Constricted variational density functional theory for spatially clearly separated charge-transfer excitations

Constricted Variational Density Functional Theory (CV-DFT) is known to be one of the successful methods in predicting charge-transfer excitation energies. In this paper, we apply the CV-DFT method to the well-known model systems ethylene-tetrafluoroethylene (C₂H₄ × C₂F₄) and the zincbacteriochlorin-bacteriochlorin complex (ZnBC-BC). The analysis of the CV-DFT energies enables us to understand the -1/R charge-transfer behaviour in CV-DFT for large separation distances R. With this we discuss the importance of orbital relaxations using the relaxed version of CV(∞)-DFT, the R-CV(∞)-DFT method. Possible effects of the optimization of the transition matrix for the relaxed self-consistent field version of CV(∞)-DFT, RSCF-CV(∞)-DFT in the case of large fragment separations are shown and we introduce two possible gradient restrictions to avoid the unwanted admixing of other transitions.