Quantum-Mechanical Hamiltonians for Constrained Systems: Application to Four-Body Systems

✍ Scribed by M. Menou; X. Chapuisat

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 1001 KB
• Volume: 159
• Category: Article
• ISSN: 0022-2852
• DOI: 10.1006/jmsp.1993.1129

✦ Synopsis

Whereas model constraints (e.g., frozen bonds, fixed bending or torsonial angles, rigid atomic groups, etc.) are often imposed in calculations of the potential energies of polyatomic molecules by quantum-chemical methods. the derivation of exact expressions for the corresponding kinetic energy operators is generally difficult. This is because of the changes in the metrics of the configuration spaces, which modify the differential operators but not the local operators. An appropriate method for overcoming this difficulty is presented, and examples for four-atom molecules and various coordinate systems are given. The coplanar-atom constraint deserves special attention, because the problem can be formulated either in (\mathbb{R}^{2}) (i.c., the molecule lies in the space-fixed plane) or in (\mathbb{P}^{3}) (i.e., the molecule is planar, but the plane, which is body-fixed. rotates with respect to the space-fixed frame). Other types of constraints are also examined. w1993 Academic Press, Inc.