NMR pecroscop: Principles and Applicaions Nagarajan Murali D - Mehods Lecure 5
D-NMR To full appreciae he workings of D NMR eperimens we need o a leas consider wo coupled spins. omeimes we need o go up o hree coupled spins, paricularl when we look a heero nuclear spins such as Carbon-3 isoope. We will sar from he simple one pulse NMR eperimen in erms of he produc operaor approach and discuss various aspecs of he pulse sequences.
Hamilonian Two pins =/ and Coupling Le us use he wo spin Hamilonian in which each spin wih spin =/ and Coupling beween hem. H H 0 0 in H for he case We can also wrie he equaion wih noaion and for he wo spins as H n subsequen discussions we will drop he ha from he operaors and represen hem as normal face ialic characer for convenience. 0 0 in roaing frame and rad s in roaing frame and rad s - -
b Pulse Calibraion bo cos b sinb cos b sinb
imple D 3 90 3 90 ) sin( ) cos( ) sin( ) cos( ) ( ) ( ) )sin( sin( ) )cos( sin( ) )sin( cos( ) )cos( cos( ) )sin( sin( ) )cos( sin( ) )sin( cos( ) )cos( cos(
90 imple D 3 90 As we know he phsical properies of he operaors we could have direcl prediced he NMR specrum from poin in he sequence. The operaors a poin are in-phase magneiaion of spins and and hus he specrum should be a in-phase double wih spliing a frequencies and. Also i is enough o follow one spin hrough he pulse sequence.
Opimum Pulse Flip Angle is no opimum o use / flip angle for he pulse as he eperimen is repeaed several imes for signal averaging and hen one should wai more han 5 imes he longiudinal relaaion ime o build up he equilibrium magneiaion. r r
Opimum Pulse Flip Angle f we assume ha he ransverse magneiaion is compleel decaed b he ime he ne signal averaging pulse is applied, we can calculae he sead sae -magneiaion and he corresponding ransverse magneiaion can be calculaed. r r M (0-) M (0-) M (0-)
Opimum Pulse Flip Angle The deeced signal can be deduced o be M (0 ) M 0 ep r T sin b ep r cos b T And he signal inensi as relaive /N ploed for various ( r / T ) as a funcion of he flip angle is given below.
Opimum Pulse Flip Angle The maimum signal is no a b=/, he opimum flip angle, known as Erns angle, b is given b cos b op ep( r / T ) For shorer reccle ime b op decreases. For r ~T, b op ~ 68 o.
Opimum Reccle Dela The opimum reccle dela for a pulse angle of b=/ can also be ploed as a funcion of he raio of r /T And he dela r ~.3 T is opimum.
D wih Decoupling The one pulse eperimen gives a double for each spins when here is a -coupling beween hem. pin muliple frequencies depend on he sae of spin in a or b sae. f selecive RF irradiaion (applied during deecion) rapidl changes mies he a and b sae of spin he spin muliple will collapse and his process is called decoupling.
D wih Decoupling H specra wih decoupling (homonuclear decoupling).
D wih Decoupling Decoupling is paricularl useful in recording 3 C specrum.
D wih Decoupling There are varians of he basic eperimen o enhance he 3 C specrum.
pin Lock 90 L During he dela he coherence of he spins do no evolve and is locked along he -ais along which he RF is applied. This process called spin locking. 6
90 80 pin Echo 90 cos( ) sin( ) 80 cos( ) sin( ) cos( sin( )cos( ) )cos( ) cos( )sin( ) sin( )sin( ) (cos ( ) sin ( )) A he end of period chemical shif evoluion is refocused.
pin Echo Modulaion Using he knowledge ha shif evoluion is refocused, he evoluion can be calculaed. 90 80 ( ) cos( ) sin( ) 4 : FD cos( sin( )cos( ) )cos( ) cos( sin( )sin( ) )sin( ) A he end of period he ani-phase coherence is generaed.
