 protons. One of the two dq of each proton is shown schematically above the simulation, which is plotted with a narrow line width so all of the lines can be resolved. Note that in this case the coupling of A and B to the X3 protons are identical, but A and B

are coupled differently to the M proton. The M proton, in addition to the AB protons, is also coupled to two others labeled P and Q.

It is fairly common for ABMX3 patterns of the CH-CHAHB-CH3 type to show nearly equal JAX, JBX, JAM and JBM. In this case the CHAHB group appears as an AB quartet of quintets. The partial NMR spectrum below shows the β CH2 signal of isopropyl 2-methylbutyrate. The downfield signal is a clean doublet of quintets, the upfield one

closer to a ddq.

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5.14 A2X2 and AA'XX' Spectra

© Copyright Hans J. Reich 2012

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In A2X2 and A2B2 patterns the two A nuclei and the two X (B) nuclei are magnetically equivalent: they have the same chemical shift by symmetry, and each A proton is

coupled equally to the two X (or B) protons. True A2X2 patterns are quite rare. Both the A and X protons are identical triplets. More complicated patterns are seen when the chemical shift difference approaches or is smaller than the JAB coupling. However, both A2B2 and AABB' always give centrosymmetric patters (A2 part mirror image of the

B2 part).

AA'XX' and AA'BB' spectra are much more common. Here each A proton is coupled differently to the B and B' protons. Some molecules with such patterns are:

Such molecules give inherently second-order pattern. Only if the JAB coupling is

identical to the JAB' coupling by accident does the system become A2B2 or A2X2, and form a first order pattern (if νAB is large enough).

AA'XX' Spectra

AA'XX' spectra consist of two identical half spectra, each a maximum of 10 lines, each symmetrical about its midpoint, νA and νX, respectively. See example B below. The appearance of the spectrum is defined by four couipling constants: JAA', JXX', JAX and JAX'. The spectrum is sensitive to the relative signs of JAX and JAX', but not to the relative signs of JAA' and JXX'. The relationship between these, and the directly measurable values K, L, M, and N are given below and in the graphic.

|K| = |JAA' + JXX'| "J" of one ab quartet

|L| = |JAX - JAX'| "δ" of both ab quartets

|M| = |JAA' - JXX'| "J" of other ab quartet

|N| = |JAX + JAX'| "doublet"

Each half-spectrum consists of a 1:1 doublet with a separation of N (intensity 50% of the half spectrum), and two ab quartets, each with "normal" intensity ratios and νab =

|L|. One has apparent couplings (Jab) of |K| and the other of |M|, as indicated. Unfortunately, K and M cannot be distinguished, the relative signs of JAA' and JXX' are not known, nor is it known which number obtained is JAA' and which is JXX'. It is also not known which coupling is JAX and which is JAX', but the relative signs of JAX and JAX'can be

determined: if |N| is larger than |L|, signs are the same. Thus the 19F and 1H spectra of 1,1-difluoroethylene (B) are identical, so it is not possible to distinguish which coupling is 2JFF and which is 2JHH, nor can one tell which is the cis JHF and which istrans JHF. This would have to be done using information about such couplings obtained from compounds where the assignments are not ambiguous.

Solving an AA'XX' Pattern. If all 10 lines are visible, and can be assigned to the large doublet and the two ab quartets, the process is straighforward, as shown for the solution

of the 19F NMR spectrum of 1,1-difluoroethylene below:

1. Determine N from the doublet separation (35.3 Hz).

.2. Measure K (41.2 and 41.4 Hz) and M (31.7, 32.0 Hz) from the appropriate line

separation ("J" of the two ab quartets).

3. Calculate L - it is the "δab" of each of the ab quartets. For the K quartet we get: SQRT[(276.2-181.3)(235.0-222.7)] = 33.8 Hz, for the M quartet: SQRT[(268.1-

189.8)(236.4-221.8)] = 34.2 Hz

4. Calculate JAA' and JXX' by summing and subtracting K and M: JAA' = (K+M)/2 = (41.3+31.8)/2 = 36.5 Hz; JXX' = (K-M)/2 = (41.3-31.8)/2 = 4.7 Hz. Because we do not

know which ab quartet is K, and which M, we do not know the relative signs of JAA' and JXX', nor do we know which coupling is which.

