Dynamical Friction Effects on the Photoisomerization of a Model Protonated Schiff Base in Solution

Intramolecular charge transfer and the function of vibronic excitons in photosynthetic light harvesting

A widely discussed explanation for the prevalence of pairs or clusters of closely spaced electronic chromophores in photosynthetic light-harvesting proteins is the presence of ultrafast and highly directional excitation energy transfer pathways mediated by vibronic excitons, the delocalized optical excitations derived from mixing of the electronic and vibrational states of the chromophores. We discuss herein the hypothesis that internal conversion processes between exciton states on the <100 fs timescale are possible when the excitonic potential energy surfaces are controlled by the vibrational modes that induce charge transfer character in a strongly coupled system of chromophores. We discuss two examples, the peridinin-chlorophyll protein from marine dinoflagellates and the intact phycobilisome from cyanobacteria, in which the intramolecular charge-transfer (ICT) character arising from out-of-plane distortion of the conjugation of carotenoid or bilin chromophores also results in localization of the initially delocalized optical excitation on the vibrational timescale. Tuning of the ground state conformations of the chromophores to manipulate their ICT character provides a natural photoregulatory mechanism, which would control the overall quantum yield of excitation energy transfer by turning on and off the delocalized character of the optical excitations.

Broadband 2DES detection of vibrational coherence in the Sx state of canthaxanthin

The nonadiabatic mechanism that mediates nonradiative decay of the bright S₂ state to the dark S₁ state of carotenoids involves population of a bridging intermediate state, S_x, in several examples. The nature of S_x remains to be determined definitively, but it has been recently suggested that S_x corresponds to conformationally distorted molecules evolving along out-of-plane coordinates of the isoprenoid backbone near a low barrier between planar and distorted conformations on the S₂ potential surface. In this study, the electronic and vibrational dynamics accompanying the formation of S_x in toluene solutions of the ketocarotenoid canthaxanthin (CAN) are characterized with broadband two-dimensional electronic spectroscopy (2DES) with 7.8 fs excitation pulses and detection of the linear polarization components of the third-order nonlinear optical signal. A stimulated-emission cross peak in the 2DES spectrum accompanies the formation of S_x in <20 fs following excitation of the main absorption band. S_x is prepared instantaneously, however, with excitation of hot-band transitions associated with distorted conformations of CAN's isoprenoid backbone in the low frequency onset of the main absorption band. Vibrational coherence oscillation maps and modulated anisotropy transients show that S_x undergoes displacements from the Franck-Condon S₂ state along out-of-plane coordinates as it passes to the S₁ state. The results are consistent with the conclusion that CAN's carbonyl-substituted β-ionone rings impart an intramolecular charge-transfer character that frictionally slows the passage from S_x to S₁ compared to carotenoids lacking carbonyl substitution. Despite the longer lifetime, the S₁ state of CAN is formed with retention of vibrational coherence after passing through a conical intersection seam with the S_x state.

Quantum and semiclassical dynamical studies of nonadiabatic processes in solution: achievements and perspectives

We concisely review the main methodological approaches to model nonadiabatic dynamics in isotropic solutions and their applications. Three general classes of models are identified as the most used to include solvent effects in the simulations. The first model describes the solvent as a set of harmonic collective modes coupled to the solute degrees of freedom, and the second as a continuum, while the third explicitly includes solvent molecules in the calculations. The issues related to the use of these models in semiclassical and quantum dynamical simulations are discussed, as well as the main limitations and perspectives of each approach.

Photophysics of First-Generation Photomolecular Motors: Resolving Roles of Temperature, Friction, and Medium Polarity

Light-driven unidirectional molecular rotary motors have the potential to power molecular machines. Consequently, optimizing their speed and efficiency is an important objective. Here, we investigate factors controlling the photochemical yield of the prototypical unidirectional rotary motor, a sterically overcrowded alkene, through detailed investigation of its excited-state dynamics. An isoviscosity analysis of the ultrafast fluorescence decay data resolves friction from barrier effects and reveals a 3.4 ± 0.5 kJ mol^-1 barrier to excited-state decay in nonpolar media. Extension of this analysis to polar solvents shows that this barrier height is a strong function of medium polarity and that the decay pathway becomes near barrierless in more polar media. Thus, the properties of the medium can be used as a route for controlling the motor's excited-state dynamics. The connection between these dynamics and the quantum yield of photochemical isomerization is probed. The photochemical quantum yield is shown to be a much weaker function of solvent polarity, and the most efficient excited-state decay pathway does not lead to a strongly enhanced quantum yield for isomerization. These results are discussed in terms of the solvent dependence of the complex multidimensional excited-state reaction coordinate.

