Coupling Constants (J) Coupling constants are a very important and useful feature of an NMR spectrum...

Coupling Constants (J)Coupling Constants (J)

• Coupling constants are a very important and useful feature of an NMR spectrum

• Importantly, coupling constants identifies pairs of nuclei that are chemically bonded to each other

• Multiplicity identifies the number of protons (or other nuclei) that are chemical bonded to the other nuclei

• The magnitude of the coupling constants identifies the coupling partner, and

provides information on dihedral angles, hydrogen bonds, the number of intervening bonds, and the type of coupled nuclei (1H, 13C, 15N, 19F, etc.)

1H 1H


BBoo

-- spin-spin coupling, scalar coupling or spin-spin coupling, scalar coupling or J-couplingJ-coupling

Random tumbling of molecules averages through-space effect of nuclear magnets to zero

BBoo

random tumbling leads to no interaction between the spin-states despite the small

magnetic fields


-- spin-spin coupling, scalar coupling or spin-spin coupling, scalar coupling or J-couplingJ-coupling

Instead, nuclear spin state is communicated through bonding electrons

Energy of electron spin states are Energy of electron spin states are

degenerate in absence of nuclear spindegenerate in absence of nuclear spin

With a nuclear spin, the electron spin With a nuclear spin, the electron spin

opposite to nuclear spin is lower energyopposite to nuclear spin is lower energy

Number of possible energy states of nuclear-Number of possible energy states of nuclear-electron spin pairs increases with the electron spin pairs increases with the

number of nuclear spinsnumber of nuclear spins

Spin state is “sensed” through bonds resulting in higher or lower energy

- aligned or anti-aligned with magnetic field

Coupling ConstantsCoupling Constants

Energy level of a nuclei are affected by covalently-bonded neighbors spin-states

Spin System One Spin System Two

Mixing of Spin Systems One and

Two


Mixing of energy levels results in additional transitions – peaks are split

I S

J (Hz)

Spin-States of covalently-bonded nuclei want to be aligned

The magnitude of the separation is called coupling constant (J) and has units of Hz

S

S

I

I

+J/4

-J/4

+J/4

J (Hz)

• Through-bond interaction that results in the splitting of a single peak into multiple peaks of various intensities Spacing in hertz (hz) between the peaks is a constant Independent of magnetic field strength

• Multiple coupling interactions may exist Increase complexity of splitting pattern

• Coupling can range from one-bond to five-bond One, two and three bond coupling are most common Longer range coupling usually occur through aromatic systems

• Coupling can be between heteronuclear and homonuclear spin pairs Both nuclei need to be NMR active i.e. 12C does not cause splitting


13C

1H1H 1H

one-bond

three-bond

1H

1H

1H

four-bond

five-bond


• Splitting pattern depends on the number of equivalent atoms bonded to the nuclei Determines the number of possible spin-pair combinations and energy levels Each peak intensity in the splitting pattern is determined by the number of spin

pairs of equivalent energy


Pascal’s triangle

• Splitting pattern follows Pascal’s triangle Number of peaks and relative peak intensity determined by the number of

attached nuclei Peak separation determined by coupling constant (J) Negative coupling reverse relative energy levels

11 1

1 2 11 3 3 1

1 4 6 4 11 5 10 10 5 1

1 6 15 20 15 6 11 7 21 35 35 21 7 1

3 attached nuclei

Quartet

1 1

3 3

Relative Intensity

JJ

J

singlet doublet triplet quartet pentet 1:1 1:2:1 1:3:3:1 1:4:6:4:1

Common NMR Splitting Patterns

Coupling Rules:1. equivalent nuclei do not interact2. coupling constants decreases with separation ( typically 3 bonds)3. multiplicity given by number of attached equivalent protons (n+1)4. multiple spin systems multiplicity (na+1)(nb+1) 5. Relative peak heights/area follows Pascal’s triangle6. Coupling constant are independent of applied field strength7. Coupling constants can be negative

IMPORTANT: Coupling constant pattern allow for the identification of bonded nuclei.



