ALBERT

Notes: The equilibrium structures, dipole moments, harmonic vibrational frequencies, and infrared intensities of NH3, FON, Be3, BeC2, and BeO2 have been determined using the coupled-cluster and Brueckner electron correlation methods. The singles and doubles coupled-cluster (CCSD) and the Brueckner doubles (BD) methods have been employed and the corresponding methods that include a perturbational estimate of connected triple excitations [i.e., CCSD(T) and BD(T)] have also been investigated. The T1 diagnostic [Int. J. Quantum Chem. Symp. 23, 199 (1989)] is found to provide a good indication of the magnitude of the difference between the results obtained with the coupled-cluster and Brueckner methods. For NH3, the T1 diagnostic is small and so the differences between results obtained from coupled-cluster and Brueckner theories are quite small. For the other four molecules the T1 diagnostic is larger, and so the differences between the coupled-cluster and Brueckner methods become larger. However, it is found for all of the molecules considered in this study that inclusion of the contribution from connected triple excitations is more important than the differences between the Brueckner and coupled-cluster correlation methods.

Notes: This is the second in a series on the ab initio calculation of the second, third, and fourth derivatives of the energy of a molecule with respect to nuclear coordinates. A knowledge of these derivatives yields, in particular, anharmonic spectroscopic constants. Here we discuss our implementation of the formula for the fourth derivative of the self-consistent-field energy and present full quartic force fields in internal coordinates for H2O and CO2.

Notes: Knowledge of a force field expanded through quartic displacements, together with a dipole field expanded through cubic displacements, yields all the harmonic and anharmonic molecular properties of interest to infrared spectroscopists. Such force fields may also explain much of the mechanism behind intramolecular vibrational energy redistribution. The ab initio quantum chemist can now calculate these fields, either at the self-consistent field level or with the inclusion of electron correlation effects. For accurate predictions, it is important to include electron correlations effects for at least the quadratic part of the force fields. Here we report studies using the second-order Møller–Plesset method for the full quartic fields. We examine the effects of using large basis sets. The quadratic force constants are calculated analytically; cubic and quartic constants are calculated using central differences of second derivatives in reduced normal coordinates. Three molecules are studied. HCCF, for which a large quantity of experimental data has been recently analyzed by Holland, Newnham, and Mills. The calculations are sufficiently accurate that errors in the experimental assignments became apparent. HFCO, where the theoretical anharmonic constants are helpful in understanding the highly excited vibrational states probed by Moore and co-workers. SiH+3, whose high resolution absorption spectra has just recently been detected by Davies and co-workers. The conclusions are that this straightforward way of calculating spectroscopic properties is an extremely valuable tool for the understanding of spectroscopy.

Notes: This is the fourth in a series of papers on the ab initio calculation of the third and fourth derivatives of the energy of a molecule. In this paper we examine anharmonic effects in the infrared and Raman spectra of benzene. The following spectroscopic properties have been calculated; ab initio anharmonic corrections (ω−ν) and estimates of the harmonic frequencies ω for all 30 vibrational modes of C6H6 and C6D6, a complete set of anharmonic constants x and g for C6H6, intensities for the infrared spectrum of C6H6 up to 6148 cm−1, and anharmonic corrections to the Raman scattering factors for the fundamental modes of C6H6. In addition, we have improved on previous calculations of the equilibrium geometry of benzene, using Møller–Plesset perturbation theory and a triple zeta plus double polarization (TZ2P) basis. We have also calculated a zero-point vibrationally averaged geometry which is in good agreement with the experimental R0 value. All these calculations are based on a Hartree–Fock quartic potential, cubic dipole surface, and quadratic polarizability surface, using a double-zeta plus polarization (DZP) basis. This is the first time a complete anharmonic potential has been obtained for a molecule of this size; the computer time required was minimized by the use of analytic derivative programs in favor of finite-difference programs. The quartic potential is presented in three coordinate systems.We discuss efficient algorithms for the nonlinear transformation of the potential from normal coordinates to valence coordinates and for symmetry checking the potential. The approximations used in our calculations have been examined and we find that the use of a Hartree–Fock DZP potential together with a perturbative treatment of the vibrational Hamiltonian is just as accurate for D6h benzene as for smaller molecules. In order to examine correlation effects in the B2u modes 14 and 15, basis-set limit second-order Møller–Plesset TZ2P+f harmonic frequencies have been calculated for these modes. It is suggested that, while these modes are very sensitive to correlation, anharmonicity has only a small effect, so a Hartree–Fock DZP anharmonic potential is adequate. Furthermore, experimental determination of anharmonic corrections to frequencies is very difficult for a molecule of this size so we hope our calculations will fill this gap.

