Photoexcitation of 11-Z-cis-7,8-dihydro retinal and 11-Z-cis retinal: A comparative computational study

M06-SX screened-exchange density functional for chemistry and solid-state physics

Screened-exchange hybrid density functionals are especially recommended for solid-state systems because they combine the advantages of hybrid functionals with the correct physics and lower computational cost associated with the attenuation of Hartree-Fock exchange at long range. We present a screened-exchange hybrid functional, M06-SX, that combines the functional form of the local revM06-L functional with a percentage of short-range nonlocal Hartree-Fock exchange. The M06-SX functional gives good results not only for a large set of training data but also for several databases quite different from the training data. The mean unsigned error (MUE) of the M06-SX functional is 2.85 kcal/mol for 418 atomic and molecular energies (AME418) in Minnesota Database 2019, which is better than all five other screened-exchange hybrid functionals tested in this work. The M06-SX functional also gives especially good results for semiconductor band gaps, molecular dissociation energies, noncovalent interactions, barrier heights, and electronic excitation energies excluding long-range charge transfer excitations. For the LC18 lattice constants database, the M06-SX functional gives an MUE of only 0.034 Å. Therefore, the M06-SX functional is well suited for studying molecular chemistry as well as solid-state physics.

Initial excited-state relaxation of locked retinal protonated schiff base chromophore. An insight from coupled cluster and multireference perturbation theory calculations

The initial S₁ excited-state relaxation of retinal protonated Schiff base (RPSB) analog with central C11C12 double bond locked by eight-membered ring (locked-11.8) was investigated by means of multireference perturbation theory methods (XMCQDPT2, XMS-CASPT2, MS-CASPT2) as well as single-reference coupled-cluster CC2 method. The analysis of XMCQDPT2-based geometries reveals rather weak coupling between in-plane and out-of-plane structural evolution and minor energetical relaxation of three locked-11.8 conformers. Therefore, a strong coupling between bonds length inversion and backbone out-of-plane deformation resulting in a very steep S₁ energy profile predicted by CASSCF/CASPT2 calculations is in clear contradiction with the reference XMCQDPT2 results. Even though CC2 method predicts good quality ground-state structures, the excited-state structures display more advanced torsional deformation leading to ca. 0.2 eV exaggerated energy relaxation and significantly red shifted (0.4-0.7 eV) emission maxima. According to our findings, the initial photoisomerization process in locked-11.8, and possibly in other RPSB analogs, studied fully (both geometries and energies) by multireference perturbation theory may be somewhat slower than predicted by CASSCF/CASPT2 or CC2 methods. © 2018 Wiley Periodicals, Inc.

Is the choice of a standard zeroth-order hamiltonian in CASPT2 ansatz optimal in calculations of excitation energies in protonated and unprotonated schiff bases of retinal?

To account for systematic error of CASPT2 method empirical modification of the zeroth-order Hamiltonian with Ionization Potential-Electron Affinity (IPEA) shift was introduced. The optimized IPEA value (0.25 a.u.), called standard IPEA (S-IPEA), was recommended but due to its unsatisfactory performance in multiple metallic and organic compounds it has been questioned lately as a general parameter working properly for all molecules under CASPT2 study. As we are interested in Schiff bases of retinal, an important question emerging from this conflict of choice, to use or not to use S-IPEA, is whether the introduction of the modified zeroth-order Hamiltonian into CASPT2 ansatz does really improve their energetics. To achieve this goal, we assessed an impact of the IPEA shift value, in a range of 0-0.35 a.u., on vertical excitation energies to low-lying singlet states of two protonated (RPSBs) and two unprotonated (RSBs) Schiff bases of retinal for which experimental data in gas phase are available. In addition, an effect of geometry, basis set, and active space on computed VEEs is also reported. We find, that for these systems, the choice of S-IPEA significantly overestimates both S₀ →S₁ and S₀ →S₂ energies and the best theoretical estimate, in reference to the experimental data, is provided with either unmodified zeroth-order Hamiltonian or small value of the IPEA shift in a range of 0.05-0.15 a.u., depending on active space and basis set size, equilibrium geometry, and character of the excited state. © 2018 Wiley Periodicals, Inc.

