Stochastic Real-Time Second-Order Green's Function Theory for Neutral Excitations in Molecules and Nanostructures
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.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2023
- DOI:
- 10.48550/arXiv.2303.06874
- arXiv:
- arXiv:2303.06874
- Bibcode:
- 2023arXiv230306874M
- Keywords:
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- Physics - Chemical Physics
- E-Print:
- J. Chem. Theory Comput. 2023, 19, 16, 5563-5571