1
|
Houston PL, Qu C, Yu Q, Pandey P, Conte R, Nandi A, Bowman JM. A New A Priori Method to Avoid Calculation of Negligible Hamiltonian Matrix Elements in CI Calculation. J Phys Chem A 2024; 128:479-487. [PMID: 38180902 DOI: 10.1021/acs.jpca.3c06985] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2024]
Abstract
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.
Collapse
Affiliation(s)
- Paul L Houston
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, United States
- Department of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, United States
| | - Chen Qu
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Qi Yu
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Priyanka Pandey
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Riccardo Conte
- Dipartimento di Chimica, Università degli Studi di Milano, via Golgi 19, 20133 Milano, Italy
| | - Apurba Nandi
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Joel M Bowman
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| |
Collapse
|