Excitation spectra of retinal by multiconfiguration pair-density functional theory

Retinal is the chromophore in proteins responsible for vision. The absorption maximum of retinal is sensitive to mutations of the protein. However, it is not easy to predict the absorption spectrum of retinal accurately, and questions remain even after intensive investigation. Retinal poses a challenge for Kohn-Sham density functional theory (KS-DFT) because of the charge transfer character in its excitations, and it poses a challenge for wave function theory because the large size of the molecule makes multiconfigurational perturbation theory methods expensive. In this study, we demonstrate that multiconfiguration pair-density functional theory (MC-PDFT) provides an efficient way to predict the vertical excitation energies of 11-Z retinal, and it reproduces the experimentally determined absorption band widths and peak positions better than complete active space second-order perturbation theory (CASPT2). The consistency between complete active space self-consistent field (CASSCF) and KS-DFT dipole moments is demonstrated to be a useful criterion in selecting the active space. We also found that the nature of the terminal groups and the conformations of retinal play a significant role in the absorption spectrum. By considering a thermal distribution of conformations, we predict an absorption spectrum of retinal that is consistent with the experimental gas-phase spectrum. The location of the absorption peak and the spectral broadening based on MC-PDFT calculations agree better with experiments than those of CASPT2.

Theoretical description of protein field effects on electronic excitations of biological chromophores

Photoinitiated phenomena play a crucial role in many living organisms. Plants, algae, and bacteria absorb sunlight to perform photosynthesis, and convert water and carbon dioxide into molecular oxygen and carbohydrates, thus forming the basis for life on Earth. The vision of vertebrates is accomplished in the eye by a protein called rhodopsin, which upon photon absorption performs an ultrafast isomerisation of the retinal chromophore, triggering the signal cascade. Many other biological functions start with the photoexcitation of a protein-embedded pigment, followed by complex processes comprising, for example, electron or excitation energy transfer in photosynthetic complexes. The optical properties of chromophores in living systems are strongly dependent on the interaction with the surrounding environment (nearby protein residues, membrane, water), and the complexity of such interplay is, in most cases, at the origin of the functional diversity of the photoactive proteins. The specific interactions with the environment often lead to a significant shift of the chromophore excitation energies, compared with their absorption in solution or gas phase. The investigation of the optical response of chromophores is generally not straightforward, from both experimental and theoretical standpoints; this is due to the difficulty in understanding diverse behaviours and effects, occurring at different scales, with a single technique. In particular, the role played by ab initio calculations in assisting and guiding experiments, as well as in understanding the physics of photoactive proteins, is fundamental. At the same time, owing to the large size of the systems, more approximate strategies which take into account the environmental effects on the absorption spectra are also of paramount importance. Here we review the recent advances in the first-principle description of electronic and optical properties of biological chromophores embedded in a protein environment. We show their applications on paradigmatic systems, such as the light-harvesting complexes, rhodopsin and green fluorescent protein, emphasising the theoretical frameworks which are of common use in solid state physics, and emerging as promising tools for biomolecular systems.

Rhodopsin Absorption from First Principles: Bypassing Common Pitfalls

Bovine rhodopsin is the most extensively studied retinal protein and is considered the prototype of this important class of photosensitive biosystems involved in the process of vision. Many theoretical investigations have attempted to elucidate the role of the protein matrix in modulating the absorption of retinal chromophore in rhodopsin, but, while generally agreeing in predicting the correct location of the absorption maximum, they often reached contradicting conclusions on how the environment tunes the spectrum. To address this controversial issue, we combine here a thorough structural and dynamical characterization of rhodopsin with a careful validation of its excited-state properties via the use of a wide range of state-of-the-art quantum chemical approaches including various flavors of time-dependent density functional theory (TDDFT), different multireference perturbative schemes (CASPT2 and NEVPT2), and quantum Monte Carlo (QMC) methods. Through extensive quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations, we obtain a comprehensive structural description of the chromophore-protein system and sample a wide range of thermally accessible configurations. We show that, in order to obtain reliable excitation properties, it is crucial to employ a sufficient number of representative configurations of the system. In fact, the common use of a single, ad hoc structure can easily lead to an incorrect model and an agreement with experimental absorption spectra due to cancelation of errors. Finally, we show that, to properly account for polarization effects on the chromophore and to quench the large blue-shift induced by the counterion on the excitation energies, it is necessary to adopt an enhanced description of the protein environment as given by a large quantum region including as many as 250 atoms.

