As the notation implies, the quantities ∆P elec and ∆P hole can be conceptualized as separate densities for the excited electron and the hole that it leaves behind in the occupied space. More precisely, this is true of the real-space densities ∆ρ elec (r) and ∆ρ hole (r) that are encoded by these density matrices. Unlike the difference density ∆ρ(r) = ∆ρ elec (r) + ∆ρ hole (r) ,