Fluorescence Anisotropy Detection of Barrier Crossing and Ultrafast Conformational Dynamics in the S2 State of β-Carotene

Carotenoids are usually only weakly fluorescent despite being very strong absorbers in the mid-visible region because their first two excited singlet states, S₁ and S₂, have very short lifetimes. To probe the structural mechanisms that promote the nonradiative decay of the S₂ state to the S₁ state, we have carried out a series of fluorescence lineshape and anisotropy measurements with a prototype carotenoid, β-carotene, in four aprotic solvents. The anisotropy values observed in the fluorescence emission bands originating from the S₂ and S₁ states reveal that the large internal rotations of the emission transition dipole moment, as much as 50° relative to that of the absorption transition dipole moment, are initiated during ultrafast evolution on the S₂ state potential energy surface and persist upon nonradiative decay to the S₁ state. Electronic structure calculations of the orientation of the transition dipole moment account for the anisotropy results in terms of torsional and pyramidal distortions near the center of the isoprenoid backbone. The excitation wavelength dependence of the fluorescence anisotropy indicates that these out-of-plane conformational motions are initiated by passage over a low-activation energy barrier from the Franck-Condon S₂ structure. This conclusion is consistent with detection over the 80-200 K range of a broad, red-shifted fluorescence band from a dynamic intermediate evolving on a steep gradient of the S₂ state potential energy surface after crossing the activation barrier. The temperature dependence of the oscillator strength and anisotropy indicate that nonadiabatic passage from S₂ through a conical intersection seam to S₁ is promoted by the out-of-plane motions of the isoprenoid backbone with strong hindrance by solvent friction.

Solvation Dynamics in Water. 4. On the Initial Regime of Solvation Relaxation

It is shown, by means of numerical and analytic work, that initial molecular momenta play little significant role in the initial fast solvation relaxation that follows electronic excitation of, and charge creation for, a standard model system of a solute in water. Instead, the nonequilibrium dynamics are predominantly described by noninertial "steering" by the torques directly generated by the newly created charge distribution. It is this process that largely overcomes inertia and drives the relaxation dynamics on a time scale of a few tens of femtoseconds in the key initial regime of the dynamics. These results are discussed in the context of commonly employed descriptions such as inertial, Gaussian, and underdamped dynamical behavior.

Ultrafast photoisomerisation of an isolated retinoid

The photoinduced excited state dynamics of gas-phase trans-retinoate (deprotonated trans-retinoic acid, trans-RA^-) are studied using tandem ion mobility spectrometry coupled with laser spectroscopy, and frequency-, angle- and time-resolved photoelectron imaging. Photoexcitation of the bright S₃(ππ*) ← S₀ transition leads to internal conversion to the S₁(ππ*) state on a ≈80 fs timescale followed by recovery of S₀ and concomitant isomerisation to give the 13-cis (major) and 9-cis (minor) photoisomers on a ≈180 fs timescale. The sub-200 fs stereoselective photoisomerisation parallels that for the retinal protonated Schiff base chromophore in bacteriorhodopsin. Measurements on trans-RA^- in methanol using the solution photoisomerisation action spectroscopy technique show that 13-cis-RA^- is also the principal photoisomer, although the 13-cis and 9-cis photoisomers are formed with an inverted branching ratio with photon energy in methanol when compared with the gas phase, presumably due to solvent-induced modification of potential energy surfaces and inhibition of electron detachment processes. Comparison of the gas-phase time-resolved data with transient absorption spectroscopy measurements on retinoic acid in methanol suggest that photoisomerisation is roughly six times slower in solution. This work provides clear evidence that solvation significantly affects the photoisomerisation dynamics of retinoid molecules.

