New vibration–rotation code for tetraatomic molecules exhibiting wide-amplitude motion: WAVR4

Abstract

A general computational method for the accurate calculation of rotationally and vibrationally excited states of tetraatomic molecules is developed. The resulting program is particularly appropriate for molecules executing wide-amplitude motions and isomerizations. The program offers a choice of coordinate systems based on Radau, Jacobi, diatom–diatom and orthogonal satellite vectors. The method includes all six vibrational dimensions plus three rotational dimensions. Vibration–rotation calculations with reduced dimensionality in the radial degrees of freedom are easily tackled via constraints imposed on the radial coordinates via the input file. Program summary Title of program: WAVR4 Catalogue number: ADUN Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADUN Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: Persons requesting the program must sign the standard CPC nonprofit use license Computer: Developed under Tru64 UNIX, ported to Microsoft Windows and Sun Unix Operating systems under which the program has been tested: Tru64 Unix, Microsoft Windows, Sun Unix Programming language used: Fortran 90 Memory required to execute with typical data: case dependent No. of lines in distributed program, including test data, etc.: 11 937 No. of bytes in distributed program, including test data, etc.: 84 770 Distribution format: tar.gz Nature of physical problem: WAVR4 calculates the bound ro-vibrational levels and wavefunctions of a tetraatomic system using body-fixed coordinates based on generalised orthogonal vectors. Method of solution: The angular coordinates are treated using a finite basis representation (FBR) based on products of spherical harmonics. A discrete variable representation (DVR) [1] based on either Morse-oscillator-like or spherical-oscillator functions [2] is used for the radial coordinates. Matrix elements are computed using an efficient Gaussian quadrature in the angular coordinates and the DVR approximation in the radial coordinates. The solution of the secular problem is carried through a series of intermediate diagonalisations and truncations. Restrictions on the complexity of the problem: (1) The size of the final Hamiltonian matrix that can be practically diagonalised; (2) The DVR approximation for a radial coordinate fails for values of the coordinate near zero—this is remedied only for one radial coordinate by using analytical integration. Typical running time: problem-dependent Unusual features of the program: A user-supplied subroutine to evaluate the potential energy is a program requirement. External routines: BLAS and LAPACK are required.