A refined ring polymer molecular dynamics theory of chemical reaction rates

We further develop the ring polymer molecular dynamics (RPMD) method for calculating chemical reaction rates [I. R. Craig and D. E. Manolopoulos, J. Chem. Phys. 122, 084106 (2005)]. We begin by showing how the rate coefficient we obtained before can be calculated in a more efficient way by considering the side functions of the ring-polymer centroids, rather than averaging over the side functions of the individual ring-polymer beads. This has two distinct advantages. First, the statistics of the phase-space average over the ring-polymer coordinates and momenta are greatly improved. Second, the resulting flux-side correlation function converges to its long-time limit much more rapidly. Indeed the short-time limit of this flux-side correlation function already provides a "quantum transition state theory" approximation to the final rate coefficient. In cases where transition state recrossing effects are negligible, and the transition state dividing surface is put in the right place, the RPMD rate is therefore obtained almost instantly. We then go on to show that the long-time limit of the new flux-side correlation function, and hence the fully converged RPMD reaction rate, is rigorously independent of the choice of the transition state dividing surface. This is especially significant because the optimum dividing surface can often be very difficult to determine for reactions in complex chemical systems.     

Quantum diffusion in liquid water from ring polymer molecular dynamics

We have used the ring polymer molecular-dynamics method to study the translational and orientational motions in an extended simple point charge model of liquid water under ambient conditions. We find, in agreement with previous studies, that quantum-mechanical effects increase the self-diffusion coefficient D and decrease the relaxation times around the principal axes of the water molecule by a factor of around 1.5. These results are consistent with a simple Stokes-Einstein picture of the molecular motion and suggest that the main effect of the quantum fluctuations is to decrease the viscosity of the liquid by about a third. We then go on to consider the system-size scaling of the calculated self-diffusion coefficient and show that an appropriate extrapolation to the limit of infinite system size increases D by a further factor of around 1.3 over the value obtained from a simulation of a system containing 216 water molecules. These findings are discussed in light of the widespread use of classical molecular-dynamics simulations of this sort of size to model the dynamics of aqueous systems.     

On the short-time limit of ring polymer molecular dynamics

We examine the short-time accuracy of a class of approximate quantum dynamical techniques that includes the centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD) methods. Both of these methods are based on the path integral molecular dynamics (PIMD) technique for calculating the exact static equilibrium properties of quantum mechanical systems. For Kubo-transformed real-time correlation functions involving operators that are linear functions of positions or momenta, the RPMD and (adiabatic) CMD approximations differ only in the choice of the artificial mass matrix of the system of ring polymer beads that is employed in PIMD. The obvious ansatz for a general method of this type is therefore to regard the elements of the PIMD (or Parrinello-Rahman) mass matrix as an adjustable set of parameters that can be chosen to improve the accuracy of the resulting approximation. We show here that this ansatz leads uniquely to the RPMD approximation when the criterion that is used to select the mass matrix is the short-time accuracy of the Kubo-transformed correlation function. In particular, we show that the leading error in the RPMD position autocorrelation function is O(t(8)) and the error in the velocity autocorrelation function is O(t(6)), for a general anharmonic potential. The corresponding errors in the CMD approximation are O(t(6)) and O(t(4)), respectively.     

New conditions for validity of the centroid molecular dynamics and ring polymer molecular dynamics

Validity of the centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD) in quantum liquids is studied on an assumption that momenta of liquid particles relax fast. The projection operator method allows one to derive the generalized Langevin equation including a memory effect for the full-quantum canonical (Kubo-transformed) correlation function. Similar equations for the CMD and RPMD correlation functions can be derived too. The comparison of these equations leads to conditions under which the RPMD and CMD correlation functions agree approximately with the full-quantum canonical correlation function. The condition for the RPMD is that the memory effects of the full-quantum and RPMD equations vanish quickly with the same time constants. The CMD correlation function requires additional conditions concerning static correlation.     

