Efficient Linear-Scaling Density Functional Theory for Molecular Systems

Abstract

Despite recent progress in linear scaling (LS) density function theory (DFT), the computational cost of the existing LS methods remains too high for a widespread adoption at present. In this work, we exploit nonorthogonal localized molecular orbitals to develop a series of LS methods for molecular systems with a low computational overhead. High efficiency of the proposed methods is achieved with a new robust two-stage variational procedure or by replacing the optimization altogether with an accurate nonself-consistent approach. We demonstrate that, even for challenging condensed-phase systems, the implemented LS methods are capable of extending the range of accurate DFT simulations to molecular systems that are an order of magnitude larger than those previously treated. Efficient linear-scaling density functional theory for molecular systems Despite recent progress in linear scaling (LS) density function theory (DFT) the computational cost of the existing LS methods remains too high for a widespread adoption at present. In this work, we exploit nonorthogonal localized molecular orbitals to develop a series of LS methods for molecular systems with a low computational overhead. High efficiency of the proposed methods is achieved with a new robust two-stage variational procedure or by replacing the optimization altogether with an accurate non-self-consistent approach. We demonstrate that even for challenging condensed phase systems, the implemented LS methods are capable of extending the range of accurate DFT simulations to molecular systems that are an order of magnitude larger than those treated before.

Efficient O( N ) divide-conquer method with localized single-particle natural orbitals

“…Noting that the computational bottleneck is mainly governed by the eigenvalue problem for the truncated clusters, and that the matrix size can be reduced by introducing LNOs compared to the conventional DC method, one can expect a considerable reduction of the computational cost as the size of the long range region increases. The idea of reducing the matrix dimension by introducing an effective representation of Hamiltonian is similar to that in the O(N ) Krylov subspace method [34] and the absolutely localized molecular orbitals (ALMO) method [23]. By solving the eigenvalue problem…”

Communication: Compact orbitals enable low-cost linear-scaling ab initio molecular dynamics for weakly-interacting systems

“…We would like to note that ALMO AIMD could not be stabilized with ∆ = 0. Neither were we able to find any values of ∆ that stabilize trajectories generated using perturbative versions of ALMO DFT [8].…”

Recent advances in QM/MM free energy calculations using reference potentials

“…In this respect, there have been a number of promising advances in the field to substantially reduce this computational challenge, in most of the cases by using a reformulation of DFT and/or applying localization constraints [13] . Some of these approaches have been shown to scale almost linearly with system size [13,55,56] , thus opening the door towards the application of DFT approaches to larger systems [13–15] . Among these developments, a few examples of note are constrained DFT [55] , where an experimentally or physically motivated constraint is applied to the density during the minimization of the DFT energy functional [57] ; orbital-free DFT [58,59] , which approximates the kinetic energy of non-interacting electrons in terms of their density; and orbital-free embedded DFT, in its different variants, such as those by Goodspaster et al [60] and Wesolowski et al [61] .…”