Common NMR Splitting Patterns


• Coupling only occurs between non-equivalent nuclei Chemical shift equivalence Magnetic equivalence For no coupling to occur, nuclei has to be BOTH chemical shift and magnetic

equivalent

c

H1

H3

H2

Cl

Ha

Hb

The CH3 protons (H1, H2, H3) are in identical environments, are equivalent, and are

not coupled to one another

The Ha and Hb protons are in different environments (proximity to Cl), are

not equivalent, and are coupled


Rules for Chemical Shift Equivalence:• Nuclei are interchangeable by symmetry operation

i. Rotation about symmetric axis (Cn)

ii. Inversion at a center of symmetry (i)

iii. reflection at a plane of symmetry ()

iv. Higher orders of rotation about an axis followed by reflection in a plane normal to this axis (Sn)

v. Symmetry element (axis, center or plane) must be symmetry element for entire molecule

C C C

Ha

Ha

Ha

Hb

Hb

Ha

Ha

Ha

Ha

Ha

Ha

Ha

Ha

Ha

Hc

Ha

Hc

Cl

Hb

Cl

Hc

Hb

Hc

Cl

Ha

Cl

180o

Symmetry planes

Examples of Chemical Shift Equivalent Nuclei

Coupling ConstantsCoupling ConstantsRules for Chemical Shift Equivalence:• Nuclei are interchangeable by a rapid process

i. > once in about 10-3 seconds

ii. Rotation about a bond, interconversion of ring pucker, etc.

Ha

Ha

Ha

Ha

Rapid

exchange

Rapid

exchange

NH2

O

HO H H

H2H2

NH2

O

HO

H H

H2H2

Examples of Chemical Shift Equivalent Nuclei

Coupling ConstantsCoupling ConstantsMagnetic Equivalence:• Nuclei must first be chemical shift equivalent

• Must couple equally to each nucleus in every other set of chemically equivalent nuclei

i. need to examine geometrical relationships

ii. the bond distance and angles from each nucleus to another chemical set must be identical

iii. Nuclei can be interchanged through a reflection plane passing through the nuclei from the other chemical set and a perpendicular to a line joining the chemical shift equivalent nuclei

Examples of Non-magnetically equivalent nuclei

Ha

Cl

Cl

Ha'

Hb'

Hb

Chemical shift equivalent, but not magnetic equivalent

C C

Fa

Fa'

Ha

Ha'

C C

Fa

Ha

Fa'

Ha'

C C

Fa

Ha

Ha'

Fa'3Jab ≠ 3Ja’b

3Jab’ ≠ 3Ja’b’

3JHaFa ≠ 3JHa’Fa

3JHaFa’ ≠ 3JHa’Fa’

Hc

Hb

Hc'

Cl

Ha

Cl

3JHaHc ≠ 3JHaHc’

3JHbHc ≠ 3JHbHc’

3JHaHc ≠ 3JHbHc

3JHaHc’ ≠ 3JHbHc’

Coupling ConstantsCoupling ConstantsMagnetic Equivalence:• Non-magnetically equivalent nuclei may lead to second order effects and very complex

splitting patterns

• Second order effects will be discussed later

i. Due to small chemical shift differences between coupled nuclei ( ~ J)

http://www.chem.wisc.edu/areas/reich/chem605/index.htm

http://www.chem.wisc.edu/areas/reich/chem605/index.htm


Multiple Spin Systemsmultiplicity (na+1)(nb+1)

C C C

Cl

Cl

Hb

H

H

Ha

Ha

HaWhat is the splitting pattern for CH2?

3JHb = 6 Hz

3JHa = 7 Hz

11 1

1 2 11 3 3 1

1 4 6 4 11 5 10 10 5 1

1 6 15 20 15 6 11 7 21 35 35 21 7 1

Coupling to Hb splits the CH2 resonance into a doublet separated by 6 Hz

3JHb = 6 Hz

Coupling to Ha splits each doublet into a quartet separated by 7 Hz

Down-field resonance Down-field resonance split into quartetsplit into quartet

up-field resonance up-field resonance split into quartetsplit into quartet


What Happens to Splitting Pattern if J changes?

