Iterative lineshape analysis of 13C-2D multiplets. I. benzaldehyde-d1

JOURNAL

OF MAGNETIC

RESONANCE

94, l-8 ( 199 1)

Iterative LineshapeAnalysis of 13C-*D Multiplets. I. Benzaldehyde-d1 IRINAF.LESHCHEVA, VLADIMIRN.TOROCHESHNIKOV, NICKOLAYM.SERGEYEV,* VYACHESLAVA.CHERTKOV, ANDVIKTORN.KHLOPKOV NA4R

Laboratory,

Department

of Chemistry,

Moscow

State

University,

Moscow

119899,

USSR

Received January 30, 1990; revised December 5, 1990 Types of NMR spectra of nuclei S (spin f ) interacting with quadrupole nuclei Q (spin I ) have been classified. For the intermediate case of poorly resolved triplets, the iterative program QUADR has been developed and applied. This program allows one to determine the spin coupling constant J(SQ) from the total lineshape analysis. In general ‘%-‘D coupling constants as small as 0.08 Hz may be obtained through this procedure. The procedure has been used for the analysis of the deuterium-coupled “C NMR spectra of benzaldehyde-d, The 13C- *D coupling constants for C, , Ci,, C,,, Conho,and C,, have been obtained. The comparison of “C-*D and 13C-‘H coupling constants has revealed several primary isotope effects on coupling constants. 0 1991 Academic hi, I~C.

For the study of small effects of isotopic substitution on NMR parameters, highly accurate NMR measurements are needed (1-3). The problem of accuracy in NMR determinations is thoroughly discussed in the literature for both the CW and the pulseFf modes (4, 5). Model calculations (5) show that the errors in the positioning of the lines in high-resolution NMR spectra can be less than both the linewidth and the digital resolution. Typically, for a linewidth of 0.1 Hz, digital resolution of 0.0 1 Hz per point, and adequate signal-to-noise ratio, the error in determining the line positions may be much less than 0.01 Hz. For multicomponent NMR spectra where iterative fitting procedures (including total lineshape analysis) can be applied, the accuracy may be improved to 0.001 Hz due to statistical averaging of the data. III many cases the study of isotope effects is related to the analysis of the quadrupole effects in the NMR spectra of magnetic nuclei S (I = j ). Up until now analysis of the quadrupole effects has been limited in its accuracy, thus hindering substantially the progress of the isotope effect studies. In this paper we report an iterative procedure to analyze the lineshape of the spin- f nuclei coupled indirectly to the quadrupolar nuclei. LINESHAPE

ANALYSIS

The interaction between magnetic nuclei of spin 1 and a quadrupole nucleus Q of spin 1 was first considered by Pople (6). He showed that the lineshape of the NMR multiplet of the S nucleus was determined by the dimensionless parameter ?I = T, (Q)J(SQ), where T,(Q) is the spin-lattice relaxation time of the quadrupolar * To whom correspondence should be addressed.

1

0022-2364191 $3.00 Copyright 0 1991 by Academic Press, Inc. All rights of reproduction in any form resewed.

2

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ET

AL.

nucleus and .Z(SQ) is the spin-spin coupling constant. However, the analytical expression obtained by Pople (6) for nuclei of spin 1 is not applicable in the limits of t + cc and 7 --* 0, since the spin-spin relaxation of the S nucleus has not been considered by Pople. The rigorous approach may be based on the Anderson-Kubo-Sack treatment ( 7, 8), where the lineshape Z(w) is expressed by Z(w) cc Re{W.(iO

+ R)-‘. l},

ill

where W is a row vector of populations of the 2Z+ 1 spin states, 1 is a (2Z+ I)dimensional vector, all of whose elements are unity, and R is a relaxation matrix. The Q,,, element of a diagonal matrix fJ with magnetic quantum number m is expressed by Dm,m = w. - w + 27rJ(SQ)m,

121

where o. is the multiplet midpoint frequency, and J( SQ) is the S, Q coupling constant. In this paper we limit ourselves to the case of interaction between a nucleus of spin 1 and a quadrupolar nucleus of spin 1 such as ‘D, 14N. To calculate the parameters of the St and R matrices, an iterative lineshape fitting procedure (QUADR) has been developed. The theoretical lineshape calculated with Eq. [l] is determined by three parameters: the spin-spin coupling constant J( SQ), the spin-lattice relaxation time of the Q nucleus, TI (Q), and the effective spin-spin relaxation time of the S nucleus, T:(S). The additional singlet (without SQ interactions) overlapping with the SQ multiplet can also be taken into consideration. This may be important for the experimental NMR spectra of deuterated compounds containing some amount of undeuterated species. DATA

