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We present a method to explore the free energy landscapes of chemical reactions with post-transition-state bifurcations using an enhanced sampling method based on well-tempered metadynamics. Obviating the need for computationally expensive DFT-level ab initio molecular dynamics simulations, we obtain accurate energetics by utilizing a free energy perturbation scheme and deep learning estimator for the single-point energies of substrate configurations. Using a pair of easily interpretable collective variables, we present a quantitative free energy surface that is compatible with harmonic transition state theory calculations and in which the bifurcations are clearly visible. We demonstrate our approach with the example of the SpnF-catalyzed Diels-Alder reaction, a cycloaddition reaction in which post-transition-state bifurcation leads to the [4+2] as well as the [6+4] cycloadduct. We obtain the free energy landscapes for different stereochemical reaction pathways and characterize the mechanistic continuum between relevant reaction channels without explicitly searching for the pertinent transition state structures., Comment: 27 pages, 5 figures

We introduce a reaction-path statistical mechanics formalism based on the principle of large deviations to quantify the kinetics of single-molecule enzymatic reaction processes under the Michaelis-Menten mechanism, which exemplifies an out-of-equilibrium process in the living system. Our theoretical approach begins with the principle of equal a priori probabilities and defines the reaction path entropy to construct a new nonequilibrium ensemble as a collection of possible chemical reaction paths. As a result, we evaluate a variety of path-based partition functions and free energies using the formalism of statistical mechanics. They allow us to calculate the timescales of a given enzymatic reaction, even in the absence of an explicit boundary condition that is necessary for the equilibrium ensemble. We also consider the large deviation theory under a closed-boundary condition of the fixed observation time to quantify the enzyme-substrate unbinding rates. The result demonstrates the presence of a phase-separation-like, bimodal behavior in unbinding events at a finite timescale, and the behavior vanishes as its rate function converges to a single phase in the long-time limit., Comment: 29 pages, 7 figures

Recent advances in machine learning and their applications have lead to the development of diverse structure-property relationship models for crucial chemical properties, and the solvation free energy is one of them. Here, we introduce a novel ML-based solvation model, which calculates the solvation energy from pairwise atomistic interactions. The novelty of the proposed model consists of a simple architecture: two encoding functions extract atomic feature vectors from the given chemical structure, while the inner product between two atomistic features calculates their interactions. The results on 6,493 experimental measurements achieve outstanding performance and transferability for enlarging training data due to its solvent-non-specific nature. Analysis of the interaction map shows there is a great potential that our model reproduces group contributions on the solvation energy, which makes us believe that the model not only provides the predicted target property but also gives us more detailed physicochemical insights., Comment: 20 pages, 5 figures

Polymer brushes normally swell in a good solvent and collapse in a poor solvent. An abnormal response of polymer brushes, so-called co-nonsolvency, is the phenomenon where the brush counter-intuitively collapses in a good solvent mixture. In this work, we employed molecular dynamics simulations to investigate the structural properties of the grafted polymers on the occurrence of co-nonsolvency. Brushes with various grafting densities were considered to study the effect of topological excluded volumes on the co-nonsolvency. We found that the brush height follows a novel scaling behavior of the grafting density $h \sim \sigma_{\text g}^{0.71}$ in the co-nonsolvent mixture. Using the scaling exponent and Alexander-de Gennes theory, an analytic function that predicts the monomer density was obtained. The many-chain effects in the co-nonsolvent lead to the formation of both intermolecular and intramolecular bridging structures. Increasing the grafting density entails lower looping events occuring because of the intermolcular bridging, causing diverse structural properties. We report how the average thickness, the polymer orientation, and the looping probability varies as the grafting density increases. Based on these observations, we constructed a phase diagram of the polymer brush system using the average thickness and orientation as order parameters. Our simulations and analytical results reveal the nature of co-nonsolvency in polymer brushes in an explicit way and will help to provide practical guidelines for applications such as drug delivery and sensor devices.

We present a coarse-graining strategy for reducing the number of particle species in mixtures to achieve a simpler system with higher diffusion while preserving the total particle number and characteristic dynamic features. As a system of application, we chose the bidisperse Lennard-Jones-like mixture discovered by Kob and Andersen [Phys. Rev. Lett. 73, 1376 (1994)] possessing a slow dynamics due to the fluid's multi-component character with its apparently unconventional choice for the pair potential of the type-A-type-B arrangement. We further established in a so-formed coarse-grained and temperature-independent monodisperse system an equilibrium structure with a radial distribution function resembling its mixture counterpart. This one-component system further possesses similar dynamic features like glass transition temperature and critical exponents while subjected to Newtonian mechanics. This strategy may finally lead to the manufacturing of new nanoparticle/colloidal fluids by experimentally modeling only the outcoming effective pair potential(s) and no other macroscopic quantity., Comment: 19 pages, 16 figures

