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(Ne5) down to O(Ne3) where Ne 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 Ne ≈ 1000 electrons.
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We have developed a stochastic resolution of identity approach to describe real-time/real-frequency spectral functions of extended systems within the second-order Green’s function formalism. The real-time approach provides a platform to compute the ionization potentials and electron affinities for open as well as periodic boundary conditions. Such an approach can also be used to generate the full-frequency quasi-particle spectral function at the same computational cost. The advantage of the stochastic formalism is that it reduces the computational scaling of the real-time sRI-GF2 from O ( N e 5 ) to O ( N e 3 ), as illustrated for a chain of hydrogen dimers. This reduced scaling opens the door to study quasi-particle excitations in extended systems within the framework of second-order Green’s function. To access the approach, we benchmarked our real-time sRI-GF2 scheme against a many-body perturbation technique within the GW approximation as well as compared the calculated ionization potentials to experimental results. We find that the sRI-GF2 results are comparable to the state-of-the-art self-consistent GW approach for a set of atoms and small molecules. While GF2 lacks the sort of screening present in the GW approximation, GF2 does include exchange effects in the self-energy, which turn out to be significant in describing the quasi-particle spectrum of molecules. R.B. gratefully acknowledges support from the Israel Science Foundation, Grant No. 800/19. D.N. and E.R. are grateful for support by the Center for Computational Study of Excited State Phenomena in Energy Materials (C2SEPEM) at the Lawrence Berkeley National Laboratory, which is funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division under Contract No. DEAC02-05CH11231 as part of the Computational Materials Sciences Program. The authors declare no competing financial interest.
R.B. gratefully acknowledges support from the Israel Science Foundation, Grant No. 800/19. D.N. and E.R. are grateful for support by the Center for Computational Study of Excited State Phenomena in Energy Materials (C2SEPEM) at the Lawrence Berkeley National Laboratory, which is funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences Materials Sciences and Engineering Division under Contract No. DEAC02-05CH11231 as part of the Computational Materials Sciences Program.
We would like to thank Felipe H. da Jornada and Steven G. Louie for helpful discussion. Resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility operated under Contract No. DE-AC02-05CH11231, are greatly acknowledged.
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