2D Multiple-Quantum Spectroscopy

447

Chapter 12

2D Multiple_ Quantum Spectroscopy 12.1 INTRODUCTION The two-dimensional h R experiments described in the earlier chapters were primarily concerned with the excitation and detection of single-quantum coherence. In this chapter, the 2D experiments involve the excitation of multiple-quantum coherence which is allowed to evolve during the ti time period before being converted and detected as single-quantum coherence. Multiple-quantum spectroscopy may therefore be considered as a generalisation of 2D correlation spectroscopy. The key difference between the two methods is the preparation and selection of coherence transfer pathways. This is illustrated in Fig. 12.1. As mentioned earlier, only single-quantum transitions can be detected directly. When there is no coupling, the isolated spin (of spin quantum number 1/2) can exist in two possible energy states, and therefore only single-quantum transitions (i.e. transitions in which the difference D M between the upper and lower energy states is equal to one) can exist (Fig. 12.2A). When coupling occurs, the nuclei depict a more complicated energy level arrangement in which zero-, single- and multiple-quantum coherences are evident (Fig. 12.2B). Multiple- and zero-quantum coherences maybe allowed to evolve before being converted to single-quantum coherence, and they are detected by the modulations of the signal as single-quantum coherence. In its simplest form the pulse sequence required to generate multiple-quantum coherence involves the application of a pair of 90 0 pulses separated by a time t which is equal to 1/4J (Fig. 12.3A). The multiple-quantum coherence generated by this sequence is not detectable, and a 900c detection pulse is applied to convert the multiple-quantum coherence into detectable transverse magnetization. The amount of double- and zero-quantum coherence detected by this procedure is a function of the offset frequencies of the single-quantum transitions. The amount of multiple-quantum coherence is therefore a function of the difference (or sum) of the chemical shifts of the coupled spins as well as the coupling constants. This chemical shift dependence can be removed by inserting a refocussing 180° pulse between the two 90° pulses (Fig. 12.3B-D). In an AB system this will result in the generation of pure double-quantum coheAence with no contributions of zero- or single-quantum coherence.Double-quantum coherence may be generated by any of the pulse

448

~

ti

A)

1

tU

2

+1 O

–1

' Preparation 2eriod +2 +1 0 –1

—————

J

–2

Fig. 12.1: Comparison between (A) 2D correlation spectroscopy and (B) 2D multiple quantumspectroscopy. The two procedures differ in the mode of preparation and in the selection of the coherence transfer pathways. In the multiple quantum experiment (B) chosen for illustration, the coherence pathways involve p = ± 2.

sequences shown in Fig. 12.3B,C and D. The multiplet components exhibit alternating signs in their intensity, and if the spectral lines are broadened by field inhomogeneities or for other reasons, the overlap between the oppositely phased multiplet components will lead to mutual cancellations. If the data is acquired immediately after the detection pulse, as in Fig. 12.3B, then it can be presented in the absolute value mode which will remove the phase information, and the spectrum will possess an absorption-mode appearance. Alternatively, instead of collecting the data immediately, a delay t = 1/2J may be inserted after the detection pulse (Fig. 12.3C) which allows the multiplet components to gain phase coherence. This works if the I H lines are narrow and there is still substantial signal after the 1/2J delay, but if the FID has decayed significantly by this time then a serious loss of sensitivity may occur, in which case the pulse sequence shown in Fig.12.3D may be employed. As in the refocussed INEPT experiment, a second pulse is applied which refocusses the multiplet components and allows them time to attain the same phase (ref.1,2).

449

Fig. 12.2: (A) Energy level diagram of spin 1/2 system in a magnetic field, Bo (B) Energy level diagram for a coupled AB spin system the magnetic field. S.Q., D.Q. and Z.Q.represent single-, double- and zero-quantum transitions respectively. The phases if the pulses can be manipulated according to the component desired to be measured (Reproduced with permission from C.L. Dumoulin, J. logo. Resonance, 64, 38-46 (1985), copyright 1985, Academic Press). The phase cycle for selection of double-quantum coherence suppresses the order p = 0, 1, 3, 4, 5, 7 but does not suppress the six-quantum signals. However as the higher order excitations are inefficient, the six-quantum excitations may be ignored for most purposes. For triple-quantum spectroscopy six experiments with 60° phase shifts are combined. Zero-quantum coherence may be generated by any of the pulse sequences shown in Fig. 12.3E, F or G. These are similar to the sequences B,C and D respectively except that the third pulse is now a 45° pulse instead of the 90° pulse used to excite doublequantum coherence. Pulse sequences B,C and D do not generate zero- or single-quantum coherence but only double-quantum coherence. The pulse sequences E,F and G however generate equal amounts of zero-quantum and double-quantum coherence but no single-quantum coherence. This results in the halving of the signal-to-noise ratio of the zero-quantum experiment in comparison to the doublequantum experiment. Furthermore, since zero-quantum transitions are not broadened by inhomogeneous magnetic fields, one can selectively eliminate undesired single- and multiple-quantum signals from zero-quantum spectroscopy using homospoil pulses. A delay (sequence F) and refocussing pulse (sequence G) are added to bring all multiplet components into the same phase, as in the pulse sequences which generate double-quantum coherence. By appropriate manipulations of the phases of the transmitter and receiver pulses, one can separate the signals arising from various coherence orders. The spectra may be obtained in

450

90° 90° (A)

c I ,

t= 1/4J

(B) (C)

90° 180° _c

90° 90° c ~i

90C

90 0

I

180° n

(E)

(F)

(G)

90°

90

t = 1/2J 180°

0

I , n ~c 90° 180° 45° 90° ,

I

A cq

ic n

90° 180° 90 0

(D)

A cq

IU

,

I

Acq

Acq

n n IU i 90° 180° 45° 90°

90° 180° 45° 90° 180° — — .. —

A cq

A cq

Fig. 123: (A) Basic pulse sequence to generate double-quantum coherence, which is dependent on the chemical shift of the coupled resonances. (B) Addition of a 1800 refocussing pulse removes dependence of the double-quantum coherence on the chemical shifts of the coupled resonances. (C) The addition of a delay after the last detection pulse allows the multiplet components to attain the same phase. (D) The broad signals are retained if a 180° refocussing pulse is applied in the middle of the delay. (E) Basic pulse sequence to generate zero-quantum coherence. (F) A delay is added to the pulse sequence in (E). (G) A refocussing pulse is added to the pulse sequence in (F). (Reproduced with permission from C.L.Dumoulin, J. logo. Resonance, 64, 38-46 (1985), copyright 1985, Academic Press).

one-dimension by applying the pulse sequences shown. Alternatively the delay between the second and third 90° pulses in sequences B,C or D, or between the 45° and 90° pulses in sequences D,E or F can be incremented, and Fourier transformation in the two dimensions will afford corresponding 2D spectra.

12.2 MULTIPLE-QUANTUM SPECTRA OF TWO-SPIN SYSTEMS If we consider the conversion of zero- and double-quantum coherence in a weakly coupled AX system into detectable single-quantum magnetization, we find that the non-selective mixing pulse of flip angle b induces sixteen coherence transfer processes (ref.3). After a complex Fourier transformation in the n1-domain, each of these processes will result in corresponding peaks in the 2D spectrum.

451

Some of the characteristic features of the multiple-quantum 2D spectrum are shown schematically in Fig. 12.4 (ref. 3). When the mixing pulse has a small flip angle (i.e. below 900), then the signals represented by large peaks will dominate. The peaks can be recognized by their characteristic geometrical disposition: (a)In the double-quantum spectrum, two doublets lie symmetrically on either side of the skew diagonal,vi = 212 (ref.4). (b) The amplitudes of the signals follow symmetry rules which differ for zero- and double-quantum peaks. When the mixing pulse has a small flip angle, then the double-quantum coherence is preferentially transferred into one quadrant. This feature has been utilised to identify the signs of the double-quantum precession frequencies (ref. 5). (c) Irrespective of the value of the flip angle, pairs of signals within any doublet always possess opposite amplitudes - hence if the coupling JAx is not resolved, the two oppositely phased signals within the pairs will cancel each other. Under these ( B)

( A)

c

- nr

OI

nc

•o

1

IC

A

I

A/ / / /

n o qn

/

/

s n

/

/

/

/ O

nr - nc

/ /

/ / /

Fig. 12.4: Some characteristic features of phase-sensitive zero- and double-quantum spectra in a weakly coupled AX spin system. (A) Peak amplitudes and locations in zero-quantum spectra (B) Peak amplitudes and locations in double quantum spectra. Filled squares represent positive peaks and empty squares represent negative peaks. (Reproduced with permission from L. Braunschweiler et al., Mo1. Phys., 48(3), 535-560 (1982), copyright 1982, Taylor & Francis Ltd.).

452

conditions (i.e. lack of resolution), coherence transfer into observable magnetization is said to be forbidden.

