Probing the Photochemical Funnel of a Retinal Chromophore Model via Zero-Point Energy Sampling Semiclassical Dynamics

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.

A Nitrogen Out-of-Plane (NOOP) Mechanism for Imine-Based Light-Driven Molecular Motors

Light-driven molecular motors have generated considerable interest due to their potential applications in material and biological systems. Recently, Greb and Lehn reported a new class of molecular motors, chiral N-alkyl imines, which undergo unidirectional rotation induced by light and heat. The mechanism of unidirectional motion in molecular motors containing a C═N group has been assumed to consist of photoinduced torsion about the double bond. In this work, we present a computational study of the photoisomerization dynamics of a chiral N-alkyl imine motor. We find that the location and energetics of minimal energy conical intersections (MECIs) alone are insufficient to understand the mechanism of the motor. Furthermore, a key part of the mechanism consists of out-of-plane distortions of the N atom (followed by isomerization about the double bond). Dynamic effects and out-of-plane distortions are critical to understand the observed (rather low) quantum yield for photoisomerization. Our results provide hints as to how the photoisomerization quantum yield might be increased, improving the efficiency of this class of molecular motors.

Internal conversion of the anionic GFP chromophore: in and out of the I-twisted S1/S0 conical intersection seam

The functional diversity of the green fluorescent protein (GFP) family is intimately connected to the interplay between competing photo-induced transformations of the chromophore motif, anionic p-hydroxybenzylidene-2,3-dimethylimidazolinone (HBDI^-). Its ability to undergo Z/E-isomerization is of particular importance for super-resolution microscopy and emerging opportunities in optogenetics. Yet, key dynamical features of the underlying internal conversion process in the native HBDI^- chromophore remain largely elusive. We investigate the intrinsic excited-state behavior of isolated HBDI^- to resolve competing decay pathways and map out the factors governing efficiency and the stereochemical outcome of photoisomerization. Based on non-adiabatic dynamics simulations, we demonstrate that non-selective progress along the two bridge-torsional (i.e., phenolate, P, or imidazolinone, I) pathways accounts for the three decay constants reported experimentally, leading to competing ultrafast relaxation primarily along the I-twisted pathway and S₁ trapping along the P-torsion. The majority of the population (∼70%) is transferred to S₀ in the vicinity of two approximately enantiomeric minima on the I-twisted intersection seam (MECI-Is). Despite their sloped, reactant-biased topographies (suggesting low photoproduct yields), we find that decay through these intersections leads to products with a surprisingly high quantum yield of ∼30%. This demonstrates that E-isomer generation results at least in part from direct isomerization on the excited state. A photoisomerization committor analysis reveals a difference in intrinsic photoreactivity of the two MECI-Is and that the observed photoisomerization is the combined result of two effects: early, non-statistical dynamics around the less reactive intersection followed by later, near-statistical behavior around the more reactive MECI-I. Our work offers new insight into internal conversion of HBDI^- that both establishes the intrinsic properties of the chromophore and enlightens principles for the design of chromophore derivatives and protein variants with improved photoswitching properties.

Trajectory surface hopping molecular dynamics simulations for retinal protonated Schiff-base photoisomerization

Global switching trajectory surface hopping molecular dynamics simulations are performed using accurate on-the-fly (TD)CAM-B3LYP/6-31G potential energy surfaces to study retinal protonated Schiff-base photoisomerization up to S₁ excitation. The simulations detected two-layer conical intersection networks: one is at an energy as high as 8 eV and the other is in the energy range around 3-4 eV. Six conical intersections within the low-layer energy region that correspond to active conical intersections under experimental conditions are found via the use of pairwise isomers, within which nonadiabatic molecular dynamics simulations are performed. Eight isomer products are populated with simulated sampling trajectories from which the simulated quantum yield in the gas phase is estimated to be 0.11 (0.08) moving from the all-trans isomer to the 11-cis (11-cis to all-trans) isomer in comparison with an experimental value of 0.09 (0.2) in the solution phase. Each conical intersection is related to one specific twist angle accompanying a related CC double bond motion during photoisomerization. Nonplanar distortion of the entire dynamic process has a significant role in the formation of the relevant photoisomerization products. The present simulation indicates that all hopping points show well-behaved potential energy surface topology, as calculated via the conventional TDDFT method, at conical intersections between S₁ and S₀ states. Therefore, the present nonadiabatic dynamics simulations with the TDDFT method are very encouraging for simulating various large systems related to retinal Schiff-base photoisomerization in the real world.

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.

