Inverse DEPT sequence. Polarization transfer from a spin-12 nucleus to n Spin-12 heteronuclei via correlated motion in the doubly rotating reference frame

JOURNAL

OF MAGNETIC

RESONANCE

s&520-526

(1983)

Inverse DEPT Sequence. Polarization Transfer from a Spin-l/2 Nucleus to IL Spin-l/2 Heteronuclei via Correlated Motion in the Doubly Rotating Reference Frame M. ROBIN BENDALL,DAVIDT.PEGG,DAVID

:M. DODDRELL, AND JAMES FIELD

School of Science, Grt@th University, Nathan Queensland 4111, Australia Received September IS, 1982 The “distortionless enhancement by polarization transfer sequence” (DEPT) is a heteronuclear multipulse sequence which provides for polarization transfer from n spinl/2 nuclei to a spin-l/2 heteronucleus subsequent to a period of simultaneous free precession (correlated motion) of both types of nuclei in the transverse plane of the doubly rotating reference frame. A new multipulse sequen~ceis described here which involves polarization transfer in the reverse direction, that is, from one spin-l/2 heteronucleus to n spin-l/2 heteronuclei again subsequent to a period of correlated motion. This inverse DEF’T sequence has similar advantages to the DEFT sequence, over INEPT and related sequences, in that it contains fewer pulses and the acquired signal is relatively insensitive to missetting the length of the free precession periods. The sequence is proved both theoretically and experimentally. INTRODUCTIOI\I

The INEPT sequence originated by Morris and Freeman (I) and extended by Doddrell and Pegs (2) and Burum and Ernst (3) may be written in terms of “CH, systems as 'H

;[x]

-

(45)-l

-

1 -

(4J)-"

-

II R---

I 4 II

1%

$byl

2

;

; II I I II -i---i

2

; decouple II I I acquire

INEPT

The A value may be set at (4J)-‘, (2.J-‘, or 3(4J)-’ set to achieve a maximum, minimum, or zero signal from different CH, gmups. The inverse INEPT sequence utilizing polarization transfer in the reverse direction, e.g., from 13C to ‘H in 13CH, systems, has been developed theoretically by Bendall et al. (4) and used by Freeman et al. (5): 13C

'H

~x]-$-;

-$-;[fy] I I TI

0022-2364/83/030520-07$03.00/0 Copyright 0 1983 by Academic F’ms, Inc. AU rights of reproduction in any form reserved.

II I J! -

2

(45)-l

-

'T -

(45)-l

-I

ldecouple I I I I acquire

inverse INEPT

INVERSE

DEFT

521

SEQUENCE

In comparing inverse INEPT to INEPT we note that the pulse labels have simply been interchanged between 13C and ‘H. More importantly for this article, we note that the variable delay period A is the last period in INEPT but the lirst delay period in reverse INEPT. In an original description of inverse INEPT (4) using the Heisenberg vector model (6) we noted a great similarity between the results of INEPT and inverse INEPT even though the various initial magnetization vectors for CH, groups are quite different between the two sequences. This similarity holds provided the variable delay period A is interchanged with the (W)-‘-set delay period as written. More recently we have developed the EPT sequence (7-9) 'H

3x1 -

(25)-l -

TI

;ca 1

I I II I

2l 2-

13C

(25)-l

I : I 71 -

-

; decouple I :I

(25)-l

----I

I

EPT

acquire

This sequence utilizes both polarization transfer and the correlated motion of coupled heteronuclei (‘H and 13C) in the transverse plane of the doubly rotating reference frame. EPT provides a “C spectrum of methine (CH) groups in which signals from methyl (CH,) and methylene (CH3 groups are suppressed to a much higher degree than can be obtained using INEPT (7, 9). Our theoretical analysis of EPT in terms of the Heisenberg vector model confirmed that only small error signals will be obtained from CHr and CH3 groups (9). The same method of analysis for inverse EPT demonstrates that this sequence will also provide an exclusive CH spectrum, a ‘H CH spectrum (9): 3x1 -