Notes: The equilibrium structure and interconversion tunneling of the van der Waals dimer of sulphur dioxide is investigated. Results with the electrostatic model are compared with those obtained ab initio at the self-consistent field level and with second order Møller–Plesset perturbation theory. This complex is shown to be a difficult problem for theoretical chemistry. We have located six stationary points on the dimer surface, two of which are probably transition states. The lowest energy region is very flat at all levels of theory but dispersion forces are likely to be responsible for the observed Cs symmetry global minimum. Substantial vibrational averaging must be invoked to explain the observed dipole moment. The tunneling splittings can be explained by a single motion proceeding via a centrosymmetric transition state and analogous to the internal rotation of acetylene dimer. A model potential gives a value of 56 cm−1 for the barrier, within the range predicted ab initio. We have also investigated three cyclic structures of the SO2 trimer, two of which are minima. The global minimum is probably nonsymmetric.

Notes: The Brueckner doubles variant of coupled cluster theory has recently been reintroduced by the authors. The use of Brueckner orbitals means that the governing equations for Tˆ2 take a particularly simple form. Here we give the details for the evaluation of the gradient of the Brueckner doubles energy for (a) the unrestricted spin–orbital formalism and (b) the closed-shell restricted formalism. Applications are presented for H2O, NH3, CH4, H2CO, C2H2, HCN, and CO2 and comparisons are made with the Hartree–Fock, second order Møller–Plesset and quadratic configuration interaction models and with experiment.

Notes: The vibrational circular dichroism (VCD) of dimethylcyclopropane is studied by ab initio techniques. The equilibrium geometry, the molecular force field, and the matrix elements for the infrared (IR) and VCD intensities are evaluated using the derivative method for molecular wave functions of SCF type. An alternative derivation of Stephens' expression for the rotational strength is presented. The results are compared with the available experimental information for the C–H stretching modes. This is an excellent demonstration of the validity of this theory for the VCD intensity of the C–H vibrations, which are easily rationalized using group theoretical arguments.

Notes: The infrared, Raman frequencies and intensities and the vibrational dichroism of the molecule have been computed using Hartree–Fock and Møller–Plesset perturbation theories. In general, the frequencies and intensities computed by perturbation theory improve the Hartree–Fock description of the spectra. For one of the spectral regions, only the values corrected by perturbation theory are entirely compatible with the measured intensities and signs.

Notes: The removal of spin contamination from unrestricted Hartree–Fock Møller–Plesset calculations is now recognized to be important. Here the Handy–Knowles formulation, previously presented, is studied. An evaluation of the energy and the energy gradient, for the removal of one- and two-spin contaminants, is described. The cost of the algorithm for the gradient is proportional to n2v3, where n and v are the number of occupied and virtual orbitals, respectively. Applications of this algorithm are presented for CN, Li3, and the abstraction of H from CH4.

Notes: The calculation of out-of-plane bending vibrations for π-bonded systems appears to be extraordinarily sensitive to the choice of a one-particle basis set. Ab initio predictions are reported for acetylene, an extreme example, at the self-consistent field (SCF), singles and doubles configuration interaction (CISD), nth order Møller–Plesset perturbation theory (MPn,n=2–4), coupled-pair functional (CPF), and singles and doubles coupled cluster (CCSD) levels of theory. It is found that the addition of a set of f basis functions to the carbon atom changes the value of the SCF πg frequency by +45 cm−1, and the value of all correlated πg frequencies by more than +100 cm−1. Evidence is presented that this behavior is present in other π-bonded systems. It is concluded that basis sets consisting of triple zeta plus two sets of polarization functions plus one set of f functions (TZ2P+f ) can predict highly accurate (∼1% average error) harmonic frequencies with the MP2, CPF, and CCSD methods, for a large number of molecules.