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Molecular dynamics (MD) simulations are used in biochemistry, physics, and other fields to study the motions, thermodynamic properties, and the interactions between molecules. Computational limitations and the complexity of these problems, however, create the need for approximations to the standard MD methods and for uncertainty quantification and reliability assessment of those approximations. In this paper, we exploit the intrinsic two-scale nature ofMDto construct a class of large-scale dynamics approximations. The reliability of these methods is evaluated here by measuring the differences between full, classical MD simulations and those based on these large-scale approximations. Molecular dynamics evolutions are non-linear and chaotic, so the complete details of molecular evolutions cannot be accurately predicted even using full, classical MD simulations. This paper provides numerical results that demonstrate the existence of computationally efficient large-scale MD approximations which accurately model certain large-scale properties of the molecules: the energy, the linear and angular momenta, and other macroscopic features of molecular motions. [ABSTRACT FROM AUTHOR]

In the preceding paper by Stork and Tavan, [J. Chem. Phys. 126, 165105 (2007)], the authors have reformulated an electrostatic theory which treats proteins surrounded by dielectric solvent continua and approximately solves the associated Poisson equation [B. Egwolf and P. Tavan, J. Chem. Phys. 118, 2039 (2003)]. The resulting solution comprises analytical expressions for the electrostatic reaction field (RF) and potential, which are generated within the protein by the polarization of the surrounding continuum. Here the field and potential are represented in terms of Gaussian RF dipole densities localized at the protein atoms. Quite like in a polarizable force field, also the RF dipole at a given protein atom is induced by the partial charges and RF dipoles at the other atoms. Based on the reformulated theory, the authors have suggested expressions for the RF forces, which obey Newton’s third law. Previous continuum approaches, which were also built on solutions of the Poisson equation, used to violate the reactio principle required by this law, and thus were inapplicable to molecular dynamics (MD) simulations. In this paper, the authors suggest a set of techniques by which one can surmount the few remaining hurdles still hampering the application of the theory to MD simulations of soluble proteins and peptides. These techniques comprise the treatment of the RF dipoles within an extended Lagrangian approach and the optimization of the atomic RF polarizabilities. Using the well-studied conformational dynamics of alanine dipeptide as the simplest example, the authors demonstrate the remarkable accuracy and efficiency of the resulting RF-MD approach. [ABSTRACT FROM AUTHOR]

In an extensive computer simulation study, the transport coefficients of the Lennard-Jones model fluid were determined with high accuracy from equilibrium molecular-dynamics simulations. In the frame of time-correlation function theory, the generalized Einstein relations were employed to evaluate the transport coefficients. This third of a series of four papers presents the results for the bulk viscosity. With comprehensive simulation data at over 350 state points, the temperature and density dependences of the bulk viscosity are characterized in this work over a wide range of fluid states. The bulk viscosity exhibits a large critical enhancement similar to that known for the thermal conductivity, but it extends much farther into the supercritical region and can be observed even at 4.5 times the critical temperature. An investigation of the pressure-fluctuation autocorrelation functions shows that the enhancement is caused by extremely slowly decaying pressure fluctuations.© 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Sets of atoms collectively behaving as rigid bodies are often used in molecular dynamics to model entire molecules or parts thereof. This is a coarse-graining strategy that eliminates degrees of freedom and supposedly admits larger time steps without abandoning the atomistic character of a model. In this paper, we rely on a particular factorization of the rotation matrix to simplify the mechanical formulation of systems containing rigid bodies. We then propose a new derivation for the exact solution of torque-free rotations, which are employed as part of a symplectic numerical integration scheme for rigid-body dynamics. We also review methods for calculating pressure in systems of rigid bodies with pairwise-additive potentials and periodic boundary conditions. Finally, simulations of liquid phases, with special focus on water, are employed to analyze the numerical aspects of the proposed methodology. Our results show that energy drift is avoided for time step sizes up to 5 fs, but only if a proper smoothing is applied to the interatomic potentials. Despite this, the effects of discretization errors are relevant, even for smaller time steps. These errors induce, for instance, a systematic failure of the expected equipartition of kinetic energy between translational and rotational degrees of freedom. [ABSTRACT FROM AUTHOR]

The multiscale coarse-graining (MS-CG) method is a method for constructing a coarse-grained (CG) model of a system using data obtained from molecular dynamics simulations of the corresponding atomically detailed model. The formal statistical mechanical derivation of the method shows that the potential energy function extracted from an MS-CG calculation is a variational approximation for the true potential of mean force of the CG sites, one that becomes exact in the limit that a complete basis set is used in the variational calculation if enough data are obtained from the atomistic simulations. Most applications of the MS-CG method have employed a representation for the nonbonded part of the CG potential that is a sum of all possible pair interactions. This approach, despite being quite successful for some CG models, is inadequate for some others. Here we propose a systematic method for including three body terms as well as two body terms in the nonbonded part of the CG potential energy. The current method is more general than a previous version presented in a recent paper of this series [L. Larini, L. Lu, and G. A. Voth, J. Chem. Phys. 132, 164107 (2010)], in the sense that it does not make any restrictive choices for the functional form of the three body potential. We use hierarchical multiresolution functions that are similar to wavelets to develop very flexible basis function expansions with both two and three body basis functions. The variational problem is solved by a numerical technique that is capable of automatically selecting an appropriate subset of basis functions from a large initial set. We apply the method to two very different coarse-grained models: a solvent free model of a two component solution made of identical Lennard-Jones particles and a one site model of SPC/E water where a site is placed at the center of mass of each water molecule. These calculations show that the inclusion of three body terms in the nonbonded CG potential can lead to significant improvement in the accuracy of CG potentials and hence of CG simulations. [ABSTRACT FROM AUTHOR]

In the quest towards coarse-grained potentials and new water models, we present an extension of the force matching technique to parameterize an all-atom force field for rigid water. The methodology presented here allows to improve the matching procedure by first optimizing the weighting exponents present in the objective function. A new gauge for unambiguously evaluating the quality of the fit has been introduced; it is based on the root mean square difference of the distributions of target properties between reference data and fitted potentials. Four rigid water models have been parameterized; the matching procedure has been used to assess the role of the ghost atom in TIP4P-like models and of electrostatic damping. In the former case, burying the negative charge inside the molecule allows to fit better the torques. In the latter, since short-range interactions are damped, a better fit of the forces is obtained. Overall, the best performing model is the one with a ghost atom and with electrostatic damping. The approach shown in this paper is of general validity and could be applied to any matching algorithm and to any level of coarse graining, also for non-rigid molecules. [ABSTRACT FROM AUTHOR]

