Chapters in 'Modem NMR Techniques for Chernistry Research' by A. E. Derorne :

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-.-, ; Chapters in 'Modem NMR Techniques for Chernistry Research' by A. E. Derorne :.Chapter.Chapter. 5 for the noe effect 6.1-6.

1 -.-, ; Chapters in 'Modem NMR Techniques for Chernistry Research' by A. E. Derorne :.Chapter.Chapter. 5 for the noe effect for the SP and NEPT techniques Other books related to the topics described in this lecture :.'Nuclear Magnetic Resonance Spectroscopy. A physicochemical View' by R. K. Harris : Chapter 4.'The Nuclear Overhauser Effect n Structural And Confonnational Analysis' by D. Neuhaus and M. Williamson: Chapters 1 and 2 ṟ

2 Enhancement Lectures 10 & of sensitivity for X nuclei Apri116, 1999, 15:37 1) ntroduction 2) The nuclear Overhause effect (noe ) r 21) 22) 23) 24) 25) 26) 27) 28) Definition Qualitative description The Solomon equations Dependence of noe on molecular motion The noe in idealistic system The noe in realistic system Homonuclear noe measurements Heteronuclear noe measurements 3) Polarization transfer 31) 32) 33) 34) Selective population transfer The NEPT experiment Refocused NEPT Characteristics of polarisation transfer experiment 4) nverse detection 41) 42) 43) What is inverse detection? Advantages The reverse NEPT r '- Page 1/17

) ntroduction Apri116, 1999, 15:37 P For X nuclei (13C, 15N.

Frequency (MHz).ya Relative sensitivityb r-"' 1H 2H 13C 14N 15N 1% 31p 99.98 0.016 1.108 99.63 0.37 100.00 100.00 1!2 1 1!1 1/2 1/2 1 1/2 100.00 15.

s-l b: At constant field r How can we increase the sensitivity of an X nucleus?

$not depends on scalar coupling r-- Depends on relaxation through di polar coupling -The noe enhancement 11(S) is detined as the fractional change in$

3 ) ntroduction Apri116, 1999, 15:37 P For X nuclei (13C, 15N...), it is difficult to obtain a good spectrum because of the low natural abundance and the reduced sensitivity sotope Natural Spin abundance Frequency (MHz).ya Relative sensitivityb r-"' 1H 2H 13C 14N 15N 1% 31p !2 1 1!1 1/2 1/2 1 1/ x x a: rad.g-l.s-l b: At constant field r How can we increase the sensitivity of an X nucleus? -By using the noe effect -By polarization Transfer -nverse detection (lh detection) 2) The noe effect 21) Definition -Manifestation of the attempt of the total system to stay at them1al equilibrium -Change in the intensity of an NMR resonance when the transitions of another one are saturated -Does not depends on scalar coupling r-- Depends on relaxation through di polar coupling -The noe enhancement 11(S) is detined as the fractional change in the intensity of on saturating S: 11(S) = (1) f', lo: equilibrium intensity of 22) Qualitative description A t wo spin system and S -At thermal equilibriumbolzmann distribution (Fig. 1 ) Page 2 / 17

4 Apri116, 1999, 15:37 Energy levels and population of a AX system -Nae experiment: saturatian af bath transitians af S (Fig. 2) N-8/2 saturated?"' a N-8/2 13a N+O/2 "' aa Saturated N+o/2 Populations after saturation of the S transitions r r" N+8/ N + o / 2 Cross-relaxatjon after saturation of S transitions 23) The SOLOMON equations The intensity of and S is proportional z and Sz are proportional to z and Sz to the population differences between the states klz = N(X(X -N(X + N(X -N (2) Page 3/17

The rate of change of z with time is: ksz = Na.a. -Na. + Na. -N k -- dt -dt dt + dt -dt (4) (3) April 16, 1999,15:37 The ways in which population can arrive at and leave from the aa state gives (Fig.

