An alternative formulation of vibrational heat-bath configuration interaction

Abstract

Recently, a selected vibrational configuration interaction method was introduced where the selection of the vibrational basis was performed using the heat-bath algorithm (VHCI). This method was adapted from the heat-bath configuration interaction (HCI) method used to solve the electronic Schrödinger equation. The selection algorithm in electronic HCI exploits the fact that most nonzero Hamiltonian matrix elements correspond to a double electronic excitation from one determinant to another and have values equal to the two-electron molecular orbital integrals such that they can be computed once, sorted, stored, and easily accessed later using a dictionary data structure. However, the Hamiltonian matrix elements in VHCI are more complicated than their electronic HCI counterparts, which lead to the possibility of different VHCI implementations. We explore one such implementation. The most significant differences compared to the original VHCI implementation is that we (i) explicitly compute all one- and two-quanta excitations, (ii) include all occupation-number contributions to the Hamiltonian matrix elements, and (iii) add individual Hartree product basis functions to the variational space rather than multiple basis functions as determined by operator products. We apply the new VHCI algorithm to ethylene oxide and naphthalene and achieve good accuracy relative to previous results at a modest computational cost.