Calculation of ionization potential of semiconductor nanoparticles using machine-learning accelerated construction of the self-energy operator

The self-energy operator in many-electron system contains information about ionization potentials (IPs) and electron-affinities (EAs). In this work, we construct the self-energy operator using ensemble learner and apply ML-driver self-energy operator for determination of ionization energies for a series of PbS, CdS, PbSe and CdSe quantum dots. One of the principle challenges in the construction of self-energy operator is the unfavorable scaling of computational cost with respect to the increasing size of the chemical system. Specifically, the conventional method of constructing requires AO-to-MO transformation of integral (N5 scaling), followed by the construction of 2-particle 1-hole and 1-particle 2-hole components of self-energy (N3 scaling). Consequently, the conventional approach becomes computationally prohibitive for nanoparticles with 300+ heavy atoms with an excess of 5000 basis functions. In this work, we address this computational bottleneck by machine-learning the self-energy operator using a stack of ensemble learner comprising of neural networks and random forests. Specifically, we start with the frequency-domain representation of the self-energy operator and transform it into a real-space 13-dimensional kernel. We then show that the kernel can be factorized into tensor products of low-dimensional irreducible tensors the ensemble learners are used to learn these low-dimensional tensors and which are then used in tandem to construct to full self-energy operator.