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Schröder B, Rauhut G. From the Automated Calculation of Potential Energy Surfaces to Accurate Infrared Spectra. J Phys Chem Lett 2024; 15:3159-3169. [PMID: 38478898 PMCID: PMC10961845 DOI: 10.1021/acs.jpclett.4c00186] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2024] [Revised: 02/20/2024] [Accepted: 02/28/2024] [Indexed: 03/22/2024]
Abstract
Advances in the development of quantum chemical methods and progress in multicore architectures in computer science made the simulation of infrared spectra of isolated molecules competitive with respect to established experimental methods. Although it is mainly the multidimensional potential energy surface that controls the accuracy of these calculations, the subsequent vibrational structure calculations need to be carefully converged in order to yield accurate results. As both aspects need to be considered in a balanced way, we focus on approaches for molecules of up to 12-15 atoms with respect to both parts, which have been automated to some extent so that they can be employed in routine applications. Alternatives to machine learning will be discussed, which appear to be attractive, as long as local regions of the potential energy surface are sufficient. The automatization of these methods is still in its infancy, and the generalization to molecules with large amplitude motions or molecular clusters is far from trivial, but many systems relevant for astrophysical studies are already in reach.
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Affiliation(s)
- Benjamin Schröder
- Institute
of Physical Chemistry, University of Goettingen, Tammannstrasse 6, Göttingen 37077, Germany
| | - Guntram Rauhut
- Institute
for Theoretical Chemistry, University of
Stuttgart, Pfaffenwaldring 55, Stuttgart 70569, Germany
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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.
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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
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Tran HK, Berkelbach TC. Vibrational heat-bath configuration interaction with semistochastic perturbation theory using harmonic oscillator or VSCF modals. J Chem Phys 2023; 159:194101. [PMID: 37965997 PMCID: PMC10653875 DOI: 10.1063/5.0172702] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2023] [Accepted: 10/23/2023] [Indexed: 11/16/2023] Open
Abstract
Vibrational heat-bath configuration interaction (VHCI)-a selected configuration interaction technique for vibrational structure theory-has recently been developed in two independent works [J. H. Fetherolf and T. C. Berkelbach, J. Chem. Phys. 154, 074104 (2021); A. U. Bhatty and K. R. Brorsen, Mol. Phys. 119, e1936250 (2021)], where it was shown to provide accuracy on par with the most accurate vibrational structure methods with a low computational cost. Here, we eliminate the memory bottleneck of the second-order perturbation theory correction using the same (semi)stochastic approach developed previously for electronic structure theory. This allows us to treat, in an unbiased manner, much larger perturbative spaces, which are necessary for high accuracy in large systems. Stochastic errors are easily controlled to be less than 1 cm-1. We also report two other developments: (i) we propose a new heat-bath criterion and an associated exact implicit sorting algorithm for potential energy surfaces expressible as a sum of products of one-dimensional potentials; (ii) we formulate VHCI to use a vibrational self-consistent field (VSCF) reference, as opposed to the harmonic oscillator reference configuration used in previous reports. Our tests are done with quartic and sextic force fields, for which we find that with VSCF, the minor improvements to accuracy are outweighed by the higher computational cost associated the matrix element evaluations. We expect VSCF-based VHCI to be important for more general potential representations, for which the harmonic oscillator basis function integrals are no longer analytic.
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Affiliation(s)
- Henry K. Tran
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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