Quantum dynamics of the femtosecond photoisomerization of retinal in bacteriorhodopsin

Classical Nuclear Motion: Comparison to Approaches with Quantum Mechanical Nuclear Motion

Ab initio molecular dynamics combines a classical description of nuclear motion with a density-functional description of the electronic cloud. This approach nicely describes chemical reactions. A possible conclusion is that a quantum mechanical description of nuclear motion is not needed. Using Occam’s razor, this means that, being the simpler approach, classical nuclear motion is preferable. In this paper, it is claimed that nuclear motion is classical, and this hypothesis will be tested in comparison to methods with quantum mechanical nuclear motion. In particular, we apply ab initio molecular dynamics to two photoreactions involving hydrogen. Hydrogen, as the lightest element, is often assumed to show quantum mechanical tunneling. We will see that the classical picture is fully sufficient. The quantum mechanical view leads to phenomena that are difficult to understand, such as the entanglement of nuclear motion. In contrast, it is easy to understand the simple classical picture which assumes that nuclear motion is steady and uniform unless a force is acting. Of course, such a hypothesis must be verified for many systems and phenomena, and this paper is one more step in this direction.

An efficient approximate algorithm for nonadiabatic molecular dynamics

We propose a modification to the nonadiabatic surface hopping calculation method formulated in a paper by Yu et al. [Phys. Chem. Chem. Phys. 16, 25883 (2014)], which is a multidimensional extension of the Zhu-Nakamura theory with a practical diabatic gradient estimation algorithm. In our modification, their diabatic gradient estimation algorithm, which is based on a simple interpolation of the adiabatic potential energy surfaces, is replaced by an algorithm using the numerical derivatives of the adiabatic gradients. We then apply the algorithm to several models of nonadiabatic dynamics, both analytic and ab initio models, to numerically demonstrate that our method indeed widens the applicability and robustness of their method. We also discuss the validity and limitations of our new nonadiabatic surface hopping method while considering in mind potential applications to excited-state dynamics of biomolecules or unconventional nonadiabatic dynamics such as radiation decay processes in ultraintense X-ray fields.

Polarizable Embedding for Excited-State Reactions: Dynamically Weighted Polarizable QM/MM

Recent interest in polarizable embedding methods for electronic excited states has so far been focused on optical absorption and emission spectra calculations. To explore the suitability of these methods for excited-state reactions, we constructed a simple molecular system with an electronic crossing coupled to a polarizable species: the triatomic LiFBe. We found that current polarizable QM/MM methods inadequately describe the potential energy surfaces in this system, particularly close to the electronic crossing, so we developed a new polarizable embedding method called dynamically weighted polarizable QM/MM. The new method reproduces the potential energy surfaces of LiFBe from full-system multireference configuration interaction singles and doubles calculations with near-quantitative accuracy.

Communication: Smoothing out excited-state dynamics: analytical gradients for dynamically weighted complete active space self-consistent field

State averaged complete active space self-consistent field (SA-CASSCF) is a workhorse for determining the excited-state electronic structure of molecules, particularly for states with multireference character; however, the method suffers from known issues that have prevented its wider adoption. One issue is the presence of discontinuities in potential energy surfaces when a state that is not included in the state averaging crosses with one that is. In this communication I introduce a new dynamical weight with spline (DWS) scheme that mimics SA-CASSCF while removing energy discontinuities due to unweighted state crossings. In addition, analytical gradients for DWS-CASSCF (and other dynamically weighted schemes) are derived for the first time, enabling energy-conserving excited-state ab initio molecular dynamics in instances where SA-CASSCF fails.

Correlated electron-nuclear dynamics with conditional wave functions

The molecular Schrödinger equation is rewritten in terms of nonunitary equations of motion for the nuclei (or electrons) that depend parametrically on the configuration of an ensemble of generally defined electronic (or nuclear) trajectories. This scheme is exact and does not rely on the tracing out of degrees of freedom. Hence, the use of trajectory-based statistical techniques can be exploited to circumvent the calculation of the computationally demanding Born-Oppenheimer potential-energy surfaces and nonadiabatic coupling elements. The concept of the potential-energy surface is restored by establishing a formal connection with the exact factorization of the full wave function. This connection is used to gain insight from a simplified form of the exact propagation scheme.

