J. CHEM. SOC. FARADAY TRANS., 1994, 90(4), 517-521 Theoretical Potential-energy Functions and the Rovibronic Spectrum of the SiH: Ion Cornelia Bauer Fachbereich Chemie der Universitat, 040439 Frankfurt, Germany David All. Hirst* Department of Chemistry, University of Warwick, Coventry, UK CV4 7AL David 1. Hall and Peter J. Sarre Department of Chemistry, University of Nottingham, University Park, Nottingham, UK NG7 2RD Pave1 Rosmus Universite de Marne la Vallee, F-93160Noisy le Grand, France ~~ Three-dimensional potential-energy functions for the 2 2Al and A 2Bl states of SiHz have been derived from extensive ab initio multi-reference configuration interaction (MRCI) calculations. Spectroscopic constants have been derived from the potential-energy functions by second-order perturbation theory.The calculated values are in very good agreement with the experimental data and also provide a secure value for the A, rotational constant for the % 2Al state. Rovibronic levels were calculated by a variational method which takes into account Renner-Teller coupling. Theoretically derived transition wavenumbers are in good agreement with experimen- tal results. Over the past few years a substantial amount of spectro- scopic data for the molecular ion SiHl has been obtained in high-resolution laser photodissociation experiments'.' in which the A 'B, +x 'A, transition has been observed by monitoring dissociation to form Si' + H, and SiH+ + H. The ground-state X'A, is bent with a bond angle of ca.120" whereas the equilibrium structure of the A state is linear. The 8 and A states are the two components of a Renner-Teller pair which correlate with 'nu for linear geometries. The SiHl ion is an important member of the 'Renner-Teller' class of AH, molecules but is of particular interest for two main reasons. First, it represents a rare example where rota- tionally resolved competitive dissociation into chemically dis- tinct channels is observed.' Secondly, while some of the SiHl ions formed by electron impact ionization of silane are gener- ated in low-lying rovibrational levels, allowing laser-excited transitions involving levels with low rotational angular momentum to be observed,' a significant proportion of the ions are formed in high-K, states with values of K, up to 25, Transitions between high-K, states give rise to a sub-band spectral structure which is wholly different from that for low K, values., Moreover, an unusual dynamical behaviour is observed in which the predissociation rates are found to decrease with increasing K, value for K, between 15 and 23.' Apart from the intrinsic interest in ab initio calculations on a prototypical Renner-Teller AH, molecule, these special spec- troscopic and dynamical aspects provided a strong motiva- tion for undertaking this work.Moreover, the calculations were conducted in the expectation that, if there were found to be good agreement between theory and experimental data, the derived potential-energy functions would be of value for future spectroscopic assignments and dynamical calculations.In the earlier experimental work,' analysis of the spectrum in the region 600-650 nm gave well determined values for the rotational constants B", C" and B'. The rotational constant A" was estimated from B" and C" with the use of inertial defect theory and from the rotational constants the geometry of the electronic ground state was obtained. The later studies in the spectral ranges 540-660 nm and 700-850 nm have been analysed in terms of transitions involving high K, values.2 These spectra have been interpreted with the aid of Renner-Teller calculations of the energy levels using an empirical potential-energy function. A fuller report of this work will be given in a forthcoming paper.3 Methods for the variational calculation of rovibronic energy levels of Renner-Teller molecules are now well estab- li~hed.