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J. Phys. Chem. 1996, 100, 8268-8272
Carbon-13 Chemical Shift Tensors and Molecular Conformation of Anisole Julio C. Facelli,† Anita M. Orendt,‡ Yi Jin Jiang,‡ Ronald J. Pugmire,*,§ and David M. Grant*,‡ Utah Supercomputing Institute, Department of Chemistry, and Department of Chemical and Fuels Engineering, UniVersity of Utah, Salt Lake City, Utah 84112-1102 ReceiVed: NoVember 28, 1995; In Final Form: February 14, 1996X
The first direct measurement of the ortho steric effect of the methoxy group on the 13C chemical shifts in anisole is reported. The ortho steric effect on the isotropic 13C chemical shifts was obtained from a lowtemperature MAS spectrum, and the effect on both the isotropic and the tensor principal components was determined from a low-temperature 2D magic angle turning (MAT) experiment. From the low-temperature MAS spectrum, the 13C chemical shift of the ortho carbon cis to the methoxy carbon is found to be 7.0 ppm lower that of the ortho carbon trans to the methoxy carbon, in good agreement with previous estimates. From the low-temperature MAT experiment, a 6.8 ppm decrease in the chemical shift is observed in the isotropic chemical shift, while the effects on the difference (cis minus trans) between the individual tensor components are measured to be -9 ppm in δ11, 1 ppm in δ22, and -14 ppm in δ33, in reasonable agreement with the results of a previous linear regression substituent analysis on several di- and trimethoxybenzenes. Comparison of the experimental results with calculations, including thermal averaging considerations, further demonstrates that at room temperature the methoxy group in anisole undergoes stochastic jumps between the two equivalent planar configurations. This work demonstrates the feasibility of using the low-temperature MAT experiment at low temperature to measure the principal values of the 13C chemical shift tensors in molecules that are liquids at room temperature.
Introduction The conformation and rotational barriers of the methoxy group in anisole and its derivatives have been studied by a variety of techniques, including electron diffraction,1 microwave spectroscopy,2 ab initio computational methods,3-5 Raman spectroscopy,6 optical spectroscopy in supersonic jet expansions,7 molecular dynamics,8 and measurement of J couplings.9 From these studies it is apparent that at room temperature and in the absence of steric interactions the heavy atoms of the methoxy group remain in the plane of the aromatic ring, jumping stochastically between the two possible minima on a time scale faster than the NMR time constant. For meta-substituted compounds the fraction of time spent at each of the planar orientations depends on the electronic structure of the molecule, as has been discussed by Biekofsky et al.10 When there is one substituent ortho to the methoxy group, the steric interaction forces the methoxy group to be trans to the substituent. Finally, when there are two substituents ortho to the methoxy group, the steric interactions force the methoxy group to adopt a conformation nearly perpendicular to the aromatic plane. These features have been previously documented by our NMR singlecrystal studies in di- and trimethoxybenzenes,11 as well as by NMR studies in the liquid phase.12 From the regression analysis of the substituent effects,13 it was determined that the steric effect decreases the isotropic or solution chemical shifts of ortho carbons cis to a methoxy group. This effect has been used for conformational identification. The single-crystal studies have also shown that the steric effects on the ortho carbons are observed not only in the isotropic chemical shift but also in the individual components of the chemical shift tensor.11 The analysis of the substituent effect in the single-crystal results indicates that the smallest shift †
Utah Supercomputing Institute. Department of Chemistry. § Department of Chemical and Fuels Engineering. X Abstract published in AdVance ACS Abstracts, April 1, 1996. ‡
S0022-3654(95)03506-4 CCC: $12.00
component, δ33, exhibits the largest decrease, while the largest shift component, δ11, shows only a modest decrease. The intermediate component, δ22, is not affected by the steric interaction. While ample indirect evidence exists for a decrease in the chemical shift of the ortho carbon cis to the methoxy group in substituted anisoles, direct evidence in the parent anisole has not previously been available. At room temperature the methoxy group in anisole undergoes rapid exchange between the two equivalent in-plane positions, making the two ortho carbons equivalent and precluding the measurement of any difference between their chemical shifts. Commonly used techniques for obtaining the principal values of the chemical shift tensors at low temperature14 are not applicable to anisole due to the extensive overlap of the tensorial bands. However, the recent development of the magic angle turning (MAT) technique15-17 and the construction of a MAT probe capable of low-temperature operation18,19 make it possible to extract the principal values of the 13C chemical shift tensor for all seven carbons in anisole. The