5. Calculate JAX and JAX' by summing and subtracting L and N: JAX = (N+L)/2 =

(35.3+34.0)/2 = 34.7 Hz, JAX' = (N-L)/2 = (35.3-34.0)/2 = 0.7 Hz. Again, we do not know which coupling is which, but the relative signs can be determined: if |N| is larger than |L|, the signs are the same, as in this case.

Special Cases of AA'XX' patterns: Unfortunately a large fraction of AA'XX' patterns

are missing lines, which means that some or all of the coupling constants may be indeterminate. Below are summarized several common (and some less common) situations where a reduced n umber of lines is seen.

In the situation where JAX = JAX' (i.e. L = 0, A2X2) the spectrum collapses to a triplet. In other words, the effective "chemical shift" of each of the ab quartets is zero, and thus each gives a single line at νA. This is more or less the situation with many compounds of the X-CH2-CH2-Y type, provided that X and Y are not too large, but cause very different chemical shifts. See example C.

In the situation where JAA' ≈ JXX' (which is often approximately the case with X-CH2-CH2-Y and p-disubstituted benzenes) the M ab quartet collapses to two lines since M = 0. See example A below.

In cases where JXX' is zero, both ab quartets will have the same Jab (M = K) and will be identical, leaving only 6 lines. This is nearly the case for situations like symmetrical o-disubstituted benzenes or 1,4-disubstituted butadienes, where JAA' is a 3-bond coupling, and JXX' a 5-bond coupling. In these situations L is small (i.e.JAX is close to JAX') and the

central lines of the K and M quartets will likely be superimposed, whereas the small outer lines may be distinct -- if the outer lines are separated by just under twice the value of JXX', the inner lines by just a fraction of JXX'.

If the signs of JAX and JAX' are different the N lines will be relatively close together. This is the case for AA'XX' patterns of the AA' vicinal type, where JAB is a geminal coupling, hence negative, and JAB' is vicinal, and hence positive. In the limit, the N lines can collapse to a singlet if JAX = -JAX'

5.15 The AA'BB' Pattern

As A and X of the AA'XX' spectrum move closer together, the lines of the 1:1 doublet

each split into two lines, for a total of twelve in each half-spectrum. The AA' and BB' parts are no longer centrosymmetric, but develop a mirror image relationship, so that the entire pattern is centrosymmetric. As is found for all AX to AB transformations, "leaning" occurs, the inner lines increase and the outer lines decrease in intensity,

culminating in just a single line when νAB = 0. AA'BB' patterns can be solved manually, but the process is difficult, and is better done with computer simulations.

Typical molecular fragments which give AA'BB' patterns are:

(a) AA' Geminal (X-CH2CH2-Y). This is the most common type of AA'BB' pattern. The

appearance can range from essentially perfect triplets, to rather complicated patterns which cannot be easily analyzed. The two spectral parameters which control appearance of the spectrum are chemical shift difference νAB, and the difference between the two vicinal coupling constants JAB andJAB'. If νAB is small (AA'BB'), then the pattern will always

be complicated, no matter what the coupling constants are. If JAB ≈ JAB'then the pattern will mimic A2X2/A2B2 and triplets will be seen if the chemical shift is large enough.

The key feature that determines the complexity of AA'BB' patterns of CH2-CH2 groups is

the relative size of JAB and JAB', which is determined largely by the conformational properties of the X-CH2CH2-Y fragment. For acyclic systems, if the X and/or Y groups are small, then the populations of the anti and gauche conformations will be close to statistical (1:2). As can be seen from the table and the simulated spectra below, the two

averaged couplings become approximately equal when there is 67% of gauche isomer, and the spectrum will mimic an A2B2 pattern -- triplets if νAB is large enough (νAB >> JAB). If X and Y are large, then the anti isomer will be favored and the pattern will be more complex. In practice, adjacent CH2 groups often look like triplets, and thus the gaucheconformation must usually be favored. For cyclic systems (e.g., N-

cyanomorpholine) the ring constrains the -CH2CH2- fragment to mostly the gauche conformation, and clean triplets are not usually seen.