12.2.1 Two Dimensional INADEQUATE

13C

NMR Spectroscopy

The iD INADEQUATE experiment described in Section 3.2 made use of filtration through double-quantum coherence to suppress signals from mono-13C isotopomers in order to record signals from the 0.01% of molecules which have two 13 C nuclei in adjacent positions. This means that the INADEQUATE experiment happens to be amongst the least sensitive experiments available in modern NMR spectroscopy to the structural chemist. However, given that sufficient amount of sample is available (generally N mg of a sample of molecular weight N for a 48 hours 1 13C recording period on a 300 MHz H/75 MHz NMR spectrometer) then it allows one to work out the entire carbon skeleton of a molecule by looking for couplings between adjacent 13C nuclei. Moreover the 2D version is significantly superior to the 1D INADEQUATE experiment since the coupled carbon atoms are readily identified as they lie symmetrically disposed as pairs of satellite signals on either side of a diagonal line, and since the pairs of coupled carbons are spread in two-dimensions so that they are located on different horizontal lines. This therefore circumvents the serious problem of overlapping peaks, isotope shifts and AB effects which make the 1D INADEQUATE experiment difficult to apply in practice. This is particularly so because in the iD INADEQUATE experiment, we were looking for the exact correspondence between the coupling constants, 1Jcc, and in molecules with more than 15 carbon atoms, it may be difficult to work out all the couplings due to peak overlap. As was mentioned earlier, the double-quantum transitions are direct transitions occurring between the highest ß b state of an AX (or AB) spin system to the lowest aa state. If a single non-selective pulse is applied to a system in thermal equilibrium, then it results in the creation of single-quantum coherence. If however the system is not in an equilibrium state, then the application of such a pulse will result in the creation of double- or multiple-quantum coherence. To detect these higher orders of coherence they must be converted into detectable single-quantum coherence by application of an additional "read" pulse. The pulse sequence used in the iD INADEQUATE experiment, as mentioned previously, involves the following two pulses: 90° X-T-180° y-T-90"X- -90° x - data acq. (x) 0

90 c-t-180° y-T -90° g- -90"y - data acq. (-y) The two FIDs obtained by the above two sequences are co-added to eliminate the signals from the isolated 13C nuclei. In the 2D INADEQUATE experiment (ref. 4,6),

453

the pulse sequence is almost identical to that in the one-dimensional experiment, except that the short switching time D is replaced by the evolution time ti which is incremented in a stepwise °manner. The spin-echo created at the end of the second delay is subjected to the 90 x pulse (i.e. the second 90° pulse in the sequence) which can result in the creation of double-quantum coherence for all directly bonded 13C nuclei, provided the value of the delay t is set at 1/(4'Jcc) ( -8 ms). This is allowed to evolve during the evolution time ti before being converted into single-quantum coherence by a "read" pulse of angle 8, and detected. The pulse sequence used may therefore be represented as: 90° f1-t-180° f2 -t-90° f1 -tl-ef3 - Acq. The most efficient conversion into single-quantum coherence is obtained if the value of the flip angle e is kept at 90° , but this makes it difficult to determine the signs of the double-quantum frequency. The phase 4,3 of the q pulse may be cycled to select the double-quantum filtered coherence transfer signal, but this requires phase shifts of 45° which may be difficult to implement in practice. Alternatively one can use a composite z-pulse (ref.4) +, or simply a read pulse of e = 135° (ref. 5). The phases of the pulses may becycled over a 256-step cycle to eliminate any pulse, phase and amplitude errors, but the following 32 steps cycle affords acceptable results: f

1 = (0123 1230 2301 3012)

f

2 = (0123 1230 2301 3012 2301 3012 0123 1230)

f3

=(0123 2301)

When the coupled carbon atoms have only a small chemical shift difference, then the efficiency of the double-quantum excitation is greatly reduced due to strong coupling, resulting in a weakening or, when chemical shifts of the two adjacent 13C nuclei are identical, complete disappearance of the signals. The double-quantum frequency 1D0 representing two adjacent 13C nuclei,13Cl - 13 CX depends on the sum of the chemical shifts of the two nuclei, 1l and Ic, and if quadrature detection is applied, on the frequencyv o of the exciting transmitter pulse which is placed in the centre of the spectrum: D0 =

1

1

A +nC -2no

+The composite z pulse consists of the sequence 900.l - Y — 900 c in which the f _y pulse affords the desired phase shift (45°).

454

(C) M

M2

4

FT M1

M3

FT

FT

FT

t1 l.ODQ M4

M2 FT

(D)

(E)

U

1

FT

3

M

O • /O •

n 2

Fig.12.5: Effect of evolution time ti on the magnetization of an AX spin system (both A and X being adjacent 13C carbons atoms) in the 2D INADEQUATE experiment. (A) Positions of vectors in the column indicate effects of increasing evolution time on the double-quantum frequencies (drawn in dotted circles to indicate that they are invisible at this stage. (B) The last read pulse of angle Q generates single quantum coherence. (C) The first Fourier transformation converts the single-quantum coherences into 13C-13C satellite spectra, comprising pairs of antiphase doublets. These are modulated by the double-quantum frequencies which characterize each pair. (D) The second Fourier transformation affords 2D INADEQUATE spectra in which both pairs of satellites appear in the same horizontal row 1l at + ', equidistant from the diagonal. The antiphase nature of the peaks within each pair of satellites is shown by hollow and filled circles. (E) A horizontal cross-section taken at nl +nc shows the two pairs of peaks for A and X carbons with alternating positive and negative amplitudes. (Reproduced with permission from J. Buddrus et al., Antgew.Chent.btt.Ed. Engl., 26, 625-642 (1987), copyright 1987, VCH Verlagsgesellschaft Press),

455

The effect of changing the evolution time ti on the magnetization of a C2 fragment is shown in Fig. 12.5. The first row contains the coherence in the double-quantum coordinate system, and this non-detectable double-quantum coherence is drawn within dotted circles to distinguish it from magnetization vectors of single-quantum coherence, which are generated after application of the last read pulse of angle 8 . As in other 2D spectra, the acquired FID signals depend on the two time variables, t1 and t2. The first set of Fourier transformations in the t2 domain results in the generation of 13C - 13C satellite spectra. The resulting AX (or AB) doublet pairs are however subjected to modulation by the individual double-quantum frequencies which characterize each pair, so that the second set of Fourier transformations in the ti domain affords the two-dimensional INADEQUATE spectrum. Thus two adjacent 13 C nuclei, A and X, will appear at the following unique coordinates: ; sA + 8c and sc ; 8A + 8X

In other words ifv l defines the vertical axis representing the double-quantum frequenciesv DO,, andvz defines the horizontal axis representing the chemical shifts of the two carbons A and X, then both pairs of satellites will lie on the same row (at NA + vc) since V DQ is the same for all four signals of an AX spin system, thus facilitating identification of the coupled nuclei. This is schematically illustrated in Fig. 12.5. The advantage of this method is that no overlap can occur, even when Jcc values are equal, as all double doublets of the coupled AX spin systems occur in different rows. The 2D INADEQUATE spectrum of a new diterpene isolated by the author from a local medicinal plant is shown in Fig. 12.6. The 13C-13C connectivities established by the 2D INADEQUATE spectrum allowed its gross structure to be established. Notice that the satellites corresponding to bonds between C-9 and C-10 did not show up in the 2D INADEQUATE plot. This serves to illustrate the fact that while the presence of double-quantum peaks in the 2D INADEQUATE spectrum provides concrete evidence of a bond, the absence of such peaks does not necessarily prove that a bond is absent. Indeed the double-quantum peaks may be weakened, resulting in their apparent disappearance, by (a) long relaxation times, particularly of quaternary carbons (b) inefficient generation of double-quantum coherence due to strong coupling among 13C nuclei with close chemical shifts and (c) large chemical shift differences between coupled 13C nuclei. This last factor is often encountered when the coupled 13C nuclei differ by more than 100 ppm in their chemical shifts (e.g. carbonyl carbons adjacent to aliphatic carbons etc.) so that pulse imperfections may occur over the widely differing chemical shifts. The 2D-INADEQUATE spectrum of sucrose (Fig. 12.7) provides another example. The pairs of coupled carbons appear on the same horizontal line, allowing them to be readily identified.

456

CDC13

C1

C-4 C1 1

C -5

C-3 C-9

C -7

C-1

C-~ i_13 ~

il

170 160 150 140 130 120 110 100 90 80 70 60 50 40 3P

C-15

20 PPM

Fig.12.6: 2D INADEQUATE spectrum of 7-hydroxyfrullanolide.

12.2.1.1 Proton Monitored INADEQUATE (INSIPID) The low sensitivity of the INADEQUATE experiment 13C is on account of the low probability (1:104) of finding isotopomers with adjacent atoms, and the low gyromagnetic ratio of the 13C nucleus. The INEPT-INADEQUATE and DEPT-INADEQUATE experiments (described in chapter 3, sections 3.2.4 and 3.2.5 respectively) result in a modest increase in sensitivity. The proton monitored INADEQUATE experiment, known as INSIPID (INadequate Sensitivity Improvement by Proton Indirect Detection) involves transfer of polarisation from 13C to protons nuclei before detection (ref. 7). The pulse sequence employed, shown in Fig. 12.8, amounts to a combination of the INADEQUATE experiment with a modified reverse INEPT experiment (ref. 8). The pulses upto pulse "d" constitute the INADEQUATE experiment while the subsequent pulses correspond to the modified reverse INEPT experiment. The 2D-INSIPID spectrum of pyridine is shown in Fig. 12.9, with the iD 1H-NMR

457

(A)

..._,~..

