Transition State Dynamics and Relaxation Processes in Solutions: A Frontier of Physical Chemistry

A Brief Discussion of Chemical Kinetics versus Chemical Dynamics

Chemical kinetics and chemical dynamics are distinct but related topics. They arise again in contemporary physical chemistry often in terms of charge carrier processes in new materials which interconvert light and electrical energy on a distribution of time scales. With this recent rise in the application of concepts in kinetics and dynamics to new problems, there has also arisen confusion about the differences and connections between the two. Here, we briefly review the relationship between kinetics and dynamics in chemical processes, with particular emphasis on the photochemical and photophysical response of a system.

Local Molecular Field Theory for Coulomb Interactions in Aqueous Solutions

Coulomb interactions play a crucial role in a wide array of processes in aqueous solutions but present conceptual and computational challenges to both theory and simulations. We review recent developments in an approach addressing these challenges─local molecular field (LMF) theory. LMF theory exploits an exact and physically suggestive separation of intermolecular Coulomb interactions into strong short-range and uniformly slowly varying long-range components. This allows us to accurately determine the averaged effects of the long-range components on the short-range structure using effective single particle fields and analytical corrections, greatly reducing the need for complex lattice summation techniques used in most standard approaches. The simplest use of these ideas in aqueous solutions leads to the short solvent (SS) model, where both solvent-solvent and solute-solvent Coulomb interactions have only short-range components. Here we use the SS model to give a simple description of pairing of nucleobases and biologically relevant ions in water.

Bond-Breaking Reactions Encounter Distinct Solvent Environments Causing Breakdown of Linear Response

Solvent effects are important for understanding solution-phase chemical reactions. Surprisingly, very few studies have explored how solvent dynamics change during the course of a reaction with solutes that encounter a wide range of configurations. Here, we use quantum simulation methods to explore the solvent dynamics during a solution-phase bond-breaking reaction: the photodissociation of Na₂⁺ in liquid Ar. We find that the solute experiences a small number of distinct solvent environments that change in a discrete fashion as the bond lengthens. In characterizing the solvent environments, we show also that linear response fails by all measures, even when nonstationarity of solvent dynamics is considered. This observation of distinct solvent response environments with a solvent that can undergo only translational motions highlights the complexity of solute-solvent interactions, but that there are only a few environments gives hope to the idea that solvation dynamics can be understood for solution-phase reactions that explore a wide configuration space.

Heavy-Atom Kinetic Isotope Effects: Primary Interest or Zero Point?

Chemists have many options for elucidating reaction mechanisms. Global kinetic analysis and classic transition-state probes (e.g., LFERs, Eyring) inevitably form the cornerstone of any strategy, yet their application to increasingly sophisticated synthetic methodologies often leads to a wide range of indistinguishable mechanistic proposals. Computational chemistry provides powerful tools for narrowing the field in such cases, yet wholly simulated mechanisms must be interpreted with great caution. Heavy-atom kinetic isotope effects (KIEs) offer an exquisite but underutilized method for reconciling the two approaches, anchoring the theoretician in the world of calculable observables and providing the experimentalist with atomistic insights. This Perspective provides a personal outlook on this synergy. It surveys the computation of heavy-atom KIEs and their measurement by NMR spectroscopy, discusses recent case studies, highlights the intellectual reward that lies in alignment of experiment and theory, and reflects on the changes required in chemical education in the area.