experimental values are in excellent agreement with those obtained from ab initio calculations. The steric shifts measured in anisole compare well with previous estimates from substituent effect studies in both the isotropic and the principal values of the chemical shift. Experimental and Calculations Materials. Anisole (J. T. Baker) was used as received after purity was confirmed by solution 13C NMR. All solid state experiments were performed on a Varian VXR-200 spectrometer, operating at a carbon frequency of 50.3185 MHz. NMR Spectroscopy. The spectrum recorded under the conditions of high-speed MAS at low temperature (approximately 180 K) was obtained with a 7 mm Doty Scientific probe, using a standard cross polarization pulse sequence and a spinning speed of approximately 4.5 kHz. A proton 90° pulse length of 4.9 µs, a recycle time of 5 s, and a cross polarization time of 7 © 1996 American Chemical Society
13C
Chemical Shifts and Molecular Conformation of Anisole
ms were used. The proton power level was increased by 3 dB during decoupling, corresponding to a decoupling field in excess of 70 kHz. The MAT15 experiment was performed using both the PHORMAT17 and the triple-echo MAT16 sequence on a homebuilt probe designed specifically to perform the MAT experiment at low temperatures.18,19 The PHORMAT spectrum gives slightly higher resolution, but at the expense of lower signal to noise; therefore, the triple-echo sequence was used for experiments from which the anisotropic information was taken. Details on the construction of the probe will be given elsewhere.19 Briefly, the probe uses a single, double-tuned coil design. The large volume coil is capable of holding approximately 1.7 g of sample and spins with a stability of (1 Hz at spinning rates of 10-30 Hz. To compensate for variations in the spinning speed over the time required for a 2D experiment (approximately 8 h), an external triggering device was used to synchronize the rf pulses with the rotor position.17 Spectral parameters of interest are as follows: proton 90° pulse of 5.1 µs (corresponding to a decoupling field of 49 kHz), contact time of 4 ms, recycle time of 2 s, acquisition length of 96 complex points, spectral width in acquisition dimension of 25 kHz, and spectral width in the evolution dimension of 8333 Hz. There were 150 complex increments acquired in the evolution dimension, resulting in a resolution of 55.6 Hz in this dimension. Twodimensional spectra using the triple-echo MAT sequence were recorded at temperatures of 215, 205, and 195 K. No differences were observed either in the projections of the evolution dimension or in the individual powder patterns obtained from the 2D data sets at different temperatures; therefore, all results presented in this paper are taken from the 205 K spectrum. All shifts presented here are referenced to an external sample of tetramethylsilane (TMS). The 2D data sets were zero filled to 1024 × 1024 points and transferred to a VAX computer for processing. No line broadening was used in either dimension. Slices containing the individual powder patterns in the vicinity of the peak maxima in the isotropic dimension were extracted from the processed 2D data set. The slices having the most intense signal were chosen for each chemically different nucleus. Individual powder patterns were fit using a Simplex routine which utilizes the POWDER method.20 The accuracy in the chemical shift values obtained by the MAT and PHORMAT experiments is comparable to that achieved for static powder patterns; this has been demonstrated by comparing the 13C chemical shifts tensors in methyl-R-glucopyranoside measured in single-crystal and powder samples.17 As with static powders, the largest sources of errors are line broadening and referencing problems; following our experience with static powders, the errors in the measurements presented here are estimated at ∼2 ppm. Calculations. The SCF and DFT calculations were performed with the Gaussian 9421 computer program, while the MP2 calculations were completed with the ACESII program.22 All calculations employed the GIAO23 (gauge invariant atomic orbitals) method with the standard Dunning24 D95 and D95** basis sets. The DFT calculations use the BLYP exchange correlation functional25 and a coupled perturbative scheme without including the magnetic field effects in the exchange correlation functional.26 The SCF and DFT calculations of the chemical shieldings were done for optimized geometries completed with the same basis set. The MP2 calculations used the structure optimized by the SCF method with the D95** basis set. In addition to the chemical shielding calculations performed on the fully optimized geometries, SCF calculations were done for partially optimized structures calculated as a function of the
J. Phys. Chem., Vol. 100, No. 20, 1996 8269 SCHEME 1: CCOCH3 Dihedral Angle in Anisole
TABLE 1: Comparison of the Parameters for the Linear Correlations between the Experimental and Calculated Principal Values Using Different Methodsa parameter
SCF
SCF (205 K)
MP2
DFT
rms intercept slope
6.0 -17.0 1.09
5.7 -16.7 1.09
7.2 -0.9 0.90
6.5 7.2 0.94
a
rms and intercept values in ppm, as described in the text.
