Assessment of TD-DFT methods and of various spin scaled CIS(D) and CC2 versions for the treatment of low-lying valence excitations of large organic dyes

We present an extension of our previously published benchmark set for low-lying valence transitions of large organic dyes [L. Goerigk et al., Phys. Chem. Chem. Phys. 11, 4611 (2009)]. The new set comprises in total 12 molecules, including two charged species and one with a clear charge-transfer transition. Our previous study on TD-DFT methods is repeated for the new test set with a larger basis set. Additionally, we want to shed light on different spin-scaled variants of the configuration interaction singles with perturbative doubles correction [CIS(D)] and the approximate coupled cluster singles and doubles method (CC2). Particularly for CIS(D) we want to clarify, which of the proposed versions can be recommended. Our results indicate that an unpublished SCS-CIS(D) variant, which is implemented into the TURBOMOLE program package, shows worse results than the original CIS(D) method, while other modified versions perform better. An SCS-CIS(D) version with a parameterization, that has already been used in an application by us recently [L. Goerigk and S. Grimme, ChemPhysChem 9, 2467 (2008)], yields the best results. Another SCS-CIS(D) version and the SOS-CIS(D) method [Y. M. Rhee and M. Head-Gordon, J. Phys. Chem. A 111, 5314 (2007)] perform very similar, though. For the electronic transitions considered herein, there is no improvement observed when going from the original CC2 to the SCS-CC2 method but further adjustment of the latter seems to be beneficial. Double-hybrid density functionals belong to best methods tested here. Particularly B2GP-PLYP provides uniformly good results for the complete set and is considered to be close to chemical accuracy within an ab initio theory of color. For conventional hybrid functionals, a Fock-exchange mixing parameter of about 0.4 seems to be optimum in TD-DFT treatments of large chromophores. A range-separated functional such as, e.g., CAM-B3LYP seems also to be promising.