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

Abstract
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.

Title of program: FRODO
Catalogue Id: ADVY_v2_0

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 (ICF) 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.

Versions of this program held in the CPC repository in Mendeley Data
ADVY_v1_0; FRODO; 10.1016/j.cpc.2005.05.002
ADVY_v2_0; FRODO; 10.1016/j.cpc.2012.09.034

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

**摘要**
一款用于实现密度算子形式约化（Formal Reduction of Density Operators, FRODO）的符号化程序，最初基于MuPAD计算机代数系统开发，旨在计算完整活性空间（Complete Active Space, CAS）框架下内部收缩函数间电子哈密顿量的矩阵元，现已基于Mathematica完成重写。

程序名称：FRODO
目录编号：ADVY_v2_0

**问题本质**
若需优化完整活性空间自洽场（Complete Active Space Self-Consistent Field, CAS-SCF）波函数，可采用多参考微扰理论，或基于内部收缩函数（Internally Contracted Functions, ICF）的组态相互作用方法；其中内部收缩函数通过激发算子作用于参考CAS-SCF波函数生成。此前基于MuPAD计算机代数系统实现的此类矩阵元计算框架，现已基于Mathematica完成重写。

**Mendeley数据中CPC程序库收录的本程序版本**
ADVY_v1_0；FRODO；10.1016/j.cpc.2005.05.002
ADVY_v2_0；FRODO；10.1016/j.cpc.2012.09.034

本程序源自贝尔法斯特女王大学馆藏的CPC程序库（1969-2018）。