The Dyson equation provides a systematic route for obtaining poles of the 1-particle Green’s function and calculating the ionization potential of chemical systems. The frequency-dependent self-energy operator in the Dyson equation contains all the necessary information about electron-correlation. However, even in its simplest form, the self-energy operator depends on 2particle-1hole (2p1h) and 1particle-2hole (1p2h) components and is computationally expensive to construct. In this work, we present the development of the stochastically enumerated stratified sampling of molecular orbitals (SESSMO) method which is designed to overcome this computational bottleneck. The SESSMO method approximates the exact self-energy operator by a stochastic self-energy operator which is constructed from sampling the 2p1h and 1p2h space. The stratified sampling is implemented to systematically identify and include high-contributing terms from the 2ph1 and 1p2h space. The SESSMO method avoids AO-to-MO integral transformation of the 2-electron integrals and calculates them directly in the MO space using real-space Monte Carlo integration. Because of the low-scaling property of SESSMO, it can be applied to obtain the entire frequency spectrum of the 1-particle Green’s function. The SESSMO method was applied to investigate the ionization potential of a series of semiconductor quantum dots Pb140S140, Pb140Se140, Cd72S72, Cd144Se144 and was used to construct the self-energy operator from a sample space of 109 2ph1 terms. A discussion on the effect of nanoparticle size, presence of surface ligands, and distortion of molecular structures on the ionization potential of quantum dots will be presented.

Development of stochastically enumerated stratified sampling of molecular orbitals for iterative solution of the Dyson equation

ACS Spring 2022

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