Search

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. [ABSTRACT FROM AUTHOR]

A database containing 17 multiplicity-changing valence and Rydberg excitation energies of p-block elements is used to test the performance of density functional theory (DFT) with approximate density functionals for calculating relative energies of spin states. We consider only systems where both the low-spin and high-spin state are well described by a single Slater determinant, thereby avoiding complications due to broken-symmetry solutions. Because the excitations studied involve a spin change, they require a balanced treatment of exchange and correlation, thus providing a hard test for approximate density functionals. We test three formalisms for predicting the multiplicity-changing transition energies. First is the ΔSCF method; we also test time-dependent density functional theory (TDDFT), both in its conventional form starting from the low-spin state and in its collinear spin-flip form starting from the high-spin state. Very diffuse basis functions are needed to give a qualitatively correct description of the Rydberg excitations. The scalar relativistic effect needs to be considered when quantitative results are desired, and we include it in the comparisons. With the ΔSCF method, most of the tested functionals give mean unsigned errors (MUEs) larger than 6 kcal/mol for valence excitations and MUEs larger than 3 kcal/mol for Rydberg excitations, but the performance for the Rydberg states is much better than can be obtained with time-dependent DFT. It is surprising to see that the long-range corrected functionals, which have 100% Hartree-Fock exchange at large inter-electronic distance, do not improve the performance for Rydberg excitations. Among all tested density functionals, ΔSCF calculations with the O3LYP, M08-HX, and OLYP functionals give the best overall performance for both valence and Rydberg excitations, with MUEs of 2.1, 2.6, and 2.7 kcal/mol, respectively. This is very encouraging since the MUE of the CCSD(T) coupled cluster method with quintuple zeta basis sets is 2.0 kcal/mol; however, caution is advised since many popular density functionals give poor results, and there can be very significant differences between the ΔSCF predictions and those from TDDFT. [ABSTRACT FROM AUTHOR]