Photo-induced electron detachment spectroscopy of anionic boron clusters, B4- and B5-, is theoretically investigated by performing electronic structure calculations and nuclear dynamics simulations. While the electronic potential energy surfaces (X1Ag, ã3B2u, b3B1u, Ã1B2u, c3B2g, and B1B2g of neutral B4 and X2B2, Ã2A1, B2B2, C2A1, D2B1, and E2A1 of neutral B5) and their coupling surfaces are constructed in this paper, the details of the nuclear dynamics on these electronic states are presented in Paper II. Electronic structure calculations are carried out at the complete active space self-consistent field - multi-reference configuration interaction level of theory employing the correlation consistent polarized valance triple zeta basis set. Using the calculated electronic structure data suitable vibronic Hamiltonians are constructed utilizing a diabatic electronic basis and displacement coordinates of the normal vibrational modes. The theoretical results are discussed in relation to those recorded in recent experiments. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations were conducted to investigate the dynamic properties of melts of nonconcatenated ring polymers and compared to melts of linear polymers. The longest rings were composed of N = 1600 monomers per chain which corresponds to roughly 57 entanglement lengths for comparable linear polymers. The ring melts were found to diffuse faster than their linear counterparts, with both architectures approximately obeying a D ∼ N-2.4 scaling law for large N. The mean-square displacement of the center-of-mass of the rings follows a sub-diffusive behavior for times and distances beyond the ring extension g2>, neither compatible with the Rouse nor the reptation model. The rings relax stress much faster than linear polymers, and the zero-shear viscosity was found to vary as η0 ∼ N1.4 ± 0.2 which is much weaker than the N3.4 behavior of linear chains, not matching any commonly known model for polymer dynamics when compared to the observed mean-square displacements. These findings are discussed in view of the conformational properties of the rings presented in the preceding paper [J. D. Halverson, W. Lee, G. S. Grest, A. Y. Grosberg, and K. Kremer, J. Chem. Phys. 134, 204904 (2011)]. [ABSTRACT FROM AUTHOR]

On the mesoscale, the molecular motion in a microporous material can be represented as a sequence of hops between different pore locations and from one pore to the other. On the same scale, the memory effects in the motion of a tagged particle are embedded in the displacement autocorrelation function (DACF), the discrete counterpart of the velocity autocorrelation function (VACF). In this paper, a mesoscopic hopping model, based on a lattice-gas automata dynamics, is presented for the coarse-grained modeling of the DACF in a microporous material under conditions of thermodynamic equilibrium. In our model, that we will refer to as central cell model, the motion of one tagged particle is mimicked through probabilistic hops from one location to the other in a small lattice of cells where all the other particles are indistinguishable; the cells closest to the one containing the tagged particle are simulated explicitly in the canonical ensemble, whereas the border cells are treated as mean-field cells in the grand-canonical ensemble. In the present paper, numerical simulation of the central cell model are shown to provide the same results as a traditional lattice-gas simulation. Along with this a mean-field theory of self-diffusion which incorporates time correlations is discussed. [ABSTRACT FROM AUTHOR]

Trotter's theorem forms the theoretical basis of most modern molecular dynamics. In essence this theorem states that a time displacement operator (a Lie operator) constructed by exponentiating a sum of noncommuting operators can be approximated by a product of single operators provided the time interval is 'very small.' In theory 'very small' implies infinitesimally small (at which point the approximate product becomes exact), while in practical analysis a finite time interval is divided into several small subintervals or steps. It follows, therefore, that the larger the number of steps the better the approximation to the exact time displacement operator. The question therefore arises: How many steps are sufficient? For bounded operators, standard theorems are available to provide the answer. In this paper we show that a very simple combinatorial formula can be derived which allows the computation of the global differences (as a function of the number of steps) between the Taylor coefficients of the exact time displacement operator and an approximate one constructed by using a finite number of steps. The formula holds for both bounded and nonbounded operators and shows, quantitatively, what is qualitatively expected-that the error decreases with increasing number of steps. Furthermore, the formula applies irrespective of the complexity of the system, boundary conditions, or the thermodynamic ensemble employed for averaging the initial conditions. The analysis yields explicit expressions for the Taylor coefficients which are then used to compute the errors. In the case of the algorithmically based practical numerical simulations in which fixed, albeit small, steps are repeatedly applied, the rise in the number of steps does not reduce the size of the steps but increases the total time of interest. The combinatorial formula shows that, here, the errors diverge. Furthermore, this work can be used to supplement other efforts such as the use of shadow Hamiltonians where the truncation of the series expansion of the latter will produce errors in the higher order propagator moments. [ABSTRACT FROM AUTHOR]

In the present paper, we report a molecular dynamics simulation of two-dimensional Lennard-Jones system with a simple square start configuration. Mean square displacement was computed showing interesting dependence on high pressure conditions in short time scale, corresponding to an abrupt restructurization. This paper is the first to report the qualitative and quantitative details of this phenomenon. [ABSTRACT FROM AUTHOR]

Attempts to simulate crystal growth of ice from liquid water and to provide a consistent microscopic description of this process have been challenging tasks. In this paper we have adapted our previously developed molecular dynamics simulation methodology to enable the investigation of steady-state directional crystal growth/melting of ice. Specifically, we examine ice/water systems of the (001), (110), and (111) faces of ice Ic and the (0001), [formula], and [formula] faces of ice Ih, where the TIP4P, TIP4P-Ew, and SPC/E water models have been utilized. The influence of different growth/melting conditions (temperature gradients and growth velocities) is investigated. Profile functions of properties of interest across the interface are obtained from nonequilibrium steady-state simulations and provide consistent descriptions of ice/water interfaces. The widths of the various crystallographic faces are found to increase in the apparent order Ic111, Ih0001 < [formula] < [formula] < Ic001 < Ic110. The observed growth rates were in agreement with experimental values and the possible dependence on the various faces is explored. The melting temperatures obtained with the present methodology for the different models are in good agreement with estimates from other work. [ABSTRACT FROM AUTHOR]

