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I x I x cos w t + I y sin w t

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.

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I x I x cos w t + I y sin w t

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  1. Chemical shift Ix IxIx coswt + Iy sin wt w Iy Ix IyIy coswt - Ix sin wt Scalar coupling Ix IxIx cos pJt + 2IySz sin pJt JIs 2IySz Ix IyIy cos pJt - 2IxSz sin pJt IxSzIxSz cos pJt + 2Iy sin pJt IySzIySz cos pJt - 2Ix sin pJt

  2. Iz Iz Iz -Ix -Ix -Iy -Iy Iy Ix Iy Iy Ix Ix -Iz -Iz JIzSz JIzSz -Iy -Ix -2IxSz -2IySz Iy 2IySz Ix 2IxSz

  3. Chemical shift evolution

  4. t I Chemical shift evolution w

  5. -Iy wI sinwIt coswIt Ix -Iy -y -Iy coswIt +IxsinwIt x

  6. scalar coupling

  7. t I S Scalar coupling pJIS

  8. -Iy JIS sinwpJIst cospJISt 2IxSz -Iy -y -Iy cospJISt +2IxSzsinwpJIst x

  9. Chemical shift evolution + scalar coupling

  10. t I S Chemical shift evolution w Scalar coupling pJ

  11. -Iy wI sinwIt coswIt Ix -Iy JIS cospJISt sinpJISt cospJISt sinpJISt IySz Ix IxSz -Iy -IycoswItcospJISt -Iy 1/2[cos(wI+pJIS)t+cos (wI-pJIS)t]

  12. Let’s play again Heteronuclear couplings Let us consider 2 different, consecutive delays

  13. t t’ I S Chemical shift evolution w Scalar coupling pJ

  14. -Iy wI coswIt sinwIt Ix -Iy JIS cospJISt cospJISt sinpJISt sinpJISt Ix -Iy 2IxSz 2IySz Ix -Iy 2IxSz 2IySz coswIt’ sinpJISt’ coswIt’ sinpJISt’ wI coswIt’ coswIt’ sinpJISt’ sinpJISt’ -Iy 2IySz Ix Iy Ix 2IxSz 2IySz -2IxSz sinpJISt’ sinpJISt’ cospJISt’ cospJISt’ cospJISt’ JIS sinpJISt’ sinpJISt’ sinpJISt’ cospJISt’ cospJISt’ cospJISt’ cospJISt’ sinpJISt’ sinpJISt’ Ix 2IySz cospJISt’ 2IySz -Ix Iy -2IxSz -2IxSz sinpJISt’ Iy -Iy 2IySz -Ix Ix 2IySz -Iy 2IxSz 2IxSz

  15. -IycoswItcospJIStcoswIt’cospJISt’ -Iycos2wItcos2pJISt Iycos2wItsin2pJISt IycoswItsinpJIStcoswIt’sinpJISt’ IysinwItcospJIStsinwIt’cospJISt’ Iysin2wItcos2pJISt -IysinwItsinpJIStsinwIt’sinpJISt’ -Iysin2wItsin2pJISt If t=t’

  16. -Iycos2wItcos2pJISt -Iycos2wIt[cos2pJISt-sin2pJISt] Iycos2wItsin2pJISt +Iysin2wIt[cos2pJISt -sin2pJISt] Iysin2wItcos2pJISt -Iysin2wItsin2pJISt -Iy[cos2wIt-sin2wIt ][cos2pJISt -sin2pJISt] Iy[coswI2t][sin2pJISt-cos2pJISt] -Iy[coswI2t][cospJIS2t]

  17. THE COSY EXPERIMENT

  18. COSY 90°x 90°x t1 t2 acq Is the “simplest” NMR experiment really simple?

  19. t I Chemical shift evolution w

  20. -Iy wI sinwIt coswIt Ix -Iy -y -Iy coswIt +IxsinwIt x

  21. t I S Scalar coupling pJIS

  22. -Iy JIS sinwpJIst cospJISt 2IxSz -Iy -y -Iy cospJISt +2IxSzsinwpJIst x

  23. t I S Chemical shift evolution w Scalar coupling pJ

  24. -Iy wI sinwIt coswIt Ix -Iy JIS cospJISt sinpJISt cospJISt sinpJISt IySz Ix IxSz -Iy -IycoswItcospJISt -Iy 1/2[cos(wI+pJIS)t+cos (wI-pJIS)t]

  25. COSY Now… if J=S

  26. -Iy wI coswIt sinwIt Ix -Iy JIS cospJISt cospJISt sinpJISt sinpJISt Ix -Iy 2IxSz 2IySz 90°x Ix -Iz 2IxSy -2IzSy coswIt’ sinpJISt’ wI coswIt’ sinpJISt’ 2IxSy -Iz Ix Iy 2IzSy -2IzSx -Iz cospJISt’ JIS sinpJISt’ sinpJISt’ 2IxSy cospJISt’ cospJISt’ sinpJISt’ sinpJISt’ cospJISt’ Iy -2IxSz -2IzSx -Iz -Sy 2IySz -Sx Ix 2IzSy 2IxSy

  27. Diagonal IysinwIt1cospJISt1sinwIt2cospJISt2 F(wI, wI) -SysinwIt1sinpJISt1sinwSt2sinpJISt2 Cross peak F(wI, ws)

  28. Diagonal IysinwIt1cospJISt1sinwIt2cospJISt2 F(wI, wI) Iy[1/2(sin(wI+pJIS)t1)+ ( sin(wI-pJIS)t1)]* [1/2(sin(wI+pJIS)t2)+ ( sin(wI-pJIS)t2)] -SysinwIt1sinpJISt1sinwSt2sinpJISt2 F(wI, ws) Cross peak Sy[1/2(cos(wI-pJIS)t1)- ( cos(wI+pJIS)t1)]* [1/2(cos(wI-pJIS)t2)- ( cos(wI+pJIS)t2)]

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