J. Phys. Chem. 1996, 100, 17485-17489
17485
Density Functional Theory Studies on Sulfur-Nitrogen Species Kausala Somasundram and Nicholas C. Handy* Department of Chemistry, UniVersity of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K. ReceiVed: July 11, 1996X
Density functional theory (DFT) calculations on SNS, S2N2, and S4N2 are reported. Both local and gradientcorrected nonlocal density functionals are used with moderate and large basis sets. The relative energies, structural parameters, and vibrational frequencies are reported for each molecule and compared with the experimental and theoretical data available in the literature. For S2N2, DFT results predicted the order of stability of the three low-energy structures as linear chain < pairwise ring < alternate ring in contrast to the MP2 results but in agreement with MRCI results. For S4N2 the order of stability is found to be (1,3) isomer < twisted form of (1,4) isomer < chair form of (1,4) isomer. We discuss identification of experimentally observed infrared absorption peaks of S2N2 and S4N2.
1. Introduction experimentally1
Sulfur-nitrogen species have been produced from the decomposition of polythiazyl, (SN)x. Among these, the disulfur dinitride (S2N2) prepared by the pyrolysis of S4N4 vapor over silver wool has been characterized by a single-crystal X-ray study.2,3 It has a planar ring of alternate atoms with D2h symmetry. The tetrasulfur dinitride (S4N2) was characterized by X-ray crystallography in 1981.4 It has a puckered ring structure with nitrogen atoms at the 1,3 positions and the fifth S atom away from the plane. In 1992, Hassanzadeh and Andrews reported5 the production of new nitrogen sulfide species by the reaction of nitrogen and sulfur in argon discharge. From the analysis of matrix isolation infrared spectra they suggest the existence of a new S2N2 isomer having an S-S bond and a new six-membered-ring S4N2 isomer with two S-S bonds and nitrogen atoms in the 1,4 positions. They also reported that the (1,4) isomer appears to be the most stable final product of the reaction between sulfur and nitrogen. For S2N2 a recent theoretical study6 at the Moller-Plesset level predicted that three structural forms are close in energy and their relative stability varies at different levels of calculation. For S4N2 a recent ab initio calculation7 showed that the (1,4) isomer has a triplet ground state at the Hartree-Fock level, but at the MP2 level there were only two singlet states. In this paper we present density functional theory results for the relative energies of ground states, equilibrium geometries, and frequencies of SNS, S2N2, and S4N2. The main purpose of this work is to investigate the performance of density functional theory on the prediction of geometries and stabilities of sulfur nitrides in which electron correlation plays an important role. There is a relatively small number of DFT studies on the structure of molecules containing sulfur atoms.8,9 In the following section we shall briefly state the different functional forms, the basis set, and the program used in this work. Then we shall go on to discuss the DFT results on the geometry, relative energies, and frequencies of each molecule separately, by comparing them with the conventional best ab initio results available in the literature. 2. Computational Methods In this study we have used the CADPAC program10 with the following combinations of functionals: LDA, which consists of Dirac-Slater exchange11 and the Vosko, Wilk, and Nusair X
Abstract published in AdVance ACS Abstracts, September 1, 1996.
