Quantum-Mechanical Description of Rigidly or Adiabatically Constrained Molecular Systems

Whereas model constraints (namely, internal degrees of freedom either frozen or stepwise adjusted by gradient methods) are often imposed for calculating the potential energies of polyatomic molecules by quantum-chemical methods, the derivation of exact expressions for the corresponding kinetic energy operators is difficult because of the changes of metrics of the configuration spaces, which modify the differential operators but not the multiplicative operators. An appropriate method for overcoming this difficulty has been designed in the case of rigid constraints (e.g., frozen groups) (M. Menou and X. Chapuisat,J. Mol. Spectrosc.159,300–328, 1993). In this article, it is generalized to the case of adiabatic constraints; i.e., the variations of certain internal degrees of freedom are adjusted to those of other degrees of freedom. Exact kinetic energy operators are derived. An example is analyzed.