Photoswitching an Isolated Donor-Acceptor Stenhouse Adduct

Donor-acceptor Stenhouse adducts (DASAs) are a new class of photoswitching molecules with excellent fatigue resistance and synthetic tunability. Here, tandem ion mobility mass spectrometry coupled with laser excitation is used to characterize the photocyclization reaction of isolated, charge-tagged DASA molecules over the 450-580 nm range. The experimental maximum response at 530 nm agrees with multireference perturbation theory calculations for the S₁ ← S₀ transition maximum at 533 nm. Photocyclization in the gas phase involves absorption of at least two photons; the first photon induces Z-E isomerization from the linear isomer to metastable intermediate isomers, while the second photon drives another E-Z isomerization and 4π-electrocyclization reaction. Cyclization is thermally reversible in the gas phase with collisional excitation.

Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces

In this Introduction, we show the basic problems of non-statistical and non-equilibrium phenomena related to the papers collected in this themed issue. Over the past few years, significant advances in both computing power and development of theories have allowed the study of larger systems, increasing the time length of simulations and improving the quality of potential energy surfaces. In particular, the possibility of using quantum chemistry to calculate energies and forces 'on the fly' has paved the way to directly study chemical reactions. This has provided a valuable tool to explore molecular mechanisms at given temperatures and energies and to see whether these reactive trajectories follow statistical laws and/or minimum energy pathways. This themed issue collects different aspects of the problem and gives an overview of recent works and developments in different contexts, from the gas phase to the condensed phase to excited states.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.

Excitation Energy Transfer by Coherent and Incoherent Mechanisms in the Peridinin-Chlorophyll a Protein

Excitation energy transfer from peridinin to chlorophyll (Chl) a is unusually efficient in the peridinin-chlorophyll a protein (PCP) from dinoflagellates. This enhanced performance is derived from the long intrinsic lifetime of 4.4 ps for the S₂ (1¹B_u⁺) state of peridinin in PCP, which arises from the electron-withdrawing properties of its carbonyl substituent. Results from heterodyne transient grating spectroscopy indicate that S₂ serves as the donor for two channels of energy transfer: a 30 fs process involving quantum coherence and delocalized peridinin-Chl states and an incoherent, 2.5 ps process initiated by dynamic exciton localization, which accompanies the formation of a conformationally distorted intermediate in 45 fs. The lifetime of the S₂ state is lengthened in PCP by its intramolecular charge-transfer character, which increases the system-bath coupling and slows the torsional motions that promote nonradiative decay to the S₁ (2¹A_g^-) state.

Torsional Dynamics and Intramolecular Charge Transfer in the S2 (1(1)Bu(+)) Excited State of Peridinin: A Mechanism for Enhanced Mid-Visible Light Harvesting

Of the carotenoids known in photosynthetic organisms, peridinin exhibits one of the highest quantum efficiencies for excitation energy transfer to chlorophyll (Chl) a acceptors. The mechanism for this enhanced performance involves an order-of-magnitude slowing of the S2 (1(1)Bu(+)) → S1 (2(1)Ag(-)) nonradiative decay pathway compared to carotenoids lacking carbonyl substitution. Using femtosecond transient grating spectroscopy with optical heterodyne detection, we have obtained the first evidence that the nonradiative decay of the S2 state of peridinin is promoted by large-amplitude torsional motions. The decay of an intermediate state termed Sx, which we assign to a twisted form of the S2 state, is substantially slowed by solvent friction in peridinin due to its intramolecular charge transfer (ICT) character.

An On-the-Fly Surface-Hopping Program JADE for Nonadiabatic Molecular Dynamics of Polyatomic Systems: Implementation and Applications

Nonadiabatic dynamics simulations have rapidly become an indispensable tool for understanding ultrafast photochemical processes in complex systems. Here, we present our recently developed on-the-fly nonadiabatic dynamics package, JADE, which allows researchers to perform nonadiabatic excited-state dynamics simulations of polyatomic systems at an all-atomic level. The nonadiabatic dynamics is based on Tully's surface-hopping approach. Currently, several electronic structure methods (CIS, TDHF, TDDFT(RPA/TDA), and ADC(2)) are supported, especially TDDFT, aiming at performing nonadiabatic dynamics on medium- to large-sized molecules. The JADE package has been interfaced with several quantum chemistry codes, including Turbomole, Gaussian, and Gamess (US). To consider environmental effects, the Langevin dynamics was introduced as an easy-to-use scheme into the standard surface-hopping dynamics. The JADE package is mainly written in Fortran for greater numerical performance and Python for flexible interface construction, with the intent of providing open-source, easy-to-use, well-modularized, and intuitive software in the field of simulations of photochemical and photophysical processes. To illustrate the possible applications of the JADE package, we present a few applications of excited-state dynamics for various polyatomic systems, such as the methaniminium cation, fullerene (C20), p-dimethylaminobenzonitrile (DMABN) and its primary amino derivative aminobenzonitrile (ABN), and 10-hydroxybenzo[h]quinoline (10-HBQ).

