The particle-hole map: formal derivation and numerical implementation

TL;DR

The paper introduces the particle-hole map (PHM), a visualization tool for electronic excitations that offers a probabilistic interpretation of electron and hole movements, derived formally from transition density matrices and implemented with localized basis sets.

Contribution

It provides a formal derivation of the PHM from the particle-hole transition density matrix and demonstrates its numerical implementation for molecular charge-transfer complexes.

Findings

PHM offers clear visualization of electron-hole dynamics.

Implementation with localized basis sets is effective.

Application to charge-transfer complex illustrates utility.

Abstract

The particle-hole map (PHM) is a tool to visualize electronic excitations, based on representations in a canonical orbital transition space. Introduced as an alternative to the transition density matrix, the PHM has a simple probabilistic interpretation, indicating the origins and destinations of electrons and holes and, hence, the roles of different functional units of molecules during an excitation. We present a formal derivation of the PHM, starting from the particle-hole transition density matrix and projecting onto a set of single-particle orbitals. We implement the PHM using atom-centered localized basis sets and discuss the example of the molecular charge-transfer complex $\rm C_2H_4 - C_2F_4$.