Configurational constant pressure molecular dynamics

We propose two new algorithms for generating isothermal-isobaric molecular dynamics. The algorithms are based on an extended phase space dynamics where two extra degrees of freedom, representing the thermostat and the barostat, are included. These new methods adopt a totally different approach towards molecular dynamics simulation in the isothermal-isobaric ensemble. They are fully configurational in the sense that only the particle positions are required in the control of the system temperature and pressure. Following on from the works of Delhommelle and Evans [Mol. Phys., 99, 1825 (2001)] and of Braga and Travis [J. Chem. Phys., 123, 134101 (2005)] concerning configurational canonical dynamics, these new algorithms can be seen as a natural extension to the isothermal-isobaric ensemble. We have validated both of our new configurational isothermal-isobaric schemes by conducting molecular dynamics simulations of a Lennard-Jones fluid and comparing the static and dynamic properties for a single state point. We find that both schemes generate similar results compared with schemes which use kinetic temperature and pressure control. We have also monitored the response of the system to a series of isothermal compressions and isobaric quenches. We find that the configurational schemes performed at least as well as the kinetic based scheme in bringing the system temperature and pressure into line with the set point values of these variables. These new methods will potentially play a significant role in simulations where the calculation of the kinetic temperature and pressure can be problematic. A well known example resides in the field of nonequilibrium simulations where the kinetic temperature and pressure require a knowledge of the streaming velocity of the fluid in order to calculate the true peculiar velocities (or momenta) that enter into their definitions. These are completely avoided by using our configurational thermostats and barostats, since these are independent of momenta. By extending the analysis of Kusnezov et al. [Ann. Phys., 204, 155 (1990)] in order to derive a set of generalized Nose-Hoover equations of motion which can generate isothermal-isobaric dynamics in a number of different ways, we are able to show that both of our new configurational barostats and Hoover's kinetic isothermal-isobaric scheme are special cases of this more general set of equations. This generalization can be very powerful in generating constant pressure dynamics for a variety of systems.     

Configurational entropy: an improvement of the quasiharmonic approximation using configurational temperature

One challenge in computational biophysics and biology is to develop methodologies able to estimate accurately the configurational entropy of macromolecules. Among many methods, the quasiharmonic approximation (QH) is most widely used as it is simple in both theory and implementation. However, it has been shown that this method becomes inaccurate by overestimating entropy for systems with rugged free energy landscapes. Here, we propose a simple method to improve the QH approximation, i.e., to reduce QH entropy. We approximate the potential energy landscape of the system by an effective harmonic potential, and request that this potential must produce exactly the configurational temperature of the system. Due to this constraint, the force constants associated with the effective harmonic potential are increased, or equivalently, entropy of motion governed by this effective harmonic potential is reduced. We also introduce the effective configurational temperature concept which can be used as an indicator to check the anharmonicity of the free energy landscape. To validate the new method we compare it with the recently developed expansion approximate method by calculating entropy of one simple model system and two peptides with 3 and 16 amino acids either in gas phase or in explicit solvent. We show that the new method appears to be a good choice in practice as it is a compromise between accuracy and computational speed. A modification of the expansion approximate method is also introduced and advantages are discussed in some detail.     

Landscapes and fragilities

The concept of fragility provides a possibility to rank different supercooled liquids on the basis of the temperature dependence of dynamic and/or thermodynamic quantities. We recall here the definitions of kinetic and thermodynamic fragility proposed in the last years and discuss their interrelations. At the same time we analyze some recently introduced models for the statistical properties of the potential energy landscape. Building on the Adam-Gibbs relation, which connects structural relaxation times to configurational entropy, we analyze the relation between statistical properties of the landscape and fragility. We call attention to the fact that the knowledge of number, energy depth, and shape of the basins of the potential energy landscape may not be sufficient for predicting fragility. Finally, we discuss two different possibilities for generating strong behavior.     

Fragility of glass-forming polymer liquids

The fragility of polymeric glass-forming liquids is calculated as a function of molecular structural parameters from a generalized entropy theory of polymer glass-formation that combines the Adam-Gibbs (AG) model for the rate of structural relaxation with the lattice cluster theory (LCT) for polymer melt thermodynamics. Our generalized entropy theory predicts the existence of distinct high and low temperature regimes of glass-formation that are separated by a thermodynamically well-defined crossover temperature T(I) at which the product of the configurational entropy and the temperature has an inflection point. Since the predicted temperature dependence of the configurational entropy and structural relaxation time are quite different in these temperature regimes, we introduce separate definitions of fragility for each regime. Experimentally established trends in the fragility of polymer melts with respect to variations in polymer microstructure and pressure are interpreted within our theory in terms of the accompanying changes in the chain packing efficiency.     

