The primary all-trans --> 13-cis photoisomerization of retinal in bacteriorhodopsin has been investigated by means of quantum chemical and combined classical/quantum mechanical simulations employing the density matrix evolution method. Ab initio calculations on an analog of a protonated Schiff base of retinal in vacuo reveal two excited states S1 and S2, the potential surfaces of which intersect along the reaction coordinate through an avoided crossing, and then exhibit a second, weakly avoided, crossing or a conical intersection with the ground state surface. The dynamics governed by the three potential surfaces, scaled to match the in situ level spacings and represented through analytical functions, are described by a combined classical/quantum mechanical simulation. For a choice of nonadiabatic coupling constants close to the quantum chemistry calculation results, the simulations reproduce the observed photoisomerization quantum yield and predict the time needed to pass the avoided crossing region between S1 and S2 states at tau1 = 330 fs and the S1 --> ground state crossing at tau2 = 460 fs after light absorption. The first crossing follows after a 30 degrees torsion on a flat S1 surface, and the second crossing follows after a rapid torsion by a further 60 degrees. tau1 matches the observed fluorescence lifetime of S1. Adjusting the three energy levels to the spectral shift of D85N and D212N mutants of bacteriorhodospin changes the crossing region of S1 and S2 and leads to an increase in tau1 by factors 17 and 10, respectively, in qualitative agreement with the observed increase in fluorescent lifetimes.

Abstract:Explicitly correlated MP2-F12 and CCSD(T)-F12 methods are reviewed. We focus on the CCSD(T)-F12x (x = a, b) approximations, which are only slightly more expensive than their non-F12 counterparts. Furthermore, local approximations in the LMP2-F12 and LCCSD-F12 methods are described, which make it possible to treat larger molecules than with standard coupled-cluster methods. We demonstrate the practicability of F12 methods by large benchmark calculations for various properties, including reaction energies, vibrational frequencies, and intermolecular interactions. In these calculations, the newly developed VnZ-F12 orbital and OPTRI auxiliary basis sets by Peterson et al. are compared to other previously used basis sets. The accuracy and efficiency of local approximations is demonstrated for reactions of large molecules. Keywords: Coupled cluster, F12 approach, Explicitly correlated, Perturbation theory, Local approximations INTRODUCTIONThe coupled-cluster method with single and double excitations and a perturbative treatment of triple excitations [CCSD(T)] is nowadays considered to be the gold standard of quantum chemistry. As long as a single-reference treatment is sufficient, it yields highly accurate results for many properties, and chemical accuracy can be reached for energy differences such as reaction enthalpies [1,2]. However, the method suffers from two major problems: the very steep scaling of the computational cost with increasing molecular size, and the extremely slow convergence of the correlation energy with respect to the basis set size. The latter problem is severe even for 573

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