Relaxation dynamics through a conical intersection: Quantum and quantum-classical studies

We study the relaxation process through a conical intersection of a photo-excited retinal chromophore model. The analysis is based on a two-electronic-state two-dimensional Hamiltonian developed by Hahn and Stock [J. Phys. Chem. B 104 1146 (2000)] to reproduce, with a minimal model, the main features of the 11-cis to all-trans isomerization of the retinal of rhodopsin. In particular, we focus on the performance of various trajectory-based schemes to nonadiabatic dynamics, and we compare quantum-classical results to the numerically exact quantum vibronic wavepacket dynamics. The purpose of this work is to investigate, by analyzing electronic and nuclear observables, how the sampling of initial conditions for the trajectories affects the subsequent dynamics.

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 minima and emission energies of retinal chromophore analogues: Performance of CASSCF and CC2 methods as compared with CASPT2

This study provides gas-phase S₁ excited-state geometries along with emission and adiabatic energies for methylated/demethylated and ring-locked analogues of protonated Schiff base retinal models comprising system of five conjugated double bonds (PSB5), using second order multiconfiguration perturbation theory (CASPT2). CASPT2 results serve as reference data to assess the performance of CC2 (second-order approximate coupled cluster singles and doubles) and a commonly used CASSCF/CASPT2 protocol, that is, complete active space self-consistent field (CASSCF) geometry optimization followed by CASPT2 energy calculation. We find that the CASSCF methodology fails to locate planar S₁ minimum energy structures for four out of five investigated planar models in contrast to CC2 and CASPT2 methods. However, for those which were found: one planar and two twisted minima, there is an excellent agreement between CASSCF and CASPT2 results in terms of geometrical parameters, one-electron properties, as well as emission and adiabatic energies. CC2 performs well for in-plane S₁ minima and their spectroscopic and electronic properties. However, this picture deteriorates for twisted minima. As expected, the CC2 description of the S₂ electronic state, with strong multireference and significant double excitation character, is very poor, exhibiting errors in transition energies exceeding 1 eV. They may be substantially diminished by recalculating transition energies with CASPT2 method. Our work shows that CASSCF/CASPT2 and CC2 shortcomings may influence gas-phase retinal analogues' excited state description in a dramatic way. © 2017 Wiley Periodicals, Inc.

Theoretical description of protein field effects on electronic excitations of biological chromophores

Photoinitiated phenomena play a crucial role in many living organisms. Plants, algae, and bacteria absorb sunlight to perform photosynthesis, and convert water and carbon dioxide into molecular oxygen and carbohydrates, thus forming the basis for life on Earth. The vision of vertebrates is accomplished in the eye by a protein called rhodopsin, which upon photon absorption performs an ultrafast isomerisation of the retinal chromophore, triggering the signal cascade. Many other biological functions start with the photoexcitation of a protein-embedded pigment, followed by complex processes comprising, for example, electron or excitation energy transfer in photosynthetic complexes. The optical properties of chromophores in living systems are strongly dependent on the interaction with the surrounding environment (nearby protein residues, membrane, water), and the complexity of such interplay is, in most cases, at the origin of the functional diversity of the photoactive proteins. The specific interactions with the environment often lead to a significant shift of the chromophore excitation energies, compared with their absorption in solution or gas phase. The investigation of the optical response of chromophores is generally not straightforward, from both experimental and theoretical standpoints; this is due to the difficulty in understanding diverse behaviours and effects, occurring at different scales, with a single technique. In particular, the role played by ab initio calculations in assisting and guiding experiments, as well as in understanding the physics of photoactive proteins, is fundamental. At the same time, owing to the large size of the systems, more approximate strategies which take into account the environmental effects on the absorption spectra are also of paramount importance. Here we review the recent advances in the first-principle description of electronic and optical properties of biological chromophores embedded in a protein environment. We show their applications on paradigmatic systems, such as the light-harvesting complexes, rhodopsin and green fluorescent protein, emphasising the theoretical frameworks which are of common use in solid state physics, and emerging as promising tools for biomolecular systems.

