Designing Conical Intersections for Light-Driven Single Molecule Rotary Motors: From Precessional to Axial Motion

In the past, the design of light-driven single molecule rotary motors has been mainly guided by the modification of their ground-state conformational properties. Further progress in this field is thus likely to be achieved through a detailed understanding of light-induced dynamics of the system and the ways of modulating it by introducing chemical modifications. In the present theoretical work, the analysis of model organic chromophores and synthesized rotary motors is used for rationalizing the effect of electron-withdrawing heteroatoms (such as a cationic nitrogen) on the topography and branching plane of mechanistically relevant conical intersections. Such an analysis reveals how the character of rotary motion could be changed from a precessional motion to an axial rotational motion. These concepts are then used to design and build quantum chemical models of three distinct types of Schiff base rotary motors. One of these models, featuring the synthetically viable indanylidenepyrroline framework, has conical intersection structures consistent with an axial rotation not hindered by ground-state conformational barriers. It is expected that this type of motor should be capable of funneling the photon energy into specific rotary modes, thus achieving photoisomerization quantum efficiencies comparable to those seen in visual pigments

Conical Intersection and Potential Energy Surface Features of a Model Retinal Chromophore: Comparison of EOM-CC and Multireference Methods

This work investigates the performance of equation-of-motion coupled-cluster (EOM-CC) methods for describing the changes in the potential energy surfaces of the penta-2,4-dieniminium cation, a reduced model of the retinal chromophore of visual pigments, due to dynamical electron correlation effects. The ground-state wave function of this model includes charge-transfer and diradical configurations whose weights vary along different displacements and are rapidly changing at the conical intersection between the ground and the first excited states, making the shape of the potential energy surface sensitive to a balanced description of nondynamical and dynamical correlation. Recently, variational (MRCISD) and perturbative (MRPT2) approaches for including dynamical correlation in CASSCF-based calculations were tested along three representative ground state paths. Here, we use the same three paths to compare the performance of single-reference EOM-CC methods against MRCISD and MRCISD+Q. We find that the spin-flip variant of EOM-CCSD with perturbative inclusion of triple excitations (dT or fT) produces potential energy profiles of the two lowest electronic states in quantitative agreement with MRCISD+Q (our highest-quality reference method). The nonparallelity errors and differences in vertical energy differences of the two surfaces along these scans are less than 1.4 kcal/mol (EOM-SF-CCSD­(dT) versus MRCISD+Q). For comparison, the largest error of MRCISD versus MRCISD+Q is 1.7 kcal/mol. Our results show that the EOM-CC methods provide an alternative to multireference approaches and may be used to study photochemical systems like the one used in this work

Inverse versus Normal Dithienylethenes: Computational Investigation of the Photocyclization Reaction

The understanding of the intimate electronic processes in photochromes is essential to optimize the properties of light-controllable devices. For one of the most studied classes of molecular switches, namely, dithienylethenes, the relative efficiencies of the normal and inverse structures remained puzzling. Indeed, despite a larger ratio of the active antiparallel conformers for the latter, the quantum yields of cyclization of inverse dithienylethenes do not exceed those of its normal counterpart. In the present contribution, we provide the first explanation of this experimental outcome using multireference ab initio quantum chemistry. We demonstrate the existence of a fluorescent intermediate on the S₁ state of the inverse system that generates a photochemically unreactive conformation in the ground state. This study paves the way toward a rational development of efficient molecular photochromes presenting a photon-quantitative response

Combined Self-Consistent-Field and Spin-Flip Tamm–Dancoff Density Functional Approach to Potential Energy Surfaces for Photochemistry

We present a new approach to calculating potential energy surfaces for photochemical reactions by combining self-consistent-field calculations for single-reference ground and excited states with symmetry-corrected spin-flip Tamm–Dancoff approximation calculations for multireference electronic states. The method is illustrated by an application with the M05-2X exchange-correlation functional to <i>cis</i>–<i>trans</i> isomerization of the penta-2,4-dieniminium cation, which is a model (with three conjugated double bonds) of the protonated Schiff base of retinal. We find good agreement with multireference configuration interaction-plus-quadruples (MRCISD+Q) wave function calculations along three key paths in the strong-interaction region of the ground and first excited singlet states

