Monte Carlo simulations of polymer dynamics: Recent advances

A brief review is given of applications of Monte Carlo simulations to study the dynamical properties of coarse-grained models of polymer melts, emphasizing the crossover from the Rouse model toward reptation, and the glass transition. The extent to which Monte Carlo algorithms can mimic the actual chain dynamics is critically examined, and the need for the use of coarse-grained rather than fully atomistic models for such simulations is explained. It is shown that various lattice and continuum models yield qualitatively similar results, and the behavior agrees with the findings of corresponding molecular dynamics simulations and experiments, where available. It is argued that these simulations significantly enhance our understanding of the theoretical concepts on the dynamics of dense macromolecular systems. © 1997 John Wiley & Sons, Inc.     

Ab initio molecular dynamics of protonated dialanine and comparison to infrared multiphoton dissociation experiments

Finite temperature Car-Parrinello molecular dynamics simulations are performed for the protonated dialanine peptide in vacuo, in relation to infrared multiphoton dissociation experiments. The simulations emphasize the flexibility of the different torsional angles at room temperature and the dynamical exchange between different conformers which were previously identified as stable at 0 K. A proton transfer occurring spontaneously at the N-terminal side is also observed and characterized. The theoretical infrared absorption spectrum is computed from the dipole time correlation function, and, in contrast to traditional static electronic structure calculations, it accounts directly for anharmonic and finite temperature effects. The comparison to the experimental infrared multiphoton dissociation spectrum turns out very good in terms of both band positions and band shapes. It does help the identification of a predominant conformer and the attribution of the different bands. The synergy shown between the experimental and theoretical approaches opens the door to the study of the vibrational properties of complex and floppy biomolecules in the gas phase at finite temperature.     

Combined electronic structure/molecular dynamics approach for ultrafast infrared spectroscopy of dilute HOD in liquid H2O and D2O

We present a new approach that combines electronic structure methods and molecular dynamics simulations to investigate the infrared spectroscopy of condensed phase systems. This approach is applied to the OH stretch band of dilute HOD in liquid D2O and the OD stretch band of dilute HOD in liquid H2O for two commonly employed models of water, TIP4P and SPC/E. Ab initio OH and OD anharmonic transition frequencies are calculated for 100 HOD x (D2O)n and HOD x(H2O)n (n = 4-9) clusters randomly selected from liquid water simulations. A linear empirical relationship between the ab initio frequencies and the component of the electric field from the solvent along the bond of interest is developed. This relationship is used in a molecular dynamics simulation to compute frequency fluctuation time-correlation functions and infrared absorption line shapes. The normalized frequency fluctuation time-correlation functions are in good agreement with the results of previous theoretical approaches. Their long-time decay times are 0.5 ps for the TIP4P model and 0.9 ps for the SPC/E model, both of which appear to be somewhat too fast compared to recent experiments. The calculated line shapes are in good agreement with experiment, and improve upon the results of previous theoretical approaches. The methods presented are simple, and transferable to more complicated systems.     

Hydration of Lanthanoids(III) and Actinoids(III): An Experimental/Theoretical Saga

The latest experimental and theoretical studies on structural and dynamical properties of lanthanoid(III) and actinoid(III) ions in water have been reviewed. In the last years, most of the issues about lanthanoid(III) hydration have been resolved combining X-ray absorption experiments and different theoretical methods. Since 2008 an effort has been made to treat the entire series thus obtaining coherent sets of experimental and theoretical results that were lately put together in such a way that it was possible to derive new basic properties, such as effective ionic radii, across the series. While for the hydration of lanthanoids(III) many experiments and simulations have been reported, the hydration of actinoids(III) was less investigated. There are some experiments performed by different research groups and few simulations that we discuss in this review. Currently, there are enough results that it is possible to gain some understanding of the hydration behavior of lanthanoids(III) and actinoids(III). The ultimate goal of this review is to provide clues on the analogies and differences between the two series. These aspects are connected to several issues: 1)?technological: the separation of these elements that is necessary for recycling and stocking of nuclear waste, 2)?practical: because experiments on actinoids need particular care, the definition of possible analogies will give the possibility to use the correct lanthanoid when the information on a specific actinoid is needed, 3)?fundamental: related to chemical similarities between the two series.     

