Probing the Photodynamics of Rhodopsins with Reduced Retinal Chromophores

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.

WFOT: A Wave Function Overlap Tool between Single- and Multi-Reference Electronic Structure Methods for Spectroscopy Simulation

We report the development of a novel diagnostic tool, named wave function overlap tool (WFOT), designed to evaluate the overlap between wave functions computed at single-reference [i.e., time-dependent density functional theory or configuration interaction singles (CIS)] and multireference (i.e., CASSCF/CASPT2) electronic structure levels of theory. It relies on truncating the single- and multireference WFs to CIS-like expansions spanning the same configurational space and maximizing the molecular orbital overlap by means of a unitary transformation. To demonstrate the functionality of the tool, we calculate the transient spectrum of acetylacetone by evaluating excited state absorption signals with multireference quality on top of single-reference on-the-fly dynamics simulations. Semiautomatic spectra generation is facilitated by interfacing the tool with the COBRAMM package, which also allows one to use WFOT with several quantum chemistry codes such as Gaussian, NWChem, and OpenMolcas. Other exciting possibilities for the utilization of the code beyond the simulation of transient absorption spectroscopy are eventually discussed.

Comparative quantum-classical dynamics of natural and synthetic molecular rotors show how vibrational synchronization modulates the photoisomerization quantum efficiency

We use quantum-classical trajectories to investigate the origin of the different photoisomerization quantum efficiency observed in the dim-light visual pigment Rhodopsin and in the light-driven biomimetic molecular rotor para-methoxy N-methyl indanylidene-pyrrolinium (MeO-NAIP) in methanol. Our results reveal that effective light-energy conversion requires, in general, an auxiliary molecular vibration (called promoter) that does not correspond to the rotary motion but synchronizes with it at specific times. They also reveal that Nature has designed Rhodopsin to exploit two mechanisms working in a vibrationally coherent regime. The first uses a wag promoter to ensure that ca. 75% of the absorbed photons lead to unidirectional rotations. The second mechanism ensures that the same process is fast enough to avoid directional randomization. It is found that MeO-NAIP in methanol is incapable of exploiting the above mechanisms resulting into a 50% quantum efficiency loss. However, when the solvent is removed, MeO-NAIP rotation is predicted to synchronize with a ring-inversion promoter leading to a 30% increase in quantum efficiency and, therefore, biomimetic behavior.

Exact-Factorization-Based Surface Hopping without Velocity Adjustment

While surface hopping has emerged as a powerful method for simulating non-adiabatic dynamics in large molecules, the ad hoc nature of the necessary velocity adjustments and decoherence corrections in the algorithm somewhat reduces its reliability. Here we propose a new scheme that eliminates these aspects by combining the nuclear equation from the quantum-trajectory surface-hopping approach with the electronic equation derived from the exact-factorization approach. The resulting method, denoted QTSH-XF, yields a surface-hopping method on firmer ground than previous and is shown to successfully capture dynamics in Tully models and in a linear vibronic coupling model of the photoexcited uracil cation.

Assessment of the Electron Correlation Treatment on the Quantum-Classical Dynamics of Retinal Protonated Schiff Base Models: XMS-CASPT2, RMS-CASPT2, and REKS Methods

We compare the performance of three different multiconfigurational wave function-based electronic structure methods and two implementations of the spin-restricted ensemble-referenced Kohn-Sham (REKS) method. The study is characterized by three features: (i) it uses a small set of quantum-classical trajectories rather than potential energy surface mapping, (ii) it focuses, exclusively, on the photoisomerization of retinal protonated Schiff base models, and (iii) it probes the effect of both methyl substitution and the increase in length of the conjugate π-system. For each tested method, the corresponding analytical gradients are used to drive the quantum-classical (Tully's FSSH method) trajectory propagation, including the recent multistate XMS-CASPT2 and RMS-CASPT2 gradients. It is shown that while CASSCF, XMS-CASPT2, and RMS-CASPT2 yield consistent photoisomerization dynamics descriptions, REKS produces, in some of these systems, qualitatively different behavior that is attributed to a flatter and topographically different excited state potential energy surface. The origin of this behavior can be traced back to the effect of the employed density functional approximation. The above studies are further expanded by benchmarking, at the CASSCF and REKS levels, the electronic structure methods using a QM/MM model of the visual pigment rhodopsin.

Biomimetic Photo-Switches Softening Model Lipid Membranes

We report the synthesis and characterization of a novel photo-switch based on biomimetic cyclocurcumin analogous and interacting with the lipid bilayer, which can be used in the framework of oxygen-independent light-induced therapy. More specifically, by using molecular dynamics simulations and free energy techniques, we show that the inclusion of hydrophobic substituents is needed to allow insertion in the lipid membrane. After having confirmed experimentally that the substituents do not preclude the efficient photoisomerization, we show through UV-vis and dynamic light scattering measurements together with compression isotherms that the chromophore is internalized in both lipid vesicles and monomolecular film, respectively, inducing their fluidification. The irradiation of the chromophore-loaded lipid aggregates modifies their properties due to the different organization of the two diastereoisomers, E and Z. In particular, a competition between a fast structural reorganization and a slower expulsion of the chromophore after isomerization can be observed in the kinetic profiles recorded during E to Z photoisomerization. This report paves the way for future investigations in the optimization of biomimetic photoswitches potentially useful in modern light-induced therapeutic strategies.

