Computational evidence in favor of a two-state, two-mode model of the retinal chromophore photoisomerization

Tuning the Photoisomerization Mechanism of Oxindole Switches with Electron-Donating Substituents

This study investigates the photoreaction mechanism of a hydroxy-substituted oxindole photoswitch using femtosecond transient absorption, fluorescence up-conversion, and computational chemistry. Deprotonation of the hydroxyl group enhances the push-pull character in the molecule, allowing tuning of the photoisomerization mechanism from a precessional to an axial motion. The neutral form of the switch exhibits longer excited-state lifetimes, while the anionic form decays rapidly within 200 fs. Computational models show that deprotonation increases the charge transfer and accessibility to conical intersections. This work highlights how varying the electron-donating strength of a substituent in a push-pull photoswitch tunes the photoreaction mechanism in designing photoswitches.

Mapping photoisomerization dynamics on a three-state model potential energy surface in bacteriorhodopsin using femtosecond stimulated Raman spectroscopy

The process of proton translocation in Halobacterium salinarum, triggered by light, is powered by the photoisomerization of all-trans-retinal in bacteriorhodopsin (bR). The primary events in bR involving rapid structural changes upon light absorption occur within subpicoseconds to picoseconds. While the three-state model has received extensive support in describing the primary events between the H and K states, precise characterization of each excited state in the three-state model during photoisomerization remains elusive. In this study, we investigate the ultrafast structural dynamics of all-trans-retinal in bR using femtosecond stimulated Raman spectroscopy. We report Raman modes at 1820 cm-1 which arise from C[double bond, length as m-dash]C stretch vibronic coupling and provide direct experimental evidence for the involvement of the I and J states with 2A- g symmetric character in the three-state model. The detection of the C[double bond, length as m-dash]C vibronic coupling mode, C[double bond, length as m-dash]N stretching mode (1700 cm-1), and hydrogen out-of-plane (HOOP) mode (954 cm-1) further supports the three-state model that elucidates the initial charge translocation along the conjugated chain accompanied by trans-to-cis photoisomerization dynamics through H(1B+ u) → I(2A- g) → J(2A- g) → K(13-cis ground state) transitions in all-trans-retinal in bR.

Fluorescent Rhodopsins: A Challenging Test for Cost-Effective QM/MM Approaches

In this study, we evaluate the performance of two cost-effective models, namely, TD-DFT and ΔSCF methods, combined with different molecular mechanics models, to predict the photophysical and photochemical properties of a set of fluorescent mutants of the microbial rhodopsin Archaerhodopsin-3. We investigate absorption energies and excited-state isomerization barriers of the embedded retinal protonated Schiff-base chromophore by comparing different DFT functionals as well as different approximations of the embedding model. For absorption energies, CAM-B3LYP demonstrates the most consistent alignment with experiments among the functionals tested, whereas the embedding potentials exhibit similar accuracy. However, incorporating linear response corrections within the polarizable TD-DFT/MM framework enhances accuracy. The photoisomerization barriers, instead, exhibit a pronounced sensitivity to the choice of embedding model, underscoring the complex role that environmental factors play in modulating predictions of excited-state processes. For the two properties here investigated, ΔSCF/MM presents qualitatively similar behavior with respect to TD-DFT for all the tested embedding models.

Machine Learning Optimization of Non-Kasha Behavior and of Transient Dynamics in Model Retinal Isomerization

Designing a model of retinal isomerization in rhodopsin, the first step in vision, that accounts for both experimental transient and stationary state observables is challenging. Here, multiobjective Bayesian optimization is employed to refine the parameters of a minimal two-state-two-mode (TM) model describing the photoisomerization of retinal in rhodopsin. The optimized retinal model predicts excitation wavelength-dependent fluorescence spectra that closely align with experimentally observed non-Kasha behavior in the nonequilibrium steady state. Further, adjustments to the potential energy surface within the TM model reduce the discrepancies across the time domain. Overall, agreement with experimental data is excellent.