1%

(25)-l -

;c*Y 1

‘II I : I

!!2 -

'H

I decouple I I

I I I

(25)-l

-

i -

(25)-l

--I

inverse EPT

acquire

Again, surprisingly, CH2 and CH3 error signals of the same magnitude are obtained for both EPT and inverse EPT, even though the initial magnetization vectors for these groups are quite different for the two sequences. For example, the CH2 group error is given by cos (a/2)( 1 + A J/J). sin ?rAJ/J, where A J is the error in J introduced when setting the (2J)-‘-see delay times. The cos (7r/2#1 + AJ/J) error term arises from the second (2J)-’ delay period for both sequences. However, the sin ?rAJ/J term comes from the last (W))’ period for EPT, but the first such period for inverse EPT. Thus EPT and inverse EPT demonstrate the same reverse symmetry for the signal magnitude as did INEPT and inverse INEPT. That is, the same result is obtained in changing to the inverse sequence if the quantitative effect of the first delay period is exchanged with the last delay period. In experimental use it became immediately obvious that EPT could be generalized to yield CH2 and CH3 signals by changing the magnitude of the second (7r/2)[H] pulse (10). This is the DEPT sequence 'H

;[x] -

(25)-l -

n

p[*yl

f 1I 13C

z-

2

I decouple I I I

I (25)-l

_

;

-

(25)-l

-I

’

acquire

CEPT

522

BENDALL

ET AL.

Convenient values of B are 7r/4, u/2 (EPT), and 37r/4. More generally, the 8 dependence of signal magnitude is given by sin 8 for CH, sin 28 for CH2, and (3/4)(sin 8 + sin 30) for CH3 (II). The question arises, is an inverse DEPT sequence viable? We know that for 8 = 7r/2 (inverse EPT) the sequence can be written. The pertinent question is then, which 7r/2 pulse in inverse EPT can be changed to a variable 8 pulse to provide the more general inverse DEPT sequence? By extending the reverse symmetry property demonstrated by inverse INEPT and inverse EPT, one would suspect that the 0 pulse should be at the beginning of the second (2.Z)’ period in inverse DEPT rather than at the end of this period as in DEPT. This is indeed the case: 1%

;cx1 -

'H

(24-l

-

y

$31

I

I I A --

i -

(25)-l

-

(25)-l

-i

; decouple I I I acquire

inverse DEPT

In this paper we show both experimentally and theoretically that the inverse DEPT sequence, as written above, does show a ‘H signal dependence corresponding to sin 28 for a “CH2 group and (3/4)(sin 8 + sin 38) for a CH3 group, and find a general expression for a i3CH, group. Although we have provided theoretical justification of the DEPT sequence we have not been able to do this in terms of the simple physical vector model (9). Correspondingly, in this article we have also had to revert to a less pictorial mathematical description for inverse DEPT, which we do in the Heisenberg picture. Nevertheless, certain properties of the inverse DEPT sequence are readily appreciated in terms of the vector model. For example, the purpose of the ?r pulses is simply to refocus chemical shift off resonance. Only one such pulse is required for each heteronucleus, placed at the midpoint of the periods in which magnetization vectors are evolving in the transverse plane of the doubly rotating plane. In this respect inverse DEPT is similar to EPT and inverse EPT (9). Second, the phase alternation of the second (7r/2)[C] pulse (with corresponding alternation of receiver phase) is necessary to reduce signals from the normal ‘H Boltzmann excess, again in a similar way to the alternation in EPT and inverse EPT (9). Inverse DEPT is potentially a very useful sequence, for example, for editing ‘H spectra. THEORETICAL

