Real-space approach to the calculation for ionization potentials, exciton, and biexciton binding energies in quantum dots using explictly-correlated electron-hole interaction kernel method

Inclusion of unoccupied states is the leading computational bottleneck for calculation of excited states for large chemical systems. In this work, we present the geminal-screened electron-hole interaction kernel (GSIK) method to address this problem. The GSIK is a real-space r12 method that avoids unoccupied orbitals for constructing the electron-hole interaction kernel by performing an infinite-order diagrammatic summation of particle-hole excitations and deriving a renormalized real-space electron-hole correlator operator. The GSIK method also bypasses the computational expensive AO-to-MO integral transformation by computing all integrals directly in the real-space numerically using permutation sampling Monte Carlo method. These two features allow GSIK method to be used for chemical systems where inclusion of a large number of unoccupied orbitals will be computationally prohibitive. In this work, the GISK method was applied to investigate exciton binding energies, biexciton binding energies, and ionization potentials for large semiconductor (Pb₁₄₀S₁₄₀, Pb₁₄₀Se₁₄₀, Cd₁₄₄Se₁₄₄) nanoparticles. The results from these calculations demonstrate the efficacy of the GSIK method for capturing electron-hole correlation in large clusters and nanoparticles.