First-passage time theory of activated rate chemical processes in electronic molecular junctions

Confined nanoscale spaces, electric fields, and tunneling currents make the molecular electronic junction an experimental device for the discovery of new out-of-equilibrium chemical reactions. Reaction-rate theory for current-activated chemical reactions is developed by combining the Keldysh nonequilibrium Green's function treatment of electrons, Fokker-Planck description of the reaction coordinate, and Kramers first-passage time calculations. The nonequilibrium Green's functions (NEGF) provide an adiabatic potential as well as a diffusion coefficient and temperature with local dependence on the reaction coordinate. Van Kampen's Fokker-Planck equation, which describes a Brownian particle moving in an external potential in an inhomogeneous medium with a position-dependent friction and diffusion coefficient, is used to obtain an analytic expression for the first-passage time. The theory is applied to several transport scenarios: a molecular junction with a single reaction coordinate dependent molecular orbital and a model diatomic molecular junction. We demonstrate the natural emergence of Landauer's blowtorch effect as a result of the interplay between the configuration dependent viscosity and diffusion coefficients. The resultant localized heating in conjunction with the bond-deformation due to current-induced forces is shown to be the determining factors when considering chemical reaction rates, each of which results from highly tunable parameters within the system.

Low-Frequency (Gigahertz to Terahertz) Depolarized Raman Scattering Off n-Alkanes, Cycloalkanes, and Six-Membered Rings: A Physical Interpretation

Molecular liquids have long been known to undergo various distinct intermolecular motions, from fast librations and cage-rattling oscillations to slow orientational and translational diffusion. However, their resultant gigahertz to terahertz spectra are far from simple, appearing as broad shapeless bands that span many orders of magnitude of frequency, making meaningful interpretation troublesome. Ad hoc spectral line shape fitting has become a notoriously fine art in the field; a unified approach to handling such spectra is long overdue. Here we apply ultrafast optical Kerr-effect (OKE) spectroscopy to study the intermolecular dynamics of room-temperature n-alkanes, cycloalkanes, and six-carbon rings, as well as liquid methane and propane. This work provides stress tests and converges upon an experimentally robust model across simple molecular series and range of temperatures, providing a blueprint for the interpretation of the dynamics of van der Waals liquids. This will enable the interpretation of low-frequency spectra of more complex liquids.

Normal mode analysis of a relaxation process with Bayesian inference

Measurements of relaxation processes are essential in many fields, including nonlinear optics. Relaxation processes provide many insights into atomic/molecular structures and the kinetics and mechanisms of chemical reactions. For the analysis of these processes, the extraction of modes that are specific to the phenomenon of interest (normal modes) is unavoidable. In this study we propose a framework to systematically extract normal modes from the viewpoint of model selection with Bayesian inference. Our approach consists of a well-known method called sparsity-promoting dynamic mode decomposition, which decomposes a mixture of damped oscillations, and the Bayesian model selection framework. We numerically verify the performance of our proposed method by using coherent phonon signals of a bismuth polycrystal and virtual data as typical examples of relaxation processes. Our method succeeds in extracting the normal modes even from experimental data with strong backgrounds. Moreover, the selected set of modes is robust to observation noise, and our method can estimate the level of observation noise. From these observations, our method is applicable to normal mode analysis, especially for data with strong backgrounds.

Polymeric microfluidic continuous flow mixer combined with hyperspectral FT-IR imaging for studying rapid biomolecular events

Early reaction intermediates in protein folding, such as those resulting in β-amyloid formation due to transient misfolding, emerge within a few hundred microseconds. Here, we report a method to obtain sub-millisecond temporal resolution and molecular structural information of protein (mis-)folding events by using a microfluidic continuous-flow mixer (MCFM) in combination with Fourier transform infrared (FT-IR) imaging. The MCFMs are made out of cyclic olefin copolymer (COC) films, because this approach allows for rapid prototyping of different mixer designs. Furthermore, COC offers high IR transparency between 1500 and 2500 cm^-1, thus maximizing the signal to noise ratio of the IR data obtained from a sample of interest. By combining narrow and wide channel widths in MCFM design, the platform provides fast mixing (460 μs) to induce protein (mis-)folding, and it maximizes the residence time in the observing area, so a wide range of reaction timescales can be captured in a single image. We validated the platform for its ability to induce and observe sub-millisecond processes by studying two systems: (i) the mixing of H₂O and D₂O and (ii) the mixing induced deprotonation of carboxylic acid. First, we observed excellent agreement between simulated and experimental data of the on-chip mixing of H₂O and D₂O, which verifies the distance-reaction time relationships based on simulation. Second, deprotonation of carboxylic acid by on-chip mixing with sodium hydroxide solution validates the ability of the platform to induce rapid pH jump that is needed for some biomolecular reactions. Finally, we studied the methanol-induced partial-unfolding of ubiquitin to show that our platform can be used to study biomolecular events 'on-pathway' using FT-IR imaging. We successfully extracted kinetic and structural details of the conformational changes along the channel. Our results are in agreement with prior studies that required more elaborate stopped flow approaches to acquire data for different time points. In summary, the reported method uses an easy-to-fabricate microfluidic mixer platform integrated with hyperspectral FT-IR imaging for rapid acquisition of structural details and kinetic parameters of biomolecular reactions. This approach does not need stopped flow or molecular imaging probes, as required respectively for alternative FT-IR spectroscopy and fluorescence approaches.

