George B. Bacskay

A quadratically convergent Hartree—Fock (QC-SCF) method. Application to closed shell systems

Using CI formalism the theory of a quadratically convergent Hartree—Fock method is developed which is shown to be a simple extension of single excitation CI and closely related to coupled Hartree-Fock perturbation theory. A computationally efficient practical scheme is proposed in which the costly four-index transformation step inherent in CI methods is avoided. Test calculations for the H2O, CO, C2H2N+ systems and for N2 perturbed by a finite electric field indicate that the current scheme is significantly more efficient than the widely used conventional Hartree—Fock method and is especially useful in coupled Hartree—Fock and finite field perturbation calculations.

Finite field method calculations. VI. Raman scatering activities, infrared absorption intensities and higher-order moments: SCF and CI calculations for the isotopic derivatives of H2O and SCF calculations for CH4

Abstract Finite-field perturbation methods are applied in calculating polarisabilities and polarisability gradients at the CI level for H 2 O, D 2 O, T 2 O, HDO, HTO and DTO. Dipole moments and dipole moment gradients are also calculated. The resulting Raman scattering activities and infrared absorption intensities are derived and compared with the SCF results in part V along with other theoretical and experimental values. Higher-order moments and polarisability tensor components are calculated for H 2 O at the SCF and CI levels and for CH 4 at the SCF level. The calculated values are compared with the results of other calculations as well as the currently available experimental values.

Finite-field method calculations. IV. Higher-order moments, dipole moment gradients, polarisability gradients and field-induced shifts in molecular properties: Application to N2, CO, CN−, HCN and HNC

Abstract In this paper, theoretical methods developed in III are applied in calculating polarisabilities, polarisability gradients and field-induced shifts, by the finite-field method. Values of dipole moment gradients and higher-order moments, calculated from the unperturbed wavefunctions, are also reported. Results for N 2 , CO, CN − , HCN and HNC have been obtained at the SCF level; some CI results for the N 2 polarisability components and moments and for the dipole moment gradients of HCN are also given. The calculated polarisability gradients and dipole moment gradients have been used to estimate the Raman scattering intensities and depolarisation ratios and the IR absorption intensities. Model calculations of field-induced shifts in bond length, vibrational levels, spectroscopic constants, force constants and dipole moment gradient are reported for N 2 and CO. The discrepancy between the SCF and experimental bond dipole moment gradients for HCN, previously noted in the literature, has been re-examined and resolved by our CI results.

The validity of electrostatic predictions of the shapes of van der Waals dimers

Abstract The interaction energies of the van der Waals dimers H 2 O-H 2 O, Cl 2 -HF, ClF-HF and N 2 O-HF have been calculated for a range of geometries using ab initio SCF techniques. The SCF binding energies have been decomposed into electrostatic, exchange, polarisation and charge-transfer contributions and the intermolecular angles optimised with respect to various combinations of the above components. The effects of exchange, polarisation and charge transfer on the shape of a given dimer are found approximately to cancel, so that in each case a purely electrostatic model is capable of predicting intermolecular angles that agree well with those of a full SCF treatment, as well as with experiment. These findings are consistent with the proposals and earlier calculations of Buckingham and Fowler.

The coupled-pair approximation in a basis of independent-pair natural orbitals

Abstract A computational method based on a rapidly convergent form of the unlinked cluster expansion is presented. Ciźeks coupled-pair approximation (CPA) is derived in a basis of partially non-orthogonal orbitals which transform each pair function to diagonal form; this produces a simple (non-variational) set of equations from which may be extracted the energy and coefficients of a wavefunction constructed from the Hartree-Fock function, all double excitations and all unlinked clusters of these. The relationship of the CPA to simpler treatments is developed using the results of Hurley, and numerical results of a simple illustrative study of the BH 3 molecule are given.

The infrared absorption intensities of the water molecule: A quantum chemical study

Using ab initio Hartree–Fock SCF, configuration interaction, and approximate coupled pair techniques, an extensive quantum chemical study of the infrared absorption intensities of the water molecule is reported. In an attempt to establish the necessary requirements for the quantitative prediction of infrared intensities four major effects were examined: (a) the magnitude of electron correlation effects, (b) the applicability of the Hellmann–Feynman theorem to the calculation of dipole moments functions, (c) basis set requirements, and (d) the accuracy of the customary harmonic approximations. The calculated infrared intensities for the water molecule and several of its isotopic derivatives are in good agreement with the available experimental data. In addition to the fundamentals the intensities of several overtone and combination bands were also calculated resulting in generally very small values that strongly depend on the potential energy surface used in the generation of vibrational wave functions.

