A New A Priori Method to Avoid Calculation of Negligible Hamiltonian Matrix Elements in CI Calculation

Hamiltonian matrices typically contain many elements that are negligibly small compared to the diagonal elements, even with methods to prune the underlying basis. Because for general potentials the calculation of H-matrix elements is a major part of the computational effort to obtain eigenvalues and eigenfunctions of the Hamiltonian, there is strong motivation to investigate locating these negligible elements without calculating them or at least avoid calculating them. We recently demonstrated an effective means to "learn" negligible elements using machine learning classification (J. Chem. Phys. 2023, 159, 071101). Here we present a simple, new method to avoid calculating them by using a cut-off value for the absolute difference in the quantum numbers for the bra and ket. This method is demonstrated for many of the same case studies as were used in the paper above, namely for realistic H-matrices of H₂O, the vinyl radical, C₂H₃, and glycine, C₂H₅NO₂. The new method is compared to the recently reported machine learning approach. In addition, we point out an important synergy between the two methods.