Over the last number of years several simulation methods have been introduced to study rare events such as nucleation. In this paper we examine the crystal nucleation rate of hard spheres using three such numerical techniques: molecular dynamics, forward flux sampling, and a Bennett-Chandler-type theory where the nucleation barrier is determined using umbrella sampling simulations. The resulting nucleation rates are compared with the experimental rates of Harland and van Megen [Phys. Rev. E 55, 3054 (1997)], Sinn et al. [Prog. Colloid Polym. Sci. 118, 266 (2001)], Schätzel and Ackerson [Phys. Rev. E 48, 3766 (1993)], and the predicted rates for monodisperse and 5% polydisperse hard spheres of Auer and Frenkel [Nature 409, 1020 (2001)]. When the rates are examined in units of the long-time diffusion coefficient, we find agreement between all the theoretically predicted nucleation rates, however, the experimental results display a markedly different behavior for low supersaturation. Additionally, we examined the precritical nuclei arising in the molecular dynamics, forward flux sampling, and umbrella sampling simulations. The structure of the nuclei appears independent of the simulation method, and in all cases, the nuclei contains on average significantly more face-centered-cubic ordered particles than hexagonal-close-packed ordered particles. [ABSTRACT FROM AUTHOR]

This paper investigates the conformational and scaling properties of long linear polymer chains. These investigations are done with the aid of Monte Carlo (MC) and molecular dynamics (MD) simulations. Chain lengths that comprise several orders of magnitude to reduce errors of finite size scaling, including the effect of solvent quality, ranging from the athermal limit over the θ-transition to the collapsed state of chains are investigated. Also the effect of polydispersity on linear chains is included which is an important issue in the real fabrication of polymers. A detailed account of the hybrid MD and MC simulation model and the exploited numerical methods is given. Many results of chain properties in the extrapolated limit of infinite chain lengths are documented and universal properties of the chains within their universality class are given. An example of the difference between scaling exponents observed in actual solvents and those observed in the extremes of “good solvents” and “θ-solvents” in simulations is provided by comparing simulation results with experimental data on low density polyethylene. This paper is concluded with an outlook on the extension of this study to branched chain systems of many different branching types. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations are used to calculate the surface tension γ and study the structural properties of the liquid–vapor interface of the simple molten salt KI. The focus of the present paper is the effect on the calculated surface tension of different terms in the interionic potential and of the way that long-ranged interactions are treated. Specifically, we analyze the dependence of γ on: (a) boundary conditions employed in the Ewald summations of Coulomb interactions; (b) truncation of dispersion interactions; (c) inclusion of polarization effects. Our results show that (a) the use of vacuum boundary conditions in the direction perpendicular to the interface helps to maintain the mechanical equilibrium of the interface; (b) an Ewald summation of dispersion interactions is necessary to avoid substantial truncation effects; (c) polarization tends to decrease γ by significant amounts, and improves the agreement with experiment. In all cases, a reduction of γ comes with a corresponding increase of the interfacial width. As a structural indicator, the tangential pair distribution functions at the interface are compared with those of the bulk liquid. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper, we present a new canonical replica exchange molecular dynamics (REMD) simulation method with normal pressure for all replicas (REMD-NV(p)T). This method is suitable for systems for which conventional constant NPT-setups are difficult to implement. In this implementation, each replica has an individual volume, with normal pressure maintained for each replica in the simulation. We derive a novel exchange term and validate this method on the structural properties of SPC/E water and dialanine (Ala2) in the bulk and in the presence of a graphene layer. Compared to conventional constant NPT-REMD and NVT-REMD simulations, we find that the structural properties of our new method are in good agreement with simulations in the NPT-ensemble at all temperatures. The structural properties of the systems considered are affected by high pressures at elevated temperatures in the constant NVT-ensemble, an effect that our method corrects for. Unprojected distributions reveal that essential motions of the peptide are affected by the presence of the barostat in the NPT implementation but that the dynamical eigenmodes of the NV(p)T method are in close quantitative agreement with the NVT-ensemble. [ABSTRACT FROM AUTHOR]

Postcollision multifragmentation which we have recently observed experimentally in C-60-surface impact is the phenomenon of a delayed multiparticle breakup of a highly collisionally vibrationally excited large molecule/cluster (the precursor species) into several polyatomic fragments, after leaving the surface. In this paper, we show that the molecular dynamics simulations of near-grazing C60 collisions with a gold surface at 300 eV impact energy (very similar to the experimental conditions) successfully reproduce the experimentally observed characteristics of the postcollision multifragmentation process. The calculated mass resolved kinetic energy distributions and the time dependent yield curves of the Cn fragments revealed a precursor mediated, velocity correlated, delayed fragmentation event along the outgoing trajectory, far away from the surface. Most of the large fragments (n = 5) are formed within a time window of 2-20 ps after leaving the surface, corresponding to the vertical distances of 3-30 nm from the surface. Analysis of delay times and actual time duration for multifragmentation reveal that a large part can be described as simultaneous postcollision (delayed) multifragmentation events. The delayed nature of the event seems to be due to an early sequence of structural transformations of the precursor. [ABSTRACT FROM AUTHOR]

Quantum effects due to the spatial delocalization of light atoms are treated in molecular simulation via the path integral technique. Among several methods, Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to investigate properties induced by spatial delocalization of atoms; however, computationally this technique is very demanding. The above mentioned limitation implies the restriction of PIMD applications to relatively small systems and short time scales. One of the possible solutions to overcome size and time limitation is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme (AdResS). AdResS requires a relatively small region treated at path integral level and embeds it into a large molecular reservoir consisting of generic spherical coarse grained molecules. It was previously shown that the realization of the idea above, at a simple level, produced reasonable results for toy systems or simple/test systems like liquid parahydrogen. Encouraged by previous results, in this paper, we show the simulation of liquid water at room conditions where AdResS, in its latest and more accurate Grand-Canonical-like version (GC-AdResS), is merged with two of the most relevant PIMD techniques available in the literature. The comparison of our results with those reported in the literature and/or with those obtained from full PIMD simulations shows a highly satisfactory agreement. [ABSTRACT FROM AUTHOR]

Understanding and controlling the transportation of water molecules across carbon nanotube (CNT) is of great importance in bio-nanotechnology. In this paper, we systematically investigate the water transporting behaviors (i.e., water flow rate) inside the CNT in the presence of lipid membranes by using all atom molecular dynamic simulations. Our results show that the hydrophilicity of CNT as well as membrane thickness can have important impacts on the water flow rate. Interestingly, since the membrane thickness is temperature-dependent, the water flow rate can exhibit thermo-responsive behaviors. Further, we also provide insights into the effect of CNT on lipid membranes. It is found that all CNTs can increase the lipid tail order parameters and thicken the membrane at 320 K; while these effects are not obvious at 290 K. Importantly, we observe that the CNT with specific hydrophobicity has the least effect on membranes. The present study may give some useful advice on future experimental design of novel devices and sensors. [ABSTRACT FROM AUTHOR]