Unlinked cluster effects in molecular electronic structure. I. The HCN and HNC molecules

Extensive calculations on the molecules HCN and HNC have been performed using our recently proposed ’’coupled‐pair approximation’’ (CPA) in a basis of nonorthogonal independent‐pair natural orbitals. A number of linear geometries are used for both systems, allowing prediction of equilibrium geometry, rotational constants and force constants for the stretching vibrational modes. The CPA values are in substantially better agreement with experimental results (where available) than those obtained from variational CI calculations including all double excitations, and can be generated with little extra computational effort. In addition, several approximate coupled‐pair techniques, which require no more effort than a CI calculation, are investigated in order to estimate their accuracy relative to the full coupled‐pair method. Using the bond‐stretching potentials, we have calculated vibrational energy levels and transition energies. Again, the values obtained by the CPA method are in better agreement with experim...

The prediction of nuclear quadrupole moments from abinitio quantum chemical studies on small molecules. I. The electric field gradients at the 14N and 2H nuclei in N2, NO, NO+, CN, CN−, HCN, HNC, and NH3

Electric field gradients (efg’s) at the nitrogen nuclei in N2, NO+, NO, CN, and CN− and at the nitrogen and hydrogen nuclei in HCN, HNC, and NH3, calculated using ab initio quantum chemical methods, are reported. Employing extensive Gaussian basis sets, the efg’s were computed at the self‐consistent field (SCF), singles and doubles configuration interaction [CI(SD)], and coupled pair functional (CPF) levels of theory as the expectation values of the efg operator and also as the energy derivatives of the appropriate perturbed Hamiltonian using the finite field method. Corrections due to zero point vibrational motions were also calculated. The effect of basis set incompleteness on the calculated efg’s, together with the experimental nuclear quadrupole coupling constants, are used to estimate the 14N and 2H nuclear quadrupole moments, and to test the quality of the correlated wave functions generated by the CI(SD) and CPF methods. The recommended values, on the basis of the present calculations, are 2.05±0.0...

Spectroscopic constants of the X̃(1A1), ã(3B1), and Ã(1B1) states of CF2, CCl2, and CBr2 and heats of formation of selected halocarbenes: An ab initio quantum chemical study

The geometries, rotational constants, harmonic force constants and frequencies, dissociation and term energies of CF2, CCl2, and CBr2 in their respective X(1A1), a(3B1) and A(1B1) states, computed by complete active space self-consistent field (CASSCF), complete active space second-order purturbation (CASPT2), and coupled-cluster with single, double and perturbative triple excitations [CCSD(T)] methods and cc-pVTZ basis sets, are reported. For CCl2 and CBr2 the barriers to linearity are also characterized. The computed spectroscopic constants are in good agreement with the available experimental data. The atomization energies and hence heats of formation at 0 and 298 K of these molecules as well as of CHF, CHCl, and CFCl, all in their lowest singlet ground states were also computed by the CCSD(T) method utilizing basis sets ranging from cc-pVDZ to aug-cc-pVQZ, cc-pCVQZ and G3large, enabling the extrapolation of the energies to a complete basis set (CBS) limit and the inclusion of core–valence correlation...

An ab initio SCF calculation of the dipole-moment derivatives and infrared-absorption intensities of the water-dimer molecule

Abstract The dipole-moment derivatives and infrared-absorption intensities of the water dimer including several deuterated species have been calculated using ab initio SCF techniques. The results are compared with the analogous, quantities for monomeric water. In addition to the highly enhanced intensity of the intramolecular OH stretch most intermolecular modes that occur in the 90–600 cm −1 region are also found to be very intense. An electrostatic model for the water dimer has been explored with a view to developing a possible scheme for the calculation of infrared intensities of larger clusters. As a result of the significant exchange and charge-transfer effects such a model is found to be unreliable in describing the dipole-moment derivatives that directly involve the hydrogen bond.