Study of Photoselectivity in Linear Conjugated Chromophores Using the XMS-CASPT2 Method

Photoisomerization, the structural alteration of molecules upon absorption of light, is crucial for the function of biological chromophores such as retinal in opsins, proteins vital for vision and other light-sensitive processes. The intrinsic selectivity of this isomerization process (i.e., which double bond in the chromophore is isomerized) is governed by both the inherent properties of the chromophore and its surrounding environment. In this study, we employ the extended multistate complete active space second-order perturbation theory (XMS-CASPT2) method to investigate photoisomerization selectivity in linear conjugated chromophores, focusing on two simple molecular models resembling retinal. By analyzing electronic energies, intramolecular charge separation, and conical intersection topographies in the gas phase, we show that the photoproduct formed by rotation around the double bond near the Schiff base is energetically favored. The topographic differences at the conical intersections leading to different photoproducts reveal differences in photodynamics. In multiphoton excitation, the primary photoproduct typically reverts to the initial configuration rather than rotating around a different double bond. Our study offers new insights into the photodynamics of photoisomerizing double bonds in π-conjugated chromophores. We anticipate that our findings will provide valuable perspectives for advancing the understanding of biological chromophores and for designing efficient photochemical switches with applications in molecular electronics and phototherapy.

Theoretical Investigation on the Reversible Photoswitch Mechanism of Benzylidene-Oxazolone System

The design and application of molecular photoswitches have attracted much attention. Herein, we performed a detailed computational study on the photoswitch benzylidene-oxazolone system based on static electronic structure calculations and on-the-fly excited-state dynamic simulations. For the Z and E isomer, we located six and four minimum energy conical intersections (MECIs) between the first excited state (S1) and the ground state (S0), respectively. Among them, the relaxation pathway driven by ring-puckering motion is the most competitive channel with the photoisomeization process, leading to the low photoisomerization quantum yield. In the dynamic simulations, about 88 % and 66 % trajectories decay from S1 to S0 for Z and E isomer, respectively, within the total simulation time of ~2 ps. The photoisomeization quantum yields obtained in our study (0.20 for Z→E and 0.12 for E→Z) agree well with the experimental measured values (0.25 and 0.11), even though the number of trajectories is limited to 50. Our study sheds light on the complexity of the benzylidene-oxazolone system 's deactivation process and the competitive mechanisms among different reaction channels, which provides theoretical guidance for further design and development of benzylidene-oxazolone based molecular photoswitches.

Ultrafast terahertz Stark spectroscopy reveals the excited-state dipole moments of retinal in bacteriorhodopsin

The photoinduced all-trans to 13-cis isomerization of the retinal Schiff base represents the ultrafast first step in the reaction cycle of bacteriorhodopsin (BR). Extensive experimental and theoretical work has addressed excited-state dynamics and isomerization via a conical intersection with the ground state. In conflicting molecular pictures, the excited state potential energy surface has been modeled as a pure S[Formula: see text] state that intersects with the ground state, or in a 3-state picture involving the S[Formula: see text] and S[Formula: see text] states. Here, the photoexcited system passes two crossing regions to return to the ground state. The electric dipole moment of the Schiff base in the S[Formula: see text] and S[Formula: see text] state differs strongly and, thus, its measurement allows for assessing the character of the excited-state potential. We apply the method of ultrafast terahertz (THz) Stark spectroscopy to measure electric dipole changes of wild-type BR and a BR D85T mutant upon electronic excitation. A fully reversible transient broadening and spectral shift of electronic absorption is induced by a picosecond THz field of several megavolts/cm and mapped by a 120-fs optical probe pulse. For both BR variants, we derive a moderate electric dipole change of 5 [Formula: see text] 1 Debye, which is markedly smaller than predicted for a neat S[Formula: see text]-character of the excited state. In contrast, S[Formula: see text]-admixture and temporal averaging of excited-state dynamics over the probe pulse duration gives a dipole change in line with experiment. Our results support a picture of electronic and nuclear dynamics governed by the interaction of S[Formula: see text] and S[Formula: see text] states in a 3-state model.