Gi

NG2 Fc

(B)

F5

,~._.r.....,,.,...,,..,,..._ .~.,...--_._..-..~.... ,--....~....,,.,.,.-

i

~.......__,..~..-

Fy

F3 ~...-..i-....._-~--•~~

(C)

h Sm

ii

F6 G3

G3

G2 G4

",..,,....

G4

1

iLl

Fig. 12.7: (A) 2D INADEQUATE spectrum of sucrose. The coupled carbons are readily identified since they lie as pairs of symmetrically disposed satellites on either side of a diagonal line. (B) Cross-sections taken of various horizontal rows of coupled carbon atoms. From these, one can readily see that the carbon marked F2 is coupled to F3 (from row 2) as well as to Fl (from row 1). (C) Broadband decoupled 13C-NMR spectrum of sucrose.

458

~-- T

~a

'b

90°

y ic

tl

t —~

INEPT 180°

—

INADEQUATE 90° 180°

90°

13 H

~—

f

e

'd

_. t _'

t —y

T

90°

'

90°

Broadband Decoupling

1B

Fig. 12.8: Pulse sequence for the proton monitored INADEQUATE (INSIPID) experiment. (Reproduced with permission from P.J. Keller et al., J. Magna. Resonance, 68,389-392 (1986), copyright 1986, Academic Press).

0

0 -0

0

C2 03

C3 C4 4 OQ

CC

3

0KHt

0'

0

-2o

9

0

-3i

300

i

0 dh

i - 300HZ

~i—

n,

Fig. 12.9: The 2D-INSIPID spectrum of pyridine. The 13C chemical shift frequencies are C2 = 2276 Hz, C3 = 319 Hz, C4 = 1232 Hz. 13C-13C double-quantum frequencies are therefore at 2595 Hz for C2-C3, and 1551 Hz for C3-C4. (Reproduced with permission from P.J. Keller et al., J.Magn. Resonance, 68, 389-392 (1986), copyright 1986, Academic Press).

459

spectrum of pyridine being plotted on thent axis. Since C-2 and C-3 chemical shifts 13C are 2276 Hz and 319 Hz respectively, the - 13C double-quantum frequencies for C-2/C-3 occur at 2276 +319 = 2595 Hz. Similarly since C-4 chemical shift is at 1232 Hz, the 13C- 13C double-quantum frequency for C-3/C-4 occurs at 319 + 1232 = 1551 Hz. Since 1H is being detected instead of 13C, one might expect an increase in sensitivity of (g g/g c)3 = 64. However on account of the polarisation transfer from 13 1 C to H, the population difference of the detected protons depends on the 13C population difference, which in turn depends on the magnitude of the heteronuclear nie. In practice a ten-fold increase in sensitivity as compared to the 2D-INADEQUATE experiment may be attained.

12.3 MULTIPLE- QUANTUM SPECTRA OF THREE-SPIN SYSTEMS 12.3.1 Double-Quantum Spectra of Three-Spin Systems A schematic representation of a phase-sensitive double-quantum spectrum of a weakly coupled AIX spin system (with Jax: Jaws: Jix = 2:5:7) is shown in Fig. 12.10. If the flip angle of the mixing pulse is < 90° , then the larger symbols again represent dominant peaks. There are two types of signals in Fig. 12.10. Some peaks (such as those on the top left) have counterparts at negativev1 frequencies with opposite algebraic signs and 0 small amplitudes for flip angle b < 90 . These involve a common nucleus in both double- and single-quantum domains (e.g. AMC i AMC). Other peaks (as on the top right) have counterparts at negative vi frequencies but with identical amplitudes for all flip angles p . These signals arise from a transfer of single-quantum magnetization to a passive spin (e.g. AMC + AMX). While conventional single-quantum COSY spectra are helpful in identifying coupled spins, certain ambiguities present themselves in the analysis of unknown networks of coupled spins. For instance in a linear fragment of A-M-C type with Jax = 0 Hz, one has to resort to delayed coherence transfer (see later) to verify that the remote nuclei A and C actually belong to the same coupling network, in order to exclude accidental superposition of two separate systems A-M and M'-X with v w1 = v i'. One also needs to identify equivalent spins, since it is sometimes difficult to identify AX2 or A2 C3 subsystems if the multiplets are not properly resolved. 12.3.1.1 Linear Systems In a linear A-M-C system, the long range couplings between nuclei A and C are often too small to be resolved (i.e. Jax — 0). The A and C nuclei therefore appear as doubly degenerate doublets in the single-quantum region of the spectrum,

460

W

M

+W c

Wr +

•o~

• c,o'

o \\ .iio

.

Wc

W1

A'

a••

io • %

Wc

5bm /

5

ß/2

6.i~. 7' , \ M

2.~i{i,~n

/ /

ß/2 cos

sin

o = - Sin ß/2 cos5 ß/2 • _ +sin 3 ß/2 cos3 ß/2 o - - sin3 ß/2 cos3 ß/ 2 • + sin5 ß/2 cos ß/2 2 o = - sin5 ß/2 cis ß/

/

ioO / ~•

=+

Wr + WM

/ o O

•

a t

C \\

W A - WM

1

aa~A

/

aa

MW •

08oi

os

/Ow O

aa

/ / oa• / oa •

•Oa af

• . •

-

I I I I // ?V

i+

W

/

IIII

1 1 1 1

N V1

A O1 h+

N

h+

W

A

- W

3 • = + sin b /2 c0s $/2 O = _ sin $/2 cos3 $/2

c

•

= + sin3$/2

u W1 W

c

•

_+

p •

= +

• _-

cos ß/2

sin3 $/2 cos 3 sin $/2 cos sin $/2 cos3

ß/2 $/2 cos ß ß

/2

cos ß

sin ß/2 cos ß/2 cos ß sin ß/2 cos ß/ 2 cos ß 3

W

Fig 1210:Schematic phase-sensitive double-quantum spectrum of a weakly coupled AIX spin system (JAx : Jlm : JMx = 2:5:7). The transitions have been assigned according to the numbering in the energy level diagram. The size of the symbols corresponds to the observed amplitudes when the flip angle of the observe pulse (3 is less then 90° (Reproduced with permission from L.Braunschweiler et al., Mo1.Phys., 48(3), 535-560 (1982), copyright 1982, Taylor & Francis Ltd.).

schematically shown in Fig. 12.11. According to the selection rules governing coherence transfer, the double-quantum signals involving both A and M nuclei (v 1= Wp + Wc) do not undergo transfer to the X region when J lc = 0. Similarly the double -quantum signals involving both M and X nuclei (i.e. signals atvi wm + Wc) do not appear in the A region. However signals do appear atvi = WA + Wc even when Jlc =0, establishing that A and X are coupled to a common nucleus M.

461

A -M -C

A

2

C

W1

- Wr + Wc

- 2W A •

• • Wc

WA

Z W2 •

o •

•

• o

•

o •

i~

/ /

/ /

- 2w

A

O • •

Fig. 12.11:Schematic phase-sensitive double-quantum spectra of (A) a linear AMC system with J,0 = 0 0, and (B) a symmetrical A2C system. When b < 90 , the larger symbols represent dominant peaks. Signals represented by diamond-like symbols vanish when b = 900. (Reproduced with permission from L. Braunschweiler et al., Mo1. Phys., 49(3), 535-560 (1982), copyright 1982, Taylor & Francis Ltd.).

In an A2C system, the double-quantum signals involving the twO A nuclei appear only in the X region. This is according to the earlier stated selection rules for transfer - as JAA does not cause peak splitting, the 2 WA double-quantum coherence is comparable to the WA+wC coherence in the AMC system with JAx= P. Double-quantum signals may be classified into the three categories shown in Fig. 12.12:

462

(A) Direct (B) Magnetic Connectivity v i Equivalence

nl

(C) Remote Connectivity

/ / /

/

/

Fig. 12.12:Characteristic signal patterns in double-quantum spectra. (Reproduced with permission from L. Braunschweiler et al., Mol.Phys., 48(3), 535-560 (1982), copyright 1982, Taylor & Francis Ltd.

(i) Signals due to Direct Connectivity: These appear as pairs of symmetrically disposed signals on either side of the skew diagonalvi = 212. When the width of the excitation pulse is kept below 90° , then the peaks in the lower quadrant appear with smaller amplitudes. (ii) Magnetically Equivalent Nuclei: When there are atleast two magnetically equivalent A nuclei coupled to a nucleus X, then a single peak appears with a ii frequency which intersects the diagonal at a chemical shift 12 = W4• The double-quantum signals for equivalent nuclei are symmetrically disposed aboutn1= 0 for all widths of the excitation pulse. (iii) Remote Nuclei: Nuclei which are not coupled to one another but share a common coupling partner give rise to a single peak, the Ii -frequency of which intersects the skew diagonal at a N2frequency which does not coincide with any of the chemical shifts. The information obtained is similar to that obtained from relayed coherence transfer experiments.