It is a common misconception that the equalization of coupling constants (and hence

the appearance of triplets) is a consequence of free rotation around the CH2-CH2 bond. In fact, there is free rotation around almost all such bonds in acyclic molecules at accessible temperatures. The appearance of more complicated patterns is the result of a preference for the anti conformation over the gauche (or vice versa), and has nothing to

do with the rate of rotation.

(b) AA' Vicinal. This type of AA'BB' pattern is much less common than type (a). It appears principally in 1,1- disubstituted cyclopropanes, 2,2-disubstituted-1,3-dioxolanes and other similar structures. The patterns are never triplets because JAB is invariably quite different from JAB'.

The N doublet peaks are close together in these patterns, often inside the K and M ab quartets, because JAX is negative, and JAX' is positive (N = JAX + JAX'). Since JAA' ≈ JXX' the K ab quartet has very small outer peaks, and the inner peaks will then be close to the N doublet peaks. These features can be seen in the dioxolane spectrum below (actually an

AA'BB' pattern), which has been simulated using the parameters shown (red trace). Peak labels are for the AA'XX' assignments. Because the A/X shift difference is diastereotopic in nature, most of these patterns tend toward AA'BB' except at very high field strength.

Here some AA'BB' spectra of dioxolanes.

Unsymmetrical 1,1-disubstituted cyclopropanes often have AA'XX' patterns that have a quartet-like appearance. Because JAA' is close to JAX', the M quartet is essentially a doublet, and the L quartet is very strongly leaning (see the spectra and simulation

below). This means that the central two line clusters have essentially 3/4 of the intensity (N+K), and the M lines 1/4, just as for a regular quartet

The half-spectrum of 1-phenyl-1-cyclocyclopropane illustrates this effect. Here JAA' and JXX' are a little more different than in the above example so the M quartet is visible as four lines. This 2-proton multiplet could be mistaken for a doublet of quartets

by the unwary spectroscopist.

(c) o-Dichlorobenzene (ODCB) Type. This kind of AA'BB' pattern never approaches

A2X2 because JAB (ortho coupling) is usually much larger than JAB' (meta coupling). It is seen in symmetrically 1,4-disubstituted dienes and ortho disubstituted benzenes. Note that for all AA'XX' / AA'BB' systems the A and X/B patterns are identical (although they have a mirror-image relationship). This is in spite of the fact that the coupling

relationships of A and X/B are often quite different in molecules of this type.

For most AA'XX' patterns of this type JXX' is a 3-bond coupling, and JAA' a 5-bond coupling, Thus the K and M ab quartets will be nearly superimposed (the Jab values differ

by 2JAA'), often leaving only 6 resolvable lines (Simulation A, naphthalene, o-dichlorobenzene). Even with the small JAA' values that are usually seen, the central lines of the K and M quartets will likely be superimposed, whereas the small outer lines may be distinct -- they will be separated by just under twice the value of JAA', the inner lines by just a fraction of JXX' (Simulation B, spectrum of biphenylene and the 1,4-

diacetoxybutadienes).

As with all such NMR spectra, the patterns get more complex when the chemical shift between the protons becomes smaller (AA'BB'). Some examples (both A and B shown):

(d) p-Disubstituted Benzene Type. These usually resemble a two AX doublets or an AB quartet, with some small extra lines.

