Restricted open-shell Kohn-Sham (ROKS) theory provides a powerful computational tool for calculating singlet excited state energies and dynamics. However, the possibility of multiple solutions to the ROKS equations - with the associated difficulty of automatically selecting the physically meaningful solution - limits its usefulness for intensive applications such as long-time Born-Oppenheimer molecular dynamics. We present an implementation of ROKS for excited states which prescribes the physically correct solution from an overlap criterion and guarantees that this solution is stationary, allowing for straightforward evaluation of nuclear gradients. The method is used to benchmark ROKS for vertical excitation energies of small and large organic dyes and for the calculation of Stokes shifts. With common density functional approximations, ROKS vertical excitation energies, and Stokes shifts show similar accuracy to those from time-dependent density functional theory and Δ-self-consistent-field approaches. Advantages of the ROKS approach for excited state structure and molecular dynamics are discussed.
Coupled-cluster and density-functional methods have been used to determine specific rotations and electronic circular dichroism (ECD) rotational strengths for (S)-2-chloropropionitrile. Coupled-cluster specific rotations using both the length- and velocity-gauge representations of the electric-dipole operator, computed with basis sets of triple-zeta quality containing up to 326 functions, compare very well with recently reported gas-phase cavity-ring-down polarimetry data. ECD rotational strengths for the six lowest-lying excited states are found to vary in sign, and the second excited state, which has a larger rotational strength than the first by a factor of 4, was found to yield a much larger contribution (by a factor of 10) to the overall negative specific rotation observed both experimentally and theoretically. However, both valence and Rydberg states appear to make substantial contributions to the total rotation, often of opposite sign from the converged/linear-response result. Furthermore, the sum-over-states approach was found to be inadequate for reproducing the specific rotations derived from the linear-response approach, even when 100 excited states (well beyond the estimated ionization limit) were included in the summation. Density-functional specific rotations using the B3LYP functional with basis sets of quadruple-zeta quality containing up to 588 functions are found to be too large compared to experiment by approximately a factor of 2. This error appears to be related to both the underestimation of the electronic excitation energies, as well as concomitant overestimation of the corresponding ECD rotational strengths. Although earlier studies reported good agreement between density-functional specific rotations and experiment when electric-field-dependent functions were used in conjunction with a double-zeta-quality basis set, the results reported here, which are near the basis-set limit, suggest that this agreement may be fortuitous.
The electronic structure of CO3 is characterized by equation-of-motion and coupled-cluster methods. C(2v) and D(3h) isomers are considered. Vertical excitation energies, transition dipoles, and the molecular orbital character of the excited states are presented for singlet and triplet manifolds. Ground-state equilibrium structures and frequencies are strongly affected by vibronic interactions with low-lying excited states. At D(3h) geometries, the vibronic interactions are enhanced by the Jahn-Teller character of the excited states. The curvature of the potential energy surface and the existence of the D(3h) minimum are very sensitive to the correlation treatment and the basis set. The correlation effects are stronger at D(3h), in agreement with a smaller HOMO-LUMO gap.
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