Two-State, Three-Mode Parametrization of the Force Field of a Retinal Chromophore Model

Mapping electronic decoherence pathways in molecules

Establishing the fundamental chemical principles that govern molecular electronic quantum decoherence has remained an outstanding challenge. Fundamental questions such as how solvent and intramolecular vibrations or chemical functionalization contribute to the decoherence remain unanswered and are beyond the reach of state-of-the-art theoretical and experimental approaches. Here we address this challenge by developing a strategy to isolate electronic decoherence pathways for molecular chromophores immersed in condensed phase environments that enables elucidating how electronic quantum coherence is lost. For this, we first identify resonance Raman spectroscopy as a general experimental method to reconstruct molecular spectral densities with full chemical complexity at room temperature, in solvent, and for fluorescent and non-fluorescent molecules. We then show how to quantitatively capture the decoherence dynamics from the spectral density and identify decoherence pathways by decomposing the overall coherence loss into contributions due to individual molecular vibrations and solvent modes. We illustrate the utility of the strategy by analyzing the electronic decoherence pathways of the DNA base thymine in water. Its electronic coherences decay in [Formula: see text]30 fs. The early-time decoherence is determined by intramolecular vibrations while the overall decay by solvent. Chemical substitution of thymine modulates the decoherence with hydrogen-bond interactions of the thymine ring with water leading to the fastest decoherence. Increasing temperature leads to faster decoherence as it enhances the importance of solvent contributions but leaves the early-time decoherence dynamics intact. The developed strategy opens key opportunities to establish the connection between molecular structure and quantum decoherence as needed to develop chemical strategies to rationally modulate it.

Significance of Energy Conservation in Coupled-Trajectory Approaches to Nonadiabatic Dynamics

Through approximating electron-nuclear correlation terms in the exact factorization approach, trajectory-based methods have been derived and successfully applied to the dynamics of a variety of light-induced molecular processes, capturing quantum (de)coherence effects rigorously. These terms account for the coupling among the trajectories, recovering the nonlocal nature of quantum nuclear dynamics that is completely overlooked in traditional independent-trajectory algorithms. Nevertheless, some of the approximations introduced in the derivation of some of these methods do not conserve the total energy. We analyze energy conservation in the coupled-trajectory mixed quantum-classical (CTMQC) algorithm and explore the performance of a modified algorithm, CTMQC-E, where some of the terms are redefined to restore energy conservation. A set of molecular models is used as a test, namely, 2-cis-penta-2,4-dienimium cation, bis(methylene) adamantyl radical cation, butatriene cation, uracil radical cation, and neutral pyrazine.

Steady State Photoisomerization Quantum Yield of Model Rhodopsin: Insights from Wavepacket Dynamics?

We simulate the nonequilibrium steady state cis-trans photoisomerization of retinal chromophore in rhodopsin on the basis of a two-state, two-mode model coupled to a thermal environment. By analyzing the systematic trends within an inhomogeneously broadened ensemble of systems, we find that the steady state reaction quantum yield (QY) correlates strongly with the excess energy above the crossing point of the system, in agreement with the prediction of the short-time dynamical wavepacket picture. However, the nontrivial dependence of the QY on the system-environment interaction indicates that a pure dynamical picture is insufficient and that environment-induced partial internal energy redistribution takes place before the reaction concludes. These results imply that a proper treatment of the photoisomerization reaction, particularly its high QY, must account for the redistribution and dissipation of energy beyond the dynamical wavepacket motion that is typically employed in the literature and that is appropriate only in the transient regime.

Quantum dynamics with curvilinear coordinates: models and kinetic energy operator

In order to simplify the numerical solution of the time-dependent or time-independent Schrödinger equations associated with atomic and molecular motions, the use of well-adapted coordinates is essential. Usually, this set of curvilinear coordinates leads to a Hamiltonian operator that is as separable as possible. Although their corresponding kinetic energy operator (KEO) expressions can be derived analytically for small systems or special kinds of coordinates, a numerical and exact approach allows one to compute them in terms of sophisticated curvilinear coordinates. Furthermore, the numerical approach enables one to easily define reduced-dimensionality or constrained models. We present here a recent implementation of this numerical approach that allows nested coordinate transformations, therefore leading to great flexibility in the definition of the curvilinear coordinates. Furthermore, this implementation has no limitations in terms of numbers of atoms or coordinate transformations. The quantum dynamics of the cis-trans photoisomerization of part of the retinal chromophore illustrates the construction of the coordinates and KEO part of a three-dimensional model. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Multi-objective optimization for retinal photoisomerization models with respect to experimental observables

The fitting of physical models is often done only using a single target observable. However, when multiple targets are considered, the fitting procedure becomes cumbersome, there being no easy way to quantify the robustness of the model for all different observables. Here, we illustrate that one can jointly search for the best model for each desired observable through multi-objective optimization. To do so, we construct the Pareto front to study if there exists a set of parameters of the model that can jointly describe multiple, or all, observables. To alleviate the computational cost, the predicted error for each targeted objective is approximated with a Gaussian process model as it is commonly done in the Bayesian optimization framework. We applied this methodology to improve three different models used in the simulation of stationary state cis-trans photoisomerization of retinal in rhodopsin, a significant biophysical process. Optimization was done with respect to different experimental measurements, including emission spectra, peak absorption frequencies for the cis and trans conformers, and energy storage. Advantages and disadvantages of previously proposed models are exposed.

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

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

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

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

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.

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.