3JHb = 7 Hz

3JHa = 7 HzLooks like a pentet!

3JHb = 6 Hz

3JHa = 3 Hz

Looks like a sextet!

Occurs because of overlap of peaks within the splitting pattern

Intensities don’t follow Pascal’s triangle (1 4 6 4 1)

Intensities don’t follow Pascal’s triangle (1 5 10 10 5 1)


Coupling Constants Provide Connectivity Information– chemical shifts identify what functional groups are present

C C C

Cl

Cl

Hb

H

H

Ha

Ha

HaNMR Peaks for coupled nuclei share the same coupling constants

CH2

CH3

CH

6 Hz 6 Hz 6 Hz

7 Hz 7 Hz

7 Hz6 Hz 7 Hz

Integral: 1 2 3


Deconvoluting a spin system– determining the J-values– determining the multiplicities present

J coupling analysis:i. Is the pattern symmetric about the center?ii. Assign integral intensity to each line, outer lines assigned

to 1iii. Are the intensities symmetric about the center?iv. Add up the assigned intensities

– Sum must be 2n, n = number of nuclei– Ex: sum = 16, n = 4

v. Separation of outer most lines is a coupling constant– Relative intensity determines the number of coupled

nuclei– Ex: intensity ratio: 1:2, 2 coupled nuclei– 1st splitting pattern is a triplet (1:2:1)

vi. Draw the first coupling patternvii. Account for all the peaks in the spin pattern by repeatedly

matching the 1st splitting patternviii. Smallest coupling constant has been assigned


Deconvoluting a spin system– determining the J-values– determining the multiplicities present

J coupling analysis:

ix. Coupling pattern is reduced to the center lines of the 1st splitting pattern.

x. Repeat process

– Ex: sum = 8, n = 3

– Ex: intensity ratio: 1:1, 1 coupled nuclei

– 2nd splitting pattern is a doublet (1:1)

xi. Repeat until singlet is generated


Demo ACD C+H NMR Viewer software– first order coupling constants

CH3CH2FCH3CH2R


Description of Spin System

– each unique set of spins is assigned a letter from the alphabet the total number of nuclei in the set are indicated as a subscript

– the relative chemical shift difference is represented by separation in the alphabet sequence

Large chemical shift differences are represented by AX or AMX (AX >> JAX)

Small chemical shift differences are represented by AB (AB < 5JAB)

Can also have mixed systems: ABX magnetically in-equivalent nuclei are differentiated by a single quote: AA’XX’ or brackets [AX]2

CH2ClCHCl2

A2X system A2M2X systemA3X2 system

Ha

Cl

Cl

Ha'

Hx'

Hx

[AX]2 or AA’XX’ system

H

H CN

Cl

AB system

O

styreneoxide

HA

HMHX

A M X

A M XTMS

A M X

J(AM)

J(AX)J(AX)

J(MX)

J(AM) J(AM)

J(MX)

J(AX) J(AX)

J(AM) = 4 Hz

J(AX) = 2.5 Hz

J(MX) = 6 Hz

Observed splitting is a result of this electron-nucleus hyperfine interaction• Coupling is measured in hertz (Hz)

Range from 0.05 Hz to thousands of Hz Can be positive or negative

o 1JC-H and many other one-bond coupling are positiveo 1JA-X is negative if are opposite sign o 2JH-H in sp3 CH2 groups are commonly negativeo 3JH-H is always positive


For an AX system, JAX is negative if the energy of the A state is lower when X has the same spin as A ( or )

The spin states and transitions are swapped

reversed

reversed

reversed


Measure the Relative Sign of Coupling Constants• Multiple experimental approaches (different NMR pulse sequences) or

simulations

E. COSY – two-dimensional NMR experiment

cross peaks identify which chemical shifts are coupled


Measure the Relative Sign of Coupling Constants• The cross-peak patterns identifies the coupling constant sign and

magnitude

Yellow-highlighted regions are expanded

Based on the slopes of the diagonal line drawn through coupling pattern

3JAX and 3JBX have the same sign

3JAB opposite sign of 3JAX and 3JBX


• Magnitude of the splitting is dependent on: Number of bonds

Bond order (single, double triple)