Comparing landscape calculations with calorimetric data on ortho-terphenyl, and the question of the configurational fraction of the excess entropy

Mossa et al. [Phys. Rev. E 65, 041205 (2002)] have calculated the total and configurational entropies of supercooled ortho-terphenyl liquid using the potential-energy landscape formalism and a simplified model of the intermolecular potential. I show here that the agreement of their calculated configurational entropy with the experimental data depends on what is assumed about the configurational fraction of the excess entropy and its temperature dependence. In particular, if the configurational fraction is taken as 0.70 and independent of temperature the agreement is excellent; if a marked temperature dependence of that fraction inferred from calorimetric data is assumed the agreement is only fair at best. This marked temperature dependence of the configurational fraction also implies some implausible behavior of contributions to the excess entropy at the Kauzmann temperature, but no obvious reason for disregarding it presents itself.     

Chiral and supramolecular model complexes for vanadium haloperoxidases: Host–guest systems and hydrogen bonding relays for vanadate species

Supramolecular interactions and hydrogen bonding play a fundamental role in determining both structure and function of vanadate in enzymatic systems and in particular for the active site of vanadium haloperoxidases. Vanadium complexes with N-salicylidene hydrazide ligands provide a versatile approach towards molecular model systems with hydrogen bonding interactions. The variation of the side chains within these hydrazone ligands provides the ability to introduce chirality in molecular model complexes by the utilization of appropriate carbohydrate fragments. Moreover, the synthetic potential and the transformation reactions found for dioxidovanadium(V) complexes with N-salicylidene hydrazide ligands are reminiscent of what is usually observed for carboxylates and can therefore be regarded as their inorganic counterpart. The anisotropy effect of the oxido groups in vanadium complexes is a valuable tool that allows for the configurational and conformational analysis of structures with corresponding chelate rings. Utilizing appropriate vanadium complexes it is possible to generate inclusion compounds with cyclodextrins. The dependence of solid state and solution structures on the ring size of the cyclodextrin is discussed.     

Dependence of the fragility of a glass former on the softness of interparticle interactions

We study the influence of the softness of the interparticle interactions on the fragility of a glass former by considering three model binary mixture glass formers. The interaction potential between particles is a modified Lennard-Jones type potential, with the repulsive part of the potential varying with an inverse power q of the interparticle distance, and the attractive part varying with an inverse power p. We consider the combinations (12,11) (model I), (12,6) (model II), and (8,5) (model III) for (q,p) such that the interaction potential becomes softer from model I to III. We evaluate the kinetic fragilities from the temperature variation of diffusion coefficients and relaxation times, and a thermodynamic fragility from the temperature variation of the configurational entropy. We find that the kinetic fragility increases with increasing softness of the potential, consistent with previous results for these model systems, but at variance with the thermodynamic fragility, which decreases with increasing softness of the interactions, as well as expectations from earlier results. We rationalize our results by considering the full form of the Adam-Gibbs relation, which requires, in addition to the temperature dependence of the configurational entropy, knowledge of the high temperature activation energies in order to determine fragility. We show that consideration of the scaling of the high temperature activation energy with the liquid density, analyzed in recent studies, provides a partial rationalization of the observed behavior.     

Laser Diagnostics of surface-emitted Na2 molecules

We report investigation on Na₂ molecules emitted from a liquid sodium surface into a vacuum. Vibrational and rotational temperatures of the emitted molecules agree with the temperature of the sodium surface, and the angular momenta of the emitted molecules are isotropically distributed. The experiments demonstrate an application of laser diagnostics for studies of a gas-liquid interface.     

Molecular dynamics simulation of liquid water and ice nanoclusters using a new effective HFD‐like model

We have determined a new two‐body interaction potential of water by the inversion of viscosity collision integrals of water vapor and fitted to achieve the Hartree–fock dispersion‐like (HFD‐like) potential function. The calculated two‐body potential generates the thermal conductivity, viscosity, and self‐diffusion coefficient of water vapor in an excellent accordance with experimental data at wide temperature ranges. We have also used a new many‐body potential as a function of temperature and density with the HFD‐like pair‐potential of water to improve the two‐body properties better than the SPC, SPC/E, TIP3P, and TIP4P models. We have also used the new corrected potential to simulate the configurational energy and the melting temperatures of the (H₂O)₅₀₀, (H₂O)₈₆₄, (H₂O)₂₀₄₈, and (H₂O)₆₉₁₂ ice nanoclusters in good agreement with the previous simulation data using the TIP4P model. The extrapolated melting point at the bulk limit is also in better agreement with the experimental bulk data. The self‐diffusion coefficients for the ice nanoclusters also simulated at different temperatures. © 2017 Wiley Periodicals, Inc.     

