Correlation of proton and carbon-13 nmr spectra by heteronuclear two-dimensional spectroscopy

JOURNAL

OF MAGNETIC

28,471-476

RESONANCE

(1977)

Correlation of Proton and Carbon-13 NMR Spectra by Heteronuclear Two-Dimensional Spectroscopy A great deal of information is contained in the proton and carbon-13 NMR spectra of a given compound, but sometimes it proves necessary to look further to discover which proton and carbon shifts are related by virtue of proximity within the molecule. This presupposes an interaction between them, usually the spin-spin coupling, and the most common technique of chemical shift correlation makes use of a series of coherent off-resonance decoupling experiments (1, 2). This communication utilizes an alternative approach based on double Fourier transformation (3, 4) that allows information about the proton spectrum to be transmitted to the carbon-13 spins. It is an application of a general experiment recently proposed and realized for the indirect detection of carbon13 resonance by Ernst and Maudsley (5,6). It is convenient to consider the proton magnetization vectors in a reference frame rotating in synchronism with the proton transmitter frequency, v,,. Proton spins with an equilibrium Z magnetization are rotated by a nonselective 90” pulse and aligned along the Y axis of this frame, where they precess freely for a variable time interval t,. Following the arguments of Ernst (5), consider first the simple CH spin system where there are just two transverse proton magnetization vectors M(a) and M(/3) precessing at frequenciesf(a) = vn - v, + iJ(CH) andf(P) = vH - v0 - +J(CH). At time t, a second 90” pulse rotates these proton vectors about the X axis, creating longitudinal magnetizations M,(a) and M,(P). These are equal to the Y components of the precessing vectors just before the second pulse, and are therefore cosine functions of the precession angles built up during t,, $44 = 2~f(Ct) t,

and

coca)= w-0

t,.

[II

These Z magnetizations correspond to nonequilibrium population differences across the proton transitions (Table 1) and are modulated as a function oft,. The populations may be thought of as being coherently “stirred” at the frequenciesf(a) andf(J). This affects the population differences across the carbon transitions, given by WA)

= 1 + + (yHIyc) lcos (4(a) - ax qca>l,

121

MN

= 1 - f (y&&J [cm q(a) - cos d.pN.

131

This time dependence of the populations introduces an amplitude modulation of the carbon- 13 signal excited by a 90” pulse. [No significant flip angle dependence can be detected in these experiments (7).] Note that the senses of the two modulations are opposite. The maxima of the cosine functions correspond to the condition that one of the proton vectors has completed an integral number of complete rotations duringt,, so that the net effect of the two 90” pulses represents a population inversion similar to that induced by a selective 180° pulse applied to one of the proton transitions. CopyrIght 0 1977 by Academic Press. Inc. All rights of reproduction in any Sorm reserved. Printed in Great Britain

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COMMUNICATIONS TABLE THE SPIN

ENERGY

LEVELS

POPULATIONS

APPROPRIATE

1

TO A CH

SPIN

Spin states Level 1 2 3 4

Carbon

; ;f

SYSTEM

AFTER Two 90° PROTON PULSES THOSE AT BO~TZMANN EQUILIBRKIM

SHOWING

COMPARED

THE WITH

Spin population9 ___-~ Proton

A A B B

At equilibrium

At time C,

-A--6 -A + 6 +A-6 -1-A + 6

’ The equilibrium population difference is 24 across across carbon-l 3 where A/S = yHIyC N 4.

-A cos $(a) - 6 -Acos$(/~)++ +Acos $(a)6 +A cos a;(/3) + 6 proton

transitions

and 26

The carbon-13 signal thus contains two modulated components and a constant component, and these are separated by Fourier transformation. Two successive transformations are carried out, the first as a function of the usual acquisition parameter t,, the second as a function of the period of free precession of the protons, t,. The result is a two-dimensional spectrum with the frequency axis F, representing the conventional proton-coupled carbon-l 3 spectrum, and the orthogonal axis F, the proton spectrum of the carbon-13-substituted molecule. For the two-spin system CH there are four modulated responses; in any given frequency dimension the pairs of responses have opposite intensities and interfere destructively if J(CH) is comparable with the linewidth. As mentioned by Ernst and Maudsley (5, 6), this is the heteronuclear analog of the double-pulse homonuclear experiment proposed by Jeener (3).