Protein Field Effect on the Dark State of 11-cis Retinal in Rhodopsin by Quantum Monte Carlo/Molecular Mechanics

The accurate determination of the geometrical details of the dark state of 11-cis retinal in rhodopsin represents a fundamental step for the rationalization of the protein role in the optical spectral tuning in the vision mechanism. We have calculated geometries of the full retinal protonated Schiff base chromophore in the gas phase and in the protein environment using the correlated variational Monte Carlo method. The bond length alternation of the conjugated carbon chain of the chromophore in the gas phase shows a significant reduction when moving from the β-ionone ring to the nitrogen, whereas, as expected, the protein environment reduces the electronic conjugation. The proposed dark state structure is fully compatible with solid-state NMR data reported by Carravetta et al. [J. Am. Chem. Soc. 2004, 126, 3948-3953]. TDDFT/B3LYP calculations on such geometries show a blue opsin shift of 0.28 and 0.24 eV induced by the protein for S1 and S2 states, consistently with literature spectroscopic data. The effect of the geometrical distortion alone is a red shift of 0.21 and 0.16 eV with respect to the optimized gas phase chromophore. Our results open new perspectives for the study of the properties of chromophores in their biological environment using correlated methods.

Axial chirality of donor-donor, donor-acceptor, and tethered 1,1'-binaphthyls: a theoretical revisit with dynamics trajectories

The circular dichroism (CD) spectra of (R)-2,2'-dimethoxy-1,1'-binaphthyl (DD) and its untethered and tethered donor-acceptor analogues (DA and DA7-DA9) were investigated experimentally and theoretically. The experimental CD spectra of DD and DA resembled each other in several aspects, displaying a positive-positive-negative Cotton effect pattern in the (1)L(b)-(1)L(a) region and a strong negative couplet at the (1)B(b) band, but significantly differed in transition energy and rotatory strength. The couplet amplitude (A) of the main band was 1.6 times larger in DA than in DD, despite the comparable extinction coefficients and seemingly analogous conformations. An additional positive Cotton effect was observed at the CT (CT) band for donor-acceptor binaphthyl DA. Our theoretical prediction of the CD spectra of binaphthyls involves three sequential first principle quantum mechanics (QM) calculations. Thus, the geometry optimizations of a series of conformers with varying dihedral angles were performed by the dispersion-corrected DFT-D method using the B97-D functional and the TZV2P basis set. The potential curve as a function of the dihedral angle (θ) was obtained by using the SCS-MP2/TZVPP single-point energy calculations with and without application of the solvent correction. The CD spectrum of each conformer was independently calculated by the second-order approximate coupled cluster calculation (CC2 method) using the TZVPP basis sets and the resolution of the identity (RI-J) approximation. The (net) theoretical CD spectrum was obtained by averaging over all possible conformers, where the dynamics trajectories based on the relative SCS-MP2 energies were taken into account. By using 17 possible conformers at θ varying from 50 to 130° by 5° intervals, the experimental CD spectra were successfully reproduced in a quantitative manner, enabling us to characterize properly almost all of the important spectral features and chiroptical properties. The two-state model, reported previously, turned out to have led to the right answer with wrong reasons. The couplet sign and amplitude A are critical functions of θ and can be used not only for (qualitatively) determining the absolute configuration but also for quantitatively analyzing the binaphthyl conformations. The angle dependence of A was already argued in the classical coupled oscillator and exciton chirality theories to provide reasonable structure elucidations but only in a qualitative or semiquantitative manner. Our method is able to predict the A value quantitatively as a function of θ. For tethered binaphthyls DA7-DA9, particular care should be exercised in the conformational assessment based on the classical treatment because the amplitude A was shown to be significantly affected by the existence of the tether itself. In the present method, the couplet amplitude A was nicely related to the dihedral angle θ of DA and DD by the state-of-the-art ab initio calculations, enabling us to gain the quantitative information about the conformation of axially chiral binaphthyls. The Cotton effect at the CT band also serves as a complementary clue for elucidating the conformation of donor-acceptor binaphthyls.

Density functional approximations for charge transfer excitations with intermediate spatial overlap

Density functional theory is now the method of choice for calculating the electronic structure of complex systems, and time-dependent density functional theory (TDDFT) is now the preferred method for calculating spectroscopic properties of large molecules. The validity of the theory depends mainly on the quality of the approximation to the unknown exchange-correlation energy. In the present paper we consider TDDFT calculations of electronic excitation energies and oscillator strengths. We show that the M06-2X and M08-HX density functionals perform as well as and better than the range-separated CAM-B3LYP functional for charge transfer excitations with intermediate spatial overlap but have better performance for bond energies, noncovalent interactions, and chemical reaction barrier heights for representative systems; we conclude that M06-2X and M08-HX should be preferred for studies requiring the exploration of potential energy surfaces as well as electronic excitation energies, provided that those excitations with the longest-range charge transfer are excluded.