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Manuscript Title: A computer program to calculate the total energy absorption cross section for the photodissociation of a diatomic molecule arising from a bound state -> repulsive state transition using time dependent quantum dynamical methods.
Authors: G.G. Balint-Kurti, S.P. Mort, C.C. Marston
Program title: PHOTO
Catalogue identifier: ACLC_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 74(1993)289
Programming language: Fortran.
Computer: MEIKO i860.
Operating system: UNIX.
RAM: 1000K words
Word size: 64
Keywords: Molecular physics, Scattering, Photon, Time dependent quantum Dynamics, Photodissociation.
Classification: 16.6.

Nature of problem:
The program calculates the total energy absorption cross section for radiation incident on a diatomic molecule as a function of photon energy. The radiation is absorbed by the molecule causing an electronic transition from an initial bound electronic state to a repulsive one. A transition dipole moment function is included in the calculation. It is through the mediation of this dipole function that the radiation interacts with and is absorbed by the molecule. The molecule is assumed initially to be in a bound vibrational state. The wavefunction of this vibrational state is computed numerically from the potential provided by the user. The user must also provide the repulsive state potential energy curve as well as the form of the transition dipole moment function. The computer program can be used as a modelling tool to extract information concerning potential energy curves and transition dipole moment functions from experimental data. It may also be used as a starting point for writing computer programs for other applications of time dependent quantum dynamics.

Solution method:
The Fourier Grid Hamiltonian method is used to generate a selected vibrational state wavefunction using the bound electronic state potential energy curve supplied by the user. This wavefunction is then multiplied by the transition dipole moment function (also supplied by the user) to yield an initial wavepacket. The wavepacket is evolved forwards in time using time dependent quantum dynamics. Its time development is governed by the (user supplied) repulsive state potential energy curve. Grid methods are used throughout, both in the computation of the initial vibrationally bound wavefunction and in the subsequent solution of the time dependent Schrodinger equation. The solution of the time dependent Schrodinger equation is accomplished through the use of the Chebychev polynomial expansion method of Tal-Ezer and Kosloff. The method requires the repeated operation of the Hamiltonian operator on the initial or current wavepacket. This wavepacket is represented by its values on a grid of evenly spaced points and discrete fast Fourier transforms are used in operating with the kinetic energy part of the Hamiltonian operator on the wavepacket. At each time step, as the time development of the wavepacket progresses, the autocorrelation function is computed by taking the overlap of the initial wavepacket with the wavepacket at the current time. The cross section is finally evaluated as the real part of the Fourier transform of the autocorrelation function. The methods yield the absorption cross section at all photon energies of interest from a single solution of the time dependent quantum dynamics.

The program is written for a 1-dimensional problem and is therefore limited to diatomics or systems being modelled using one mathematical dimension. The number of grid points must be a power of 2 (e.g. 128, 256) due to the nature of the Fourier transform algorithm used.

Running time:
54 seconds on Meiko, 8 minutes 9 seconds on SUN.