NMR Spectroscopy: Principles and Applications. Nagarajan Murali 2D NMR Homonuclear 2D Lecture 6

Transcription

1 NMR pecroscopy: Principles and pplicaions Nagarajan Murali D NMR Homonuclear D Lecure 6

2 D-NMR Two dimensional NMR is a novel and non-rivial exension of D NMR specroscopy. n he simples form of undersanding he a D specrum is a plo of inensiy vs frequency whereas he b D NMR specrum is a plo of inensiy vs wo independen frequency axes.

3 NMR ignal in Two-Time Periods We know ha NMR signals are deeced as a funcion of ime and D NMR hus implies we have NMR signal as a funcion of wo independen ime periods. ny D NMR scheme can be represened in general as below.

4 NMR ignal in Two-Time Periods n he preparaion period equilibrium magneizaion is buil-up and ransformed ino coherences ha evolve during he evoluion period. The evoluion period is incremened sysemaically in successive experimens. During he mixing period a coherence /magneizaion ransfer is effeced which hen ge deeced during he deecion period.

5 NMR ignal in Two-Time Periods The sysemaic incremenaion of he inerval and direc deecion of NMR signal during gives wo dimensional ime domain daa. spcral widh N * spcral widh

6 NMR ignal in Two-Time Periods The ime domain signal up on wo dimensional Fourier ransform yields wo dimensional specrum.

7 Correlaed pecroscopy COY Le us now focus on he very basic D NMR experimen called COY. We analyzed a special case in he D secion as a selecive correlaion experimen. Here we analyze he D version ha gives correlaion beween all J coupled proons. The pulse sequence is give an as follows: The experimen is repeaed N imes wih sysemaic incremenaion of he ime and he daa colleced is subjeced o double FT o yield D specrum.

8 Correlaed pecroscopy COY ypical COY specrum will have wo ypes of peaks diagonal peaks ha correlae he shifs of he same spins in boh and dimensions and cross peaks ha correlae spin wih spin by he process of coherence ransfer by he second pulse in he sequence.

9 Hamilonian Two pins =/ and J Coupling Le us again use he wo spin Hamilonian in which each spin wih spin =/ and J Coupling beween hem. H z z J z z in Hz for he case J H J z z z z in roaing frame and rad s - n subsequen discussions we will drop he ha from he operaors and represen hem as normal face ialic characer for convenience.

10 COY Experimen Le us consider wo proons coupled o each oher and we apply he COY pulse sequence ha has wo non selecive 9 o x- pulses. Le us jus follow spin and by inducion we can wrie for spin. z cos sin x cos sin x y cos J cos J cos J cos J z y x z x y cos sin cos sin sin J sin J sin J sin J x x y x z z z y y J cos sin z z Deecable erms

11 COY Experimen Focusing jus on he deecable erms we have he signal a he sar of as sin cos J x sin sin J z y The x erm will give a double a frequency in he dimension and is modulaed in by sin giving rise o he diagonal peak. The erm z y will give an ani-phase double a frequency in he dimension and is modulaed in by sin giving rise o he cross peak. n he dimension he double srucure of he diagonal peak is in-phase cosine funcion whereas ha of he cross peak is ani-phase sine funcion.

12 COY Experimen Focusing jus on he deecable erms we have he signal a he sar of as sin cos J x sin sin J z y

13 COY Experimen Le us analyze he cross peak muliple srucure. sin cos J x sin sin J z y sin sin J cos J cos J z y cross peak srucure cos cos J J

14 COY Experimen Le us analyze he diagonal peak muliple srucure. sin cos J x sin sin J z y sin cos J sin J sin J x diagonal peak srucure sin sin J J

15 COY Experimen The cross peaks and diagonal peaks will have differen phases as hey are 9 ou of phase in boh and dimension. x diagonal peak srucure z y sin sin J J cos cos J J

16 COY Experimen The diagonal peak will be dispersive mode in boh dimension and he cross peak will be in absorpive mode. D absorpion mode lineshape D dispersion mode lineshape

17 COY Experimen The ani-phase srucure of he cross peaks is a problem because if he line widh exceeds he J coupling hen he ani-phase double overlap and he peak vanishes. Whereas he diagonal peaks have in-phase muliples and add in signal srengh in overlap siuaions exacerbaing he problem. a imulaion shows he effec of overlap and in b a real siuaion wih added noise is shown. The line widh is abou /5 of J value on he lef mos specrum. n a he smalles coupling consan J max /64 is sill visible bu in b due o noise even J max /3 is barly visible. Thus he abiliy o see a cross peak for small coupling depends on linewidh and noise.

