Fast two-dimensional correlation spectroscopy

JOURNAI.

OF MAGNETIC

RESONANCE

83,649-655

(1989)

Fast Two-Dimensional Correlation Spectroscopy LISA MCINTYRE

AND

RAY

FREEMAN

University Chemical Laboratories, Cambridge University, Cambridge, England Received

March

2 1, 1989

Correlation spectroscopy (COSY) has emerged as one of the most powerful methods of two-dimensional Fourier transform NMR (1-4). It provides clear and unequivocal evidence of scalar coupling through the detection of cross peaks in the spectrum, and it also provides a measure of the active and passive coupling constants. In this latter application, however, digital resolution can be a limiting factor in the F, dimension, being determined (for a given spectral width) by the number oft, increments employed. Fine digitization can mean a very protracted COSY experiment (5) particularly when sophisticated phase cycling is used. Since the COSY experiment gathers strong NMR signals on every t, increment, it enjoys a sensitivity (per unit time) comparable with that of one-dimensional spectroscopy (I, 6). In many applications of COSY to proton NMR at high field, sensitivity is more than adequate, and no time averaging need be employed beyond that imposed by the phase-cycling procedures. However, we must not be misled into assuming that the experiment cannot be improved, indeed we show below that much of the information recorded in a conventional COSY experiment is redundant, raising the possibility that the essential information may be acquired more rapidly. We describe here an alternative to the COSY experiment which achieves comparable results in a significantly shorter time. It arose out of an earlier study aimed at separating overlapping two-dimensional COSY cross peaks, and it is helpful to describe some of the principles of this method first. A COSY cross peak has a particular type of symmetry. For a two-spin (IS) system it is a square pattern of four absorptionmode signals alternating in sign in both frequency dimensions (2~). The splitting is the same in both dimensions and is determined by active coupling Jrs. For more complicated spin systems (for example, the ISR case) this primitive square pattern is further split by the passive couplings (those not directly involved in the coherence transfer betyeen spins I and S). Thus there might be an additional splitting JIR in the F, dimension and an additional splitting JsR in the F2 dimension. Passive splittings do not cause any further alternation in the sign of the signal intensity. Consequently a cross peak representing I + S coherence transfer would consist of 16 lines (Fig. 1) and could be decomposed into four primitive square patterns of the form (f~). On the opposite side of the principal diagonal, the other cross peak (corresponding to S + I transfer) has an identical pattern except that it is reflected with respect to the principal diagonal. These same principles continue to apply as more passive spins are introduced. We disregard the lineshape distortions attributable to correlation of B, 649

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0

l

0

t

b h FIG. I. Representation of a typical COSY cross peak for an ISR spin system as a contour diagram with negative-going signals shown in black. The primitive pattern is a square of side JIs showing sign alternation in both dimensions. This is further split by the passive coupling JIR in one dimension and the other passive coupling JRs in the other dimension. The entire cross peak can be constructed by multiplying the intensity ordinates of the two orthogonal sections S(F, , a) and S(b, F2).

inhomogeneity effects in the two frequency dimensions (7) which can give rise to intensity contours in the form of a tilted ellipse. These effects, associated with coherence-transfer echoes (8, 9), are usually quite small in many cases of practical interest. There is an important consequence ofthis form of symmetry. The entire cross peak can be reconstructed by multiplying together the intensity ordinates of two orthogonal sections, one parallel to the F1 axis and one parallel to the F2 axis. We can see this most simply by assuming initially that the two orthogonal sections pass through exact resonance for four of the component lines in each dimension (Fig. 1). Clearly pointby-point multiplication preserves the sign alternation of the intensities of each primitive square pattern. It also reproduces the correct two-dimensional lineshape of each individual resonance line (as can be confirmed by computer simulation). At first sight it is perhaps less obvious that the reconstruction of the two-dimensional cross peak is successful wherever the F, and F2 sections are located, they need not pass through exact resonance in either dimension. Naturally they must pick up appreciable intensity from the tails of the lines, well above the background noise level, and they must not cut through any extraneous signal responses. Normalization of the intensities is achieved by dividing by the intensity ordinate at the point (a, b) where the two sections intersect. Thus if the sections are represented as S( F, , a) and S(b, F2) then the two-dimensional cross peak is constructed by multiplying intensity ordinates S(AF1, a) and S(b, AF’*) within the appropriate narrow frequency regions AF, and A&:

These symmetry rules can be expressed mathematically by writing the cross peak due to I + S coherence transfer in a three-spin (ISR) system as a product of timedomain signals (remembering that we disregard coherence-transfer echo effects),

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while the cross peak due to S + I coherence transfer is WI 3 f2 ) = WI

Mf2

[31

)>

where g(t,) = sin(2~61tl)sin(~JIst,)~~s(?rJ1Rt,

)exp(-t, /T2)

141

h(t2) = sin(2a~st2)sin(~JIS~2)~~s(~JSR~~)e~p(-t2/TZ).

[51

In the frequency domain the cross peak is centered at (6,) 6s); JIR and JSR are passive couplings while JIs is the active coupling. It is a standard property of Fourier transforms that the corresponding two-dimensional spectrum can be written as the product WI

>J.2

I=

WI

WV’2

13

bl

where G(F,) and H(F2) are the Fourier transforms of g(t,) and h(t2), respectively. This is a surface in three-dimensional space having the property that any section parallel to the F, axis has afixed profile defined by G(F,); only the amplitude (and sign) may change as the F2 coordinate of the section is changed. Similarly, each section parallel to the F2 axis has a fixed profile defined by H(F,). The ordinate at any point on the surface is determined by the product of G(F,) and H(F2), normalized by dividing by the intensity S(a, 6) at the point where the two sections cross. Consequently the entire surface can be reconstructed from a knowledge of G(F, ) and H(F,) measured at arbitrary positions. Exceptions to this rule occur at the rare condition where section G(F,) or H(F2) is identically zero (midway between a positive and negative peak). Now it so happens that a recent experiment called pseudo-correlation spectroscopy or +COSY (10-14) permits the measurement of a section S(F2) that has the same form as the corresponding section through a COSY cross peak. Consider the case of two sites with chemical shifts P and Q Hz (Fig. 2). Briefly, +COSY is a coherencetransfer experiment (P + Q) initiated by a soft half-Gaussian pulse (15) at the frequency P Hz, giving a section S(P, F2). Digitization in the F2 domain can be as fine as necessary without significantly prolonging the experiment. Although +-COSY does not give the orthogonal section S(F,, Q) of this same cross peak, this information comes directly from the corresponding (Q --f P) coherence-transfer experiment (Fig. 2). Since the two-dimensional spectrum has reflection symmetry about the principal diagonal, the section S(Q, F2) is equivalent to the required section S(F, , Q). In contrast to the conventional COSY experiment, each correlation affords only one twodimensional cross peak. From just two +COSY measurements the entire PQ cross peak can be constructed, well digitized in both frequency dimensions. No large two-dimensional data matrices are involved, and only the usual one-dimensional Fourier transformation is used. The time expended in displaying the result on a digital recorder is limited to plotting the cross peak itself; none of the remainder of the spectrum need be involved. The known values of the chemical shifts P and Q determine the area of two-dimensional frequency space where the cross peak must appear. In the more general case of a multispin system with well-separated chemically

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FIG. 2. Representation of a +COSY spectrum showing cross peaks (shaded rectangular areas) for coherence transfer between sites with chemical shifts P and Q Hz. Traces can only be recorded in the F2 dimension, for example, the sections S(P, F2) and S(Q, F2), but the latter is equivalent to the section S(F, , Q) (dashed line) because of the reflection symmetry about the principal diagonal.