Investigation of ultrafast intermediate states during singlet fission in lycopene H-aggregate using femtosecond stimulated Raman spectroscopy

The singlet fission process involves the conversion of one singlet excited state into two triplet states, which has significant potential for enhancing the energy utilization efficiency of solar cells. Carotenoid, a typical π conjugated chromophore, exhibits specific aggregate morphologies known to display singlet fission behavior. In this study, we investigate the singlet fission process in lycopene H-aggregates using femtosecond stimulated Raman spectroscopy aided by quantum chemical calculation. The experimental results reveal two reaction pathways that effectively relax the S2 (11Bu+) state populations in lycopene H-aggregates: a monomer-like singlet excited state relaxation pathway through S2 (11Bu+) → 11Bu- → S1 (21Ag-) and a dominant sequential singlet fission reaction pathway involving the S2 (11Bu+) state, followed by S* state, a triplet pair state [1(TT)], eventually leading to a long lifetime triplet state T1. Importantly, the presence of both anionic and cationic fingerprint Raman peaks in the S* state is indicative of a substantial charge-transfer character.

Color Tuning in Bovine Rhodopsin through Polarizable Embedding

Bovine rhodopsin is among the most studied proteins in the rhodopsin family. Its primary activation mechanism is the photoisomerization of 11-cis retinal, triggered by the absorption of a UV-visible photon. Different mutants of the same rhodopsin show different absorption wavelengths due to the influence of the specific amino acid residues forming the cavity in which the retinal chromophore is embedded, and rhodopsins activated at different wavelengths are, for example, exploited in the field of optogenetics. In this letter, we present a procedure for systematically investigating color tuning in models of bovine rhodopsin and a set of its mutants embedded in a membrane bilayer. Vertical excitation energy calculations were carried out with the polarizable embedding potential for describing the environment surrounding the chromophore. We show that polarizable embedding outperformed regular electrostatic embedding in determining both the vertical excitation energies and associated oscillator strengths of the systems studied.

Retinal photoisomerization versus counterion protonation in light and dark-adapted bacteriorhodopsin and its primary photoproduct

Discovered over 50 years ago, bacteriorhodopsin is the first recognized and most widely studied microbial retinal protein. Serving as a light-activated proton pump, it represents the archetypal ion-pumping system. Here we compare the photochemical dynamics of bacteriorhodopsin light and dark-adapted forms with that of the first metastable photocycle intermediate known as "K". We observe that following thermal double isomerization of retinal in the dark from bio-active all-trans 15-anti to 13-cis, 15-syn, photochemistry proceeds even faster than the ~0.5 ps decay of the former, exhibiting ballistic wave packet curve crossing to the ground state. In contrast, photoexcitation of K containing a 13-cis, 15-anti chromophore leads to markedly multi-exponential excited state decay including much slower stages. QM/MM calculations, aimed to interpret these results, highlight the crucial role of protonation, showing that the classic quadrupole counterion model poorly reproduces spectral data and dynamics. Single protonation of ASP212 rectifies discrepancies and predicts triple ground state structural heterogeneity aligning with experimental observations. These findings prompt a reevaluation of counter ion protonation in bacteriorhodopsin and contribute to the broader understanding of its photochemical dynamics.

Recommendations for Velocity Adjustment in Surface Hopping

This study investigates velocity adjustment directions after hopping in surface hopping dynamics. Using fulvene and a protonated Schiff base (PSB4) as case studies, we investigate the population decay and reaction yields of different sets of dynamics with the velocity adjusted in either the nonadiabatic coupling, gradient difference, or momentum directions. For the latter, in addition to the conventional algorithm, we investigated the performance of a reduced kinetic energy reservoir approach recently proposed. Our evaluation also considered velocity adjustment in the directions of approximate nonadiabatic coupling vectors. While results for fulvene are susceptible to the adjustment approach, PSB4 is not. We correlated this dependence to the topography near the conical intersections. When nonadiabatic coupling vectors are unavailable, the gradient difference direction is the best adjustment option. If the gradient difference is also unavailable, a semiempirical vector direction or the momentum direction with a reduced kinetic energy reservoir becomes an excellent option to prevent an artificial excess of back hoppings. The precise velocity adjustment direction is less crucial for describing the nonadiabatic dynamics than the kinetic energy reservoir's size.

From a one-mode to a multi-mode understanding of conical intersection mediated ultrafast organic photochemical reactions

This review discusses how ultrafast organic photochemical reactions are controlled by conical intersections, highlighting that decay to the ground-state at multiple points of the intersection space results in their multi-mode character.