Quantum statistics and classical mechanics: real time correlation functions from ring polymer molecular dynamics

We propose an approximate method for calculating Kubo-transformed real-time correlation functions involving position-dependent operators, based on path integral (Parrinello-Rahman) molecular dynamics. The method gives the exact quantum mechanical correlation function at time zero, exactly satisfies the quantum mechanical detailed balance condition, and for correlation functions of the form C(Ax)(t) and C(xB)(t) it gives the exact result for a harmonic potential. It also works reasonably well at short times for more general potentials and correlation functions, as we illustrate with some example calculations. The method provides a consistent improvement over purely classical molecular dynamics that is most apparent in the low-temperature regime.     

On combining molecular dynamics and stochastic dynamics simulations to compute reaction rates in liquids

An approach that combines molecular dynamics and stochastic dynamics calculations for obtaining reaction rates in liquids is investigated by studying the cis-->trans isomerization of HONO in liquid krypton. The isomerization rates are computed for several liquid densities by employing full-dimensional molecular-dynamics simulations. The rates are also computed by employing the stochastic dynamics method for a wide range of collision frequencies. Comparisons of the two sets of the computed rates show that for a wide range of liquid densities there is a simple linear relation between the liquid density rho and the collision frequency alpha, that is, alpha=crho. This suggests that once the constant c is determined from a molecular-dynamics calculation at a single density, the reaction rates can be obtained from stochastic dynamics calculations for the entire range of liquid densities where alpha=crho holds. The applicability of the combined molecular dynamics and stochastic dynamics approach provides a practical means for obtaining rate constants at considerable savings of computer time compared to that required by using full-dimensional molecular-dynamics simulations alone.     

An efficient molecular dynamics simulation method for calculating the diffusion-influenced reaction rates

We present a molecular dynamics (MD) simulation method for calculating the diffusion-influenced reaction rates in the limit of low reactant concentrations. To calculate the reaction rate coefficient, we use MD trajectories of a nonreactive equilibrium system that are initiated with a pair of reactant molecules in reactive configuration. Hence reaction systems involving complicated reactant molecules with geometrically restricted reactivities can be treated with comparable efficiency as the simple hard-sphere reaction system. Compared to the similar MD method proposed by Van Beijeren, Dong, and Bocquet [J. Chem. Phys. 114, 6265 (2001)], the present method has a couple of advantages. First, reactions involving more general sink functions can be treated. Second, more accurate results can be obtained when the reaction probability upon collision is less than unity. As an application, we investigate the effects of nondiffusive dynamics and hydrodynamic interaction of reactants on the reaction rate.     

Quantum mechanical correlation functions, maximum entropy analytic continuation, and ring polymer molecular dynamics

The maximum entropy analytic continuation (MEAC) and ring polymer molecular dynamics (RPMD) methods provide complementary approaches to the calculation of real time quantum correlation functions. RPMD becomes exact in the high temperature limit, where the thermal time betavariant Planck's over 2pi tends to zero and the ring polymer collapses to a single classical bead. MEAC becomes most reliable at low temperatures, where betavariant Planck's over 2pi exceeds the correlation time of interest and the numerical imaginary time correlation function contains essentially all of the information that is needed to recover the real time dynamics. We show here that this situation can be exploited by combining the two methods to give an improved approximation that is better than either of its parts. In particular, the MEAC method provides an ideal way to impose exact moment (or sum rule) constraints on a prior RPMD spectrum. The resulting scheme is shown to provide a practical solution to the "nonlinear operator problem" of RPMD, and to give good agreement with recent exact results for the short-time velocity autocorrelation function of liquid parahydrogen. Moreover these improvements are obtained with little extra effort, because the imaginary time correlation function that is used in the MEAC procedure can be computed at the same time as the RPMD approximation to the real time correlation function. However, there are still some problems involving long-time dynamics for which the RPMD+MEAC combination is inadequate, as we illustrate with an example application to the collective density fluctuations in liquid orthodeuterium.     