~Recent applications include H20 ,5 BH, ,6 CO; 7*8+ and CH, .9 These methods require accurate potential-energy surfaces for the two components of the Renner-Teller pair.There have been a number of theoretical treatments of the SiH; but none of these has yielded potential- energy surfaces of sufficient accuracy for the calculation of rovibronic levels for comparison with experiment and pos- sessing predictive value. In this paper we report ab initio potential-energy surfaces for the 8'A1 and A2B1 states of SiHi calculated with large basis sets and with extensive treatment of electron correlation.These data have been fitted to polynomial functions which have been used in variational calculations of rovibronic levels. Molecular parameters are derived and compared with experimental data. Ab initio Calculations The basis for Si consisted of the 17s12p Gaussian basis set of Partridge17 contracted to 1ls8p (with the outer ten s and seven p functions uncontracted) augmented with four sets of Cartesian d functions (with exponents 2.1, 0.9, 0.4 and O.l5/ag) and two sets of Cartesian f functions (with exponents 1.6 and 0.55/a;). The hydrogen basis was the 8s basis of van Duijneveldt18 contracted to 4s with the addition of three sets of p functions (with exponents 1.8, 0.6 and 0.2/a;) and one set of d functions with exponent 0.7/a;.This resulted in a total of 117 basis functions. Molecular orbitals for the R'A, and A2Bl states were obtained in separate CASSCF calculations for each state.For the 'A, state the active space consisted of the orbitals 4al-7al, 2b1, 2b2-4b, whereas for the 'B, state the orbitals 4al-6al, 2b1, 3b1, 2b2-4b, constituted the active space. The CASSCF orbitals were used in MRCI calculations in which all single and double excitations were generated with respect to a set of reference configurations. For the 'A, state the ref- erence set of configurations consisted of all configurations obtained by distributing five electrons amongst the orbitals 4a,-6al, 2b2-4b, resulting in 499 180 configurations. In the -289.70 *J. CHEM. SOC. FARADAY TRANS., 1994, VOL.90 the range 180"-100". The ab initio calculations were made with the GAMESS-UK suite of program^.'^ -289.72. Adiabatic Potential-energy Functions (APEF) -289.74. The MRCI total energies, in terms of the bond lengths T,, r2 and the included angle a, were fitted to polynomial expan- sions -289.76 I v(r1, r2 a) = 1cijk RiR', Ok (1)S ijk%& -289.78 in terms of the coordinates R,, R, and 0.R, and R, werez chosen as dimensionless Simon-Parr-Finlan coordinates,Q) Ri = (1 -rref/ri).For 0the displacement coordinate 0= (a-289.80 -aref)(in radians) was employed. For the electronic ground state we used polynomials up to sixth order in R,, R, and -289.82 seventh order in 0.The corresponding orders for the upper state were set to be 5 (Rl, R2)and 6 (0).The surfaces were expanded around the calculated minimum geometry ()7: ,A, -289.84 state) and a near-minimum geometry (A2B1,rref= 2.8a0, aref= 180').The fits included 84 geometries for the A2Bl state because each ab initio point corresponds to two geome- -289.86 ' I tries on the surface. For the ground state 101 calculated ener- 180.0 160.0 140.0 120.0 100.0 80.0 60.0 gies for the z2A, state were augmented by 28 linearaldegrees geometries calculated for the A state in order to ensure Fig. 1 Cut of the potentialenergy functions of the 8 'A, and a 2Bl degeneracy of the two surfaces for linear geometries. The states of SiH; along the bending coordinate for rl = r2= 1.482 A bending potential-energy curves for r, = r2 equal to 2.8~~ (1.482 A) are illustrated in Fig.1. With these APEFs, which are valid for bond lengths 1.3 < MRCI calculations for the ,B, state 386 335 configurations r/A < 2.1 and angles between 90" and 180°, we were able to resulted from a set of reference configurations in which five reproduce the ab initio energies within a range of 6 cm- '. electrons were distributed amongst the orbitals 4a,-6al, 2b,, However, variational