S0022-3654(96)02072-2 CCC: $12.00
TABLE 1: Density Functional Calculations on the Structure (Å, deg) and Frequencies (cm-1) of the SNS Radical with C2W Symmetry method
RN-S
∠SNS
ω1
ω2
ω3
LDA/6-31G* BLYP/6-31G* BLYP/TZ2P B3LYP/TZ2P UMP2/DZP7 CISD/TZ2P20 expt5
1.565 1.593 1.579 1.557 1.575 1.546
150.2 148.1 148.6 150.9 146.2 151.3 153 ( 5
678 634 638 675 832 728 ∼660
295 303 296 288 332 307
1288 1164 1161 1238 1437 1296 1225.2
(VWN)12 correlation terms; BLYP, which consists of LDA, the exchange correction of Becke (B88X),13 and the correlation function of Lee, Yang, and Parr (LYP);14 BP86, which consists of LDA, B88X, and the correlation function of Perdew 86;15 B3P86, which is a hybrid function16 consisting of LDA, SCF exchange, LDA(Dirac) exchange, B88X, and the correlation function of Perdew 86; B3LYP, which is also a hybrid function17 like B3P86, but it uses the LYP correlation function. Initially full geometry optimizations were carried out with a 6-31G* basis set using LDA and BLYP functionals. First a medium quadrature scheme was used to locate the stationary points, and then the calculations were repeated using a highquadrature scheme. To test any variation by the use of different functional forms, single-point calculations were performed at the reported MP2/6-31G* geometry using the various combinations of functionals stated above. To test the effect of basis set, the geometry optimizations of the low-energy structures were carried out with larger TZ2P and TZ2P+f basis sets using the BLYP and B3LYP functionals. The above basis sets are derived from Dunning’s (9s,6p) contraction18 of Huzinaga’s (12s,9p) primitive sets for sulfur and Dunning’s (5s,4p) contraction18 of Huzinaga’s (10s,6p) primitive sets for nitrogen. The d polarization functions have exponents of 2.12, 0.67, and 0.23 for sulfur and 1.35 and 0.45 for nitrogen. The f polarization functions have exponents of 0.8 and 0.65 on N and S, respectively. Analytical second-derivative calculations were carried out using the high-quadrature scheme at the DFT(LDA)/6-31G*, DFT(BLYP)/6-31G*, DFT(B3P86)6-31G*, and DFT(B3LYP)/ TZ2P levels. In the case of open shell molecular radicals the unrestricted formalism was used. 3. Results and Discussion (a) SNS. Several structural forms are possible for this radical. However, we have studied only the bent SNS (2A1), as it is the © 1996 American Chemical Society
17486 J. Phys. Chem., Vol. 100, No. 44, 1996
Somasundram and Handy
TABLE 2: Density Functional Relative Energies in kcal mol-1 of Different Structural Forms of S2N2 at Various Levels method
linear chain (a)
pairwise ring (b)
alternate ring (c)
Y-shape (SNN)-S (d)
cis NSSN (e)
LDA/6-31G* BLYP/6-31G* MP2/6-31G*6 BLYP/TZ2P B3LYP/TZ2P B3LYP/TZ2P+f MP4SDTQ(Ref. 6) LDA/6-31G*//MP2/6-31G* BLYP/6-31G*//MP2/6-31G* BP86/6-31G*//MP2/6-31G* B3LYP/6-31G*//MP2/6-31G* B3P86/6-31G*//MP2/6-31G*
0 0 0 0 0 0 0 0 0 0 0 0
15.1 14.9 18.5 11.7 8.1 8.3 9.3 14.7 16.4 13.2 10.8 8.3
23.5 27.4 12.3 17.0 12.8 11.2 4.9 22.9 26.3 22.0 22.1 18.5
35.9 31.4
65.9 49.1
TABLE 3: Optimized Geometries of the Three Low-Energy Structures of S2N2 Calculated at Various Levels
method
Figure 1. First five low-energy structural forms of S2N2.
experimentally predicted form5 and there is no controversy between the experimental and high-level theoretical calculations.19,20 This work presents the DFT calculations for comparison purposes. Table 1 shows the structural parameters and the harmonic frequencies calculated using density functional theory together with the available experimental and other theoretical values. Comparison of the second and third rows of Table 1 shows that the DFT results are not very sensitive to changes in basis set. The change in bond length is 0.01 Å and the change in bond angle is 0.5° on going from 6-31G* to TZ2P. For this radical, only the bond angle is known experimentally although with some uncertainty, and all of our calculated values lie within the error limit. Among these, DFT(LDA)/6-31G* and DFT(B3LYP)/TZ2P values are close to the experimental average value. In their matrix infrared characterization, Hassanzadeh and Andrews assigned5 the band at 1225.2 cm-1 to the antisymmetric stretching mode of SNS and reported that this mode is nearly harmonic. They predicted that the symmetric stretching frequency of SNS is near 660 cm-1. We have listed our calculated harmonic frequencies in Table 1. Best results are obtained at the