Analytic energy gradients for constrained DFT-configuration interaction.

The constrained density functional theory-configuration interaction (CDFT-CI) method has previously been used to calculate ground-state energies and barrier heights, and to describe electronic excited states, in particular conical intersections. However, the method has been limited to evaluating the electronic energy at just a single nuclear configuration, with the gradient of the energy being available only via finite difference. In this paper, we present analytic gradients of the CDFT-CI energy with respect to nuclear coordinates, which gives the potential for accurate geometry optimization and molecular dynamics on both the ground and excited electronic states, a realm which is currently quite challenging for electronic structure theory. We report the performance of CDFT-CI geometry optimization for representative reaction transition states as well as molecules in an excited state. The overall accuracy of CDFT-CI for computing barrier heights is essentially unchanged whether the energies are evaluated at geometries obtained from quadratic configuration-interaction singles and doubles (QCISD) or CDFT-CI, indicating that CDFT-CI produces very good reaction transition states. These results open up tantalizing possibilities for future work on excited states.

Communication: Conical intersections using constrained density functional theory-configuration interaction.

The constrained density functional theory-configuration interaction (CDFT-CI) method has previously been used to calculate ground-state energies and barrier heights. In this work, it is examined for use in computing electronic excited states, for the challenging case of conical intersections. Conical intersections are a prevalent feature of excited electronic surfaces, but conventional time-dependent density functional theory calculations are found to be entirely unsatisfactory at describing them, for two small systems. CDFT-CI calculations on those systems are found to be in qualitative agreement with reference CAS surfaces. These results suggest that with a suitable definition of atomic populations and a careful choice of constrained states, CDFT-CI could be the basis for a seamless description of electronic degeneracy.

The diabatic picture of electron transfer, reaction barriers, and molecular dynamics.

Diabatic states have a long history in chemistry, beginning with early valence bond pictures of molecular bonding and extending 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 summary of the challenges and prospects for the further application of diabatic states in chemistry.

An "optimal" spawning algorithm for adaptive basis set expansion in nonadiabatic dynamics.

The full multiple spawning (FMS) method has been developed to simulate quantum dynamics in the multistate electronic problem. In FMS, the nuclear wave function is represented in a basis of coupled, frozen Gaussians, and a "spawning" procedure prescribes a means of adaptively increasing the size of this basis in order to capture population transfer between electronic states. Herein we detail a new algorithm for specifying the initial conditions of newly spawned basis functions that minimizes the number of spawned basis functions needed for convergence. "Optimally" spawned basis functions are placed to maximize the coupling between parent and child trajectories at the point of spawning. The method is tested with a two-state, one-mode avoided crossing model and a two-state, two-mode conical intersection model.

Constrained density functional theory based configuration interaction improves the prediction of reaction barrier heights.

In this work, a constrained density functional theory based configuration interaction approach (CDFT-CI) is applied to calculating transition state energies of chemical reactions that involve bond forming and breaking at the same time. At a given point along the reaction path, the configuration space is spanned by two diabaticlike configurations: reactant and product. Each configuration is constructed self-consistently with spin and charge constraints to maximally retain the identities of the reactants or the products. Finally, the total energy is obtained by diagonalizing an effective Hamiltonian constructed in the basis spanned by these two configurations. By design, this prescription does not affect the energies of the reactant or product species but will affect the energy at intermediate points along the reaction coordinate, most notably by modifying the reaction barrier height. When tested with a large set of reactions that include hydrogen transfer, heavy atom transfer, and nucleophilic substitution, CDFT-CI is found to improve the prediction of barrier heights by a factor of 2-3 for some commonly used local, semilocal, and hybrid functionals. Thus, just as CDFT can be used to cure energy errors in charge localized states, CDFT-CI can recover the correct energy for charge delocalized states by approximating the true wave function as a linear combination of localized configurations (e.g., reactant and product). The well-defined procedure and the promising results of CDFT-CI suggest that it could broaden the applicability of traditional DFT methods for reaction barrier heights.