Susan M. Colwell

The derivation of vibration-rotation kinetic energy operators in internal coordinates. II

A straightforward method for the derivation of kinetic energy operators for molecular vibration-rotation problems is described. It is assumed that internal coordinates are used for the molecular vibrations. The operator is derived by starting with the kinetic energy operator in cartesian coordinates, followed by a succession of transformations using the chain rule. Euler angles are treated in the same way as internal coordinates. At the end derivatives with respect to Euler angles are replaced by angular momentum operators. Such operators have been derived for triatomic and tetra-atomic molecules using a computer algebra program.

The density functional calculation of nuclear shielding constants using London atomic orbitals

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...

Frequency dependent hyperpolarizabilities with application to formaldehyde and methyl fluoride

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/lle...

The determination of hyperpolarisabilities using density functional theory

Abstract The theory for the calculation of the static polarisability α and hyperpolarisability β using density functional theory is presented. In particular the computational implementation of the coupled-perturbed Kohn—Sham equations is discussed. Calculations on CH 2 O and CH 3 CN are reported using large basis sets and accurate quadrature using the local density approximation (S-VWN). The results suggest that DFT is a promising method for the determination of these properties. Finally it is argued that the theory of Vignale, Rasolt and Geldart can be used as a basis for the determination of frequency-dependent polarisabilities.

The vibrational energy levels of ammonia

A variational 6-dimensional method is used to determine the low lying vibrational energy levels of ammonia. The six internal coordinates were chosen to be appropriate for the symmetry and inversion motion of the molecule; they were the three NH bond lengths, r1, r2, r3, the unique angle β which each bond makes with the trisector of them, and two (of the three) angles, θ2 and θ3, between the bonds when projected on to a plane perpendicular to the trisector. The Wilson G matrix was determined for these internal coordinates both by computer algebra and by hand. An appropriate Jacobian for the motion was determined and the full Hermitian kinetic energy operator was obtained using the Podolsky transformation. Expansion functions were in the usual product form. Special attention was given to the θ2, θ3 expansion functions so that appropriate A1, A2 and E symmetry vibrational modes were obtained explicitly. Matrix elements of the kinetic energy operator were expressed in terms of one-dimensional integrals.Variat...

The determination of hyperpolarizabilities using density functional theory with nonlocal functionals

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.

Higher analytic derivatives. II. The fourth derivative of self‐consistent‐field energy

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.

Reaction path curvature effects in the isomerization of the methoxy radical

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%.

The determination of magnetisabilities using density functional theory

Abstract The theory for the calculation of magnestisabilities using current density functional theory is presented, following on from the original theory of Vignale, Rasolt and Geldart. It is shown that a Hellmann-Feynman identity holds for the first derivative of the energy with respect to a magnetic field. The magnetic Hessian which arises in the coupled perturbed Kohn-Sham equations contains an extra term involving the current density operator as well as the density itself. It is now in a form for computation.

The calculation of frequency-dependent polarizabilities using current density functional theory

Abstract The formalism of Colwell, Handy and Lee for the calculation of frequency-dependent properties using current density functional theory has been implemented using local, non-local or hybrid functionals. This theory has been applied to the calculation of frequency-dependent polarizabilities and dispersion coefficients in a variety of small molecules. The results obtained are in good agreement with experimental data. The effect of the terms which depend upon the current density is found to be small.