Jeffrey F. Gaw

Analytic Raman intensities from molecular electronic wave functions

An analytic method for the evaluation of Ramanintensities from closed−shell self‐consistent‐field wave functions is presented. Predictioinsf or ethylenemolecule are also reported. (AIP)

Analytic evaluation and basis set dependence of intensities of infrared spectra

Equations are presented for the analytic determination of dipole moment derivatives with respect to nuclear coordinates for closed‐shell, open‐shell unrestricted, and open‐shell restricted Hartree–Fock wave functions. The efficient evaluation of these derivatives and the resulting infrared intensities simultaneously with determination of the vibrational frequencies is discussed. Intensities are presented for a selection of test molecules with a wide variety of basis sets. It is concluded that basis sets of double‐zeta polarized or higher quality usually give correct qualitative information about the ordering of the intensities, while smaller basis sets may not even predict the most intense mode correctly. Quantitative accuracy using the larger basis sets seems to be limited primarily by the use of the double harmonic approximation.

The elimination of singularities in derivative calculations

Abstract The evaluation of gradients and second derivatives of the electronic energy of a molecule is discussed for two methods which include electron correlation effects - configuration interaction and perturbation theory. It is shown that numerically stable procedures can be devised using the fact that the energy is invariant to certain orbital rotations amongst occupied and amongst virtual orbitals. Some details are given on the implementation of this procedure for closed-shell second-order perturbation theory second derivatives.

Unified theoretical treatment of analytic first and second energy derivatives in open-shell Hartree—Fock theory

Abstract Second derivatives of polyatomic potential energy hypersurfaces are of widespread importance to problems in theoretical chemistry. A formalism is presented which allows the analytic evaluation of energy second derivatives from restricted Hartree—Fock wavefunctions for arbitrary closed- or open-shell molecular systems. The present method makes use of previously reported integral second-derivative techniques and earlier advances in the solution of the open-shell coupled perturbed Hartree—Fock equations. The applicability of the new method is demonstrated in studies of the first excited singlet state of formaldehyde, for which the equilibrium geometry and vibrational frequencies have been determined with two different basis sets.

Analytic energy second derivatives for general MCSCF wave functions

Expressions for the determination of analytic energy second derivatives for general MCSCF wave functions are presented. Equations for two distinct approaches: (1) direct differentiation of the energy expression and associated Lagrangian condition; and (2) power series expansion of the Hamiltonian and exponential‐i‐lambda transformation of the wave function, are developed. The problem of the nonzero nullity of the Hessian, and the resultant existence of redundant variables in the coupled perturbed multiconfiguration Hartree Fock (CPMCHF) equations, is discussed and a straightforward solution proposed. The viability of the methods presented in this paper are illustrated by a sample calculation on formaldehyde, using a double zeta (DZ) basis set and including 325 MCSCF configurations in the state space.

The H+5 potential energy hypersurface: Characterization of ten distinct energetically low‐lying stationary points

Ab initio molecular electronic structure theory has been used in an attempt to characterize the low‐lying stationary points on the H+5 potential energy hypersurface. Three distinct levels of theory have been used: the self‐consistent‐field (SCF) method, configuration interaction (CI) including all single and double excitations, and full configuration interaction. Four different basis sets were used: double zeta (DZ), double zeta plus polarization (DZP), an extended basis set designated H (6s2p/4s2p), and a second extended basis set designated H (8s3p/6s3p). The higher levels of theory are in agreement that the only minimum for H+5 is a C2v structure, with three other stationary points (of D2d, C2v, and D2h symmetries) lying less than 1 kcal/mol higher in energy. The predicted dissociation energy D0 is 5.5 kcal/mol, which is estimated to be about 1 kcal/mol less than the exact D0. Furthermore, there are six other stationary points lying less than 8 kcal/mol above the minimum. Vibrational frequencies, dipol...

Generalization of analytic energy third derivatives for the RHF closed‐shell wave function: Derivative energy and integral formalisms and the prediction of vibration–rotation interaction constants

The general restricted Hartree–Fock (RHF) closed‐shell energy analytic third derivative method is presented together with details concerning its implementation and that of the derivative integral algorithm. The viability of the energy equation and the integral techniques are illustrated by calculations on water, hydrogen cyanide, and formaldehyde with double zeta (DZ), double zeta plus polarization (DZP), triple zeta (TZ), triple zeta plus polarization (TZP), and triple zeta plus two sets of polarization (TZ2P) basis sets. Cubic force constants in reduced normal coordinates are reported for these basis sets. The cubic force constants are then applied in the prediction of the vibration–rotation interaction constants αBr (B=A, B, C) for these molecules.

Molecular clustering about a positive ion. Structures, energetics, and vibrational frequencies of the protonated hydrogen clusters H+3, H+5, H+7, and H+9

The positive hydrogen clusters H+(H2)n for n=1, 2, 3, 4 have been studied via nonempirical molecular electronic structure theory. Using double zeta (DZ) and double zeta plus polarization (DZ+P) basis sets, wave functions are reported at both the self‐consistent field (SCF) and configuration interaction including all single and double excitations (CISD) levels of theory. In each case analytic gradient techniques have been used to locate stationary point geometries and to predict harmonic vibrational frequencies. The effects of electron correlation are shown to be greater for these loose molecular complexes than for ordinary molecules. Although H+5 in its lowest energy conformation is not qualitatively described as H+3⋅H2, the larger molecular ions do fit the qualitative picture H+3(H2)n, with H+3 as a nucleating center. Of special interest here are the ‘‘new’’ normal modes of these clusters, i.e., those modes having no counterpart in the isolated H+3 or H2 species. There are 15 such vibrational degrees of ...

Analytic energy second derivatives for general correlated wavefunctions, including a solution of the first-order coupled-perturbed configuration-interaction equations

Abstract The first theoretical method for the analytic determination of energy second derivatives for configuration-interaction wave-functions is presented. Several test cases are reported, the largest being an 8385 configuration formaldehyde wavefunction.

A study of the ground electronic state of hydrogen peroxide

Abstract A quartic force field for H 2 O 2 is presented in terms of curvilinear displacement coordinates, the result of an ab initio calculation with DZP, TZ2P, and TZ2P+ f basis sets. The MP2 method was used for the quadratic part with the SCF method used for the cubic and quartic parts. The MP2 calculations suggest that the equilibrium torsional angle is near 115°, rather than the currently accepted experimental value of 112°. Use of second-order perturbation theory leads to predictions for fundamentals which are within 1% of observed values. The quartic field was then changed so that the torsional part was represented in terms of cos nφ , to give a better description of the large amplitude motion. The vibrational energy levels of this new force field were then calculated by a six-dimensional variational vibrational analysis using an exact representation of the kinetic energy operator. Good agreement with experimental data was again achieved including low-lying torsional vibrations. Variationally calculated vibrational levels up to 6000 cm −1 are presented. The new potential is therefore shown, by the variational method, to be a good representation of the potential for H 2 O 2 in the region of the equilibrium geometry.