dihedral CCOCH3 (see Scheme 1) angle at 10° increments. The shieldings and energies calculated as a function of this angle were used to calculate the thermally averaged chemical shifts assuming the Boltzmann distribution. Transformation of the calculated chemical shieldings to the TMS scale was achieved by scaling the calculated values by a linear correlation with the experimental principal shift values for all the carbon resonances. The relevant scaling parameters are given in Table 1. The intercept with zero on the experimental shift axis corresponds to the estimated TMS chemical shielding, which was obtained from the calculated shielding in methane, for a given theoretical method and basis set, minus the 7 ppm reported as the difference between liquid TMS and gas phase methane.27 The large deviations, up to 17 ppm, observed from this zero intercept indicate that a significant referencing problem still exists between calculated and experimental chemical shifts. The similarities of the rms (root mean square) scatter between the calculated and experimental values for the different theoretical methods indicate that they all produce results of similar quality. Note that this comparison is biased against the MP2 results which used a basis set without polarization functions, due to limitations in the computer program. Only a minor correction is observed between the rms of the SCF results with and without thermal averaging, indicating that these corrections may be important only for a highly refined shift analysis. Results and Discussion The measured and calculated isotropic values of the 13C chemical shift tensors in anisole are presented in Table 2. The assignments in the table for the solid state spectra are based on the corresponding calculated values. The fact that the methyl carbon gives rise to two signals will be discussed below. This splitting, however, has negligible consequences in the measurement of the ortho steric effect. The experimental values include those obtained from a room-temperature solution spectrum, the low-temperature MAS spectrum, and the isotropic chemical shift measured from the evolution dimension projection of the lowtemperature 2D MAT spectrum. All the solid state values agree
8270 J. Phys. Chem., Vol. 100, No. 20, 1996
Facelli et al.
TABLE 2: Comparison of Measured and Calculated Isotropic Chemical Shifts for Anisole carbon assignment
solution MASa LT-MATb calc, RTc Calc, LTc
1
methoxyd
2 3 4 5,6
ortho-cise ortho-transe para metaf
114.2 114.2 120.9 129.8
7
ipso
160.2
54.6
54.1 55.5 111.8 118.8 122.5 131.1 132.4 160.8
53.1 54.6 111.3 118.2 122.0 130.7 132.1 160.3
59.5
58.9
113.2 121.5 122.4 135.0 135.9 159.9
112.1 121.2 122.0 135.1 136.0 159.7
a
MAS spectrum taken at a temperature of 180 K and a spinning speed of 4.5 kHz. b Values from the isotropic projection of the 2D MAT spectrum using the PHORMAT method. c Boltzmann average chemical shifts at RT ) 300 K and LT ) 205 K. Calculations using the SCF method and the D95** basis set were scaled as explained in the text. d NMR spectra (both MAS and MAT) show a splitting that is postulated to be due to crystal packing effects (see text) and therefore not reproduced in the calculations on a single molecule. e Assignments to cis and trans carbons based on agreement with theory. f There is no basis for differentiating between two meta carbons due to small differences observed in the isotropic chemical shift and the absence of measurable differences in components.