Ultrafast dynamics in reverse micelles,microemulsions, and vesicles

Recently techniques of solvation dynamics have been applied to reverse micelles, microemulsions and vesicular systems. The dynamical data obtained provides a complement to steady-state experiments and builds an understanding of the details of these systems. Recent molecular dynamics simulations show the power of combined experiments and simulations.     

Temporal asymmetry of fluctuations in nonequilibrium steady states: links with correlation functions and nonlinear response

The presence of temporal asymmetries in fluctuation paths of nonequilibrium systems has recently been confirmed numerically in nonequilibrium molecular dynamics simulations of particular deterministic systems. Here we show that this is a common feature of homogeneously driven and thermostatted, reversible, deterministic, chaotic, nonequilibrium systems of interacting particles. This is done by expressing fluctuation paths as correlation functions. The theoretical arguments look rather general, and we expect them to easily extend to other forms of driving and thermostats. The emergence of asymmetry is also justified using the transient time correlation function expression of nonlinear response theory. Numerical simulations are used to verify our arguments.     

Energy transfer in the nanostar: the role of coulombic coupling and dynamics

We present a theoretical investigation of energy transfer in the phenylene ethynelene dendrimer known as the nanostar. Data from extensive molecular dynamics simulations are used to model the dynamical effects caused by torsional motion of the phenyl groups. We compare rate constants for energy transfer between the two-ring chromophore and the three-ring chromophore obtained via the F?rster model, the ideal dipole approximation (IDA), and the transition density cube (TDC) method, which has as its limit an exact representation of the Coulombic coupling. We find that the rate constants obtained with the TDC are extremely sensitive to the phenyl group rotation, whereas the constants computed with the F?rster model and the IDA are not. The implications of these results for the interpretation of recent pump-probe experiments on the nanostar are discussed in detail. Finally, we predict the temperature dependence of the rate constant for energy transfer.     

Liquid-vapor interfaces of water-acetonitrile mixtures of varying composition

Detailed molecular-dynamics simulations are carried out to investigate the equilibrium and dynamical properties of water-acetonitrile mixtures of varying composition. Altogether, we have simulated eight different systems of different concentrations of acetonitrile. The inhomogeneous density and anisotropic orientational profiles at interfaces, surface tension, and also the distribution of hydrogen bonds are calculated for both water and acetonitrile molecules. The dynamical aspects of the interfaces are investigated in terms of the anisotropic diffusion and dipole orientational relaxation of interfacial water and acetonitrile molecules. For both structural and dynamical properties, the behaviors of the interfaces are compared with those of the corresponding bulk phases. A comparison between the present theoretical results and experimental findings, wherever available, is also made to verify the usefulness of the molecular models employed in the present study for predicting interfacial properties.     

Mode-coupling theory for multiple-time correlation functions of tagged particle densities and dynamical filters designed for glassy systems

The theoretical framework for higher-order correlation functions involving multiple times and multiple points in a classical, many-body system developed by Van Zon and Schofield [Phys. Rev. E 2002, 65, 011106] is extended here to include tagged particle densities. Such densities have found an intriguing application as proposed measures of dynamical heterogeneities in structural glasses. The theoretical formalism is based upon projection operator techniques which are used to isolate the slow time evolution of dynamical variables by expanding the slowly evolving component of arbitrary variables in an infinite basis composed of the products of slow variables of the system. The resulting formally exact mode-coupling expressions for multiple-point and multiple-time correlation functions are made tractable by applying the so-called N-ordering method. This theory is used to derive for moderate densities the leading mode coupling expressions for indicators of relaxation type and domain relaxation, which use dynamical filters that lead to multiple-time correlations of a tagged particle density. The mode coupling expressions for higher order correlation functions are also successfully tested against simulations of a hard sphere fluid at relatively low density.     

Experimental and theoretical study of the photodissociation of bromo-3-fluorobenzene

The UV photodissociation of bromo-3-fluorobenzene under collisionless conditions has been studied as a function of the excitation wavelength between 255 and 265 nm. The experiments were performed using ultrafast pump-probe laser spectroscopy. To aid in the interpretation of the results, it was necessary to extend the theoretical framework substantially compared to previous studies, to also include quantum dynamical simulations employing a two-dimensional nuclear Hamiltonian. The nonadiabatic potential energy surfaces (PES) were parameterized against high-level MS-CASTP2 quantum chemical calculations, using both the C-Br distance and the out-of-plane bending of the bromine as nuclear parameters. We show that the wavelength dependence of the photodissociation via the S0-->1pipi*-->1pisigma* channel, accessible with a approximately 260 nm pulse, is captured in this model. We thereby present the first correlation between experiments and theory within the quantitative regime.     

