I x I x cos w t + I y sin w t
description
Transcript of I x I x cos w t + I y sin w t
![Page 1: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/1.jpg)
![Page 2: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/2.jpg)
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
![Page 3: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/3.jpg)
Iz
IxIy
-Iy -Ix
Iz
-Iz
IxIy
-Iy
Iz
Ix
-Ix
-IzIy
JIzSz
Ix 2IySz
-2IySz -Ix
Iy
-2IxSz
2IxSz
-Iy
JIzSz
![Page 4: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/4.jpg)
![Page 5: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/5.jpg)
Chemical shift evolution
![Page 6: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/6.jpg)
I
Chemical shift evolution
![Page 7: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/7.jpg)
-Iy
I
-IyIx
cosI sinI
-Iy cosIxsinI
x
-y
![Page 8: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/8.jpg)
![Page 9: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/9.jpg)
scalar coupling
![Page 10: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/10.jpg)
I
S
Scalar coupling JIS
![Page 11: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/11.jpg)
-Iy cosJISxSzsinJIs
x
-y
-Iy
JIS
-Iy2IxSz
cosJIS sinJIs
![Page 12: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/12.jpg)
Chemical shift evolution + scalar coupling
![Page 13: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/13.jpg)
I
S
Chemical shift evolution
Scalar coupling J
![Page 14: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/14.jpg)
-Iy
I
-IyIx
-IyIxSz
IxIySz
JIS
cosI sinI
cosJIScosJISsinJIS
sinJIS
-IycosIcosJIS-Iy 1/2[cos(I+JIS)cos (I-JIS)
![Page 15: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/15.jpg)
![Page 16: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/16.jpg)
![Page 17: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/17.jpg)
Let’s play again
Heteronuclear couplings
Let us consider 2 different, consecutive delays
![Page 18: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/18.jpg)
’I
S
Chemical shift evolution
Scalar coupling J
![Page 19: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/19.jpg)
-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’
![Page 20: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/20.jpg)
-IycosIcosJIScosI’cosJIS’
IycosIsinJIScosI’sinJIS’
IysinIcosJISsinI’cosJIS’
-IysinIsinJISsinI’sinJIS’
If =’
-Iycos2Icos2JIS
Iycos2Isin2JIS
Iysin2Icos2JIS
-Iysin2Isin2JIS
![Page 21: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/21.jpg)
-Iycos2Icos2JIS
Iycos2Isin2JIS
Iysin2Icos2JIS
-Iysin2Isin2JIS
-Iy[cos2Isin2Icos2JISsin2JIS
+Iysin2Icos2JISsin2JIS
-Iycos2Icos2JISsin2JIS
Iy[cosI2sin2JIScos2JIS
-Iy[cosI2cosJIS2
![Page 22: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/22.jpg)
![Page 23: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/23.jpg)
THE COSY EXPERIMENT
![Page 24: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/24.jpg)
Is the “simplest” NMR experiment really simple?
COSY90°x 90°x
t1 t2
acq
![Page 25: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/25.jpg)
![Page 26: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/26.jpg)
I
Chemical shift evolution
![Page 27: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/27.jpg)
-Iy
I
-IyIx
cosI sinI
-Iy cosIxsinI
x
-y
![Page 28: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/28.jpg)
I
S
Scalar coupling JIS
![Page 29: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/29.jpg)
-Iy cosJISxSzsinJIs
x
-y
-Iy
JIS
-Iy2IxSz
cosJIS sinJIs
![Page 30: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/30.jpg)
I
S
Chemical shift evolution
Scalar coupling J
![Page 31: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/31.jpg)
-Iy
I
-IyIx
-IyIxSz
IxIySz
JIS
cosI sinI
cosJIScosJISsinJIS
sinJIS
-IycosIcosJIS-Iy 1/2[cos(I+JIS)cos (I-JIS)
![Page 32: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/32.jpg)
Now… if J=S COSY
![Page 33: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/33.jpg)
-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
![Page 34: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/34.jpg)
IysinIt1cosJISt1sinIt2cosJISt2
-SysinIt1sinJISt1sinSt2sinJISt2
F(I, I) Diagonal
F(I, s) Cross peak
![Page 35: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/35.jpg)
![Page 36: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/36.jpg)
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)]
![Page 37: I x I x cos w t + I y sin w t](https://reader035.fdocuments.in/reader035/viewer/2022062222/56815a91550346895dc80726/html5/thumbnails/37.jpg)