Rotational dynamics and conformational kinetics in liquid crystals

Abstract

Two particular aspects of solute dynamics in ordered media are analysed on the basis of the solution of multivariate diffusion equations: the effects of the solvation dynamics on the rotational motions of dipolar probes in liquid crystal solvents, and the alteration of reaction pathways in isomerization kinetics caused by the solvent order. The introduction of a suitable solvent coordinate allows the interpretation of high frequency contributions in the rotational correlation functions observed by spectroscopic techniques, namely dielectric dispersion, IR and Raman spectroscopy, ESR lineshapes and optical Kerr effect. For molecular systems undergoing conformational changes, a method is offered to evaluate the modification of the torsional barriers resulting from the anisotropic torques modulated by the molecular shape changes along the reaction coordinate.     

Dynamics of a supercooled ionic liquid studied by optical and dielectric spectroscopy

We have measured the dynamics of solvation of a triplet state probe, quinoxaline, in the glass-forming ionic liquid dibutylammonium formate near its glass transition temperature Tg=153 K. The Stokes-shift correlation function displays a relaxation time dispersion of considerable magnitude and the optical line width changes systematically along the solvation coordinate. The solvent dynamics in the viscous regime is compared with the rotational behavior of the solute and with the dielectric relaxation of the ionic liquid. Among the different quantities derived from the dielectric experiments, the relaxation of the macroscopic electric field, i.e., the modulus Mt, matches best the solvent response Ct regarding time scale and stretching exponent. Many other properties are reminiscent of the behavior of polar molecular liquids which lack the ionic character.     

Free energy landscapes of electron transfer system in dipolar environment below and above the rotational freezing temperature

Electron transfer reaction in a polar solvent is modeled by a solute dipole surrounded by dipolar molecules with simple rotational dynamics posted on the three-dimensional distorted lattice sites. The interaction energy between the solute and solvent dipoles as a reaction coordinate is adopted and free energy landscapes are calculated by generating all possible states for a 26 dipolar system and by employing Wang-Landau sampling algorithm for a 92 dipolar system. For temperatures higher than the energy scale of dipole-dipole interactions, the free energy landscapes for the small reaction coordinate region have quadratic shape as predicted by Marcus [Rev. Mod. Phys. 65, 599 (1993)] whereas for the large reaction coordinate region, the landscapes exhibit a nonquadratic shape. When the temperature drops, small notched structures appear on the free energy profiles because of the frustrated interactions among dipoles. The formation of notched structure is analyzed with statistical approach and it is shown that the amplitude of notched structure depend upon the segment size of the reaction coordinate and is characterized by the interaction energy among the dipoles. Using simulated free energy landscapes, the authors calculate the reaction rates as a function of the energy gap for various temperatures. At high temperature, the reactions rates follow a bell shaped (inverted parabolic) energy gap law in the small energy gap regions, while it becomes steeper than the parabolic shape in a large energy gap regions due to the nonquadratic shape of the free energy landscape. The peak position of parabola also changes as the function of temperature. At low temperature, the profile of the reaction rates is no longer smooth because of the many local minima of the free energy landscape.     

The dynamical role of solvent on the ICN photodissociation reaction: connecting experimental observables directly with molecular dynamics simulations

The ICN photodissociation reaction is the prototype system for understanding energy disposal and curve crossing in small molecule bond-breaking. The wide knowledge base on this reaction in the gas phase makes it an excellent test case to explore and understand the influence of a liquid solvent on the photo-induced reaction dynamics. Molecular dynamics simulations that include surface-hopping have addressed numerous aspects of how the solvent should influence non-adiabatic transitions and energy flow and ultimately determine product branching for this reaction system. In this paper, we report femtosecond transient absorption work directly combined with new molecular dynamics simulations that make direct connection with the spectroscopic observables. The full spectral evolution after initiating ICN photodissociation at 266 nm in water and ethanol is recorded with unprecedented time resolution, fast enough to see the nascent products emerge before interacting with the solvent cage. Use of a 266 nm pump maximizes the probability of subsequent caging on the upper diabat while launching large rotational energy release for trajectories emerging on the lower diabat. The 2D dataset yields a map of the different products and how they interconvert. In particular, information on the branching ratio and spectral evolution of the product bands is revealed as the products relax their electronic and rotational degrees of freedom. An evolution from rotationally hot gas-phase like CN (sharp band, at 390 nm) to equilibrated and solvated CN radicals (broad, at 326 nm in water and 415 nm in ethanol) is clearly observed in both solvents, and signals assignable to I* are also captured. The non-adiabatic molecular dynamics simulations focus on identifying when trajectories curve cross, filtering the trajectory ensemble into spectroscopically distinct sub-populations and analyzing the rotational energy for the CN product population. The experimental results, taken together with the MD simulations, establish the initial surface crossing probability and suggest multiple passes through the curve crossing region determine the final product yields and provide a source of freshly torqued CN radicals that continues to top up the population of rotationally hot photoproduct over the first few picoseconds.     