Renner-Teller calculations of the 2b,, 3b,. Calculations were made at 65 geometries for the transition frequencies between the 8,A, and A 2B, states ground state for bond angles in the range 90"-160". For the implied an error in the barrier to linearity of at least 10 cm-I *B, state 55 geometries were included with bond angles in (see next section).In order to improve the agreement between Table 1 Expansion coefficients" of the three-dimensional modified MRCI near-equilibrium potential-energy functions of the 8 2A, and A 2Bl states of SiH; x2A, state coo,: 289.845 159 46 c100: O.OOOOOO00 coo1 : O.OOOOOO00 0.716918 62 '110: -0.024 675 56 c101: 0.007 986 88 0.059 158 80 c300: -0.217 446 30 c120: -0.035 965 22 0.005 224 35 c111: -0.024 643 63 c012: -0.028 226 75 -0.012 770 25 c400: -0.546 603 86 c310: -0.095 198 88 c220: 0.067 331 32 '301 : 0.036271 12 c121: -0.034 61 129 c202: -0.081 139 73 '112: 0.024 40401 c013: 0.022 605 17 c004: 0.OOO261 32 '500: -0.741 254 12 c410: -0.345 089 11 '320' 0.217 267 25 '401 0.123 604 57 c311: -0.146 16454 c221: -0.049 335 11 '302' 0.025 463 73 c122: 0.041 141 24 '203 0.026 846 04 '113: -0.052 436 24 c014: 0.017 865 66 coos : -0.001 456 29 c600: -0.003 14092 Cs10: 0.001 799 56 c420: -0.OOO268 21 '330: 0.002 220 26 Cso1: 0.404232 67 '411: 0.329 033 11 '321 : -0.205 719 29 c402: -0.017 771 55 0.224 433 64 c222: -0.158 569 94 '303 : -0.051 31258 -0.038 26 193 '204' 0.046 908 83 cl 14: 0.042 667 9 1 -0.010 185 80 c006: O.OO0 894 55 coo,: -0.008 815 15 A2Bl state coo,: 289.807 478 53 c100: 0.011 999 95 c200 0.721 704 10 -0.032 501 02 coo,: 0.026 23 1 73 c300: -0.210894 13 -0.07 1106 26 c012: -0.013 121 22 c400: -0.437 889 09 -0.160 562 60 c040: -0.437 889 09 c112: 0.020 8 19 95 -0.030 59 140 '004' 0.003 008 15 c212: 0.086 91 1 33 -0.00301005 csoo: -0.315 390 35 '114: 0.011 608 09 -0.08 584 18 0.00000167 c222: -2.697 129 1 1 " The coefficients C, and cjik are equal by symmetry.Each coefficient cijk is given in the table in hartree units E,. * The coordinates are Ri = 1 -rrcf/r, i = 1, 2 with rrcf= re = 1.482 A for the ground state and rref= 2.8 a, for the upper state and 0= a -arefwith aref= a, for both states. For the R and A states aref= 119" and 180°, respectively. R, and R, are dimensionless. 0is given in radians. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 the calculated and experimental data, we have slightly modi- fied the original height of the barrier to linearity in the 2Al state. This was done by adding 10 cm-' to the Cooocoeffi-cient in the expansion of the APEF for the A2B, state.All energies for linear geometries of the Z2A, state were increased accordingly. In the fit for the electronic ground state no energies for angles 160 < a/degrees < 180 were con- sidered. For linear geometries the APEFs in Table 1 are degenerate to within 1 cm-' for bond lengths in the range 1.1 c r/A < 2.1. The expansion coefficients of the modified potentials are given in Table 1. The barrier to linearity for the 8 2Al state is now determined to be 8247.7 cm-' relative to the bottom of the potential-energy well. After determining the equilibrium bond length and angles of both states, the APEFs were used in the calculation of some spectroscopic constants. First, the quartic force field in internal coordinates was cal- culated. This was then transformed by /-tensor algebra22 to the force field in dimensionless normal coordinates.Using second-order perturbation theory the equilibrium rotational constants, harmonic vibrational frequencies and other con- stants were determined. At this stage the Renner-Teller coup- ling as well as spin-orbit interaction were neglected. The rotational constants for the individual vibrational levels were then obtained by using the equilibrium rotational constants and the set of a, values. Our constants, which are given in Table 2 together with some previously obtained data, are very close to the experimental