Angles between bonds

H3C CH3 H2C CH2

3JHH 8 Hz 3JHH 11.6 & 19.1 Hz

H

X

Y

H

H

X

H

Y

trans 3JHH ~ 17 Hz cis 3JHH ~10 Hz

HC CH

3JHH 9.1 Hz

X

Y

H

H

geminal 2JHH ~2.5 Hz

HA

HB HC

HD

3JAB 9.4 Hz4JAC 1.1 Hz5JAB 0.9 Hz


• Magnitude of the splitting is dependent on: dihedral angle

− Fixed or average conformation


• Magnitude of the splitting is dependent on: Cyclohexanes dihedral angles


3Jaa 9-12 Hz3Jee or 3Jea 3-4 Hz

3Jaa >> 3Jee,3Jea

Dual Karplus curves for the axial and equatorial protons

• Magnitude of the splitting is dependent on: Cyclohexanes dihedral angles

− examples



• Magnitude of the splitting is dependent on: Cyclopentanes dihedral angles



• Magnitude of the splitting is dependent on: Comparison between Cyclohexanes and Cyclopentanes

Because of range of cyclopentane conformations, vicinal couplings are variable: Jcis > Jtrans and Jcis > Jtrans

Only in rigid cyclopentanes can a stereochemistry be defined: Jcis > Jtrans

In chair cyclohexane, only one vicinal

coupling can be large (>7 Hz)

In cyclopentane, two or three vicinal

coupling can be large (>7 Hz)


• Magnitude of the splitting is dependent on: Cyclobutanes are flatter than cyclopentanes, so: Jcis > Jtrans

− unless structure features induce strong puckering of the ring or electronegative substituents are present

Cyclopropanes are rigidly fixed, so Jcis > Jtrans is always true


• Magnitude of the splitting is dependent on: Orientation

− unless structure features induce strong puckering of the ring or electronegative substituents are present

− Internal hydrogen bonds may lead to constrained conformations and distinct different coupling constants

Since methyl groups can freely rotate, the observed coupling is the average of the three individual coupling constants


Magnitude of the splitting is dependent on: Electronegativity of Substituents

3JH-H coupling constant decreases as electronegativity increases

3JH-H decreases even more with two electronegative substituents


3JH-H coupling constant decreases as electronegativity of substituents

increases for cycloalkenes

3JH-H coupling constant decreases as electronegativity of substituents

increases for alkenes

Magnitude of the splitting is dependent on: Electronegativity of Substituents


Magnitude of the splitting is dependent on: Ring Size

− Coupling constants decrease as ring size gets smaller

− Coupling constants also decrease as ring is formed and gets smaller


Magnitude of the splitting is dependent on: Bond order

− Coupling constant decreases as bond order decreases

Heterocycles

– Heterocycles have smaller coupling constants compared to hydrocarbons systems

3JH-H = 8.65 x (n bond order) + 1.66

• Magnitude of the splitting is dependent on: Proportional to ab

s character of bonding orbital

– Increases with increasing s-character in C-H bond


H3C CH31JC-H 125 Hz

H3C NH21JN-H 95 Hz Br

F

Cl

F

H

F

2JF-H 48.2 Hz

• Magnitude of the splitting is dependent on: Attenuated as the number of bonds increase

– Usually requires conjugated systems (aromatic, allylic, propargylic, allenic) or favorable geometric alignment (W-coupling)

– Not usually seen over more than 4 to 5 bonds (acetylenes and allenes)



Magnitude of the splitting is dependent on: Geminal protons (H-C-H) fall into two major groups

– Unstrained sp3 CH2 protons: 2JH-H -12 Hz

– Vinyl sp2 CH protons: 2JH-H 2 Hz


Magnitude of the splitting is dependent on: Geminal protons coupling constants are effected by the electronic effects of

substituents

– Based on the interaction between the filled and empty orbitals of the CH2 fragment

Note: opposite trend


Magnitude of the splitting is dependent on electronic effects: In acyclic and unstrained ring systems: 2JH-H ~ -10 to -13 Hz

