Performance of the Density Functional Theory/Multireference Configuration Interaction Method on Electronic Excitation of Extended π-Systems

Abstract

The combined density functional theory/multireference configuration interaction (DFT/MRCI) method [Grimme and Waletzke. J. Chem. Phys. 1999, 111, 5645] has been employed to study the 1 L a and 1 L b states of linear polyacenes and the low-lying triplet and singlet states of linear polyenes and diphenyl-polyenes. We have systematically investigated the dependence of the electronic state properties on technical parameters of the calculations such as the atomic orbital basis set or the geometry optimization approach. The choice of basis set appears to be of minor importance whereas the excitation energies of the polyenes are quite sensitive to the ground-state geometry parameters. The DFT/MRCI energies at the B3-LYP optimized geometries systematically underestimate the experimental values, but we do not observe a bias toward one or the other type of state. The energy gaps between the electronically excited states are reproduced very well. In particular, this applies also to the first excited singlet 2 1 A g and the optically bright 1 B u + state of the polyenes. The latter appears to be the S 3 or even S 4 state in longer polyenes where the multiconfigurational 1 B u state represents S 2 . Frequencies and intensities of the excited-state absorption from the 2 1 A g state are found to be strongly geometry dependent.

Electronic excitations in long polyenes revisited

“…46 According to these results the 1B − u state becomes the S 2 state for N 22 at the chosen Franck-Condon geometry, while the 3A − g singlet excitation stays above the 1B + u state in all polyenes considered. In summary, the quoted calculations 26,[43][44][45] and, here, particularly Refs. 43 and 45, essentially confirmed the early PPP/MRCI descriptions of the low-lying electronically excited singlet states concerning the relative spacings of the covalent and ionic states in the polyenes.…”

“…26,[43][44][45] For instance, in 2004 Kurashige et al 43 studied the alltrans-polyenes with 6 ≤ N ≤ 28π -electrons in a correlated ab initio setting, which restricted the active space for full CI expansions to the five highest occupied and five lowest unoccupied molecular orbitals (MOs), and estimated σ -π interactions by second order perturbation theory. According to these calculations the vertical transition to the 1B − u state appears below the 1B + u transition at N ≥ 14 and the transition to the 3A − g state at N ≥ 22.…”

“…Similarly, the "density matrix renormalization group" approach (DMRG), which was combined with complete active space self-consistent field (CASSCF) calculations, of Ghosh et al, 26 which were carried out for polyenes with N = 8, 12, 16, 20, 24 π -electrons, placed already at N = 8 the covalent excitations 2A − g ,1B − u , and 3A − g below the optical transition. Finally, Marian and Gilka 45 applied the "density functional theory multireference configuration interaction" method (DFT/MRCI) to polyenes with 6 ≥ N ≥ 26 using extended basis sets, geometries optimized for single determinant Kohn-Sham ground states, and described dynamic correlations by MRCI expansions "kept short by extensive configuration selection at a few thousand configuration state functions." 46 According to these results the 1B − u state becomes the S 2 state for N 22 at the chosen Franck-Condon geometry, while the 3A − g singlet excitation stays above the 1B + u state in all polyenes considered.…”

“…Here, the question arises, which level of theory one should choose for the computation of ground state geometries. This question is important, because calculated vertical excitation energies will differentially and sensitively depend on the bond length alternation in the chosen ground state geometry 7,18,45 (cf. also Sec.…”

Theoretical predictions of red and near-infrared strongly emitting X-annulated rylenes

“…15 They ascribed the ordering anomaly to the electron correlation effects. Since then, there have been continuous and considerable investigations, such as by Tavan and Schulten, 16 Cave and Davidson, 17 Nakayama et al, 18 Hsu et al, 19 Serrano-Andres et al, 20 Starcke et al, 21 Marion and Gilka, 22 Shahi et al, 23 in calculating the 2A g /1B u orderings for the short unsubstituted polyene and Shukla 24 for the substituted polyene [poly(diphenylacetylene)]. It is found that the 2A g state has important contributions from electron double excitation configuration in the molecular orbital picture.…”