Generation of molecular symmetry orbitals for the point and double groups
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. All commonly applied point and double groups are supported by the program including, in addition, the access to their group-theoretical data such as the symmetry operators, characters, or irreducible representations. Program summary Title of program: BETHE Catalogue identifier: ADVU Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADVU Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: none Computer for which the program is designed: All computers with a license of the computer algebra package MAPLE (Maple is a registered trademark of Waterloo Maple Inc.) Installations: University of Kassel (Germany) Operating systems or monitors under which the program has been tested: Linux 8. 1 + and Windows2000 Programming language used: MAPLE 7 and 8 Memory required to execute with typical data: 10-30 MB No. of lines in distributed program, including test data, etc.: 14 190 No. of bytes in distributed program, including test data, etc.: 370 795 Distribution format: tar.gz Nature of the physical 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 and double groups, i.e. for nonrelativistic and relativistic computations. Method of solution: Projection operator techniques are applied to generate the symmetry-adapted orbital functions as a linear combinations of atomic orbitals. Restrictions onto the complexity of the problem: The generation of the symmetry orbitals is supported for the cyclic and related groups C-i, C-s, C-n, C-nh, C-nv, the dihedral groups D-n, D-nh, D-nd, the improper cyclic groups S-2n (n <= 10), the cubic groups 0, T, O-h, T-h, T-d as well as the icosahedral groups I and I-h. In all these cases, the symmetry orbitals can be obtained for either the point-or double groups by using a norrelativistic or, respectively, relativistic framework for the computations. Unusual features of the program: All commands of the BETHE program are available for interactive work. Apart from the symmetry orbitals generation, the program also provides a simple access to the group theoretical data for the presently implemented groups from above. The notation of the symmetry operations and the irreducible representations follows the compilation by Altmann and Herzig [Point-Group Theory Tables, Clarendon Press, Oxford, 1994]. For a quick reference to the program, a description of all user-relevant commands is given in the (user) manual Bethe-cormands ps and is distributed together with the code. Typical running time: Although the program replies 'promptly' on most requests, the running time depends strongly on the particular task. (C) 2005 Elsevier B.V. All rights reserved.
symmetry orbital double group projection operator atomic and molecular orbital point group