The Two-Dimensional Spectrum of Ethanol The application of this technique may be illustrated by the shift correlation spectrum of ethanol, measured as a slightly acidified sample containing deuterochloroform as internal lock material. The Varian CFT-20 spectrometer used a computer program for double Fourier transformation described elsewhere (8). Proton pulses of 40-psec duration were obtained by pulsing the proton decoupler in the coherent mode. Note that the frequency of the decoupler determines the frequency zero of the F, dimension. For the sake of simplicity Fig. 1 displays the spectrum in the absolute-value mode (8), the relative signs of the intensities having been verified in separate phase-sensitive experiments. A characteristic feature of Fig. 1 is the strong conventional proton-coupled carbon13 spectrum that runs along the line F, = 0 and represents the unmodulated carbon populations. At the F, coordinate of each of these responses, a horizontal trace runs out in the F, dimension carrying the corresponding proton responses. These traces are equivalent to the carbon- 13 satellites of a conventional proton spectrum except that the two halves have oppoposite intensities (not apparent in the absolute-value display of Fig. 1). For example, in the left foreground of Fig. 1 there is a trace originating from the methylene protons showing a doublet [J(CH) = 141.3 Hz] of quartets [J(HH) = 7.1 Hz]. In the background of the diagram there is a doublet [J(CH) = 125.5 Hz] of triplets

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LJ(HH) = 7.1 Hz] from the protons of the methyl group. These responses provide the chemical shifts of the CH, and CH, protons even though the spectrometer detects only carbon-13 signals, and the proton and carbon shifts are correlated through the direct couplings. These traces are repeated at the F, frequencies corresponding to the carbon- 13 lines, but instead of the usual 1 : 2 : 1 intensity ratio for the triplet and 1 : 3 : 3 : 1 intensity ratio for a quartet, these have become 1 : 0 : 1 and 1: 1: 1: 1, respectively, as predicted and

-0

C

FIG. 1. Two-dimensional spectrum of carbon-13 in natural abundance in ethanol, obtained by a pulse technique which permits the indirect detection of the proton resonance frequencies. and the correlation of the proton and carbon chemical shifts.

demonstrated by Ernst (5). A simple extension of the population “stirring” calculations of Table 1 establishes that the expected intensity ratios for a triplet should be -1:O: + 1, the zero arising because the population effects cancel for the intermediate symmetric levels while the antisymmetric levels remain unaffected. Similarly it is easy to show that the quartet intensities are - 1 : -1 : + 1 : + 1. (exactly equivalent results apply for the population changes induced by a selective 180° pulse on one of the proton lines.) Population transfer also occurs through long-range coupling, as illustrated by the three triplets in the right foreground and the four quartets in the left background of Fig. 1. The former are actually doublets [J(CCH) = 4.2 Hz1 of triplets [J(HH) = 7.1 Hz] in

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the F, dimension but the long-range coupling is not resolved, although it is large enough to prevent mutual cancellation of these opposed signals. Similarly, in the F, dimension there is an unresolved 4.2-Hz splitting (a 1 : 1 : 1 : 1 quartet) and a well-resolved I : 2: 1 triplet due to coupling to the “passive” protons of the methylene group. The weaker responses in the left background of Fig. 1 belong to the methylene protons of molecules with carbon- 13 in the methyl group. Here the long-range coupling [J(CCH) = 2.5 H z 1 is small enough to cause appreciable cancellation in both frequency dimensions. This leaves an apparent 1 : 3 : 3 : 1 quartet (in F2) of 1 : 3 : 3 : 1 quartets (in FJ due to coupling to the “passive” methyl protons. Simplification of the Spectra For many of the applications to larger molecules it is important to simplify these twodimensional correlation spectra, and this can be achieved by greatly reducing the splitting due to protons in both frequency dimensions. Since the algebraic sum of the intensities of the multiplet components of the modulated responses is zero, noise

i, Hz

560

PffOTO/v SPECTRUM

2. A splittings have factor of 3 by the long-range

1, except that the proton-carbon two-dimensional spectrum of ethanol similar to Fig. and scaled down in the F, dimension by a been coherently decoupled in the F, dimension, a partial refocusing technique. Note the almost complete elimination of the responses due to coupling.