Combining simulation and model theories, this paper analyses the impact of pair dynamics on the intermolecular nuclear Overhauser effect (NOE) in liquids. For the first time, we give a distance resolved NOE. When applied to the ionic liquid 1-ethyl-3-methyl-imidazolium tetrafluoroborate the NOE turns out to be of long-range nature. This behaviour translates to the experimentally measured cross- and longitudinal relaxation rates.We were able to calculate the heteronuclear NOE from simulation data, despite the high computational effort.Model theories are computationally less demanding and cover the complete frequency range of the respective spectral density function, they are usually based on a very simple pair distribution function and the solution of the diffusion equation. In order to model the simulated data sufficiently, these simplifications in structure and dynamics have to be generalised considerably. [ABSTRACT FROM AUTHOR]

We have performed large-scale Lennard-Jones molecular dynamics simulations of homogeneous vapor-to-liquid nucleation, with 109 atoms. This large number allows us to resolve extremely low nucleation rates, and also provides excellent statistics for cluster properties over a wide range of cluster sizes. The nucleation rates, cluster growth rates, and size distributions are presented in Diemand et al. [J. Chem. Phys. 139, 74309 (2013)], while this paper analyses the properties of the clusters. We explore the cluster temperatures, density profiles, potential energies, and shapes. A thorough understanding of the properties of the clusters is crucial to the formulation of nucleation models. Significant latent heat is retained by stable clusters, by as much as ΔkT = 0.1ϵ for clusters with size i = 100. We find that the clusters deviate remarkably from spherical-with ellipsoidal axis ratios for critical cluster sizes typically within b/c = 0.7 ± 0.05 and a/c = 0.5 ± 0.05. We examine cluster spin angular momentum, and find that it plays a negligible role in the cluster dynamics. The interfaces of large, stable clusters are thinner than planar equilibrium interfaces by 10%-30%. At the critical cluster size, the cluster central densities are between 5% and 30% lower than the bulk liquid expectations. These lower densities imply larger-than-expected surface areas, which increase the energy cost to form a surface, which lowers nucleation rates. [ABSTRACT FROM AUTHOR]

Molecular mechanisms of the steady-state growth of the chain folded lamella and the cold crystallization across the glass transition temperature Tg are investigated by molecular dynamics simulation for a system of long polyethylene (PE)-like polymers made of 512 united atoms C512. The present paper aims to reconsider results of our previous simulations for short PE-like polymers C100 by carrying out very long simulations up to 1 μs for more realistic systems of much longer chains, thereby to establish the firm molecular image of chain-folded crystallization and clarify the specific molecular process of cold crystallization. We observe that the chain-folded lamella shows fast thickening-growth keeping marked tapered growth front. Despite the fast growth in much longer chains, the fold-surface is found to be predominantly of adjacent-reentry. Detailed inspections of the molecular pathway give an insightful image that can explain the apparently contradicting results. In addition, the fold-structure with specific spatial heterogeneity is found to give rise to heterogeneous mobility within the crystalline region. On the other hand, investigations of the cold crystallization during slow heating of the glassy film across Tg is found to give a granular texture made of small crystallites. The crystallites are found to nucleate preferentially near the free surfaces having lower Tg, and to be dominantly edge-on showing a definite tendency to orient their chain axes parallel to the free surface. [ABSTRACT FROM AUTHOR]

Most of today's molecular-dynamics simulations of materials are based on the Born-Oppenheimer approximation. There are many cases, however, in which the coupling of the electrons and nuclei is important and it is necessary to go beyond the Born-Oppenheimer approximation. In these methods, the non-adiabatic coupling vectors are fundamental since they represent the link between the classical atomic motion of the nuclei and the time evolution of the quantum electronic state. In this paper we analyze the calculation of non-adiabatic coupling vectors in a basis set of local orbitals and derive an expression to calculate them in a practical and computationally efficient way. Some examples of the application of this expression using a local-orbital density functional theory approach are presented for a few simple molecules: H3, formaldimine, and azobenzene. These results show that the approach presented here, using the Slater transition-state density, is a very promising way for the practical calculation of non-adiabatic coupling vectors for large systems. [ABSTRACT FROM AUTHOR]

This paper demonstrates a method for calculating the tension of a system with a curved interface from a molecular dynamics simulation. To do so, the pressure of a subset of the system is determined by applying a local (virtual) mechanical deformation, fitting the response to that of a bulk fluid, and then using the Young-Laplace equation to infer the tension of the interface. The accuracy of the method is tested by calculating the local pressure of a series of water simulations at various external pressures. The tension of a simulated curved octane-water interface is computed with the method and compares well with the planar tension (≈ 46.7 dyn/cm). Finally, an ambiguity is resolved between the Harasima and Irving-Kirkwood methods of calculating the local pressure as a means for computing the tension. [ABSTRACT FROM AUTHOR]

Hydrodynamic interactions play an important role in the dynamics of macromolecules. The most common way to take into account hydrodynamic effects in molecular simulations is in the context of a Brownian dynamics simulation. However, the calculation of correlated Brownian noise vectors in these simulations is computationally very demanding and alternative methods are desirable. This paper studies methods based on Krylov subspaces for computing Brownian noise vectors. These methods are related to Chebyshev polynomial approximations, but do not require eigenvalue estimates. We show that only low accuracy is required in the Brownian noise vectors to accurately compute values of dynamic and static properties of polymer and monodisperse suspension models. With this level of accuracy, the computational time of Krylov subspace methods scales very nearly as O(N2) for the number of particles N up to 10 000, which was the limit tested. The performance of the Krylov subspace methods, especially the 'block' version, is slightly better than that of the Chebyshev method, even without taking into account the additional cost of eigenvalue estimates required by the latter. Furthermore, at N = 10 000, the Krylov subspace method is 13 times faster than the exact Cholesky method. Thus, Krylov subspace methods are recommended for performing large-scale Brownian dynamics simulations with hydrodynamic interactions. [ABSTRACT FROM AUTHOR]

