Structure of the intersection space associated with Z/E photoisomerization of retinal in rhodopsin proteins

Understanding the Photoprocesses in Biological Systems: Need for Accurate Multireference Treatment

Light-matter interaction is crucial to life itself and revolves around many of the central processes in biology. The need for understanding these photochemical and photophysical processes cannot be overemphasized. Interaction of light with biological systems starts with the absorption of light and subsequent phenomena that occur in the excited states of the system. However, excited states are typically difficult to understand within the mean field approximation of quantum chemical methods. Therefore, suitable multireference methods and methodologies have been developed to understand these phenomena. In this Perspective, we will describe a few methods and methodologies suitable for these descriptions and discuss some persisting difficulties.

The development of the QM/MM interface and its application for the on-the-fly QM/MM nonadiabatic dynamics in JADE package: Theory, implementation, and applications

Understanding the nonadiabatic dynamics of complex systems is a challenging task in computational photochemistry. Herein, we present an efficient and user-friendly quantum mechanics/molecular mechanics (QM/MM) interface to run on-the-fly nonadiabatic dynamics. Currently, this interface consists of an independent set of codes designed for general-purpose use. Herein, we demonstrate the ability and feasibility of the QM/MM interface by integrating it with our long-term developed JADE package. Tailored to handle nonadiabatic processes in various complex systems, especially condensed phases and protein environments, we delve into the theories, implementations, and applications of on-the-fly QM/MM nonadiabatic dynamics. The QM/MM approach is established within the framework of the additive QM/MM scheme, employing electrostatic embedding, link-atom inclusion, and charge-redistribution schemes to treat the QM/MM boundary. Trajectory surface-hopping dynamics are facilitated using the fewest switches algorithm, encompassing classical and quantum treatments for nuclear and electronic motions, respectively. Finally, we report simulations of nonadiabatic dynamics for two typical systems: azomethane in water and the retinal chromophore PSB3 in a protein environment. Our results not only illustrate the power of the QM/MM program but also reveal the important roles of environmental factors in nonadiabatic processes.

Topology of Conical Intersection Seams and the Geometric Phase

In this paper, we demonstrate two topological properties of crossing seams, that is, the sets of points in the N-dimensional space of nuclear coordinates where two electronic eigenstates are degenerate. We shall examine the typical case of states of the same spin with accidental degeneracies, whereby the crossing seam is of dimension N - 2. The first property we demonstrate is that a crossing seam has no boundary, therefore, it must either extend asymptotically to infinite values of one or more coordinates or wrap on itself. The second property is that two (or more) crossing seams can intersect each other but in such a way that neither of them ends at the intersection. When N = 3, the crossing seam is a line in a 3D space; this is so in triatomic molecules but also in reduced dimensionality treatments of larger polyatomics. The above-mentioned rules then mean that the crossing seam is a line of infinite length or a closed loop and can split into three branches but not in two. The example of the first two excited 1A' states of H2Cl+ illustrates these rules and shows their usefulness for computational search and characterization of crossing seams.

Photocycle dynamics of the Archaerhodopsin 3 based fluorescent voltage sensor Archon2

The retinal photocycle dynamics of the fluorescent voltage sensor Archon2 in pH 8 Tris buffer was studied. Archon2 is a mutant of Archaerhodopsin 3 (Arch) from Halorubrum sodomense obtained by a robotic multidimensional directed evolution approach (Archon2 = Arch T56P-P60S-T80P-D95H-T99S-T116I-F161V-T183I-L197I-A225C). The samples were photo-excited to the first absorption band of the protonated retinal Schiff base (PRSB) Ret_586 (absorption maximum at λ_max = 586 nm, excitation wavelengths λ_exc = 590 nm and 632.8 nm). The photocycle dynamics were studied by recording absorption spectra during light exposure and after light exposure. Ret_586 photoisomerized to Ret_535 (main component) and Ret_485 (minor component). Ret_535 backward photoisomerized to Ret_586 in light-adapted state (named Ret_586_la) and partly deprotonated to neutral retinal Schiff base (RSB) Ret_372 in light adapted state (named Ret_372_la, same isomer form as Ret_535). After excitation light switch-off Ret_372_la recovered to Ret_372 in dark-adapted state (Ret_372_da) which slowly re-protonated to Ret_535, and Ret_535 slowly isomerized back to Ret_586 in dark-adapted state (Ret_586_da). Photocycle schemes and reaction coordinate diagrams are developed and photocycle parameters are determined.

Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections

Nonadiabatic effects are ubiquitous in photophysics and photochemistry, and therefore, many theoretical developments have been made to properly describe them. Conical intersections are central in nonadiabatic processes, as they promote efficient and ultrafast nonadiabatic transitions between electronic states. A proper theoretical description requires developments in electronic structure and specifically in methods that describe conical intersections between states and nonadiabatic coupling terms. This review focuses on the electronic structure aspects of nonadiabatic processes. We discuss the requirements of electronic structure methods to describe conical intersections and nonadiabatic couplings, how the most common excited state methods perform in describing these effects, and what the recent developments are in expanding the methodology and implementing nonadiabatic couplings.

A systematic model study quantifying how conical intersection topography modulates photochemical reactions

Despite their important role in photochemistry and expected presence in most polyatomic molecules, conical intersections have been thoroughly characterized in a comparatively small number of systems. Conical intersections can confer molecular photoreactivity or photostability, often with remarkable efficacy, due to their unique structure: at a conical intersection, the adiabatic potential energy surfaces of two or more electronic states are degenerate, enabling ultrafast decay from an excited state without radiative emission, known as nonadiabatic transfer. Furthermore, the precise conical intersection topography determines fundamental properties of photochemical processes, including excited-state decay rate, efficacy, and molecular products that are formed. However, these relationships have yet to be defined comprehensively. In this article, we use an adaptable computational model to investigate a variety of conical intersection topographies, simulate resulting nonadiabatic dynamics, and calculate key photochemical observables. We varied the vibrational mode frequencies to modify conical intersection topography systematically in four primary classes of conical intersections and quantified the resulting rate, total yield, and product yield of nonadiabatic decay. The results reveal that higher vibrational mode frequencies reduce nonadiabatic transfer, but increase the transfer rate and resulting photoproduct formation. These trends can inform progress toward experimental control of photochemical reactions or tuning of molecules' photochemical properties based on conical intersections and their topography.

Photochemistry and photophysics at extended seams of conical intersection

The role of extended seams of conical intersection in excited-state mechanisms is reviewed. Seams are crossings of the potential energy surface in many dimensions where the decay from the excited to the ground state can occur, and the extended seam is composed of different segments lying along a reaction coordinate. Every segment is associated with a different primary photoproduct, which gives rise to competing pathways. This idea is first illustrated for fulvene and ethylene, and then it is used to explain more complex cases such as the dependence of the isomerisation of retinal chromophore isomers on the protein environment, the dependence of the efficiency of the azobenzene photochemical switch on the wavelength of irradiation and the direction of the isomerisation, and the coexistence of different mechanisms in the photo-induced Wolff rearrangement of diazonaphthoquinone. The role of extended seams in the photophysics of the DNA nucleobases and the relationship between two-state seams and three-state crossings is also discussed. As an outlook, the design of optical control strategies based on the passage of the excited molecule through the seam is considered, and it is shown how the excited-state lifetime of fulvene can be modulated by shaping the energy of the seam.

Aborted double bicycle-pedal isomerization with hydrogen bond breaking is the primary event of bacteriorhodopsin proton pumping

Quantum mechanics/molecular mechanics calculations based on ab initio multiconfigurational second order perturbation theory are employed to construct a computer model of Bacteriorhodopsin that reproduces the observed static and transient electronic spectra, the dipole moment changes, and the energy stored in the photocycle intermediate K. The computed reaction coordinate indicates that the isomerization of the retinal chromophore occurs via a complex motion accounting for three distinct regimes: (i) production of the excited state intermediate I, (ii) evolution of I toward a conical intersection between the excited state and the ground state, and (iii) formation of K. We show that, during stage ii, a space-saving mechanism dominated by an asynchronous double bicycle-pedal deformation of the C10═C11─C12═C13─C14═N moiety of the chromophore dominates the isomerization. On this same stage a N─H/water hydrogen bond is weakened and initiates a breaking process that is completed during stage iii.