PROCESSING

PROCEDURE

Depending on the T, J value we distinguish three types of SQ multiplets: “clearly resolved triplet,” with 2 < T, J, “poorly resolved triplet,” with 0.2 -C T, J < 2, and “broadened singlet,” with T, J -C 0.2. These cases are now considered in detail. a. Clearly resolved triplet. The difference between the coupling constants J(SQ) and the observed splitting can be calculated using the standard theory of perturbation (9) as AJ=

’ 10a2T2J1 ohs*

t3j

For T, J > 2 this reduction effect does not exceed 0.2% and may as a rule be neglected. In general the observed linewidth of the nucleus S is the sum of two parts AU112

=

AVQ

+

Au,,

[41

where Avo is the quadrupole broadening and Av, is the contribution of ail nonquadrupole mechanisms of relaxation. For clearly resolved triplets, the quadrupole contribution AVQ depends on the spin state of the Q nucleus (6). The corresponding values for the central (Z,(Q) = 0) and the side components ( Zz(Q) = + 1) may be expressed as

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CARBON-DEUTERIUM

a"~,,,

=

MULTIPLETS

3

3 5aT1 (Q)

The difference in the linewidths of the side and the central components may be used to estimate the time TI (Q) using Eqs. [5a] and [ 5b]. To consider in more detail the nonquadrupole contributions AU, to the linewidth, we limit ourselves to i3C NMR spectra with broadband proton decoupling. In this case one should consider the following contributions to the linewidth: AvNQ = 7

1

= A# + AvF + AvD + AvE.

aT2

Here AvR is the spin-spin relaxation contribution ( 1/ ?cT2), AvF is the factor of magnetic field inhomogeneity, AvD is the residual undecoupled linewidth in the broadband decoupling mode, and AvE is a possible exchange broadening. b. Poorly resolved triplet. Each of the triplet components is noticeably broadened and the direct measurement of the coupling constants may lead to substantial errors. The analysis reveals that, for a poorly resolved triplet, simultaneous determination of all three parameters TI (Q), J( SQ), and T:(S) is impossible due to their strong correlation. Hence at least one of these parameters needs to be predetermined by some independent experiments. In particular, the relaxation time T1 (Q) can be measured directly or taken from the data for clearly resolved triplets in the same spectrum. The contribution AvR can be determined from the spin-lattice relaxation time T1 of the nucleus S (supposing T1 (S) = T,(S)). Contributions AvF and AvD can be evaluated using the reference spectral lines. c. Broadened singlet. According to the lineshape analysis made by Cunliffe and Harris (20) the additional broadening is expressed as AvQ = 2 T~T~(Q)J(SQ)~.

171

The analysis shows -that for the broadened singlets two parameters must be predetermined in order to calculate the third one. In particular, to estimate the spin-spin coupling constant, both times T, (Q) and TT (S) should be known. “C-‘D

COUPLING

CONSTANTS

IN

BENZALDEHYDE-d,

Isotope effects on r3C chemical shifts and 13C-lH coupling constants have been obtained by comparing the data for benzaldehyde C6HSCH0 (I) with those for benzaldehyde-dl C6HSCD0 (II). Comparison of the 13C-‘H coupling constants with the ’ 3C--2D coupling constants has been performed using the converted coupling J*: J*( 13C-‘H) = (Y&,,)J(‘~C-~D). The most accurate value of Yu/Yo al. (II) was used. Previously the coupling constant by Hansen and Jakobsen as cited between the formyl proton and the

[81

= 6.5 1439940 -t 6 * lop8 obtained by Neronov et ’ J( 13C- ‘H) for the carbonyl carbon was measured in Ref. (12) while the other coupling constants aromatic carbons were measured in (13). Taking

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ET AL.

TABLE I “C-‘H ‘J(C-H) 175.171 (0.025)

Coupling Constants of Formyl Proton in Benzaldehyde (in Hertz)’ ‘J(C-H) 24.193 (0.005)

“J(C-H)

‘J(C-H)

2.080 (0.005)

0.478 (0.005)

5J(C-H)

0.161 (0.005)

a Standard deviations are given in parentheses.