We describe a replica exchange strategy where trial swap configurations are generated by nonequilibrium switching simulations. By devoting simulation time to the switching simulations, one can systematically increase an effective overlap between replicas, which leads to an increased exchange acceptance rate and less correlated equilibrium samples. In this paper, we derive our method for a general class of stochastic dynamics, and discuss various strategies for enhancing replica overlap through novel dynamical schemes and prudent choices of switching protocols. We then demonstrate our method on a model system of alanine dipeptide in implicit solvent, characterizing decreases in data correlations and gains in sampling efficiency. [ABSTRACT FROM AUTHOR]

The dynamics of complex systems often involve thermally activated barrier crossing events that allow these systems to move from one basin of attraction on the high dimensional energy surface to another. Such events are ubiquitous, but challenging to simulate using conventional simulation tools, such as molecular dynamics. Recently, E and Zhou [Nonlinearity 24(6), 1831 (2011)] proposed a set of dynamic equations, the gentlest ascent dynamics (GAD), to describe the escape of a system from a basin of attraction and proved that solutions of GAD converge to index-1 saddle points of the underlying energy. In this paper, we extend GAD to enable finite temperature simulations in which the system hops between different saddle points on the energy surface. An effective strategy to use GAD to sample an ensemble of low barrier saddle points located in the vicinity of a locally stable configuration on the high dimensional energy surface is proposed. The utility of the method is demonstrated by studying the low barrier saddle points associated with point defect activity on a surface. This is done for two representative systems, namely, (a) a surface vacancy and ad-atom pair and (b) a heptamer island on the (111) surface of copper. [ABSTRACT FROM AUTHOR]

In this paper, the conformation and dynamics properties of polyethylene oxide (PEO) and polypropylene oxide (PPO) polymer chains at 298 K have been studied in the melt and at infinite dilution condition in water, methanol, chloroform, carbon tetrachloride, and n-heptane using molecular dynamics simulations. The calculated density of PEO melt with chain lengths of n = 2, 3, 4, 5 and, for PPO, n = 7 are in good agreement with the available experimental data. The conformational properties of PEO and PPO show an increasing gauche preference for the O-C-C-O dihedral in the following order water>methanol>chloroform>carbon tetrachloride = n-heptane. On the contrary, the preference for trans conformation has a maximum in carbon tetrachloride and n-heptane followed in the order by chloroform, methanol, and water. The PEO conformational preferences are in qualitative agreement with results of NMR studies. PEO chains formed different types of hydrogen bonds with polar solvent molecules. In particular, the occurrence of bifurcated hydrogen bonding in chloroform was also observed. Radii of gyration of PEO chains of length larger than n = 9 monomers showed a good agreement with light scattering data in water and in methanol. For the shorter chains the observed deviations are probably due to the enhanced hydrophobic effects caused by the terminal methyl groups. For PEO the fitting of end-to-end distance distributions with the semi-flexible chain model at 298 K provided persistence lengths of 0.375 and 0.387 nm in water and methanol, respectively. Finally, the radius of gyration of Pluronic P85 turned out to be 2.25 ± 0.4 nm at 293 K in water in agreement with experimental data. [ABSTRACT FROM AUTHOR]

Energy is commonly dissipated in molecular dynamics simulations by using a thermostat. In non-isothermal shear simulations of confined liquids, the choice of the thermostat is very delicate. We show in this paper that under certain conditions, the use of classical thermostats can lead to an erroneous description of the dynamics in the confined system. This occurs when a critical shear rate is surpassed as the thermo-viscous effects become prominent. In this high-shear-high-dissipation regime, advanced dissipation methods including a novel one are introduced and compared. The MD results show that the physical modeling of both the accommodation of the surface temperature to liquid heating and the heat conduction through the confining solids is essential. The novel method offers several advantages on existing ones including computational efficiency and easiness of application for complex systems. [ABSTRACT FROM AUTHOR]

Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper, we introduce a multiscale methodology suitable to address this problem, assuming that the evolution of the slow species in the system is well approximated by a Langevin process. It is based on the conditional stochastic simulation algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the constrained multiscale algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Fokker-Planck equation approximation, we can in turn approximate average switching times in stochastic chemical systems. [ABSTRACT FROM AUTHOR]

While the interaction of colloidal particles (sizes in excess of 100 nm) with liquid interfaces may be understood in terms of continuum models, which are grounded in macroscopic properties such as surface and line tensions, the behaviour of nanoparticles at liquid interfaces may be more complex. Recent simulations [D. L. Cheung and S. A. F. Bon, Phys. Rev. Lett. 102, 066103 (2009)] of nanoparticles at an idealised liquid-liquid interface showed that the nanoparticle-interface interaction range was larger than expected due, in part, to the action of thermal capillary waves. In this paper, molecular dynamics simulations of a Lennard-Jones nanoparticle in a binary Lennard-Jones mixture are used to confirm that these previous results hold for more realistic models. Furthermore by including attractive interactions between the nanoparticle and the solvent, it is found that the detachment energy decreases as the nanoparticle-solvent attraction increases. Comparison between the simulation results and recent theoretical predictions [H. Lehle and M. Oettel, J. Phys. Condens. Matter 20, 404224 (2008)] shows that for small particles the incorporation of capillary waves into the predicted effective nanoparticle-interface interaction improves agreement between simulation and theory. [ABSTRACT FROM AUTHOR]

The reported work extends previously published research on transport in aqueous ionic solutions through carbon nanotubes. Specifically, the effects of the nanotube radius, solute concentration, and applied external electric fields on the solution structuring are investigated in terms of spatial density distributions, pair distribution functions, and electrostatic potential profiles. Several simulated structural features are consistent with general theoretical results of nanofluidics and can be interpreted fairly well with respect to these (such as the Donnan-type voltages established at the channel apertures depending on the logarithm of the maximum ion concentration). The simulated properties are based on averages over the largest data collection times reported in the literature (0.8 μs), providing accurate estimates of the measured quantities. [ABSTRACT FROM AUTHOR]

The present investigations continue previous research on transport in aqueous ionic solutions through carbon nanotubes. Specifically, the effects of the nanotube radius, solute concentration, and applied external electric fields on the transport properties are investigated in terms of mobilities, currents, and pairing times of the solute ions. The simulated transport features are corroborated with general theoretical results of nanofluidics (such as the linear log-log regime of the nanochannel conductance as function of the solute concentration and the current-voltage curve of the channel). Discontinuities in the partial ionic currents are explained on the basis of a recent theoretical model of quantized ionic conductance in nanopores, developed by Zwolak et al. Correlations between the structural and dynamic properties are established, linking causally the highly structured spatial density profiles, the ion pairing phenomenon and the ionic currents. [ABSTRACT FROM AUTHOR]