Additive and epistatic effects influence spectral tuning in molluscan retinochrome opsin

The relationship between genotype and phenotype is nontrivial due to often complex molecular pathways that make it difficult to unambiguously relate phenotypes to specific genotypes. Photopigments, an opsin apoprotein bound to a light-absorbing chromophore, present an opportunity to directly relate the amino acid sequence to an absorbance peak phenotype (λmax). We examined this relationship by conducting a series of site-directed mutagenesis experiments of retinochrome, a non-visual opsin, from two closely related species: the common bay scallop, Argopecten irradians, and the king scallop, Pecten maximus. Using protein folding models, we identified three amino acid sites of likely functional importance and expressed mutated retinochrome proteins in vitro. Our results show that the mutation of amino acids lining the opsin binding pocket are responsible for fine spectral tuning, or small changes in the λmax of these light sensitive proteins Mutations resulted in a blue or red shift as predicted, but with dissimilar magnitudes. Shifts ranged from a 16 nm blue shift to a 12 nm red shift from the wild-type λmax. These mutations do not show an additive effect, but rather suggests the presence of epistatic interactions. This work highlights the importance of binding pocket shape in the evolution of spectral tuning and builds on our ability to relate genotypic changes to phenotypes in an emerging model for opsin functional analysis.

Spectroscopy and photoisomerization of protonated Schiff-base retinal derivatives in vacuo

The protonated Schiff-base retinal acts as the chromophore in bacteriorhodopsin as well as in rhodopsin. In both cases, photoexcitation initializes fast isomerization which eventually results in storage of chemical energy or signaling. The details of the photophysics for this important chromophore is still not fully understood. In this study, action-absorption spectra and photoisomerization dynamics of three retinal derivatives are measured in the gas phase and compared to that of the protonated Schiff-base retinal. The retinal derivatives include C₉C₁₀trans-locked, C₁₃C₁₄trans-locked and a retinal derivative without the β-ionone ring. The spectroscopy as well as the isomerization speed of the chromophores are altered significantly as a consequence of the steric constraints.

Control of Protonated Schiff Base Excited State Decay within Visual Protein Mimics: A Unified Model for Retinal Chromophores

Artificial biomimetic chromophore-protein complexes inspired by natural visual pigments can feature color tunability across the full visible spectrum. However, control of excited state dynamics of the retinal chromophore, which is of paramount importance for technological applications, is lacking due to its complex and subtle photophysics/photochemistry. Here, ultrafast transient absorption spectroscopy and quantum mechanics/molecular mechanics simulations are combined for the study of highly tunable rhodopsin mimics, as compared to retinal chromophores in solution. Conical intersections and transient fluorescent intermediates are identified with atomistic resolution, providing unambiguous assignment of their ultrafast excited state absorption features. The results point out that the electrostatic environment of the chromophore, modified by protein point mutations, affects its excited state properties allowing control of its photophysics with same power of chemical modifications of the chromophore. The complex nature of such fine control is a fundamental knowledge for the design of bio-mimetic opto-electronic and photonic devices.

Light-Induced Conformational Alterations in Heliorhodopsin Triggered by the Retinal Excited State

Heliorhodopsins are a recently discovered diverse retinal protein family with an inverted topology of the opsin where the retinal protonated Schiff base proton is facing the cell cytoplasmic side in contrast to type 1 rhodopsins. To explore whether light-induced retinal double-bond isomerization is a prerequisite for triggering protein conformational alterations, we utilized the retinal oxime formation reaction and thermal denaturation of a native heliorhodopsin of Thermoplasmatales archaeon SG8-52-1 (TaHeR) as well as a trans-locked retinal analogue (TaHeR_L) in which the critical C₁₃=C₁₄ double-bond isomerization is prevented. We found that both reactions are light-accelerated not only in the native but also in the “locked” pigment despite lacking any isomerization. It is suggested that light-induced charge redistribution in the retinal excited state polarizes the protein and triggers protein conformational perturbations that thermally decay in microseconds. The extracted activation energy and the frequency factor for both the reactions reveal that the light enhancement of TaHeR differs distinctly from the earlier studied type 1 microbial rhodopsins.