into consideration the temperature and concentration dependence of the coupling constants we have prepared the identical 20% volume solution of I and II in acetoned6 and again measured the 13C- ‘H coupling constants in I (Table 1) . For the lineshape analysis of the 13C NMR spectra of benzaldehyde-dl a sample containing 4% of the undeuterated form I was used. To measure very small isotope shifts for C,,, and C,, carbons a sample with 33% of I was used. The C, signal is a clearly resolved triplet with 13C-2D splittings of about 26 Hz. The reduction effect can be neglected for this case (as being less than 0.0004 Hz according to Eq. [ 3 ] ) . We have considered the components of the triplet as nonoverlapping Lorentzians and their positions and linewidths have been found with the standard fitting procedure. These results are given in Table 2 and Table 3. The spin-lattice relaxation time T,(D) and the quadrupole contributions Au, were obtained using Eqs. [5a] and [ 5b]. The value thus obtained (0.9 1 -+ 0.10 s) is very close to the value of 0.94 + 0.06 s measured in the *D inversion-recovery experiments. The ’ J( 13C-*D) coupling constant and the corresponding J* coupling constant are given in Table 3. The Cimo signal is a triplet with approximately 3.7 Hz splitting. The reduction effect values are comparable with the error estimates for the 13C-2D coupling constants. Hence total lineshape analysis has been applied (Table 3 ) . Pairs of experimental and best calculated spectra are given in Fig. 1 (a, b, c, and d for Cipm, Cortho, C,,,, and C para, respectively). Small deviations are observed systematically at the maxima of the absorption lines, which indicates some inadequacy of the model chosen. We believe that this discrepancy is mainly due to the magnetic field inhomogeneity. For the C,, signal the predicted value of the 13C-2H coupling constant is 0.025 Hz (neglecting the isotope effects), which cannot be measured in the spectrum of II. The isotope shift for &, is given in Table 3.

TABLE 2 Separate Component Analysis Data of the C, Multiplet in Benzaldehyde-d, Component Triplet side components Triplet central component Singlet of the protonated form I

0.323 0.253 0.145

0.209 0.140 0.0

0.114 0.113 0.145

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TABLE 3

-

13C-‘D Coupling Constants (Hertz), Converted “C-‘H Coupling Constants (Hertz), Isotope Effects on “C-‘H Coupling Constants (Hertz), and “C(H/D) Isotope Shifts (ppb) in Benzaldehyde with Formyl Proton Substituted for Deuterium”

Caribon

C, C qso C onho C “leta C nwa

J( 13C-*D) 26.847 (0.002) 3.661 (0.002) 0.323 (0.002) 0.080 (0.003) 0.025’

J*(‘3C-‘H)b 174.892 (0.013) 23.888 (0.013) 2.104 (0.013) 0.52 I (0.0 19) 0.161’

A/’ -0.279 (0.028) -0.305 (0.014) 0.024 (0.014) 0.043 (0.020) 0.0’

A6d -293.3 -72.4 -10.1 -5.1 +I.8

’ Standard 0 errors are given in parentheses. ’ J*(13C-‘H) = (-&rn)J(‘3C-2D). ’ 4 J = J*(13C-‘H) - J(13C-‘H) (for the “C-‘H data see Table 1). d Aa = 6,, - 6r. “The values are calculated using the “C-‘H data (Table I), neglecting isotope effects.

The C,, singlet has been analyzed using the fixed values of J( 13C-2D), T, (D), and the isotope shift. The sum of the AvF and hYD contributions has been found to be 10.089 Hz. This value was used in the analysis of C,, and CoBhosignals since one may suppose that the AuD contributions are quite similar for all aromatic carbons. The AvR contribution can be found from the T1 ( i3C) measurements (Table 4). The Cortho signal is a poorly resolved triplet with distinct indication of a singlet of I (Fig. lb). The lineshape analysis of this signal with a fixed T: value from the q, calculations leads to a significant deviation between the experimental and calculated spectra. Several attempts have been made to minimize this deviation by varying the T: value. In all the cases an additional broadening of about 0.05 Hz has been established for the Cortho signal. This contribution may be assigned to a rotation of the formyl group around the Cipso-C, bond in benzaldehyde ( 14, 1.5). For C,, Ciw, and C,,,, these contributions are absent because of symmetry reasons. To estimate the exchange contribution for Corthowe used the data on the activation parameters A# (34.7 k 0.8 kJ/mol-‘) and AS* (15.0 -t 5.0 kJ/mol-‘) from (14). The linewidth AuE at temperatures above the collapse may be estimated from the Meiboom formula (16) for degenerate two-site exchange. Using the rate-constant theory with AH* and AS* values from (14) we have obtained the rate constant k of 3.2 - 10’ s-’ at 300 K. The data for the Au value have been taken from the low-temperature ( 139 K) 13C NMR spectrum of benzaldehyde ( 15), where AvorthOis about 800 Hz for a 90 MHz resonance frequency. Thus we obtained additional exchange broadening equal to about 0.03 Hz. Although this value is somewhat different from the experimental estimate (0.05 Hz) we may still conclude that the exchange process does contribute noticeably to the linewidth. The difference may be attributed to the inaccurate estimate of the rate constant k. This additional broadening may be neglected for the &,a carbon as the Au value does not exceed 100 Hz according to the low-temperature spectrum (14, 15).

