The Evolution of Electronic Structure in Conjugated Molecules Revealed by Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory and Density-Based Analyses: I. Polyenes

Spin-flip time-dependent density functional theory (SF-TDDFT) extends linear-response TDDFT to diradicals, bond breaking, conical intersections, and excited states with doubly excited character. The mixed-reference SF-TDDFT (MRSF-TDDFT) formulation provides spin-purified states while keeping the simplicity of the original formalism. Previous benchmarks of MRSF-TDDFT have focused on energies, structures, and permanent and transition dipole moments. Here we look at the state and transition densities. Using natural orbitals, natural transition orbitals, natural difference orbitals, and exciton descriptors, we examine the number of effectively unpaired electrons, the singly excited character of the transitions, exciton sizes, and electron–hole correlation in conjugated molecules of increased sizes. Here we consider all-trans polyenes and in a companion paper we consider polyacenes. In polyenes, the ground state remains predominantly closed shell, the bright 1 1Bu+ state remains singly excited, and the covalent 2 1Ag− and 1 1Bu− states gain progressively more doubly excited character. Exciton descriptors, in particular electron–hole separation and correlation, highlight the differences in state characters arising due to differences in treatment of electron correlation. MRSF-TDDFT captures the main trends in state ordering as compared to the high-level correlated methods as well as the evolution of states’ characters. The results illustrate the utility of MRSF-TDDFT and density-based analyses in describing electronic structure of large conjugated systems.