with each other within experimental error. The splitting of the resonances of the two ortho carbons is readily apparent for all the low-temperature measurements, with the resonance of the carbon cis to the methoxy carbon being an average of 7 ppm lower than the ortho carbon trans to the methoxy carbon. The average chemical shift value for the two ortho carbons is equal, within experimental error, to the liquid value for the combined ortho resonances observed in solution. The -7 ppm difference (cis minus trans) between the two ortho carbon resonances is in good agreement with previous estimates of the ortho steric effect, e.g. -7.7 ppm from substituent effects in liquids,13 -11.8 ppm from single-crystal studies in polysubstituted methoxybenzenes,11 -6.2 ppm from the average difference in solid parasubstituted anisoles,28 and -10 ppm from IGLO calculations.13 In all cases the ortho-cis carbon has the smaller chemical shift. For the calculations performed for this paper, the isotropic values differ by -10 ppm at the SCF level, -12 ppm at the MP2 level, and -9 ppm at the DFT level. If the thermal effects are included in the calculations (SCF), a splitting of -8 ppm (at room temperature) or -9 ppm (at 205 K) is predicted between the two ortho carbons. Thus, the thermal corrections make only modest contributions to the calculated values. The splitting observed in the meta carbons is much smaller, with a difference of 1.3 ppm observed in the MAS spectrum. This difference is comparable to the SCF calculations at 205 K, which predict a splitting of 0.9 ppm, and to the MP2 calculations with a splitting of 1.7 ppm. The DFT method predicts no difference between the isotropic chemical shifts of the two meta carbons. The SCF and MP2 calculations predict that the meta carbon with the largest isotropic chemical shift is trans to the methoxy group and adjacent to the ortho carbon with the largest chemical shift. A comparison of the high-resolution spectra of anisole is given in Figure 1. Included in this figure is the roomtemperature liquid spectrum (Figure 1a), the MAS spectrum recorded at a temperature of 180 K before and after annealing (Figure 1b,c, respectively), and the isotropic shift projection of the PHORMAT spectrum recorded at 205 K (Figure 1d). One feature in the low-temperature MAS spectrum (and in the isotropic projection of the low-temperature MAT 2D spectrum) that remains to be interpreted is the shoulder or splitting observed on the methoxy carbon resonance. This spectral feature was present, either as a shoulder or as a definite splitting,
Figure 1. High-resolution spectra of anisole: (a) room-temperature liquid spectrum; (b) MAS spectrum at 180 K before annealing; (c) MAS spectrum at 180 K after annealing at 225 K; (d) isotropic projection of the PHORMAT spectrum at 205 K. In (b) and (c) an asterisk denotes spinning sidebands of the isotropic resonances.
regardless of the method employed in freezing the sample (i.e., samples frozen quickly by immersion in liquid nitrogen before being placed in a precooled probe or cooled somewhat slower, by placing the sample in the probe at room temperature and then cooling it down over a period of approximately 10 min). The splitting observed in the methyl group appears to be independent of both the strength and the offset of the decoupler field. In an attempt to remove this minor splitting the MAS sample was annealed by holding the stationary sample at a temperature only slightly lower than the melting point (225 K) of anisole. After this annealing period the sample was again
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Chemical Shifts and Molecular Conformation of Anisole
J. Phys. Chem., Vol. 100, No. 20, 1996 8271
TABLE 3: Principal Values of the Chemical Shift Tensor for Carbons of Anisolea carbon assignment
δ11
δ22
δ33
1 2 3 4 5,6
methoxyb ortho-cis ortho-trans para metac
7
ipso
78, 79 (80, 89, 90) 194 (195, 195, 196) 203 (207, 207, 204) 222 (223, 227, 222) 234 (244, 234, 237) - (244, 235, 235) 243 (251, 237, 236)
69, 69 (76, 80, 81) 133 (126, 119, 123) 132 (131, 126, 130) 134 (129, 125, 126) 146 (146, 133, 138) - (148, 135, 139) 167 (168, 179, 181)
12, 15 (20, 4, 4) 6 (13, 7, 7) 20 (26, 25, 21) 8 (15, 9, 10) 11 (17, 12, 13) - (17, 14, 14) 70 (61, 67, 71)
a
All values in ppm referenced to TMS. The calculated values have been scaled as explained in the text. Experimental values from the fit of slices from the triple-echo MAT at 205 K. These values have an estimated error of ∼2 ppm. The serial values in parentheses correspond to the SCF, MP2, and DFT calculations, respectively. b NMR spectra (both MAS and MAT) show a splitting that is postulated to be due to crystal packing effects (see text) and therefore not reproduced in the calculations; hence two experimental shifts are recorded here. c Calculated principal values in the first row are for the meta carbon adjacent to the ortho-cis carbon; second row values are for the meta carbon adjacent to the orthotrans carbon.
