Exploring Chemical Concepts and Reactivity from Conceptual Density Functional Theory in Excited States via the ΔSCF Approach

Along with the recent development of the ΔSCF approach for excited state electronic structure description using density functional theory (DFT), we extend and develop conceptual density functional theory (CDFT) for evaluating chemical concepts and reactivity descriptors for both ground and excited states. Thereby, the fundamental energy functionalEJ[{npσ},v(r)] based on the generalized adiabatic connection Kohn–Sham (GAC-KS) theorem is introduced. Offering a straightforward interpretation of the reactivity of excited states analogous to that of the ground state. In this framework, ground state CDFT naturally emerges as a special case when the derivative with respect to the number of electrons is taken at the frontier orbital occupation, i.e., dN = dnf. Starting from the ground state system, the spin-polarized analytical linear response function (LRF) is tested to examine the atomic shell structure for alkali atoms as well as the reactive region upon electron addition and removal processes using the Fukui kernel. The behavior of the LRF is then illustrated for ground, singly excited, and doubly excited states of a set of molecular systems, revealing the expected trends and nature of bond polarizability and bonding character. The analytical Fukui function is also presented here for its ability to describe local electrophilicity and nucleophilicity for ground and excited states. An inverse relationship for the condensed electrophilic and nucleophilic Fukui functions is observed between the ground and excited states for a set of small molecules, including substituted benzenes. The dual descriptor obtained from the analytical Fukui function via a finite difference approximation is applied to interpret the Woodward–Hoffmann (WH) rules for pericyclic reactions. For both thermally driven and photoinduced ring cyclization processes at the ground and excited states, respectively, the dual descriptor successfully translates the WH rules from molecular orbital context into a purely density-based language.