Dissipative dynamics at conical intersections: simulations with the hierarchy equations of motion method

The effect of a dissipative environment on the ultrafast nonadiabatic dynamics at conical intersections is analyzed for a two-state two-mode model chosen to represent the S₂(ππ*)–S₁(nπ*) conical intersection in pyrazine (the system) which is bilinearly coupled to infinitely many harmonic oscillators in thermal equilibrium (the bath). The system–bath coupling is modeled by the Drude spectral function. The equation of motion for the reduced density matrix of the system is solved numerically exactly with the hierarchy equation of motion method using graphics-processor-unit (GPU) technology. The simulations are valid for arbitrary strength of the system–bath coupling and arbitrary bath memory relaxation time. The present computational studies overcome the limitations of weak system–bath coupling and short memory relaxation time inherent in previous simulations based on multi-level Redfield theory [A. Kühl and W. Domcke, J. Chem. Phys. 2002, 116, 263]. Time evolutions of electronic state populations and time-dependent reduced probability densities of the coupling and tuning modes of the conical intersection have been obtained. It is found that even weak coupling to the bath effectively suppresses the irregular fluctuations of the electronic populations of the isolated two-mode conical intersection. While the population of the upper adiabatic electronic state (S₂) is very efficiently quenched by the system–bath coupling, the population of the diabatic ππ* electronic state exhibits long-lived oscillations driven by coherent motion of the tuning mode. Counterintuitively, the coupling to the bath can lead to an enhanced lifetime of the coherence of the tuning mode as a result of effective damping of the highly excited coupling mode, which reduces the strong mode–mode coupling inherent to the conical intersection. The present results extend previous studies of the dissipative dynamics at conical intersections to the nonperturbative regime of system–bath coupling. They pave the way for future first-principles simulations of femtosecond time-resolved four-wave-mixing spectra of chromophores in condensed phases which are nonperturbative in the system dynamics, the system–bath coupling as well as the field-matter coupling.

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.

Valence-bond non-equilibrium solvation model for a twisting monomethine cyanine

We propose and analyze a two-state valence-bond model of non-equilibrium solvation effects on the excited-state twisting reaction of monomethine cyanines. Suppression of this reaction is thought responsible for environment-dependent fluorescence yield enhancement in these dyes. Fluorescence is quenched because twisting is accompanied via the formation of dark twisted intramolecular charge-transfer (TICT) states. For monomethine cyanines, where the ground state is a superposition of structures with different bond and charge localizations, there are two possible twisting pathways with different charge localizations in the excited state. For parameters corresponding to symmetric monomethines, the model predicts two low-energy twisting channels on the excited-state surface, which leads to a manifold of TICT states. For typical monomethines, twisting on the excited state surface will occur with a small barrier or no barrier. Changes in the solvation configuration can differentially stabilize TICT states in channels corresponding to different bonds, and that the position of a conical intersection between adiabatic states moves in response to solvation to stabilize either one channel or the other. There is a conical intersection seam that grows along the bottom of the excited-state potential with increasing solvent polarity. For monomethine cyanines with modest-sized terminal groups in moderately polar solution, the bottom of the excited-state potential surface is completely spanned by a conical intersection seam.

Non-adiabatic dynamics close to conical intersections and the surface hopping perspective

Conical intersections play a major role in the current understanding of electronic de-excitation in polyatomic molecules, and thus in the description of photochemistry and photophysics of molecular systems. This article reviews aspects of the basic theory underlying the description of non-adiabatic transitions at conical intersections, with particular emphasis on the important case when the dynamics of the nuclei are treated classically. Within this classical nuclear motion framework, the main aspects of the surface hopping methodology in the conical intersection context are presented. The emerging picture from this treatment is that of electronic transitions around conical intersections dominated by the interplay of the nuclear velocity and the derivative non-adiabatic coupling vector field.

