Acceleration of self-consistent-field convergence in ab initio molecular dynamics and Monte Carlo simulations and geometry optimization

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Abstract

We propose a novel acceleration method for self-consistent-field calculations in direct ab initio molecular dynamics/Monte Carlo (AIMD/AIMC) simulations and geometry optimization. This acceleration method, so-called LSMO, predicts an initial guess of molecular orbitals (MOs) for the next simulation step by using the geometric information with the least-squares technique. Numerical tests confirm that the LSMO method is both effective and feasible in the AIMD/AIMC simulations and geometry optimization.

Graphical abstract

We propose a novel acceleration method for self-consistent-field (SCF) calculations in direct ab initio molecular dynamics/Monte Carlo (AIMD/AIMC) simulations and geometry optimization. This acceleration method, which is called LSMO, predicts an initial guess of the SCF by using the geometric information with the least-squares technique. Numerical tests confirm the effectiveness and feasibility of the LSMO method.

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Introduction

Molecular simulations based on molecular dynamics (MD) and Monte Carlo (MC) methods are useful tools to study various processes in complex systems. Since Car and Parrinello proposed a combination between the first principle electronic structure calculation and the MD simulation [1], the method of ab initio MD (AIMD) has become popular [2]. One of the advantages of the AIMD method is the capability for reproducing dynamical processes of chemical reactions following covalent bond breaking and/or forming because ab initio molecular orbital (MO) or density functional theory (DFT) calculations performed ‘on the fly’ ensure reliable Born–Oppenheimer (BO) potential energies and atomic forces even in the bond breaking region. Similarly, the ab initio MC (AIMC) method [3] has been widely used for surveying free energy surfaces under the canonical ensemble.

In the AIMD and AIMC simulations, the practical methods for the electronic structure calculations are commonly limited to the Hartree–Fock (HF) and Kohn–Sham (KS) DFT methods because the highly correlated methods such as the second-order Møller–Plesset perturbation theory (MP2) and the coupled cluster with singles and doubles (CCSD) require high cost of computation even for single-point calculation of a complex system. The AIMD/AIMC simulations with the HF/DFT methods still need high expense in comparison with the classical MD/MC ones. A major bottleneck is the self-consistent-field (SCF) procedure. So far, various efforts [4], [5], [6], [7], [8], [9], [10], [11], [12], [13] have been carried out for accelerating the SCF convergence. One of the famous techniques for the rapid SCF convergence is a direct inversion in the iterative subspace (DIIS) method [6], [8], which extrapolates the Fock matrix in the SCF process.

In a previous study [14], we have developed an acceleration technique for the SCF convergence which is specific to the AIMD simulations. This method predicts the initial guess of the MOs at the next MD step by a linear combination of the converged MOs at previous MD steps. The linear combination coefficients are determined by the Lagrange interpolation (LI) technique [15] with the information of the physical time of the MD simulations. Thus, it is named LIMO. However, the LIMO technique cannot be applied to the AIMC simulations straightforwardly for the lack of the time information. Therefore, the present study aims to develop an alternative technique which is applicable to AIMC. The method uses the geometric information instead of the time and determines the linear combination coefficients of MOs by the least-squares (LS) method as seen in DIIS. Thus, it is named LSMO.

The construction of this Letter is as follows: Theoretical backgrounds, namely the LIMO and DIIS methods, are briefly summarized in Section 2, and the new LSMO technique is explained. Section 3 demonstrates the computational method (3.1) and numerical applications to AIMD (3.2), AIMC (3.3), and geometry optimization (3.4). The conclusion is presented in Section 4.

Section snippets

LIMO

The basic idea of LIMO is that an effective initial guess of MOs (or KS orbitals) at the (n + 1)th step in an AIMD simulation, Cprd(n+1), is constructed by a linear combination of several converged MOs up to the nth step, Ccnv(n-i) (i = 0, 1, 2, …), as follows:Cprd(n+1)=iciCcnv(n-i)TpSCF(n-i)(n),where symbols {ci} (i = 0, 1, 2, …) denote the coefficients of linear combination. Since the HF manifold as well as the KS density is defined only by occupied orbitals, Cprd(n+1) and Ccnv(n-i) have a dimension of

Computational method

This section describes numerical applications of the LSMO method to AIMD/AIMC simulations and a geometry optimization. The LSMO method was implemented into the original MD/MC program. Ab initio calculations for computing BO potential energies and atomic forces were carried out using the Gaussian03 suite of programs [16]. Test systems for the AIMD/AIMC simulations were methanol (CH3OH), benzene (C6H6), water clusters [(H2O)4, (H2O)4+, and (H2O)14], 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) (C6H

Conclusion

We have proposed in this study an alternative method for predicting initial guesses for the SCF calculations in the AIMD/AIMC simulations and geometry optimization. The present method, called LSMO, is based on the idea of our previous LIMO method [14], which expresses the initial guess of MOs at the next step in an AIMD simulation by a linear combination of previous converged MOs. Since the time information was required for determining the linear combination coefficients, the LIMO method was

Acknowledgments

Part of the present calculations were performed at the Research Center for Computational Science (RCCS), Okazaki Research Facilities, and National Institutes of Natural Sciences (NINS). This study was supported in part by a Grant-in-Aid for Scientific Research on Priority Areas ‘Molecular Theory for Real Systems’ KAKENHI 18066016 from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan; by the Nanoscience Program in the Next Generation Super Computing Project of the

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