FRODO: a MuPAD program to calculate matrix elements between contracted wavefunctions

Abstract

A symbolic program performing the Formal Reduction of Density Operators (FRODO) has been developed in the MuPAD computer algebra system with the purpose of evaluating the matrix elements of the electronic Hamiltonian between internally contracted functions in a complete active space (CAS) scheme. The program is illustrated making use of two meaningful examples. Program summary Title of program:FRODO Catalogue identifier:ADVY Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADVY Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer:Any computer on which the MuPAD computer algebra system can be installed Operating systems under which the program has been tested:Linux Programming language used:MuPAD vs. 2.5.3 for Linux No. of lines in distributed program, including test data, etc.:3939 No. of bytes in distributed program, including test data, etc.:19 661 Distribution format:tar.gz Nature of physical problem: In order to improve on the CAS–SCF wavefunction one can resort to multireference perturbation theory or configuration interaction based on internally contracted functions (ICF) which are obtained by application of the excitation operators to the reference CAS–SCF wavefunction. The formulation of such matrix elements is quite cumbersome and a computer algebra system like MuPAD appears ideally suited to perform such a task. Method of solution: The method adopted consists in successively eliminating all occurrences of inactive orbital indices (core and virtual) from the products of excitation operators which appear in the definition of the ICF's and in the electronic Hamiltonian expressed in the second quantization formalism. Restrictions due to the complexity of the problem: The program is limited to no more than doubly excited ICF's.