Discrete breathers for understanding reconstructive mineral processes at low temperatures

Reconstructive transformations in layered silicates need a high temperature in order to be observed. However, very recently, some systems have been found where transformation can be studied at temperatures 600 degrees C below the lowest experimental results previously reported, including sol-gel methods. We explore the possible relation with the existence of intrinsic localized modes, known as discrete breathers. We construct a model for nonlinear vibrations within the cation layer, obtain their parameters, and calculate them numerically, obtaining their energies. Their statistics show that, although there are far less breathers than phonons, there are much more above the activation energy, making them good candidates to explain the reconstructive transformations at low temperatures.     

Denaturation of Drew-Dickerson DNA in a high salt concentration medium: molecular dynamics simulations

We have performed molecular dynamics simulation on B-DNA duplex (CGCGAATTGCGC) at different temperatures. The DNA was immerged in a salt-water medium with 1 M NaCl concentration to investigate salt effect on the denaturation process. At each temperature, configurational entropy is estimated using the covariance matrix of atom-positional fluctuations, from which the melting temperature (T(m)) was found to be 349 K. The calculated configuration entropy for different bases shows that the melting process involves more peeling (including fraying from the ends) conformations, and therefore the untwisting of the duplex and peeling states form the transition state of the denaturation process. There is a narrow minor groove in the AATT sequence that becomes wider by increasing temperature which disappears at high temperatures, especially above the melting temperature. We have also calculated the fraction of denatured base pairs, f-curve, from which T(m) was found to be 340 K, close to experimental value of 341 K. We found that DNA at high salt concentrations has few hydrogen bonds even at temperatures higher than the T(m). Our calculations show the fact that adding salt leads to increase of T(m) and stabilization of DNA.     

Configurational temperature control for atomic and molecular systems

A new configurational temperature thermostat suitable for molecules with holonomic constraints is derived. This thermostat has a simple set of motion equations, can generate the canonical ensemble in both position and momentum space, acts homogeneously through the spatial coordinates, and does not intrinsically violate the constraints. Our new configurational thermostat is closely related to the kinetic temperature Nosé-Hoover thermostat with feedback coupled to the position variables via a term proportional to the net molecular force. We validate the thermostat by comparing equilibrium static and dynamic quantities for a fluid of n-decane molecules under configurational and kinetic temperature control. Practical aspects concerning the implementation of the new thermostat in a MOLECULAR DYNAMICS code and the potential applications are discussed.     

Non-Gaussian energy landscape of a simple model for strong network-forming liquids: Accurate evaluation of the configurational entropy

We present a numerical study of the statistical properties of the potential energy landscape of a simple model for strong network-forming liquids. The model is a system of spherical particles interacting through a square-well potential, with an additional constraint that limits the maximum number of bonds Nmax per particle. Extensive simulations have been carried out as a function of temperature, packing fraction, and Nmax. The dynamics of this model are characterized by Arrhenius temperature dependence of the transport coefficients and by nearly exponential relaxation of dynamic correlators, i.e., features defining strong glass-forming liquids. This model has two important features: (i) Landscape basins can be associated with bonding patterns. (ii) The configurational volume of the basin can be evaluated in a formally exact way, and numerically with an arbitrary precision. These features allow us to evaluate the number of different topologies the bonding pattern can adopt. We find that the number of fully bonded configurations, i.e., configurations in which all particles are bonded to Nmax neighbors, is extensive, suggesting that the configurational entropy of the low temperature fluid is finite. We also evaluate the energy dependence of the configurational entropy close to the fully bonded state and show that it follows a logarithmic functional form, different from the quadratic dependence characterizing fragile liquids. We suggest that the presence of a discrete energy scale, provided by the particle bonds, and the intrinsic degeneracy of fully bonded disordered networks differentiates strong from fragile behavior.     

