A truncation/recoupling method for basis set calculations of eigenvalues and eigenvectors

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Abstract
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 H0 plus a remainder H1. A new subset of basis functions is obtained by diagonalizing H0. 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 d r e s s e d e i g e n f u n c t i o n s are then augmented by the component of the original direct‐product basis in which H0 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.