Stochastic Resolution of Identity for Real-Time Second-Order Green's Function: Ionization Potential and Quasi-Particle Spectrum

Wenjie Dou; Tyler Y Takeshita; Ming Chen; Roi Baer; Daniel Neuhauser; Eran Rabani

doi:10.1021/acs.jctc.9b00918

Stochastic Resolution of Identity for Real-Time Second-Order Green's Function: Ionization Potential and Quasi-Particle Spectrum

J Chem Theory Comput. 2019 Dec 10;15(12):6703-6711. doi: 10.1021/acs.jctc.9b00918. Epub 2019 Nov 11.

Authors

Wenjie Dou¹, Tyler Y Takeshita², Ming Chen^{1

3}, Roi Baer⁴, Daniel Neuhauser⁵, Eran Rabani^{1

3

6}

Affiliations

¹ Department of Chemistry , University of California Berkeley , Berkeley , California 94720 , United States.
² Mercedes-Benz Research and Development North America , Sunnyvale , California 94085 , United States.
³ Materials Sciences Devision , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States.
⁴ Fritz Haber Research Center for Molecular Dynamics, Institute of Chemistry , The Hebrew University of Jerusalem , Jerusalem 9190401 , Israel.
⁵ Department of Chemistry and Biochemistry , University of California Los Angeles , Los Angeles , California 90095 , United States.
⁶ The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science , Tel Aviv University , Tel Aviv 69978 , Israel.

PMID: 31652067
DOI: 10.1021/acs.jctc.9b00918

Abstract

We develop a stochastic resolution of identity approach to the real-time second-order Green's function (real-time sRI-GF2) theory, extending our recent work for imaginary-time Matsubara Green's function [ Takeshita et al. J. Chem. Phys. 2019 , 151 , 044114 ]. The approach provides a framework to obtain the quasi-particle spectra across a wide range of frequencies and predicts ionization potentials and electron affinities. To assess the accuracy of the real-time sRI-GF2, we study a series of molecules and compare our results to experiments as well as to a many-body perturbation approach based on the GW approximation, where we find that the real-time sRI-GF2 is as accurate as self-consistent GW. The stochastic formulation reduces the formal computatinal scaling from O(N_e⁵) down to O(N_e³) where N_e is the number of electrons. This is illustrated for a chain of hydrogen dimers, where we observe a slightly lower than cubic scaling for systems containing up to N_e ≈ 1000 electrons.