Impact of Electronic State Mixing on the Photoisomerization Time Scale of the Retinal Chromophore

Spectral data show that the photoisomerization of retinal protonated Schiff base (rPSB) chromophores occurs on a 100 fs time scale or less in vertebrate rhodopsins, it is several times slower in microbial rhodopsins and it is between one and 2 orders of magnitude slower in solution. These time scale variations have been attributed to specific modifications of the topography of the first excited state potential energy surface of the chromophore. However, it is presently not clear which specific environment effects (e.g., electrostatic, electronic, or steric) are responsible for changing the surface topography. Here, we use QM/MM models and excited state trajectory computations to provide evidence for an increase in electronic mixing between the first and the second excited state of the chromophore when going from vertebrate rhodopsin to the solution environments. Ultimately, we argue that a correlation between the lifetime of the first excited state and electronic mixing between such state and its higher neighbor, may have been exploited to evolve rhodopsins toward faster isomerization and, possibly, light-sensitivity

Systematic Excited State Studies of Reversibly Switchable Fluorescent Proteins

The reversibly switchable fluorescent proteins Dronpa, rsFastLime, rsKame, Padron, and bsDronpa feature the same chromophore but display a 40 nm variation in absorption maxima and an only 18 nm variation in emission maxima. In the present contribution, we employ QM/MM models to investigate the mechanism of such remarkably different spectral variations, which are caused by just a few amino acid replacements. We show that the models, which are based on CASPT2//CASSCF level of QM theory, reproduce the observed trends in absorption maxima, with only a 3.5 kcal/mol blue-shift, and in emission maxima, with an even smaller 1.5 kcal/mol blue-shift with respect to the observed quantities. In order to explain the variations across the series, we look at the chromophore’s electronic structure change during absorption and emission. Such analysis indicates that a change in charge-transfer character, which is more pronounced during absorption, triggers a cascade of hydrogen-bond-network rearrangements, suggesting preparation to an isomerization event. We also show how the contribution of Arg 89 and Arg 64 residues to the chromophore conformational changes correlate with the spectral variations in absorption and emission. Furthermore, we describe how the conical intersection stability is related to the protein’s photophysical properties. While for the Dronpa, rsFastLime, and rsKame triad, the stability correlates with the photoswitching speed, this does not happen for bsDronpa and Padron, suggesting a less obvious photoisomerization mechanism

Relationship between Excited State Lifetime and Isomerization Quantum Yield in Animal Rhodopsins: Beyond the One-Dimensional Landau–Zener Model

We show that the speed of the chromophore photoisomerization of animal rhodopsins is not a relevant control knob for their light sensitivity. This result is at odds with the momentum-driven tunnelling rationale (i.e., assuming a one-dimensional Landau–Zener model for the decay: Zener, C. Non-Adiabatic Crossing of Energy Levels. <i>Proc. R. Soc. London, Ser. A</i> <b>1932,</b> 137 (833), 696–702) holding that a faster nuclear motion through the conical intersection translates into a higher quantum yield and, thus, light sensitivity. Instead, a model based on the phase-matching of specific excited state vibrational modes should be considered. Using extensive semiclassical hybrid quantum mechanics/molecular mechanics trajectory computations to simulate the photoisomerization of three animal rhodopsin models (visual rhodopsin, squid rhodopsin and human melanopsin), we also demonstrate that phase-matching between three different modes (the reactive carbon and hydrogen twisting coordinates and the bond length alternation mode) is required to achieve high quantum yields. In fact, such “phase-matching” mechanism explains the computational results and provides a tool for the prediction of the photoisomerization outcome in retinal proteins