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ET AL.

b

-1.00 -0 50

0.00

0 50

1.00

-0.60

HZ

FIG.

(d) &.

-0 30

0.00

0 30

0.60

HZ

1. Experimental and calculated “C NMR spectra of benzaldehyde-d, : (a) Ci,, (b) CO,,,,, (c) C,,,,, The difference spectra are shown above.

The C,, signal is a broadened singlet (Fig. 1c) not allowing even a qualitative estimate of the 13C-2D coupling constant. As mentioned above, estimation of 13C2D coupling constants requires that all other parameters be known. Hence we have determined the isotope shift for C,,,,@ and used it together with T,(D) and the sum of the AuF and AvD values found in the calculations of the & signal. All the measured 13C-2D coupling constants, the converted couplings J*( 13C- ‘H), and the isotope effects on chemical shifts and on coupling constants are given in Table 3. EXPERIMENTAL

Twenty percent volume solutions of benzaldehyde and benzaldehyde-d, in acetonede were used for the NMR measurements with the 2D lock on the signal of acetoned6. We used two samples of the deuterated compound with high (96%) and low (67% ) isotopic purity. Benzaldehyde-dr was kindly provided to us by A. N. Rushin, to whom the authors express their gratitude. The r3C NMR spectra were measured on Bruker AM-360 and Varian VXR-400 spectrometers using WALTZ proton decoupling and digital resolution of 0.01-0.03 Hz/point. The value of ‘J( 13C- ‘H) was measured from the proton-coupled 13CNMR

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TABLE 4 The Spin-Lattice Relaxations Times T, of “C Nuclei of C C o*r c mela>cwa in Benzaliehyde-d, ’ Carbon

T, (4

Cm C ~pso cwa C meta C Onho

41.5 + 30.8 f 10.0 f 12.5 + 13.6 +

5.0 2.9 0.2 0.2 0.3

’ Inversion-recovery method, T = 300 K.

spectrum of I and ‘J(13C- ‘H) couplings were obtained from two-dimensional J-resolved NMR spectra with selective excitation ( 17) of the formyl proton on a Bruker AM-360 spectrometer with the “SELJRES” pulse sequence. Digital resolution on the J coordinate was 0.002 Hz/point. The “J( 13C-H) values were determined as doublet splittings in J cross sections of the 2D spectra with errors not exceeding 0.005 Hz. The spin-lattice relaxation times were measured using the inversion-recovery method with a l8Oo-r-90’ pulse sequence. The iterative program QUADR was written for the IBM PC/AT and used in the interactive mode. The program is available on request from Dr. V. N. Torocheshnikov. DISCUSSION

The data obtained show that the study of isotope effects (especially on the coupling constants) needs ultraprecise NMR experiments. For benzaldehyded,, the isotope effects are observed unambiguously only for one-bond and two-bond 13C- ‘H coupling constants (Table 3). For other spin-spin coupling constants, the isotope effects do not exceed 0.05 Hz. We think that the level of 0.1 Hz is a quite reasonable threshold for studying isotope effects on coupling constants if the errors for the NMR data are within 0.03405 Hz limits. In the case of H/D isotope effects, the requirements for the accuracy of the spectral data lead to the necessity of highquality 13C-*D coupling constant data with errors of the 0.0014003 Hz order. For poorly resolved triplets and for broadened singlets total lineshape analysis is necessary. We now comment on the applicability of the 13C-‘H coupling constants measurement technique using corresponding 13C-‘D coupling constants proposed by Giinther et al. ( 18). An important advantage of this technique is the possibility of avoiding second-order effects in the analysis of the proton-coupled 13C NMR spectra‘ Possible diradvantages of this technique are those of neglecting primary isotope effects on r3C‘H coupling constants as well as some evident difficulties in measuring small r3C-*D sphttings. As far as the former are concerned, the data we obtained and the data from the literature show that the isotope effects do not exceed 1% of the magnitude (exceptions are PHs ( 19) and H$ ( 20)). Hence these are not necessary for the estimation of all r3C- ‘H coupling constants of less than 10 Hz (i.e., practically for all long-range 13C2 ‘H coupling constants (21)) . As for the latter difficulties, they are very serious

