Constrained Density Functional Theory and Its Application in Long-Range Electron Transfer.

Recently, we have proposed an efficient method in the Kohn-Sham density functional theory (DFT) to study systems with a constraint on their density (Phys. Rev. A 2005, 72, 24502). In our approach, the constrained state is calculated directly by running a fast optimization of the constraining potential at each iteration of the usual self-consistent-field procedure. Here, we show that the same constrained DFT approach applies to systems with multiple constraints on the density. To illustrate the utility of this approach, we focus on the study of long-range charge-transfer (CT) states. We show that constrained DFT is size-consistent:  one obtains the correct long-range CT energy when the donor-acceptor separation distance goes to infinity. For large finite distances, constrained DFT also correctly describes the 1/R dependence of the CT energy on the donor-acceptor separation. We also study a model donor-(amidinium-carboxylate)-acceptor complex, where experiments suggest a proton-coupled electron-transfer process. Constrained DFT is used to explicitly calculate the potential-energy curves of both the donor state and the acceptor state. With an appropriate model, we obtain qualitative agreement with experiments and estimate the reaction barrier height to be 7 kcal/mol.