results. This work provides a secure value for the A, constant in the 2 state for the first time. Variational Calculations The rovibronic levels were obtained using the approach of Carter and Handy,23*24 which accounts for the full dimen- sionality, anharmonicity, rotation-vibration, electronic angular momenta and electron spin coupling effects. Some additional approximations were made.First, the L,, L, operators and the geometry dependence of the L, , L: operators were disregarded. The expectation values of the latter operators were set to unity. As Brommer et aL7 showed, this simplification makes only a small contri- bution to the relative positions of the rovibronic levels. Furthermore, the spin-orbit coupling constant Aso was set to zero. A value of ca. 140 cm-'has been obtained from a fit of experimental results obtained for high K values, but no sufficiently resolved data are available for lower K values as these levels are too strongly predissociated.2 ' In the variational calculations 24 symmetry-adapted har- monic oscillator functions were employed for each stretching symmetry coordinate Si = (l/&)(Ar, fAr2) using the inter- nal force constantsf, +LRwithf, andf,, obtained from per- turbation theory (see above).The basis set for the bending mode comprised 48 associated Legendre functions. We calculated the rovibronic levels up to 17000 cm-'for N = 0, 1 (N = J -S) covering the K, values 0 and 1. The energies are converged up to 1 cm-'. In Table 3 we give the bending levels up to 18000 cm-'. As no stretching and com- bination levels are known experimentally, they are tabulated up to 8000 cm-' for the electronic ground state and some selected levels are given for the upper state.The symmetric and antisymmetric stretching frequencies for the electronic ground state are predicted to be 2097.5 cm-' and 2174.6 cm-', respectively (for N = K, = 0). For the 'pure' bending levels with higher quantum numbers it is not always possible to assign them in terms of two different electronic states and harmonic vibrational quantum numbers (see footnotes to Table 3), especially for K, 3 1, where effects due to electron-nuclear motion coup- ling occur. For instance, the wavefunctions of the (0, 2, 0) levels of the A state for N = K = 1 are strongly mixed with the j?: state bending levels (0, 11, 0) with N = K, = 1 (for the linear state u2 is given in linear notation and K = IA + 1 I), the bending quantum number for the electronic ground state is vbent.,cf.Table 3). The analysis of the two-dimensional bend contraction reveals that the (0, 2, 0) levels of the upper state in fact belong ca. 50% to the ground state. The same holds for the (0, 11, 0) levels, which cannot be unambiguously assigned to either electronic state. The K, reordering in the bending levels of the electronic ground state starts with ub;"* = 9, which we expected from the height of the barrier to linearity. For this bending quantum Table 2 Spectroscopic constants for SiH: SCF spectroscopic constants experiment ref. 1 ref. 12 ref. 11 ref. 10 UHF ref. 14 MRCI ref.13 MRCI this work ~ ~~ 8 2A, a Jdegrees rJA 1.49 & 0.01 119 f 0.5 1.465 120.09 1.490 119.20 1.4737 119.95 1.49 120 1.482 120 1.4819 119.77 A,/cm-' a 15.75 f 0.25 5.094 (2) 3.772 (4) 2268 966 10404 f81 7469 k2 A 'B, rJA 1.465 a Jdegrees B,,,/cm-' o,/cm -02/cm- 3.956 (1) 03/cm-' a Calculated from the full set of a-constants obtained from the potentials in Table 1. components as 'C+states. 'Results for SCF calculations. 