Construction of Bayesian mixture model for efficient calculation of electron-hole interaction kernel in quantum dots*

This work presents the development and implementation of the Bayesian mixture model for a computationally efficient calculation of electronically excited states in semiconductor quantum dots. In the Bayesian quasiparticle kernel method, the electron-hole interaction kernel is constructed iteratively from real-space sampling of the single-particle states in the quantum dot. For a given particle-hole excitation, the transition density matrix is expressed as a Gaussian Mixture Model and the mixing coefficients are obtained using an iterative Bayesian updating procedure. The quasiparticle kenel was constructed using 2nd-order many-body perturbation theory and was applied for the calculation of exciton binding energies and biexciton binding energies in PbS, CdS, PbSe, and CdSe quantum dots. The quality of the Bayesian quasiparticle kernel was independently tested by comparing the ionization potentials obtained from non-machine-learning based methods for these quantum dots. The results from these calculations highlight the application of Bayesian quasiparticle kernel method as a fast and accurate first-principles method for investigating excited states properties of large chemical systems.