Coherent ultrafast torsional motion and isomerization of a biomimetic dipolar photoswitch

Femtosecond fluorescence up-conversion, UV-Vis and IR transient absorption spectroscopy are used to study the photo-isomerization dynamics of a new type of zwitterionic photoswitch based on a N-alkylated indanylidene pyrroline Schiff base framework (ZW-NAIP). The system is biomimetic, as it mimics the photophysics of retinal, in coupling excited state charge translocation and isomerization. While the fluorescence lifetime is 140 fs, excited state absorption persists over 230 fs in the form of a vibrational wavepacket according to twisting of the isomerizing double bond. After a short "dark" time window in the UV-visible spectra, which we associate with the passage through a conical intersection (CI), the wavepacket appears on the ground state potential energy surface, as evidenced by the transient mid-IR data. This allows for a precise timing of the photoreaction all the way from the initial Franck-Condon region, through the CI and into both ground state isomers, until incoherent vibrational relaxation dominates the dynamics. The photo-reaction dynamics remarkably follow those observed for retinal in rhodopsin, with the additional benefit that in ZW-NAIP the conformational change reverses the zwitterion dipole moment direction. Last, the pronounced low-frequency coherences make these molecules ideal systems for investigating wavepacket dynamics in the vicinity of a CI and for coherent control experiments.

Electrostatic control of the photoisomerization efficiency and optical properties in visual pigments: on the role of counterion quenching

Hybrid QM(CASPT2//CASSCF/6-31G*)/MM(Amber) computations have been used to map the photoisomerization path of the retinal chromophore in Rhodopsin and explore the reasons behind the photoactivity efficiency and spectral control in the visual pigments. It is shown that while the electrostatic environment plays a central role in properly tuning the optical properties of the chromophore, it is also critical in biasing the ultrafast photochemical event: it controls the slope of the photoisomerization channel as well as the accessibility of the S(1)/S(0) crossing space triggering the ultrafast decay. The roles of the E113 counterion, the E181 residue, and the other amino acids of the protein pocket are explicitly analyzed: it appears that counterion quenching by the protein environment plays a key role in setting up the chromophore's optical properties and its photochemical efficiency. A unified scenario is presented that discloses the relationship between spectroscopic and mechanistic properties in rhodopsins and allows us to draw a solid mechanism for spectral tuning in color vision pigments: a tunable counterion shielding appears as the elective mechanism for L<-->M spectral modulation, while a retinal conformational control must dictate S absorption. Finally, it is suggested that this model may contribute to shed new light into mutations-related vision deficiencies that opens innovative perspectives for experimental biomolecular investigations in this field.

Optimizing conical intersections without derivative coupling vectors: application to multistate multireference second-order perturbation theory (MS-CASPT2)

We introduce a new method for optimizing minimal energy conical intersections (MECIs), based on a sequential penalty constrained optimization in conjunction with a smoothing function. The method is applied to optimize MECI geometries using the multistate formulation of second-order multireference perturbation theory (MS-CASPT2). Resulting geometries and energetics for conjugated molecules including ethylene, butadiene, stilbene, and the green fluorescent protein chromophore are compared with state-averaged complete active space self-consistent field (SA-CASSCF) and, where possible, benchmark multireference single- and double-excitation configuration interaction (MRSDCI) optimizations. Finally, we introduce the idea of "minimal distance conical intersections", which are points on the intersection seam that lie closest to some specified geometry such as the Franck-Condon point or a local minimum on the excited state.

Tracking the excited-state time evolution of the visual pigment with multiconfigurational quantum chemistry

The primary event that initiates vision is the photoinduced isomerization of retinal in the visual pigment rhodopsin (Rh). Here, we use a scaled quantum mechanics/molecular mechanics potential that reproduces the isomerization path determined with multiconfigurational perturbation theory to follow the excited-state evolution of bovine Rh. The analysis of a 140-fs trajectory provides a description of the electronic and geometrical changes that prepare the system for decay to the ground state. The data uncover a complex change of the retinal backbone that, at approximately 60-fs delay, initiates a space saving "asynchronous bicycle-pedal or crankshaft" motion, leading to a conical intersection on a 110-fs time scale. It is shown that the twisted structure achieved at decay features a momentum that provides a natural route toward the photoRh structure recently resolved by using femtosecond-stimulated Raman spectroscopy.