Figure 2. (Left) Individual slices from the aromatic region of the MAT spectrum of anisole at 205 K. (Right) Best fit simulation of the corresponding powder patterns from the left. Patterns are identified by the isotropic chemical shifts.
cooled to about 180 K and a second MAS spectrum was recorded. The shoulder changed to a definite splitting of 1.4 ppm. In addition, the other resonances were broadened, with a shoulder forming on the ortho-cis carbon resonance. Additional annealing did not lead to any other changes in the spectrum. These observations suggest that anisole may occupy at least two magnetically nonequivalent positions in the crystal lattice and that direct or indirect crystal packing effects are reflected as splittings in the NMR spectrum. In the absence of any diffraction data for anisole it is not possible to discuss further these anomalies observed in the NMR spectra. Table 3 reports the experimental and calculated principal values of the anisole chemical shift tensors. Individual slices
of the six aromatic carbons, from which the principal values were obtained, are shown in Figure 2 along with their best fit simulations. The experimental values are taken from the spectrum recorded at 205 K. In all cases the average of the three principal values agrees with the values obtained from the isotropic projection within 1.2 ppm. As the thermal averaging produces only modest changes in the calculated values, only those values for the absolute minimum energy configuration have been included in Table 3. The steric effects in the principal components of the ortho carbons are found to be -9 ppm for δ11, 1 ppm for δ22, and -14 ppm for δ33. These differences are in qualitative agreement with the values of -4.5, -1.9, and
8272 J. Phys. Chem., Vol. 100, No. 20, 1996 -11.4 ppm, for δ11, δ22, and δ33, respectively, obtained from the single-crystal study of di- and trimethoxybenzenes.11 Results of the SCF, MP2, and DFT theoretical methods are included in Table 3. In most cases the calculated values are in reasonable agreement with the experimental values. All the calculations reproduce the essence of the steric effects on the individual components; however, they predict a larger splitting in the δ22 component of the ortho carbons than observed experimentally. The experiment does not resolve any differences in the principal values for the two meta carbons. This is in qualitative agreement with the calculations, which predict differences smaller than 2 ppm (about the spectral resolution in the experimental spectrum). The DFT and MP2 calculations more faithfully reproduce the difference between δ11 and δ22 in the methoxy carbon than do the SCF calculations. Comparison of the calculated results with the experimental values fails to support any apparent advantages for any of the three calculation methods. This may be an indication that, in addition to the quality of the wave function, other factors such as intermolecular effects, molecular geometry, and vibrational corrections could still be important limiting factors in calculating chemical shift tensors. The calculations are needed, however, to provide the orientation of the principal axis system of the chemical shift tensor; such information is not available from experiments on powder samples. For the aromatic carbons the calculations place δ11 approximately along the C-H or C-O bonds, δ33 perpendicular to the aromatic plane, and δ22 in the aromatic plane and perpendicular to δ11. This is consistent with previous results obtained from single-crystal NMR on aromatic compounds.29 For the methyl carbon, δ33 is approximately along the O-CH3 bond and the other two components are perpendicular to this bond. Conclusions This paper demonstrates the utility of the low-temperature MAT experiment measuring and analyzing the chemical shift principal values in complex molecules which are liquids at low temperature. The calculated results in anisole show that the thermal averaging of the chemical shift tensors over the CCOCH3 angle has a very small effect on the calculated values, indicating that at room temperature the methoxy group stochastically jumps between the two equivalent positions with all the heavy atoms in the plane. While the calculations indicate the configuration with the methoxy group perpendicular to the plane is a local minimum of the energy, its value is too high to have any significant population and therefore its contribution to the thermally averaged shielding is negligible. This result is consistent with NMR measurements of the long-range coupling constants,9 even when taking into consideration that the barrier in the condensed phases may be lower than that in the gas phase, as discussed by Spellmeyer et al.8 Finally the agreement found between previous estimates of the ortho steric effect, using substituent effect correlations, with its direct measurement using low-temperature MAT experiments supports the use of these empirical correlations when a direct observation is not available.