Dissipative particle dynamics simulations of polymer melts. I. Building potential of mean force for polyethylene and cis-polybutadiene

We present the derivation of coarse-grained force fields for two types of polymers, polyethylene (PE), and cis-polybutadiene (cis-PB), using the concept of potential of mean force. Coarse-grained force fields were obtained from microscopic simulations for several coarse-graining levels, i.e., different number of monomers lambda per mesoscopic unit called "bead." These force fields are then used in dissipative particle dynamics (DPD) simulations to study structural and dynamical properties of polymer melts of PE and cis-PB. The radial distribution functions g(R), the end-to-end distance R0, the end-to-end vector relaxation time tau, and the chain center of mass self-diffusion D(CM), are computed for different chain lengths at different coarse-graining factor lambda. Scaling laws typical of the Rouse regime are obtained for both polymers for chain lengths ranging from 6 to 50 beads. It is found that the end-to-end distance R0 obtained from DPD simulations agree well with values obtained from both microscopic simulations and experiments. The dependence of the friction coefficient used in DPD simulations versus the coarse-graining level is discussed in view of the overall scaling of the dynamical properties.     

Molecular dynamics of C-peptide of ribonuclease A studied by replica-exchange Monte Carlo method and diffusion theory

Generalized-ensemble algorithm and diffusion theory have been combined in order to compute the dynamical properties monitored by nuclear magnetic resonance (NMR) experiments from efficient and reliable evaluation of statistical averages. Replica-exchange Monte Carlo simulations have been performed with a C-peptide analogue of ribonuclease A, and the Smoluchowski diffusion equation has been applied. A fairly good agreement between the calculated and measured ¹H-NOESY NMR cross peaks has been obtained. The combination of these advanced and continuously improving statistical tools allows the calculation of a wide variety of dynamical properties routinely obtained by experiments.     

Dynamic coupling between the LID and NMP domain motions in the catalytic conversion of ATP and AMP to ADP by adenylate kinase

The catalytic conversion of adenosine triphosphate (ATP) and adenosine monophosphate (AMP) to adenosine diphosphate (ADP) by adenylate kinase (ADK) involves large amplitude, ligand induced domain motions, involving the opening and the closing of ATP binding domain (LID) and AMP binding domain (NMP) domains, during the repeated catalytic cycle. We discover and analyze an interesting dynamical coupling between the motion of the two domains during the opening, using large scale atomistic molecular dynamics trajectory analysis, covariance analysis, and multidimensional free energy calculations with explicit water. Initially, the LID domain must open by a certain amount before the NMP domain can begin to open. Dynamical correlation map shows interesting cross-peak between LID and NMP domain which suggests the presence of correlated motion between them. This is also reflected in our calculated two-dimensional free energy surface contour diagram which has an interesting elliptic shape, revealing a strong correlation between the opening of the LID domain and that of the NMP domain. Our free energy surface of the LID domain motion is rugged due to interaction with water and the signature of ruggedness is evident in the observed root mean square deviation variation and its fluctuation time correlation functions. We develop a correlated dynamical disorder-type theoretical model to explain the observed dynamic coupling between the motion of the two domains in ADK. Our model correctly reproduces several features of the cross-correlation observed in simulations.     

Establishing effective simulation protocols for beta- and alpha/beta-peptides. II. Molecular mechanical (MM) model for a cyclic beta-residue

All-atom molecular mechanical (MM) force field parameters are developed for a cyclic beta-amino acid, amino-cyclo-pentane-carboxylic acid (ACPC), using a multi-objective evolutionary algorithm. The MM model is benchmarked using several short, ACPC-containing alpha/beta-peptides in water and methanol with SCC-DFTB (self consistent charge-density functional tight binding)/MM simulations as the reference. Satisfactory agreements are found between the MM and SCC-DFTB/MM results regarding the distribution of key dihedral angles for the tetra-alpha/beta-peptide in water. For the octa-alpha/beta-peptide in methanol, the MM and SCC-DFTB/MM simulations predict the 11- and 14/15-helical form as the more stable conformation, respectively; however, the two helical forms are very close in energy (2-4 kcal/mol) at both theoretical levels, which is also the conclusion from recent NMR experiments. As the first application, the MM model is applied to an alpha/beta-pentadeca-peptide in water with both explicit and implicit solvent models. The stability of the peptide is sensitive to the starting configuration in the explicit solvent simulations due to their limited length ( approximately 10-40 ns). Multiple ( approximately 20 x 20 ns) implicit solvent simulations consistently show that the 14/15-helix is the predominant conformation of this peptide, although substantially different conformations are also accessible. The calculated nuclear Overhauser effect (NOE) values averaged over different trajectories are consistent with experimental data, which emphasizes the importance of considering conformational heterogeneity in such comparisons for highly dynamical peptides.     

