A NEW GRID-BASED METHOD FOR THE DIRECT COMPUTATION OF EXCITED MOLECULAR VIBRATIONAL-STATES - TEST APPLICATION TO FORMALDEHYDE

A new method is presented for the direct computation of excited vibrational energy levels of molecules. The method combines the advantages of grid-based approaches to molecular dynamics problems with those of the Davidson diagonalization technique, which has found widespread usage in molecular electronic structure theory. It permits the direct computation of a prespecified vibrational state without the need to compute all lower lying levels. The wavefunctions used in the present test applications are extremely accurate and are the vibrational analogues of ''full configuration interaction (CI)'' wavefunctions in electronic structure theory. The method is applicable to large problems in that it requires the storage of only a few vectors, between six and eleven in the examples given, and no large matrices need to be retained. The theory of the new method is presented, first for the case of a single degree of vibrational freedom and then for the general case. Test results are given both for a diatomic model system and for a realistic ab initio potential energy surface computed for the formaldehyde molecule. The method is expected to provide a starting point for the development of future techniques for computing highly accurate vibrational wavefunctions for much larger molecules, As with all grid-based methods, no matrix elements of the potential need to be evaluated. The value of the potential is required only at the grid points of the multidimensional grid in coordinate space.