Molecular mechanism of diaminomaleonitrile to diaminofumaronitrile photoisomerization: an intermediate step in the prebiotic formation of purine nucleobases

The photoinduced isomerization of diaminomaleonitrile (DAMN) to diaminofumaronitrile (DAFN) was suggested to play a key role in the prebiotically plausible formation of purine nucleobases and nucleotides. In this work we analyze two competitive photoisomerization mechanisms on the basis of state-of-the-art quantum-chemical calculations. Even though it was suggested that this process might occur on the triplet potential-energy surface, our results indicate that the singlet reaction channel should not be disregarded either. In fact, the peaked topography of the S1 /S0 conical intersection suggests that the deexcitation should most likely occur on a sub-picosecond timescale and the singlet photoisomerization mechanism might effectively compete even with a very efficient intersystem crossing. Such a scenario is further supported by the relatively small spin-orbit coupling of the S1 and T2 states in the Franck-Condon region, which does not indicate a very effective triplet bypass for this photoreaction. Therefore, we conclude that the triplet reaction channel in DAMN might not be as prominent as was previously thought.

Nonadiabatic dynamics of photoinduced proton-coupled electron transfer: comparison of explicit and implicit solvent simulations

Theoretical approaches for simulating the ultrafast dynamics of photoinduced proton-coupled electron transfer (PCET) reactions in solution are developed and applied to a series of model systems. These processes are simulated by propagating nonadiabatic surface hopping trajectories on electron-proton vibronic surfaces that depend on the solute and solvent nuclear coordinates. The PCET system is represented by a four-state empirical valence bond model, and the solvent is treated either as explicit solvent molecules or as a dielectric continuum, in which case the solvent dynamics is described in terms of two collective solvent coordinates corresponding to the energy gaps associated with electron and proton transfer. The explicit solvent simulations reveal two distinct solvent relaxation time scales, where the faster time scale relaxation corresponds to librational motions of solvent molecules in the first solvation shell, and the slower time scale relaxation corresponds to the bulk solvent dielectric response. The charge transfer dynamics is strongly coupled to both the fast and slow time scale solvent dynamics. The dynamical multistate continuum theory is extended to include the effects of two solvent relaxation time scales, and the resulting coupled generalized Langevin equations depend on parameters that can be extracted from equilibrium molecular dynamics simulations. The implicit and explicit solvent approaches lead to qualitatively similar charge transfer and solvent dynamics for model PCET systems, suggesting that the implicit solvent treatment captures the essential elements of the nonequilibrium solvent dynamics for many systems. A combination of implicit and explicit solvent approaches will enable the investigation of photoinduced PCET processes in a variety of condensed phase systems.

Backbone modification of retinal induces protein-like excited state dynamics in solution

The drastically different reactivity of the retinal chromophore in solution compared to the protein environment is poorly understood. Here, we show that the addition of a methyl group to the C═C backbone of all-trans retinal protonated Schiff base accelerates the electronic decay in solution making it comparable to the proton pump bacteriorhodopsin. Contrary to the notion that reaction speed and efficiency are linked, we observe a concomitant 50% reduction in the isomerization yield. Our results demonstrate that minimal synthetic engineering of potential energy surfaces based on theoretical predictions can induce drastic changes in electronic dynamics toward those observed in an evolution-optimized protein pocket.

Isotope Effects on the Nonequilibrium Dynamics of Ultrafast Photoinduced Proton-Coupled Electron Transfer Reactions in Solution

The hydrogen/deuterium isotope effects on the ultrafast dynamics of photoinduced proton-coupled electron transfer (PCET) are investigated with a recently developed nonadiabatic dynamics approach. An ensemble of surface hopping trajectories is propagated according to a Langevin equation on electron-proton vibronic free energy surfaces that depend on a collective solvent coordinate. The calculations illustrate that ultrafast PCET reactions could exhibit a significant normal isotope effect, where PCET is faster for hydrogen than deuterium, but could also exhibit a negligible isotope effect or even a slight inverse isotope effect. The isotope effect is very small or absent when highly excited electron-proton vibronic states dictate the nonadiabatic dynamics and increases with greater participation of lower vibronic states. Thus, although the presence of a significant isotope effect strongly suggests that proton motion is coupled to electron transfer, the absence of an isotope effect does not exclude the possibility that proton transfer accompanies electron transfer in ultrafast photoinduced charge transfer processes.