Development and Efficient Implementation of Electron-Hole Interaction Kernel for Investigation of Electronic Excitations in Semiconductor and Metallic Nanoparticles
The focus of this work is to construct theoretical methods or approaches to tackle computationally challenging problems in quantum chemistry. The primary topic of the work will focus on efficient theories that allow for capturing electron-correlation in semiconductor or metallic nanoparticles. These systems are computationally challenging due to the size of the systems, the number of electrons per atom, and the degeneracy of the particle-hole states. Three methods presented here are aimed at providing novel theoretical methods towards computationally inexpensive electronic excited state calculations. The frequency-dependent geminal-screened electron-hole interaction kernel (FD-GSIK) method provides a real-space approach towards eliminating the virtual space reducing the computational effort present in most excited state methods. Dressed molecular orbital basis is presented to compress the configuration space in metallic nanoparticles, resulting in a cheap multi-reference approach to obtaining electron-correlation. Finally, the moment generated molecular orbital basis is derived to provide an alternative approach that utilizes moments of the reference function to decouple particle and hole states. A secondary focus within this work is to provide efficient Monte Carlo sampling techniques for modeling and integration. Monte Carlo provides an efficient pathway to sampling experimental models and evaluation of complicated integrals which are normally computationally costly. The theoretical developments presented in this work allow for understanding theoretical properties in semiconductor or metallic nanoparticles which normally would be computationally prohibited
