Density functional theory with fractionally occupied frontier orbitals and the instabilities of the Kohn–Sham solutions for defining diradical transition states: Ring-opening reactions

Abstract

Density functional theory with fractionally occupied frontier orbitals was combined with an analysis of the instability of the Kohn–Sham solutions and applied to the study of the ring-opening reactions of 1,2-dioxetene, 1,2-dithiete, 1,2-diselenete, and 1,2-ditellurete. These molecules possess transition structures and reactive intermediates for the ring-opening reactions which exhibit strong nondynamical electron correlation. All restricted density functional theory (DFT) solutions for the closed shell transition state structures for all these species are unstable. The solutions with the hybrid Hartree–Fock DFT functionals, B3LYP and B3PW91, are triplet unstable, while for the pure DFT functional BLYP the instability is due to a violation of the Aufbau principle. The same types of instabilities were found for the 1,2-diselenete and 1,2-ditellurete intermediates. Lower energy stable solutions for the diradical transition structures were found with unrestricted DFT methods allowing fractionally occupied orbitals. This DFT approach indicates a decrease in the active orbital space from four fractionally occupied natural orbitals in earlier multireference predictions to two fractionally occupied Kohn–Sham orbitals.