VIBRATIONAL-ENERGY LEVELS OF FORMALDEHYDE CALCULATED FROM AN INTERNAL COORDINATE HAMILTONIAN USING THE LANCZOS-ALGORITHM

By choosing the discrete points associated with basis functions which compactly represent vibrational wavefunctions, but yield a sparse Hamiltonian matrix with a well-defined, easily exploitable structure, we are able to apply Lanczos' algorithm efficiently to compute the lowest eigenvalues of variational matrices as large as 1000000 x 1000000 to obtain many vibrational states. We use an exact kinetic energy operator in bond angle-bond length coordinates to calculate energy levels of formaldehyde.