Nuclear Magneic Resonance Principles Nagarajan Murali Rugers, The ae Universi of New Jerse
References Undersanding NMR pecroscop James Keeler John Wile & ons (006,007 pin Dnamics Basics of Nuclear Magneic Resonance Malcolm H. Levi John Wile & ons (007
Overview Larmor Precession Bulk Magneiaion Roaing Frame RF Pulse in Roaing Frame FD Produc Operaors Foundaion for Fuure Lecures pw calibraion, pw calibraion b Nuaion imple D pin Echo T Relaaion T - Relaaion pin Lock D Correlaion pecroscop (COY D NOEY D ROEY pw calibraion HMQC and HQC
Nuclear Magneic Momen The nucleus of man aoms behaves like a in bar magne we sa he nucleus possesses a magneic momen m. The magneic momens arise from a fundamenal proper of he nucleus known as pin which gives rise o an angular momenum and given as μ gromagneic raio specific for a nucleus and can be posiive (m and are parallel or negaive (m and are ani-parallel.
Larmor Precession The magneic momen m in a magneic field B 0 eperiences a orque dμ μ d The sie of he magneic momen m is fied - he effec of he orque is o roae he magneic momen around he magneic field. This roaion is called Larmor precession and he frequenc is Larmor frequenc. B 0 > 0 Larmor frequenc rad s - 0 B 0 0 B 0 H
Bulk Magneiaion n NMR eperimens we observe a large number of such nuclear magneic momens. When an eernal magneic field is applied o a sample he magneic momens give a ne conribuion called a magneiaion along he direcion of he applied magneic field. A equilibrium he individual magneic momens are predominanl oriened a an angle and precess on he surface of a cone a he Larmor frequenc wih no ne magneiaion perpendicular o he field.
Alignmen of Nuclear Magneic Momens No eernal magneic field Eernal Field induces ne magneiaion Ne magneiaion is ero M 0 m 0 N B 3kT ( 0 N number of spins, gromagneic raio, Planks consan, spin qunum number, m 0 permeabili of free space, B 0 Applied magneic field srengh (inducion, K - Bolman consan, T emperaure.
Alignmen of Nuclear Magneic Momens akes a finie ime o induce he magneiaion b he eernal field and he ime consan T is known as longiudinal relaaion ime. Eernal Field induces ne magneiaion M 0 m 0 N B 3kT ( 0 N number of spins, gromagneic raio, Planks consan, spin qunum number, m 0 permeabili of free space, B 0 Applied magneic field srengh (inducion, K - Bolman consan, T emperaure.
ignal > 0 0 B 0 rad s - 0 B 0 H f b some means he bulk magneiaion is iled, all individual magneic momens are also iled and as he momens precess around he field he bulk magneiaion also precesses and induces a signal in a coil placed perpendicular o he applied field. uppose he vecor is iled b an angle b from ais owards he ais hen he observed signal will be along ais M M 0 sinb cos( 0 Along a coil in ais, i would be M M 0 sinb sin( 0
> 0 Radio Frequenc Pulse 0 B 0 rad s - 0 B 0 H A radio frequenc (RF pulse a or near (resonance he Larmor frequenc applied along he -ais can il he magneiaion and is represened as B cos( 0 B is he ampliude of rf field and is he frequenc and is he duraion of he pulse.
Moion in he presence of RF dμ d m ( B 0 B ( The moion of he magneic momens is now complicaed as he field is ime-dependan due o he RF. The dnamics can be simplified in a roaing frame where he field appears saic.
Roaing Frame n he op figure a vecor roaes in - plane, in boom figure he - aes ssem is roaing and he vecor is alwas along - ais
Roaing Frame Le s use he roaing frame o undersand he effec of RF pulses. a he applied field B 0 is along Z-ais and an RF field B cos( applied along he X-ais of he laboraor frame. Then he figures below show he fields in he roaing frame roaing a a frequenc given b he aes ssem (. 0 B B 0 0 ( B 0 B B B eff eff B B eff B f B >>B hen he effecive field is along B and he magneiaion vecor will roae abou he -ais.