Response of biophotonic device using retinoid

The authors focus on the retina in the human eye and consider retinoic acid to be the most appropriate for use in photoreceptive devices. The authors fabricated retinoic acid–chitosan film by using the layer-by-layer self-assembly process. The photocurrent value of the devices increased from 4·0 to 7·0 mA when used in optimized conditions. One of the best responses of these manually fabricated photoreceptive devices was that the photocurrent was 7 mA and the photocurrent response continued during the longest period to date of 9 h, which is an 81 times longer life time than before. The authors calculated the external quantum efficiency of the photocurrent response for devices with the best performance. The estimated external quantum efficiency of the photocurrent response for the best device was 4·53. In comparison, for one of the gel-type devices, the efficiency was 0·004. The mechanism of the photocurrent response of biophotonic devices seems to be the radical reaction rather than any ionic or charged carrier reaction.

Control Mechanisms of Photoisomerization in Protonated Schiff Bases

We performed ab initio excited-state molecular dynamics simulations of a gas-phase photoexcited protonated Schiff base (C1-N2═C3-C4═C5-C6) to search for control mechanisms of its photoisomerization. The excited molecule twists by ∼90° around either the N2C3 bond or the C4C5 bond and relaxes to the ground electronic state through a conical intersection with either a trans or cis outcome. We show that a large initial distortion of several dihedral angles and a specific normal vibrational mode combining pyramidalization and double-bond twisting can lead to a preferential rotation of atoms around the C4C5 bond. We also show that selective pretwisting of several dihedral angles in the initial ground state thermal ensemble (by analogy to a protein pocket) can significantly increase the fraction of photoreactive (cis → trans) trajectories. We demonstrate that new ensembles with higher degrees of control over the photoisomerization reaction can be obtained by a computational directed evolution approach on the ensembles of molecules with the pretwisted geometries.

Photochemical reaction dynamics of the primary event of vision studied by means of a hybrid molecular simulation

The photoisomerization reaction dynamics of a retinal chromophore in the visual receptor rhodopsin was investigated by means of hybrid quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations. The photoisomerization reaction of retinal constitutes the primary step of vision and is known as one of the fastest reactions in nature. To elucidate the molecular mechanism of the high efficiency of the reaction, we carried out hybrid ab initio QM/MM MD simulations of the complete reaction process from the vertically excited state to the photoproduct via electronic transition in the entire chromophore-protein complex. An ensemble of reaction trajectories reveal that the excited-state dynamics is dynamically homogeneous and synchronous even in the presence of thermal fluctuation of the protein, giving rise to the very fast formation of the photoproduct. The synchronous nature of the reaction dynamics in rhodopsin is found to originate from weak perturbation of the protein surroundings and from dynamic regulation of volume-conserving motions of the chromophore. The simulations also provide a detailed view of time-dependent modulations of hydrogen-out-of-plane vibrations during the reaction process, and identify molecular motions underlying the experimentally observed dynamic spectral modulations.

An Ab Initio Study of the Excited States, Isomerization Energy Profiles and Conical Intersections of a Chiral Cyclohexylidene Derivative

The excited valence and Rydberg states of the chiral (4-methylcyclohexylidene) fluoromethane (4MCF) have been investigated using multiconfigurational CASSCF and CASPT2, and coupled-cluster methods (RI-CC2). A 3s Rydberg state is predicted below the valence (1)pipi* state. To gain insight into the photophysics of the cis-trans isomerization of this olefin, potential energy profiles for the valence (10pipi* state along the twisting and pyramidalization reaction coordinates have been computed using variational methods (CASSCF and multireference configuration interaction with singles and doubles (MR-CISD)). Starting from geometries with energies close to degeneracy in the valence and ground-state curves, three minima on the crossing seam that can be correlated with the conical intersections known for fluoroethylene, have been found. On the basis of these features, the photochemistry of 4MCF is discussed.

Calculation of nonadiabatic couplings with restricted open-shell Kohn-Sham density-functional theory

This paper generalizes the recently proposed approaches for calculating the derivative couplings between adiabatic states in density-functional theory (DFT) based on a Slater transition-state density to transitions such as singlet-singlet excitations, where a single-determinant ansatz is insufficient. The proposed approach is based on restricted open-shell Frank et al. [J. Chem. Phys. 108, 4060 (1998)] theory used to describe a spin-adapted Slater transition state. To treat the dependence of electron-electron interactions on the nuclear positions, variational linear-response density-functional perturbation theory is generalized to reference states with an orbital-dependent Kohn-Sham Hamiltonian and nontrivial occupation patterns. The methods proposed in this paper are not limited to the calculation of derivative coupling vectors, but can also be used for the calculation of other transition matrix elements. Moreover, they can be used to calculate the linear response of open-shell systems to arbitrary external perturbations in DFT.