Probing the Photodynamics of Rhodopsins with Reduced Retinal Chromophores

While the light-induced population dynamics of different photoresponsive proteins has been investigated spectroscopically, systematic computational studies have not yet been possible due to the phenomenally high cost of suitable high level quantum chemical methods and the need of propagating hundreds, if not thousands, of nonadiabatic trajectories. Here we explore the possibility of studying the photodynamics of rhodopsins by constructing and investigating quantum mechanics/molecular mechanics (QM/MM) models featuring reduced retinal chromophores. In order to do so we use the sensory rhodopsin found in the cyanobacterium Anabaena PCC7120 (ASR) as a benchmark system. We find that the basic mechanistic features associated with the excited state dynamics of ASR QM/MM models are reproduced using models incorporating a minimal (i.e., three double-bond) chromophore. Furthermore, we show that ensembles of nonadiabatic ASR trajectories computed using the same abridged models replicate, at both the CASPT2 and CASSCF levels of theory, the trends in spectroscopy and lifetimes estimated using unabridged models and observed experimentally at room temperature. We conclude that a further expansion of these studies may lead to low-cost QM/MM rhodopsin models that may be used as effective tools in high-throughput in silico mutant screening.

Assessment of Approximate Coupled-Cluster and Algebraic-Diagrammatic-Construction Methods for Ground- and Excited-State Reaction Paths and the Conical-Intersection Seam of a Retinal-Chromophore Model

As a minimal model of the chromophore of rhodopsin proteins, the penta-2,4-dieniminium cation (PSB3) poses a challenging test system for the assessment of electronic-structure methods for the exploration of ground- and excited-state potential-energy surfaces, the topography of conical intersections, and the dimensionality (topology) of the branching space. Herein, we report on the performance of the approximate linear-response coupled-cluster method of second order (CC2) and the algebraic-diagrammatic-construction scheme of the polarization propagator of second and third orders (ADC(2) and ADC(3)). For the ADC(2) method, we considered both the strict and extended variants (ADC(2)-s and ADC(2)-x). For both CC2 and ADC methods, we also tested the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) variants. We have explored several ground- and excited-state reaction paths, a circular path centered around the S1/S0 surface crossing, and a 2D scan of the potential-energy surfaces along the branching space. We find that the CC2 and ADC methods yield a different dimensionality of the intersection space. While the ADC methods yield a linear intersection topology, we find a conical intersection topology for the CC2 method. We present computational evidence showing that the linear-response CC2 method yields a surface crossing between the reference state and the first response state featuring characteristics that are expected for a true conical intersection. Finally, we test the performance of these methods for the approximate geometry optimization of the S1/S0 minimum-energy conical intersection and compare the geometries with available data from multireference methods. The present study provides new insight into the performance of linear-response CC2 and polarization-propagator ADC methods for molecular electronic spectroscopy and applications in computational photochemistry.

Molcas 8: New capabilities for multiconfigurational quantum chemical calculations across the periodic table

In this report, we summarize and describe the recent unique updates and additions to the Molcas quantum chemistry program suite as contained in release version 8. These updates include natural and spin orbitals for studies of magnetic properties, local and linear scaling methods for the Douglas-Kroll-Hess transformation, the generalized active space concept in MCSCF methods, a combination of multiconfigurational wave functions with density functional theory in the MC-PDFT method, additional methods for computation of magnetic properties, methods for diabatization, analytical gradients of state average complete active space SCF in association with density fitting, methods for constrained fragment optimization, large-scale parallel multireference configuration interaction including analytic gradients via the interface to the Columbus package, and approximations of the CASPT2 method to be used for computations of large systems. In addition, the report includes the description of a computational machinery for nonlinear optical spectroscopy through an interface to the QM/MM package Cobramm. Further, a module to run molecular dynamics simulations is added, two surface hopping algorithms are included to enable nonadiabatic calculations, and the DQ method for diabatization is added. Finally, we report on the subject of improvements with respects to alternative file options and parallelization.

Modelling retinal chromophores photoisomerization: from minimal models in vacuo to ultimate bidimensional spectroscopy in rhodopsins

Modelling of retinal photoisomerization in different environments is reviewed and ultimate ultrafast electronic spectroscopy is proposed for obtaining new insights.

Computational Photobiology and Beyond

In this paper we review the results of a group of computational studies of the spectroscopy and photochemistry of light-responsive proteins. We focus on the use of quantum mechanics/molecular mechanics protocols based on a multiconfigurational quantum chemical treatment. More specifically, we discuss the use, limitations, and application of the ab initio CASPT2//CASSCF protocol that, presently, constitutes the method of choice for the investigation of excited state organic molecules, most notably, biological chromophores and fluorophores. At the end of this Review we will also see how the computational investigation of the visual photoreceptor rhodopsin is providing the basis for the design of light-driven artificial molecular devices.

