We report a test of 30 density functionals, including several recent ones, for their predictions of 69 singlet-to-singlet excitation energies of 11 molecules. The reference values are experimental results collected by Caricato et al. for 30 valence excitations and 39 Rydberg excitations. All calculations employ time-dependent density functional theory in the adiabatic, linear-response approximation. As far as reasonable, all of the assignments are performed by essentially the same protocol as used by Caricato et al., and this allows us to merge our mean unsigned errors (MUEs) with the ones they calculated for both density functional and wave function methods. We find 21 of the 30 density functionals calculated here have smaller MUEs for the 30 valence states than what they obtained (0.47 eV) for the state-of-the-art EOM-CCSD wave function. In contrast, for all of density functionals the MUE for 39 Rydberg states is larger than that (0.11 eV) of EOM-CCSD. Merging the 30 density functionals calculated here with the 26 calculated by Caricato et al. makes a set of 56 density functionals. Averaging the unsigned errors over both the valence excitations and the Rydberg excitations, none of the 56 density functionals shows a lower mean unsigned error than that (0.27 eV) of EOM-CCSD. Nevertheless, two functionals are successful in having an overall mean unsigned error of 0.30 eV, and another nine are moderately successful in having overall mean unsigned errors in the range 0.32-0.36 eV. Successful or moderately successful density functionals include seven hybrid density functionals with 41% to 54% Hartree-Fock exchange, and four range-separated hybrid density functionals in which the percentage of Hartree-Fock exchange increases from 0% to 19% at small interelectronic separation to 65%-100% at long range.

The calculation of redox potentials involves large energetic terms arising from gas phase ionization energies, thermodynamic contributions, and solvation energies of the reduced and oxidized species. In this work we study the performance of a wide range of wave function and density functional theory methods for the prediction of ionization energies and aqueous one-electron oxidation potentials of a set of 19 organic molecules. Emphasis is placed on evaluating methods that employ the computationally efficient local pair natural orbital (LPNO) approach, as well as several implementations of coupled cluster theory and explicitly correlated F12 methods. The electronic energies are combined with implicit solvation models for the solvation energies. With the exception of MP2 and its variants, which suffer from enormous errors arising at least partially from the poor Hartree-Fock reference, ionization energies can be systematically predicted with average errors below 0.1 eV for most of the correlated wave function based methods studies here, provided basis set extrapolation is performed. LPNO methods are the most efficient way to achieve this type of accuracy. DFT methods show in general larger errors and suffer from inconsistent behavior. The only exception is the M06-2X functional which is found to be competitive with the best LPNO-based approaches for ionization energies. Importantly, the limiting factor for the calculation of accurate redox potentials is the solvation energy. The errors in the predicted solvation energies by all continuum solvation models tested in this work dominate the final computed reduction potential, resulting in average errors typically in excess of 0.3 V and hence obscuring the gains that arise from choosing a more accurate electronic structure method.

Time-dependent density functional theory (TDDFT) holds great promise for studying photochemistry because of its affordable cost for large systems and for repeated calculations as required for direct dynamics. The chief obstacle is uncertain accuracy. There have been many validation studies, but there are also many formulations, and there have been few studies where several formulations were applied systematically to the same problems. Another issue, when TDDFT is applied with only a single exchange-correlation functional, is that errors in the functional may mask successes or failures of the formulation. Here, to try to sort out some of the issues, we apply eight formulations of adiabatic TDDFT to the first valence excitations of ten molecules with 18 density functionals of diverse types. The formulations examined are linear response from the ground state (LR-TDDFT), linear response from the ground state with the Tamm-Dancoff approximation (TDDFT-TDA), the original collinear spin-flip approximation with the Tamm-Dancoff (TD) approximation (SF1-TDDFT-TDA), the original noncollinear spin-flip approximation with the TDA approximation (SF1-NC-TDDFT-TDA), combined self-consistent-field (SCF) and collinear spin-flip calculations in the original spin-projected form (SF2-TDDFT-TDA) or non-spin-projected (NSF2-TDDFT-TDA), and combined SCF and noncollinear spin-flip calculations (SF2-NC-TDDFT-TDA and NSF2-NC-TDDFT-TDA). Comparing LR-TDDFT to TDDFT-TDA, we observed that the excitation energy is raised by the TDA; this brings the excitation energies underestimated by full linear response closer to experiment, but sometimes it makes the results worse. For ethylene and butadiene, the excitation energies are underestimated by LR-TDDFT, and the error becomes smaller making the TDA. Neither SF1-TDDFT-TDA nor SF2-TDDFT-TDA provides a lower mean unsigned error than LR-TDDFT or TDDFT-TDA. The comparison between collinear and noncollinear kernels shows that the noncollinear kernel drastically reduces the spin contamination in the systems considered here, and it makes the results more accurate than collinear spin-flip TDDFT for functionals with a low percentage of Hartree-Fock exchange and sometimes for functionals with a higher percentage of Hartree-Fock exchange, but it yields less accurate results than ground-state TDDFT.

Application of the Artificial Force Induced Reaction (AFIR) method to the prediction of cyclization/ rearrangement pathways for carbocation precursors to sesquiterpenes is described. This method captures many of the features revealed in previous studies as well as new ones, including a pathway to asesquiterpene not yet isolated in nature that we suspect will be isolated in time.

We add higher-order electronic polarization effects to the molecular tailoring approach (MTA) by embedding each fragment in background charges as in combined quantum mechanical and molecular mechanical (QM/MM) methods; the resulting method considered here is called electrostatically embedded MTA (EE-MTA). We compare EE-MTA to MTA for a test peptide, Ace-(Ala)20-NMe, and we find that including background charges (embedding charges) greatly improves the performance. The fragmentation is performed on the basis of amino acids as monomers, and several sizes of fragment are tested. The fragments are capped with either hydrogen cap atoms or tuned fluorine cap atoms. The effective core potential of the tuned fluorine cap atom is optimized so as to reproduce the proton affinity for seven types of tetrapeptide, and the proton affinity calculated with the tuned cap atom shows a lower mean unsigned error than that obtained by using a hydrogen cap atom. In the application to the test peptide, these generically tuned cap atoms show better performance compared with the hydrogen cap atom for both the electronic energy and the energy difference between an α helix and a β sheet (in the latter case, 1.0% vs 2.7% when averaged over three sizes of fragments and two locations for cut bonds). Also, we compared the accuracy of several charge redistribution schemes, and we find that the results are not particularly sensitive to these choices for the Ace-(Ala)20-NMe peptide. We also illustrate the dependence on the choice of charge model for the embedding charges, including both fixed embedding charges and embedding charges that depend on conformation.