Calculation of ionization potential of boron nitride clusters and quantum dots from iterative solution of the Dyson equation

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 stratified stochastic enumeration of molecular orbitals (SSE-MO) method which is designed to overcome this computational bottleneck. The SSE-MO 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 SSE-MO method was applied to investigate the ionization potential of a series of semiconductor boron nitride clusters and quantum dots 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 impact of defect sites on the ionization potential of quantum dots will be presented.