DFT(B3LYP)/TZ2P level, which predicts the symmetric and antisymmetric stretching frequencies within 1% and 2% of the experimental values, respectively. Both MP2 and CISD methods overestimate the frequencies. (b) S2N2. Several ab initio calculations have been reported21-23 for the various structural forms of S2N2. Recently Warren et al.6 have performed a systematic study on all the possible structural forms of S2N2 at the SCF and MP2 levels with reasonably large basis sets. They found five structural forms within 50 kcal mol-1. Here we report our DFT results on those first five low-energy structures (see Figure 1). Structures a-d successfully optimized, but the planar cis NSSN form (e) either converged to a linear structure or separated into two NS fragments. It is to be noted that for e, the MP2/6-31G* geometry reported by Warren et al.6 has an S-S distance of 2.937 Å, which is much greater than the S-S single-bond length of 2.02-2.18 Å. The first two rows of Table 2 give the relative energies for these five structures using LDA and BLYP functionals with
LDA/6-31G* BLYP/6-31G* MP2/6-31G*6 BLYP/TZ2P B3LYP/TZ2P B3LYP/TZ2P+f expt2,3
linear chain (D2h) (a) RN-S RN-N
pairwise ring (C2V) (b) RN-S RN-N RS-S
alternate ring (D2h) (c) RN-S
1.571 1.603 1.570 1.596 1.586 1.580
1.738 1.804 1.723 1.775 1.737 1.726
1.660 1.702 1.684 1.683 1.652 1.646 1.651-1.657
1.159 1.167 1.190 1.158 1.139 1.142
1.265 1.269 1.301 1.273 1.260 1.264
2.122 2.192 2.100 2.170 2.132 2.112
the 6-31G* basis set. These are compared with the MP2/631G* results. The linear SNNS form (a) is the lowest energy structure. DFT results shows that the second lowest energy structure is the pairwise ring (b), which is 8.4 and 12.5 kcal mol-1 lower in energy compared to the alternate ring (c) at the LDA and BLYP levels, respectively, whereas MP2 results predicted that the alternate ring is lower in energy by 6.2 kcal mol-1. The fourth, fifth, and sixth rows of Table 2 show the relative energies of the first three low-energy structures, calculated with large basis sets. Increasing the size of the basis set stabilizes both ring structures. The pairwise ring remains lower in energy by about 5 kcal mol-1 compared to the alternate ring. Addition of an f function further stabilizes both ring structures, but still the pairwise ring is lower in energy by 3 kcal mol-1. In the seventh row we have given the best relative energies of Warren et al. calculated at the MP4SDTQ/6311G(2df) level using the MP2/6311G(2df) geometry. This result predicted that the alternate ring is lower in energy by 4.4 kcal mol-1. We have noticed that the weight of the reference function at the MP2 level is 0.88, which indicates that these structures have multireference character. We therefore undertook a multiconfiguration calculation using the MOLPRO program.24 A complete active space SCF (CASSCF)25 calculation at the DFT/ TZ2P geometry using the 2p orbitals of N and 3p orbitals of S as its active space predicted that the pairwise ring is lower in energy than the alternate ring by 6.5 kcal mol-1. A further multireference configuration interaction (MRCISD)26 calculation using those configurations of the above CASSCF wave function with coefficients greater than 0.05 reduced this energy difference to 3.3 kcal mol-1. The conclusion is therefore that the most sophisticated quantum chemistry calculation supports the DFT prediction. In the last five rows we have compared the DFT relative energies of the first three low-energy structures, calculated at the MP2/6-31G* geometry using various functionals. It is clear that the different functional forms did not make any change in their order of stability. On average the difference in energy between the ring structures is nearly 10 kcal mol-1. The geometry of the three low-energy structures calculated at various levels are presented in Table 3 together with the
DFT Study on Sulfur-Nitrogen Species
J. Phys. Chem., Vol. 100, No. 44, 1996 17487
TABLE 4: DFT/TZ2P Harmonic Frequencies (cm-1) of the Three S2N2 Structures linear chain (a) Σg Σg Πg Σu Πu
pairwise ring (b)
B3LYP
MP26
2196 520 335 934 156
1910 551 116 1037 152
A1 A1 A1 A2 B2 B2
alternate ring (c)
B3LYP
MP26
1408 655 482 498 845 439
1116 771 516 499 859 500
ω1-Ag ω2-Ag ω3-Bg ω4-B1u ω5-B2u ω6-B3u
B3LYP
MP26
938 643 922 477 650 777
851 620 886 475 783 791
expt28
expt29
665.1 90.9 476.2 785
474 663 795
Figure 2. Possible cyclic forms of tetrasulfur dinitride.