463

12.3.2 Triple-Quantum Spectra of Three-Spin Systems The generalisations presented above were applicable to transfer of double-quantum coherence. However in three-spin systems, triple-quantum coherence transfer can also occur. In an AIX system, the triple-quantum spectrum will comprise two rows of signals atvi = f (wl + WM + Wc), and the coherence will be transferred into twelve single-quantum transitions, provided all three couplings are resolved. In a linear system with Jlc = 0, the triple-quantum coherence transfer is restricted to the doubly coupled central M nucleus. In a weakly coupled A2C system, the triple-quantum signals (ni= 21l +nc) will occur only in the C region. Triple-quantum spectra are specially useful in that they allow a distinction to be made between an A2C subunit and an A3C fragment, since the latter affords additional signals at vi = 3 wA andn2 = wx. In the case of systems with more than three spins, the multiple-quantum spectra will give rise to additional combination lines. Table 12.1 shows some common multiplet structures which are obtained along the i domain in multiple-quantum spectra. When analysing such spectra, primary emphasis should be given to identifying the chemical shifts where the signals are occurring, and the multiplicity of the signals should be used only for purposes of confirmation, as they are often not fully resolved, particularly in large molecules. A double-quantum spectrum of deuterated 3-aminopropanol serves as a representative example of an AA'II'XX' system. The high resolution single-quantum spectrum showed that the protons in the aliphatic -CH2CH2CH2chain have negligible long range couplings, and almost equal vicinal couplings, so that the system may be approximated to an A2M2C2 system. Examination of the spectrum (Fig. 12.13) shows that there are two pairs of multiplets in which the peaks lie symmetrically situated on either side of the diagonal. These appear at Vi wp + III and n i = WM + Wc, corresponding to couplings between A and M, and between M and C respectively, and they can be assigned to the first type of cross-peaks due to direct connectivity mentioned above. The rest of the signals, five in all, do not have symmetrical counterparts on the other side of the diagonal. If one draws horizontal lines from the peaks to the diagonal, they are seen to meet the diagonal at the chemical shifts of the nuclei A,' and C on then2 axis. One can conclude from the occurrence of these signals that the spin system contains atleast two equivalent nuclei of each type of nucleus, A, M and C, and the signals represent the second type of peaks (i.e. those due to magnetic equivalence) found in double-quantum spectra. The horizontal line (marked III) from one of the signals does not intersect the diagonal at the chemical shifts,12, of any of the nuclei A,' or C. The intersection falls between wA and Wc (o n2), and the peaks therefore represent the remote nuclei A and C (i.e. they are not coupled to each other but share a common coupling partner, M). The position of the cross-peak along vi corresponds to wA + Wc, hence establishing the chemical shifts of the remote nuclei responsible for it.

464

Table-12.1: Multiplicities of multiple-quantum signals in commonly occurring spin systems .

Spin Systems

Multiplicity and splittings+ +

2-spin-26hT + AIX AIX AAC A2C AMKX AMC2 AMXX AMC2 ACC2 AC2C AMMC2 AM2C2 AMMCC AAMMC2

D(JAx + JMx) D(JAM +JMx) D(JAx) D(2JAx) D(JAK + Jmk) x D(JAx +JMx) T (JAX+Jmc) D(JAi + Jix) x D(JAx) D(2JAx) x D(2JMx) T(JAx) D(2JAx) D(JAM) c T(JAx + JMx) D(2JAM) x T(2JMx) D(JAM + Jlc)cT(Jmc) T(JAM) C T(JAx + JMx) T(2JAM) c T(2JAx)

A2M2C2

3-s2in-3GliT AMKX AMXX AMC2 AC2C AC3 AMMCC A12C2 AM2CC AAMMCC A2MMC2 A3M2C

+

D(JAx + JMc + JKx) D(JAx + JMx) D(JAM+2JMx) D(JAx) D(3JAx) D(JaM+JMx) x D(JAx+JMx) T(JAx + 2Jritx) D(2JAM+JAx) c D(2JMx) D(JAM+JAx) x D(JAM+JMx) x D(JAM+JMx) D(2JAM) x T(2JAx+JMx) T(3JAM) c D(3JAx)

465

4-spin-2Q.T AMKSX

D ( J A X + J M X + JKX-JSX)

AMjXX

D ( - J A X + 2JMX)

AM2XX

D ( + JAX + 2JMX)

AAM2XX

D ( 2 J A M + J A X ) X D ( - J A X + 2JMX)

A3MMX

D(3JAX-JMX) X D(3JAM)

5-SDin-30T" AMKKX2

D ( - J A K + J M K + 2JKX)

AMK2X2

D ( - J A M + 2JMK + 2JMX)

^ Spins that flip in the transition are in boldface. ^ ^ D and Τ stand for double and triple. * Spins that flip with Am = -1 are in boldface with overbar. (Reproduced with permission from L. Braunschweiler et al., Mol Phys., 48(3), 535-560 (1982), copyright 1982, Taylor and Francis Ltd.).

While 2D COSY experiments (and of course the conventional selective double resonance experiments) only provide information about direct connectivity in coupling networks, multiple-quantum spectra provide information about direct connectivity, remote connectivity and magnetic equivalence. Relayed magnetization transfer experiments (presented earlier) also provide information about direct and remote connectivity but cannot identify magnetic equivalence. Furthermore in 2D COSY experiments (both conventional and relayed) some of the magnetization components (including solvent signals) are not involved in coherence transfer processes and therefore give rise to a dominant diagonal ridge along v i = V2 . As multiple-quantum spectroscopy is exclusively concerned with the portion of the magnetization which is involved in coherence transfer, this problem does not arise. Further, one can record various spectra corresponding to the respective orders of coherence and accumulate information about various spin systems - this offers a powerful way of obtaining "filtered" information exclusively concerned about certain sub-units (this is so because a p-quantum spectrum will afford information only about subunits concerned with ρ spin systems). This may prove to be a powerful method for analysing different spin systems in large molecules.

466

1.6 kHz

w

2

.o• • p•

e

+

W A WC

2w c

a

M

t~

W W

W M+WC

\ $

~

II

\

2W

g

~

~

0.8kHz

\

W

A

Wc

m

\ \

\

W1

Fig. 12.13:AbsoIute value double-quantum spectrum of 3-aminopropanol. Signals representing direct connectivity (I), magnetic equivalence (II) and remote connectivity (III) can be readily identified. The multiplets have been enlarged on the left. (Reproduced with permission from L. Braunschweiter et a1., Mol. Phys., 48(3), 535-560 (1982), copyright 1982, Taylor & Francis Ltd..

12.3.2.1 Constant Time Double-Quantum Spectroscopy 13 While C-NMR spectroscopy, its 1 double-quantum spectroscopy has found use in use in H-NMR spectroscopy is less widespread. This is because in 13C-NMR spectroscopy (the INADEQUATE experiment, to be more precise) one is looking for direct connectivity corresponding to 13C- I3C couplings, and these are easily

467

recognized because of the symmetrical disposition of the 13C doublets on either side of the diagonal. In 1H-NMR spectroscopy, however the multiplets obtained during double-quantum experiments along the vi axis do not correspond to the multiplets along the ½axis, so that the chemist needs to familiarise himself with their appearance before undertaking the task of interpreting the data. Moreover signals appear in multiple-quantum spectroscopy which have no precedence in COSY spectra - for instance one obtains signals at (UA + Wc) on the viaxis even when there is no coupling between the A and X nuclei. A method has therefore been developed which suppresses the homonuclear couplings along the vi axis so that the unusual multiplets found along the Vi axis are not observed (ref. 9). During this experiment the overall evolution time is kept constant (ref. 10,11) and a 180° pulse is applied during the evolution period which serves to interconvert those coherences which involve all the spin labels being interchanged. The pulse sequence used is: 90° -t -180° -t-90° -(T- ti/2) - 180° - (tj!2) - 90° - Acq The method, known as constant time double quantum spectroscopy, affords single lines along the i. axis arising only from direct connectivities, and the method has greater sensitivity than that in which the homonuclear couplings are not suppressed.

12.4 MULTIPLE QUANTUM SPECTRA IN FOUR-SPIN SYSTEMS Fig. 12.14 shows the various coherence transfer processes which may occur in a weakly-coupled four-spin system of AMC2 type with Jlc = 0. Fig. 12.14b shows a typical single-quantum transfer process between nuclei A and M in conventional 2D spectroscopy. The symbols i indicate the transfer of antiphase coherence, the transfer from A to M being symbolically represented as:

I1M _± Il Fig. 12.14(c) portrays relayed coherence transfer, while Fig. 12.14(d), (e) and (f) correspond to three coherence transfer processes found in double-quantum NMR: the first of these (Fig. 12.14d) corresponds to excitation and conversion of double-quantum coherence associated with direct connectivity, while Fig. 12.14e represents double-quantum coherences involving two nuclei which are not directly coupled together but share a common coupling partner nucleus (an example of "remote connectivity"). Fig.12.14f corresponds to coherence transfer to magnetically equivalent spins. Fig.12.12 shows how these three types of coherence transfer processes (d,e and f) give rise to corresponding characteristic patterns in double-quantum 2D-NMR spectra.