5 The rate of change of z with time is: ksz = Na.a. -Na. + Na. -N k -- dt -dt dt + dt -dt (4) (3) April 16, 1999,15:37 The ways in which population can arrive at and leave from the aa state gives (Fig. 3): = -(Wl + WlS + w v No-a + Wl No- + WlS No-+ W2 N + constant(5) At thermal equilibrium, = O with Ni(O) = equilibrium population (Wl1 + WlS + W2) Naa(O) -Wl1 Naf3(O) -WlS Nf3a(O) -W2 Nf3f3(O) = constant (6) r'tbe population differences from equilibrium can be written (Ni -Ni(O)) = ni. Therefore: =-(Wl+WlS+W2) naa+wlnap+wlsnpa+w2npp (7) r, dz.:;ind the similar expressions for dt ' dt ' and dt : and calculate dt = -(W + W1S + W2) n(x(x + W n(x + W1S n(x+ W2 n + (W+ W1S + WO) no; -W n(x(x -W1S n -Wo n(x -(W+ W1S + WO) n(x + W n + W1S n(x(x + Won(X + (W + W1S + W2) n -Wln(X -W1S n(x -W2 n(x(x (8) (9) Combination of (2) and (3) gives: 2 (N -Naa) = -k (z + Sz) and 2 (Na -Na) = -k (z -Sz) JS wel as: 2 (n -naa) = -k (z -z(o) + Sz -Sz(O)) and 2 (na -na) = -k (z -z(o) -Sz + Sz(O)) (10) Substitution of (10) into (9) gives: dz dt = -(z -z(o) + Sz -Sz(O» (Wl + W2) -(z -z(o) -Sz + Sz(O» (W + WO) which gives the Solomon equation: dlz dt = -(z -z(o» (WO + 2 Wl + W2) -(Sz -Sz(O» (W2- WO) (11) At steady state, dlz / dt = O and Sz = O, giving: D= -(z- z(d» (WO + 2Wl1 + W2) + Sz(D) (W2 -WO) Thus, z -z(o) / Sz(O) = W2 -Wo Wo + 2 W 11 + W2 (12) since Sz(O) = "f's yl Page 4 / 17

6 (l -10) - W2.Wo Tl(S) = Wo + 2 Wli + W2 (13) April 16, 1999, (W2- WO)

-Wo fastest when the molecules tumbles at a rate of about 1kHz W 1 fastest at a tumbling rate of = 400 MHz W2 fastest at a tumbling rate of = 800 MHz April 16, 1999, 15:37 P Small molecules in non

7 -Wo fastest when the molecules tumbles at a rate of about 1kHz W 1 fastest at a tumbling rate of = 400 MHz W2 fastest at a tumbling rate of = 800 MHz April 16, 1999, 15:37 P Small molecules in non viscous solvents tumble at a rate of around 1011 Hz, while large molecules tumble at rates about 107 H z For small molecules, W 2 > Wo For large molecule, WO> W 2 ntermediate size molecules, W 2 = Wo positive noe negative noe no noe w 242) Quantitative considerations log '.c FCURE 2-5 Varia:ion 01 dipolar transiljon probabilities \'1,- W,- and.. with r.- sho'nn for spectrome:cr frequencies of CO and 270.Hz. Calculated ror a pair or protons Å apart. -Extreme narrowing limit 'tc very short, ro 'tc «1:.Small molecules in non viscous solvents Wo & 2 'tc (19); Wl & c 3 'tc (20); 7 r6 W2& r6 (21) 25) The noe in idealistic system )J.le can now write the noe enhancement in term of molecular tumble rate (22) (23) and 1l1(S) = yl PS -For a homonuclear S system yl = ys, ro -= ros 5 + 0)2 'tc2-40)4 'tc4 «(1)1 -(l)s) 'tc «1 (S) = (1)2 'tc2 + 40)4 'tc4 (24) Page 6 / 17

April 16, 1999, 15:37 "' -n extreme narrowing conditions ro 'tc «1 -For large molecules (proteins, nucleic acids) W} ==W} ==O 111(8) = 2 111(8) '= - " -For a heteronuclear S system n extreme

8 April 16, 1999, 15:37 "' -n extreme narrowing conditions ro 'tc «1 -For large molecules (proteins, nucleic acids) W} ==W} ==O 111(8) = 2 111(8) '= - " -For a heteronuclear S system n extreme narrowing conditions ro 'tc «T11(S) = 2 yl Examples 1) 13C () signal up on saturation of lh (S) resonance = 4 noemax13c (lh) = 2 ')C 13C{1H} ) 1) SN () signal upon saturation of lh (S) resonance 1SN { 1H} r-"\ :r!:! noemax13c (lh) negative noe enhancement 'YN -When ro 'tc increases, "(S) decreases and can become negative The zero crossing is then given by 'tc = { 5 } 1/2 «(J) + (J)S)2-6 «(J) -(J)S)2

