The calculation of vibrational eigenstates by MINRES filter diagonalization

A spectral filtering method reported recently [Faraday Disc. 102, 17 (1996)], which utilizes the optimal expansion of the Green operator in a finite Lanczos subspace, is used to construct a new scheme for the calculation of bound vibrational stales by filler diagonalization. The method requires storage of only two real vectors in the primary representation, i.e., those required to generate the Lanczos subspace. Calculations for the HO2 molecule show that the new scheme efficiently generates converged eigenvalues within a nominated energy window which may be scanned through the bound spectrum, and utilizes just a single Lanczos subspace (generated once only). It not only is more efficient than the regular Lanczos algorithm for computing high-lying eigenstates, but also has the interesting property of eliminating duplicated and ghost eigenvalues, which can cause problems in interpretation of the regular Lanczos spectrum.