Dynamics of an enzymatic substitution reaction in haloalkane dehalogenase

Reactive flux molecular dynamics simulations have been carried out using a combined QM/MM potential to study the dynamics of the nucleophilic substitution reaction of dichloroethane by a carboxylate group in haloalkane dehalogenase and in water. We found that protein dynamics accelerates the reaction rate by a factor of 2 over the uncatalyzed reaction. Compared to the thermodynamic effect in barrier reduction, protein dynamic contribution is relatively small. However, analyses of the friction kernel reveal that the origins of the reaction dynamics in water and in the enzyme are different. In aqueous solution, there is significant electrostatic solvation effect, which is reflected by the slow reorganization relaxation of the solvent. On the other hand, there is no strong electrostatic coupling in the enzyme and the major effect on reaction coordinate motion is intramolecular energy relaxation.     

Proton transfer in a polar solvent from ring polymer reaction rate theory

We have used the ring polymer molecular dynamics method to study the Azzouz-Borgis model for proton transfer between phenol (AH) and trimethylamine (B) in liquid methyl chloride. When the A-H distance is used as the reaction coordinate, the ring polymer trajectories are found to exhibit multiple recrossings of the transition state dividing surface and to give a rate coefficient that is smaller than the quantum transition state theory value by an order of magnitude. This is to be expected on kinematic grounds for a heavy-light-heavy reaction when the light atom transfer coordinate is used as the reaction coordinate, and it clearly precludes the use of transition state theory with this reaction coordinate. As has been shown previously for this problem, a solvent polarization coordinate defined in terms of the expectation value of the proton transfer distance in the ground adiabatic quantum state provides a better reaction coordinate with less recrossing. These results are discussed in light of the wide body of earlier theoretical work on the Azzouz-Borgis model and the considerable range of previously reported values for its proton and deuteron transfer rate coefficients.     

Molecular dynamics coupled with a virtual system for effective conformational sampling

An enhanced conformational sampling method is proposed: virtual‐system coupled canonical molecular dynamics (VcMD). Although VcMD enhances sampling along a reaction coordinate, this method is free from estimation of a canonical distribution function along the reaction coordinate. This method introduces a virtual system that does not necessarily obey a physical law. To enhance sampling the virtual system couples with a molecular system to be studied. Resultant snapshots produce a canonical ensemble. This method was applied to a system consisting of two short peptides in an explicit solvent. Conventional molecular dynamics simulation, which is ten times longer than VcMD, was performed along with adaptive umbrella sampling. Free‐energy landscapes computed from the three simulations mutually converged well. The VcMD provided quicker association/dissociation motions of peptides than the conventional molecular dynamics did. The VcMD method is applicable to various complicated systems because of its methodological simplicity. © 2018 Wiley Periodicals, Inc.     

Molecular Dynamics of Excited State Intramolecular Charge Transfer in Solution by Coherent Nuclear Wave Packets

Revealing a proper reaction coordinate in a chemical reaction is the key step towards elucidation of the molecular reaction dynamics. In this report, we investigated the dynamics of intramolecular charge transfer (ICT) of 8-aminopyrene-1,3,6-trisulfonic acid (APTS) occurring in the excited state by time-resolved fluorescence (TF) and TF spectra. Accurate reaction rates and rate-dependent nuclear wave packets in the product state allow detailed investigation of the molecular reaction dynamics. The ICT rate is solvent dependent: (34 fs)⁻¹, (87 fs)⁻¹, and (∞)⁻¹ in water, formamide, and dimethylformamide, respectively. By recording spectra of the nuclear wave packets for different reaction rates, chemical species responsible for the emission spectra can be positively identified. The origin of the wave packets can be deduced from the amplitude change of the wave packets at different reaction rates, and the vibrational modes that are associated with the reaction coordinate could be identified. Theoretical calculations of the vibrational reorganization energies reproduce the experimental spectrum of the nuclear wave packets and corroborate the conclusions.     

