The Application of Constricted Variational Density Functional Theory to Excitations Involving Electron Transitions...

We have applied the constricted variational density functional method (CV(n)-DFT) to n → π* transitions in which an electron is moved from an occupied lone-pair orbital n to a virtual π* orbital. A total of 34 transitions involving 16 different compounds were considered using the local density approximation (LDA), Becke, three-parameter, Lee-Yang-Parr (B3LYP), and BHLYP functionals. The DFT-based results were compared to the "best estimates" (BE) from high-level ab initio calculations. With energy terms included to second order in the variational parameters (CV(2)-DFT), our theory is equivalent to the adiabatic version of time-dependent density functional theory (DFT). We find that calculated excitation energies for CV(2)-DFT using LDA and BHLYP differ substantially from BE with root-mean-square-deviations (rmsd) of 0.86 and 0.69 eV, respectively, whereas B3LYP affords an excellent fit with BE at rmsd = 0.18 eV. Resorting next to CV(∞)-DFT, where energy terms to all orders in the variational parameters are included, results in all three functionals in too high excitation energies with rmsd = 1.69, 1.14, and 0.93 eV for LDA, B3LYP, and BHLYP, respectively. Adding in orbital relaxation considerably improves the results with rmsd = 0.54, 0.30, and 0.48 eV for LDA, B3LYP, and BHLYP, respectively. It is concluded that CV(∞)-DFT with orbital relaxation is a robust method for which the accuracy is less functionally dependent than that of CV(2)-DFT or adiabatic TDDFT.