MP2/6-31G* values. Available experimental results are also given. For most of the structures, the LDA/6-31G* values are close to the MP2 values. Only the alternate ring structure has been experimentally well characterized. For this structure, our calculated LDA value is close to the experimental value. Recently Parr and Yang stated in their review paper27 that LDA has been remarkably successful in structure prediction. The BLYP/6-31G* value is as usual too long by 0.045 Å. Again the basis set effect on the structural parameter is not large. For the alternate ring structure, DFT(B3LYP)/TZ2P agrees well with experiment, but DFT(BLYP)/TZ2P is still in error by 0.03 Å. Since the suggestion5 for the existence of a new isomer came from the observation of an infrared absorption peak at 1167.5 cm-1, in Table 4 we have listed our B3LYP/TZ2P calculated frequencies together with the best available MP2 and experimental frequencies. The infrared spectrum of solid S2N2 has been recorded,28,29 and the frequencies were assigned to the alternate ring structure of D2h symmetry. For some modes our calculated values are very different from the experimental frequencies. In particular our calculated value for the ring puckering mode is 477 cm-1 compared to the experimental value28 of 90.9 cm-1. The MP2 results show a value of 475 cm-1, and experimental results of Warn and Chapman29 show a value of 474 cm-1 for this mode. The similar values of DFT, MP2,6 and Warn and Chapman29 question the experimental assignment of Bragin et al.28 for this mode. For this alternate ring structure (c), the maximum difference between our DFT frequencies and the MP2 frequencies is ∼130 cm-1. For the linear chain (a) and pairwise ring (b) experimental frequencies are not available, and a comparison is made with the MP2 frequencies. Some modes, in particular the highest frequency Σg mode of the linear chain and the highest frequency A1 mode of the pairwise ring, which Warren et al.6 matched up with the experimental frequency of 1167.5 cm-1, differ by more than 250 cm-1. In our calculation we could not find any frequency close to 1167.5 cm-1, and therefore on this DFT evidence, we doubt whether the new structure was seen. (c) S4N2. Earlier theoretical studies30 considered only the (1,3) isomer (Figure 2a) and obtained a nonplanar structure in agreement with experiment.4 Recently Chandler et al.7 reported an ab initio calculation on the possible cyclic forms, the (1,2), (1,3), and (1,4) isomers, of S4N2 (see Figure 2) at the MP2 level with a DZP type basis set. They found only one minimum with a puckered structure for the (1,3) isomer; two minima (symmetric chair and twisted planar forms), with the symmetric chair lower in energy, for the (1,4) isomer; and no minima for the (1,2) isomer.
Figure 3. Geometry (bond lengths in angstroms and bond angles in degrees) of (1,3) tetrasulfur dinitride at various levels of theory.
Figure 4. Geometry (bond lengths in angstroms and bond angles in degrees) of (1,4) tetrasulfur dinitride at various levels of theory.
Here we report DFT calculations on the (1,3) and (1,4) isomers using LDA, BLYP, and B3LYP functionals with a 6-31G* basis set. For the (1,3) isomer, our results support the recent MP2 work and the experimental results, predicting the puckered ring is the only minimum. The structural parameters calculated at various levels are compared in Figure 3. As for SNS and S2N2 the DFT(BLYP) bond lengths are too long, the DFT(LDA) values are close to the experimental values, but the DFT(B3P86) values give the best agreement.
17488 J. Phys. Chem., Vol. 100, No. 44, 1996
Somasundram and Handy
TABLE 5: DFT Harmonic Frequencies (cm-1) of the Three Minima of S4N2a (1,3) isomer
(1,4) chair form
(1,4) twisted form
mode
B3P86 (6-31G*)
MP27 (DZP)
expt31
mode
B3P86 (6-31G*)
MP27 (DZP)
mode
B3P86 (6-31G*)
ω1-A′ ω2 ω3 ω4 ω5 ω6 ω7 ω8-A′′ ω9 ω10 ω11 ω12
968 (3) 626 (16) 590 (1) 458 (4) 368 (18) 272 (4) 160 (1) 1065 (30) 639 (51) 384 (0) 323 (1) 143 (12)
820 611 547 475 378 274 156 1066 680 389 320 171
929 (s) 620 (s)
ω1-Ag ω2 ω3 ω4 ω5-Bg ω6 ω7-Au ωg ω9 ω10-Bu ω11 ω12
657 (1) 454 (4) 310 (1) 295 (11) 896 (1) 273 (0) 840 (11) 431 (2) 60 (11) 600 (117) 563 (34) 156 (65)
693 451 322 282 864 267 971 463 54b 1378 545 328
ω2-A′ ω2 ω3 ω4 ω5 ω6 ω7-A′′ ω8 ω9 ω10 ω11 ω12
726 (0) 696 (120) 471 (93) 381 (0) 121 (0) 85 (1) 1077 (23) 1038 (53) 342 (22) 310 (41) 124 (0) 63 (22)
a
470 (w) 377 (m) 266 (vw) 1033 (s) 629 (s) 320 (w)
The numbers in parentheses are the calculated intensities in km/mol. b Reference 32.