An efficient time-dependent importance sampling method is developed for the Monte Carlo calculation of time correlation functions via the initial value representation (IVR) of semiclassical (SC) theory. A prefactor-free time-dependent sampling function weights the importance of a trajectory based on the magnitude of its contribution to the time correlation function, and global trial moves are used to facilitate the efficient sampling the phase space of initial conditions. The method can be generally applied to sampling rare events efficiently while avoiding being trapped in a local region of the phase space. Results presented in the paper for two system-bath models demonstrate the efficiency of this new importance sampling method for full SC-IVR calculations. [ABSTRACT FROM AUTHOR]

CdTe and CdTe-based Cd1-xZnxTe (CZT) alloys are important semiconductor compounds that are used in a variety of technologies including solar cells, radiation detectors, and medical imaging devices. Performance of such systems, however, is limited due to the propensity of nano- and micro-scale defects that form during crystal growth and manufacturing processes. Molecular dynamics simulations offer an effective approach to study the formation and interaction of atomic scale defects in these crystals, and provide insight on how to minimize their concentrations. The success of such a modeling effort relies on the accuracy and transferability of the underlying interatomic potential used in simulations. Such a potential must not only predict a correct trend of structures and energies of a variety of elemental and compound lattices, defects, and surfaces but also capture correct melting behavior and should be capable of simulating crystalline growth during vapor deposition as these processes sample a variety of local configurations. In this paper, we perform a detailed evaluation of the performance of two literature potentials for CdTe, one having the Stillinger-Weber form and the other possessing the Tersoff form. We examine simulations of structures and the corresponding energies of a variety of elemental and compound lattices, defects, and surfaces compared to those obtained from ab initio calculations and experiments. We also perform melting temperature calculations and vapor deposition simulations. Our calculations show that the Stillinger-Weber parameterization produces the correct lowest energy structure. This potential, however, is not sufficiently transferrable for defect studies. Origins of the problems of these potentials are discussed and insights leading to the development of a more transferrable potential suitable for molecular dynamics simulations of defects in CdTe crystals are provided. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations were conducted to investigate the structural properties of melts of nonconcatenated ring polymers and compared to melts of linear polymers. The longest rings were composed of N = 1600 monomers per chain which corresponds to roughly 57 entanglement lengths for comparable linear polymers. For the rings, the radius of gyration squared, g2>, was found to scale as N4/5 for an intermediate regime and N2/3 for the larger rings indicating an overall conformation of a crumpled globule. However, almost all beads of the rings are 'surface beads' interacting with beads of other rings, a result also in agreement with a primitive path analysis performed in the next paper [J. D. Halverson, W. Lee, G. S. Grest, A. Y. Grosberg, and K. Kremer, J. Chem. Phys. 134, 204905 (2011)]. Details of the internal conformational properties of the ring and linear polymers as well as their packing are analyzed and compared to current theoretical models. [ABSTRACT FROM AUTHOR]

Markov state models of molecular kinetics (MSMs), in which the long-time statistical dynamics of a molecule is approximated by a Markov chain on a discrete partition of configuration space, have seen widespread use in recent years. This approach has many appealing characteristics compared to straightforward molecular dynamics simulation and analysis, including the potential to mitigate the sampling problem by extracting long-time kinetic information from short trajectories and the ability to straightforwardly calculate expectation values and statistical uncertainties of various stationary and dynamical molecular observables. In this paper, we summarize the current state of the art in generation and validation of MSMs and give some important new results. We describe an upper bound for the approximation error made by modeling molecular dynamics with a MSM and we show that this error can be made arbitrarily small with surprisingly little effort. In contrast to previous practice, it becomes clear that the best MSM is not obtained by the most metastable discretization, but the MSM can be much improved if non-metastable states are introduced near the transition states. Moreover, we show that it is not necessary to resolve all slow processes by the state space partitioning, but individual dynamical processes of interest can be resolved separately. We also present an efficient estimator for reversible transition matrices and a robust test to validate that a MSM reproduces the kinetics of the molecular dynamics data. [ABSTRACT FROM AUTHOR]

In this paper, molecular dynamics simulation was performed to investigate the liquid/vapor interfacial structure of neat polar liquids. Large-scale ensembles of liquid pyridine and its alkyl derivatives, 4-methylpyridine and 4-ethylpyridine, were simulated by classical molecular dynamics at 298 K. For the liquid system of low polarity, the surface density profile of the atoms meet exactly at the middle of interfacial region, and atoms of hydrophobic nature can be hardly discriminated from hydrophilic ones in either vapor or liquid sides. For a liquid system of high polarity, the density profile of atoms with different nature is highly discriminated all over the interfacial region, and as the polarity increases, a dense region of atomic density is clearly developed in the subsurface region. The recognized bivariate method was also used to study the molecular orientational distribution quantitatively. Orientational analysis of the three liquid systems indicates that the pyridine ring plane in the outmost surface tends to be vertical. Its tendency in the innermost interfacial region is parallel. The orientational states available to 4-ethylpyridine and pyridine are discriminated by predicting the possibility of a bisector-wise tumbling for the ring plane in pyridine and a side-wise tumbling in 4-ethylpyridine. The orientational distribution maps explain the trend of experimental surface tension and surface entropy. As the dipole moment of these liquids increases with the alkyl chain length, the surface structural profile changes from a regular definite one to a surface of complex atomic structure involving a dense phase near the interface. The development of dense region in alkyl derivatives is the result of segregation of molecules due to the alkyl group, which is captured and discriminated by molecular dynamics simulation even when the length of a short alkyl chain is increased by one carbon atom. [ABSTRACT FROM AUTHOR]

