Discriminating Clockwise and Counterclockwise Photoisomerization Paths in Achiral Photoswitches by Excited-State Electronic Circular Dichroism

Despite the numerous investigations of photoisomerization reactions from both the computational and experimental points of view, even in complex environments, to date there is no direct demonstration of the direction of rotation of the retinal chromophore, initiating the vision process in several organisms, occurring upon light irradiation. In the literature, many proposals have been formulated to shed light on the details of this process, most of which are extracted from semiclassical simulations. Although high hopes are held in the development of time-resolved X-ray spectroscopy, I argue in this work that simpler but less known techniques can be used to unravel the details of this fascinating photochemical process. In fact, chiroptical spectroscopy would unambiguously prove the direction of the rotatory motion of the chromophore during the photoisomerization process by probing excited state chirality, a piece of information that, so far, has been exclusively extracted from atomistic simulations. I demonstrate this statement by computing the expected chiroptical response along photoisomerization pathways for several models of the retinal chromophores that are found in nature bound to rhodopsins, including nuclear ensemble spectra from semiclassical dynamics simulations, that can be compared with time-resolved experiments.

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.

The impact of different geometrical restrictions on the nonadiabatic photoisomerization of biliverdin chromophores

The photoisomerization mechanism of the chromophore of bacterial biliverdin (BV) phytochromes is explored via nonadiabatic dynamics simulation by using the on-the-fly trajectory surface-hopping method at the semi-empirical OM2/MRCI level. Particularly, the current study focuses on the influence of geometrical constrains on the nonadiabatic photoisomerization dynamics of the BV chromophore. Here a rather simplified approach is employed in the nonadiabatic dynamics to capture the features of geometrical constrains, which adds mechanical restrictions to the specific moieties of the BV chromophore. This simplified method provides a rather quick approach to examine the influence of geometrical restrictions on photoisomerization. As expected, different constrains bring distinctive influences on the photoisomerization mechanism of the BV chromophore, giving either strong or minor modification of both involved reaction channels and excited-state lifetimes after the constrains are added in different ring moieties. These observations not only contribute to the primary understanding of the role of the spatial restriction caused by biological environments in photoinduced dynamics of the BV chromophore, but also provide useful ideas for the artificial regulation of the photoisomerization reaction channels of phytochrome proteins.

Coupled- and Independent-Trajectory Approaches Based on the Exact Factorization Using the PyUNIxMD Package

We present mixed quantum-classical approaches based on the exact factorization framework. The electron-nuclear correlation term in the exact factorization enables us to deal with quantum coherences by accounting for electronic and nuclear nonadiabatic couplings effectively within classical nuclei approximation. We compare coupled- and independent-trajectory approximations with each other to understand algorithms in description of the bifurcation of nuclear wave packets and the correct spatial distribution of electronic wave functions along with nuclear trajectories. Finally, we show numerical results for comparisons of coupled- and independent-trajectory approaches for the photoisomerization of a protonated Schiff base from excited state molecular dynamics (ESMD) simulations with the recently developed Python-based ESMD code, namely, the PyUNIxMD program.

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.

Ultrafast excited-state dynamics of promising nucleobase ancestor 2,4,6-triaminopyrimidine

The ultrafast excited-state dynamics of 2,4,6-triaminopyrimidine - thought to be a promising candidate for a proto-RNA nucleobase - have been investigated via static multireference quantum-chemical calculations and mixed-quantum-classical/trajectory surface-hopping dynamics with a focus on the lowest-lying electronic states of the singlet manifold and with a view towards understanding the UV(C)/UV(B) photostability of the molecule. Ultrafast internal conversion channels have been identified that connect the lowest-lying ππ* electronically-excited state of 2,4,6-triaminopyrimidine with the ground electronic state, and non-radiative decay has been observed to take place on the picosecond timescale via a ππ* out-of-plane NH2 ("oop-NH2") minimum-energy crossing point. The short excited-state lifetime is competitive with the excited-state lifetimes of the canonical pyrimidine nucleobases, affirming the promise of 2,4,6-triaminopyrimidine as an ancestor. Evidence for energy-dependent excited-state dynamics is presented, and the open question of intersystem crossing is discussed speculatively.

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.

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

In recent years, the potential energy surfaces of the penta-2,4-dieniminium cation have been investigated using several electronic structure methods. The resulting pool of geometrical, electronic, and energy data provides a suitable basis for the construction of a topographically correct analytical model of the molecule force field and, therefore, for a better understanding of this class of molecules, which includes the chromophore of visual pigments. In the present contribution, we report the construction of such a model for regions of the force field that drive the photochemical and thermal isomerization of the central double bound of the cation. While previous models included only two modes, it is here shown that the proposed three-mode model and corresponding set of parameters are able to reproduce the complex topographical and electronic structure features seen in electronically correlated data obtained at the XMCQDPT2//CASSCF/6-31G* level of theory.

