Compact Real-Space Representation of Excited States Using Frequency-Dependent Explicitly Correlated Electron–Hole Interaction Kernel

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. The FD-GSIK is a parameter-free, first-principles method derived from excited-state wave function that was both frequency-dependent and r12-explicitly correlated. The FD-GSIK avoids using unoccupied orbitals for kernel construction by performing an infinite-order summation of particle-hole excitation and representing it as a compact real-space operator. It bypasses the computationally demanding steps of evaluation, storage, and transformation of atomic-orbital integrals by directly evaluating molecular orbital integrals in real space using the stratified Monte Carlo method. We demonstrate and discuss the advantages of this method by presenting excitation and electron–hole binding energies of large nanoparticles including Pb₁₄₀S₁₄₀, Pb₁₄₀Se₁₄₀, Cd₁₄₄Se₁₄₄, and Cd₇₂S₇₂.