From A to B in free energy space

The authors present a new method for searching low free energy paths in complex molecular systems at finite temperature. They introduce two variables that are able to describe the position of a point in configurational space relative to a preassigned path. With the help of these two variables the authors combine features of approaches such as metadynamics or umbrella sampling with those of path based methods. This allows global searches in the space of paths to be performed and a new variational principle for the determination of low free energy paths to be established. Contrary to metadynamics or umbrella sampling the path can be described by an arbitrary large number of variables, still the energy profile along the path can be calculated. The authors exemplify the method numerically by studying the conformational changes of alanine dipeptide.     

Water-protein dynamic coupling and new opportunities for probing it at low to physiological temperatures in aqueous solutions

Both the structure and dynamics of biomolecules are known to be essential for their biological function. In the dehydrated state, the function of biomolecules, such as proteins, is severely impeded, so hydration is required for bioactivity. The dynamics of the hydrated biomolecules and their hydration water are related - but how closely? The problem involves several layers of complexity. Even for water in the bulk state, the contribution from various dynamic components to the overall dynamics is not fully understood. In biological systems, the effects of confinement on the hydration water further complicate the picture. Even if the various components of the hydration water dynamics are properly understood, which of them are coupled to the protein dynamics, and how? The studies of protein dynamics over the wide temperature range, from physiological to low temperatures, provide some answers to these question. At low temperatures, both the protein and its hydration water behave as solids, with only vibrational degrees of freedom. As the temperature is increased, non-vibrational dynamic components start contributing to the measurable dynamics and eventually become dominant at physiological temperatures. Thus, the temperature dependence of the dynamics of protein and its hydration water may allow probing various dynamic components separately. In order to suppress the water freezing, the low-temperature studies of protein rely on either low-hydrated samples (essentially, hydrated protein powders), or cryo-protective solutions. Both approaches introduce the hydration environments not characteristic of the protein environments in living systems, which are typically aqueous protein solutions of various concentrations. In this paper, we discuss the coupling between the dynamic components of the protein and its hydration water by critical examining of the existing literature, and then propose that proteins can be studied in an aqueous solution that is remarkably similar in its dynamic properties to pure water, yet does not freeze down to about 200 K, even in the bulk form. The first experiment of this kind using quasielastic neutron scattering is discussed, and more experiments are proposed.     

Multi-overlap molecular dynamics methods for biomolecular systems

We propose a molecular dynamics method for the multi-overlap algorithm. By utilizing a non-Boltzmann weight factor, this method realizes a random walk in the overlap space at a constant temperature and explores widely in the configurational space, where the overlap of a configuration with respect to a reference state is a measure for structural similarity. We can obtain detailed information about the free-energy landscape and the transition states among any specific reference conformations at that temperature. We also introduce a multi-dimensional extension of the multi-overlap algorithm. Appling this multi-dimensional method to a penta peptide, Met-enkephalin, we demonstrate its effectiveness.     

Activation processes with memory

We propose a mathematical treatment of the activated processes governed by stochastic Langevin dynamics with a colored random force, corresponding to a noise generated by an Ornstein-Uhlenbeck process. Such non-Markovian dynamics take place in a variety of chemical and biological systems. Using the path integral approach, we constructed the conditional probability for passing between two stationary states in configurational space. Our relations can be used for Monte Carlo sampling of evolution trajectories for systems with many degrees of freedom as well as for determining the reaction coordinate used in transition state theory. On the basis of our relation for a conditional probability, we generalize the method of determining the most probable path to the case of colored random force. Using the simple three-hole potential, we examine numerically the effect of nonzero correlation time (memory) on the evolution of the most probable path for a finite temperature.     

Free energy of the solid C60 fullerene orientational order-disorder transition

The free energies of the orientationally ordered crystal phase of C60 at low temperatures and the disordered crystal phase at high temperatures are calculated to an accuracy of +/-0.05 kJ/mol using the expanded ensemble Monte Carlo method with the potential model of Sprik et al. [J. Phys. Chem. 96, 2027 (1992)]. The order-disorder transition temperature at zero pressure is determined directly from these free energies, and is found to be consistent with the abrupt changes in configurational energy and unit cell size also found in simulation. A modification of the potential results in predictions of the transition temperature of 257 K and the entropy change of 18.1 J/mol K at this transition, which are in good agreement with the experimental values of 260 K and 19 J/mol K, respectively. The orientational distinguishability in the ordered phase and the indistinguishability in the disordered phase lead to a contribution to the entropy difference of k ln 60, with 60 being the symmetry number of C60. This quantum mechanical correction is important for the accurate prediction of the phase transition properties of the C60 crystals.