Structural analysis and dynamics of retinal chromophore in dark and meta I states of rhodopsin from 2H NMR of aligned membranes

Rhodopsin is a prototype for G protein-coupled receptors (GPCRs) that are implicated in many biological responses in humans. A site-directed (2)H NMR approach was used for structural analysis of retinal within its binding cavity in the dark and pre-activated meta I states. Retinal was labeled with (2)H at the C5, C9, or C13 methyl groups by total synthesis, and was used to regenerate the opsin apoprotein. Solid-state (2)H NMR spectra were acquired for aligned membranes in the low-temperature lipid gel phase versus the tilt angle to the magnetic field. Data reduction assumed a static uniaxial distribution, and gave the retinylidene methyl bond orientations plus the alignment disorder (mosaic spread). The dark-state (2)H NMR structure of 11-cis-retinal shows torsional twisting of the polyene chain and the beta-ionone ring. The ligand undergoes restricted motion, as evinced by order parameters of approximately 0.9 for the spinning C-C(2)H(3) groups, with off-axial fluctuations of approximately 15 degrees . Retinal is accommodated within the rhodopsin binding pocket with a negative pre-twist about the C11=C12 double bond that explains its rapid photochemistry and the trajectory of 11-cis to trans isomerization. In the cryo-trapped meta I state, the (2)H NMR structure shows a reduction of the polyene strain, while torsional twisting of the beta-ionone ring is maintained. Distortion of the retinal conformation is interpreted through substituent control of receptor activation. Steric hindrance between trans retinal and Trp265 can trigger formation of the subsequent activated meta II state. Our results are pertinent to quantum and molecular mechanics simulations of ligands bound to GPCRs, and illustrate how (2)H NMR can be applied to study their biological mechanisms of action.

Quantum Chemical Methods for the Investigation of Photoinitiated Processes in Biological Systems: Theory and Applications

With the advent of modern computers and advances in the development of efficient quantum chemical computer codes, the meaningful computation of large molecular systems at a quantum mechanical level became feasible. Recent experimental effort to understand photoinitiated processes in biological systems, for instance photosynthesis or vision, at a molecular level also triggered theoretical investigations in this field. In this Minireview, standard quantum chemical methods are presented that are applicable and recently used for the calculation of excited states of photoinitiated processes in biological molecular systems. These methods comprise configuration interaction singles, the complete active space self-consistent field method, and time-dependent density functional theory and its variants. Semiempirical approaches are also covered. Their basic theoretical concepts and mathematical equations are briefly outlined, and their properties and limitations are discussed. Recent successful applications of the methods to photoinitiated processes in biological systems are described and theoretical tools for the analysis of excited states are presented.

Solvent Effects on the Low-Lying Excited States of a Model of Retinal

The low-lying excited states of a solution in alcohol of a five-double-bond model of the rhodopsin protein chromophore, the protonated 11-cis-retinal Schiff base (PSB11), are studied theoretically. We combine a multireference perturbational treatment in the description of the solute molecule with molecular dynamics calculations in the description of the solvent. The geometry, charge distribution, and electronic spectra are strongly influenced by the solvent. The solvent shift values show a marked dependence on the use of relaxed geometries in solution and on the nature of the states involved in the excitation process. The dynamic correlation has a strong effect on the order of the excited states. In solution, the first two excited states almost become degenerate.