Effects of the Protein Environment on the Spectral Properties of Tryptophan Radicals in <i>Pseudomonas aeruginosa</i> Azurin

Many biological electron-transfer reactions involve short-lived tryptophan radicals as key reactive intermediates. While these species are difficult to investigate, the recent photogeneration of a long-lived neutral tryptophan radical in two <i>Pseudomonas aeruginosa</i> azurin mutants (Az48W and ReAz108W) made it possible to characterize the electronic, vibrational, and magnetic properties of such species and their sensitivity to the molecular environment. Indeed, in Az48W the radical is embedded in the hydrophobic core while, in ReAz108W it is solvent-exposed. Here we use density functional theory and multiconfigurational perturbation theory to construct quantum-mechanics/molecular-mechanics models of Az48W^• and ReAz108W^• capable of reproducing specific features of their observed UV–vis, resonance Raman, and electron paramagnetic resonance spectra. The results show that the models can correctly replicate the spectral changes imposed by the two contrasting hydrophobic and hydrophilic environments. Most importantly, the same models can be employed to disentangle the molecular-level interactions responsible for such changes. It is found that the control of the hydrogen bonding between the tryptophan radical and a single specific surface water molecule in ReAz108W^• represents an effective means of spectral modulation. Similarly, a specific electrostatic interaction between the radical moiety and a Val residue is found to control the Az48W^• excitation energy. These modulations appear to be mediated by the increase in nitrogen negative charge (and consequent increase in hydrogen bonding) of the spectroscopic D₂ state with respect to the D₀ state of the chromophore. Finally, the same protein models are used to predict the relaxed Az48W^• and ReAz108W^• D₂ structures, showing that the effect of the environment on the corresponding fluorescence maxima must parallel that of D₀ absorption spectra

Assessment of Density Functional Theory for Describing the Correlation Effects on the Ground and Excited State Potential Energy Surfaces of a Retinal Chromophore Model

In the quest for a cost-effective level of theory able to describe a large portion of the ground and excited potential energy surfaces of large chromophores, promising approaches are rooted in various approximations to the exact density functional theory (DFT). In the present work, we investigate how generalized Kohn–Sham DFT (GKS-DFT), time-dependent DFT (TDDFT), and spin-restricted ensemble-DFT (REKS) methods perform along three important paths characterizing a model retinal chromophore (the penta-2,4-dieniminium cation) in a region of near-degeneracy (close to a conical intersection) with respect to reference high-level multiconfigurational wave function methods. If GKS-DFT correctly describes the closed-shell charge transfer state, only TDDFT and REKS approaches give access to the open-shell diradical, one which sometimes corresponds to the electronic ground state. It is demonstrated that the main drawback of the usual DFT-based methods lies in the absence of interactions between the charge transfer and the diradicaloid configurations. Hence, we test a new computational scheme based on the State-averaged REKS (SA-REKS) approach, which explicitly includes these interactions into account. The State-Interaction SA-REKS (SI-SA-REKS) method significantly improves on the REKS and the SA-REKS results for the target system. The similarities and differences between DFT and wave function-based approaches are analyzed according to (1) the active space dimensions of the wave function-based methods and (2) the relative electronegativities of the allyl and protonated Schiff base moieties

Origin of Fluorescence in 11-<i>cis</i> Locked Bovine Rhodopsin

The excited state lifetime of bovine rhodopsin (Rh) increases from ca. 100 fs to 85 ps when the C11C12 bond of its chromophore is locked by a cyclopentene moiety (Rh5). To explain such an increase, we employed <i>ab initio</i> multiconfigurational quantum chemistry to construct computer models of Rh and Rh5 and to investigate the shape of their excited state potential energy surfaces in a comparative way. Our results show that the observed Rh5 fluorescence (λ_max^f = 620 nm) is due to a previously unreported locally excited intermediate whose lifetime is controlled by a small energy barrier. The analysis of the properties and decay path of such an intermediate provides useful information for engineering rhodopsin variants with augmented fluorescence efficiencies