Generation of molecular symmetry orbitals for the point and double groups

Abstract Symmetry-adapted molecular basis functions are widely applied for the electronic structure computations of molecules and clusters. These functions are obtained by exploiting the symmetry of the system and often help to simplify the computations considerably. In order to facilitate their use in algebraic and numerical computations, here we provide a set of Maple procedures which generates these functions by means of projection operators, both within the nonrelativistic and relativistic theory.... Title of program: BETHE Catalogue Id: ADUH_v2_0 [ADVU] Nature of problem Molecular and solid-state quantum computations can be simplified considerably if the symmetry of the systems with respect to the rotation and inversion of the coordinates is taken into account. To exploit such symmetries, however, symmetry-adapted basis functions need to be constructed instead of using -- as usual -- the atomic orbitals as the (one-particle) basis. These so-called symmetry orbitals are invariant with respect to the symmetry operations of the group and are different for the point ... Versions of this program held in the CPC repository in Mendeley Data ADUH_v1_0; BETHE.; 10.1016/j.cpc.2004.06.088 ADUH_v2_0; BETHE; 10.1016/j.cpc.2005.03.112 ADUH_v3_0; BETHE; 10.1016/j.cpc.2006.01.001 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)摘要 对称适配分子基函数（symmetry-adapted molecular basis functions）被广泛应用于分子与团簇的电子结构计算。此类函数通过利用体系的对称性构建，通常可显著简化计算流程。为便于其在代数与数值计算中的应用，本文提供了一套Maple程序集，可通过投影算子（projection operators）生成此类函数，涵盖非相对论与相对论两种理论框架。 程序名称：BETHE 目录编号：ADUH_v2_0 [ADVU] 问题本质 若在分子与固态量子计算中考虑体系对坐标旋转与反演的对称性，可大幅简化计算流程。但要利用此类对称性，需构建对称适配基函数，而非像常规那样以原子轨道作为（单粒子）基组（one-particle basis）。这类被称为对称轨道（symmetry orbitals）的函数在群的对称操作下保持不变，且针对不同点群…… 本程序在Mendeley数据的CPC程序库中的存档版本如下： ADUH_v1_0; BETHE.; 10.1016/j.cpc.2004.06.088 ADUH_v2_0; BETHE; 10.1016/j.cpc.2005.03.112 ADUH_v3_0; BETHE; 10.1016/j.cpc.2006.01.001 本程序源自贝尔法斯特女王大学馆藏的CPC程序库（1969-2018）