Exponential probe rotation in glass-forming liquids

Using time resolved optical depolarization, we have studied the rotational behavior of molecular probes in supercooled liquids near the glass transition temperature T(g). Simultaneously, the dynamics of the liquid immediately surrounding these rigid probes is measured by triplet state solvation experiments. This direct comparison of solute and solvent dynamics is particularly suited for assessing the origin of exponential orientational correlation functions of probe molecules embedded in liquids which exhibit highly nonexponential structural relaxation. Polarization angle dependent Stokes shift correlation functions demonstrate that probe rotation time and solvent response time are locally correlated quantities in the case of smaller probe molecules. Varying the size of both guest and host molecules shows that the size ratio determines the rotational behavior of the probes. The results are indicative of time averaging being at the origin of exponential rotation of probes whose rotational time constant is slower than solvent relaxation by a factor of 20 or more.     

Solvent reorganization of electron transitions in viscous solvents

We develop a model of electron transfer reactions at conditions of nonergodicity when the time of solvent relaxation crosses the observation time window set up by the reaction rate. Solvent reorganization energy of intramolecular electron transfer in a charge-transfer molecule dissolved in water and acetonitrile is studied by molecular dynamics simulations at varying temperatures. We observe a sharp decrease of the reorganization energy at a temperature identified as the temperature of structural arrest due to cage effect, as discussed by the mode-coupling theory. This temperature also marks the onset of the enhancement of translational diffusion relative to rotational relaxation signaling the breakdown of the Stokes-Einstein relation. The change in the reorganization energy at the transition temperature reflects the dynamical arrest of the slow, collective relaxation of the solvent related to the relaxation of the solvent dipolar polarization. An analytical theory proposed to describe this effect agrees well with both the simulations and experimental Stokes shift data. The theory is applied to the analysis of charge-transfer kinetics in a low-temperature glass former. We show that the reorganization energy is substantially lower than its equilibrium value for the low-temperature portion of the data. The theory predicts the possibility of discontinuous changes in the dependence of the electron transfer rate on the free energy gap when the reaction switches between ergodic and nonergodic regimes.     

Femtosecond infrared study of the dynamics of solvation and solvent caging.

The ultrafast reaction dynamics following 295-nm photodissociation of Re2CO10 were studied experimentally with 300-fs time resolution in the reactive, strongly coordinating CCl4 solution and in the inert, weakly coordinating hexane solution. Density-functional theoretical (DFT) and ab initio calculations were used to further characterize the transient intermediates seen in the experiments. It was found that the quantum yield of the Re-Re bond dissociation is governed by geminate recombination on two time scales in CCl4, approximately 50 and approximately 500 ps. The recombination dynamics are discussed in terms of solvent caging in which the geminate Re(CO)5 pair has a low probability to escape the first solvent shell in the first few picoseconds after femtosecond photolysis. The other photofragmentation channel resulted in the equatorially solvated dirhenium nonacarbonyl eq-Re2(CO)9(solvent). Theoretical calculations indicated that a structural reorganization energy cost on the order of 6-7 kcal/mol might be required for the unsolvated nonacarbonyl to coordinate to a solvent molecule. These results suggest that for Re(CO)5 the solvent can be treated as a viscous continuum, whereas for the Re2(CO)9 the solvent is best described in molecular terms.     

Communication: exploring the reorientation of benzene in an ionic liquid via molecular dynamics: effect of temperature and solvent effective charge on the slow dynamics

The rotational time correlation function (RTCF) of solute benzene molecules in the ionic liquid (1-butyl-3-methylimidazolium chloride) has been studied using classical molecular dynamics simulation. The effect of solvent charge on the functional form of RTCF was investigated by comparing four force fields for the solvent where the total charge on the anion and the cation was set to ±1e, ±0.7e, ±0.5e, and 0, respectively. For all three charged solvent models, the RTCF exhibits a long-time tail where the relaxation rate exhibits a significant slowdown. This feature is strengthened by higher solvent charges as well as lower temperatures, indicating the influence of the strong Coulombic fields arising from the solvent charges. The long-time tail is caused by the extraordinarily slow solvent structural relaxation of ionic liquids compared to the time scale of their local vibrational and librational dynamics.     