We propose the thermodynamic integration along a spatial reaction coordinate using the molecular dynamics simulation combined with the three-dimensional reference interaction site model theory. This method provides a free energy calculation in solution along the reaction coordinate defined by the Cartesian coordinates of the solute atoms. The proposed method is based on the blue moon algorithm which can, in principle, handle any reaction coordinate as far as it is defined by the solute atom positions. In this article, we apply the present method to the complex formation process of the crown ether 18-Crown-6 (18C6) with the potassium ion in an aqueous solution. The separation between the geometric centers of these two molecules is taken to be the reaction coordinate for this system. The potential of mean force (PMF) becomes the maximum at the separation between the molecular centers being ∼4 Å, which can be identified as the free energy barrier in the process of the molecular recognition. In a separation further than the free energy barrier, the PMF is slightly reduced to exhibit a plateau. In the region closer than the free energy barrier, approach of the potassium ion to the center of 18C6 also decreases the PMF. When the potassium ion is accommodated at the center of 18C6, the free energy is lower by -5.7 ± 0.7 kcal/mol than that at the above mentioned plateau or converged state. By comparing the results with those from the free energy calculation along the coupling parameters obtained in our previous paper [T. Miyata, Y. Ikuta, and F. Hirata, J. Chem. Phys. 133, 044114 (2010)], it is found that the effective interaction in water between 18C6 and the potassium ion vanishes beyond the molecular-center-separation of 10 Å. Furthermore, the conformation of 18C6 is found to be significantly changed depending upon the 18C6-K+ distance. A proper conformational sampling and an accurate solvent treatment are crucial for realizing the accurate PMF, and we believe that the proposed method is useful to evaluate the PMF in a solution. A discussion upon the PMF in terms of the three-dimensional distribution function for the solvent is also presented. [ABSTRACT FROM AUTHOR]

In this paper we calculate the interfacial resistances to heat and mass transfer through a liquid-vapor interface in a binary mixture. We use two methods, the direct calculation from the actual nonequilibrium solution and integral relations, derived earlier. We verify, that integral relations, being a relatively faster and cheaper method, indeed gives the same results as the direct processing of a nonequilibrium solution. Furthermore we compare the absolute values of the interfacial resistances with the ones obtained from kinetic theory. Matching the diagonal resistances for the binary mixture we find that kinetic theory underestimates the cross coefficients. The heat of transfer is, as a consequence, correspondingly larger. [ABSTRACT FROM AUTHOR]

The use of discrete variable representation (DVR) basis sets within ab initio molecular dynamics calculations allows the latter to be performed with converged energies and, more importantly, converged forces. In this paper, we show how to carry out ab initio molecular dynamics calculations in the isothermal-isobaric ensemble with fully flexible simulation boxes within the DVR basis set framework. In particular, we derive the appropriate DVR based expression for the pressure tensor when the electronic structure is represented using Kohn-Sham density functional theory, and we examine the convergence of this expression as a function of the basis set size. An illustrative example using 64 silicon atoms in a fully flexible box using a combination of the Martyna-Tobias-Klein [Martyna et al., J. Chem. Phys. 101, 4177 (1994)] and Car-Parrinello [Car and Parinello, Phys. Rev. Lett. 55, 2471 (1985)] algorithms is presented to demonstrate the efficacy of the approach. [ABSTRACT FROM AUTHOR]

In this work, our previous simulation method on the calculation of solubility of nonpolar solutes in nonpolar polymers [H. Eslami and F. Müller-Plathe, Macromolecules 40, 6413 (2007)] has been extended to the case of solubility calculation for water, as a polar penetrant, in poly(ethylene terephthalate), as a polar polymer. The chemical potentials of water in the polymer phase and in the gas phase have been calculated by employing our grand canonical ensemble molecular dynamics simulation method [H. Eslami and F. Müller-Plathe, J. Comput. Chem. 28, 1763 (2007)]. In this paper it is shown that performing just two independent simulations, one in the polymer phase and one in the vapor phase, in the grand canonical ensemble, is sufficient to calculate the phase coexistence point. The calculated solubilities, diffusion coefficients, and permeability coefficients are in good agreement with experimental data. Also the calculated glass transition temperature of the wet polymer is shown to be in a very good agreement with experiment. [ABSTRACT FROM AUTHOR]

In this paper, a new solvation model is proposed for simulations of biomolecules in aqueous solutions that combines the strengths of explicit and implicit solvent representations. Solute molecules are placed in a spherical cavity filled with explicit water, thus providing microscopic detail where it is most needed. Solvent outside of the cavity is modeled as a dielectric continuum whose effect on the solute is treated through the reaction field corrections. With this explicit/implicit model, the electrostatic potential represents a solute molecule in an infinite bath of solvent, thus avoiding unphysical interactions between periodic images of the solute commonly used in the lattice-sum explicit solvent simulations. For improved computational efficiency, our model employs an accurate and efficient multiple-image charge method to compute reaction fields together with the fast multipole method for the direct Coulomb interactions. To minimize the surface effects, periodic boundary conditions are employed for nonelectrostatic interactions. The proposed model is applied to study liquid water. The effect of model parameters, which include the size of the cavity, the number of image charges used to compute reaction field, and the thickness of the buffer layer, is investigated in comparison with the particle-mesh Ewald simulations as a reference. An optimal set of parameters is obtained that allows for a faithful representation of many structural, dielectric, and dynamic properties of the simulated water, while maintaining manageable computational cost. With controlled and adjustable accuracy of the multiple-image charge representation of the reaction field, it is concluded that the employed model achieves convergence with only one image charge in the case of pure water. Future applications to pKa calculations, conformational sampling of solvated biomolecules and electrolyte solutions are briefly discussed. [ABSTRACT FROM AUTHOR]

This paper presents comparisons between molecular dynamics simulations (MDSs) and the Keilson and Storer (KS) model for collision-induced translational velocity changes in pure H2 at room temperature from four different points of view. The first considers various autocorrelation functions associated with the velocity. The second and third comparisons are made for the collision kernels and for the time evolutions of some conditional probabilities for changes in the velocity modulus and orientation. Finally, the evolutions, with density, of the half widths of the Q(1) lines of the isotropic Raman (1–0) fundamental band and of the (2–0) overtone quadrupole band are investigated. The results demonstrate that, while the KS approach gives a poor description of detailed velocity-to-velocity changes, it leads to accurate results for the correlation functions and spectral shapes, quantities resulting from large averages over the velocity. On the opposite, collision kernels derived from MDS lead to accurate predictions of all considered quantities. The results open promising perspectives for modeling of the spectral shapes of other systems. They also stress the value of direct calculations of speed-dependent broadening and shifting parameters from the intermolecular potential to avoid their determination from measured spectra and permit fully meaningful tests of the models. [ABSTRACT FROM AUTHOR]

We present results from molecular dynamics simulations for the anisotropic self-diffusion tensor and the velocity autocorrelation functions of monodisperse systems of dense linear chain molecules under flow. Two molecular models are used in these simulations: The finitely extensible nonlinear elastic chain and the freely jointed tangent sphere chain. Nonequilibrium molecular dynamics is used to simulate these systems under planar Couette flow and planar extensional flow. Under planar extensional flow, results presented here are the first, from simulation, for diffusion and velocity autocorrelation functions of molecules, while for planar Couette flow, we compare the broadest range of conditions. An explicit derivation is provided of the Green–Kubo expression for the diffusion tensor. This expression is then used to derive the relation involving the mean-squared displacement—an often used alternative method to calculate diffusion coefficients. Velocity autocorrelation functions have been used, in combination with results on the alignment of molecules from a previous paper, to provide some details of the molecular scale dynamics that influence diffusive transport under flow. [ABSTRACT FROM AUTHOR]

