Direct optimization method to study constrained systems within density-functional theory

Consider a system with an arbitrary constraint on its electron density (e.g., that there are $N$ charges on a certain group of atoms). We show that in Kohn-Sham density functional theory, the minimum energy state consistent with the constraint is actually a maximum with respect to the constraint potential, and that this solution is unique. This leads us to an efficient algorithm for calculations on constrained systems. Illustrative studies are shown for charge transfer in the zincbacteriochlorin-bacteriochlorin complex, polyene and alkane chains.

Figure 1

Molecular structures of the linked zincbacteriochlorin-bacteriochlorin complex and the model complex. $R$ refers to the distance between the two carbon atoms that are formerly linked.

Figure 2

(a) The lowest CT-state energies of the ZnBC-BC model complex at different distances as compared to its ground-state energy at 5.84 Å. Lower line, ${\mathrm{ZnBC}}^{+}\text{−}{\mathrm{BC}}^{-}$. Upper line, ${\mathrm{ZnBC}}^{-}\text{−}{\mathrm{BC}}^{+}$. (b) Applied potential vs charge transfer for the model complex at 5.84Å.

Figure 3

Applied potential vs charge transfer for ${\mathrm{C}}_6{\mathrm{H}}_8$ (dots) and ${\mathrm{C}}_6{\mathrm{H}}_{14}$ (triangles).

Figure 4

Applied potential vs charge transfer for ${\mathrm{C}}_4{\mathrm{H}}_9\mathrm{F}$. Dots, B3LYP. Triangles, CCSD.