We investigate the dimensional dependence of dynamical fluctuations related to dynamic heterogeneity in supercooled liquid systems using kinetically constrained models. The $d$-dimensional spin-facilitated East model with embedded probe particles is used as a representative super-Arrhenius glass forming system. We investigate the existence of an upper critical dimension in this model by considering decoupling of transport rates through an effective fractional Stokes-Einstein relation, $D\sim{\tau}^{-1+\omega}$, with $D$ and $\tau$ the diffusion constant of the probe particle and the relaxation time of the model liquid, respectively, and where $\omega > 0$ encodes the breakdown of the standard Stokes-Einstein relation. To the extent that decoupling indicates non mean-field behavior, our simulations suggest that the East model has an upper critical dimension which is at least above $d=10$, and argue that it may be actually be infinite. This result is due to the existence of hierarchical dynamics in the East model in any finite dimension. We discuss the relevance of these results for studies of decoupling in high dimensional atomistic models., Comment: 7 pages, 7 figures

We numerically investigate the dynamic heterogeneity and its length scale found in the coarse-grained ionic liquid model systems. In our ionic liquid model systems, cations are modeled as dimers with positive charge, while anions are modeled as monomers with negative charge, respectively. To study the effect of the charge distributions on the cations, two ionic liquid models with different charge distributions are used and the model with neutral charge is also considered as a counterpart. To reveal the heterogeneous dynamics in the model systems, we examine spatial distributions of displacement and time distributions of exchange and persistence times. All the models show significant increase of the dynamic heterogeneity as the temperature is lowered. The dynamic heterogeneity is quantified via the well-known four-point susceptibility which measures the fluctuation of a time correlation function. The dynamic correlation length is calculated by fitting the dynamic structure factor, S4(k,t), with Ornstein-Zernike form at the time scale at which the dynamic heterogeneity reaches the maximum value. Obtained time and length scales exhibit a power law relation at the low temperatures, similar to various supercooled liquid models. Especially, the charged model systems show unusual crossover behaviors which are not observed in the uncharged model system. We ascribe the crossover behavior to the enhanced cage effect caused by charges on the particles.

Kinetically constrained models (KCMs) have gained much interest as models that assign the origins of interesting dynamic properties of supercooled liquids to dynamical facilitation mechanisms that have been revealed in many expreiments and numerical simulations. In this work, we investigate the dynamic heterogeneity in the fragile-to-strong liquid via Monte Carlo method using the model that linearly interpolates between the strong-liquid like behavior and the fragile-liquid like behavior by an asymmetry parameter b. When the asymmetry parameter is sufficiently small, smooth fragile-to-strong transition is observed both in the relaxation time and the diffusion constant. Using these physical quantities, we investigate fractional Stokes-Einstein relations observed in this model. When b is fixed, the system shows constant power law exponent under the temperature change, and the exponent has the value between that of the FA model and the East model. Furthermore, we investigate the dynamic length scale of our systems and also find the crossover relation between the relaxation time. We ascribe the competition between energetically favored symmetric relaxation mechanism and entropically favored asymmetric relaxation mechanism to the fragile-to-strong crossover behavior.

Diffusion of long ring polymers in a melt is much slower than the reorganization of their internal structures. While direct evidences for entanglements have not been observed in the long ring polymers unlike linear polymer melts, threading between the rings is suspected to be the main reason for slowing down of ring polymer diffusion. It is, however, difficult to define the threading configuration between two rings because the rings have no chain end. In this work, evidences for threading dynamics of ring polymers are presented by using molecular dynamics simulation and applying a novel analysis method. The simulation results are analyzed in terms of the statistics of persistence and exchange times that have proved useful in studying heterogeneous dynamics of glassy systems. We find that the threading time of ring polymer melts increases more rapidly with the degree of polymerization than that of linear polymer melts. This indicates that threaded ring polymers cannot diffuse until unthreading event occurs, which results in the slowing down of ring polymer diffusion.

We study structural properties of a ring polymeric melt confined in a film in comparison to a linear counterpart using molecular dynamics simulations. Local structure orderings of ring and linear polymers in the vicinity of the surface are similar to each other because the length scale of surface-monomer excluded volume interaction is smaller than the size of an ideal blob of the ring. In a long length scale, while the Silberberg hypothesis can be used to provide a physical origin of confined linear polymer results, it no longer holds for a ring polymer case. We also present different structural properties of ring and linear polymers in a melt, including the size of polymers, an adsorbed amount, and the coordination number of a polymer. Our observation reveals that a confined ring in a melt adopts highly segregated conformation due to a topological excluded volume repulsion, which may provide a new perspective to understand the nature of biological processes, such as territorial segregation of chromosomes in eukaryotic nuclei.

