NMR Spectroscopy: Principles and Applicationsnmurali/nmr_course/Chem_542_Spring...pulse NMR...
Transcript of NMR Spectroscopy: Principles and Applicationsnmurali/nmr_course/Chem_542_Spring...pulse NMR...
NMR Spectroscopy: Principles and Applications
Nagarajan Murali
1D - Methods
Lecture 5
1D-NMR
To fully appreciate the workings of 1D NMR experiments we need to at least consider two coupled spins. Sometimes we need to go up to three coupled spins, particularly when we look at hetero nuclear spins such as Carbon-13 isotope. We will start from the simple one pulse NMR experiment in terms of the product operator approach and discuss various aspects of the pulse sequences.
HamiltonianTwo Spins I=1/2 and J Coupling
Let us use the two spin Hamiltonian in which each spin with spin I=1/2 and J Coupling between them.
We can also write the equation with notation I and S for the two spins as
In subsequent discussions we will drop the hat from the operators and represent them as normal face italic character for convenience.
1202012112202101 case for the Hzin JJ zzzz IIIIH
s rad and frame rotatingin 2 1-2 zzzz SISIH
ISSI J
s rad and frame rotatingin 2 1-21122211 zzzz IIIIH
J
Pulse Calibration
1 2
bx
t
zz SI bbbb sincossincos yzyz SSII bo
x
Simple 1D
1 2 3
90x
tI S
J
1
2
3
zz SI
90x
yy SI
)sin()cos(
)sin()cos(
tStS
tItI
SxSy
IxIy
tSI zSzI )(
tSIJ zzIS )2()sin()sin(2)cos()sin(
)sin()cos(2)cos()cos(
)sin()sin(2)cos()sin(
)sin()cos(2)cos()cos(
tJtIStJtS
tJtIStJtS
tJtSItJtI
tJtSItJtI
ISSzyISSx
ISSzxISSy
ISIzyISIx
ISIzxISIy
Simple 1D
1 2 3
90x
tI S
J
1
2
zz SI
90x
yy SI
As we know the physical properties of the operators we could have directly predicted the NMR spectrum from point 2 in the sequence. The operators at point 2 are in-phase y magnetization of spins I and S and thus the spectrum should be a in-phase doublet with splitting J at frequencies I and S. Also it is enough to follow one spin through the pulse sequence.
Optimum Pulse Flip Angle
It is not optimum to use /2 flip angle for the pulse as the experiment is repeated several times for signal averaging and then one should wait more than 5 times the longitudinal relaxation time to build up the equilibrium magnetization.
tr tr
Optimum Pulse Flip Angle
If we assume that the transverse magnetization is completely decayed by the time the next signal averaging pulse is applied, we can calculate the steady state z-magnetization and the corresponding transverse magnetization can be calculated.
Mz(0-) Mz(0-) Mz(0-)
tr tr
Optimum Pulse Flip Angle
The detected signal can be deduced to be
And the signal intensity as relative S/N plotted for various (tr / T 1) as a function of the flip angle is given below.
b
b
sin
cosexp1
exp1
)0(
1
10
T
t
T
t
MMr
r
x
Optimum Pulse Flip Angle
The maximum signal is not at b=/2, the optimum flip angle, known as Ernst angle, b is given by
For shorter recycle time bopt decreases. For tr~T1, bopt ~ 68o .
)/exp(cos 1Ttropt b
Optimum Recycle Delay
The optimum recycle delay for a pulse angle of b=/2 can also be plotted as a function of the ratio of tr/T1
And the delay tr ~ 1.3 T1 is optimum.
1D with Decoupling
The one pulse experiment gives a doublet for each spins when there is a J-coupling between them. Spin 1 multipletfrequencies depend on the state of spin 2 in a or b state. If selective RF irradiation (applied during detection) rapidly changes mixes the a and b state of spin 2 the spin multipletwill collapse and this process is called decoupling.
1D with Decoupling
1H – spectra with decoupling (homonuclear decoupling).
1D with Decoupling
Decoupling is particularly useful in recording 13C spectrum.
1D with Decoupling
There are variants of the basic experiment to enhance the 13C spectrum.
Spin Lock
90x SLy
zI yI yI
yI1
16
During the delay t the Iy coherence of the spins do not evolve and is locked along the y-axis along which the RF is applied. This process called spin locking.
Spin Echo90x
180y
At the end of 2 period chemical shift evolution is refocused.
zI90x
yI )sin()cos( IxIy II
zI I
)sin()cos( IxIy II 180y
yI
))(sin)((cos)sin()sin()cos()sin(
)sin()cos()cos()cos(22
IIy
IIyIIx
IIxIIyI
II
II
zI I
Spin Echo –J Modulation
90x
180y
At the end of 2 period the anti-phase coherence is generated.
SI
J
t
)2sin(2)2cos( ISzxISy JSIJI yI zzIS SIJ 2)2(
:4
1
J zxSI2
)sin()sin()cos()sin(2
)sin()cos()cos()cos(2
JttIJttSI
JttIJttSI
IxIzy
IyIzx
FID
Using the knowledge that shift evolution is refocused, the J evolution can be calculated.
Spin Echo –J Modulation –Spectrum Editing
The dependence of echo on J coupling can be used to edit carbon spectrum to identify C, CH, CH2, CH3 type carbons.