Solvent dynamics in a model system

We report herein a study of the solvent reorganization process in an electron transfer reaction. The calculations are based on a model consisting of 26 or 62 solvent particles. Molecular dynamics simulations are performed to calculate the electric field fluctuations during the orientational and translational motion of the solvent molecules. The changes in the electric fields at various points near the reacting sites in the system are evaluated as a function of time. From these electric fields, electric field time correlation functions are calculated. The main conclusion in this work is that it requires nearly 3 ps for the model solvent to reorient during the charge transfer. These results suggest ways of incorporating solvent dynamics based on molecular models into theoretical studies of electron transfer rates in condensed media.     

Dynamics of proton transfer and vibrational relaxation in dilute hydrofluoric acid

The molecular mechanisms in both vibrational relaxation and proton transfer (PT) associated with infrared (IR)-induced PT in a dilute hydrofluoric acid solution at ambient temperature are studied by molecular dynamics (MD) simulations with the multistate empirical valence bond model. To investigate the solvation dynamics, a collective solvent coordinate and its perpendicular bath modes are defined from the diabatic energy gap and their motions are examined by the generalized Langevin equation (GLE) formalism. The GLE analysis using the equilibrium MD simulation shows that the major solvent reorganizations in the PT are represented by the libration and hindered translation. In particular, the libration gives the stronger coupling to the solvent reorganization and the faster relaxation. The nonequilibrium MD simulation demonstrated that both the HF stretching vibration and the solvent reorganization relax on a similar time scale and thus compete in the PT. It also supported the "presolvation mechanism" for the PT in this system.     

Polymer reversal rate calculated via locally scaled diffusion map

A recent study on the dynamics of polymer reversal inside a nanopore by Huang and Makarov [J. Chem. Phys. 128, 114903 (2008)] demonstrated that the reaction rate cannot be reproduced by projecting the dynamics onto a single empirical reaction coordinate, a result suggesting the dynamics of this system cannot be correctly described by using a single collective coordinate. To further investigate this possibility we have applied our recently developed multiscale framework, locally scaled diffusion map (LSDMap), to obtain collective reaction coordinates for this system. Using a single diffusion coordinate, we obtain a reversal rate via Kramers expression that is in good agreement with the exact rate obtained from the simulations. Our mathematically rigorous approach accounts for the local heterogeneity of molecular configuration space in constructing a diffusion map, from which collective coordinates emerge. We believe this approach can be applied in general to characterize complex macromolecular dynamics by providing an accurate definition of the collective coordinates associated with processes at different time scales.     

Chemical reaction dynamics within anisotropic solvents in time-dependent fields

The dynamics of low-dimensional Brownian particles coupled to time-dependent driven anisotropic heavy particles (mesogens) in a uniform bath (solvent) have been described through the use of a variant of the stochastic Langevin equation. The rotational motion of the mesogens is assumed to follow the motion of an external driving field in the linear response limit. Reaction dynamics have also been probed using a two-state model for the Brownian particles. Analytical expressions for diffusion and reaction rates have been developed and are found to be in good agreement with numerical calculations. When the external field driving the mesogens is held at constant rotational frequency, the model for reaction dynamics predicts that the applied field frequency can be used to control the product composition.     

Oxidation of methionine residues in aqueous solutions: free methionine and methionine in granulocyte colony-stimulating factor

The free energy barriers and a mechanism of the oxidation of the amino acid methionine in water and in granulocyte colony-stimulating factor (G-CSF) are analyzed via combined quantum mechanical and molecular mechanical (QM/MM) methods, constrained molecular dynamics, and committor probability calculations. The computed free energy barrier of free methionine amino acid is very close to the measured value (14.7 +/- 1.2 versus 15.5 +/- 0.02 kcal/mol). The reaction coordinate was found to be the difference between the O-O bond of H2O2 and the S-O bond, where the S is the sulfur atom of the methionine residue. It was confirmed by computing the committor probability distribution and the distribution of constrained forces that this coordinate is not coupled to the activation of other degrees of freedom. The computed free energies of the oxidation of methionine residues in G-CSF indicate that the protein environment has insignificant effects on the reaction barriers of oxidation. This result further validates our proposal that the access of solvent to methionine sites, as measured by the two-shell water coordination number, governs the kinetics of the oxidation reaction of methionine groups in a protein molecule. We also found that the number of hydrogen bonds between the distal oxygen of H2O2 and the water molecules near the methionine increases along the reaction coordinate as oxidation progresses, indicating that the charge separation developed during the oxidation by H2O2 is stabilized by specific interactions with water molecules, such as hydrogen bonding.