On the fluorescence enhancement of arch neuronal optogenetic reporters

The lack of a theory capable of connecting the amino acid sequence of a light-absorbing protein with its fluorescence brightness is hampering the development of tools for understanding neuronal communications. Here we demonstrate that a theory can be established by constructing quantum chemical models of a set of Archaerhodopsin reporters in their electronically excited state. We found that the experimentally observed increase in fluorescence quantum yield is proportional to the computed decrease in energy difference between the fluorescent state and a nearby photoisomerization channel leading to an exotic diradical of the protein chromophore. This finding will ultimately support the development of technologies for searching novel fluorescent rhodopsin variants and unveil electrostatic changes that make light emission brighter and brighter.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

The Quest to Simulate Excited-State Dynamics of Transition Metal Complexes

This Perspective describes current computational efforts in the field of simulating photodynamics of transition metal complexes. We present the typical workflows and feature the strengths and limitations of the different contemporary approaches. From electronic structure methods suitable to describe transition metal complexes to approaches able to simulate their nuclear dynamics under the effect of light, we give particular attention to build a bridge between theory and experiment by critically discussing the different models commonly adopted in the interpretation of spectroscopic experiments and the simulation of particular observables. Thereby, we review all the studies of excited-state dynamics on transition metal complexes, both in gas phase and in solution from reduced to full dimensionality.

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.

Dynamical correction to the Bethe-Salpeter equation beyond the plasmon-pole approximation

The Bethe-Salpeter equation (BSE) formalism is a computationally affordable method for the calculation of accurate optical excitation energies in molecular systems. Similar to the ubiquitous adiabatic approximation of time-dependent density-functional theory, the static approximation, which substitutes a dynamical (i.e., frequency-dependent) kernel by its static limit, is usually enforced in most implementations of the BSE formalism. Here, going beyond the static approximation, we compute the dynamical correction of the electron-hole screening for molecular excitation energies, thanks to a renormalized first-order perturbative correction to the static BSE excitation energies. The present dynamical correction goes beyond the plasmon-pole approximation as the dynamical screening of the Coulomb interaction is computed exactly within the random-phase approximation. Our calculations are benchmarked against high-level (coupled-cluster) calculations, allowing one to assess the clear improvement brought by the dynamical correction for both singlet and triplet optical transitions.

Modern quantum chemistry with [Open]Molcas

MOLCAS/OpenMolcas is an ab initio electronic structure program providing a large set of computational methods from Hartree-Fock and density functional theory to various implementations of multiconfigurational theory. This article provides a comprehensive overview of the main features of the code, specifically reviewing the use of the code in previously reported chemical applications as well as more recent applications including the calculation of magnetic properties from optimized density matrix renormalization group wave functions.

Combining Graphics Processing Units, Simplified Time-Dependent Density Functional Theory, and Finite-Difference Couplings to Accelerate Nonadiabatic Molecular Dynamics

Starting from our recently published implementation of nonadiabatic molecular dynamics (NAMD) on graphics processing units (GPUs), we explore further approaches to accelerate ab initio NAMD calculations at the time-dependent density functional theory (TDDFT) level of theory. We employ (1) the simplified TDDFT schemes of Grimme et al. and (2) the Hammes-Schiffer-Tully approach to obtain nonadiabatic couplings from finite-difference calculations. The resulting scheme delivers an accurate physical picture while virtually eliminating the two computationally most demanding steps of the algorithm. Combined with our GPU-based integral routines for SCF, TDDFT, and TDDFT derivative calculations, NAMD simulations of systems of a few hundreds of atoms at a reasonable time scale become accessible on a single compute node. To demonstrate this and to present a first, illustrative example, we perform TDDFT/MM-NAMD simulations of the rhodopsin protein.

Induced Night Vision by Singlet-Oxygen-Mediated Activation of Rhodopsin

In humans, vision is limited to a small fraction of the whole electromagnetic spectrum. One possible strategy for enhancing vision in deep-red or poor-light conditions consists of recruiting chlorophyll derivatives in the rod photoreceptor cells of the eye, as suggested in the case of some deep-sea fish. Here, we employ all-atom molecular simulations and high-level quantum chemistry calculations to rationalize how chlorin e6 (Ce6), widely used in photodynamic therapy although accompanied by enhanced visual sensitivity, mediates vision in the dark, shining light on a fascinating but largely unknown molecular mechanism. First, we identify persistent interaction sites between Ce6 and the extracellular loops of rhodopsin, the transmembrane photoreceptor protein responsible for the first steps in vision. Triggered by Ce6 deep-red light absorption, the retinal within rhodopsin can be isomerized thus starting the visual phototransduction cascade. Our data largely exclude previously hypothesized energy-transfer mechanisms while clearly lending credence to a retinal isomerization indirectly triggered by singlet oxygen, proposing an alternative mechanism to rationalize photosensitizer-mediated night vision.