We consider the diffusion constant, D, of a probe particle coupled to the East model, extending previous numerical results for this model to encompass a total of twelve orders of magnitude in relaxation time, {\tau}. Our considerations thus cover the full range of relaxation times relevant to experimental studies of reversible glass formers. Throughout this range, we show that the results of the model are consistent with a fractional Stokes-Einstein law, D \propto {\tau}^{-{\xi}} with {\xi} \approx 0.77. The same data can also be fit by relating D{\tau} to the East model excitation concentration q, specifically, D{\tau} \sim 1/q^{\alpha} with {\alpha} \approx 1.6. In either case, breakdown of the Stokes-Einstein relation in this kinetically constrained model is unquestionable and large., Comment: 1 page, 1 figure

Dynamics of a coarse-grained model for the room-temperature ionic liquid, 1-ethyl-3-methylimidazolium hexafluorophosphate, couched in the united-atom site representation are studied via molecular dynamics simulations. The dynamically heterogeneous behavior of the model resembles that of fragile supercooled liquids. At or close to room temperature, the model ionic liquid exhibits slow dynamics, characterized by nonexponential structural relaxation and subdiffusive behavior. The structural relaxation time, closely related to the viscosity, shows a super-Arrhenius behavior. Local excitations, defined as displacement of an ion exceeding a threshold distance, are found to be mainly responsible for structural relaxation in the alternating structure of cations and anions. As the temperature is lowered, excitations become progressively more correlated. This results in the decoupling of exchange and persistence times, reflecting a violation of the Stokes-Einstein relation., Comment: Published on the Phys. Chem. Chem. Phys. website

To understand the non-exponential relaxation associated with solvation dynamics in the ionic liquid 1-ethyl-3-methylimidazolium hexafluorophosphate, we study power spectra of the fluctuating Franck-Condon energy gap of a diatomic probe solute via molecular dynamics simulations. Results show 1/f dependence in a wide frequency range over 2 to 3 decades, indicating distributed relaxation times. We analyze the memory function and solvation time in the framework of the generalized Langevin equation using a simple model description for the power spectrum. It is found that the crossover frequency toward the white noise plateau is directly related to the time scale for the memory function and thus the solvation time. Specifically, the low crossover frequency observed in the ionic liquid leads to a slowly-decaying tail in its memory function and long solvation time. By contrast, acetonitrile characterized by a high crossover frequency and (near) absence of 1/f behavior in its power spectra shows fast relaxation of the memory function and single-exponential decay of solvation dynamics in the long-time regime., Comment: 10 pages, 4 figures

We investigate statistics of dynamical exchange events in coarse--grained models of supercooled liquids in spatial dimensions $d=1$, 2, and 3. The models, based upon the concept of dynamical facilitation, capture generic features of statistics of exchange times and persistence times. Here, distributions for both times are related, and calculated for cases of strong and fragile glass formers over a range of temperatures. Exchange time distributions are shown to be particularly sensitive to the model parameters and dimensions, and exhibit more structured and richer behavior than persistence time distributions. Mean exchange times are shown to be Arrhenius, regardless of models and spatial dimensions. Specifically, $ \sim c^{-2}$, with $c$ being the excitation concentration. Different dynamical exchange processes are identified and characterized from the underlying trajectories. We discuss experimental possibilities to test some of our theoretical findings., Comment: 11 pages, 14 figures, minor corrections made, paper published in Journal of Chemical Physics

A theory is formulated for time dependent fluctuations of the spectrum of a single molecule in a dynamic environment. In particular, we investigate the photon counting statistics of a single molecule undergoing a spectral diffusion process. Based on the stochastic optical Bloch equation, fluctuations are characterized by Mandel's $Q$ parameter yielding the variance of number of emitted photons and the second order intensity correlation function, $g^{(2)}(t)$. Using a semi-classical approach and linear response theory, we show that the $Q$ parameter can be described by a three-time dipole correlation function. This approach gene ralizes the Wiener-Khintchine formula that gives the average number of fluorescent photons in terms of a one-time dipole correlation function. We classify the time ordering properties of the three-time dipole correlation function, and show that it can be represented by three different pulse shape functions similar to those used in the context of nonlinear spectroscopy. An exact solution is found for a single molecule whose absorption frequency undergoes a two state random telegraph process (i.e., the Kubo-Anderson sudden jump process.) Simple expressions are obtained from the exact solution in the slow and fast modulation regimes based on appropriate approximations for each case. In the slow modulation regime $Q$ can be large even in the long time limit, while in the fast modulation regime it becomes small.

