Effective Hamiltonian Theory and Molecular Dynamics

Abstract

The theory of effective Hamiltonians was developed within nuclear physics in the 1960s by Bloch (I) and Des Cloizeaux (2) as a method for determining the effective interactions between nucleons. Subsequently it was adapted to quantum chemistry (3, 4a,b) and used to overcome some limitations of both ab initio and semiempirical methods (5, 6). A more recent application of the theory is in molecular dynamics, where the basic processes studied are full collisions, in which energy transfers and structural modifications appear between molecular bound states and molecular continua (7), and half colli­ sions, in which one participating continuum is a photon continuum and the other one is an ionization or dissociation continuum (7a). Most of the recent theoretical treatments of collisions discretize the molecular continua by adding absorbing spatial boundaries and by working with a bounded range of radial coordinates in conjunction with finite basis sets of square integrable functions. Wave packet propagation methods have often been used to integrate these systems by using discrete representations (8). Because the required computer processor unit CPU time rapidly becomes prohibitively long when wave packets are propagated on multidimensional grids, new attempts have been made to derive time-independent treatments from the time-dependent ones. A solution within the framework of the Floquet theory