Role of Water in the Reaction Mechanism and endo/exo Selectivity of 1,3-Dipolar Cycloadditions Elucidated by Quantum Chemistry and Machine Learning

Asymmetric 1,3-dipolar cycloadditions of azomethine ylides with activated olefins are among the most important and versatile methods for the synthesis of enantioenriched pyrroline and pyrrolidine derivatives. Despite both theoretical and practical importance, the role of water molecules in the reactivity and endo/exo selectivity remains unclear. To explore how water accelerates the reactions and improves the endo/exo selectivity of the cycloadditions of 1,3-dipole phthalazinium-2-dicyanomethanide (1) and two dipolarophiles, an ab initio-quality neural network potential that overcomes the computational bottleneck of explicitly considering water molecules was used. It is demonstrated that not only the nature of both the dipolarophile and the 1,3-dipole, but also the solvent medium, can perturb or even alter the reaction mechanism. An extreme case was found for the reaction of 1,3-dipole 1 with methyl vinyl ketone, in which the reaction mechanism changes from a concerted to a stepwise mode on going from MeCN to H₂ O as solvent, with formation of a zwitterionic intermediate that is a very shallow minimum on the energy surface. Thus, high stereocontrol can still be expected despite the stepwise nature of the mechanism. The results indicate that water can induce global polarization along the reaction coordinate and highlight the role of microsolvation effects and bulk-phase effects in reproducing the experimentally observed aqueous acceleration and enhanced endo/exo selectivity.

Ultrafast ring-opening and solvent-dependent product relaxation of photochromic spironaphthopyran

Combined experiment and theory shed light on the dominant pathways involved in the photochemical reaction of spiropyran.

Isomerization kinetics of flexible molecules in the gas phase: Atomistic versus coarse-grained sampling

Isomerization kinetics of molecules in the gas phase naturally falls on the microcanonical ensemble of statistical mechanics, which for small systems might significantly differ from the more traditional canonical ensemble. In this work, we explore the examples of cis-trans isomerization in butane and bibenzyl and to what extent the fully atomistic rate constants in isolated molecules can be reproduced by coarse-graining the system into a lower dimensional potential of mean force (PMF) along a reaction coordinate of interest, the orthogonal degrees of freedom acting as a canonical bath in a Langevin description. Time independent microcanonical rate constants can be properly defined from appropriate state residence time correlation functions; however, the resulting rate constants acquire some time dependence upon canonical averaging of initial conditions. Stationary rate constants are recovered once the molecule is placed into a real condensed environment pertaining to the canonical ensemble. The effective one-dimensional kinetics along the PMF, based on appropriately chosen inertia and damping parameters, quantitatively reproduces the atomistic rate constants at short times but deviates systematically over long times owing to the neglect of some couplings between the system and the bath that are all intrinsically present in the atomistic treatment. In bibenzyl, where stronger temperature effects are noted than in butane, the effective Langevin dynamics along the PMF still performs well at short times, indicating the potential interest of this extremely simplified approach for sampling high-dimensional energy surfaces and evaluating reaction rate constants.