468

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 12.14:Coherence transfer processes in an A1C2 spin system.

12.5 UNIFORM EXCITATION OF MULTIPLE- QUANTUM COHERENCE In conventional multiple-quantum spectroscopy, the multiple-quantum coherence is excited by a sequence of three pulses: 90° -T -180° -T -90° (Fig.12.15a). The excitation depends on the generation of antiphase coherence during the preparation period under the influence of spin-spin couplings (ref. 3,12). The magnitude of the excitation depends on the coupling constant, and it may vary from nucleus to nucleus. This leads to an unpredictability in the relative intensity of the peaks for a given period. As mentioned earlier, remote and direct connectivities are distinguished from each other in double-quantum spectra from their appearance as lone multiplets, and as pairs of symmetrically situated multiplets across the diagonal respectively. The variation of signal amplitudes may cause one of the pairs of

469

180°

90° (a)

F

F

T

f+Y

T/2

/2

90°

90°

.

Y

¤ tl ~~

90° 90°

180°

100y

90°

180° F

90°

(with Z -filter)

(b) t/2

T/2

tl

T/2

T

/2

(with purging pulse)

90° 90°

90° '1''

90° (c) t

t 1—

90°

Y+ ~

(with Z-filter)

'·

(with purging pulse)

Fig.12.15:Pulse sequences for multiple-quantum spectroscopy. (a) Conventional sequence. (b) Sequence with symmetrical excitation/detection. The lower trace has a purging pulse at its end, while the upper trace contains a z-filter; both serve to suppress antiphase magnetization. (c) Symmetrical excitation/detection but without the 180° refocussing pulses present in (b). (Reproduced with permission from M. Rance et al., J. Magn. Resonance, 61, 67-80 (1985), copyright 1985, Academic Press).

multiplets to "disappear", making it erroneously appear as a remote connectivity or as originating from magnetic equivalence. These limitations can be overcome to a great extent by symmetrizing the pulse sequence (ref. 13). This is done by insertion of a rephasing interval after the evolution period (Fig. 12.15b). A purging pulse (ref. 2) is incorporated before acquisition to remove any defects due to incomplete t averaging. Alternatively a z- filter may be

470

inserted prior to acquisition (ref. 14), which comprises two additional pulses. The first of these rotates any in-phase magnetization components along the y' axis to the z axis, while the second pulse is phase-cycled, usually in 90° steps, along with the receiver (Fig. 12.15b, lower-trace). Thus only selected in-phase magnetization (or whatever exists as zero-quantum coherence during T z) will pass the z-filter. The undesired zero-quantum coherence is eliminated by averaging over a number of t z values. In another modification of the symmetrical excitation/detection sequence (Fig. 12.15c), the 180° refocussing pulses of the above sequence are removed. Compared to conventional multiple-quantum spectroscopy, the spectra obtained by the above sequences are in pure absorption, with positive peaks appearing for direct connectivities and negative peaks for remote connectivities. This provides a useful new method for spectral editing.

12.6 MULTIPLE- QUANTUM FILTERED COSY SPECTRA An important method for obtaining "filtered" information about connectivities between nuclear spins through scalar J couplings is that of multiple-quantum filtration. You will recall that in the conventional COSY experiment, the pulse 900 sequence involved the application of two pulses which were separated by a variable delay time ti. The response to these two pulses was measured during the detection period, t2. The responses on the diagonal in the conventional COSY spectrum arise due to components of the in-phase magnetization which are not affected by the second (mixing) pulse. The multiplet components of the peaks along the diagonal therefore possess the same phase and exhibit binomial peak intensity ratios. The cross-peaks, on the other hand, arise by the transfer of antiphase magnetization of one spin to the antiphase magnetization of another directly coupled spin (e.g. A to X in an AX system). This results in the cross-peak multiplets exhibiting alternating signs with respect to the coupling which generates the cross-peak, and the

90°

ti

Filter 90 0

t2

Fig.12.16.Pulse scheme for multiple quantum filtration. The application of two closely spaced rf pulses results in the mixing process which involves transfer of coherence in two steps - first from single into p-quantum coherence and then back to detectable single-quantum coherence. The result is a p-quantuu»m filtered spectrum.

471

intensity ratio may be depicted as an antiphase triangle (see Fig. 8.30). It also confers on the cross-peaks an "opposite" sense in terms of absorption and dispersion with respect to the diagonal peaks - when the cross-peaks are phased to appear in pure 2D absorption lineshapes, then the diagonal peaks appear in pure 2D dispersion lineshapes and vice versa. This is due to the sinusoidal variation of in-phase to antiphase magnetization during the evolution and detection periods. The presence of long dispersion tails in the diagonal peaks tends to mask any cross-peaks lying near the diagonal. Moreover when the multiplet components of cross-peaks are incompletely resolved, it can cause their mutual cancellation (because they have alternating signs) leading to a suppression of their intensities in comparison to diagonal peak multiplets which have been generated from in-phase magnetizations. This can cause cross-peaks to "disappear". + We have already discussed some of the characteristics of multiple-quantum coherence previously. The most important of these is the differential sensitivity of various orders of coherence to phase changes in its excitation sequence - a doublequantum coherence being twice as sensitive, triple-quantum coherence thrice as sensitive and, in general terms, a p-quantum coherence being p times as sensitive as a single-quantum coherence to phase changes of the excitation pulses. This provides us with a method for selecting the desired order of coherence when recording spectra (ref. 15-17). In practice this is done by applying a third 90° x pulse almost immediately after the second (mixing) pulse in the COSY sequence. The modified sequence may be represented as shown in Fig. 12.16. The third 90° pulse serves to convert multiple-quantum coherence created by the second pulse into detectable single-quantum coherence. Suitable phase cycling can then select out the signals which have been generated from different orders of coherence (ref. 2,3). Thus if we shift the phases of the first two pulses by 90° , it will have the same effect as if a 180° pulse was applied to a single-quantum coherence i.e. lead to signal inversion. It is notable that only signals due to double-quantum + While the presence of cross-peaks may be considered as evidence of coupling between corresponding protons, the absence of cross-peaks must be interpreted with caution. If the peaks have been weakened due to mutual cancellation (when not properly resolved, and when the spectrum is presented in the absolute value mode) they may fall below the threshold at which the lowest contour has been plotted. They may appear on plotting at a lower level. Other reasons for presence of weak cross-peak signals may be small couplings, wide T2 variation (particularly evident among exchanging protons, which leads to a mismatch of the window function and the FID envelope), and widely varying Ti values which lead to an incorrect repetition rate. Of these the most common cause of cross-peak weakening and disappearance is small coupling constants. These will lead firstly to the cancellation of antiphase pairs by overlap if not properly resolved, as already stated, and secondly the signals due to very small couplings will be weakened by relaxation processes much more than those due to larger couplings. This is because magnetization t

transfer between nuclei is dependent on the J values, being proportional to: e i/T2 sin pJti.

472

coherences are inverted by the 90° pulse. If the receiver phase is correspondingly inverted, then only signals created by the double-quantum coherence are detected In the case of a triple-quantum coherence spectrum, the signal inversion will be caused by a 60° phase shift (because the triple-quantum coherence is 3 times as sensitive to phase shifts as a single-quantum coherence, and 3/2 times as sensitive as a double-quantum coherence). In general if we wish to select a p-quantum coherence, then we have to step the phase of the excitation pulses through the sequence 0,180 ° /p, 2x180° /r...(2r-1)x180° /p, while simultaneously alternating the receiver phase. Quad detection may be employed inv l in the usual manner, the 90° phase changes being affected by (90/p)° phase shifts for quad detection of p-quantum coherence spectra. As all other coherences have been filtered out, only the desired p-quantum coherences are modulated as a function of t I* The resulting spectra are therefore much less complicated, and hence easier to interpret. Thus in a double-quantum COSY experiment, couplings due to AX or AB spin systems will appear while solvent protons, which cannot produce double-quantum coherence, or signals due to triple-quantum coherence (for instance in 3-spin systems) will be eliminated. A significant spectral simplification is hence achieved, since p-quantum coherence can arise only from atleast p-coupled spins of spin quantum number 1/2. Peaks arising from spin systems with less than p-spins are eliminated. Direct connectivities are represented in double-quantum spectra by pairs of signals situated symmetrically on the two sides of the diagonal, whereas remotely connected or magnetically equivalent protons give rise to lone multiplets. This purging operation is known as multiple-quantum filtration, and the spectra are referred to as p-quantum filtered COSY spectra, or more simply asp-QF COSYspectra. Using the procedure outlined above for a double-quantum coherence COSY experiment, the antiphase magnetization of one spin will be converted by the second mixing pulse into double-quantum coherence. This is then immediately converted by the third pulse into single-quantum coherence with antiphase magnetization either on the same spin (producing a diagonal peak) or on the other coupled spin involved in the double-quantum coherence (producing a cross-peak). Both the diagonal and the cross-peaks will now possess antiphase character, and it is possible to phase them simultaneously to produce pure 2D absorption lineshapes in both. Strictly speaking, this is not true. Other orders of coherence which will also be detected are represented by the formula r(2m + 1) where "r" will be 2 in double-quantum coherence spectra, 3 in triple-quantum coherence spectra etc., and "m" is any integer 0,1,2,3 etc. Thus for a double-quantum coherence experiment other orders detected will include 2(2x1 + 1) = 6, 2(2x2 + 1) =10 etc. but as the higher order coherences are weak, they are often not detected in practice. Some dispersive contributions may pass the filter, but these signals are usually weak.