Investigation of the dynamics of two coupled oscillators with mixed quantum-classical methods

The dynamics of two coupled oscillators can become quite complex if anharmonic potential energy functions are employed. This type of system therefore represents a good model for an investigation of the performance of mixed quantum-classical methods. In this work, the motion of two coupled particles with a mass ratio of one to ten is studied with three different mixed quantum-classical methods in the presence of anharmonic potential terms for a comparison with exact quantum mechanical calculations. The mixed quantum-classical approaches include the multitrajectory Ehrenfest, the mixed quantum-classical Bohmian (MQCB), and the so-called coupled Schrödinger equations (CSE) formalisms. The analysis shows that while the description of a weakly anharmonic system by the Ehrenfest and MQCB schemes is accurate if proper sampling techniques are applied, both approximations break down rapidly if the anharmonic terms are increased. The performance of the simple CSE prescription, which corresponds to a reduction of the full two-dimensional wave function to two one-dimensional wave functions representing two quantum oscillators coupled via the potential energy in a classical fashion, decreases if the width of the initial wave packet is enlarged. The dependence of the CSE method on the diffuseness of the initial wave packet is therefore opposite to that of the MQCB method, which is more accurate for wide wave packets. Overall, the multitrajectory Ehrenfest ansatz is found to be most successful in reproducing the exact quantum results.

Locating the lowest free-energy point on conical intersection in polar solvent: Reference interaction site model self-consistent field study of ethylene and CH2NH2+

We present a theoretical method for locating the lowest free-energy points on conical intersections (CIs) in solution using the reference interaction site model self-consistent field (RISM-SCF) theory. Based on the linear-response theory, the nonequilibrium free energy is defined as a quadratic function of solvation coordinates, the parameters in which are directly obtained by ab initio RISM-SCF calculations. This free energy is easily incorporated into an efficient CI optimization procedure in gas phase. The present method is applied to the cis-trans photoisomerizations of ethylene and methaniminium cation (CH2NH2(+)) in polar solvents. We show that the geometries and energies of CIs are largely affected by the solute-solvent electrostatic interaction. In particular, the hydrogen migration of ethylene observed at CIs in the gas phase disappears in protic solvents due to the large stabilization of the zwitterionic state.

The retinal chromophore/chloride ion pair: structure of the photoisomerization path and interplay of charge transfer and covalent states

Ab initio multi-reference second-order perturbation theory computations are used to explore the photochemical behavior of two ion pairs constituted by a chloride counterion interacting with either a rhodopsin or bacteriorhodopsin chromophore model (i.e., the 4-cis-gamma-methylnona-2,4,6,8-tetraeniminium and all-trans-nona-2,4,6,8-tetraeniminium cations, respectively). Significant counterion effects on the structure of the photoisomerization paths are unveiled by comparison with the paths of the same chromophores in vacuo. Indeed, we demonstrate that the counterion (i) modulates the relative stability of the S0, S1, and S2 energy surfaces leading to an S1 isomerization energy profile where the S1 and S2 states are substantially degenerate; (ii) leads to the emergence of significant S1 energy barriers along all of the isomerization paths except the one mimicking the 11-cis --> all-trans isomerization of the rhodopsin chromophore model; and (iii) changes the nature of the S1 --> S0 decay funnel that becomes a stable excited state minimum when the isomerizing double bond is located at the center of the chromophore moiety. We show that these (apparently very different) counterion effects can be rationalized on the basis of a simple qualitative electrostatic model, which also provides a crude basis for understanding the behavior of retinal protonated Schiff bases in solution.

Conical intersections and semiclassical trajectories: Comparison to accurate quantum dynamics and analyses of the trajectories

Semiclassical trajectory methods are tested for electronically nonadiabatic systems with conical intersections. Five triatomic model systems are presented, and each system features two electronic states that intersect via a seam of conical intersections (CIs). Fully converged, full-dimensional quantum mechanical scattering calculations are carried out for all five systems at energies that allow for electronic de-excitation via the seam of CIs. Several semiclassical trajectory methods are tested against the accurate quantum mechanical results. For four of the five model systems, the diabatic representation is the preferred (most accurate) representation for semiclassical trajectories, as correctly predicted by the Calaveras County criterion. Four surface hopping methods are tested and have overall relative errors of 40%-60%. The semiclassical Ehrenfest method has an overall error of 66%, and the self-consistent decay of mixing (SCDM) and coherent switches with decay of mixing (CSDM) methods are the most accurate methods overall with relative errors of approximately 32%. Furthermore, the CSDM method is less representation dependent than both the SCDM and the surface hopping methods, making it the preferred semiclassical trajectory method. Finally, the behavior of semiclassical trajectories near conical intersections is discussed.