Vibrational coherence transfer in the ultrafast intersystem crossing of a diplatinum complex in solution

We investigate the ultrafast transient absorption response of tetrakis(μ-pyrophosphito)diplatinate(II), [Pt₂(μ-P₂O₅H₂)₄]^4- [hereafter abbreviated Pt(pop)], in acetonitrile upon excitation of its lowest singlet ¹A_2u state. Compared with previously reported solvents [van der Veen RM, Cannizzo A, van Mourik F, Vlček A, Jr, Chergui M (2011) J Am Chem Soc 133:305-315], a significant shortening of the intersystem crossing (ISC) time (<1 ps) from the lowest singlet to the lowest triplet state is found, allowing for a transfer of vibrational coherence, observed in the course of an ISC in a polyatomic molecule in solution. Density functional theory (DFT) quantum mechanical/molecular mechanical (QM/MM) simulations of Pt(pop) in acetonitrile and ethanol show that high-lying, mostly triplet, states are strongly mixed and shifted to lower energies due to interactions with the solvent, providing an intermediate state (or manifold of states) for the ISC. This suggests that the larger the solvation energies of the intermediate state(s), the shorter the ISC time. Because the latter is smaller than the pure dephasing time of the vibrational wave packet, coherence is conserved during the spin transition. These results underscore the crucial role of the solvent in directing pathways of intramolecular energy flow.

Taking the plunge: chemical reaction dynamics in liquids

The dynamics of chemical reactions in liquid solutions are now amenable to direct study using ultrafast laser spectroscopy techniques and advances in computer simulation methods. The surrounding solvent affects the chemical reaction dynamics in numerous ways, which include: (i) formation of complexes between reactants and solvent molecules; (ii) modifications to transition state energies and structures relative to the reactants and products; (iii) coupling between the motions of the reacting molecules and the solvent modes, and exchange of energy; (iv) solvent caging of reactants and products; and (v) structural changes to the solvation shells in response to the changing chemical identity of the solutes, on timescales which may be slower than the reactive events. This article reviews progress in the study of bimolecular chemical reaction dynamics in solution, concentrating on reactions which occur on ground electronic states. It illustrates this progress with reference to recent experimental and computational studies, and considers how the various ways in which a solvent affects the chemical reaction dynamics can be unravelled. Implications are considered for research in fields such as mechanistic synthetic chemistry.

Quantum stochastic trajectories: the Smoluchowski-Bohm equation

Molecular systems are quantum systems, but the complete characterization of molecular motions within a fully quantum framework might appear to be an unfeasible task because it would require that the actual nuclear positions are established at any time. One would like to use a quantum molecular trajectory that defines the instantaneous nuclear positions and satisfies the predictions of quantum mechanics in terms of its statistical properties. Even though it can be proven that the single Bohm trajectory provides a representation of the quantum molecular trajectory, this solves the issue only on a theoretical ground: exact solutions of the Schrödinger-Bohm dynamical system are extremely computationally demanding. Therefore, we derive a stochastic equation of Smoluchowski type from the Schrödinger-Bohm dynamics, through projection operator techniques, in order to characterize the molecular motions of open quantum systems. The main quantum features of the motions emerge from the equilibrium distribution, i.e., the wave function's squared modulus integrated on the environment degrees of freedom. Furthermore, we verify the accuracy of the stochastic equation by comparing its predictions with those of the deterministic dynamics for a model system of six interacting harmonic oscillators. The indisputable advantage of this full quantum mechanical approach is that of representing the molecular dynamics, which controls important phenomena like vibrational relaxation, conformational transitions and activated processes, in a self consistent way and at the low computational cost of solving simple stochastic equations.