473

The appearance or absence of peaks in p-quantum filtered COSY spectra of weakly coupled nuclei is governed by the following selection rules (ref. 17): (i) The appearance of a diagonal peak in a p-quantum filtered spectrum leads to the conclusion that the spin has resolved couplings to p-1 equivalent or non-equivalent spins. (ii) The appearance of a cross-peak between two spins in a p-quantum filtered spectrum suggests that in addition to their direct coupling, there are non-vanishing couplings to a common set of atleast p-2 additional spins. Fig. 12.17A shows the upfield region of a phase-sensitive COSY spectrum of basic pancreatic trypsin inhibitor (BPTI). The cross-peaks near the diagonal cannot be seen because of the dispersion tails of the peaks on the diagonal. Fig. 12.17B shows the same region in a phase-sensitive double-quantum-filtered (DQF) COSY spectrum. The elimination of the dispersive character of the diagonal peaks in the phase-sensitive DQF-COSY spectrum allows the identification of the cross-peaks lying near the diagonal. In principle it is possible to eliminate dispersion by using a pseudoecho filter but this requires presentation of the structure in the absolute value mode with its accompanying drawbacks discussed earlier. As we are restricting the coherence to a particular order, we may expect the sensitivity of multiple-quantum spectra to be less than that of conventional COSY spectra. The sensitivity of DQF- COSY can therefore be reduced by a factor of 2. In COSY spectra, the effective sensitivity is not determined by the signal-to-noise ratio but by the amount of thermal noise (i.e. by the signal-to-thermal noise ratio), the extent of thermal noise being indicated by the ti noise. Also of relevance, when plotting conventional COSY spectra, are the signs of the dispersion tails of the diagonal peaks in comparison to the cross-peaks. These criteria determine the lowest contour level which can be plotted without incorporating too much noise into the spectrum. In practice, the sensitivity of DFQ-COSY is comparable to that of the conventional phase-sensitive COSY experiment. Fig. 12.18 shows the schematic calculated cross-peak multiplet patterns obtained for COSY, double-quantum filtered COSY(a-c), and triple-quantum filtered COSY spectra. In Fig. 12.18a, the active coupling is larger than the passive couplings in both dimensions. In Fig. 12.18b, both passive couplings are larger than the active coupling. In Fig. 12.18c one passive coupling is greater than the active coupling, while the other passive coupling is smaller than the active coupling. All three couplings are active in Fig. 12.18d. Knowledge of the multiplet patterns can thus help in the recognition of active and passive couplings and in the assignment of coupling constants. Unless the data are collected under conditions of high digital resolution and the observed couplings are significantly larger than the natural linewidths, cancellation will occur by overlap of unresolved peaks whenever more than one coherence pathway contributes to the cross-peak intensity, leading to changes in the actual appearance of the multiplets.

474

n2

1

2

Fig. 12.17:(A) Conventional phase-sensitive COSY spectrum of basic pancreatic trypsin inhibitor. (B) Corresponding region in the phase-sensitive double-quantum filtered (DQF) COSY spectrum. The singlet resonances and solvent signal are largely suppressed. (Reproduced with permission from M. Rance et al., Biochern. Biophys. Res. Comm., 117(2), 479-485 (1983), copyright 1983, Academic Press).

475

(a)

—

r. Ja Ja

G

+ i

(c )

(b)

Jpr'i

r— l. Jp

+• • O O

L+ . . O O rL 1 00•• ~ 00••

Jp

~r + JP Ja,A'l ~Ja _

++• O• O

[ 1~ 0.0. +

G+• 0 • O ~ O•0 ~

Jp

Ja

+G

G LL

+ ~ +

..

~ Ja i~ Jp

+• • O O O

O

i + ~+ • • O O ~ OO .•

(d )

Ja J a

Ja —~ t--t hJa { +

+ • O 0• ~ r O ~ •O +• 00 •

Fig. 12.1&(a) - (c) Calculated fine structure patterns of multiplets obtained in COSY and double-quantum filtered COSY spectra (d) Same for triple-quantum filtered COSY spectrum. The active and passive couplings are indicated by "a' and "p" signs. (Reproduced with permission from J. Boyd et al., J. Magn. Resonance, 68, 67-84 (1986), copyright 1986, Academic Press).

It is possible to reduce the flip angle of the second mixing pulse in multiple-quantum filtered COSY spectra. As in COSY-45 spectra, reduction of the flip angle leads to suppression of multiplets generated by unconnected double-quantum transitions compared to the connected transitions.

12.7 H0MONUCLEAR ZERO-QUANTUM SPECTROSCOPY When one applies a pulse sequence of 90° -T -90° - T '- b , the signal obtained contains contributions from longitudinal magnetization present prior to the application of the final pulse, as well as the zero-quantum coherence which is converted to detectable magnetization by the final pulse. In homonuclear zero-quantum 2D NMR spectra, the signals originating from longitudinal magnetization occur atvi= 0 in the absence of nuclear Overhauser effect or chemical exchange. It is possible to discriminate between the longitudinal magnetization and zero-quantum coherence contributions to the final spectrum by utilising the differences in intensities of the two contributions. The inter_sity I of the signals from longitudinal magnetization is proportional to sin b12 (where p is the flip angle of the final pulse), while for an AX spin system, the signals arising from the conversion 3 of zero-quantum coherence into detectable magnetization are proportional to sin b/2 cos b/2 if the spin flip of the observed transition is of the same sense as the zero-quantum transition, and proportional to sin R/2cos 3 p/2 if it is of the opposite sense (ref. 18). Thus if two separate experiments are carried out, one with a flip angle ° b and the other with an angle b + 90 , then the difference between the two experiments will lead to elimination of the contributions from longitudinal magnetization, and the signals obtained will correspond essentially to those arising from zero-quantum coherence contributions (ref. 19). There are several advantages in recording zero-quantum spectra. Firstly homonuclear zero-quantum resonances are independent of inhomogeneities of the

476

magnetic field. Secondly zero-quantum frequencies comprise frequency differences, which are independent of the spectral window chosen. The standard pulse sequence 90° x-T -180° -t -90° x used to excite double-quantum resonance does not lead to the generation of zero-quantum resonance in weakly coupled homonuclear spin systems. The simpler sequence 90° x-t- 90° x does excite zero-quantum resonance but the signal amplitudes depend both on the couplings and on the chemical shifts (ref. 18,20). A method has been developed for mapping networks of spin-spin couplings via zero-quantum coherence which suppresses the chemical shift modulation of the amplitudes of excited zero-quantum coherences (ref. 21). The pulse sequence used (which is a modification of the Jeener pulse sequence (ref. 22)), is shown in Fig. 12.19. The chemical shift terms are suppressed by the 180 0y pulse. At the end of the evolution period ti, the zero-quantum coherence is converted back into transverse magnetization by a non-selective pulse of flip angle a . The efficiency of the zeroquantum coherence excitation depends on the delay t and the J values. If the value of t is small, then signals due to direct couplings are intensified while those due to long range couplings are suppressed.If desired, one can remove this sensitivity to the value of t by incrementing in step with t1 in a fixed proportion, kti (ref.3).

II I

i i

90° ~

: F2

1

i F

i

180°

f

180°

90°

~~ i

i

I

1

'

t

i

90° or 45F

45°

: f3

45°

F

2

i

i

F

4

a

i F4

3

ti

;~

t

2

Fig.12.19:Pulse segi&nce used in zero-quantum experiments. The 180° pulse serves to suppress the chemical shift effects. The homogeneity spoil pulse at tj = 0 may or may not be incorporated. The detection pulse at the end of the evolution period ti may have angle of 90° or 45° as in (a) or have an arbitrary flip angle a , as in (b). This last pulse converts the zero-quantum coherence into transverse magnetization which is recorded. (Reproduced with permission from L. Muller, J. Magna. Resonance, 59, 326-331 (1984), copyright 1984, Academic Press).

477

Fig. 12.20 shows the 2D 1H/1H zero-quantum spectrum of n-butanol with the final pulse set at 90° . The connectivity between protons is visualised by their occurrence on the same horizontal axis, and the strong zero-quantum peaks between vicinal protons can be readily recognized. The spectrum is symmetrical about v1= 0. If the flip angle of the detection pulse is reduced to 45° , then the connectivity is seen from lines lying along the anti-diagonal direction (v 2,21 (Fig. 12.21). In general if the value of the detection pulse is between 0° and 90° , then the cross-peaks appear along the anti-diagonal, whereas if the value of this pulse is between 90° and 180° , then the

- 2.5--

-1.5--

- 0.5Hz

N

M i~

t-

,

0.5-

M

1.5.5n1

h

4.