Excited-State Charge Transfer at a Conical Intersection: Effects of an Environment

The influence of a polar and polarizable environment on charge transfer processes at a conical intersection (CI) can be described by a diabatic free energy model yielding coupled surfaces as a function of both molecular coordinates and a solvent coordinate. We extend and apply this model for the S1-S0 CI in protonated Schiff bases, representing a model for retinal isomerization (Faraday Discuss. 2004, 127, 395, 2004). A dielectric continuum description of the solvent is combined with a minimal, two-electron-two-orbital electronic structure model according to Bonacić-Koutecký, Koutecký, and Michl (Angew. Chem. 1987, 26, 170), which characterizes the charge translocation effects at the CI. The model predicts that the nonequilibrium solvent state resulting from the S0-->S1 Franck-Condon transition can entail the disappearance of the CI, such that solvent motion is necessary to reach the CI seam. The concerted evolution of the intramolecular coordinates and the solvent coordinate is illustrated by an excited-state minimum energy path.

Photoinduced conformational dynamics of a photoswitchable peptide: a nonequilibrium molecular dynamics simulation study

Employing nonequilibrium molecular dynamics simulations, a comprehensive computational study of the photoinduced conformational dynamics of a photoswitchable bicyclic azobenzene octapeptide is presented. The calculation of time-dependent probability distributions along various global and local reaction coordinates reveals that the conformational rearrangement of the peptide is rather complex and occurs on at least four timescales: 1) After photoexcitation, the azobenzene unit of the molecule undergoes nonadiabatic photoisomerization within 0.2 ps. 2) On the picosecond timescale, the cooling (13 ps) and the stretching (14 ps) of the photoexcited peptide is observed. 3) Most reaction coordinates exhibit a 50-100 ps component reflecting a fast conformational rearrangement. 4) The 500-1000 ps component observed in the simulation accounts for the slow diffusion-controlled conformational equilibration of the system. The simulation of the photoinduced molecular processes is in remarkable agreement with time-resolved optical and infrared experiments, although the calculated cooling as well as the initial conformational rearrangements of the peptide appear to be somewhat too slow. Based on an ab initio parameterized vibrational Hamiltonian, the time-dependent amide I frequency shift is calculated. Both intramolecular and solvent-induced contributions to the frequency shift were found to change by < or = 2 cm(-1), in reasonable agreement with experiment. The potential of transient infrared spectra to characterize the conformational dynamics of peptides is discussed in some detail.

Femtosecond primary events in bacteriorhodopsin and its retinal modified analogs: Revision of commonly accepted interpretation of electronic spectra of transient intermediates in the bacteriorhodopsin photocycle

Femtosecond primary events in bacteriorhodopsin (BR) and its retinal modified analogs are discussed. Ultrafast time resolved electronic spectra of the primary intermediates induced in the BR photocycle are discussed along with spectral and kinetic inconsistencies of the previous models proposed in the literature. The theoretical model proposed in this paper based on vibrational coupling between the electronic transition of the chromophore and intramolecular vibrational modes allows us to calculate the equilibrium electronic absorption band shape and the hole burning profiles. The model is able to rationalize the complex pattern of behavior for the primary events in BR and explain the origin of the apparent inconsistencies between the experiment and the previous theoretical models. The model presented in the paper is based on the anharmonic coupling assumption in the adiabatic approximation using the canonical transformation method for diagonalization of the vibrational Hamiltonian instead of the commonly used perturbation theory. The electronic transition occurs between the Born-Oppenheimer potential energy surfaces with the electron involved in the transition being coupled to the intramolecular vibrational modes of the molecule (chromophore). The relaxation of the excited state occurs by indirect damping (dephasing) mechanisms. The indirect dephasing is governed by the time evolution of the anharmonic coupling constant driven by the resonance energy exchange between the intramolecular vibrational mode and the bath. The coupling with the intramolecular vibrational modes results in the Franck-Condon progression of bands that are broadened due to the vibrational dephasing mechanisms. The electronic absorption line shape has been calculated based on the linear response theory whereas the third order nonlinear response functions have been used to analyze the hole burning profiles obtained from the pump-probe time-resolved measurements. The theoretical treatment proposed in this paper provides a basis for a substantial revision of the commonly accepted interpretation of the primary events in the BR photocycle that exists in the literature.