18 COY Experimen The COY specrum below illusrae he usefulness of he experimen in idenifying he spin sysem in a molecule. zo-sugar

19 COY Experimen The COY specrum below illusrae he usefulness of he experimen in idenifying he spin sysem in a molecule. Carbopepoid

20 D FT We have seen in deail D FT in Lecure 3. We summarize he resul here as exp iexp R id Where is he absorpion mode lineshape and D is he dispersion mode line shape. Furhermore we can also do cosine and sine FT. FT cos exp R sin FT cos exp R cosft sin exp R sin FT sin exp R cosinft D D

21 NMR ignal in Two-Time Periods a Time domain signal cosine modulaed in and. b cos-ft wih respec o and c cos-ft wih respec o.

22 D FT cosine Modulaion ypical D ime domain signal will usually be cos exp R exp i exp R The D ime domain signal is cosine modulaed wih respec o. n he signal is complex due o quadraure deecion. We will now have o do wo FTs wih he D ime domain signal one wih respec o and anoher wih respec o.

23 D FT cosine Modulaion FT wih respec o yields Then D we do a cosine FT wih respec o. where is he absorpion mode lineshape along axis. The real par of he above expression gives a D specrum wih absorpion lineshape in boh frequency axes. exp cos FT id R s cos cos FT FT D i id s

24 D FT The D specrum of he expression below is a double absorpion lineshape D peak. Re

25 D FT sine Modulaion omeime we can also have a sine modulaed signal as The FT along gives hen Then we do a sine FT wih respec o. where is he absorpion mode lineshape along axis. The real par of he above expression gives as before a D specrum wih absorpion lineshape in boh frequency axes. exp sin FT id R s sin sin FT FT D i id s exp exp exp sin R i R

26 D FT cosine/sine Modulaion The disadvanage of having jus a cosine or sine modulaion in is ha here is no frequency sign discriminaion. We can see his from he properies of FT. complexft exp iexp R cosinft cos exp R sin FT cos exp R cosft sin exp R sin FT sin exp R D D id cos cos sin sin

27 D FT cosine + sine Modulaion We can however generae D signals ha is boh sine and cosine modulaed in s c sin exp R exp i exp R cos exp R exp i exp R is useful o collec boh signals usually in wo experimens so ha frequency sign discriminaion can be achieved in he ime domain.

28 D FT cosine + sine Modulaion complex modulaion in can be generaed as P-ype signal and N-ype signal The resuling specrum from hese complex signals will be frequency discriminaed. exp exp exp exp exp exp exp sin cos R i R i R i R i i P s c P exp exp exp exp exp exp exp sin cos R i R i R i R i i N s c N

29 D FT P-ype Modulaion D FT of he complex signal is wrien as complex FT along yields a specrum plo of eiher he real par or he imaginary par will yield a phase wised lineshape. ] [ exp exp P id R i ] [ ] [ ] ][ [ P D D i D D id id Real Par maginary Par

30 D FT P-ype Modulaion ypical phase wised lineshape is shown below. uch a lineshape is undesirable in high resoluion work.

31 D FT N-ype Modulaion D FT of he complex signal is wrien as complex FT along yields a specrum plo of eiher he real par or he imaginary par will yield a phase wised lineshape. ] [ exp exp N id R i ] [ ] [ ] ][ [ N D D i D D id id Real Par maginary Par

32 D Hyper Complex Daa We can use he cosine and sine modulaed daa o form a hyper complex D daa ha will yield a pure absorpion specrum daa. ar wih cosine modulaed signal and do a FT along We hen ake he real par of he signal We do he same process for he sine modulaed signal. Now we form a new complex signal from hese wo signals exp cos c id R exp cos R c R exp sin R s R exp exp ]exp sin [cos R s R c R i R i i

33 D Hyper Complex Daa The usual complex FT along will hen yield he desired specrum. We hen ake he real par of he D FT o ge double absorpion lineshape wih frequency discriminaion. This mehod of daa collecion and Fourier ransform is known as aes-haberkorn-ruben mehod or simply aes mehod. ] [ exp exp id id R i

34 Time Proporional Phase ncremenaion TPP We need complex daa along o discriminae posiive frequency from negaive frequency. u by some means if we can se all frequencies o be posiive hen we don no need complex signal. One way o achieve his is o se he reference frequency a he end of he specrum and leave he negaive frequency region empy. u his wases daa space. n TPP we leave he reference frequency a he cener bu move he offses o look like all he frequencies are posiive.

