Symmetry-adapted polynomial basis for global potential energy surfaces-applications to XY4 molecules

被引:18
作者
Cassam-Chenai, Patrick [1 ]
Patras, Frederic [1 ]
机构
[1] Univ Nice, CNRS, UMR 6621, Lab Math J Dieudonne, F-06108 Nice 2, France
关键词
D O I
10.1007/s10910-008-9354-y
中图分类号
O6 [化学];
学科分类号
0703 ;
摘要
The nuclear potential energy surfaces (PES) used in quantum chemistry inherit the symmetry of the whole molecular system, and are therefore invariant under the action of the nuclear permutation-translation-rotation-inversion group. One can take advantage of this property, both theoretically and numerically. The present article is the prolongation of the works of Schmelzer and Murrell and of Collins and Parsons on the subject. It presents a simplified technique to obtain symmetry-adapted polynomial basis for global PES, together with algorithmic recipes that make the problem computationally tractable. The method is illustrated in detail on XY4 type of molecules for which a full description of the algebra of invariant polynomials under the full symmetry group of the molecule is given.
引用
收藏
页码:938 / 966
页数:29
相关论文
共 14 条
[1]  
Benson D.J., 1993, LONDON MATH SOC LECT, V190
[2]  
Borel A., 1969, LINEAR ALGEBRAIC GRO
[3]  
Burnside W., 1911, Theory of groups of finite order
[4]   INVARIANTS OF FINITE GROUPS GENERATED BY REFLECTIONS [J].
CHEVALLEY, C .
AMERICAN JOURNAL OF MATHEMATICS, 1955, 77 (04) :778-782
[5]   IMPLICATIONS OF ROTATION-INVERSION-PERMUTATION INVARIANCE FOR ANALYTIC MOLECULAR-POTENTIAL ENERGY SURFACES [J].
COLLINS, MA ;
PARSONS, DF .
JOURNAL OF CHEMICAL PHYSICS, 1993, 99 (09) :6756-6772
[6]  
Cox DA, 1996, IDEALS VARIETIES ALG
[7]   COHEN-MACAULAY RINGS, INVARIANT THEORY, AND GENERIC PERFECTION OF DETERMINANTAL LOCI [J].
HOCHSTER, M ;
EAGON, JA .
AMERICAN JOURNAL OF MATHEMATICS, 1971, 93 (04) :1020-&
[8]  
HOCHSTER M, 1974, ADV MATH, V13, P125
[9]   Symmetry, invariants, topology.: Basic tools [J].
Michel, L ;
Zhilinskií, BI .
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 2001, 341 (1-6) :11-84
[10]   THE GENERAL ANALYTIC-EXPRESSION FOR S-4-SYMMETRY-INVARIANT POTENTIAL FUNCTIONS OF TETRA-ATOMIC HOMONUCLEAR MOLECULES [J].
SCHMELZER, A ;
MURRELL, JN .
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, 1985, 28 (02) :287-295