Noniterative Doubles Corrections to the Random Phase and Higher Random Phase Approximations: Singlet and Triplet Excitation Energies.

Pi A B Haase,Stephan P A Sauer,Rasmus Faber,Patricio F Provasi

doi:10.1002/jcc.26074

Abstract

The second‐order noniterative doubles‐corrected random phase approximation (RPA) method has been extended to triplet excitation energies and the doubles‐corrected higher RPA method as well as a shifted version for calculating singlet and triplet excitation energies are presented here for the first time. A benchmark set consisting of 20 molecules with a total of 117 singlet and 71 triplet excited states has been used to test the performance of the new methods by comparison with previous results obtained with the second‐order polarization propagator approximation (SOPPA) and the third order approximate coupled cluster singles, doubles and triples model CC3. In general, the second‐order doubles corrections to RPA and HRPA significantly reduce both the mean deviation as well as the standard deviation of the errors compared to the CC3 results. The accuracy of the new methods approaches the accuracy of the SOPPA method while using only 10–60% of the calculation time. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

Highlights

A powerful tool for studying excited states in molecules is the polarization propagator known as the linear response function.[1,2] The polarization propagator describes how a system responds to a time-dependent perturbation and is used for calculating both excitation energies and various response properties
0 0 −1 correction should improve the higher RPA method (HRPA)(D) excitation energies, the results presented in this study show that the systematic underestimation of HRPA(D) energies is eliminated upon inclusion of the correction in eq (31)
The performance of the two new methods, HRPA(D) and s-HRPA(D), for determining singlet excitation energies will be compared to the well-known methods random phase approximation (RPA), RPA(D), HRPA, and second-order polarization propagator approximation (SOPPA)

Summary

Introduction

A powerful tool for studying excited states in molecules is the polarization propagator known as the linear response function.[1,2] The polarization propagator describes how a system responds to a time-dependent perturbation and is used for calculating both excitation energies and various response properties. An alternative strategy is to define appropriate approximations to the polarization propagator in a consistent manner with the aid of Møller–Plesset perturbation theory by evaluating the propagator with respect to the order in the fluctuation potential to which the propagator, excitation energies, and transition moments are correct This allows for the construction of a hierarchy with respect to accuracy, similar to that of the CC-based methods. In the HRPA method, second-order contributions to the A, B, and S matrices are included.[19,20] This is equivalent to letting h1 again span the excitation operator manifold, employing the second-order Møller–Plesset wave function as reference state and keeping only terms through second order in the fluctuation potential in the E and S matrices. Sf0g ωfj 0gSf1g Rfj 0g ð19Þ where Rðj 0Þ is the RPA eigenvector augmented with a doubleexcitation part wherein all elements are zero: Rfj 0g

CCCCA: ð20Þ

Benchmark Results

Conclusions