35 Time Proporional Phase ncremenaion TPP Le us sar wih he cosine and sine modulaed signals: c s cos exp R exp i exp R sin exp R exp i exp R We know sine and cosine funcions differ only in phase a shif of one quarer period or a phase of / radians convers one o he oher. cos cos cos sin sin sin for

36 Time Proporional Phase ncremenaion TPP We can hen simply add a phase o he cosine modulaed funcion ha is defined as cos add add exp R exp i exp R cos[ add ] exp R exp iexp R f we se he phase =f max * hen we can shif all he frequencies will be shifed o he righ.

37 oh aes and TPP mehods have advanages and hus combining hem in a D experimens is ideal. COY experimen wih aes-tpp mehod can be represened as below. aes TPP Mehod ' * spcral widh N * spcral widh

38 COY Experimen D-FT of FD from such an experimen yields a specrum wih he diagonal peak in dispersive mode in boh dimension and he cross peak in absorpive mode. D absorpion mode lineshape D dispersion mode lineshape

39 Double Quanum Filered COY DQFC The disadvanages of COY can be alleviaed by double quanum filered COY experimen in which he diagonal muliples are also ani-phase like he cross peaks and in same phase. This leads o beer resoluion near diagonal and cleaner looking specrum. The pulse sequence is shown below.

40 DQFC Up ill he second pulse he sequence resembles COY bu beween he second and hird 9 o pulse double quanum DQ coherences are reained which hen convered in o observable single quanum coherences by he hird 9 o pulse. DQ - coherences

41 DQFC f we follow he evoluion of spin from he analysis of COY we have righ afer he second 9 o pulse cos sin cos J cos J z x cos sin sin J sin J x z y y Only he erm highlighed is reained and is sum of double quanum and zero quanum erm.

42 DQFC fer he second 9 o pulse we reaiin only he DQC. sin cos sin cos sin cos x z z x x x y y x x y y x y x J J J DQ ZQ Third 9 o pulse

43 DQFC The firs erm yields he diagonal peaks and he second erm yields he cross peaks. cos sin J x z z x lso boh he diagonal and cross peaks are aniphase muliples in boh and dimensions and have same phase characerisics in boh dimensions.

44 COY vs DQFC comparison of properly phased a COY and b DQFC illusraes he advanage of DQFC. There is a loss of signal by a facor of in DQFC compared o COY.

45 COY vs DQFC region of DQFC of andrographolide illusraes he advanage of DQFC. Cross peaks close o diagonals can be seen beer.

46 Toal Correlaion pecroscopy TOCY COY and DQFC connec via cross peaks spins ha have coupling beween hem which can eiher be shor range or long range. n a spin nework le s say spin is coupled spin bu no o spin C and spin is coupled spin C i.e. J C = J J C. Then in COY or DQFC here will be a cross peak beween spin and spin spin and spin C bu no cross peak beween spin and spin C. n a TOCY experimen spin o spin C cross peak will also appear and idenify spins and C as a unique group of coupled spins.

47 Toal Correlaion pecroscopy TOCY COY TCOY

48 Toal Correlaion pecroscopy TOCY ypical TOCY pulse sequence is given below. The key par of he experimen is isoropic mixing caused by he spin locking field in he mixing period. soropic mixing convers z x and y o z x and y.

49 Toal Correlaion pecroscopy TOCY Le us say we reain z a poin in he pulse sequence. The evoluion of z during isoropic mixing yields a poin. z isoropic mixing cosj cosj sinj mix mix y z x x y mix z

50 Toal Correlaion pecroscopy TOCY f we jus focus on he z erms he las 9 o pulse would roae z o y which will produce in phase double in. The z erm arose from he y in period ha had cosine modulaions wih respec o J coupling which will is also be an in-phase double. cosj cosj cosj cosj mix mix z x y nalyical soluions are no feasible for more han wo spin sysem and he qualiaive analysis does no show how a cross peak appear when he coupling is absen. mix mix z y

51 Toal Correlaion pecroscopy TOCY n a exended coupled nework of spins z a poin in he pulse sequence ransferred as o of z which hen ge ransferred as 3z and so on during isoropic mixing. The ransfer exends o more remoe spins as he mixing ime is increased.

52 Toal Correlaion pecroscopy TOCY TOCY of he azo-sugar. On he righ he COY is shown.