FIG.

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decoupling during acquisition of the carbon-13 signal is not feasible. However, since the proton transmitter is normally set off-resonance in this experiment, coherent decoupling can be used, leaving a small residual splitting in the F, dimension, sufficient to prevent mutual cancellation of the opposed signals, but not necessarily large enough to be resolved in the two-dimensional display (Fig. 2). An equivalent simplification may be achieved in the F, dimension by the introduction of a 180° refocusing pulse on the carbon spins, slightly delayed with respect to $,, so that the refocusing of the GIand p proton vectors is not quite complete. In practice this pulse was applied at 2t,/3, reducing the splittings by a factor of 3. This partial refocusing acts on the long-range couplings in a similar way, and the reduced splittings become comparable with the linewidths, causing destructive interference. In this way shift correlations based on long-range coupling are eliminated, leaving only correlations based on the large directly bonded couplings, a considerable simplification of the spectrum. Figure 2 shows the ethanol spectrum modified by these two devices, the only strong responses representing populations transferred through J(CH,) = 125.5 Hz and J(CH,) = 141.3 Hz, with a very weak response through the long-range coupling J(13C. CH,). The center frequencies of these two groups of lines indicate the chemical shifts of the protons with respect to the decoupler frequency vO.The relative shift is 195 Hz (~2.5 ppm at 80 MHz).

Conclusions The preliminary results with this technique show considerable promise for increasing the information content of carbon-13 spectroscopy by introducing correlated proton shift information. The two-dimensional spectrum may show the detailed coupling scheme as pointed out by Ernst (5), as in Fig. 1, or it may be considerably simplified as in Fig. 2. It is primarily the modulated spin populations that are of interest, and since steady-state saturation of the carbon-13 spins affects only the unmodulated signals, the method should be applicable to carbon- 13 nuclei with long spin-lattice relaxation times. Sensitivity is thus determined by the spin-lattice relaxation of protons, which is often more favorable than that of carbon-13. Furthermore the population pumping mechanism operates through population differences appropriate to protons (d) rather than for carbon (4, where A/6 z 4, so there is a sensitivity advantage similar to that obtained through the nuclear Overhauser effect. ACKNOWLEDGMENTS This research was supported by an equipment grant from the Science Research Council. and a Scholarship from the Salters’ Company (G.B.). The idea of detecting nuclear resonance indirectly bl observation of the coherent signal transferred to another nucleus was originally suggested and experimentally verified by R. R. Ernst and A. A. Maudsley (5, 6). One of the authors (R.F.) is pleased to acknowledge an illuminating discussion with Professor Ernst. REFERENCES I.

H. J. REICH, M. JAUTELAT. M. T. MESSE, F. J. WEIGERT. AND J. D. ROBERTS, J. Amer. Chem. Sot. 91, 7445 (1969). 2. L. F. JOHNSON, Tenth Experimental NMR Conference, Pittsburgh, Pa. 1969. 3. J. JEENER, Ampere International Summer School II, Basko Polje, 1971: Second European Experimental NMR Conference, Enschedi, Holland, 1975.

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4. W. P. AUE, E. BARTHOLDI, AND R. R. ERNST,J. Chem. Phys. 64, 2229 (1976); R. R. ERNST, W. P. AUE, P. BACHMANN, J. KARHAN, A. KUMAR, AND L. MOLLER, Nineteenth Congress Ampere, Heidelberg, 1976. 5. R. R. ERNST, Eighteenth Experimental NMR Conference, Asilomar, Calif., 1977; Sixth International Symposium on Magnetic Resonance, Banff, Canada, 1977. 6. A. A. MAUDSLEY AND R. R. ERNST, Chem. Phys. Lett., in press. 7. S. SCH~UBLIN, A. HGHENER, AND R. R. ERNST, J. Magn. Resonance 13, 196 (1974). 8. G. BODENHAUSEN, R. FREEMAN, R. NIEDERMEYER, AND D. L. TURNER, J. Magn. Resonance 26, 133 (1977).

GEOFFREY

Physical Chemistry Laboratory, Oxford University, Oxford, England. Received July 19,1977

BODENHAUSEN RAY FREEMAN