Reduced-Scaling Approach for Configuration Interaction Singles and Time-Dependent Density Functional Theory Calculations Using Hybrid Functionals.

Dávid Mester,Mihály Kállay

doi:10.1021/acs.jctc.8b01199

Abstract

An approximation is presented which can efficiently decrease the computational expenses of configuration interaction singles (CIS) and time-dependent density functional theory (TDDFT) methods employing hybrid functionals. The approach is the adaptation of the local density fitting scheme developed for Hartree-Fock (HF) calculations for excited states and reduces the quartic scaling of the methods to cubic. It can also be applied to related methods, such as the time-dependent HF and Tamm-Dancoff approximation TDDFT approaches. Our benchmark calculations show that, for molecules of 50-100 atoms, average speedups of 2-4 can be achieved for CIS and TDDFT calculations at the expense of negligible errors in the calculated excitation energies and oscillator strengths, but for bigger systems or molecules of localized electronic structure significantly larger speedups can be gained. We also demonstrate that the approximation enables excited-state calculations on a single processor even for molecules of 1000 atoms using basis sets augmented with diffuse functions including more than 17 000 atomic orbitals.

Highlights

In the past decades, the demand for an accurate theoretical description of excited-state properties has been steadily increasing, especially in photochemistry, molecular biology, and spectroscopy
Time-dependent density functional theory (TDDFT), which is derived from density functional theory (DFT) through the linear-response formalism, is the most common choice to investigate time-dependent properties of molecular systems, such as excitation energies, polarizabilities, and chiroptical properties.[1−5] The developed analytical time-dependent density functional theory (TDDFT) gradients enable the efficient calculation of excited-state equilibrium structures and other molecular properties.[6−9] The time-dependent Hartree−Fock (TDHF) method[10] is an analogue of TDDFT where one chooses the Hartree−Fock (HF) solution as the ground-state reference
In this work an efficient scheme has been presented for calculating excitation energies and transition moments at the configuration interaction singles (CIS) and TDDFT levels, as well as for the related TDHF and Tamm−Dancoff approximation (TDA)-TDDFT methods

Summary

Introduction

The demand for an accurate theoretical description of excited-state properties has been steadily increasing, especially in photochemistry, molecular biology, and spectroscopy. Time-dependent density functional theory (TDDFT), which is derived from density functional theory (DFT) through the linear-response formalism, is the most common choice to investigate time-dependent properties of molecular systems, such as excitation energies, polarizabilities, and chiroptical properties.[1−5] The developed analytical TDDFT gradients enable the efficient calculation of excited-state equilibrium structures and other molecular properties.[6−9] The time-dependent Hartree−Fock (TDHF) method[10] is an analogue of TDDFT where one chooses the Hartree−Fock (HF) solution as the ground-state reference It is well-known that TDDFT is generally more accurate despite the similar computational requirements, at least for valence excitations,[11−15] due to the consideration of dynamic electron correlation. In the corresponding calculations for extended systems, the time spent on the initial canonical CIS calculation, due to the effective approximations for the correlated model, is significant compared to the overall computation time

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