shifted species (first-order coupling) the procedure is straightforward. A one-dimensional high-resolution spectrum is displayed on a computer monitor screen. The operator decides which shift correlations would be of interest and then sets a frequency cursor near each selected chemical shift, located by preference on one of the peaks of the spin multiplet. Suppose there were N such frequency choices made (N might be of the order of 10). With this information, the computer sets up and performs N coherence-transfer experiments according to the +COSY recipe (10-13) producing Nsections through the two-dimensional spectrum. These sections are then examined in pairs, for example, the traces S(P, F2) and S(Q, F2) which pass through the (P + Q) and (Q + P) cross peaks. A narrow frequency range S(P, AF*) spanning the region around the frequency F2 = Q Hz is extracted and multiplied by S(Q, aF,) near the frequency Fz = P Hz. This reconstructs the PQ two-dimensional cross peak. Since P and Q are known frequencies, the two ordinates corresponding to S(P, Q) and S(Q, P) can be measured (they should be equal) and used for normalization. A practical example is illustrated in Fig. 3. This shows one of the cross peaks from the 400 MHz proton spectrum of the four-spin system of meta-bromonitrobenzene (Scheme 1) dissolved in acetone-&. This three-dimensional “net” representation was constructed by multiplying two +COSY traces, involving selective irradiation of lines of the M and P protons. The selective pulse consisted of a train of 602 DANTE pulses modulated according to a coarse 14-step half-Gaussian envelope with an overall duration of 1.6 s. Phase alternation of the final hard 90” pulse eliminated the signals of the conventional spectrum, leaving only coherence-transfer responses (IO). When used purely for correlation purposes, the +COSY experiment simply records None-dimensional traces one beneath the other, showing the coherence-transfer responses. Figure 4 illustrates results from the proton four-spin system in metabromonitrobenzene. Comparison of the four +COSY traces with the conventional one-dimensional spectrum reveals all the scalar coupling interactions including the

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FIG. 3. An experimental cross peak in the 400 MHz proton correlation spectrum of meta-bromonitrobenzene representing coherence transfer between protons M and P. It was constructed by multiplying, tht appropriate 15 Hz regions of two I)-COSY traces.

weak para coupling. This mode of display is just as convenient as the more familial two-dimensional COSY plot and avoids recording extraneous data (16, 17). Traces with poor signal-to-noise ratio can be enhanced by time averaging without ai%cting the rest of the experiment. By judicious choice of the frequency of the selective pulse. overlapping cross peaks may be separated into their constituents,

A

Br

M SCHEME]

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x

P

M

A

a

d

FIG. 4. Chemical-shift correlation achieved MHz spectrum of meru-bromonitrobenzene. (b) the A multiplet, (c) the M multiplet, (d) coherence transfer through the para coupling,

by recording one-dimensional +COSY traces from the 400 Selective pulses were applied to an arbitrarily chosen line of the P multiplet, (e) the X multiplet. Note the appreciable JAX = 0.4 Hz.

The COSY experiment is now well-established and widely used and has the advantage of requiring no operator intervention; all the correlations are obtained in a single two-dimensional experiment. However, much of this information is redundant; all the essential shift correlation information could be extracted from a small number of $-COSY traces. Each correlation requires only one coherence-transfer trace and no time need be wasted examining the empty regions between chemically shifted groups or in stepping through an entire spin multiplet. Very fine digital resolution is achieved without significantly increasing the length of the experiment. The problem of “tl noise” (18, 19), which can be a limiting factor in some conventional COSY spectra, does not arise in this new form of correlation spectroscopy. For samples of low concentration, the amount of time averaging can be matched to the sensitivity requirements of each individual trace, thereby using the available time more efficiently. These one-dimensional experiments contain all the useful coupling information, and the assignment procedure has less need for complex pattern recognition routines (2022) than the conventional COSY experiment. These advantages suggest that $-COSY should provide shift correlation information appreciably faster than the conventional COSY method, and with better definition of scalar coupling information. The time saving is particularly marked in situatons where the operator knows which correlations are important and is prepared to plan the #-COSY experiment accordingly.

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ACKNOWLEDGMENTS This work was made possible by an equipment grant from the Science and Engineering Research Council. We are indebted to the Association of Commonwealth Universities for a scholarship (L.M.) and the Australian Federation of University Women, Victoria, for a Lady Leitch Prize (L.M.). We thank several Cambridge colleagues who eventually dissuaded us from adopting the name turbo-COSY (T-COSY) for the new technique. REFERENCES 1. J. JEENER, “Ampere International 2. 3. 4. 5. 6. 7. 8. 9. 10. I I. 12. 13.

14. 15. 16. 17. 18. 19. 20. 21. 22.

Summer School, Bask0 Polje, Yugoslavia, 197 1.”

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