Time-dependent quantum methods for large systems

This review focuses on time-dependent methods suitable for simulating the quantum dynamics of processes in large clusters and condensed-phase environments. A number of mean field, quantum-classical, and quantum statistical approximations that avoid the conventional exponential scaling with the number of degrees of freedom are reviewed. In addition, rigorous semiclassical and path integral approaches are described that are feasible in certain physical situations. Select chemical applications illustrating the capabilities of these methods are discussed.

A global investigation of excited state surfaces within time-dependent density-functional response theory

This work investigates the capability of time-dependent density functional response theory to describe excited state potential energy surfaces of conjugated organic molecules. Applications to linear polyenes, aromatic systems, and the protonated Schiff base of retinal demonstrate the scope of currently used exchange-correlation functionals as local, adiabatic approximations to time-dependent Kohn-Sham theory. The results are compared to experimental and ab initio data of various kinds to attain a critical analysis of common problems concerning charge transfer and long range (nondynamic) correlation effects. This analysis goes beyond a local investigation of electronic properties and incorporates a global view of the excited state potential energy surfaces.

Molecular dynamics simulation of bacteriorhodopsin's photoisomerization using ab initio forces for the excited chromophore

Retinal proteins are photoreceptors found in many living organisms. They possess a common chromophore, retinal, that upon absorption of light isomerizes and thereby triggers biological functions ranging from light energy conversion to phototaxis and vision. The photoisomerization of retinal is extremely fast, highly selective inside the protein matrix, and characterized through optimal sensitivity to incoming light. This article describes the first report of an ab initio quantum mechanical description of the in situ isomerization dynamics of retinal in bacteriorhodopsin, a microbial retinal protein that functions as a light-driven proton pump. The description combines ab initio multi-electronic state molecular dynamics of a truncated retinal chromophore model (N-methyl-gamma-methylpenta-2,4-dieniminium cation fragment) with molecular mechanics of the protein motion and unveils in complete detail the photoisomerization process. The results illustrate the essential role of the protein for the characteristic kinetics and high selectivity of the photoisomerization: the protein arrests inhomogeneous photoisomerization paths and funnels them into a single path that initiates the functional process. Supported by comparison with dynamic spectral modulations observed in femtosecond spectroscopy, the results identify the principal molecular motion during photoisomerization.

Structural changes during the formation of early intermediates in the bacteriorhodopsin photocycle

Early intermediates of bacteriorhodopsin's photocycle were modeled by means of ab initio quantum mechanical/molecular mechanical and molecular dynamics simulations. The photoisomerization of the retinal chromophore and the formation of photoproducts corresponding to the early intermediates were simulated by molecular dynamics simulations. By means of the quantum mechanical/molecular mechanical method, the resulting structures were refined and the respective excitation energies were calculated. Two sequential intermediates were found with absorption maxima that exhibit red shifts from the resting state. The intermediates were therefore assigned to the K and KL states. In K, the conformation of the retinal chromophore is strongly deformed, and the N--H bond of the Schiff base points almost perpendicular to the membrane normal toward Asp-212. The strongly deformed conformation of the chromophore and weakened interaction of the Schiff base with the surrounding polar groups are the means by which the absorbed energy is stored. During the K-to-KL transition, the chromophore undergoes further conformational changes that result in the formation of a hydrogen bond between the N--H group of the Schiff base and Thr-89 as well as other rearrangements of the hydrogen-bond network in the vicinity of the Schiff base, which are suggested to play a key role in the proton transfer process in the later phase of the photocycle.

Following evolution of bacteriorhodopsin in its reactive excited state via stimulated emission pumping

New information concerning the photochemical dynamics of bacteriorhodopsin (BR) is obtained by impulsively stimulating emission from the reactive fluorescent state. Depletion of the excited-state fluorescence leads to an equal reduction in production of later photoproducts. Accordingly, chromophores which are forced back to the ground state via emission do not continue on in the photocycle, conclusively demonstrating that the fluorescent state is a photocycle intermediate. The insensitivity of depletion dynamics to the "dump" pulse timing, throughout the fluorescent states lifetime, and the biological inactivity of the dumped population suggest that the fluorescent-state structure is constant, well-defined, and significantly different than that where crossing to the ground state takes place naturally. In conjunction with conclusions from comparing the photophysics of BR with those of synthetic analogues containing "locked" retinals, present results show that large-amplitude torsion around C13=C14 is required to go between the above structures.

