A TRUNCATION RECOUPLING METHOD FOR BASIS SET CALCULATIONS OF EIGENVALUES AND EIGENVECTORS

We describe a new method to truncate and recouple basis functions in general variational calculations based on a direct-product representation of multidimensional wave functions. The method is presented for molecular vibrations; however, the procedure is quite general and can be used in any basis set expansion method. The direct-product Hamiltonian matrix H is decomposed into a block diagonal matrix H(o) plus a remainder H1. A new subset of basis functions is obtained by diagonalizing H(o). This subset of basis functions is shown to be eigenfunctions of a Hamiltonian in a reduced dimensionality space, "dressed" by the remaining degrees of freedom. These dressed eigenfunctions are then augmented by the component of the original direct-product basis in which H(o) is diagonal. The new basis is recoupled using an energy selection criterion, yielding a substantial reduction in the size of the final full Hamiltonian matrix. The method also suggests a generalization of the vibrational self-consistent field method, in which explicit correlation is included in the reduced dimensionality space. An illustrative example of the truncation/recoupling method is given for the vibrational states of HCO, where a major reduction in the order of the Hamiltonian matrix is achieved relative to the conventional direct-product method.