Diabatic states have a long history in chemistry, beginning with early valence bond pictures of molecular bonding and stretching through the construction of model potential energy surfaces to the modern proliferation of methods for computing these elusive states. In this review we summarize the basic principles that define the diabatic basis and demonstrate how they can be applied in the specific context of constrained density functional theory. Using illustrative examples from electron transfer and chemical reactions, we show how the diabatic picture can be used to extract qualitative insight and quantitative predictions about energy landscapes. The review closes with a brief resumé of the challenges and prospects for the further application of diabatic states in chemistry.

Existing density functional theory (DFT) methods are typically very effective in capturing dynamic correlation, but run into difficulty treating near-degenerate systems where static correlation becomes important. In this work, we propose a configuration interaction (CI) method that allows one to use a multireference approach to treat static correlation but incorporates DFT's efficacy for the dynamic part as well. The new technique uses localized charge or spin states built by a constrained DFT approach to construct an active space in which the effective Hamiltonian matrix is built. These local configurations have significantly less static correlation compared to their delocalized counterparts and possess an essentially constant amount of self-interaction error. Thus their energies can be reliably calculated by DFT with existing functionals. Using a small number of local configurations as different references in the active space, a simple CI step is then able to recover the static correlation missing from the localized states. Practical issues of choosing configurations and adjusting constraint values are discussed, employing as examples the ground state dissociation curves of H(2) (+), H(2), and LiF. Excellent results are obtained for these curves at all interatomic distances, which is a strong indication that this method can be used to accurately describe bond breaking and forming processes.

No abstract

We utilize excited state density functional theory (eDFT) to study Rydberg states in atoms. We show both analytically and numerically that semilocal functionals can give quite reasonable Rydberg energies from eDFT, even in cases where time dependent density functional theory (TDDFT) fails catastrophically. We trace these findings to the fact that in eDFT the Kohn-Sham potential for each state is computed using the appropriate excited state density. Unlike the ground state potential, which typically falls off exponentially, the sequence of excited state potentials has a component that falls off polynomially with distance, leading to a Rydberg-type series. We also address the rigorous basis of eDFT for these systems. Perdew and Levy have shown using the constrained search formalism that every stationary density corresponds, in principle, to an exact stationary state of the full many-body Hamiltonian. In the present context, this means that the excited state DFT solutions are rigorous as long as they deliver the minimum noninteracting kinetic energy for the given density. We use optimized effective potential techniques to show that, in some cases, the eDFT Rydberg solutions appear to deliver the minimum kinetic energy because the associated density is not pure state v-representable. We thus find that eDFT plays a complementary role to constrained DFT: The former works only if the excited state density is not the ground state of some potential while the latter applies only when the density is a ground state density.

We analyze spin-charge separation in molecular wires using a combination of real-time density-functional simulations and model Hamiltonian calculations. By considering the ab initio electron dynamics of positively charged ͑C 50 H 52 + ͒ and negatively charged ͑C 50 H 52 − ͒ polyacetylene chains under a chemical potential bias, we are able to extract information about the mobility of electrons, holes, and spins in these molecules. Our results indicate that charges move more rapidly than spins in these molecules. We further supplement our ab initio data with empirical calculations employing the Pariser-Parr-Pople ͑PPP͒ model Hamiltonian. Our modeling indicates that the degree of spin-charge separation responds very strongly to the nonlocal exchange interaction, while showing little sensitivity to Coulombic forces. In particular, in order to reproduce the B3LYP results within the PPP model, it is necessary to reduce the strength of the exchange interaction by ca. 50% in the latter. We therefore conclude that many of the features present in the B3LYP spin current response are a direct result of self-interaction error in the functional.