James R. Henderson

Highly excited rovibrational states using a discrete variable representation: The H+3 molecular ion

A formulation of the rovibrational problem in Jacobi coordinates is presented which employs a discrete variable representation for the angular internal coordinate. Rotational excitation is implemented via a two‐step procedure and symmetry (for AB2 systems) included using a computationally efficient method. Energies for the lowest 180 vibrational states of H+3 are presented and their wavefunctions analyzed graphically. J=1←0 excitation energies are presented for the lowest 41 vibrational states. The significance of the regular states in the high‐energy regime of H+3 is discussed.

All the vibrational bound states of H+3

Abstract Vibrational calculations are presented for three H + 3 potential energy surfaces using a discrete variable representation in all three internal coordinates. These calculations converge all the J =0 bound states of H + 3 to within 10 cm −1 giving at least 881 states for each potential. The wavefunctions of these states have been analysed in an attempt to find assignable or spatially localised states of the system. The significance of this work to the unassigned near-dissociation spectra of H + 3 is discussed.

DVR3D - FOR THE FULLY POINTWISE CALCULATION OF RO-VIBRATIONAL SPECTRA OF TRIATOMIC-MOLECULES

The DVR3D program suite calculates energy levels, wavefunctions, and where appropriate dipole transition moments, for rotating and vibrating triatomic molecules. Potential energy, and where necessary, dipole surfaces must be provided. The programs use an exact (within the Born-Oppenheimer approximation) Hamiltonian, offer a choice of Jacobi or Radau internal coordinates and several body-fixed axes. Rotationally excited states are treated using an efficient two-step algorithm. The programs uses a Discrete Variable Representation (DVR) based on Gauss-Legendre and Gauss-Laguerre quadrature for all 3 internal coordinates and thus yields a fully pointwise representation of the wavefunctions. The vibrational step uses successive diagonalisation and truncation which is implemented for 4 of the 6 possible coordinate orderings. The rotational and transition dipole programs exploit the major savings offered by performing integrals on a DVR grid.

All the bound vibrational states of H3+ : a reappraisal

The 3D discrete variable representation (DVR) calculations of Henderson and Tennyson [Chem. Phys. Lett. 173, 133 (1990)] are reanalyzed to find the source of the nonvariational behavior highlighted by Carter and Meyer [J. Chem. Phys. 96, 2424 (1992)]. The discrepancy is found to be caused not by the use of incorrect boundary conditions, but by a failure of the quadrature approximation commonly used in DVR calculations. Corrected DVR calculations show variational but slow convergence. Calculations using the same intermediate vectors as the nonvariational calculations and a corrected final Hamiltonian show greatly enhanced convergence. The vibrational band origins computed with this method are converged to within 2 cm−1 up to 35u2009000 cm−1. A complete list of these is presented and comparisons made with previous predictions.

DVR3D: programs for fully pointwise calculation of vibrational spectra

Abstract DVR3D calculates rotationless ( J =0) vibrational energy levels and wavefunctions for triatomic systems using scattering (Jacobi) coordinates, or optionally unsymmetrised Radau coordinates, for a given potential energy surface. The program uses a discrete variable representation (DVR) based on Gauss-Legendre and Gauss-Laguerre quadrature for all 3 internal coordinates and thus yields a fully pointwise representation of the wavefunctions. Successive diagonalisation and truncation is implemented for 4 of the possible 6 possible coordinate orderings. DVR3D is best used for problems for which many (several hundred) vibrational states are required. Given appropriate dipole surfaces, the accompanying program DIPJ0DVR computes vibrational band intensities for wavefunctions generated by DVR3D.

Optical Spectrum of Single‐Crystal Nd2S3

Rare‐earth sesquisulfide crystals have been grown by the Czochralski method. The crystals as grown are opaque n‐type semiconductors. Diffusion of sulfur into semiconducting crystals at 1200°C produces transparent insulators having the same crystal structure, lattice parameters, bandgap, and optical spectrum as the semiconductors. Electrical conductivity can be controlled over 12 orders of magnitude by heating crystals in an atmosphere of sulfur. Assignments of Nd3+ J levels observed in the spectrum of insulator‐type Nd2S3 are made with the aid of a calculation of free‐ion wavefunctions and energy levels. A crystal‐field calculation based on Oh symmetry describes the details of the observed spectrum. Even at 4°K observed 4fu2009→u20094f transitions in Nd2S3 are broader than in other Nd3+ salts and are shifted about 300 cm−1 to the red of the Nd2O3 spectrum.

Nonlinear normal modes and local bending vibrations of H+3 and D+3

The structure of bending overtones of the H3+ and D3+ molecular ions at the energies below the barrier to linearity is analyzed using energies and wave functions from full three‐dimensional discrete variable representation calculations. The lowest‐in‐energy states of the vibrational polyads ν2=4,5,6 are shown to follow the localization pattern of local bending modes, three equivalent‐by‐symmetry principal periodic trajectories of the corresponding classical two‐mode system near the equilibrium.

VERY HIGHLY EXCITED VIBRATIONAL-STATES OF LICN USING A DISCRETE VARIABLE REPRESENTATION

Calculations are presented for the lowest 900 vibrational (J = 0) states of the LiCN floppy system for a two dimensional potential energy surface (r CN frozen). Most of these states lie well above the barrier separating the two linear isomers of the molecule and the point where the classical dynamics of the system becomes chaotic. Analysis of the wavefunctions of individual states in the high energy region shows that while most have an irregular nodal structure, a significant number of states appear regular—corresponding to solutions of standard, ‘mode localized’ hamiltonians. Motions corresponding in zero-order to Li-CN and Li-NC normal modes as well as free rotor states are identified. The distribution of level spacings is also studied and yields results in good agreement with those obtained by analysing nodal structures.

Gateway states and bath states in the vibrational spectrum of H+3

Abstract Vibrational band intensities are obtained from discrete variable representation calculations of eigenstates for H + 3 . Transitions linking highly excited states to the ground state show large variations in intensities, with gateway states corresponding to highly excited bending motion (“horseshoes”) which leak intensity into the nearby bath states. It is suggested that these gateway states may be observable. Implications of these results for the interpretation of the infrared predissociation spectra of H + 3 are discussed.

DVR1D: programs for mixed pointwise/ basis set calculation of ro-vibrational spectra

Abstract DVR1D calculates vibrational energy levels and wavefunctions for triatomic molecules in either scattering (Jacobi) or Radau coordinates for a given potential. The program uses a discrete variable representation (DVR) for the angular coordinate and a choice of basis functions for the radial coordinates. The program is particularly appropriate for high lying vibrational states. The accompanying program ROTLEV2 is driven by DVR1D and calculates rotationally excited states of AB 2 molecules such as water using Radau coordinates and a “bisector” axis embedding which properly reflects the symmetry of the system. DVR1D can also drive ROTLEVD, DIPOLE and hence SPECTRA from the TRIATOM program suite (Tennyson et al., Comput. Phys. Commun., previous article).