Capturing the Elusive Curve-Crossing in Low-Lying States of Butadiene with Dressed TDDFT.

A striking example of the need to accurately capture states of double-excitation character in molecules is seen in predicting photoinduced dynamics in small polyenes. Due to the coupling of electronic and nuclear motions, the dark 2Ag state, known to have double-excitation character, can be reached after an initial photoexcitation to the bright 1Bu state via crossings of their potential energy surfaces. However, the shapes of the surfaces are so poorly captured by most electronic structure methods, that the crossing is missed or substantially mis-located.

Reformulation of Time-Dependent Density Functional Theory for Nonperturbative Dynamics: The Rabi Oscillation Problem Resolved.

Rabi oscillations have long been thought to be out of reach in simulations using time-dependent density functional theory (TDDFT), a prominent symptom of the failure of the adiabatic approximation for nonperturbative dynamics. We present a reformulation of TDDFT which requires response quantities only, thus enabling an adiabatic approximation to predict such dynamics accurately because the functional is evaluated on a density close to the ground state, instead of on the fully nonperturbative density. Our reformulation applies to any real-time dynamics, redeeming TDDFT far from equilibrium.

Oscillator strengths and excited-state couplings for double excitations in time-dependent density functional theory.

Although useful to extract excitation energies of states of double-excitation character in time-dependent density functional theory that are missing in the adiabatic approximation, the frequency-dependent kernel derived earlier [Maitra et al., J. Chem.

Curing the Divergence in Time-Dependent Density Functional Quadratic Response Theory.

The adiabatic approximation in time-dependent density functional theory is known to give an incorrect pole structure in the quadratic response function, leading to unphysical divergences in excited state-to-state transition probabilities and hyperpolarizabilties. We find the form of the exact quadratic response kernel and derive a practical and accurate approximation that cures the divergence. We demonstrate our results on excited state-to-state transition probabilities of a model system and of the LiH molecule.