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The theory for the coupled perturbed Kohn–Sham calculation of hyperpolarizabilities using nonlocal density functionals is presented. Results for calculations on formaldehyde, acetonitrile, and methyl fluoride using moderate size basis sets are reported. These results are compared with previous density functional calculations using the local density approximation, Hartree–Fock, and correlated methods, and with the experimental values. © 1994 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The reaction path Hamiltonian is used to investigate the isomerization CH3O→CH2OH, the reaction path and necessary properties being determined by ab initio methods. In this paper a careful analysis of the effects of the curvature of the path on the temperature dependent rate constants is presented; curvature affects the log of these rate constants by about 5%. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Methods for the determination of the frequency dependent hyperpolarizabilities, β(-2ω;ω,ω), β(-ω;ω,0), and β(0;ω,-ω) at the self-consistent field (SCF) level of theory are discussed and compared. Two efficient alternatives are proposed; one involves determination of appropriate response vectors which arise in first-order perturbation theory at frequency ω, and the other involves solving first-order perturbation theory equations at frequency 0 (static), ω and 2ω. Neither approach involves solution of the second-order perturbation theory equations. The method is illustrated with application to formaldehyde and methyl fluoride using large one-particle basis sets. The basis set requirement for convergence of this property at the SCF level of theory is investigated. Basis sets including up to d functions on first row atoms and p functions on hydrogen incorporating diffuse functions appear to be adequate. The effect of electron correlation on the static hyperpolarizability is estimated using second-order Mo\ller–Plesset theory. Comparison is made with experimental values where available. [ABSTRACT FROM AUTHOR]

The theory for the calculation of nuclear shielding constants with London atomic orbitals using density functional theory is presented. The theory includes the use of a local exchange–correlation functional which depends on both the electron density ρ(r) and the paramagnetic current density jp(r). The resulting coupled-perturbed Kohn–Sham equations are presented, together with the working expression for the nuclear shielding tensor. The entire theory has been programmed and exhaustively checked, using standard Gaussian basis sets. A variety of ρ(r) dependent exchange–correlation functionals have been used, together with a current dependence suggested by Vignale, Rasolt, and Geldart. Certain numerical difficulties arose with this form which necessitated a cutoff in its evaluation for low densities. Calculations have been performed on HF, N2, CO, F2, H2O, and CH4. Including the current dependence is seen here to have a slightly deshielding effect. The major deficiency in the reported calculations appears to arise from the use of local functionals which give poor values for the Kohn–Sham eigenvalues. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]