We present a real-time second-order Green’s function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of O(Ne3), where Ne is the number of electrons. The cubic scaling is achieved by adopting the stochastic resolution of the identity to decouple the 4-index electron repulsion integrals. To improve the time propagation and the spectral resolution, we adopt the dynamic mode decomposition technique and assess the accuracy and efficiency of the combined approach for a chain of hydrogen dimer molecules of different lengths. We find that the stochastic implementation accurately reproduces the deterministic results for the electronic dynamics and excitation energies. Furthermore, we provide a detailed analysis of the statistical errors, bias, and long-time extrapolation. Overall, the approach offers an efficient route to investigate excited states in extended systems with open or closed boundary conditions.
Bibliographical noteFunding Information:
C.Y., D.R.R., and E.R. are grateful for support from the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research and Office of Basic Energy Sciences, Scientific Discovery through Advanced Computing (SciDAC) program, under award no. DE-SC0022088. Some of the methods used in this work were provided by the “Center for Computational Study of Excited State Phenomena in Energy Materials (C2SEPEM)”, which is funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences, and Engineering Division, via contract no. DE-AC02-05CH11231 as part of the Computational Materials Sciences program. Resources of the National Energy Research Scientific Computing Center (NERSC) and a U.S. Department of Energy Office of Science User Facility operated under contract no. DE-AC02-05CH11231 are also acknowledged. R.B. and E.R. acknowledge support from the US-Israel Binational Science Foundation BSF-201836.
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