Facelli et al. Acknowledgment. This work was partially supported by the Pittsburgh Energy Technology Center through the Consortium for Fossil Fuel Liquefaction Science through Contract No. DEFC22-89PC89852 and the National Science Foundation through Grant No. CHE-9006357. Computer resources were provided by the Utah Supercomputing Institute at the University of Utah. References and Notes (1) Seip, H. M.; Seip, R. Acta Chem. Scand. 1973, 27, 4024. (2) Onda, M.; Toda, A.; Mori, S.; Yamaguchi, I. J. Mol. Struct. 1986, 144, 47. (3) Facelli, J. C. J. Mol. Struct. (THEOCHEM) 1992, 276, 307. (4) Vincent, M. A.; Hillier, I. H. Chem. Phys. 1990, 140, 35. (5) Contreras, R. H.; Biekofsky, R. R.; de Kowalewski, D. G.; Orendt, A. M.; Facelli, J. C. J. Phys. Chem. 1993, 97, 91. (6) Konschin, H.; Tylli, H.; Grundfelt-Forsius, C. J. Mol. Struct. 1981, 77, 51. (7) Breen, P. J.; Bernstein, E. R.; Secor, H. V.; Seeman, J. I. J. Am. Chem. Soc. 1989, 111, 1958. (8) Spellmeyer, D. C.; Grootenhuis, P. D. J.; Miller, M. D.; Kuyper, L. F.; Kollman, P. A. J. Phys. Chem. 1990, 94, 4483. (9) Schaefer, T.; Sebastian, R. Can. J. Chem. 1989, 67, 1148. (10) Biekofsky, R. R.; Pomilio, A. B.; Aristegui, R. A.; Contreras, R. H. J. Mol. Struct. 1995, 344, 143. (11) Carter, C. M.; Facelli, J. C.; Alderman, D. W.; Grant, D. M.; Dalley, N. K.; Wilson, B. E. J. Chem. Soc., Faraday Trans. 1 1988, 84, 3673. (12) Biekofsky, R. R.; Pomilio, A. B.; Contreras, R. H.; de Kowalewski, D. G.; Facelli, J. C. Magn. Reson. Chem. 1989, 27, 158. (13) Bromilow, J.; Brownlee, R. T. C.; Craik, D. J.; Sadek, M.; Taft, R. J. Org. Chem. 1980, 45, 2429. (14) Orendt, A. M. Chemical Shift Tensor Measurement in Solids. In Encyclopedia of Nuclear Magnetic Resonance, Grant, D. M., Harris, R. K., Eds.; John Wiley: London, 1996, p 1282. (15) Gan, Z. J. Am. Chem. Soc. 1992, 114, 8307. (16) Hu, J. Z.; Orendt, A. M.; Alderman, D. W.; Pugmire, R. J.; Ye, C.; Grant; D. M. Solid State NMR 1994, 3, 181. (17) Hu, J. Z.; Wang, W.; Liu, F.; Solum, M. S.; Alderman, D. W.; Pugmire, R. J.; Grant, D. M. J. Magn. Reson., Ser. A 1995, 113, 210. (18) Jiang, Y. J.; Orendt, A. M.; Bai, S.; Solum, M. S.; Alderman, D. W.; Mayne, C. L.; Pugmire, R. J.; Grant, D. M. Poster 281 at 37th Annual Rocky Mountain Conference on Analytical Chemistry; Rocky Mountain Section, Society for Applied Spectroscopy, and Colorado Section, American Chemical Society, Denver, CO, July 1995. (19) Jiang, Y. J.; Pugmire, R. J.; Grant, D. M. Manuscript in preparation. (20) Alderman, D. W.; Solum, M. S.; Grant, D. M. J. Chem. Phys. 1986, 84, 3717. (21) Frisch, M. J.; Trucks, G. W.; Schegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T. A.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Ciolowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; HeadGordon, M.; Gonzales, C.; Pople, J. A. Gaussian 94, Revision A.1; Gaussian, Inc.: Pittsburgh, PA, 1995. (22) Stanton, J. F.; Gauss, J.; Watts, J. D.; Lauderdale, W. J.; Bartlett, R. J. ACESII Program System Release 2.0; QTP, University of Florida: Gainesville, FL. (23) Ditchfield, R. Mol. Phys. 1974, 27, 789. (24) Dunning, T. H. J. Chem Phys. 1970, 53, 2823. (25) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. 1988, B37, 785. Becke, A. D. Phys. ReV. 1988, A38, 3098. (26) Fox, D. Personal communication. (27) Jameson, A. K.; Jameson, C. J. Chem. Phys. Lett. 1981, 134, 461. (28) Penner, G. H.; Wasylishen, R. E. Can. J. Chem. 1989, 67, 525. (29) Iuliucci, R. J.; Facelli, J. C.; Alderman, D. W.; Grant, D. M. J. Am. Chem. Soc. 1995, 117, 2336, and previous papers in series.
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