Systems chemistry seeks to find fundamental insights into the emergent properties of complex systems and living matter. Thus chemists use a “bottom-up” approach for the design and integration of simple elements as a means of producing self-organized systems that can serve as feasible models. Toward this end, networks of replicating molecules have been produced and their dynamic behavior was analyzed both experimentally and by simulation. In this paper we describe our analysis of the reaction mechanisms which build up these systems. To do so, we revisit models for self-replication and template assisted catalysis and expand them to describe the kinetics of small catalytic networks. From symmetry requirements and reasonable chemical assumptions, it is shown that the construction of increasingly complex networks requires higher order catalysis. Specifically, we explain why low order catalysis, in which a monomeric molecule serves as a template, is incapable of efficiently activating cooperative cross catalytic elements and basic asymmetric sequentially linked units, so that at least second order catalysis, in which dimeric molecules serve as templates, is necessary. These cooperative and asymmetric linked units are required components of more complex molecular networks. We compare our results with other experimental evidence for the centrality of higher order catalysis and discuss the implications of our results on molecular self-organization and other aspects of systems chemistry. [ABSTRACT FROM AUTHOR]

In this paper, we construct an effective model for the dynamics of an excluded-volume chain under confinement by extending the formalism of Rouse modes. We make specific predictions about the behavior of the modes for a single polymer confined to a tube. The results are tested against Monte Carlo simulations using the bond-fluctuation algorithm which uses a lattice representation of the polymer chain with excluded-volume effects. [ABSTRACT FROM AUTHOR]

In a previous paper [G. Rickayzen and D. M. Heyes, J. Chem. Phys. 126, 234503 (2007)] we investigated by theory and molecular dynamics (MD) simulation the force and velocity autocorrelation functions of a fluid of molecules interacting through steeply varying potentials of the form [lowercase_phi_synonym](r)=4[variant_greek_epsilon][z2(r)-z(r)], where z(r)=(σ/r)n, [variant_greek_epsilon] and σ set the energy and length scale of the interaction, respectively, and n is an adjustable exponent (n=72 and 144 were considered in that work). Discrepancies between the theory and simulation were found except at the shortest times for some of the state points. In order to identify the origin(s) of these discrepancies, we have investigated here another fluid, in which the particles interact via the Morse potential in which z(r)=exp(-κ(r-σ)/σ), where κ is now the “steepness” parameter. The parameter κ is the analog of n, and this potential form is used in order to compare with previous results and establish better the origin of the differences between theory and simulation. It is shown in a further development of the theory that the actual form of the potential in the steep and short-ranged attractive limit is immaterial, and there exists a law of corresponding states for such potentials. This conclusion is confirmed by the MD simulations with the two potential forms for κ=n=144. The difference between the theory and simulation correlation functions increases with density, and it is concluded that these differences probably originate in many-body effects in time, which are absent in the theory. For packing fractions below about 0.2 the agreement between the theory and MD simulation force and velocity autocorrelation functions is nevertheless very good at all accessible times. [ABSTRACT FROM AUTHOR]

Molecular mechanisms of crystal growth and homogeneous nucleation from the melt of polyethylene-like linear polymer are investigated by molecular dynamics simulations. The present paper is aimed at extending our previous work with respect to the system size and the boundary condition, thereby enabling detailed studies on the structures of sufficiently large lamellae and fully equilibrated melt. Lamellae of uniform thickness but with marked tapered edges are found to grow at constant velocity from the substrate. Three-dimensional shape of the growing lamellae exhibits peculiar undulation at the growth front, the origin of which is suggested to be the inhomogeneous thickness distribution within the lamellae. Trajectories of chains crystallizing onto the growth front reveal an unexpected pathway for chain folding, where a partially attached chain stem forms a new fold by plunging its head back into a neighboring stem position through slithering snake motions of the chain. Detailed statistics of folds and cilia show that the folds are rather neat and mostly make re-entries into the nearest or the second or third nearest neighboring stem positions, whereas the cilia are generally short but with a small number of longer cilia forming thick amorphous layers. Structure of supercooled melt investigated versus temperature reveals that, at moderate degree of supercooling, the overall chain conformation remains Gaussian random coil but the persistent length of chains increases monotonically with increasing supercooling. Exceptions are at the largest supercooling where homogeneous nucleation takes place; usual melt structure becomes rapidly unstable and emerges many crystallites of random orientations. During early 10–20 ns after the quench, density of melt, radius of gyration of chains, and fraction of kinked bonds show marked alterations. These structural changes are highly cooperative and are considered simply due to the emergence of many embryonic crystals in the melt. Conformations of the chains forming nuclei are also traced to reveal that the homogeneous nuclei are fringed micelle like aggregates of chains, but the chains as a whole have folded conformations, which are similar to those reported in previous simulations on a single polyethylene in a vacuum. [ABSTRACT FROM AUTHOR]

Milestoning is a procedure to compute the time evolution of complicated processes such as barrier crossing events or long diffusive transitions between predefined states. Milestoning reduces the dynamics to transition events between intermediates (the milestones) and computes the local kinetic information to describe these transitions via short molecular dynamics (MD) runs between the milestones. The procedure relies on the ability to reinitialize MD trajectories on the milestones to get the right kinetic information about the transitions. It also rests on the assumptions that the transition events between successive milestones and the time lags between these transitions are statistically independent. In this paper, we analyze the validity of these assumptions. We show that sets of optimal milestones exist, i.e., sets such that successive transitions are indeed statistically independent. The proof of this claim relies on the results of transition path theory and uses the isocommittor surfaces of the reaction as milestones. For systems in the overdamped limit, we also obtain the probability distribution to reinitialize the MD trajectories on the milestones, and we discuss why this distribution is not available in closed form for systems with inertia. We explain why the time lags between transitions are not statistically independent even for optimal milestones, but we show that working with such milestones allows one to compute mean first passage times between milestones exactly. Finally, we discuss some practical implications of our results and we compare milestoning with Markov state models in view of our findings. [ABSTRACT FROM AUTHOR]