In the case of the (1,4) isomer we also found two minima, the chair and twisted forms. At the DFT(LDA) and DFT(B3P86) levels, the twisted form is lower in energy by 3.0 and 2.3 kcal mol-1, respectively. With the B3LYP functional the twisted stationary point had one imaginary frequency (i24 cm-1). With the BLYP(6-31G*) functional, no stationary point could be determined from the twisted form, the molecule preferring to fall apart into SNS+SNS. Among the (1,3) and (1,4) isomers, the (1,3) isomer is lower in energy by 12.9 and 17.4 kcal mol-1 at the LDA and B3P86 levels, respectively. For the (1,4) isomer LDA, B3LYP, and B3P86 structural parameters calculated with the 6-31G* basis set are shown in Figure 4. For the chair form our DFT results are similar to the MP2 results, whereas for the twisted form the structural parameters vary significantly. Here again, the suggestion5 for a new (1,4) isomer came from the observation of infrared absorption peaks at 773.0 and 882.3 cm-1, which were proposed as symmetric and antisymmetric stretching of NS2 group(s), respectively. We have calculated the harmonic frequencies and listed them in Table 5 together with the available MP2 and experimental frequencies.31 The vibrational spectrum in CS2 solution was recorded for the (1,3) isomer in 1983,31 but the labeling of the peaks is not given. Here we have labeled them as in ref 7. Our DFT(B3P86) frequencies agree very well with the experimental frequencies. The maximum difference is only 39 cm-1. Moreover, in the experimental spectrum, the peaks at ω2, ω8, and ω9 had strong absorption, and our calculated infrared intensities also support this observation. For the chair form of the (1,4) isomer we could not find any frequency near the MP2 value of 1378 cm-1. Our calculated frequencies for the symmetric stretching mode of the NS2 group(s) are 657 and 600 cm-1 and for the antisymmetric stretching mode of the NS2 group(s) are 896 and 840 cm-1. Among these the frequencies at 600 and 840 cm-1 are intense. For the twisted form, our calculated values of 696 and 726 cm-1 correspond to the symmetric stretching mode and 1038 and 1077 cm-1 correspond to the antisymmetric stretching mode with the frequencies at 696 and 1038 cm-1 being intense. On the basis of these DFT calculations we suggest that the observed frequency of 773 cm-1 may be the symmetric stretching of the twisted form and the observed frequency of 882 cm-1 may be the antisymmetric stretching of the chair form. 4. Conclusion From these studies we have gained the following information on sulfur-nitrogen species. (i) SNS (2A1). The DFT studies give better agreement with observed frequencies than either MP2 or CI. (ii) S2N2. The DFT calculations predict the order of stability to be linear chain < pairwise ring < alternate ring, in con-
tradiction to MP2 studies (linear chain < alternate ring < pairwise ring). Our MRCI studies support the DFT predictions. DFT studies cannot make an identification of an absorption peak at 1167.5 cm-1. (iii) S4N2. The DFT studies show that the twisted form of the (1,4) isomer is lower than the chair form, opposite to the conclusion from MP2 calculations. We may have identified the two infrared absorption peaks at 773.0 and 882.3 cm-1. Acknowledgment. We thank Dr. D. Mok for performing the reported MRCI calculation. K.S. would like to acknowledge the British Council for financial assistance. References and Notes (1) Teichman, R. A., III; Nixon, E. R. Inorg. Chem. 1976, 15, 1993. (2) Mikulski, C. M.; Russo, P. J.; Saran, M. S.; MacDiarmid, A. G.; Garito, A. F.; Heeger, A. J. J. Am. Chem. Soc. 1975, 97, 6358. (3) Cohen, H. J.; Garito, A. F.; Heeger, A. J.; MacDiarmid, A. G.; Mikulski, C. M.; Saran, M. S.; Kleppinger, J. J. Am. Chem. Soc. 1976, 98, 3844. (4) Chivers, T.; Codding, P. W.; Oakley, R. T. J. Chem. Soc., Chem. Commun. 