Photophysics of the pi,pi* and n,pi* states of thymine: MS-CASPT2 minimum-energy paths and CASSCF on-the-fly dynamics

The photodynamics along the main decay paths of thymine after excitation to the lowest pi,pi* state have been studied with MS-CASPT2 calculations and semiclassical CASSCF dynamics calculations including a surface hopping algorithm. The static calculations show that there are two decay paths from the Franck-Condon structure that lead to a conical intersection with the ground state. The first path goes directly to the intersection, while the second one is indirect and involves a minimum of the pi,pi* state, a small barrier, and a crossing between the pi,pi* and n,pi* states. From the static calculations, both paths have similar slopes. The dynamics calculations along the indirect path show that, after the barrier, part of the trajectories are funneled to the intersection with the ground state, where they are efficiently quenched to the ground state. The remaining trajectories populate the n,pi* state. They are also quenched to the ground state in less than 1 ps, but the static calculations show that the decay rate of the n,pi* state is largely overestimated at the CASSCF level used for the dynamics. Overall, these results suggest that both direct and indirect paths contribute to the subpicosecond decay components found experimentally. The indirect path also provides a way for fast population of the n,pi* state, which will account for the experimental picosecond decay component.

Controlling S1/S0 decay and the balance between photochemistry and photostability in benzene: a direct quantum dynamics study

In this work, we investigate general mechanistic principles that control reaction selectivity following S(1)/S(0) internal conversion in benzene. A systematic relationship is drawn between the varying topology of an extended seam of conical intersection and the balance between two competitive radiationless decay channels: photophysical (benzene reactant regeneration) and photochemical (prefulvene product formation). This is supported by a model quantum dynamics study, using a direct dynamics approach based on variational multiconfiguration Gaussian wavepackets, where initial excitation of specific vibrational modes is designed to generate dynamical pathways that reach selected targets regions of the seam. High-energy regions of the seam are found to be sloped and in favor of the photophysical channel, while lower-energy regions are peaked and give access to the photochemical channel. This changeover could in principle be exploited to define targets for optimal control, by exciting different combinations of specific vibronic levels in S(1), accessing different regions of the seam, and giving different products.

Acceleration of the Z to E photoisomerization of penta-2,4-dieniminium by hydrogen out-of-plane motion: theoretical study on a model system of retinal protonated Schiff base

We report the result of comparison between two reaction coordinates [on the potential energy surface of the first excited state (S(1))] produced by CASSCF and these energies recalculated by MRMP2 in the Z to E photoisomerization of penta-2,4-dieniminium (PDI) as the minimal model of the retinal protonated Schiff base (RPSB). One coordinate is the S(1) state minimum-energy-path (MEP) in mass-weighted coordinates from the S(1) vertically excited point, where a strong hydrogen-out-of plane (HOOP) motion is not exhibited. The energy profile of the S(1) MEP at the MRMP2//CASSCF level shows a barrier for the rotation around the reactive C-C and hits the S(1)/S(0) degeneracy space where the central C-C-C-C dihedral angle is distorted by 65 degrees . The other coordinate is an S(1) coordinate obtained by the relaxed scan strategy. The relaxed coordinate along the central C-C-C-C dihedral angle, which we call the HOOP coordinate, shows strong HOOP motion. According to the MRMP2//CASSCF calculation, there is no barrier on the HOOP coordinate. Furthermore, the S(1) to S(0) transition may be possible without the large skeletal deformation by HOOP motion because the HOOP coordinate encounters the S(1)/S(0) degeneracy space where the central C-C-C-C dihedral angle is distorted by only 40 degrees . Consequently, if PDI is a suitable model molecule for the RPSB as often assumed, the 11-cis to all-trans photoisomerization is predicted to be accelerated by the HOOP motion.

Simulation of the photodeactivation of formamide in the nO-pi* and pi-pi* states: an ab initio on-the-fly surface-hopping dynamics study

The short-time photodynamics (1 ps) of formamide in its low-lying singlet excited n(O)-pi(*) and pi-pi(*) states have been investigated by the direct trajectory surface-hopping method based on multiconfigurational ab initio calculations. The simulations showed that in both states, the primary deactivation process is C-N bond dissociation. In the ground state, the energy is transferred to (a) translational motion of the HCO and NH(2) fragments, (b) additional C-H dissociation from the vibrationally hot HCO fragment, or (c) formation of NH(3) and CO. In addition to the C-N dissociation pathway, C-O bond fission is found to be an additional primary deactivation path in the pi-pi(*) dynamics. From fractional occupations of trajectories, lifetimes of formamide were estimated: tau(S(1))=441 fs and tau(S(2))=66 fs.