Liquid-vapor interfacial properties of water-ammonia mixtures: dependence on ammonia concentration

The equilibrium and dynamical properties of the liquid-vapor interfaces of water-ammonia mixtures are investigated by means of molecular-dynamics simulations. Altogether, we have simulated seven different systems of different concentration of ammonia. The inhomogeneous density, anisotropic orientational profiles, surface tension, and the pattern of hydrogen bonding are calculated for both water and ammonia molecules in order to characterize the location, width, thermodynamic aspects, and microscopic structure of the liquid-vapor interfaces of each of the water-ammonia systems. The dynamical aspects of the interfaces are investigated in terms of the anisotropic diffusion and dipole orientational relaxation of water and ammonia molecules. The properties of the interfaces are compared with those of the corresponding bulk phases. The present theoretical results are also compared with experimental findings wherever available.     

Multiple time scale molecular dynamics for fluids with orientational degrees of freedom. I. Microcanonical ensemble

We propose a new approach to eliminate the resonance instabilities inherent in multiple time step molecular dynamics simulations. The approach is developed within the microcanonical ensemble on the basis of an energy-constrained technique in the presence of orientational degrees of freedom. While the single and standard multiscale methods are restricted to small time steps of 5 and 8 fs, respectively, it is shown in simulations of water that the algorithms we have derived postpone the appearance of the instabilities to larger steps of about 16 fs. Such steps are close to the upper theoretical limit of 20 fs peculiar to the microcanonical ensemble and can be used without affecting static and dynamical properties.     

Extending the fluctuation theorem to describe reaction coordinates

The fluctuation theorem describes the distribution of work done on small systems which have been pushed out of equilibrium in response to an external field. The theorem has recently been a subject of much interest for describing single-molecule experiments and simulations. In this communication, it is shown how the fluctuation theorem can be extended to describe fluctuations not only in the work done on a system, but also in a reaction coordinate. The extension explored in this work allows for a generalized derivation of Hummer and Szabo's expression (G. Hummer and A. Szabo, Proc. Natl. Acad. Sci. 98, 3658 (2001)) for reconstructing the potential of mean force from nonequilibrium trajectories. The derivation demonstrates how implementation of this expression can be more easily facilitated. Atomistic simulations of a biomolecular system are presented which support these results.     

Real-space, real-time calculation of dynamic hyperpolarizabilities

The finite-difference method to calculate hyperpolarizabilities is generalized for dynamical case. The calculation of the dynamical hyperpolarizabilities from non-perturbative, explicitly time-dependent single particle states obtained in the framework of the time-dependent density functional theory, is implemented in real space and real time. The optical response functions up to the third order are extracted in frequency domain. The present approach is free of deficiencies associated with atom centered basis sets and allows treatment of large molecules. The calculated results are in good agreement with experiments and with other theoretical calculations for various test cases.     

Coarse-grained description of polymer blends as interacting soft-colloidal particles

We present a theoretical approach which maps polymer blends onto mixtures of soft-colloidal particles. The analytical mesoscale pair correlation functions reproduce well data from united atom molecular dynamics simulations of polyolefin mixtures without fitting parameters. The theory exactly recovers the analytical expressions for density and concentration fluctuation structure factors of soft-colloidal mixtures (liquid alloys).     

Non-meanfield deterministic limits in chemical reaction kinetics

A general mechanism is proposed by which small intrinsic fluctuations in a system far from equilibrium can result in nearly deterministic dynamical behaviors which are markedly distinct from those realized in the meanfield limit. The mechanism is demonstrated for the kinetic Monte Carlo version of the Schnakenberg reaction where we identified a scaling limit in which the global deterministic bifurcation picture is fundamentally altered by fluctuations. Numerical simulations of the model are found to be in quantitative agreement with theoretical predictions.