Effec of Radio Frequenc Pulse Radio Frequenc (RF pulses a a frequenc 0 and srengh B roaes he magneiaion. b B pw pw 90 0 roaion 80 0 roaion n he roaing frame, he saic field along -direcion is ero on-resonance. The RF field appears saic along -ais. The roaion angle b increases wih increasing pulse widh for a given RF srengh.
One Pulse Eperimen Wih a 90 0 pulse along ais, he magneiaion vecor roaed from o and evolves wih a precession frequenc 0 ro M M M M 0 0 cos( sin(
Free nducion Deca - FD Wih a 90 0 pulse along ais, he magneiaion vecor roaed from o hen he observed FD is ( ( ( ( M M M 0 0 ( im / T ( e / T (cos( isin( e e i e / T T is he deca consan of he signal in he plane or he ransverse relaaion ime consan. M ( M ( Fourier Transform ( ( e i d
Transverse relaaion T The relaaion rae consan in erms of half he line widh a half maimum T Line widh (LW=d is usuall measured in unis of H, herefore T d * LW ( H
Proon NMR pecrum Proon NMR specrum illusraing major funcional groups. The solven is deueraed dimehlsulfoide.
Chemical hif d TM TM d( ppm 0 6 d ppm TM 6 ( 0 TM d ( ppm 0 6 ( TM 6 ( d ( ppm 0 ( d ( ppm 0 6 0 TM TM TM d ( ppm 0 6 TM TM ince he frequenc increases wih he field srengh he chemical shif difference beween wo peaks is larger in frequenc unis. ppm a 400MH = 400H; ppm a 500MH = 500H.
Tools for Undersanding NMR Eperimens To undersand NMR eperimens wih more han one pe of spins and man pulses we need more sophisicaed ools developed based on quanum mechanics and is popularl known as Produc Operaor Formalism (POF. The sae of he magneiaions (spin saes of differen species are represened b operaors and heir producs o describe he ime evoluion of he spin saes.
Operaors Approach Operaors for wo species and Longiudinal Magneiaion ingle Quanum Coherence X Magneiaion ingle Quanum Coherence Y Magneiaion Ani-phase X Coherence Ani-phase Y Coherence E deni operaor Muliple Quanum Coherence (MQC,,, Longiudinal - pin Order + Zero Quanum Coherence (ZQC - Double Quanum Coherence (DQC - ZQC + DQC J Hamilonian Pars pin Chemical hif pin Chemical hif J Coupling beween pins &
Operaors Approach b b b cos b cos b sin b sin b b b b cos b cos b sin b sin b b b b cos b cos b sin b sin b NMR Eperimens can be undersood b following he evoluion of operaors.
Pulse Calibraion b b cos b sinb cos b sinb
PW-Calibraion b Nuaion B p p 4 ( H Ref: Rapid pulse lengh deerminaion in high-resoluion NMR Peer.C. Wu, Gofried Oing, J. Magn. Reson 76(, 5, 005
imple D 3 90 J 3 90 sin( cos( sin( cos( ( J ( sin( sin( cos( sin( sin( cos( cos( cos( sin( sin( cos( sin( sin( cos( cos( cos( J J J J J J J J
90 80 pin Echo 90 cos( sin( 80 cos( sin( cos( cos( sin( cos( cos( sin( sin( sin( (cos ( sin ( A he end of period chemical shif evoluion is refocused.
pin Echo J Evoluion 90 80 J ( J cos( J sin( J 4J : FD cos( cos( J sin( cos( J cos( sin( J sin( sin( J A he end of period he ani-phase coherence is generaed.