Excluded volume effects on polymer reaction rates

The rates of reaction of acid chloride groups with nitrophenol groups were measured with the groups attached to polymer chains. The average degree of substitution was kept low, near to one or less groups per chain. It was found that the interpolymer reaction rates decreased several fold in dilute solution for high polymers compared with the rates in more concentrated solutions or with those for low-molecular-weight polymers. The results were compared with the models proposed by Morawetz and the effect was of the predicted magnitude. The results also confirmed Morawetz' prediction that smaller effects could be expected for terminally substituted than for randomly substituted polymers.     

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.     

Fast predictions of liquid-phase acid-catalyzed reaction rates using molecular dynamics simulations and convolutional neural networks

The rates of liquid-phase, acid-catalyzed reactions relevant to the upgrading of biomass into high-value chemicals are highly sensitive to solvent composition and identifying suitable solvent mixtures is theoretically and experimentally challenging. We show that the complex atomistic configurations of reactant–solvent environments generated by classical molecular dynamics simulations can be exploited by 3D convolutional neural networks to enable accurate predictions of Brønsted acid-catalyzed reaction rates for model biomass compounds. We develop a 3D convolutional neural network, which we call SolventNet, and train it to predict acid-catalyzed reaction rates using experimental reaction data and corresponding molecular dynamics simulation data for seven biomass-derived oxygenates in water–cosolvent mixtures. We show that SolventNet can predict reaction rates for additional reactants and solvent systems an order of magnitude faster than prior simulation methods. This combination of machine learning with molecular dynamics enables the rapid, high-throughput screening of solvent systems and identification of improved biomass conversion conditions.

Solvent-mediated, acid-catalyzed reaction rates relevant to the upgrading of biomass into high-value chemicals are accurately predicted using a combination of molecular dynamics simulations and 3D convolutional neural networks.     

Discontinuous molecular dynamics simulation study of polymer collapse

Discontinuous molecular dynamics simulations were used to study the coil-globule transition of a polymer in an explicit solvent. Two different versions of the model were employed, which are differentiated by the nature of monomer-solvent, solvent-solvent, and nonbonded monomer-monomer interactions. For each case, a model parameter lambda determines the degree of hydrophobicity of the monomers by controlling the degree of energy mismatch between the monomers and solvent particles. We consider a lambda-driven coil-globule transition at constant temperature. The simulations are used to calculate average static structure factors, which are then used to determine the scaling exponents of the system in order to determine the theta-point values lambda(theta) separating the coil from the globule state. For each model we construct coil-globule phase diagrams in terms of lambda and the particle density rho. Additionally, we explore for each model the effects of varying the range of the attractive interactions on the phase boundary separating the coil and globule phases. The results are analyzed in terms of a simple Flory-type theory of the collapse transition.     

Nanoparticle dispersion and aggregation in polymer nanocomposites: insights from molecular dynamics simulation

It is a great challenge to fully understand the microscopic dispersion and aggregation of nanoparticles (NPs) in polymer nanocomposites (PNCs) through experimental techniques. Here, coarse-grained molecular dynamics is adopted to study the dispersion and aggregation mechanisms of spherical NPs in polymer melts. By tuning the polymer-filler interaction in a wide range at both low and high filler loadings, we qualitatively sketch the phase behavior of the PNCs and structural spatial organization of the fillers mediated by the polymers, which emphasize that a homogeneous filler dispersion exists just at the intermediate interfacial interaction, in contrast with traditional viewpoints. The conclusion is in good agreement with the theoretically predicted results from Schweizer et al. Besides, to mimick the experimental coarsening process of NPs in polymer matrixes (ACS Nano 2008, 2, 1305), by grafting polymer chains on the filler surface, we obtain a good filler dispersion with a large interparticle distance. Considering the PNC system without the presence of chemical bonding between the NPs and the grafted polymer chains, the resulting good dispersion state is further used to investigate the effects of the temperature, polymer-filler interaction, and filler size on the filler aggregation process. It is found that the coarsening or aggregation process of the NPs is sensitive to the temperature, and the aggregation extent reaches the minimum in the case of moderate polymer-filler interaction, because in this case a good dispersion is obtained. That is to say, once the filler achieves a good dispersion in a polymer matrix, the properties of the PNCs will be improved significantly, because the coarsening process of the NPs will be delayed and the aging of the PNCs will be slowed.     

