  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 $\rm C_2H_4 - C_2F_4$.