pin Echo Modulaion pecrum Ediing The dependence of echo on coupling can be used o edi carbon specrum o idenif C, CH, CH, CH 3 pe carbons. CH: ( ) cos( ) sin( ) cos sin wih ( ) K CH : cos K sin cos sin cos 4 K sin cos CH 3 : cos 3 ( ) L L sin cos...
pin Echo Modulaion pecrum Ediing The funcional dependence can be used o idenif he proonaion of carbon. For =, C and CH ampliudes are opposie of CH and CH 3 carbons. or : o 80 cos C : CH : cos CH CH 3 : cos : cos 3
pin Echo Modulaion pecrum Ediing Each muliple in he carbon specrum of he spin ssem ma be represened b a vecor, hen he evoluion can be picoriall represened.
APT-Aached Proon Tes The APT eperimen uses he funcional dependence of and edis he carbon specrum (a) Normal carbon D, (b) edied specrum wih =, and (c) = / onl he quaernar carbon is seleced. The firs carbon pulse is no a / pulse o opimie /N wih fas repeiion imes.
Polariaion Transfer There is a class of eperimens ha are called polariaion ransfer eperimens and he ransfer magneiaion of abundan high g nuclei magneiaion o low abundan low g nuclei such as proon o carbon. One such pe of eperimen is called NEPT (nsensiive Nuclear Enhancemen b Polariaion Transfer).
NEPT + - b-a g,,( ) g g cos( cos( ) g ) g sin( ), sin( ) sin g sin( ) g cos wih FD f = H and = 3 C hen g /g =4, we have 4 imes more signal han normal D. s
NEPT One can also illusrae he evoluion picoriall.
Refocused NEPT The NEPT sequence can be eended o give in-phase muliple so ha decoupling can be performed. uch a pulse sequence is called refocused NEPT. g wih g cos sin cos sin
Ediing wih Refocused NEPT The refocused NEPT can also be used o edi carbon specrum as we did wih APT eperimen. wih CH CH CH 3 : sin : sin cos : 3sin cos
Ediing wih DEPT To Edi using he refocused NEPT one has o var he dela o ge he desired. nsead, we modif he pulse sequence o achieve he same effec. The flip angle of H pulse is varied o achieve he same resul. CH : sin; CH : sin cos; CH3 : 3sin cos
Ediing wih DEPT A suiable linear combinaion of he four specra on he lef ields he edied specra on he righ. 0.707CH +.0CH +.06 CH 3 DEPT-35 o DEPT-90 o DEPT-90 o CH DEPT-45 o 0.707CH +.0CH +.06 CH 3
APT vs DEPT n APT eperimen quaernar carbon is also seen whereas in he DEPT onl carbons aached o proons are seen. DEPT allows separaion of carbons, hus aiding unambiguous idenificaion. APT wih =35 o CH and CH 3 are down; C and CH are up. DEPT
X-Nucleus PW Calibraion 90 80 b ( ) b=0 he signal is maimum. b =90 0 here is no signal as he muliple quanum coherence is unobservable. cos( ) b cos b sinb ( ) sin( ) cos b sinb
Coherence Transfer g,,( ) g g cos( cos( ) g sin(, ) g sin( ) ) The conversion of o is an imporan aspec of pulsed NMR and is known as he coherence ransfer sep. Coherence ransfer is eensivel used o obain coupling ne work informaion in muli dimensional NMR.
Coherence Transfer elecive Correlaion Eperimen Le us consider wo proons coupled o each oher and in he eperimen (a) we appl a selecive 90 o -pulse on spin and afer a dela appl a non selecive 90 o pulse along ha roaes boh proons. n (b) we do he same bu he selecive pulse on spin is applied along -. Also sa ha we are on resonance o spin i.e. =0.
Coherence Transfer elecive Correlaion Eperimen sin cos ) ( ) ( a b sin cos sin cos sin cos sin cos 0 0
Coherence Transfer elecive Correlaion Eperimen 0 0 cos sin cos sin An uncoupled hird spin ( c) ( b) ( a) cos sin