Towards Understanding the Solvent-Dynamic Control of the Transport and Heterogeneous Electron-Transfer Processes in Ionic Liquids

The impact of temperature-induced changes in solvent dynamics on the diffusion coefficient and standard rate constant k⁰ for heterogeneous electron transfer (ET) of ethylferrocene (EFc) in 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF₆ ]) is investigated. The results are analysed to understand the impact of solvent-dynamic control, solute-solvent interactions and solvent friction on the transport of redox probes and k⁰ . Concentration dependence of the diffusion coefficient of EFc in [BMIM][PF₆ ] is observed. This is attributed to the solute-induced enhancement of the structural organisation of the ionic liquid (IL), which is supported by the concentration-dependent UV/Vis absorption and photoluminescence responses of EFc/[BMIM][PF₆ ] solutions. Similar values of the activation energies for mass transport and ET and a linear relationship between the diffusion coefficient and the heterogeneous ET rate is observed. The ratio between the diffusion coefficient and the heterogeneous rate constant allows a characteristic length L_d , which is temperature-independent, to be introduced. The presented results clearly establish that mass transport and heterogeneous ET of redox probes are strongly correlated in ILs. It is proposed that the apparent kinetics of heterogeneous ET reactions in ILs can be explained in terms of their impact on thermal equilibration, energy dissipation and thermal excitation of redox-active probes.

Controlling Selectivity by Controlling Energy Partitioning in a Thermal Reaction in Solution

The comparison of experimental and predicted kinetic isotope effects in the α-cleavage of alkoxy radicals is used here to judge the applicability of statistical rate theories. It is found that the governing rate theory and the statistical versus nonstatistical nature of the cleavage depend on the cleavage barrier and how much energy is imparted to the radical. The latter can then be controlled by changing the size of substituents in the system. With a large alkyl group substituent, the vibrational energy of the alkoxy radical is increased, but this energy is not statistically distributed, leading to a lower isotope effect than predicted by statistical theories. The observed isotope effect can be approximately rationalized using a semistatistical localized RRKM model.

Broadband Transient Absorption and Two-Dimensional Electronic Spectroscopy of Methylene Blue

Broadband transient absorption and two-dimensional electronic spectroscopy (2DES) studies of methylene blue in aqueous solution are reported. By isolating the coherent oscillations of the nonlinear signal amplitude and Fourier transforming with respect to the population time, we analyzed a significant number of coherences in the frequency domain and compared them with predictions of the vibronic spectrum from density function theory (DFT) calculations. We show here that such a comparison enables reliable assignments of vibrational coherences to particular vibrational modes, with their constituent combination bands and overtones also being identified via Franck–Condon analysis aided by DFT. Evaluation of the Fourier transform (FT) spectrum of transient absorption recorded to picosecond population times, in coincidence with 2D oscillation maps that disperse the FT spectrum into the additional excitation axis, is shown to be a complementary approach toward detailed coherence determination. Using the Franck–Condon overlap integrals determined from DFT calculations, we modeled 2D oscillation maps up to two vibrational quanta in the ground and excited state (six-level model), showing agreement with experiment. This semiquantitative analysis is used to interpret the geometry change upon photoexcitation as an expansion of the central sulfur/nitrogen containing ring due to the increased antibonding character in the excited state.

Excited-State Proton Transfer in Resveratrol and Proposed Mechanism for Plant Resistance to Fungal Infection

Steady-state and time-resolved fluorescence techniques were employed to study the photophysics and photochemistry of trans-resveratrol. trans-Resveratrol is found in large quantities in fungi-infected grapevine-leaf tissue and plays a direct role in the resistance to plant disease. We found that trans-resveratrol in liquid solution undergoes a trans-cis isomerization process in the excited state at a rate that depends partially on the solvent viscosity, as was found in previous studies on trans-stilbene. The hydroxyl groups of the phenol moieties in resveratrol are weak photoacids. In water and methanol solutions containing weak bases such as acetate, a proton is transferred to the base within the lifetime of the excited state. When resveratrol is adsorbed on cellulose (also a component of the plant's cell wall), the cis-trans process is slow and the lifetime of the excited state increases from several tens of picoseconds in ethanol to about 1.5 ns. Excited-state proton transfer occurs when resveratrol is adsorbed on cellulose and acetate ions are in close proximity to the phenol moieties. We propose that proton transfer from excited resveratrol to the fungus acid-sensing chemoreceptor is one of the plant's resistance mechanisms to fungal infection.