2148.4' 834.6' 208 3.1 ' 7867.5 16.7723 5.0379 3.8022 2.8466 -0.0490 0.5158 0.0235 2189.7 912.6 2267.1 8247.7 1.472 1.468 180 2237.1' 21 16.5' 676.5" 1.4693 3.9434 180 2220.1 621.1 2346.8 These results were obtained treating both Renner-Teller J. CHEM. SOC. FARADAY TRANS., 1994, VOL.90 Table 3 Rovibronic levels for the A-f( system of SiHi (in cm-') (a) Bending levels, (ul = u3 = 0) 8 'A1' A 'Bib ,,lin c ubent 000 101 111 110 2 001 101 110 1122 18 1725 1 .3' 17260.e 17830.8' 17832.9' 15 17979.8 17988.0 17 16121.7 16130.6 16684.0 16686.2 14 17298.3' 1 7299.9' 16 14987.2 14995.9 14456.7 14458.8 13 16684.0 16692.2 16025.215 13771.7 13780.1* 13 150.9 13 152.9 12 16025.5 14 12575.2 12584.e 12283.8 12285.6 11 15394.1 15402.2 13 11657.8 1 1666.7 11324.4' 11326.2' 10 14740.4 14740.9 12 10490.7 10499.6' 101 3 1.9 10133.9 9 14111.4 141 19.4 11 9582.7 9591.6 9220.3" 9222.0" 8 1 3474.6' 13475.3' 10 8692.0 8700.9 8501.6 8503.1 7 12836.7 12844.4 9 7823.3 7832.2 7790.3 7792.0 6 12156.4 12157.0 8 6971.1 6980.0 7006.0 7007.7 5 11571.3 11579.2 7 6123.8 6132.7 6170.5 6172.2 4 10853.3 10853.9 6 5272.1 528 1.0 5314.9 5316.5 3 10316.4 10324.3 5 4412.0 4420.9 4448.8 4450.4 2 9605.3" 9605.7" 4 3543.3 3552.2 3575.1 3576.6 1 9073.4 908 1.2 3 2666.9 2675.8 2694.7 2696.2 2 1783.6 1792.6 1808.5 1809.9 1 894.6 903.5 917.1 918.4 0 0.0 8.96 20.6 21.9 (b) Stretching motion and combination levels in the ft state (in cm-')11 1 ~~ 0 0 2097.5 2106.3 2117.8 21 19.0 0 0 1 2174.6 2183.5 2194.8 2 196.0 1 1 0 2980.3 2989.1 3002.5 3003.8 0 1 1 3054.4 3063.2 3076.4 3077.7 1 2 0 3858.8 3867.6 3883.3 3884.7 0 2 1 3929.4 3938.2 3953.6 3955.0 2 0 0 4139.6 4148.3 4159.6 4160.8 1 0 1 4186.8 4195.5 4206.6 4207.8 0 0 2 43 15.4 4324.2 4335.2 4336.4 0 3 1 4799.1 4807.9 4826.1 4827.6 1 3 0 4732.3 4741.1 4759.8 4761.3 1 1 1 5054.5 5063.2 5076.2 5077.5 2 1 0 5010.3 5019.0 5032.1 5033.5 0 4 1 5662.7 567 1.5 5693.4 5695.0 0 1 2 5180.5 5189.2 5202.0 5203.3 1 2 1 59 18.7 5927.4 5942.6 5944.0 1 4 0 5599.8 5608.6 5631.3 5632.8 2 0 1 6132.2 6140.8 6151.7 6152.9 2 2 0 5877.9 5886.6 5902.1 5903.4 0 0 3 6411.0 6419.6 6430.4 6431.6 0 2 2 6041.5 6050.3 6065.2 6066.6 0 5 1 6519.3 6528.1 6554.8 6556.4 3 0 0 61 12.4 6121.0 6132.0 6133.2 1 3 1 6778.6 6787.3 6805.5 6806.8 1 0 2 6274.2 6282.8 6293.7 6294.9 2 1 1 6987.6 6996.2 7008.9 7010.2 1 5 0 6460.2 6469.0 6496.6 6498.2 2 3 0 674 1.4 6750.1 6768.6 6770.1 0 3 2 6898.0 6906.7 6924.4 6925.8 3 1 0 6970.0 6978.5 699 1.4 6992.7 (c) Stretchin g motio n and combination level s in the A s tate (in cm-')b u3 even u3 odd 2u1 u;" 03 001 101 110 112 u1 din 03 001 101 110 112 1 1 0 10316.4 11203.6 0 1 1 11312.6 11320.3 1 2 0 11771.9" 11773.3' 0 2 1 11821.9 11822.8 2 1 0 13269.1 13276.6 1 1 1 13360.1 13367.7 0 1 2 13510.6 13518.2 2 2 0 13822.6' 13824.0' 0 2 2 13947.5' 13948.2" ~~ ~ ~~ a The notation for the levels of the fi.'A, state is NKaK,. For the linear A 'B, state we used the notation NK,.u:" = 2uyn' + K + 1 with K = I A + I I. 'These levels are perturbed by anharmonic resonances; assignment ambiguous. 'There is a strong Renner-Teller interaction between the levels )7 (ul, 11, u3)and A (ul, 2, u3)for N = K = 1.number for the first time the K, = 1 levels lie below the cor- Conclusion responding K, = 0 level. The theoretically derived transition wavenumbers between The potential-energy functions for the 2 2A, and A 2B,states the two states are compared with the experimental data in of SiHl were used to calculate rovibronic levels up to 18OOO Table 4. After correcting the barrier by 10 cm-' as described cm-' for K = 0, 1. The transition wavenumbers between in the previous section our theoretically calculated data cor- both states were obtained and compared with experimental respond closely with the experimental results. data. In general the agreement between the theoretical and J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 521 Table 4 Comparison of transition wavenumbers obtained from experiment and variational calculations using both original and modified potentials (N = 1)" 0';v; 0;" 4 2 K U; exp. pot. Id pot. IIe level separations in the electronic ground state 'A, 0 1' 0 0 2' 0 00 0' 1' 0 0 890.3 889.6 896.5 891.4 level separations in the excited electronic state 2Bl 0 9' 0 0 7' 0 1261.0 1275.0 0 1 lo 0 0 9' 0 1280.2 1282.9 0 13' 0 0 11' 0 1296.7 1289.9 0 15' 0 0 13' 0 1300.7 1295.8 transition wavenumbers in the A-8 system 0 7' 0 0 0' 0 12831.8 12812.4 12823.8 0 9' 0 0 0' 0 14092.8 14087.1 14098.8 0 1 1' 0 0 0' 0 15373 15369.9 1538 1.7 0 13' 0 0 0' 0 16669.3 16659.8 1667 1.6 0 15' 0 0 0' 0 17970 17955.9 17967.4 0 13' 0 0 1' 0 15779 15759.1 15775.1 0 15' 0 0 1' 0 17076 17055.2 17070.9 u2 are either given in ubCn'for the electronic ground state or ulin for the excited electronic state with din= ubcn' notation, the superscript K means K,, for the linear 2B,state K ations.