For AA'XX patterns of this type, the two 3J meta couplings (JAA' = JXX') are likely to be very close in size so that the M ab quartet collapses to two lines since M = 0 or very small (Simulation B). In addition, the para-coupling (JAX') is nearly zero, which makes L

≈ N. Thus the two lines of the M quartet will appear at or close to the chemical shift of the N doublet, leaving only a doublet and one ab quartet, whose doublets will be on both sides of the N+M lines (simulation A). This is why p-substituted benzenes are often

incorrectly described as doublets, since the extra lines corresponding to the K quartet

amount to only 1/4 of the total intensity, and appear fairly close to the dominant M+N doublet.

When the chemical shift between A and B is small (as in p-bromochlorobenzene below), the usual leaning effects are seen, additional lines appear, and the extra lines become more pronounced.

(e) Miscellaneous. In the 1,3-substituted cyclobutane below

the 4JHH (JAA', JBB' and JAB') are large enough that the expected first-order AB quartet is not seen, but a much more complicated pattern. In this case, as in the p-disubstituted benzene case above the "AB" character dominates the appearance of the multiplet, largely because the coupling interactions between either of the AB protons and the A'B'

protons are much weaker than the A to B and the A' to B' couplings (i.e. the AB pair is nearly isolated from the A'B' pair).

Trans-1,2-disubstituted cyclopropanes can form AA'BB' patterns. Some examples

Origin of Complexity in Patterns of the AA'XX'... Type

There are two situations where spin systems containing AA'XX' type do not show unusual complexity. One is where JAX = JAX', in which case the pattern becomes first order A2X2.

The second is systems in which there is no coupling between both of the chemical shift

equivalent protons, i.e., JAA' = JXX' = 0. In such cases the degeneracy between spin states is no longer present, and first order systems result. Consider two examples. A monosubstituted benzene is nn AA'BB'C or AA'MM'X system. A simulated spectrum is shown below

If we recalculate the spectrum after setting JAA' = 0 and JMM' = 0 then the spectrum becomes essentially first order (it would be completely first order if the chemical shifts between A, M and X were made larger).

For this reason, some spin systems which are formally of the AA'XX' type, but in which there is no significant spin-spin coupling between the equivalent protons show first order spectra. For example, the fairly common spin system below of the AA'BB'X type shows

no unusual complexity (beyond that of normal ABX patterns) because there is no coupling between the A and A' protons, nor between the B and B' protons. Such systems are sometimes defined as (AB)2X to indicate that magnetic inequivalence is not a factor.

Contrast this with the NMR spectrum of dibromosulfolane below.

Why is this spectrum so complex? In this AA'MM'XX' system, although there is no significant coupling between A and A' or M and M', there is coupling between X and X', making the whole system a highly second order one (remember: anything coupled to a strongly coupled pair like the XX' protons becomes second order)..

If we remove the XX' coupling, the system becomes essentially first order (two isolated AMX patterns). We could better describe it as an (AMX)2 rather than an AA'MM'XX' spin system.

Another example of the same spin system is shown below.

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5.16 Virtual Coupling

© Copyright Hans J. Reich 2012

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The term "virtual coupling" refers to an NMR phenomenon in which apparently first-order multiplets contain false coupling information. In extreme cases, protons that are not actually coupled will show splitting. More commonly, the magnitude of coupling constants obtained by first-order analysis is incorrect. All virtual coupling effects arise when protons, well isolated from other protons in chemical shift, are coupled to a group

of other protons which are strongly coupled to each other. By strongly coupled we mean that these protons are both close in chemical shift and coupled to each other with J > Δν.

On the following pages are examples which illustrate the virtual coupling phenomenon in several different systems. One simple way to summarize these effects is as follows: when two or more protons are strongly coupled, then any protons coupled to them will give multiplets with false coupling information and/or unexpectedly complex multiplet structure. Furthermore, the strongly coupled protons themselves will contain misleading

multiplet structure. Virtual coupling effects are also frequently encountered inheteronuclear magnetic equivalence NMR situations, e.g. in transition metal phosphine complexes (see Sect. 7-MULTI-2)