For mathematical

ANALYSIS

convenience let us rewrite the inverse DEPT sequence as

(Z,?r/2)-(2J)-‘-(SXB)(ZX~)-(2J)-L-(ZX

-r/2)-(2.Z)‘-decouple

Z and acquire S,

where Z is a single spin-l/2 heteronucleus (e.g., 13C) coupled to n S spin- l/2 heteronuclei (e.g., ‘H). The pulse no tation has been changed from our usual form to facilitate the subsequent mathematics. Thus (Z,?r/2) means a 7r/2 Z pulse on the y axis of the doubly rotating frame. All pulses are arbitrarily applied along the x axis except for the first pulse which must have a 90” phase shift relative to the last r/2 Z pulse. The phase alternation of the latter pulse, which in practice inverts the final signal phase, is not considered here. To simplify the mathematics without losing anything essential, we assume that the pulses are all on resonance and have omitted the refocusing ?r pulse for S spins. For convenience, however, we retain the ?r pulse for Z spins, and write the (Z, - 7r/2) pulse as (ZX7r/2)(ZX- ?r).

INVERSE

523

DEPT SEQUENCE

The free evolution time periods, of length (2J)-’ are described in the doubly rotating frame by the time-evolution operator exp(-iI&r) which follows from the Hamiltonian 27rJI&. The operators I and S represent the I and S angular momenta, respectively. For a IS, group,

s = c s’,

111

where the summation is over the n spins of type S. Because of its conceptual directness, we work in the Heisenberg picture, where the states remain constant and the operators evolve. This evolution may be calculated from the Heisenberg equation of motion, which gives us S(t) = u-‘(t,

o)su(t, O),

where U is the time-evolution operator. Operators such as S(t) which show explicitly the time dependence are He&&erg operators and operators such as I and S which do not have a time dependence are Schroedinger operators. In this experiment we measure the expectation values (S,(t)) and (S,,(f)), so we first calculate S,(t), that is, S,(t) = u-‘(l, o)s,u(t, 0). PI The time-displacement U(t, 0) = exp(-iZ&r)

operator for the sequence as described is

exp(-iZgr/2)

exp(iIgr) exp(-iZ&r) X exp(-i&8)

exp(--iZ,?r)

exp(-iI&)

exp(-iZyr/2).

[3]

We simplify this by using the following expressions which can be derived from the angular momentum relations such as described in Refs. (22) and (13) exp(il,u)

exp(-iZ&r)

exp(iI&r)

exp(-iS,fl)

exp(-il,?r)

= exp(iI&r)

exp(iI,S,u)

= exp[-ifl(S,. cos I,?r - S, sin Ip)]

[41

PI

= exp(iSyIz2t9), for spin I = l/2. This yields U(t, 0) = exp(-iZ&r)

exp(-il,?r/2)

exp(iS,I,28)

exp(-iZ,?r/2)

PI

and so from [2] S,(t) = exp( i&r/2)

exp(-iS,I,28)

exp(il,?r/2) exp(iI&r)

X S, exp(--iI&r)

exp(-iIx7r/2)

exp(iS,I,2B) exp(-il,?r/2).

[7]

We simplify this by use of the relations, for spin I = l/2, exp(iZ&r)S,

exp(-iZ&?r)

exp(iZX7r/2)Iz exp(- iIgr/2) exp(-iSyIz2~)Zy exp(iS,I,28) exp(iIy7r/2)ZX exp(-iIy7r/2)

= -21sy,

VI

= Iy ,

191

= Iy cos s,2e - I, sin s,2e,

1101

= I,.

ill1

These relations give us the remarkably simple result for the x component Heisenberg vector spin operator at the end of the sequence,

of the

524

BENDALL

ET

9.L.

SJt) = -2S,(Z, cos S,2fI -- Z, sin $20).

1121

The expectation value (S,(t)) will be, because t.he Heisenberg states do not evolve, found in terms of the initial S and Z states, which are all fz eigenstates. Thus the term involving I,, in [ 121 will give a zero contribution because it is not diagonal in these states. Our result is then (S,(t))

= 2(Z,)(S,

sin $28).