Quantum mechanical methods for enzyme kinetics

This review discusses methods for the incorporation of quantum mechanical effects into enzyme kinetics simulations in which the enzyme is an explicit part of the model. We emphasize three aspects: (a) use of quantum mechanical electronic structure methods such as molecular orbital theory and density functional theory, usually in conjunction with molecular mechanics; (b) treating vibrational motions quantum mechanically, either in an instantaneous harmonic approximation, or by path integrals, or by a three-dimensional wave function coupled to classical nuclear motion; (c) incorporation of multidimensional tunneling approximations into reaction rate calculations.

Molecular dynamics simulations of biological reactions

This review considers the author perspective on the emergence of molecular dynamics (MD) simulations of biological processes. It starts with the 1976 simulation of the primary event in rhodopsin, moves to the earliest simulations of enzymatic reactions and electron transfer reactions and ends up with recent simulations of proton translocations and ion transport in proteins. The emphasis is placed on our progress in simulations of actual biological reactions and functional properties, rather than on studies of general properties such as structure and thermal motions. In most cases it has been possible to develop special strategies that capture the relevant dynamics of the given biological process. The predictive power of our early simulations of fast biological process (e.g. vision and photosynthesis) and the insight obtained from these studies is pointed out. Critical examinations of dynamical effects in different biological processes is reviewed. This includes the finding that dynamical effects are unlikely to contribute significantly to enzyme catalysis or to other processes with significant activation barriers. Even in the case of ion channels it is found that the most important effects are associated with energetics rather than dynamics. Nevertheless, MD simulations provide what is probably the most realistic description of the actual reactive events. The resulting insight is crucial in studies of fast photobiological reactions and instructive in cases of slower processes.

The role of intersection topography in bond selectivity of cis-trans photoisomerization

Ab initio methods are used to characterize the ground and first excited state of the chromophore in the rhodopsin family of proteins: retinal protonated Schiff base. Retinal protonated Schiff base has five double bonds capable of undergoing isomerization. Upon absorption of light, the chromophore isomerizes and the character of the photoproducts (e.g., 13-cis and 11-cis) depends on the environment, protein vs. solution. Our ab initio calculations show that, in the absence of any specific interactions with the environment (e.g., discrete ordered charges in a protein), energetic considerations cannot explain the observed bond selectivity. We instead attribute the origin of bond selectivity to the shape (topography) of the potential energy surfaces in the vicinity of points of true degeneracy (conical intersections) between the ground and first excited electronic states. This provides a molecular example where a competition between two distinct but nearly isoenergetic photochemical reaction pathways is resolved by a topographical difference between two conical intersections.

Molecular dynamics study of the nature and origin of retinal's twisted structure in bacteriorhodopsin

The planarity of the polyene chain of the retinal chromophore in bacteriorhodopsin is studied using molecular dynamics simulation techniques and applying different force-field parameters and starting crystal structures. The largest deviations from a planar structure are observed for the C(13)==C(14) and C(15)==N(16) double bonds in the retinal Schiff base structure. The other dihedral angles along the polyene chain of the chromophore, although having lower torsional barriers in some cases, do not significantly deviate from the planar structure. The results of the simulations of different mutants of the pigment show that, among the studied amino acids of the binding pocket, the side chain of Trp-86 has the largest impact on the planarity of retinal, and the mutation of this amino acid to alanine leads to chromophore planarity. Deletion of the methyl C(20), removal of a water molecule hydrogen-bonded to H(15), or mutation of other amino acids to alanine did not show any significant influence on the distortion of the chromophore. The results from the present study suggest the importance of the bulky residue of Trp-86 in the isomerization process, in both ground and excited states of the chromophore, and in fine-tuning of the pK(a) of the retinal protonated Schiff base in bacteriorhodopsin. The dark adaptation of the pigment and the last step of the bacteriorhodopsin photocycle imply low barriers against the rotation of the double bonds in the Schiff base region. The twisted double bonds found in the present study are consistent with the proposed mechanism of these ground state isomerization events.