A low-storage filter-diagonalization method to calculate expectation values of operators non-commutative with the Hamiltonian: Vibrational assignment of HOCl

A method based on the Hellmann–Feynman theorem is proposed for calculating expectation values of operators non-commutative with the system Hamiltonian, Ĥ0. It is applicable in both the low-storage filter-diagonalization (LSFD) and Lanczos methods. Specifically, LSFD is used to determine eigenvalues of Ĥ0 and a perturbed Hamiltonian consisting of Ĥ0 and the non-commutative operator Ĥ′: Ĥλ=Ĥ0+λĤ′. The difference between the two spectra yields the expectation values of Ĥ′ without explicit calculating the eigenstates. For an appropriate choice of Ĥ′, information about vibrational assignments can be obtained. As an example, the vibrational assignment of HOCl and its Fermi resonances are analyzed.