Transverse relaaion T The relaaion rae consan in erms of half he line widh a half maimum T Line widh (LW=d is usuall measured in unis of H, herefore T d * LW ( H
T B pin Echo Mehod M ( M 0 e / T pin Echo principle is used o measure he ransverse relaaion ime T
inensi 9.498 66.763 9.39694 6.995 Eponenial daa analsis: T Relaaion inde freq(ppm peak T error 0.66 0.0905 0.47 0.0599 peak number T = 0.63 error = 0.09 ime observed calculaed difference 0.05 66.8 65.3.43 0.05 58.7 59.4-0.756 0. 46.5 49. -.58 0. 36.7 33.6 3. 0.4 4. 5.8 -.5 0.8 3.8 3.53 0.84.6 0.4 0.79 0.3 3. -0.0 0.7-0.7 6.4 0.0 0.7-0.0969 peak number T = 0.47 error = 0.06 ime observed calculaed difference 0.05 6. 64. -.94 0.05 59.5 58.47 0. 49.7 47.4.3 0. 9.5 3.7 -.7 0.4 4. 4. 0.036 0.8 3.6.96 0.655.6 0.9 0.9-0.004 3. -0.0 0.83-0.03 6.4 0.0 0.83-0.63
T Relaaion nversion Recover ( ( / 0 T e M M null null null T T T null T T e M e M e M M null null null.44 ln ln ( 0 ( / 0 / 0 / 0
T Relaaion inde freq(ppm inensi 7.7598 50.485 7.73657 54.945 Eponenial daa analsis: peak T error 9.67 0.57 9.75 0.4794 peak number T = 9.7 error = 0.57 ime observed calculaed difference 0.065-4. -4.3-0.859 0.5-4. -4 -. 0.5-40.4-40.5 0.034 0.5-39. -39.3 0.8-37. -37. 0.073-3.3-3.8 0.498 4-3.9-4.9.0 8-0. -.3.05 6 9.9 8.94 0.48 3 30 3.4 -.38 64 44.7 45.7 -.0 8 50.5 49..4 peak number T = 9.8 error = 0.479 ime observed calculaed difference 0.065-45 -44. -0.98 0.5-43.7-43.8 0.55 0.5-4.5-43. 0.683 0.5-4.6-4 -0.558-40. -39.6-0.456-35. -35-0.0456 4-5.9-6.6 0.643 8-0.9 -.9.04 6 0. 9.73 0.45 3 3.7 33.8 -.5 64 48. 49.3 -.06 8 54.3 53.3
pin Lock 90 L During he dela he coherences of he spins are locked along he ais along which RF is applied. Oher componens roae abou -ais (nuaion and deca.
D Correlaed pecroscop - COY 90 90 90 ( cos( sin( ( J cos( sin( cos( J cos( J cos( sin( sin( J sin( J 90 Diagonal Peak Cross Peak cos( sin( cos( J cos( J cos( sin( sin( J sin( J
D pecrum sin( sin( cos( sin( J J J Diagonal Peaks cos( cos( sin( sin( J J J Cross Peaks
D COY pecrum Line hape Cross Peaks Diagonal Peaks
D Nuclear Overhauser pecroscop - NOEY 90 ( 90 90 90 m cos( sin( ( J cos( sin( cos( J cos( J 90 cos( sin( sin( J sin( J cos( sin( cos( J cos( J cos( sin( sin( J sin( J Relaaion in m cos( cos( J a ( m 90 cos( cos( J a ( m cos( cos( J a ( cos( cos( J a ( m m
D Roaing Frame Overhauser pecroscop - ROEY 90 ( cos( sin( ( J 90 L m cos( sin( cos( J cos( J L Relaaion in m cos( sin( sin( J sin( J cos( cos( cos( J cos( J a a r r ( ( m m
X-Nucleus PW Calibraion 90 80 J b ( J b=0 he signal is maimum. b =90 0 here is no signal as he muliple quanum coherence is unobservable. cos( J b cos b sinb ( J sin( J cos b sinb
HMQC - pe 90 b 80 b=0 he signal is maimum. b= 90 0 he signal is maimum. b J cos( J ( J b cos b sinb sin( J b sinb cos b sin b ( J sin b cos b in b
PWX-Calibraion b Nuaion p p 4 ( H Ref: DEAL- A fas single scan mehod for X pulse widh calibraion Nagarajan Murali, J. Magn. Reson 83, 4, 006
D-HMQC J ( J 90 80 90 90 cos( J sin( J Decoupling RF ( J,( s cos( s sin( s cos( s in( s
D-HQC 90 80 80 90 80 90 90 90 80 80 4J cos( J ( J sin( J Decoupling RF,( s ( J cos( s sin( s cos( s in( s
D-HQC/HMQC For each pair here will be one peak. f here are homonuclear coupling ha will spli he lines along he Proon ( dimension.