Automated evaluation of matrix elements between contracted wavefunctions: A Mathematica version of the FRODO program

A symbolic program performing the Formal Reduction of Density Operators (FRODO), formerly 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, has been rewritten in Mathematica. New version : A program summary Program title: FRODO Catalogue identifier: ADV Y _v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADVY_v2_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3878 No. of bytes in distributed program, including test data, etc.: 170729 Distribution format: tar.gz Programming language: Mathematica Computer: Any computer on which the Mathematica computer algebra system can be installed Operating system: Linux Classification: 5 Catalogue identifier of previous version: ADV Y _v1_0 Journal reference of previous version: Comput. Phys. Comm. 171(2005)63 Does the new version supersede the previous version?: No Nature of 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 (ICFs) which are obtained by application of the excitation operators to the reference CAS-SCF wavefunction. The previous formulation of such matrix elements in the MuPAD computer algebra system, has been rewritten using Mathematica. Solution method: 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 ICFs and in the electronic Hamiltonian expressed in the second quantization formalism. Reasons for new version: Some years ago we published in this journal a couple of papers [1, 2] hereafter to be referred to as papers I and II, respectively dedicated to the automated evaluation of the matrix elements of the molecular electronic Hamiltonian between internally contracted functions [3] (ICFs). In paper II the program FRODO (after Formal Reduction Of Density Operators) was presented with the purpose of providing working formulas for each occurrence of the ICFs. The original FRODO program was written in the MuPAD computer algebra system [4] and was actively used in our group for the generation of the matrix elements to be employed in the third-order n -electron valence state perturbation theory (NEVPT) [5–8] as well as in the internally contracted configuration interaction (IC-CI) [9]. We present a new version of the program FRODO written in the Mathematica system [10]. The reason for the rewriting of the program lies in the fact that, on the one hand, MuPAD does not seem to be any longer available as a stand-alone system and, on the other hand, Mathematica, due to its ubiquitousness, appears to be increasingly the computer algebra system most widely used nowadays. Restrictions: The program is limited to no more than doubly excited ICFs. Running time: The examples described in the Readme file take a few seconds to run. References: [1] C. Angeli, R. Cimiraglia, Comp. Phys. Comm. 166 (2005) 53. [2] C. Angeli, R. Cimiraglia, Comp. Phys. Comm. 171 (2005) 63. [3] H.-J. Werner, P. J. Knowles, Adv. Chem. Phys. 89 (1988) 5803. [4] B. Fuchssteiner, W. Oevel: http://www.mupad.de Mupad research group, university of Paderborn. Mupad version 2.5.3 for Linux. [5] C. Angeli, R. Cimiraglia, S. Evangelisti, T. Leininger, J.-P. Malrieu, J. Chem. Phys. 114 (2001) 10252. [6] C. Angeli, R. Cimiraglia, J.-P. Malrieu, J. Chem. Phys. 117 (2002) 9138. [7] C. Angeli, B. Bories, A. Cavallini, R. Cimiraglia, J. Chem. Phys. 124 (2006) 054108. [8] C. Angeli, M. Pastore, R. Cimiraglia, Theor. Chem. Acc. 117 (2007) 743. [9] C. Angeli, R. Cimiraglia, Mol. Phys. in press, DOI:10.1080/00268976.2012.689872 [10] http://www.wolfram.com/Mathematica . Mathematica version 8 for Linux.