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Chemical shift. I x. I x I x cos w t + I y sin w t. w. I y. I x. I y I y cos w t - I x sin w t. Scalar coupling. I x. I x I x cos p Jt + 2 I y S z sin p Jt. J Is. 2I y S z. I x. I y I y cos p Jt - 2 I x S z sin p Jt. I x S z I x S z cos p Jt + 2 I y sin p Jt. - PowerPoint PPT Presentation
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Ix Ix cost + Iy sin t
Iy Iy cost - Ix sin t
Ix Ix cos Jt + 2IySz sin Jt
Iy Iy cos Jt - 2IxSz sin Jt
IxSz IxSz cos Jt + 2Iy sin Jt
IySz IySz cos Jt - 2Ix sin Jt
Ix
Ix Iy
Ix
Ix 2IySzJIs
Chemical shift
Scalar coupling
Iz
IxIy
-Iy -Ix
Iz
-Iz
IxIy
-Iy
Iz
Ix
-Ix
-IzIy
JIzSz
Ix 2IySz
-2IySz -Ix
Iy
-2IxSz
2IxSz
-Iy
JIzSz
Chemical shift evolution
I
Chemical shift evolution
-Iy
I
-IyIx
cosI sinI
-Iy cosIxsinI
x
-y
scalar coupling
I
S
Scalar coupling JIS
-Iy cosJISxSzsinJIs
x
-y
-Iy
JIS
-Iy2IxSz
cosJIS sinJIs
Chemical shift evolution + scalar coupling
I
S
Chemical shift evolution
Scalar coupling J
-Iy
I
-IyIx
-IyIxSz
IxIySz
JIS
cosI sinI
cosJIScosJISsinJIS
sinJIS
-IycosIcosJIS-Iy 1/2[cos(I+JIS)cos (I-JIS)
Let’s play again
Heteronuclear couplings
Let us consider 2 different, consecutive delays
’I
S
Chemical shift evolution
Scalar coupling J
-IyI
-IyIx
-Iy 2IxSz
Ix 2IySz
JIS
-Iy
2IxSz
Ix 2IySz-Iy
Ix 2IxSz2IySz Ix Iy 2IySz -2IxSz
I
JIS
-Iy 2IxSz
Ix 2IySz
2IxSz
Iy
2IySz -Ix
Ix2IySz
Iy -2IxSz
2IySz-Ix
-2IxSz -Iy
cosI sinI
cosJIS cosJISsinJIS sinJIS
cosI’ cosI’ cosI’ cosI’sinJIS’ sinJIS’ sinJIS’ sinJIS’
cosJIS’
sinJIS’
cosJIS’cosJIS’
cosJIS’
cosJIS’
cosJIS’
cosJIS’
cosJIS’sinJIS’ sinJIS’
sinJIS’
sinJIS’
sinJIS’ sinJIS’sinJIS’
-IycosIcosJIScosI’cosJIS’
IycosIsinJIScosI’sinJIS’
IysinIcosJISsinI’cosJIS’
-IysinIsinJISsinI’sinJIS’
If =’
-Iycos2Icos2JIS
Iycos2Isin2JIS
Iysin2Icos2JIS
-Iysin2Isin2JIS
-Iycos2Icos2JIS
Iycos2Isin2JIS
Iysin2Icos2JIS
-Iysin2Isin2JIS
-Iy[cos2Isin2Icos2JISsin2JIS
+Iysin2Icos2JISsin2JIS
-Iycos2Icos2JISsin2JIS
Iy[cosI2sin2JIScos2JIS
-Iy[cosI2cosJIS2
THE COSY EXPERIMENT
Is the “simplest” NMR experiment really simple?
COSY90°x 90°x
t1 t2
acq
I
Chemical shift evolution
-Iy
I
-IyIx
cosI sinI
-Iy cosIxsinI
x
-y
I
S
Scalar coupling JIS
-Iy cosJISxSzsinJIs
x
-y
-Iy
JIS
-Iy2IxSz
cosJIS sinJIs
I
S
Chemical shift evolution
Scalar coupling J
-Iy
I
-IyIx
-IyIxSz
IxIySz
JIS
cosI sinI
cosJIScosJISsinJIS
sinJIS
-IycosIcosJIS-Iy 1/2[cos(I+JIS)cos (I-JIS)
Now… if J=S COSY
-IyI
-IyIx
-Iy 2IxSz
Ix 2IySz
JIS
-Iz
2IxSy
Ix -2IzSy-Iz
2IxSy Ix Iy 2IzSy -2IzSx
I
JIS
Ix2IySz
Iy -2IxSz
2IzSy-Sx
-2IzSx -Sy
cosI sinI
cosJIS cosJISsinJIS sinJIS
cosI’ cosI’sinJIS’ sinJIS’
cosJIS’
cosJIS’
cosJIS’
cosJIS’sinJIS’
sinJIS’ sinJIS’sinJIS’
90°x
-Iz
-Iz
2IxSy
2IxSy
IysinIt1cosJISt1sinIt2cosJISt2
-SysinIt1sinJISt1sinSt2sinJISt2
F(I, I) Diagonal
F(I, s) Cross peak
IysinIt1cosJISt1sinIt2cosJISt2
-SysinIt1sinJISt1sinSt2sinJISt2
F(I, I) Diagonal
F(I, s) Cross peak
Iy[1/2(sin(I+JIS)t1)+ ( sin(I-JIS)t1)]* [1/2(sin(I+JIS)t2)+ ( sin(I-JIS)t2)]
Sy[1/2(cos(I-JIS)t1)- ( cos(I+JIS)t1)]* [1/2(cos(I-JIS)t2)- ( cos(I+JIS)t2)]
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