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and the previous practice of using the technique ( 18) is usually limited only by the one-bond 13C-lH couplings (see, e.g., data for pyridine in Ref. (18)). However, on the basis of the present study, we may state that the total lineshape analysis allows us to measure i3C-‘D coupling constants as small as 0.080 Hz (with a standard error of 0.003 Hz), which corresponds to 13C- ‘H coupling constants of about 0.5 Hz. This reasonable level of accuracy is probably high enough to meet all practical problems of the structural chemistry of organic compounds. Finally we briefly comment on the caveat concerning the effect of molecular alignment in high magnetic fields put forward recently by Bastiaan et al. (22). By using their estimates for naphthalene with a AX value of -2.0 * lop6 in the magnetic fields of 7- 15 T one can conclude that the biggest correction should be for one-bond 13C‘H coupling constants. For the benzene derivatives with AX values of about - 1.O -1 Oe6 (see the data in (23))) and in the magnetic field of 10 T we used in our experiments, the corresponding correction for the ’ J( 13Col-’ H ) coupling constant should be around 0.03 Hz. Thus it may indeed affect the data for ‘J(13C,- ‘H) in I. However, here we are interested mainly in isotope effects on coupling constants. Hence we should have considered the isotope effects on the direct dipole-dipole contributions D,, which should obviously be negligible (l-3% of the 0.03 Hz correction mentioned above). REFERENCES 1. C. J. JAMESON, Bull. Magn. Resort. 3, 3 ( 1980). 2. N. M. SERGEYEV, in “NMR Basic Principles and Progress” (P. Diehl, E. Fluck, and R. Kosfeld, Eds.), Vol. 22, p. 3 1, Springer-Verlag, Berlin, 1990. 3. A. ALLERHAND, R. E. ADDLEMAN, AND D. OSMAN, .I Am. Chem. Sot. 107,5809 (1985). 4. J. C. LINDON AND A. G. FERRDGE, Prog. NMR Spectrosc. 14,21 ( 1980). 5. G. H. WEISS, J. A. FERRETII, AND J. E. KIEFER, J. Magn. Resort. 46,69 ( 1982). 6. J. A. POPLE, Mol. Phys. 1, 168 (1958). 7. A. ABRAGAM, “The Principles of Nuclear Magnetism,” Clarendon Press, Oxford, 196 1. 8. J. I. KAPLAN AND G. FRAENKEL, “NMR of Chemically Exchanging Systems,” Academic Press, New York, 1980. 9. N. M. SERGEYEV AND L. F. KOBEZ, unpublished results. 10. A. V. CUNLIFFE AND R. K. HARRIS, Mol. Phys. 15,4 13 ( 1968 ). 11. Yu. I. NERONOV, A. E. BARZAKH, AND KH. MUKHAMADIEV, Z/I. Eksp. Teor. Fiz. 69, 1872 ( 1975 ). 12. P. DIEHL, J. JOKISAARI, AND J. AMREIN, Org. Magn. Reson. 13,451 ( 1980). 13. L. ERNST, V. WRAY, V. A. CHERTKOV, AND N. M. SERGEYEV, J. Magn. Reson. 25, 123 (1977). 14. T. DRAKENBERG, R. JOST, AND J. SOMMER, J. Chem. Sot. Chem. Commun., 1011 ( 1974). 15. L. LUNAZZI, D. MACCIANTELLI, AND A. C. BOICELLI, Tetrahedron Lett., 1205 ( 1975 ). 16. G. BINSCH, in “Dynamic NMR Spectroscopy” (L. M. Jackman and F. A. Cotton, Ed%), p. 175, Academic Press, New York, 1975. 17. A. BAX AND R. FREEMAN, J. Am. Chem. Sot. 104, 1099 ( 1982). 18. H. GUNTHER, H. SEEL, AND H. SCHMICKLER, J. Magn. Reson. 28, 145 ( 1977). 19. A. K. JAMESON AND C. J. JAMESON, J. Magn. Resort. 32,455 ( 1978). 20. H. J. JAKOBSEN, A. J. ZQZULIN, P. D. ELLIS, AND J. D. ODOM, J Magn. Reson. 38,219 ( 1980). 21. P. E. HANSEN, Prog. NMR Spectrosc. 14, 175 (1981). 22. E. W. BASTIAAN, J. BULTHUIS, AND C. MACLEAN, Magn. Reson. Chem. 24,723 ( 1986). 23. W. H. FLYGARE, Chem. Rev. 74,653 (1974).