On the quantum theory of molecules.

Transition state theory was introduced in 1930s to account for chemical reactions. Central to this theory is the idea of a potential energy surface (PES). It was assumed that such a surface could be constructed using eigensolutions of the Schrödinger equation for the molecular (Coulomb) Hamiltonian but at that time such calculations were not possible.

Vibrational energy levels with arbitrary potentials using the Eckart-Watson Hamiltonians and the discrete variable representation.

An effective and general algorithm is suggested for variational vibrational calculations of N-atomic molecules using orthogonal, rectilinear internal coordinates. The protocol has three essential parts. First, it advocates the use of the Eckart-Watson Hamiltonians of nonlinear or linear reference configuration.

Use of a nondirect-product basis for treating singularities in triatomic rotational-vibrational calculations.

A technique has been developed which in principle allows the determination of the full rotational-vibrational eigenspectrum of triatomic molecules by treating the important singularities present in the triatomic rotational-vibrational kinetic energy operator given in Jacobi coordinates and the R(1) embedding. The singular term related to the diatom-type coordinate, R(1), deemed to be unimportant for spectroscopic applications, is given no special attention. The work extends a previous [J.

Adiabatic Jacobi corrections for H2+-like systems.

The Coulomb three-body problem in Jacobi coordinates was solved by treating the distance of the particles having equal charge as a parameter. This method allows computation of electronic energies with finite nuclear masses while maintaining the notion of a potential energy curve. The rotationless ground-state electronic and the so-called adiabatic Jacobi correction (AJC) energies are presented for H2+, D2+, and HD+ at fixed internuclear separations.

Molecular structure calculations without clamping the nuclei.

A number of recent papers have considered ways in which molecular structure may be calculated when both the electrons and the nuclei are treated from the outset as quantum particles. This is in contrast to the conventional approach in which the nuclei initially have their positions fixed and so merely provide a potential for electronic motion. The usual approach is generally assumed to be justified by the 1927 work of Born and Oppenheimer.