Dynamics of solvent response in methanol-chloroform binary solvent mixture: a case of synergistic solvation

Steady-state absorption, emission, and femtosecond transient absorption spectroscopies were used to ascertain the static and dynamic nature of the solvent response of methanol-chloroform binary solvent mixtures of different stoichiometric ratios using 4-(dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4H-pyran (DCM) as the probe molecule. The appearance of synergistic solvation behavior in the steady-state absorption measurements can be explained in terms of solvent-solvent interactions through an extended hydrogen-bonding network. The disappearance of such synergistic behavior in the excited state of the DCM dye was recently proposed by us to be due to the weak nature of the intermolecular interactions present in binary solvent mixtures (J. Phys. Chem. B 2012, 116, 1345). It was anticipated and subsequently confirmed by the dynamics of the solvent response that the disruption of the weak interactive solvent network is the main reason for the absence of the synergism in the excited state. As expected, we observed the slowest dynamics for the mixture with X(MeOH) = 0.45, with an average solvation time of 12.03 ps, which is much higher than the values for the pure bulk counterparts (⟨τ(s)⟩(Methanol) = 4.32 ps and ⟨τ(s)⟩(Chloroform) = 1.32 ps). The unprecedented slowing of solvation for DCM is probably due to the rigid interactive methanol-chloroform solvent system in the first solvation shell, followed by solvent rearrangements around the solute dipole. Overall interactions present within the methanol-chloroform binary solvent mixture furnish clear evidence of solvent association through weak hydrogen bonding.

Perspective: Bimolecular chemical reaction dynamics in liquids

Bimolecular reactions in the gas phase exhibit rich and varied dynamical behaviour, but whether a profound knowledge of the mechanisms of isolated reactive collisions can usefully inform our understanding of reactions in liquid solutions remains an open question. The fluctuating environment in a liquid may significantly alter the motions of the reacting particles and the flow of energy into the reaction products after a transition state has been crossed. Recent experimental and computational studies of exothermic reactions of CN radicals with organic molecules indicate that many features of the gas-phase dynamics are retained in solution. However, observed differences may also provide information on the ways in which a solvent modifies fundamental chemical mechanisms. This perspective examines progress in the use of time-resolved infra-red spectroscopy to study reaction dynamics in liquids, discusses how existing theories can guide the interpretation of experimental data, and suggests future challenges for this field of research.

[Ru(bpy)3]2+* and other remarkable metal-to-ligand charge transfer (MLCT) excited states

In 1974, the metal-to-ligand charge transfer (MLCT) excited state, [Ru(bpy)3]2+*, was shown to undergo electron transfer quenching by methylviologen dication (MV2+), inspiring a new approach to artificial photosynthesis based on molecules, molecular-level phenomena, and a “modular approach”. In the intervening years, application of synthesis, excited-state measurements, and theory to [Ru(bpy)3]2+* and its relatives has had an outsized impact on photochemistry and photophysics. They have provided a basis for exploring the energy gap law for nonradiative decay and the role of molecular vibrations and solvent and medium effects on excited-state properties. Much has been learned about light absorption, excited-state electronic and molecular structure, and excited-state dynamics on timescales from femtoseconds to milliseconds. Excited-state properties and reactivity have been exploited in the investigation of electron and energy transfer in solution, in molecular assemblies, and in derivatized polymers and oligoprolines. An integrated, hybrid approach to solar fuels, based on dye-sensitized photoelectrosynthesis cells (DSPECs), has emerged and is being actively investigated.