C. Ruth Le Sueur

Triatom: programs for the calculation of ro-vibrational spectra of triatomic molecules

Abstract The TRIATOM program suite calculates energy levels, wavefunctions, and where appropriate, dipole transition moments and spectra, 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 several body-fixed, internal coordinate systems based on two distances and an included angle and employ basis function expansions of orthogonal polynomials. The calculations are variational, and rotational excitation is treated using an efficient two-step algorithm. Constituent programs are TRIATOM which solves the vibrational problem and also performs the first step for rotationally excited systems. SELECT which optionally preselects basis functions for TRIATOM. ROTLEVD which performs the second step for rotationally excited states. DIPOLE computes either line or band transition intensities. SPECTRA uses the data generated by the other programs to give simulated absorption or emission spectra.

On the use of variational wavefunctions in calculating vibrational band intensities

It is shown that vibrational band intensities calculated using variational wavefunctions and dipole surfaces give results which depend on how the Cartesian axes of the dipole surface are defined. It is suggested that the most consistent definition of these axes uses the rules proposed by Eckart for separating rovibrational motion. The consequences of this choice of axis system for the calculated band intensities of H2S, LiNC and H3 +, and the apparent validity of Honl-London factors are discussed. Computed band intensities are presented for H2S, HDS and D2S which correct previous literature values.

Vibration-rotation levels of water beyond the Born-Oppenheimer approximation

Abstract The value of the adiabatic correction to the Born-Oppenheimer electronic energy is calculated as a function of geometry for water using SCF wavefunctions. A mass-dependent adiabatic function is combined with high-accuracy ab initio electronic structure calculations due to Partridge and Schwenke. Vibrational band origins for H 2 O, D 2 O, T 2 O, HDO, HTO and DTO are analysed. Unlike previous calculations on the H 3 + system, it is suggested that non-adiabatic effects are more important than adiabatic surface and effective masses of the heavy particles intermediate between the nuclear and atomic masses is found to significantly improve predictions of rotational term values. The adiabatic correction is found to be of particular importance for rotational levels with high K a .

Practical schemes for distributed polarizabilities

A general formalism for distributed molecular polarizabilities has already been established [1]. It requires the matrix elements of the multipole moment operators to be partitioned between a number of regions of the molecule. In the present paper, various partitioning methods are investigated. One partitioning scheme, based on Gauss-Hermite quadrature, stands out as more stable than others which can be applied to general geometries. Symmetry requirements, however, are not automatically fulfilled when this scheme is used, so symmetrization schemes are also discussed. Calculations of the Rayleigh-Schrodinger induction energy using these distributed polarizabilities are used as a guide for judging the usefulness of the partitioning schemes. Morokuma analysis is used as a standard for comparison. The results support the view that the partitioning scheme based on Gauss-Hermite quadrature is preferred because of its greater stability.

Ab initio ro-vibrational levels of H3+ beyond the Born-Oppenheimer approximation

Abstract The value of the adiabatic correction to the Born-Oppenheimer electronic energy is calculated as a function of geometry for H3+ using SCF wavefunctions. A mass-dependent adiabatic function is combined with the near-Born-Oppenheimer electronic structure calculations of Rohs, Kutzelnigg, Jaquet and Klopper and the rotation-vibration energy levels of H3+ and D3+ are calculated. The levels for H3+ are significantly better than any previous ab initio estimates but are less accurate than those obtained by recent spectroscopically determined effective H3+ potentials. The adiabatic correction is less important for the heavier D3+. For both ions rotational levels are obtained to near experimental accuracy. Small, systematic shifts in the vibrational bands may be attributable to residual errors in the Born-Oppenheimer potential.

Localization methods for distributed polarizabilities

The response of a molecule to external electric fields can be described in terms of distributed polarizabilities. Such polarizabilities include both local and non-local effects. Methods of transforming the non-local polarizabilities into local ones are explored in this paper. Such transformations have to satisfy certain restrictions. The results for saturated and conjugated hydrocarbons suggest that full localization is not satisfactory, but that a scheme in which some charge-flow polarizabilities are retained gives values that are reasonably transferable between molecules. The paper also suggests how a transferable polarizability scheme may be developed for other kinds of molecules.

Asymmetric adiabatic correction to the rotation–vibration levels of H2D+ and D2H+

Calculations on H2D+ and D2H+ have shown that the energy levels of these asymmetric isotopomers of H3+ cannot be reproduced using effective potential energy surfaces with D3h symmetry. It is shown that for these ions the adiabatic correction to the Born–Oppenheimer approximation has an asymmetric component which can be expressed as a mass‐independent surface multiplied by a mass factor. An expression for this function is obtained from ab initio calculations. Use of this adiabatic correction is found to resolve the discrepancy with the levels of H2D+ and D2H+. The ab initio calculations reported reproduce the observed H2D+ transitions with an average error (obs−calc) of −8 MHz for the rotational transitions, −0.06 cm−1 for the ν1 band, −0.13 cm−1 for ν2, and −0.19 cm−1 for ν3. These errors are nearly constant for all transitions within a vibrational band. This gives a very accurate ab initio framework for predicting unobserved transition frequencies.

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.

Stationary points on the potential energy surfaces of (SO2)2 and (SO2)3

The equilibrium structure and interconversion tunneling of the van der Waals dimer of sulphur dioxide is investigated. Results with the electrostatic model are compared with those obtained ab initio at the self‐consistent field level and with second order Mo/ller–Plesset perturbation theory. This complex is shown to be a difficult problem for theoretical chemistry. We have located six stationary points on the dimer surface, two of which are probably transition states. The lowest energy region is very flat at all levels of theory but dispersion forces are likely to be responsible for the observed Cs symmetry global minimum. Substantial vibrational averaging must be invoked to explain the observed dipole moment. The tunneling splittings can be explained by a single motion proceeding via a centrosymmetric transition state and analogous to the internal rotation of acetylene dimer. A model potential gives a value of 56 cm−1 for the barrier, within the range predicted ab initio. We have also investigated three ...

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.