We develop a time-dependent second-order Green's function theory (GF2) for calculating neutral excited states in molecules. The equation of motion for the lesser Green's function (GF) is derived within the adiabatic approximation to the Kadanoff-Baym (KB) equation, using the second-order Born approximation for the self-energy. In the linear response regime, we recast the time-dependent KB equation into a Bethe-Salpeter-like equation (GF2-BSE), with a kernel approximated by the second-order Coulomb self-energy. We then apply our GF2-BSE to a set of molecules and atoms and find that GF2-BSE is superior to configuration interaction with singles (CIS) and/or time-dependent Hartree-Fock (TDHF), particularly for charge-transfer excitations, and is comparable to CIS with perturbative doubles (CIS(D)) in most cases.
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We would like to thank Yang-Hao Chen, Daniel Neuhauser, Vojtech Vlcek for helpful discussions. R.B. gratefully acknowledges support from the U.S.–Israel Binational Science Foundation (No. BSF-201836). E.R. and D.R.R. are grateful for support by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing (SciDAC) program, under Award No. DE-SC0022088. The stochastic 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), 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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