First principle excited state calculations using a frequency–dependent geminal–screened electron-hole interaction kernel

A primary computational limitation for excited state methods is the inclusion of virtual or unoccupied states in the calculations. The inclusion of these states increases the calculation cost for excited state calculations. We present the frequency–dependent geminal–screened electron–hole interaction kernel (FD–GSIK) method for describing electron–hole correlation in electronically excited many–electron systems. FD–GSIK avoids using unoccupied orbitals for kernel construction by performing infinite–order summation of particle–hole excitation and representing it as a compact real–space operator. The central idea of our approach is to use Löwdin partitioning technique to construct a frequency–dependent and r12–explicitly correlated operator for treating electron–hole correlation for the excited state wave function that is derived from first principles and is parameter–free. Evaluation of all integrals were performed in real space using stratified Monte Carlo, which avoided the steep computational cost of evaluation, storage and transformation of the atomic orbitals to molecular orbitals. The FD–GSIK was applied to large nanoparticles including Pb₁₄₀S₁₄₀, Pb₁₄₀Se₁₄₀, and Cd₁₄₄Se₁₄₄, to obtain excitation and electron–hole binding energies.