9 7 maj 1996, (j;s PS = 2 O'S,,1(S) - -(PS + P*) 1 2p* -=2+- 1l(S) PS " La - & r6 11(S) 'tc : NOE s. - % 4a - '\'»- )a -'. -, 1- -la-j. -2.S....-U...-.S S.. OgClTc Fig. 7: Reduction of steady state noe due to leakagc as a function of (J)'tc, with different intemuclear distance rs. P* is constant at 0.1 s-. r---...' a r. 2.0 (" b r = NOE NOE X 1- -sa -sa -.la J OgWTc oj -2 -' 2 Fig. 8: Reduction of steady state noe due to leakage as a function of rott, with different values of P*. The dotted curves are for P* = O. The other curves are from top to bottom, P* = 0.02, 0.05, 0.1, 0.2 and 0.5 s-l. Page 9117

$theoritical noe enhancement on rox 'tc for X { 1 H} experiments 26) The noe in realistic system (External relaxation rate P* ) 1l(S) = "y'swo + 2 w l + W2 {\ W2-WO -- ys (}S = yl PS 0"15 Cross$

10 April 16, 1999, 15:37 F WTc Fig. 6: Dependence of max. theoritical noe enhancement on rox 'tc for X { 1 H} experiments 26) The noe in realistic system (External relaxation rate P* ) 1l(S) = "y'swo + 2 w l + W2 {\ W2-WO -- ys (}S = yl PS 0"15 Cross relaxation rate between and S (JS > O when noe > O W2 > Wo (JS < O when noe < O W2 < Wo (j)'tc < 1 (j)'tc > 1 PS direct dipolar relaxation rate constant for relaxation of spin by spin S. -n a realistic system, PS is not the only relaxation mechanism P* 1: spin-rotation, c sa, quadrupolar relaxation etc P* inteffi1olecular dipole-dipole relaxation by paramagnetic species rhe noe enhancement becomes P* reduce the noe enhancement P* is independent of!s since it refers to interaction of lother than that with spin S. f fs is reduced, bath als and ps increase The cantributian af P* decreases and the nae increases taward its thearitical value noe depends on internuclear distance, hut only when there is external relaxation -Effect of P* on the Steady state noe Page 8/17

11 HomoDuclear Doe measuremedts Apri116, 1999,15:37 Practical considerations -Detection of few percent of intensity changes -mportant Sample preparation Frequency stability -Solvent A void protonated solvents ncrease the rate of intermolecular dipole-dipole relaxation r-- Reduce the intramolecular enhancement (increase of p*) Avoid solvents with broad deuterium lock signals DMSO and Acetone -d6 strong and sharp lock signal good solvents for noe CDCl3 weak lock signal no good for noe D20 broad lock signal no good for noe -Sample Removal of all impurities that lead to spin-lattice relaxation paramagnetic metal ions molecular oxygen The noe difference experiment n theory Saturate one resonance and then compare the intensities of others with their equilibrillm vallles. ntegration of resonances with and without a period of presaturation n practice Not accurate enollgh to detect small noe's Noe difference method (A) n (B) Page 10/17

$lh Ul {\ OFF r--l Decoupler Spectrum PD Acq Coupled, no noe Coupled, with noe Decoupled, no noe$

12 . " 28) Heteronuclear noe measurements Gated decoupling experiments Apri116, 1999, 15:37 13C-NMR spectra decoupled with noe 13C lh ON Decoupling OFFr". 13C-NMR spectra deccupled withcut nce f" 13C lh ON n n OFF -13C-NMR spectra coupled with noe 13C f" lh Ul {\ OFF r--l Decoupler Spectrum PD Acq Coupled, no noe Coupled, with noe Decoupled, no noe Decoupled, with noe OFF ON OFF ON OFF OFF ON ON Page / 17

$3) Polarisation transfer April 16, 1999, 17:12 31) Selective population transfer (SP) n = -L\H ap + L\C = -3L\.$