When CH2 is substituted with a -acceptor, like carbonyl or cyano coupling becomes more negative: 2JH-H ~ -16 to -25 Hz

− Reliable and can help with structure assignments

Conjugated aryl, alkene and alkyne substituents also makes coupling becomes more negative


Magnitude of the splitting is dependent on electronic effects: In unsaturated carbons: 2JH-H ~ 2.5 Hz

Electronegative substituents (F,O) behave as -acceptors with a negative effect with 2JH-H close to zero

Electropositive substituents (Si, Li) behave as -donors with a negative effect with 2JH-H

Oxygen substituents can behave as a strong -acceptor and strong -donor (lone pair), both positive effects leading to a large 2JH-H or as a strong p-acceptor leading to large negative coupling

Coupling Constants (J)Coupling Constants (J)Magnitude of the splitting is dependent on electronic effects:

Summary of effects, and acceptors have opposite effects on coupling, as do and donors


Weak coupling or first-order approximation• Up to now, we have assumed the frequency difference (chemical shift) between the

coupled nuclei is large

i. >> J

• Second order effects come into play when this assumption is no longer valid

i. < 5J

• Second order effects lead to very complex splitting patterns that are difficult, if not impossible to interpret manually and leads to incorrect chemical shifts and coupling constants

• Interpreting NMR spectra with second-order effects usually requires software


Second-Order Effects (Strong Coupling)

– occurs when chemical shift differences is similar in magnitude to coupling constants (/J < 5)

chemical shifts and coupling constants have similar energy and intermingle results from mixing of the equivalent and spin states

none of the transitions are purely one nuclei described by quantum mechanical wave functions

AB spin system


Second-Order Effects (Strong Coupling) perturbs peak intensity and position

as chemical shift differences decrease, intensity of outer lines become weaker and internal lines become stronger the multiplet leans towards each other (“roof” effect) which increases as chemical shift difference decreases

AB spin system

Second-Order Effects (Strong Coupling) becomes easier to interpret at higher magnetic field strengths


Higher field increases /J



– hierarchy of coupling constants with increasing second-order effects

1. AX and all other first order systems (AX2, AMX, A3X2, etc.)

2. AB

i. Line intensities start to lean

ii. J can be measured, can be calculated

3. AB2

i. Extra lines

ii. Both J and have to be calculated

4. ABX, ABX2, ABX3

i. JAB can be measured, everything else requires calculation

5. ABC

i. Both J and have to be determined from computer simulation

6. AA’XX’

i. Do not become first order even at high magnetic fields

ii. Both J and have to be determined from computer simulation

7. AA’BB’

8. AA’BB’X

9. Etc.



– general effect of strong couplings on NMR spectra

1. Line intensities are no longer integral ratios, no longer follow Pascal’s triangle

2. Line positions are no longer symmetrically related to chemical shift position

i. Multiplet center may no longer be chemical shift (AB and higher)

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

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

5. Additional lines over the number predicted by simple coupling rules appear

i. Peaks with intensities of 2 or more are split into individual components

More lines then the expected triplet for the boxed CH2 pair



– general effect of strong couplings on NMR spectra

6. Coupling between equivalent nuclei (JAA’ or JXX’) affects line count and position

i. Second order effects appear even if /J is large for groups of magnetically non-equivalent protons with identical chemical shifts which are coupled

i. Do not get simpler at higher fields

7. Computer analysis becomes mandatory to extract accurate J and values (ABC and higher)

8. Ultimately spectra become so complex that the only useful information is integration, chemical shift and general appearance.


