Sanibel Symposium

Electron-hole or quasiparticle representation plays a central role in describing electronic excitations in many-electron systems. For charge-neutral excitation, the electron-hole interaction kernel is the quantity of interest for calculating important excitation properties such as optical gap, optical spectra, electron-hole recombination and electron-hole binding energies. The electron-hole interaction kernel can be formally derived from the density-density correlation function using both Green’s function and TDDFT formalism. The accurate determination of the electron-hole interaction kernel remains a significant challenge for precise calculations of optical properties in the GW+BSE formalism.

Traditional approaches, such as MBPT formalism, use unoccupied states (which are defined with respect to Fermi vacuum) to construct the electron-hole interaction kernel. However, the inclusion of unoccupied states has long been recognized as the leading computational bottleneck that limits the application of this approach for larger finite systems. In this work, we present an alternative derivation that avoids using unoccupied states to construct the electron-hole interaction kernel. The central idea of our approach is to use explicitly correlated geminal functions for treating electron-electron correlation for both ground and excited state wave functions.

The geminal-screened electron-hole interaction kernel (GSIK) is a real-space representation for describing electron-hole correlation in charge-neutral excitations. The GSIK method avoids using virtual or unoccupied orbitals for constructing the electron-hole interaction kernel by performing a complete infiniteorder diagrammatic summation of a subset of particle-hole excitation. [1] The GSIK method also bypasses the computational expensive AO-to-MO integral transformation step by computing the necessary MO integrals directly in the real-space representation numerically using stratified Monte Carlo method. [2]

These two features allow GSIK method to be used for chemical systems where inclusion of large number of unoccupied orbitals will be computational prohibitive. In this work, the GISK method was applied to large metallic (Au300 and Ag200) and semiconductor (Pb150S150, Cd150Se150) nanoclusters for calculation of excitation energies and electron-hole binding energies. The results from these calculations demonstrate the efficacy of the GSIK method for capturing electron-hole correlation in large clusters and nanoparticles.

References:

[1] Bayne, M.G., Scher, J.A., Ellis, B.H., Chakraborty, A. “Linked-Cluster Formulation of Electron-Hole Interaction Kernel in Real-Space Representation without Using Unoccupied States” (2018) Journal of Chemical Theory and Computation, 14 (7), pp. 3656-3666. DOI:10.1021/acs.jctc.8b00123
[2] Bayne, M.G. and Chakraborty, A. “Development of composite control-variate stratified sampling approach for efficient stochastic calculation of molecular integrals” (2018) https://arxiv.org/abs/1804.01197