Ground and Excited States of Retinal Schiff Base Chromophores by Multiconfigurational Perturbation Theory
We have studied the wavelength dependence of retinal Schiff base absorbencies on the protonation state of the chromophore at the multiconfigurational level of theory using second order perturbation theory (CASPT2) within an atomic natural orbital basis set on MP2 optimized geometries. Quantitative agreement between calculated and experimental absorption maxima was obtained for protonated and deprotonated Schiff bases of all-trans- and 11-cis-retinal and intermediate states covering a wavelength range from 610 to 353 nm. These data will be useful as reference points for the calibration of more approximate schemes.Retinal is the chromophore in several photosensitive proteins where it converts light energy into structural changes (1): in the visual pigments or rhodopsins, the light-induced isomerization of 11-cis-retinal to all-trans initiates the visual cycle. In hacteriorhodopsin. all-trans-retinal is transformed by light into the 13-cis isomer, which starts the proton pumping cycle across the bacterial cell wall of Halobacterium salinarium
One particular aspect in retinal protein chemistry concerns the ultraviolet-visible spectral changes in these pigments, which serve specific needs: from ancient bacteria that use sensory rhodopsins to test the composition of light (2) to the human eye where three different rhodopsins enable the perception of colors (3). Understanding the physical origin of these changes has been a major challenge to theory ever since the original concept of the external point charge model has been introduced in the literature (4). Advances in x-ray crystallography have provided a multitude of bacteriorhodopsin structures, including intermediates of the proton pumping cycle (5) and have culminated recently in the threedimensional structure of bovine rhodopsin (6) and its first photointermediate, bathorhodopsin (7). These structures, which reveal the geometry of the retinal chromophore and its environment in atomic detail, have been instrumental for theoretical studies of retinal protein spectral shuts using diverse quantum-mechanical schemes (8-13). The dilemma that these studies face is exemplified by the fact that two of them arrive at very reasonable values for the theoretically calculated ahsorhance of rhodopsin, yet their results for the simple 11-cis-retinal protonated Schilf base (pSb). which forms the basis for the ensuing quantum mechanical and molecular mechanical (QM/MM) calculations, differ by 0.56 eV or 176 nm.
Recently the gas phase absorption spectra of several retinal Schiff bases in different protonation states have been determined (14.15) and found to peak at 610/620 nm (transpSb in Scheme 1 ). 487 nm (trans-SbN^sup +^), and 610 nm (cis-pSb). These data define much needed reference points for the calculation of retinal protein spectra, both for the protonated chromophores in vacuo and for the effect of a positive charge in a defined relative orientation to the chromophore. To cover the short-wavelength region of retinal Schiff base spectra, we also include the neutral species trans-Sb whose absorbance in the nonpolar solvent 3-methylpentane peaks at 353 nm (16). In the following, we show that CASPT2 theory at a very high level of sophistication is able to quantitatively reproduce these data.
In view of the huge computational requirements, the /(-butyl group in Scheme 1 was reduced to methyl (the solvent spectra of the two pSbs are essentially identical) (17) and N(CH^sub 3^)^sub 3^^sup +^ to NH^sub 3^^sup +^. Geometry optimization at the CASPT2 level for systems of this size is still prohibitive in computer resources. We therefore resorted to MP2 and its analytical gradients, which allow for an efficient geometry search with a correlated wave function. Starting with the DFT-optimized structures (18). the chromophores were reoptimized with MP2 using a 6-31G** basis set (19).
All four chromophores exhibit strong bond alternation (Fig. 1), which is. however, significantly reduced between C9 and N16 in the three positively charged systems. A further reduction is observed in trans- and cis-pSb, where the positive charge is part of the ?-system. From C6 to N16, all chromophores are essentially planar with the exception of r/.s-pSb. which is twisted by 7° and 3° about the C11=C12 and the C12-C13 bonds, respectively, and moves the C13-N16 fragment away from the bulky ?-ionone ring.
Ground and excited state energies were calculated with the CASSCF method as provided by the MOLCAS set of routines (20). Six-root state-averaged wave functions were expanded in an atomic natural orbital basis set (21) with the contraction C,N[4s3p1d)/H[2s]. The active space was (12,12), i.e.. all pseudo ?-clectrons and valence pscudo ?-orbitals were considered. Second-order corrections to the CASSCF energies were calculated with CASPT2. All core orbitals were kept frozen during the calculations. To avoid the effect of intruder states, the level shift was set uniformly to 0.3 au. These parameters are identical to the ones we used in recent studies on retinal model
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