Synthesis, spectroscopy and QM/MM simulations of a biomimetic ultrafast light-driven molecular motor

A molecular motor potentially performing a continuous unidirectional rotation is studied by a multidisciplinary approach including organic synthesis, transient spectroscopy and excited state trajectory calculations. A stereogenic center was introduced in the N-alkylated indanylidene-pyrroline Schiff base framework of a previously investigated light-driven molecular switch in order to achieve the unidirectional C[double bond, length as m-dash]C rotary motion typical of Feringa's motor. Here we report that the specific substitution pattern of the designed chiral molecule must critically determine the unidirectional efficiency of the light-induced rotary motion. More specifically, we find that a stereogenic center containing a methyl group and a hydrogen atom as substituents does not create a differential steric effect large enough to fully direct the motion in either the clockwise or counterclockwise direction especially along the E→Z coordinate. However, due to the documented ultrafast character and electronic circular dichroism activity of the investigated system, we find that it provides the basis for development of a novel generation of rotary motors with a biomimetic framework and operating on a picosecond time scale.

A QM/MM study of the initial excited state dynamics of green-absorbing proteorhodopsin

The primary photochemical reaction of the green-absorbing proteorhodopsin is studied by means of a hybrid quantum mechanics/molecular mechanics (QM/MM) approach. The simulations are based on a homology model derived from the blue-absorbing proteorhodopsin crystal structure. The geometry of retinal and the surrounding sidechains in the protein binding pocket were optimized using the QM/MM method. Starting from this geometry the isomerization was studied with a relaxed scan along the C13[double bond, length as m-dash]C14 dihedral. It revealed an "aborted bicycle pedal" mechanism of isomerization that was originally proposed by Warshel for bovine rhodopsin and bacteriorhodopsin. However, the isomerization involved the concerted rotation about C13[double bond, length as m-dash]C14 and C15[double bond, length as m-dash]N, with the latter being highly twisted but not isomerized. Further, the simulation showed an increased steric interaction between the hydrogen at the C14 of the isomerizing bond and the hydroxyl group at the neighbouring tyrosine 200. In addition, we have simulated a nonadiabatic trajectory which showed the timing of the isomerization. In the first 20 fs upon excitation the order of the conjugated double and single bonds is inverted, consecutively the C13[double bond, length as m-dash]C14 rotation is activated for 200 fs until the S1-S0 transition is detected. However, the isomerization is reverted due to the specific interaction with the tyrosine as observed along the relaxed scan calculation. Our simulations indicate that the retinal - tyrosine 200 interaction plays an important role in the outcome of the photoisomerization.

Fluorescence Enhancement of a Microbial Rhodopsin via Electronic Reprogramming

The engineering of microbial rhodopsins with enhanced fluorescence is of great importance in the expanding field of optogenetics. Here we report the discovery of two mutants (W76S/Y179F and L83Q) of a sensory rhodopsin from the cyanobacterium Anabaena PCC7120 with opposite fluorescence behavior. In fact, while W76S/Y179F displays, with respect to the wild-type protein, a nearly 10-fold increase in red-light emission, the second is not emissive. Thus, the W76S/Y179F, L83Q pair offers an unprecedented opportunity for the investigation of fluorescence enhancement in microbial rhodopsins, which is pursued by combining transient absorption spectroscopy and multiconfigurational quantum chemistry. The results of such an investigation point to an isomerization-blocking electronic effect as the direct cause of instantaneous (subpicosecond) fluorescence enhancement.

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.

The effect of solvent relaxation in the ultrafast time-resolved spectroscopy of solvated benzophenone

Modeling time-resolved spectra to unravel ultra fast solvent reorganization.

Photoisomerization of Arylazopyrazole Photoswitches: Stereospecific Excited-State Relaxation

Electronic structure calculations and nonadiabatic dynamics simulations (more than 2000 trajectories) are used to explore the Z-E photoisomerization mechanism and excited-state decay dynamics of two arylazopyrazole photoswitches. Two chiral S1 /S0 conical intersections with associated enantiomeric S1 relaxation paths that are barrierless and efficient (timescale of ca. 50 fs) were found. For the parent arylazopyrazole (Z8) both paths contribute evenly to the S1 excited-state decay, whereas for the dimethyl derivative (Z11) each of the two chiral cis minima decays almost exclusively through one specific enantiomeric S1 relaxation path. To our knowledge, the Z11 arylazopyrazole is thus the first example for nearly stereospecific unidirectional excited-state relaxation.