2.53.5

3.0

2.5

2.0

1.5

PPM

n2 1

1

Fig. 12.20: H- H zero-quantum spectrum of n-butanol. The proton-proton connectivities are shown by horizontal lines. (Reproduced with permission from L. Muller, J. Magn. Resonance, 59, 326-331 (1984), copyright 1984, Academic Press).

478

n2

Fig. 12.21:Rroton-rroton zero quantum spectrum of n-butanol obtained with the flip angle of the detection pulse reduced to 45° . (Reproduced with permission from L.Muller, J. Magn. Resonance, 59, 326-311 (1984), copyright 1984, Academic Press).

cross-peaks appear in the diagonal (v 2, 211 ) direction. The spectrum obtained by the 45° pulse is cleaner than that from the 90° pulse as the small transfer of zero-quantum coherence to passive spins due to weak long-range couplings, visible in the spectrum from the 90° detection pulse, is absent from the spectrum with the 45° detection pulse

12.7.1 Improved HZQC Method An improved pulse sequence for recording zero-quantum coherence (ZQC) spectra reported by Muller (ref. 21) is shown in Fig. 12.22 (ref. 23). It overcomes the major drawback of ZQC spectra i.e. their dependence on spin-spin coupling constants

479

980

1

.—

H omospoil

45° pulse

180°,

t

--- t

.. -t l —~

Fig.12.22:Pulse sequence for recording homonuclear zero-quantum coherence spectra. The duration of the a-pulse may be 90° or 45° . (Reproduced with permission from A.S. Zektzer et al., J. Nat. Prod., 50, 455-462 (1987), copyright 1987, American Society of Pharmacognosy).

and chemical shifts. The homonuclear zero-quantum coherence (HZQC) method appears to possess significant advantages over the proton double-quantum INADEQUATE (HDQC) experiment, particularly in saving recording time and resolution, though it may not have the ability of HDQC in elucidating coupling pathways when very small J h,1 couplings are involved. Since zero-quantum transitions are insensitive, HZQC spectra can be recorded in relatively inhomogeneous magnetic fields (ref. 24). Moreover it is convenient to consider zero-quantum coherence as a rotating monopole, single-quantum coherence as a dipole, and double-quantum coherence as a quadrupole and so on, so that ZQC may be expected to be relatively insensitive to the phases of the applied pulses, thereby allowing a simpler 4-step cycle to be used in comparison to the 32-step time-consuming phase cycling procedure required in the HDQC experiment (ref. 25,26). The ZQC spectrum of strychnine is shown in Fig. 12.23 (ref. 23). There are a number of features of this spectrum which should be noticed. The ZQTs appear in the n (zero-quantum) frequency domain at the algebraic differences between the chemical shift frequencies of the coupled resonances, relative to the transmitter frequency. If a 900 conversion pulse was employed, then the ZQT responses would be expected to occur as symmetrical pairs on either side of thevi = 0 axis. However the use of a 45° conversion pulse removes half of each pair, thereby resulting in a simpler contour plot. The connectivities shown by solid lines represent zero-quantum transitions, and they occur along parallel lines with a slope of 21 2=11. The axis marked "á" has the minimal residual single-quantum coherences located on it, while incompletely cancelled double-quantum coherences appear symmetrically about the skew diagonal marked "b" (Fig. 12.23). Weak error image peaks can sometimes occur as a pair of responses along 212 = -n 1. The HZQ experiment may have certain advantages in some cases over the COSY experiment, particularly when peaks on the diagonal in COSY spectra mask the cross-peaks of protons having very close chemical shifts. It has however not been widely employed in structural studies.

~ O

O -~

-200 -400 -600 -800 Hz

480

--

r

O

~ f O

O

O O

-O

.' . . _

1

i . . '

i

-

I

'

. . .

O

i

G~

400 200 400 -200 -400 -600 -800 1000 Hz

Fig. 1223:Homonuclear zero-quantum spectrum of strychnine. (Reproduced with permission from A.S. Zektzer et al., J. Nat. Prod., 50, 455-462(1987), copyright 1987, American Society of Pharmacognosy). 13C/13C

connectivities as in the The method can also be used for establishing INADEQUATE experiment. This is illustrated in the zero-quantum 13C spectrum of n-butanol (Fig. 12.24). The appearance of the spectra is similar to the SECSY spectra (ref. 27) in which single-quantum transitions are correlated by spin echoes. In SECSY spectra one usually finds a large ridge of only partially resolved peaks nearvi= 0. In zero-quantum spectra, however, the signals atvi =0 are suppressed, and the overlap of peaks is reduced since there are usually only half as many zero-quantum peaks as single-quantum peaks. However larger data matrices are necessary to cover the completevi dimension which is twice as large as the 12 dimension.

481

-2000 .

0-

2000 —

4000 H z 4500

3500

~

t 2500

~

~ 1500

~

~ 500

0

12 Fig. 12.24:Carbon-carbon zero-quantum spectrum of n-butanol. (Reproduced with permission from L.Mu11er, J. Magn. Resonance, 59, 326-331 (1984), copyright 1984, Academic Press).

12.7.2 SUCZESS A modification of the sequence, known as SUCZESS (successivezero-quantum single-quantum coherences for spin correlation) has been developed which requires a smaller data matrix (ref. 28). The pulse sequence used is shown in Fig. 12.25. The phase cycling used is shown in Table 12.2. The first 8 cycles are sufficient to afford an acceptable spectrum, though better compensation of pulse imperfections is achieved if 16 or 32 phase cycles are used. A SUCZESS spectrum of a mixture of L-alanyl-L-alanine and L- alanine in D20 is shown in Fig. 12.26. The antidiagonal line is seen to be clean and a good resolution is achievable. Since the data matrix in ni dimension is reduced, significant savings can be made in recording time. Furthermore if a value of t = 0.15/3J is chosen, then the AC, AC2 and AC3 spin systems are evenly excited (ref. 29) and the long range coupling correlations are reduced, resulting in a simpler spectrum.

482

90°

180° 2

F1

45°

135°

Receiver

F4

I

F5

~~ ti i i

t

i

i

~~

i

t

G

I t1/2

ii

ii

i

~ ~

i

t1/2

i ~

t2

Fig.12.25:Pulse sequence for the SUCZESS experiment. (Reproduced with permission from J. Santoro et al.,J. Magn. Resonance, 64,151-154 (1985), copyright 1985, Academic Press).

- 500

I,

a

- 400

- 300 S1( Hz)

- 200 - 100 i

0

~~

i 1200 1000 800

600

i 400

i 200

r 0

F2 (Hz) Fig. 1226:1H SUCZESS spectrum of a mixture of Ala-Ala and Ala. (Reproduced with permission from J. Santoro et al., J. Magn. Resonance, 64, 151-154 (1985), copyright 1985, Academic Press).

483

*

TabIe-12.2: Phase Cycling for SUCZESS Experiments

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

F1

f2

c c

y y y

c

U

c

c

x x c

-x -c -x -x -x -x -x -c x c c

x c c c c

-x -x -x -x -c -x -c -x

y y y y y y y y y y y y -y -y -y -y -y -y -y -y -y -y -y -y -y -y -y -y

F3 g

F4

F5

-y -y

-y -y

U

c c

-c

y -y y -y y y -y y -y y -y y

U

-c

-x -y y y -y x -x -x

-g

c

y -y y -y y -y y -y y -y y -y y -y -y -y

y -y -y y -x

-x c c

c c

-x -y y y -y c

-x -x x

(receiver)

y y -y -y x c -c

-x y y -y -y c

x -x -x y y -y -y c

x -x -c y y y -y

(Reproduced with permission from J. Santoro et al.,3. logo. Resonance, 64,151-154 (1985), copyright 1985, Academic Press).