By applying the concept of dynamical facilitation and analyzing the excitation lines that result from this facilitation, we investigate the origin of decoupling of transport coefficients in supercooled liquids. We illustrate our approach with two classes of models. One depicts diffusion in a strong glass former, and the other in a fragile glass former. At low temperatures, both models exhibit violation of the Stokes-Einstein relation, $D\sim\tau^{-1}$, where $D$ is the self diffusion constant and $\tau$ is the structural relaxation time. In the strong case, the violation is sensitive to dimensionality $d$, going as $D\sim\tau^{-2/3}$ for $d=1$, and as $D\sim \tau^{-0.95}$ for $d=3$. In the fragile case, however, we argue that dimensionality dependence is weak, and show that for $d=1$, $D \sim \tau^{-0.73}$. This scaling for the fragile case compares favorably with the results of a recent experimental study for a three-dimensional fragile glass former., Comment: 7 pages, 7 figures, submitted to Phys. Rev. E

Recent experimental observations have found two different kinds of ``strange kinetic behaviors" in individual semiconductor nanocrystals (or quantum dots). Fluorescence intermittency observed in the quantum dots shows power--law statistics in both {\it on} and {\it off} times. Spectral diffusion of the quantum dots is also described by power--law statistics in the sojourn times. Motivated by these experimental observations we consider two different but related problems: (a) a stochastic lineshape theory for the Kubo-Anderson oscillator whose frequency modulation follows power-law statistics and (b) photon counting statistics of quantum dots whose intensity fluctuation is characterized by power-law kinetics. In the first problem, we derive an analytical expression for the lineshape formula and find rich type of behaviors when compared with the standard theory. For example, new type of resonances and narrowing behavior have been found. We show that the lineshape is extremely sensitive to the way the system is prepared at time $t=0$ and discuss the problem of stationarity. In the second problem, we use semiclassical photon counting statistics to characterize the fluctuation of the photon counts emitted from quantum dots. We show that the photon counting statistics problem can be mapped onto a L\'evy walk process. We find unusually large fluctuations in the photon counts that have not been encountered previously. In particular, we show that $Q$ may increase in time even in the long time limit., Comment: accepted for publication in Chemical Physics, special issue on Strange Kinetics

F\"{o}rster-Dexter theory for excitation energy transfer is generalized for the account of short time nonequilibrium kinetics due to the nonstationary bath relaxation. The final rate expression is presented as a spectral overlap between the time dependent stimulated emission and the stationary absorption profiles, which allows experimental determination of the time dependent rate. For a harmonic oscillator bath model, an explicit rate expression is derived and model calculations are performed in order to examine the dependence of the nonequilibrium kinetics on the excitation-bath coupling strength and the temperature. Relevance of the present theory with recent experimental findings and possible future theoretical directions are discussed., Comment: published in {\it Chemical Physics} (special issue on Photoprocesses in Multichromophoric Molecular Assemblies)

Electron transfer processes in Debye solvents are studied using a spectral analysis method recently proposed. Spectral structure of a nonadiabatic two-state diffusion equation is investigated to reveal various kinetic regimes characterized by a broad range of physical parameters; electronic coupling, energy bias, reorganization energy, and solvent relaxation rate. Within this unified framework, several kinetic behaviors of the electron transfer kinetics, including adiabatic Rabi oscillation, crossover from the nonadiabatic to adiabatic limits, transition from the incoherent to coherent kinetic limits, and dynamic bath effect, are demonstrated and compared with results from previous theoretical models. Dynamics of the electron transfer system is also calculated with the spectral analysis method. It is pointed out that in the large reorganization energy case the nonadiabatic diffusion equation exhibits a non-physical behavior, yielding a negative eigenvalue., Comment: submitted for a publication in Journal of Chemical Physics

We present a general relation between Mandel's $Q$ parameter describing variance of number of photons emitted from a single molecule and a three time correlation function describing a spectral diffusion process the molecule is undergoing. For a prototype of such a stochastic process an exact solution is found which exhibits rich types of physical behaviors.

Motivated by recent experiments we consider a stochastic lineshape theory for the case when the underlying process obeys power-law statistics, based on a generalized Anderson-Kubo oscillator model. We derive an analytical expression for the lineshape and find rich type of behaviors when compared with the standard theory, for example, new type of resonances and narrowing phenomena. We show that the lineshape is extremely sensitive to the way the system is prepared at time $t=0$ and discuss the problem of stationarity.