1981, 584. (5) Hassanzadeh, P.; Andres, L. J. Am. Chem. Soc. 1992, 114, 83. (6) Warren, D. S.; Zhao, M.; Gimarc, B. M. J. Am. Chem. Soc. 1995, 117, 10345. (7) Chandler, G. S.; Jayatilaka, D.; Wajrak, M. Chem. Phys. 1995, 198, 1691. (8) Altmann, J. A.; Handy, N. C.; Ingamells, V. E. Int. J. Quantum Chem. 1996, 57, 533. (9) Ziegler, T.; Gutsev, G. L. J. Chem. Phys. 1992, 96, 7623. (10) CADPAC: Cambridge Analytical Derivative Package Issue 6.0 Cambridge (1995). A suite of quantum chemistry programs developed by Amos, R. D. with contributions from Alberts, I. L.; Andrews, J. S.; Colwell, S. M.; Handy, N. C.; Jayatilaka, D.; Knowles, P. J.; Kobayashi, R.; Koga, N.; Laidig, K. E.; Lee, A. M.; Maslen, P. E.; Murray, C. W.; Rice, J. E.; Sanz, J.; Simandiras, E. D.; Stone, A. J.; Su, M.-D. (11) Dirac, P. A. M. Cambridge Philos. Soc. 1930, 26, 376. (12) Vosko, S. J.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200. (13) Becke, A. D. Phys. ReV. 1988, A38, 3098. (14) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. 1988, B37, 785. (15) Perdew, J. P. Phys. ReV. 1986, B33, 8822. (16) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (17) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, R.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzales, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. GAUSSIAN92/DFT, Revision G.2; Gaussian, Inc.: Pittsburgh, PA, 1993. (18) Dunning, T. H. J. Chem. Phys. 1971, 55, 716. (19) Kaldor, U. Chem. Phys. Lett. 1991, 185, 131. (20) Yamaguchi, Y.; Xie, Y.; Grev, R. S.; Schaefer, H. F., III. J. Chem. Phys. 1990, 92, 3683. (21) Janssen, R. A. J. J. Phys. Chem. 1993, 97, 6384. (22) Haddon, R. C.; Wasserman, S. R.; Wudl, F.; Williams, G. R. J. J. Am. Chem. Soc. 1980, 102, 6687. (23) Collins, M. P. S.; Duke, B. J. J. Chem. Soc., Chem. Commun. 1976, 701. (24) MOLPRO (1994): A package of ab initio programs written by Werner, H.-J.; Knowles, P. J., with contributions from Almlo¨f, J.; Amos,
DFT Study on Sulfur-Nitrogen Species R. D.; Deegan, M. J. O.; Elbert, S. T.; Hampel, C.; Meyer, W.; Peterson K.; Pitzer, R.; Stone, A. J.; Taylor, P. R. (25) Werner, H.-J.; Knowles, P. J. J. Chem. Phys. 1985, 82, 5053. Knowles, P. J.; Werner, H.-J. Chem. Phys. Lett. 1985, 115, 259. (26) Werner, H.-J.; Knowles, P. J. J. Chem. Phys. 1988, 89, 5803. Knowles, P. J.; Werner, H.-J. Chem. Phys. Lett. 1988, 145, 514. (27) Parr, R. G.; Yang, W. Annu. ReV. Phys. Chem. 1995, 46, 701. (28) Bragin, J.; Evans, M. V. J. Chem. Phys. 1969, 51, 268.
J. Phys. Chem., Vol. 100, No. 44, 1996 17489 (29) Warn, J. R. W.; Chapman, D. Spectrochim. Acta. 1966, 22, 1371. (30) Palmer, M. H.; Wheeler, J. R.; Findlay, R. H.; Westwood, N. P. C.; Lau, W. M. J. Mol. Struct. (THEOCHEM) 1981, 86, 193. (31) Chivers, T.; Codding, P. W.; Laidlaw, W. C.; Liblong, S. W.; Oakley, R. T.; Trsic, M. J. Am. Chem Soc. 1983, 105, 1186. (32) Jayatilaka, D. Private communication.
JP962072B