= PEFs with corrected barrier. experimental molecular parameters is good. Given that the experimental constants were obtained from spectra which are intrinsically low-resolution owing to lifetime broadening of the excited state, it may be that the accuracy of the rotational constants obtained from the theoretical potentials now exceeds that of the current experimental values.We may con- clude that the theoretical potentials and parameters now provide a sound basis on which further theoretical and experimental studies can be based. These include: (a)dynami-cal calculations directed towards an understanding of the predissociative decay mechanism(s) and lifetimes, interpreta- tion of the partitioning between the two dissociation channels from well defined rovibronic levels, and prediction of the internal quantum state distributions of the products, (b) further high-resolution laser-based photodissociation studies in both frequency and time domains, and (c) experimental searches for spectra of the SiH; ion in silane discharges and, conceivably, in interstellar clouds. C.B. and P.R. thank S. Carter and N.C. Handy for providing them with access to the variational Renner-Teller program. This work was supported by the Deutsche Forschungsge- meinschaft, Fonds der Chemischen Industrie and by the SERC. D.I.H. thanks BP for a research studentship. References M. C. Curtis, P. A. Jackson, P. J. Sarre and C. J. Whitham, Mol. Phys., 1985,56,485. D. I. Hall, A. P. Levick, P. J. Sarre, C. J. Whitham, A. Alijah and G. Duxbury, J. Chem. SOC.,Faraday Trans., 1993,89,177. D. I. Hall, A. P. Levick, P. J. Sarre and C. J. Whitham, in prep- aration. S. Carter, N. C. Handy, P. Rosmus and G. Chambaud, Mol. Phys., 1990, 71, 605. 2ubcn1+ K + 1. In the case of the = 1 A + 1 I. Upper state. 'Lower state. Original PEFs without alter- 5 M. Brommer, B.Weis, B. Follmeg, P. Rosmus, S. Carter, N. C. Handy, H-J. Werner and P. J. Knowles, J. Chem. Phys., 1993,98, 5222. 6 M. Brommer, P. Rosmus, S. Carter and N. C. Handy, Mol. Phys., 1992, 77, 549. 7 M. Brommer, G. Chambaud, E-A. Reinsch, P. Rosmus, A. Spiel-fiedel, N. Feautrier and H-J. Werner, J. Chem. Phys., 1991, 94, 8070. 8 G. Chambaud, W. Gabriel, P. Rosmus and J. Rostas, J. Phys. Chem., 1992,%, 3285. 9 W. H. Green, N. C. Handy, P. J. Knowles and S. Carter, J. Chem. Phys., 1991,94,118. 10 J. R. Ball and C. Thomson, Int. J. Quantum Chem., 1978, 14, 39. 11 M. S. Gordon, Chem. Phys. Lett., 1978,59,410. 12 J. M. Dyke, N. Jonathan, A. Morris, A. Ridha, M. J. Winter, Chem. Phys., 1983,81,481. 13 D. M. Hirst and M. F. Guest, Mol. Phys., 1986,59, 141. 14 M. Gonhlez, R. Sayos, F. Mota and A. Aguilar, Chem. Phys., 1987,113,417. 15 R. S. Grev and H. F. Schaefer, J. Chem. Phys., 1992,97,8389. 16 J-P. Gu, M-B. Huang, F. Kong and S-H. Liu, J. Mol. Struct. (Theochem),1992,253,217. 17 H. Partridge, NASA Technical Memorandum 89449, Ames Research Center, Moffett Field, CA, 1987. 18 F. B. van Duijneveldt, IBM Technical Research Report RJ-94.5, 1971. 19 M. F. Guest and P. Sherwood, GAMESS-UK, User's Guide and Reference Manual, 1992, SERC Daresbury Laboratory, UK. 20 S. Carter and N. C. Handy, J. Chem. Phys., 1987,87,4294. 21 P. J. Sarre, Faraday Discuss. Chem. SOC., 1991,91,414. 22 A. R. Hoy, I. M. Mills and G. Strey, Mol. Phys., 1972, 24, 1265. 23 S. Carter and N. C. Handy, Mol. Phys., 1984,52, 1367. 24 S. Carter, N. C. Handy, P. Rosmus and G. Chambaud, Mol. Phys., 1990, 71, 605. Paper 3/05836K; Received 28th September, 1993