Investigation of Ionization Potential in Quantum Dots Using the Stratified Stochastic Enumeration of Molecular Orbitals Method.

The overarching goal of this work is to investigate the size-dependent characteristics of the ionization potential of PbS and CdS quantum dots. The ionization potentials of quantum dots provide critical information about the energies of occupied states, which can then be used to quantify the electron-removal characteristics of quantum dots. The energy of the highest-occupied molecular orbital is used to understand electron-transfer processes when invesigating the energy-level alignment between quantum dots and electron-accepting ligands. Ionization potential is also important for investigating and interpreting electron-detachment processes induced by light (photoelectron spectra), external voltage (chemiresistance), and collision with other electrons (impact ionization). Accurate first-principles calculations of ionization potential continue to be challenging because of the computational cost associated with the construction of the frequency-dependent self-energy operator and the numerical solution of the associated Dyson equation. The computational cost becomes prohibitive as the system size increases because of the large number of 2particle-1hole (2p1h) and 1particle-2hole (1p2h) terms needed for the calculation. In this work, we present the Stratified Stochastic Enumeration of Molecular Orbitals (SSE-MO) method for efficient construction of the self-energy operator. The SSE-MO method is a real-space method and the central strategy of this method is to use stochastically enumerated sampling of molecular orbitals and molecular-orbital indices for the construction of the 2p1h and 1p2h terms. This is achieved by first constructing a composite MO-index Cartesian coordinate space followed by transformation of the frequency-dependent self-energy operator to this composite space. The evaluation of both the real and imaginary components of the self-energy operator is performed using a stratified Monte Carlo technique. The SSE-MO method was used to calculate the ionization potentials and the frequency-dependent spectral functions for a series of PbS and CdS quantum dots by solving the Dyson equation using both single-shot and iterative procedures. The ionization potentials for both PbS and CdS quantum dots were found to decrease with increasing dot size. Analysis of the frequency-dependent spectral functions revealed that for PbS quantum dots the intermediate dot size exhibited a longer relative lifetime whereas in CdS the smallest dot size had the longest relative lifetime. The results from these calculations demonstrate the efficacy of the SSE-MO method for calculating accurate ionization potentials and spectral functions of chemical systems.

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.