1131

The value of (II) will be the usual Boltzmann excess population of Z spins, which is proportional to the gyromagnetic ratio yI. To calculate [ 131 we write -2(S,, sin $28)

= d/d&(cos S,,28).

v41

Using [ 11 we expand cos S,26 as cos (2 $28) i

= j-J cos $28 + r(sin S$28),

P51

i

where T represents terms involving at least one factor of the form sin S$28, and thus the expectation value of all these T terms in terms of the initial compound proton state n ]~yl~)will vanish. This is because sin S$28 is completely off diagonal in the k

fz eigenstates Im,). Also, because the spin of each individual S spin is one-half, the first term of [ 151 is simply cos” 8, and so the expectation value will also be just cos” 8, which is completely independent of the initial S state. Finally, substitution of this into [ 141 and [ 131 gives us (&(t))

a yrn cos”-,I e sin e.

[I61

By a similar procedure we can show that (S,,(t)) vanishes, so the final signal is given by [ 161. It should be noted that this has the same dependence on 8 and n as does the DEPTdecoupled proton signal (II). For example, for a CHz group we have 2 X cos fl sin 0 = sin 28 and for a CH3 group we have 3 co8 8 sin 6 = (3/4)(sin B + sin X 38). Recently (23) we established a remarkable correspondence between the DEPT 8 pulse and the INEPT A time for spin- l/2 nuclei, namely, that the two sequences give identical proton-decoupled carbon spectra when e = ?rJA. This correspondence is also found between inverse DEPT and INEPT (and presumably inverse INEPT) because we have previously noted (see Eq. [20], Ref. (14)) that for spin- l/2 heteronuclei the dependence of the INEPT signal on A and n is given by n cos”-’ X ?rJA sin rJA. EXPERIMENTAL

RESULTS

A modified Bruker CXP-300 spectrometer was employed; IO-MHz rf was multiplied up and fed through a 90-MHz phase shifter (normally used to provide four phases at 300 MHz for DEPT and INEPT by mixing with 210 MHz rf). The phaseshifted 90-MHz rf was mixed with 14.54 MHz from the same synthesiser used to provide the lo-MHz rf, thus yielding four phases for i3C irradiation. 13C decoupling was not available. A 75.46-MHz fixed-frequency lo-mm probe provided with a ‘H coil was used. Presaturation by ‘H decoupling (0.5 watts) was employed. The inverse DEPT sequence was tested using a mixture of i3CH31 and CH3i3CH21. The signal magnitude dependence on the length of the B pulse is shown in Fig. 1, the results confIrming the viability of the sequence and the expected f3 dependence.

INVERSE

il

525

DEFT SEQUENCE

, 5

ii

e

in

FIG. 1. Dependence of ‘H signal intensity on the 0 pulse length in the inverse DEFT sequence for (a) 13CHJ and (b) the 13CH2group in CH3”CHJ. Experimental points (H and 0, respectively) and theoretical curves ((3/4)[sin 0 + sin 3191and sin 20, respectively) are shown. A sample comprising approximately 20% “CHSI, 20% CH3”CHJ, and 6O?GCDC13 was used. Eight transients were collected for each experimental point, after four dummy transients, using a recycle time of 30 sec. The experimental points are the average of the intensities in the %coupled ‘H doublet.

The decrease in signal intensity for larger 8 pulses results from inhomogeneity in the pulse. The carbon 7r/2 pulse time, found by obtaining a nil signal when either of the (?r/ 2)[C] pulses in inverse DEPT are misset at u radians, corresponded within 5% to that measured using the sequence (7r/2)[H]-(W)-‘-(7r/2)[C],

acquire ‘H signal,

for which a nil signal is obtained for any 13CH, group provided the (rr/2)[C] pulse time is accurately set. A positive or negative signal results depending on whether the ‘H pulse time is shorter or longer than n/2, respectively. This set-up procedure is the inverse of one used to set up INEPT and DEPT type sequences (15). CONCLUSIONS