The 3s Rydberg state as a doorway state in the ultrafast dynamics of 1,1-difluoroethylene

The deactivation dynamics of 1,1-difluoroethylene after light excitation is studied within the surface hopping formalism in the presence of 3s and 3p Rydberg states using multi-state second order perturbation theory (MS-CASPT2).

On the decay of the triplet state of thionucleobases

The double-well triplet state of thionucleobases allows for a two-step mechanistic control of their triplet decay lifetime.

Mechanism of ultrafast non-reactive deactivation of the retinal chromophore in non-polar solvents

Counterion sensitive photodynamics of the retinal chromophore in solution.

Photoexcitation and relaxation kinetics of molecular systems in solution: towards a complete in silico model

A theoretical–computational method is proposed for modelling the complete kinetics – from photo-excitation to relaxation – of a chromophore in solution.

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.

Simulation of femtosecond two-dimensional electronic spectra of conical intersections

We have simulated femtosecond two-dimensional (2D) electronic spectra for an excited-state conical intersection using the wave-function version of the equation-of-motion phase-matching approach. We show that 2D spectra at fixed values of the waiting time provide information on the structure of the vibronic eigenstates of the conical intersection, while the evolution of the spectra with the waiting time reveals predominantly ground-state wave-packet dynamics. The results show that 2D spectra of conical intersection systems differ significantly from those obtained for chromophores with well separated excited-state potential-energy surfaces. The spectral signatures which can be attributed to conical intersections are discussed.

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.

Nonadiabatic photodynamics of a retinal model in polar and nonpolar environment

The nonadiabatic photodynamics of the all-trans-2,4-pentadiene-iminium cation (protonated Schiff base 3, PSB3) and the all-trans-3-methyl-2,4-pentadiene-iminium cation (MePSB3) were investigated in the gas phase and in polar (aqueous) and nonpolar (n-hexane) solutions by means of surface hopping using a multireference configuration-interaction (MRCI) quantum mechanical/molecular mechanics (QM/MM) level. Spectra, lifetimes for radiationless deactivation to the ground state, and structural and electronic parameters are compared. A strong influence of the polar solvent on the location of the crossing seam, in particular in the bond length alternation (BLA) coordinate, is found. Additionally, inclusion of the polar solvent changes the orientation of the intersection cone from sloped in the gas phase to peaked, thus enhancing considerably its efficiency for deactivation of the molecular system to the ground state. These factors cause, especially for MePSB3, a substantial decrease in the lifetime of the excited state despite the steric inhibition by the solvent.

Nonlinear dimensionality reduction for nonadiabatic dynamics: the influence of conical intersection topography on population transfer rates

Conical intersections play a critical role in the nonadiabatic relaxation of excited electronic states. However, there are an infinite number of these intersections and it is difficult to predict which are actually relevant. Furthermore, traditional descriptors such as intrinsic reaction coordinates and steepest descent paths often fail to adequately characterize excited state reactions due to their highly nonequilibrium nature. To address these deficiencies in the characterization of excited state mechanisms, we apply a nonlinear dimensionality reduction scheme (diffusion mapping) to generate reaction coordinates directly from ab initio multiple spawning dynamics calculations. As illustrated with various examples of photoisomerization dynamics, excited state reaction pathways can be derived directly from simulation data without any a priori specification of relevant coordinates. Furthermore, diffusion maps also reveal the influence of intersection topography on the efficiency of electronic population transfer, providing further evidence that peaked intersections promote nonadiabatic transitions more effectively than sloped intersections. Our results demonstrate the usefulness of nonlinear dimensionality reduction techniques as powerful tools for elucidating reaction mechanisms beyond the statistical description of processes on ground state potential energy surfaces.

Semiclassical dynamics simulations of charge transport in stacked π-systems

Charge transfer processes within stacked π-systems were examined for the stacked ethylene dimer radical cation with inclusion of a bridge containing up to three formaldehyde molecules. The electronic structure was treated at the complete active space self-consistent field and multireference configuration interaction levels. Nonadiabatic interactions between electronic and nuclear degrees of freedom were included through semiclassical surface hopping dynamics. The processes were analyzed according to fragment charge differences. Static calculations explored the dependence of the electronic coupling and on-site energies on varying geometric parameters and on the inclusion of a bridge. The dynamics simulations gave the possibility for directly observing complex charge transfer and diabatic trapping events.

Photodynamics of the adenine model 4-aminopyrimidine embedded within double strand of DNA

On-the-fly surface hopping nonadiabatic photodynamical simulations using hybrid quantum mechanical/molecular mechanical approach of 4-aminopyrimidine were performed to model the relaxation mechanism of adenine within DNA double strand. The surrounding bases do not affect the overall ring-puckering relaxation mechanisms significantly, however, interesting hydrogen-bond dynamics is observed. First, formation of intra-strand hydrogen bonds is found. It is shown that this effect speeds up the decay process. In addition, the Watson–Crick structure is altered by breaking one of the inter-strand hydrogen bonds also leading to a decrease of the life time.