MOLECULAR HAMILTONIANS FOR HIGHLY CONSTRAINED MODEL SYSTEMS

We describe a simple approach for constructing the molecular Hamiltonian which is ideal for studying large molecular systems in which many constraints are imposed. The present procedure allows one to evaluate the correct classical G matrix for highly constrained model systems in the absence of total angular momentum, using matrices that are no larger than the number of active vibrations in the model. A straightforward prescription for constructing the appropriate quantum kinetic energy operator for these systems is then introduced. This prescription is a modification of the Podolsky procedure and it allows one to incorporate constraints in the quantum operators without the extensive use of differential calculus. Finally, the extension of the constrained system Hamiltonian to nonzero total angular momentum is made and methods for reducing the effective Hamiltonian to the minimum number of degrees of freedom using the Augustin-Miller canonical transformation are described. The present approach is illustrated with several molecular examples including arbitrary bent equilibrium triatomic molecules, weakly bound van der Waals complexes, and large molecules with low frequency, large amplitude vibrations.