R. Wallace

A theory of nuclear motion in polyatomic molecules based upon the morse oscillator: I. Application to the stretching overtone spectra of water and benzene molecules

Abstract A theory of molecular vibrations is presented which is based upon the Morse, as opposed to the harmonic, oscillator. As a first application of this model, the stretching overtone spectra of the benzene and water molecules have been calculated, these examples being chosen on account of the high degree of anharmonicity characterizing their potentials and the availability of suitable experimental data.

Procedures leading to a variety of orthonormal Jacobi-type coordinates of relevance to large-amplitude vibration and scattering problems

Abstract Algorithms are developed to produce transformation matrices to convert from scalar bond distance—angle coordinates to scalar coordinates corresponding to a variety of Jacobi-type orthonormal coordinates defined by the usual Gram—Schmidt process, or by alternates taking into account symmetries inherent in the molecular hamiltonian. The transformations have been developed with computer implementation in mind.

The selection of coordinate systems for describing large-amplitude nuclear motion in triatomic molecules

Abstract A family of mass-scaled coordinate systems is presented for the triatom i75n which the kinetic energy operator for large-amplitude vibrational motion is diagonal (unlike that in current local-mode theories). For any particular potential, a procedure is described to choose the coordinate system in which the hamiltonian most closely approaches separability. This optimal system is applied to the calculation of vibrational excitation energies of water and related isotopic molecules. The relationship of the family of large- amplitude coordinates to normal coordinates is discussed.

Large amplitude vibration in polyatomic molecules. I. A polar representation of orthogonal relative coordinates

Abstract A general expression for the rovib kinetic energy operator in a system of orthogonal internal coordinates is derived for arbitrary amplitudes of motion. Plots of the molecular potential in such coordinates serve to determine coordinate subsets in which the potential approaches separability. A revision of previous theory for the three-body problem is presented. A rovib hamiltonian for non-branched four-atom molecules (such as C2H2) is derived. Certain features of application to polyatomic (five-atom) molecules are considered.

The determination of generalized Jacobi vectors (GJVs) for common types of small molecules

Abstract Methods previously described to define generalized Jacobi vectors for N-body systems are elaborated for common types of small molecules to define a variety of orthonormal coordinates describing relative motion.

Form of the quantum kinetic energy operator for relative motion of a group of particles in a general non-inertial reference frame

Abstract A form is derived for the quantum kinetic energy operator for relative motion of a group of particles in a general non-inertial reference frame. Rotational coordinates are integrated out leaving an expression in terms of internal Cartesian coordinates and rotational quantum numbers. The operator reduces to standard forms for conventional choices of reference frames (such as instantaneous principal axes of inertia) and serves as a general starting point from internal curvilinear coordinates describing large-amplitude internal motion.

Search for curvilinear coordinates to separate the torsional motion in ethylene from other internal modes

Abstract Despite the fact that the observed progression of torsional overtone transitions in ethylene appears “pure”, qualitatively correct theoretical potentials indicate substantial coupling of the torsional mode with CC stretching. An attempt is made to recover a single mode description by invoking an internal curvilinear coordinate which follows the minimum energy torsional pathway, together with a corresponding orthogonal coordinate. A theoretical spectrum is computed for the new “torsional” motion and this is shown to be in good agreement with experiment.

Large-amplitude vibration in triatoms. III. Application to linear molecules: Vibrational states of HCN

Abstract Within the context of a recently proposed model, the angle-bending Schrodinger equation for linear molecules is cast in the form of the Legendre equation with an added potential. This is solved by a complete set expansion in terms of associated Legendre functions. The resulting solutions are incorporated into the existing model. Computation of the lower vibrational excitations of HCN is carried out.

Large-amplitude vibration in triatoms. II. Introduction of potential refinement within a LAV model applied to the sulfur dioxide molecule

Abstract The recent theoretical approach of Wallace to LAV in triatoms is applied to sulfur dioxide in a form which permits least-squares potential refinement. Close agreement of the model with twenty-five fundamentals, overtones, and combination bands is attained.

A model for describing large amplitude vibrations of triatomic molecules

Abstract A coordinate system developed by Smith and Whitten for describing scattering states of three body systems is applied to the problem of large amplitude The SW equations are simplified and a form of potential found which permits a separation of the SW Schrodinger equation. The model is applied to the description of large amplitude vibrations in the water molecule and it is shown that the assumed form of potential satisfac A model for arbitrary amplitude vibrations of H 2 O is obtained in terms of three separate one-dimensional equations.