13 3) Polarisation transfer April 16, 1999, 17:12 31) Selective population transfer (SP) n = -L\H ap + L\C = -3L\.7 H2 n = -L\H -L\C = -5L\ f:' H1 f3a r- H-[\C=+3[\ n = [\H + [\C = + 5[\ 'YH ::z 4 'Yc L\H = 4 L\C AC=A 13C population C2 transition = Cl transition = 2A r-' H n = + 5L\ inverted H2 n=-5l\.!!!!:- 3A n = -3A 13C population Cl transition = C2 transition = Gain in intensity by -3, +5 compared to normal spectrum

r...32) The NEPT experiment Apri116, 1999, 17:14 p (nsensitive Nuclei Enhanced by Polarisation Transfer) 90 180. 90 x x y "' ntntnlh x 90. ffi;>,., a z r.

14 r...32) The NEPT experiment Apri116, 1999, 17:14 p (nsensitive Nuclei Enhanced by Polarisation Transfer) x x y "' ntntnlh x 90. ffi;>,., a z r. / x' c d e f uc, " fl(' " / /< y' - r. r >'1:. x', Hr, - H,,-, 1'1lf. ",1,"l(. X x i - g 9' z / h z 'LH(HO 11 H, / tt H, l C / 'C, -.r 'HM, C / X' -- Page 13/17

15 r '33 April 16, 1999, 17:14 p 9Oox 180 x 90 :f:y 180 y lh tntn n x "" 9' z h 1 z 1 r: 1 Page 14/17

$99-1.52 3.98 5.03 15N -3.94 9.87 57Fe 16.48 30.95 '""'-' The repetition rate of the pulse sequence is determined by Tt of protons The il delay -Maximum sensitivity:for an Sn system: L\ = sin-1-.$

16 -?4 Characteristics of polarisation transfer experiment Apri116, 1999, 17:02 p Sensitivity -Enhancement of sensitivity of by Error! NEPT = lo Error! Nucleus Max noe NEPT 31p "" 13C 29Si N Fe '""'-' The repetition rate of the pulse sequence is determined by Tt of protons The il delay -Maximum sensitivity:for an Sn system: L\ = sin-1-.!.- 1tJ n 1/2 -ectrum editing according to multiplicity CH: CH2 C..3 & sin (n J A) & sin (2 n J A) & [sin (n J A) + sin (3 n J)] -6 : i CH CH2 CHJ 6.,,. " '. J, Jo J' JO ' ". Page 15/17

. y 4) nverse detection 7 maj 1996, 19.45 What is inverse detection? -Use of the sateites lh-{x} only some % of the principal peak.

17 . y 4) nverse detection 7 maj 1996, What is inverse detection? -Use of the sateites lh-{x} only some % of the principal peak. which are in the feet of the peaks in the proton spectum and which represents -Example lh spectrum <?fchc3 '"""" 12C.o. o 00 o. o o..,.o 12' C e) 'O " le -58 -e3 -ll3 H(rl = O 99% no coupling with 1 H one peak of intensity 99 14C 1=0 Traces. 13C = 1/ % Coupling with 1 H a doublet of intensity 1 % r width lj13c-lh and symmetric / major peak -The NMR information is transfered from the X nucleus to the proton detected nucleus. t (\ :-T-"--- --,.- \...:.--,,, '.. :--.,,,- J...,. '",...1..,"."..1...,.". 1 H spectrum of CHC13 in inverse detection Page 16/17

18 . -42) Advantages Apri116, 1999, 17:02 p Gain in sensitivity Obtention of NMR parameters for nuclei with low 'Y The reverse NEPT experiment 180:. 90:. 'Hn n r=1/4j rf')n1. -J.;;iJr"" z H Cp H t (. (" 1j( 90, x '1 '. y' cx.n.:-.:a b c d (e) f g /'! HCH. 'C. 130, 90 i ',. o.(., n r:1/l. ) r1')n..,..-., 90..iaOO y' - 11(/1 H (. af} :..J.:...:r a b ( d (el f 9 11( H. f" 90, x HS ( (+21 z 90.. Page :

Nuclear OverhauserEffect (NOE) and its effects in NMR spectroscopy

Nuclear OverhauserEffect (NOE) and its effects in NMR spectroscopy S. SANKARARAMAN Department of Chemistry Indian Institute of Technology Madras Chennai 600036 sanka@iitm.ac.in Nuclear spin polarization