Comparison of Many-Particle Representations for Selected Configuration Interaction: II. Numerical Benchmark Calculations

Vijay Gopal Chilkuri,Frank Neese

doi:10.1021/acs.jctc.1c00081

Abstract

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 (MalrieuJ. 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 CH4, C2H4, and C4H6. 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.

Highlights

The selected configuration interaction method has recently seen a resurgence and has established itself as a powerful tool for quantum chemistry as evidenced by various recent studies.[1−11] As the use of sCI methods becomes more widespread, the need for a thorough understanding of various characteristics of sCI methods such as convergence thresholds, extrapolation techniques, and error bars, becomes increasingly important
There have been attempts toward a thorough benchmark of sCI methods by various groups recently, such as the benchmarking of the Gaussian-2 set using semistochastic heat-bath configuration interaction[12] (SHCI) by Yao et al.[13]. Stochastic methods such as the full configuration interaction quantum Monte Carlo (FCIQMC) method pioneered by Alavi and co-workers have their own standardized algorithms for benchmarking and extrapolation, which depends on the type of FCIQMC algorithm used.[14−17] Another such effort is illustrated by the recent work of the adaptive sampling CI by Tubman et al.[16,18]
The accuracy of the iterative configuration expansion (ICE) algorithm for DETs, CFGs, and configuration state functions (CSFs) is performed by comparison of the molecules in the FCI21 set with the FCI energy

Summary

Introduction

The selected configuration interaction (sCI) method has recently seen a resurgence and has established itself as a powerful tool for quantum chemistry as evidenced by various recent studies.[1−11] As the use of sCI methods becomes more widespread, the need for a thorough understanding of various characteristics of sCI methods such as convergence thresholds, extrapolation techniques, and error bars, becomes increasingly important. Recent collaborative initiatives on comparing various approaches together with sCI have appeared.[20,21]

Methods

Results

Conclusion