PuCO体系的分子反应动力学研究

基于多体项展式理论方法导出的PuCO分子基态(X^7A")的分析势能函数,用准经典的Monte-Carlo轨线法对Pu(^7Fg)+CO(0,0)和O(^3Pg)+PuC(0,0)的分子反应动力学过程进行了计算。结果表明：Pu(^7Fg)与CO(0,0)碰撞易生成PuCO配合物分子,该反应是无阈能反应,反应截面σ随能量Et的升高而下降,当Et=502.1kJ.mol^-^1时,σ几乎为零。O(^3Pg)与PuC(0,0)碰撞易发生生成Pu+CO的交换反应,该反应无阈能。     

Chemical reaction paths—VI : A pericyclic ring closure

Structural data from several crystal structure analyses of 1,6-methano annulenes and related molecules are used to map the reaction path for the pericyclic 1,6-ring-closure reaction. A possible structural expression of the attractive interaction between the reacting atoms can be detected.     

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.     

Identifying the mechanisms of polymer friction through molecular dynamics simulation

Mechanisms governing the tribological behavior of polymer-on-polymer sliding were investigated by molecular dynamics simulations. Three main mechanisms governing frictional behavior were identified. Interfacial "brushing" of molecular chain ends over one another was observed as the key contribution to frictional forces. With an increase of the sliding speed, fluctuations in frictional forces reduced in both magnitude and periodicity, leading to dynamic frictional behavior. While "brushing" remained prevalent, two additional irreversible mechanisms, "combing" and "chain scission", of molecular chains were observed when the interfaces were significantly diffused.     

Recent advances in polymer molecular dynamics simulation and data analysis

Significant advances in molecular simulation methodology over the past decade have greatly reduced the traditional size-timescale bottleneck in molecular dynamics calculations. The development of the geometric statement function method allows for systems up to several hundred thousand atoms to be simulated for up to several nanoseconds in reasonable times on standard workstations. For constant energy simulations, the use of symplectic integrators ensures accurate dynamics, even at long simulation times, without velocity or other artificial rescaling schemes. Finally, new methods of frequency estimation allow for accurate vibrational mode frequency calculations even in the presence of chaotic motion on time scales twenty times shorter than the standard fast Fourier transform, with an additional improvement in the sensitivity of the results when initial dynamics conditions are carefully chosen.     

Conformational analysis of six- and twelve-membered ring compounds by molecular dynamics

A molecular dynamics (MD)-based conformational analysis has been performed on a number of cycloalkanes in order to demonstrate the reliability and generality of MD as a tool for conformational analysis. MD simulations on cyclohexane and a series of methyl-substituted cyclohexanes were performed at temperatures between 400 and 1200 K. Depending on the simulation temperature, different types of interconversions (twist-boat–twist-boat, twist- boat–chair and chair–chair) could be observed, and the MD simulations demonstrated the expected correlation between simulation temperature and ring inversion barriers. A series of methyl-substituted 1,3- dioxanes were investigated at 1000 K, and the number of chair–chair interconversions could be quantitatively correlated to the experimentally determined ring inversion barrier. Similarly, the distribution of sampled minimum-energy conformations correlated with the energy-derived Boltzmann distribution. The macrocyclic ring system cyclododecane was subjected to an MD simulation at 1000 K and 71 different conformations could be sampled. These conformations were compared with the results of previously reported conformational analyses using stochastic search methods, and the MD method provided 19 out of the 20 most stable conformations found in the MM2 force field. Finally, the general performance of the MD method for conformational analysis is discussed.