Extreme Parametric Sensitivity in the Steady-State Photoisomerization of Two-Dimensional Model Rhodopsin

We computationally studied the photoisomerization reaction of the retinal chromophore in rhodopsin using a two-state two-mode model coupled to thermal baths. Reaction quantum yields at the steady state (10 ps and beyond) were found to be considerably different than their transient values, suggesting a weak correlation between transient and steady-state dynamics in these systems. Significantly, the steady-state quantum yield was highly sensitive to minute changes in system parameters, while transient dynamics was nearly unaffected. Correlation of such sensitivity with standard level spacing statistics of the nonadiabatic vibronic system suggests a possible origin in quantum chaos. The significance of this observation of quantum yield parametric sensitivity in biological models of vision has profound conceptual and fundamental implications.

QM/MM Investigation of the Spectroscopic Properties of the Fluorophore of Bacterial Luciferase

We employ replica-exchange molecular dynamics (REMD) and a hybrid ab initio multiconfigurational quantum mechanics/molecular mechanics (QM/MM) approach to model the absorption and fluorescence properties of bacterial luciferin-luciferase. Specifically, we employ complete active space perturbation theory (CASPT2) and study the effect of active space, basis set, and IPEA shift on the computed energies. We discuss the effect of the protein environment on the fluorophore's excited-state potential energy surface and the role that the protein plays in enhancing the fluorescence quantum yield in bacterial bioluminescence.

Quantum and Quantum-Classical Studies of the Photoisomerization of a Retinal Chromophore Model

We report an in-depth analysis of the photo-induced isomerization of the 2-cis-penta-2,4-dieniminium cation: a minimal model of the 11-cis retinal protonated Schiff base chromophore of the dim-light photoreceptor rhodopsin. Based on recently developed three-dimensional potentials parametrized on ab initio multi-state multi-configurational second-order perturbation theory data, we perform quantum-dynamical studies. In addition, simulations based on various quantum-classical methods, among which Tully surface hopping and the coupled-trajectory approach derived from the exact factorization, allow us to validate their performance against vibronic wavepacket propagation and, therefore, a purely quantum treatment. Quantum-dynamics results uncover qualitative differences with respect to the two-dimensional Hahn-Stock potentials, widely used as model potentials for the isomerization of the same chromophore, due to the increased dimensionality and three-mode correlation. Quantum-classical simulations show, instead, that three-dimensional model potentials are capable of capturing a number of features revealed by atomistic simulations and experimental observations. In particular, a recently reported vibrational phase relationship between double-bond torsion and hydrogen-out-of-plane modes critical for rhodopsin isomerization efficiency is correctly reproduced.

Excited-State Vibronic Dynamics of Bacteriorhodopsin from Two-Dimensional Electronic Photon Echo Spectroscopy and Multiconfigurational Quantum Chemistry

Owing to the ultrafast time scale of the photoinduced reaction and high degree of spectral overlap among the reactant, product, and excited electronic states in bacteriorhodopsin (bR), it has been a challenge for traditional spectroscopies to resolve the interplay between vibrational dynamics and electronic processes occurring in the retinal chromophore of bR. Here, we employ ultrafast two-dimensional electronic photon echo spectroscopy to follow the early excited-state dynamics of bR preceding the isomerization. We detect an early periodic photoinduced absorptive signal that, employing a hybrid multiconfigurational quantum/molecular mechanical model of bR, we attribute to periodic mixing of the first and second electronic excited states (S1 and S2, respectively). This recurrent interaction between S1 and S2, induced by a bond length alternation of the retinal chromohore, supports the hypothesis that the ultrafast photoisomerization in bR is initiated by a process involving coupled nuclear and electronic motion on three different electronic states.

Trans-to-cis photoisomerization of cyclocurcumin in different environments rationalized by computational photochemistry

Cyclocurcumin is a turmeric component that has attracted much less attention compared to the well-known curcumin. In spite of the less deep characterization of its properties, cyclocurcumin has shown promising anticancer effects when used in combination with curcumin. Especially, due to its peculiar molecular structure, cyclocurcumin can be regarded as an almost ideal photoswitch, whose capabilities can also be exploited for relevant biological applications. Here, by means of state-of-the-art computational methods for electronic excited-state calculations (TD-DFT, MS-CASPT2, and XMS-CASPT2), we analyze in detail the absorption and photoisomerization pathways leading from the more stable trans isomer to the cis one. The different molecular surroundings, taken into account by means of the electrostatic solvent effect and compared with available experimental data, have been found to be critical in describing the fate of irradiated cyclocurcumin: when in non-polar environments, an excited state barrier prevents photoisomerization and favours fluorescence, whereas in polar solvents, an almost barrierless path results in a striking decrease of fluorescence, opening the way toward a crossing region with the ground state and thus funneling the photoproduction of the cis isomer.