Second-Order Effects

– as the chemical shifts coalesce intensity of outer lines decrease inner peaks eventually collapse to singlet nuclei become chemically and magnetically equivalent

AB spin system

May be misinterpreted as a quartet

Weaker outer lines may be overlooked and interpreted as a doublet


Second-Order Effects (AB)

– analysis of second-order splitting patterns remember: resonance positions are also perturbed separation between outer lines and inner lines (a-b, c-d) yields coupling constant

JAB = (a-b) = (c-d)

true chemical shift is not the doublet centers center = ½(b+c)

AB = √ (a-d) (b-c)

A = center + ½AB

B = center - ½AB

A B


Second-Order Effects (AB2)

– as the chemical shifts coalesce

line intensities no longer follow simple rules

arithmetic average of the line positions no longer give true chemical shifts

JAB can still be measured directly from spectrum

none of the line separation correspond to JAB

additional lines appear

AB2 spin system

Note: splitting of intense lines



– four A lines 1 – 4 and four B lines 5 – 8 and the very weak combination line 9

– calculation of A, B, and JAB is simple:

– how to report an AB2 spin system in a journal manuscript:

report the two chemical shifts as an AB2 multiplete (m):

2.63, 2.69 (AB2m, 3H, JAB = 12.2 Hz)



– unique features of second-order splitting pattern for AB2 system

Spectrum depends only on the ratio /J

lines 1 to 4 correspond to the one proton part (A)

lines 5 to 8 correspond to the two-proton part (B2)

line 5 (5) is the most intense line

lines 5 and 6 often do not split up

when /J << 1, the spectrum appears nearly symmetrical

lines 1,2, 8 1, 2 ,8) become very weak

looks like a distorted triplet with 1:10:1 area ratio

JAB and JBB do not affect the spectrum

Second-Order Effects (ABX)

– most complex spin-system that can still be manually analyzed

– ABX has a common appearance AB – unsymmetrical 8-line pattern that integrates to 2 protons AB – 4 doublets with the same separation JAB with strong leaning

X – symmetric 6-line pattern that integrates to 1 proton X – 5th and 6th lines are small and not often seen, apparent doublet of doublet JAB and X are directly measurable from spectrum

JAX, JBX, A and B need to be calculated


XAB

X - center of peaks


– Many ABX patterns are sufficiently close to AMX (AB >> JAB)

first-order solution has an excellent chance of being correct

– First, identify the distorted doublet of doublets for both A and B

– Remove the splitting (identify the center of each doublet), which leaves an AB pattern

– Solve AB pattern as before to get JAB, A, and B

large errors when JAX and JBX are very different or AB small compared to JAB


A & B doublet of doubletseparation is JAX & JBX

Center doublets and get AB pattern


– Correct analysis of ABX patterns Reverse the order of extracting coupling constants to approximate solution

– First, identify the two AB quartets separation between the four pairs of lines are identical tall inner line associated with shorter outer line (leaning)


Identify the two AB quartetsJab+ = Jab-


– Correct choice of ab quartet

– Incorrect choice of ab quartet



– Solve the two ab quartets

Treat as normal AB patterns and obtain four chemical shifts (a+,b+,a-,b-)

Don’t know which half is a and which is b - two possible solutions



– Solution 1 and Solution 2 – depends on the relative sign of JAX and JBX

Solution 1: JAX and JBX same sign

Solution 2: JAX and JBX different sign


Swap the a & b labels


– Which solution is the correct one?

– Several criteria can be used:

1. Magnitude of the couplings – one solution may give dubious (very large or very small) couplings

2. Signs of coupling constants – the signs can sometimes be predicted and rule out a solution all vicinal 3J couplings are positive,

geminal 2J couplings at sp3 carbons are usually negative

CHXCHAHB – JAX and JBX have the same sign

CHACHBHX – JAX and JBX have different signs

• Analysis of the X-part – the intensities of the lines in the X-part are always different – most reliable way to identify the correct solution


Two different X patterns depending on relative sign of

JAX and JBX


– Effective of relative sign of JAX and JBX on AB pattern


Solution 1JAX and JBX same sign

Solution 2JAX and JBX different sign


– AB pattern from ABX spin

system as a function of

changing AB



– AB pattern from ABX spin

system as a function of

the relative sign and

Magnitude of JAX and JBX

Coupling Constants (J)Coupling Constants (J)JAX and JBX same sign JAX and JBX different sign


Demo ACD C+H NMR Viewer software– second order coupling constants

Coupling Constants (J) Coupling constants are a very important and useful feature of an NMR spectrum...

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Transcript of Coupling Constants (J) Coupling constants are a very important and useful feature of an NMR spectrum...