484

12.8 PROBLEMS (2D-INADEQUATE) 12.8.1 Problem-1 Compound A having the molecular formula C5H1o0 afforded the 2DINADEQUATE spectrum shown in Fig. 12.27. Assign the connectivities on the spectrum and deduce the structure of the compound. The 13C-chemical shift assignments of compound A are, a: 817.9 (CH3); b: 834.0 (CH); c: 834.7 (CH2); : d67.6 (CH2), e: 874.7 (CH2). e

C

a

_ I PPM

80

I

70

60

50

40

30 II

Fig. 12.27

I

I ................ I...................................................................................................................................................................... I I.......................I 20

10 u

G

0

485

12.8.2 Problem-2 Compound B having the molecular formula C7H7C1O, afforded the 2DINADEQUATE spectrum shown in Fig. 12.28. Assign the connectivities on the spectrum and deduce the structure of the compound. The 13C-chemical shift assignments of compound B are, a: d19.9 (CH3); b: 8114.1 (CH); c: d117.8 (CH); d: d126.3 (C); e: d129.8 (CH); f: d137.5 (C); g: d153.3 (C). a

cb

e

g

)

PPM 160

i

i

140

120

N

II II

Fig. 12.28

i II

i 100

i

i 80

i

i

60

i

i

40

i

i

20

0

486

12.8.3 Problem-3 Compound C having the molecular formula C6H7N afforded the 2D-INADEQUATE spectrum presented in Fig. 12.29. Assign the connectivities on the spectrum and propose a structure for the compound. The 13C-chemical shift assignments of compound C are, a: 824.3 (CH3); b: 8120.6 (CH); c: 8123.0 (CH); d: d135.9 (CH); e: d149.4 (CH); f: d158.6 (C).

i

i

i

'

i

PPM 160 140 120 100 80

h

Fig. 12.29

II

i

60

i

i

i

40

20

0

487

12.9 SOLUTIONS TO PROBLEMS (2D-INADEQUATE) 12.9.1 Solution to Problem-1 In order to establish connectivities between different carbons from the 2D-INADEQUATE spectrum, draw a diagonal line such that satellite peaks occur at equal distances on either side of the diagonal. Then pick out any satellite peak, say the one marked A, which corresponds to the carbon at d17.9 (signal a). Now draw a horizontal line from A to another cross-peak B, which establishes that the carbon at 817.9 is connected to the one at X34.0 (signal b). Next draw a vertical line from B downwards to B2. In doing so, one comes across the pair of satellites B1, which has another pair of satellites, C, on the same horizontal axis thereby establishing connectivity between carbons at d34.0 and d34.7 (signal c). Similarly the satellite B2 has the satellite E as its partner, thereby establishing connectivity between carbons at d34.0 and d74.7 (signal e). By dropping a vertical line from the satellite peak C one reaches Ci. Its "mirror image" partner satellite on the other side of the diagonal line is D, hence establishing the connectivity between the carbon at d34.7 with the carbon at d67.6 (signal d). In this way one can solve the 2D-INADEQUATE connectivities in the spectrum. Fig. 12.30 represents the assigned connectivities of compound A, with its structure. d

e

~ PPM

/i

.......... 1 .......

70

80

60

50

30

40

bj cH D/

e

ß - Methyl tetrahydrofuran Cl D,,.

l ~I

Fig. 12.30

i

....... . i . __....._ i 10 0 ..

.'

20

hA

a

d

a

B

488

12.9.2 Solution to Problem-2 Fig. 12.31 represents the assigned connectiuities of compound B, with its structure.

I PPM 160

b

e

g

f

I

I

1 140

L i

120

G

i 100

i 80

60

20

40

l1

‚1-

OH

a

CH 3 CI 4-Chl oro-3-m eth yl phenol

Fig. 12.31

0

489

12.9.3 Solution to Problem-3 Fig. 12.32 represents the assigned connectivities of compound C with its structure.

I

I

I

I

I

I

I

I

~

PPM 160 140 120 100 80 60 40

~

~

20

, 0

- - - - - - - - - - - - - - - - - - - - - - - - - - - -i/ ---------

m

Ih

7i- - - - - - -

Fig. 12.32

REFERENCES 1 C.L. Dumoulin, The application of multiple-quantum techniques for the suppression of water signals in 1H-NMR spectra, J. Magn. Resonance, 64 (1985) 38-46. 2. O.W. Sorensen, M.H. Levitt and R.R. Ernst, Uniform excitation of multiple-quantum coherence: Application to multiple quantum filtering, J. Magn. Resonance, 55 (1983) 104-113. 3. L. Braunschweiler, G. Bodenhausen and R.R. Ernst, Analysis of networks of coupled spins by multiple-quantum NMR, Mo1. Phys., 48(3) (1982) 535-560. 4. A. Bax, R. Freeman, T.A. Frenkiel and M.H. Levitt, Assignment of carbon-13 NMR spectra via double quantum coherence, J. Magn. Resonance, 43 (1981) 478-483.

490

5.

6. 7. 8.

9. 10. 11.

12.

13.

14. 15. 16.

17. 18.

19. 20.

T.H. Mareci and R. Freeman, Echoes and antiechoes in coherence transfer NMR: determining the signs of double-quantum frequencies. J. Magn. Resonance, 48 (1) (1982) 158-163. A. Bax, R. Freeman and T.A. Frenkiel, An NMR technique for tracing out the carbon skeleton of an organic molecule, J. Am. Chem. Soc., 103 (1981) 2102-2104. P.J. Keller and K.E. Vogele, Sensitivity enhancement of INADEQUATE by proton monitoring, J. Magn. Resonance, 68 (1986) 389-392. R. Freeman, T.H. Mareci and G.A. Morris, Weak selective signals in high resolution NMR spectra: separating the wheat from the chaff, J. Magn. Resonance, 42 (1981) 341-345. J.A. Wilde and P.H. Bolton, Suppression of couplings in homonuclear multiple-quantum spectroscopy, J. Magn. Resonance, 67 (1986) 570-574. A. Bax and R. Freeman, Investigation of complex networks of spin-spin coupling by two-dimensional NMR, J. Magn. Resonance, 44(1981)542-561. M. Rance, G. Wagner, O.W. Sorensen, K. Wuethrich and R.R. Ernst, Application of wi-decoupled 2D correlation spectra to the study of proteins, J. Magn. Resonance, 59 (1984) 250-261. O.W. Sorensen, G.W. Eich, M.H. Levitt, G. Bodenhausen and R.R. Ernst, Product operator formalism for the description of NMR pulse experiments, Prig. NucL Magn. Resin., 16 (1983) 163-192. M. Rance, O.W. Sorensen, W. Leupin, H. Kugler, K. Wuethrich and R.R. Ernst, Uniform excitation of multiple quantum coherence. Application to two-dimensional double quantum spectroscopy, J. Magn. Resonance, 61 (1985) 67-80. O.W. Sorensen, M. Rance and R.R. Ernst, the z filters for purging phase- or multiplet-distorted spectra, J. Magn. Resonance, 56 (3) (1984) 527-534. A.J. Shaka and R. Freeman, Simplification of NMR spectra by filtration through multiple-quantum coherence, J. Magn. Resonance, 51 (1983) 169-173. M. Rance, O.W. Sorensen, G. Bodenhausen, G. 1Wagner, R.R. Ernst and K. Wuethrich, Improved spectral resolution in COSY H-NMR spectra of proteins via double quantum filtering, Biochem. Biophys. Res. Cimmun., 117(2) (1983) 479-485. U. Piantini, O.W. Sorensen and R.R. Ernst, Multiple quantum filters for elucidating NMR coupling networks, J. Am. Chem. Soc., 104 (1982) 6800-6801. W.P. Aue, E. Bartholdi and R.R. Ernst, Two-dimensional spectroscopy. Application to nuclear magnetic resonance, J. Chem. Phys., 64 (5) (1976) 2229-2246. P.H. Bolton, Flip-angle filters, J. Magn. Resonance, 60 (1984) 342-346. G. Pouzard, S. Sukumar and L.D. Hall, High resolution zero- quantum transition (two-dimensional) NMR spectroscopy: spectral analysis, J. Am. Chem. Soc. 103 (14) (1981) 4209- 4215.

491

21. L.Muller, Mapping of spin-spin coupling via zero-quantum coherence, J. Magn. Resonance, 59 (1984) 326-331. 22. J.Jeener and P. Broekaert, Nuclear magnetic resonance in solids : thermodynamic effects of a pair of rf (radii frequency) pulses, Phys. Rev., 157 (2) (1967) 232-240. 23. A.S. Zektzer and G.E. Martin, Proton zero quantum two-dimensional NMR spectroscopy. J. Natl. Prod., 50(3) (1987) 455-462. 24. A. Wokaun and R.R. Ernst, Selective detection of multiple quantum transitions in NMR by two-dimensional spectroscopy, Chem. Phys. Lett., 52(3) (1977) 407-412. 25. G.E. Martin, R. Sanduja and M. Alam, Two-dimensional NMR studies of marine natural products. 2. Utilization of two-dimensional proton double quantum coherence NMR spectroscopy in natural products structure elucidation determination of long-range couplings in plumericin, J. Org. Chem., 50(3) (1985) 2383-2386. 26. S.W. Fesik, T.J. Perun and A.M. Thomas, 1H-Assignments of glycopeptide antibiotics by double quantum NMR and relayed correlation spectroscopy, Magn. Resin. Chem., 23 (8) (1985) 645-648. 27. K. Nagayama, K. Wuethrich and R.R. Ernst, Two-dimensional spin echo 1 correlated spectroscopy (SECSY) for H-NMR studies of biological macromolecules, Biochem. Biophys. Res. Commun., 90(1) (1979) 305-311. 28. J. Santoro, F.J. Bermejo and M. Rico, Successive zero- quantum single quantum coherences for spin correlation, J. Magn. Resonance, 64 (1985) 151-154. 29. D.P. Burum and R.R. Ernst, Net polarization transfer via a J-ordered state for signal enhancement of low-sensitivity nuclei, J. Magn. Resonance, 39(1) (1980) 163-168.