Acid-base equilibrium of the chromophore counterion results in distinct photoisomerization reactivity in the primary event of proteorhodopsin

Proteorhodopsin (PR) is a proton-pumping rhodopsin, and it is known to exhibit a multi-phasic decay of the excited-state population in the primary process. So far, this complex excited-state decay has been attributed to the branching of the relaxation pathway on the excited-state potential energy surface. However, a recent ultrafast spectroscopic study on a sodium-pumping rhodopsin suggested that such a complex decay may originate from the heterogeneity in the ground state due to the acid-base equilibrium of the counterion of the protonated retinal Schiff base (PRSB). In this study, we studied the excited-state dynamics of PR at pH 11 and 4, in which the counterion of the PRSB, Asp97, is completely deprotonated and protonated, respectively. The obtained time-resolved absorption data revealed that the excited-state lifetime is decisively governed by the protonation state of Asp97, and the photoisomerization of the PRSB chromophore proceeds faster and more efficiently when Asp97 is deprotonated. This conclusion was further supported by high similarity of the excited-state dynamics between PR at pH 4 and the D97N mutant in which Asp97 is replaced with neutral Asn. The results of this study suggest that the protonation state of the PRSB counterion plays a decisive role in determining the excited-state dynamics and the photoisomerization reactivity of rhodopsins in general, by making a significant influence on the exited-state potential energy surface of the PRSB chromophore.

Multistate Multiconfiguration Quantum Chemical Computation of the Two-Photon Absorption Spectra of Bovine Rhodopsin

Recently, progress in IR sources has led to the discovery that humans can detect infrared (IR) light. This is hypothesized to be due to the two-photon absorption (TPA) events promoting the retina dim-light rod photoreceptor rhodopsin to the same excited state populated via one-photon absorption (OPA). Here, we combine quantum mechanics/molecular mechanics and extended multiconfiguration quasi-degenerate perturbation theory calculations to simulate the TPA spectrum of bovine rhodopsin (Rh) as a model for the human photoreceptor. The results show that the TPA spectrum of Rh has an intense S₀ → S₁ band but shows also S₀ → S₂ and S₀ → S₃ transitions whose intensities, relative to the S₀ → S₁ band, are significantly increased when compared to the corresponding bands of the OPA spectrum. In conclusion, we show that IR light in the 950 nm region can be perceived by rod photoreceptors, thus supporting the two-photon origin of the IR perception. We also found that the same photoreceptor can perceive red (i.e., close to 680 nm) light provided that TPA induces population of S₂.

Quantum Mechanical and Molecular Mechanics Modeling of Membrane-Embedded Rhodopsins

Computational chemistry provides versatile methods for studying the properties and functioning of biological systems at different levels of precision and at different time scales. The aim of this article is to review the computational methodologies that are applicable to rhodopsins as archetypes for photoactive membrane proteins that are of great importance both in nature and in modern technologies. For each class of computational techniques, from methods that use quantum mechanics for simulating rhodopsin photophysics to less-accurate coarse-grained methodologies used for long-scale protein dynamics, we consider possible applications and the main directions for improvement.

Far Red Fluorescent Proteins: Where Is the Limit of the Acylimine Chromophore?

The search for new near-infrared probes for fluorescence imaging applications is a rapidly growing field of research. Monomeric fluorescent proteins that autocatalyze their chromophore are the most versatile markers for in vivo applications, but the development of bright far-red fluorescent proteins (RFPs) has proven difficult. In this contribution, we search for the theoretical limit of the red shift and how it can be reached without sacrificing the fluorescence quantum yield. Through extensive excited-state pathway calculations, molecular dynamics sampling, and statistical modeling using QM/MM schemes, we provide a new understanding of the chromophore's photophysics including the role of its acylimine extension, which is the main difference from other families of fluorescent proteins. The excited-state dynamics of the mPlum RFP and its mutants provide an ideal basis due to mPlum's flexible binding pocket and extended dynamic Stokes shift. We found a large number of structural species with red-shifted emission that differ in rotamer states and H-bonds between key amino acid residues in the binding pocket. By analyzing their spectral and structural features, we derive guidelines for future rational genetic design strategies.