A typical example of virtual coupling is provided by the epoxide below. HA and HB are more or less first order when the spectrum is taken in CDCl3 (although typical second

order effects are starting to appear) because HA and HB have a significant chemical shift. However, in acetrone-d6, HA and HB are essentially superimposed, and HC appears as a triplet, as if HA and HB were equally coupled to HC, leading to a very different structure assignment. The small coupling visible for HB and HC in CDCl3 is probably not entirely real

- it is the beginning of the "virtual coupling" effect which eventually leads to a triplet for HC

These effects can be understood by examining the behavior of the X part of an ABX system as ΔνAB becomes small. In this simulation, JAX is set to 0; nevertheless when ΔνAB < 15 Hz the X part shows clear indications of coupling to HA, as does the AB part, i.e. virtual coupling.

Virtual Coupling in X of an ABX system

As the chemical shift between HA and HB becomes smaller, the αβ state begins to mix with the βα state, and the βα state mixes with the αβ (the mixing coefficient is Q). This results in their energies becoming closer together, and eventually, when νAB = 0, Q becomes 1, and the two energy levels consist of equal parts αβ and βα, and their energies are identical (the X part becomes a triplet).

"Virtual Coupling" Effects

An important generalization in this area is that the severity of the "virtual coupling" effects is very strongly dependent on JAB - ifJAB is larger than JAX and JBX then the X part is profoundly changed (i.e. doublet to triplet). On the other hand, when JAB is smaller

than JAX or JBX then the perturbations are much less dramatic, leading to small additional lines and minor errors in apparent coupling constants. A case of this type is provided by

the three compounds below. The aromatic protons are well separated in 1 and 3 and

thus are pretty much first order, but in 2 HA appears nearly on top of HB. As a result, HX shows non-first order structure.

One of the main reasons that complex NMR spectra are simpler to interpret at higher field strengths is that many virtual coupling effects are ameliorated or disappear

altogether as chemical shift differences (in Hz) become larger. Exceptions are AA'BB', AA'XX' patterns and more complicated analogs (such as AA'BB'X). These are always non-first order (if there is coupling between A and A' or B and B') because they always satisfy the criteria for virtual coupling: A and A' have zero chemical shift at any field strength. If

A and A' are also coupled to each other (JAA' > 0) then the A and B protons, or any other protons coupled to A or B can give complex or misleading multiplets.

What are those Impurities? A student in the course brought me the NMR spectrum of acrolein shown below, with the question: why can't I get rid of the impurities, I've

distilled the compound twice?

The answer? The compound is perfectly pure, as shown by its NMR spectrum in benzene-d6, which is essentially first order. The problem with the spectrum in CDCl3 is that two of the protons are nearly superimposed, so that all the others which are coupled to them become very complicated. Benzene, like other aromatic solvents, causes significant upfield shifts which removes the degeneracy and leads to a first-order spectrum.

Exercise: Use WINDNMR to simulate first the benzene-d6 spectrum, and then the CDCl3 spectrum (all you should need to do is adjust the chemical shifts). Which two protons are superimposed in the CDCl3 spectrum?

Is it the Right Stuff? Accidental coincidences of chemical shifts and the resulting

virtual coupling effects can lead to surprisingly deceptive NMR spectra, sufficiently so that the unwary researcher could conclude that a synthesis had failed. An interesting case is the phenyl region of the NMR spectrum below:

Taken at face value the aromatic region looks like a 4H doublet and a 1H multiplet

(pentet or sextet) with J of 4.3 Hz, hardly compatible with a monosubstituted phenyl group. Yet this is simply a phenyl group in which the ortho and meta protons accidentally have identical chemical shifts (or nearly so). Since they are strongly coupled to each other the four protons behave as a unit, and the para proton appears to be equally coupled to all four, leading to the apparent doublet and pentet - a classical case of

virtual coupling. The apparent coupling constant of 4.3 Hz is the average of the meta and para couplings.

In the trans isomer below the meta and para protons are a little further apart, and

easily recognized for what they are.

