Computation of vertical excitation energies of retinal and analogs: scope and limitations

A comprehensive survey of computational methods: semiempirical (ZINDO/S), Time-Dependent Hartree-Fock (TD-HF), Configuration Interaction Singles (CIS), and several approximate functionals within the Time-Dependent Density Functional Theory (TD-DFT) has been carried out for the description of vertical excitation energies and oscillator strengths of retinal and related polyenals. ZINDO and TD-DFT computations showed the best agreement with the experimental data. In particular, hybrid functionals including approximately 25% of exact exchange (B3LYP, B3P86, and PBE0) were found to perform best with these highly conjugated polyenes. A systematic average error of 0.18-0.22 eV has been found after a simple one-parameter correction. Thus, 0.18 eV might be considered the upper limit of accuracy for current one-determinant methods in the computation of vertical excitation energies. The consideration of adiabatic excitations, conformational sampling, solvation, and nondynamic correlation should describe this processes more accurately, but this leads to highly demanding methods beyond feasibility for these large polyenes. The trends observed, particularly the good performance of the ZINDO/S method, should pave the way for the prediction of excited states properties in natural and artificial photoreceptor proteins, thus advancing towards the description of their light-transducing biological role in Nature.