)sin(2)cos( ISzxISy JISJS yS zzIS SIJ 2)( CH:
ISzxy JISS with sin2cos
CH2:
zzIS SKJ 2)(
cossin4cossin2cossin2cos 22zzyzxzxy KISISKSS
CH3:zzIS SLJ 2)(
....cossin2cos3 zxy LSS
Spin Echo –J Modulation –Spectrum Editing
The functional dependence can be used to identify the protonation of carbon. For =, C and CH2 amplitudes are opposite of CH and CH3 carbons.
33
22
cos:
cos:
cos:
1:
CH
CH
CH
C
o180or
1cos :1
ISIS
JJ
Spin Echo –J Modulation –Spectrum Editing
Each multiplet in the carbon spectrum of the spin system may be represented by a vector, then the evolution can be pictorially represented.
APT-Attached Proton Test
The APT experiment uses the functional dependence of and edits the carbon spectrum (a) Normal carbon 1D, (b) edited spectrum with =, and (c) = /2 only the quaternary carbon is selected. The first carbon pulse is not a /2 pulse to optimize S/N with fast repetition times.
Polarization Transfer
There is a class of experiments that are called polarization transfer experiments and they transfer magnetization of abundant high g nuclei magnetization to low abundant low gnuclei – such as proton to carbon. One such type of experiment is called INEPT (Insensitive Nuclear Enhancement by Polarization Transfer).
INEPT
)sin(2)cos( ISzxIISyI JSIJI ggyI Ig zzISxx SIJSI 2)(,,
yy SI2
,2
)sin(2)cos( ISxzIISyI JSIJI gg
+y -y b-a
IS
ISs2J
1 with Jsincos)sin(2 ttSJSI yI
FIDISxzI gg
If I=1H and S=13C then gI/gS=4, we have 4 times more signal than normal 1D.
INEPTOne can also illustrate the evolution pictorially.
Refocused INEPTThe INEPT sequence can be extended to give in-phase multiplet so
that decoupling can be performed. Such a pulse sequence is called refocused INEPT.
g
g
sincos22
with
sincos22
2
2
222
2
2
yxzSIJ
xzI
IS
ISyISxzSIJ
xzI
SSISI
J
JSJSISI
zzIS
zzIS
Editing with Refocused INEPTThe refocused INEPT can also be used to edit carbon spectrum as
we did with APT experiment.
23
2
2
cossin3:
cossin2:
sin:
with
CH
CH
CH
J
Editing with DEPTTo Edit using the refocused INEPT one has to vary the delay to get
the desired . Instead, we modify the pulse sequence to achieve the same effect. The flip angle of 1H pulse is varied to achieve the same result.
232 cossin3:;cossin2:;sin: CHCHCH
Editing with DEPTA suitable linear combination of the four spectra on the left yields
the edited spectra on the right.
DEPT-45o
DEPT-90o
DEPT-90o
DEPT-135o
0.707CH + 1.0CH2 + 1.061 CH3
0.707CH + 1.0CH2 + 1.061 CH3
CH
APT vs DEPT
In APT experiment quaternary carbon is also seen whereas in the DEPT only carbons attached to protons are seen. DEPT allows separation of carbons, thus aiding unambiguous identification.
APT with =135o CH and CH3 are down; C and CH2 are up. DEPT
X-Nucleus PW Calibration
J2
1
90x
180y
bx
zx
ISzxISy
SI
JSIJI
2
)sin(2)cos(
yI
zzIS SIJ 2)(
yx IS b
bb sin2cos2 yxzx SISI
zzIS SIJ 2)(
bb sin2cos yxy SII
b=0 the signal is maximum.b =900 there is no signal as the multiple quantum coherence is unobservable.
Coherence Transfer
)sin(2)cos( ISzxIISyI JSIJI ggyI Ig zzISxx SIJSI 2)(,,
yy SI2
,2
)sin(2)cos( ISxzIISyI JSIJI gg
The conversion of 2IxSz to 2IzSx is an important aspect of pulsed NMR and is known as the coherence transfer step. Coherence transfer is extensively used to obtain coupling net work information in multi dimensional NMR.
Coherence Transfer – Selective Correlation Experiment
Let us consider two protons coupled to each other and in the experiment (a) we apply a selective 90o x-pulse on spin 1 and after a delay apply a non selective 90o pulse along y that rotates both protons. In (b) we do the same but the selective pulse on spin 1 is applied along -x. Also say that we are on resonance to spin 1 i.e. 1=0.
Coherence Transfer – Selective Correlation Experiment
1221121 sin2cos)()( JIIJIab xzy
xxzy
yy
zzxy
zz
zy
x
zz
IJIIJI
II
IJIIJI
IIJ
II
I
II
21221121
21
21221121
2112
21
1
21
sin2cos
2
sin2cos
2
2
xxzy
yy
zzxy
zz
zy
x
zz
IJIIJI
II
IJIIJI
IIJ
II
I
II
21221121
21
21221121
2112
21
1
21
sin2cos
2
sin2cos
2
2
01 01
Coherence Transfer – Selective Correlation Experiment
1221121 sin2cos)()()( JIIJIabc xyzy
xxzy IJIIJI 21221121 sin2cos xxzy IJIIJI 21221121 sin2cos
01 01
An uncoupled third spin