Why is my Spectrum so Ugly? In this spectrum there is an accidental superposition of two protons, HM and HN, which are coupled to each other. All of the protons coupled to these two, HA, HB, HX, and HY, show strongly second order distorted multiplets, with extra lines and non-centrosymmetric structure. A simple method to address this kind of problem is to take the spectrum in an aromatic solvent (or even just add a few drops to

the sample), which in many cases moves the protons around enough that the second-order effects are reduced or eliminated. When the spectrum is taken in benzene, HM and HN are shifted away from each other, and HA and HB now show more or less first oder multiplets.

Methyl Region AMX3 ---> ABX3 ---> AA'X3

Methyl groups usually give reliably simple multiplets in NMR spectra. However, if a methyl group is coupled to a proton which is part of a strongly-coupled system, then its NMR signal can give complex and misleading information

© 2012 Hans J. Reich, All Rights Reserved

Web page created by WINPLT. Last updated 01/29/2012 01:04:36

NMR Solvents

Solvent Formula 1H shifts 13C shifts mp °C

bp °C

Acetic Acid-d4 CD3COOD 2.0, 11.7 20.0, 180.0 16.6 117.9

Acetone-d6 CD3COCD3 2.09 29.9, 206.7 -94.7 56.1

Acetonitrile-d3 CD3CN 1.94 1.4, 118.7 -43.8 81.6

Benzene-d6 C6D6 7.16 128.4 5.5 80.1

Carbon Disulphide CS2 none 192.8 -11.6 46.3

Carbon Tetrachloride CCl4 none 96.7 -23.0 76.8

Chloroform-d CDCl3 7.24 77.23 -63.5 61.3

Dichloromethane-d2 CD2Cl2 5.32 54.0 -95.1 40.8

Diethyl Ether (-100 °C) (CH3CH2)2O 1.21, 3.45 ?, 66.51 -

116.3 34.6

Dimethyl Ether (-100 °C)

CH3OCH3 3.2 60.08 -

138.5 -23

N,N-Dimethyl formamide-

d7 Me2NCHO

2.95, 2.75,

8.03 29.8, 34.9, 163.2 -61.? 153.?

Dimethyl Sulfoxide-d6 CD3SOCD3 2.50 39.5 18.6 189.0

1,4-Dioxan (OCH2CH2)2 3.53 66.7 11.8 101.4

Ethanol-d6 CD3CD2OD 1.11, 3.56,

5.19 17.3, 57.0 -117 78.3

Methanol-d4 CD3OD 3.31, 4.78 49.2 -97.8 64.6

Nitrobenzene C6D5NO2 7.5, 7.7, 8.1 123, 129, 135 5.7 210.8

Nitromethane-d3 CD3NO2 4.3 57.3 -28.6 101.2

Pyridine-d5 C5D5N 7.22, 7.58, 8.74

123.9, 135.9, 150.2

-41.6 115.3

1,1,2,2-Tetrachloroethane

CHCl2CHCl2 5.96 75.5 -43.8 146.3

Tetrahydrofuran-d8 C4D8O 1.73, 3.58 25.4, 67.6 -

108.5 65.4

Tetrahydrofuran -100 °C C4H8O

?, 67.96

Toluene-d8 C6D5CD3 2.09, 6.98, 7.00, 7.09

20.4, 125.5, 128.3, 129.4, 137.9

-94.9 110.6

Trichlorofluoromethane CFCl3 none 117.6 -111 23.7

Trifluoroacetic Acid-d4 CF3COOD 11.5 116.6, 164.2 -15.3 72.4

Trifluoroethanol-d3 CF3CD2OD 3.88, 5.02 61.5, 126.3 -15.3 72.4

Water D2O 4.8 none 0.0 100.0

Solvent Formula 1H shifts 13C shifts mp °C

bp °C

More detail, actual spectra,

NMR Chemical Shifts of Common Laboratory Solvents as Trace Impurities, Gottlieb, H. E.; Kotlyar, V.;

Nudelman, A. J. Org. Chem. 1997, 62 7512 - 7515. DOI