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arXiv · 2303.06874

Stochastic Real-Time Second-Order Green's Function Theory for Neutral Excitations in Molecules and Nanostructures

Leopoldo Mejía·Jia Yin·David R. Reichman·Roi Baer·Chao Yang·Eran Rabani
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Abstract

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 $O(N_{\rm e}^3$), where $N_{\rm e}$ 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 (ERI). To improve the time-propagation and the spectral resolution, we adopt the dynamic mode decomposition (DMD) 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.

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Leopoldo Mejía, Jia Yin, David R. Reichman, Roi Baer, Chao Yang, Eran Rabani. 2023-03-13. Stochastic Real-Time Second-Order Green's Function Theory for Neutral Excitations in Molecules and Nanostructures. https://doi.org/10.1021/acs.jctc.3c00296

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