Evaluation of full valence correlation energies and gradients

Complete-active-space self-consistent field (CASSCF) wave functions are central to understanding strongly correlated molecules as they capture the entirety of electronic interactions within a subset of the orbital space. The most interesting case for CASSCF is the full valence limit, where all bonding and an equal number of virtual orbitals are included in the active space, and no approximation is made in selecting the important valence orbitals or electrons. While conventional algorithms require exponential computational time to evaluate full valence CASSCF, this article shows that the method of increments can do the same with polynomial effort, in a new method denoted iCASSCF. The method of increments can also provide density matrices and other necessary ingredients for the construction of the nuclear gradient. These goals are met through a many-body expansion that breaks the problem into smaller pieces that are subsequently reassembled to form close approximations of conventional CAS results. Practical demonstrations on a number of medium-sized molecules, with up to 116 valence electrons correlated in 116 orbitals, show the power of this methodology.

Bacteriorhodopsin: Structural Insights Revealed Using X-Ray Lasers and Synchrotron Radiation

Directional transport of protons across an energy transducing membrane—proton pumping—is ubiquitous in biology. Bacteriorhodopsin (bR) is a light-driven proton pump that is activated by a buried all- trans retinal chromophore being photoisomerized to a 13- cis conformation. The mechanism by which photoisomerization initiates directional proton transport against a proton concentration gradient has been studied by a myriad of biochemical, biophysical, and structural techniques. X-ray free electron lasers (XFELs) have created new opportunities to probe the structural dynamics of bR at room temperature on timescales from femtoseconds to milliseconds using time-resolved serial femtosecond crystallography (TR-SFX). Wereview these recent developments and highlight where XFEL studies reveal new details concerning the structural mechanism of retinal photoisomerization and proton pumping. We also discuss the extent to which these insights were anticipated by earlier intermediate trapping studies using synchrotron radiation. TR-SFX will open up the field for dynamical studies of other proteins that are not naturally light-sensitive.

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.

Direct evidence for hula twist and single-bond rotation photoproducts

Photoisomerization reactions are quintessential processes driving molecular machines and motors, govern smart materials, catalytic processes, and photopharmacology, and lie at the heart of vision, phototaxis, or vitamin production. Despite this plethora of applications fundamental photoisomerization mechanisms are not well understood at present. The famous hula-twist motion—a coupled single and double-bond rotation—was proposed to explain proficient photoswitching in restricted environments but fast thermal follow-up reactions hamper identification of primary photo products. Herein we describe an asymmetric chromophore possessing four geometrically distinct diastereomeric states that do not interconvert thermally and can be crystallized separately. Employing this molecular setup direct and unequivocal evidence for the hula-twist photoreaction and for photoinduced single-bond rotation is obtained. The influences of the surrounding medium and temperature are quantified and used to favor unusual photoreactions. Based on our findings molecular engineers will be able to implement photo control of complex molecular motions more consciously.

Photoisomerization mechanisms govern important (bio)catalytic reactions and lie at the core of many functional materials. Here, the authors report a molecular setup that allows for the direct and separate observation of three fundamental photoreactions, namely the hula twist, single-bond rotation, as well as double-bond isomerization.

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. Proc. R. Soc. London, Ser. A 1932, 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.

Retinal isomerization in bacteriorhodopsin captured by a femtosecond x-ray laser

Ultrafast isomerization of retinal is the primary step in photoresponsive biological functions including vision in humans and ion transport across bacterial membranes. We used an x-ray laser to study the subpicosecond structural dynamics of retinal isomerization in the light-driven proton pump bacteriorhodopsin. A series of structural snapshots with near-atomic spatial resolution and temporal resolution in the femtosecond regime show how the excited all-trans retinal samples conformational states within the protein binding pocket before passing through a twisted geometry and emerging in the 13-cis conformation. Our findings suggest ultrafast collective motions of aspartic acid residues and functional water molecules in the proximity of the retinal Schiff base as a key facet of this stereoselective and efficient photochemical reaction.

