Open AccessComparison of Many-Particle Representations for Selected Configuration Interaction: II. Numerical Benchmark Calculations
Author(s) -
Vijay Gopal Chilkuri,
Frank Neese
Publication year - 2021
Publication title -
journal of chemical theory and computation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.001
H-Index - 185
eISSN - 1549-9626
pISSN - 1549-9618
DOI - 10.1021/acs.jctc.1c00081
Subject(s) - extrapolation , benchmark (surveying) , wave function , slater determinant , configuration interaction , set (abstract data type) , convergence (economics) , limit (mathematics) , computer science , function (biology) , ground state , statistical physics , full configuration interaction , physics , mathematics , quantum mechanics , atomic orbital , statistics , electron , mathematical analysis , molecule , biology , geography , geodesy , evolutionary biology , economic growth , economics , programming language
The present work is the second part in our three-part series on the comparison of many-particle representations for the selected configuration interaction (CI) method. In this work, we present benchmark calculations based on our selected CI program called the iterative configuration expansion (ICE) that is inspired by the CIPSI method of Malrieu and co-workers (Malrieu J. Chem. Phys. 1973, 58, (12), 5745-5759). We describe the main parameters that enter in this algorithm and perform benchmark calculations on a set of 21 small molecules and compare ground state energies with full configuration interaction (FCI) results (FCI21 test set). The focus is the comparison of the performance of three different types of many-particle basis functions (MPBFs): (1) individual Slater determinants (DETS), (2) individual spin-adapted configuration state functions (CSFs), and (3) all CSFs of a given total spin that can be generated from spatial configurations (CFGs). An analysis of the cost of the calculation in terms of the number of wavefunction parameters and the energy error is evaluated for the DET-, CFG-, and CSF-based ICE. The main differences for the three many-particle basis representations show up in the number of wavefunction parameters and the rate of convergence toward the FCI limit with the thresholds of the ICE. Next, we analyze the best way to extrapolate the ICE energies toward the FCI results as a function of the thresholds. The efficiency of the extrapolation is investigated relative to the FCI21 test set as well as near FCI calculations on three moderately sized hydrocarbon molecules CH 4 , C 2 H 4 , and C 4 H 6 . Finally, we comment on the size-inconsistency error for the three many-particle representations and compare it with the error in the total energy. The implication for selected CI implementations with any of the three many-particle representations is discussed.