Fractional spin in reduced density-matrix functional theory.

We study the behavior of different functionals of the one-body reduced density matrix (1RDM) for systems with fractional z-component of the total spin. We define these systems as ensembles of integer spin states. It is shown that, similarly to density functional theory, the error in the dissociation of diatomic molecules is directly related to the deviation from constancy of the atomic total energies as functions of the fractional spin. However, several functionals of the 1RDM show a size inconsistency which leads to additional errors. We also investigate the difference between a direct evaluation of the energy of an ensemble of integer-spin systems and a direct minimization of the energy of a fractional-spin system.

Theoretical investigation on the effect of protonation on the absorption and emission spectra of two amine-group-bearing, red "push-pull" emitters, 4-dimethylamino-4'-nitrostilbene and 4-(dicyanomethylene)-2-methyl-6-p-(dimethylamino) styryl-4H-pyran, by DFT and TDDFT calculations.

A theoretical investigation on the electronic structure of 4-dimethylamino-4'-nitrostilbene (DANS), 4-(dicyanomethylene)-2-methyl-6-p-(dimethylamino) styryl-4H-pyran (DCM), and their protonated forms is presented in an effort to rationalize recent experimental results on the tuning of the emitted color of organic light-emitting diodes through photochemically induced protonation. Density functional theory (DFT) and time-dependent density functional theory (TDDFT) calculations have been carried out on the neutral and protonated forms of DANS and DCM, employing both the B3LYP and the CAM-B3LYP functionals. It was found that the CAM-B3LYP functional leads to better agreement than the B3LYP of the calculated with the experimental absorption lambda(max) for DANS, whereas B3LYP is more appropriate than CAM-B3LYP for DCM. The results of the calculations aid in a rationalization of the observed differences of the spectra of DANS and DCM upon protonation, and in particular those differences that make DANS a more attractive system for absorbance and emission tuning.