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.

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.

Engineering the vibrational coherence of vision into a synthetic molecular device

The light-induced double-bond isomerization of the visual pigment rhodopsin operates a molecular-level optomechanical energy transduction, which triggers a crucial protein structure change. In fact, rhodopsin isomerization occurs according to a unique, ultrafast mechanism that preserves mode-specific vibrational coherence all the way from the reactant excited state to the primary photoproduct ground state. The engineering of such an energy-funnelling function in synthetic compounds would pave the way towards biomimetic molecular machines capable of achieving optimum light-to-mechanical energy conversion. Here we use resonance and off-resonance vibrational coherence spectroscopy to demonstrate that a rhodopsin-like isomerization operates in a biomimetic molecular switch in solution. Furthermore, by using quantum chemical simulations, we show why the observed coherent nuclear motion critically depends on minor chemical modifications capable to induce specific geometric and electronic effects. This finding provides a strategy for engineering vibrationally coherent motions in other synthetic systems.

The ultrafast, vibrationally coherent photoisomerization of rhodopsin is a model of efficient photomechanical energy conversion at the molecular scale. Here, the authors demonstrate a similar photoreaction in synthetic compounds, unraveling the underlying mechanism and discussing its implications.

Dynamics of recombination via conical intersection in a semiconductor nanocrystal

Conical intersections are well known to introduce nonradiative decay pathways in molecules, but have only recently been implicated in nonradiative recombination processes in materials. Here we apply excited state ab initio molecular dynamics simulations based on a multireference description of the electronic structure to defective silicon nanocrystals up to 1.7 nm in diameter to search for accessible nonradiative recombination pathways. Dangling bond defects are found to induce conical intersections between the ground and first excited electronic states of five systems of various sizes. These defect-induced conical intersections are accessible at energies that are in the visible range (2.4-2.7 eV) and very weakly dependent on particle size. The dynamic simulations suggest that these intersections are accessed 40-60 fs after creation of a defect-localized excitation. This ultrafast recombination is attributed to the fact that Jahn-Teller distortion on the first excited state drives the defect directly towards a conical intersection with the ground electronic state.

The origin of absorptive features in the two-dimensional electronic spectra of rhodopsin

A three-state three-mode model Hamiltonian reveals the origin of the absorptive features in the two-dimensional electronic spectra of rhodopsin.

Coupling Real-Time Time-Dependent Density Functional Theory with Polarizable Force Field

Real-time time-dependent density functional theory (RT-TDDFT) is a powerful tool for obtaining spectroscopic observables and understanding complex, time-dependent properties. Currently, performing RT-TDDFT calculations on large, fully quantum mechanical systems is not computationally feasible. Previously, polarizable mixed quantum mechanical and molecular mechanical (QM/MMPol) models have been successful in providing accurate, yet efficient, approximations to a fully quantum mechanical system. Here we develop a coupling scheme between induced dipole based QM/MMPol and RT-TDDFT. Our approach is validated by comparing calculated spectra with both real-time and linear-response TDDFT calculations. The model developed within provides an accurate method for performing RT-TDDFT calculations on extended systems while accounting for mutual polarization between the quantum mechanical and molecular mechanical regions.

Coherent control of an opsin in living brain tissue

Retinal-based opsins are light-sensitive proteins. The photoisomerization reaction of these proteins has been studied outside cellular environments using ultrashort tailored light pulses^1-5. However, how living cell functions can be modulated via opsins by modifying fundamental nonlinear optical properties of light interacting with the retinal chromophore has remained largely unexplored. We report the use of chirped ultrashort near-infrared pulses to modulate light-evoked ionic current from Channelrhodopsin-2 (ChR2) in brain tissue, and consequently the firing pattern of neurons, by manipulating the phase of the spectral components of the light. These results confirm that quantum coherence of the retinal-based protein system, even in a living neuron, can influence its current output, and open up the possibilities of using designer-tailored pulses for controlling molecular dynamics of opsins in living tissue to selectively enhance or suppress neuronal function for adaptive feedback-loop applications in the future.