In our most recent work we have found that the DEPT sequence is superior to INEPT and to spin-echo sequences for the purpose of editing i3C spectra (IO, 11, 16). The major reason for this is that DEPT spectra are relatively insensitive to missetting the sequence delay periods away from that determined by the value of J. The latter are impossible to set accurately for all CH, groups in a sample because of variation in the 13C-‘H single-bond J values. However, signal errors that occur from this source in 13C subspectra are smaller than those found in subspectra using spinecho sequences and very much smaller than those in equivalent INEPT subspectra. Inverse DEPT will also have this advantage. A simple explanation of the advantage over inverse INEPT is that inverse DEPT signals depend, in the 6rst approximation, on the length of the 13pulse rather than on rJA as does inverse INEPT. In addition, inverse DEPT contains fewer pulses than inverse INEPT and is consequently less prone to pulse errors. Consequently inverse DEPT is an important new sequence.

526

BENDALL

ET

AL.

‘H spectra may be edited by adding and subtracting spectra obtained using inverse DEPT with 8 = 7r/4, u/2, and 37r/4 in a similar way to editing 13C spectra using DEPT (10, II). However, for largely technical reasons, this paper is a preliminary account of the inverse DEPT sequence. For applications in ‘H spectroscopy, 13C decoupling is required and as yet this is not readily available. Second, the problem of suppressing ‘H signals from ‘?H, groups has been noted (5, 17). These need to be suppressed to less than 0.05% for application to unenriched samples, an accuracy which is very likely unobtainable on present-day spectrometers. Nevertheless the desirability of obtaining separate ‘H spectra of CH, CH2, and CH3 groups is likely to accelerate spectrometer development to this end. ACKNOWLEDGME.NT The

Bruker

CXP-300

is owned

by the Brisbane

NMR

Ceatre

and sited at Griffith

University.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

II. 12. 13. II. 15. 16. 17.

A. MORRIS AND R. FREEMAN, .I. Am. Chem. Sot. 101,760 (1979). M. DODDRELL AND D. T. PEGC, J. Am. Chem. Sot. 102,638s (1980). P. BURUM AND R. R. ERNST, J. Magn. Reson. 39, 163 ( 1980). R. BENDALL, D. T. F%GG, AND D. M. DODDRELL, J. Mugn. Reson. 45, 8 ( 198 1). FREEMAN, T. H. MARECI, AND G. A. MORRIS, J. Magn. Reson. 42, 341 (198 1). T. PEXX, M. R. BENDALL, AND D. M. DODDRELL, .I. Mugn. Reson. 44, 238 (1981). R. BENDALL, D. T. PEGG, AND D. M. DODDRELL, J. Chem. Sot. Chem. Commun., 872 (1982). R. BENDALL, D. T. PEGG, D. M. DODDRELL, AND D. H. WILLIAMS, J. Org. Chem. 47, 3021 (1982). M. R. BENDALL, D. T. PEGG, AND D. M. DODDRELL, J. Magn. Res.. in press. D. M. DODDRELL, D. T. F+ECG, AND M. R. BENDALL, J. Mczgn. Reson. 48, 323 (1982). D. T. PEGG, D. M. DODDRELL, AND M. R. BENDALL, L Chem. Phys. 77,2745 (1982). D. M. BRINK AND G. R. SATCHLER, “Angular Momentum,” Oxford Univ. Press (Clarendon), Oxford, 1968. D,T.FWx, D.M. DODDRELL, ANDM.R.BENDALL,J. Magn. Res., 51,264(1983). D. T. PEGG, D. M. DODDRELL, W. M. BROOKS, AND M. R. BENDALL, J. Magn. Reson. 44,32 (1981). D. M. THOMAS, M. R. BENDALL, D. T. PEGG, D. M. DOIDDRELL, AND J. FIELD, J. Mugn. Reson. 42, 298 (1981). M. R. BENDALL, D. T. PECK, AND D. M. DODDRELL, unpublished results. M. R. BENDALL, D. T. pu;G, D. M. DODDRELL, AND J. FIELD, J. Am. Chem. Sot. 103,934 (1981).

G. D. D. M. R. D. M. M.