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.     

A configurational temperature Nosé-Hoover thermostat

We propose two new thermostats which can be employed in computer simulations to ensure that two different variants of the configurational temperature fluctuate around their equilibrium values. These new thermostats differ from one previously introduced by Delhommelle and Evans [Mol. Phys. 99, 1825 (2001)] in several important ways. First, our thermostats are derived in the same spirit as the Nosé-Hoover thermostat and therefore generate the canonical phase-space distribution. Second, our thermostats involve simpler equations of motion, which do not involve spatial gradients of the configurational temperature. They do not suffer from problems stemming from stiff equations of motion and furthermore, in large temperature perturbation simulations, the measured temperature follows the set-point temperature without any overshoot, and with good damping of oscillations. We show that both of our configurational thermostats are special cases of a more general set of Nosé-Hoover equations proposed by Kusnezov et al. [Ann. Phys. 204, 155 (1990)]. The new thermostats are expected to be highly useful in nonequilibrium simulations, particularly those characterized by spatial inhomogeneities. They should also find applicability in simulations involving large changes in temperature over small time scales, such as temperature quench molecular dynamics and radiation damage modeling.     

An isothermal-isobaric Langevin thermostat for simulating nanoparticles under pressure: application to Au clusters.

We present a method for simulating clusters or molecules subjected to an external pressure, which is exerted by a pressure-transmitting medium. It is based on the canonical Langevin thermostat, but extended in such a way that the Brownian forces are allowed to operate only from the region exterior to the cluster. We show that the frictional force of the Langevin thermostat is linked to the pressure of the reservoir in a unique way, and that this property manifests itself when the particle it acts upon is not pointlike but has finite dimensions. By choosing appropriately the strength of the random forces and the friction coefficient, both temperature and pressure can be controlled independently. We illustrate the capabilities of this new method by calculating the compressibility of small gold clusters under pressure.     

A configurational temperature for molecules with hard-core or discontinuous interactions

We extend the usual formula for a configurational temperature so that it applies to condensates in which the molecules interact through hard-core or discontinuous potentials. The new formula involves extra terms which may be calculated during the course of a simulation. The formula is tested by its application to a number of systems with discontinuous or hard-core potentials in thermodynamic equilibrium. Metropolis Monte Carlo simulations were performed on these systems in a canonical ensemble and the configurational temperature is compared with the input temperature. The two are in agreement to within less than 0.1%.     

Configurational temperatures and interactions in charge-stabilized colloid

A system's temperature can be expressed in terms of its constituents' instantaneous positions rather than their momenta. Such configurational temperature definitions offer substantial benefits for experimental studies of soft condensed matter systems, most notably their applicability to overdamped systems whose instantaneous momenta may not be accessible. We demonstrate that the configurational temperature formalism can be derived from the classical hypervirial theorem, and introduce a hierarchy of hyperconfigurational temperature definitions, which are particularly well suited for experimental studies. We then use these analytical tools to probe the electrostatic interactions in monolayers of charge-stabilized colloidal spheres confined by parallel glass surfaces. The configurational and hyperconfigurational temperatures, together with a thermodynamic sum rule, provide previously lacking self-consistency tests for interaction measurements based on digital video microscopy, and thereby cast light on controversial reports of confinement-induced like-charge attractions. We further introduce a method to determine unknown parameters in a model potential by using consistency of the configurational and hyperconfigurational temperatures as a set of constraints. This approach, in principle, also should provide the basis for a model-free estimation of the pair potential.     

玻璃化液体中构型熵与展宽弛豫函数关系的研究

The relationship between the transport properties and thermodynamic properties in glass forming liquids was investigated. The configurational entropy of Adam-Gibbs theory on cooperatively rearranging regions and the theoretic function derived from extremal value model were used to propose a brief that non-exponential stretched exponent in KWW form relaxation function is equal to the relative configurational entropy of cooperatively rearranging region in liquids, and is inversely proportional to the critical number of molecules occurring configurational transformation in a cooperatively rearranging region. Therefore, the new physical significance on glassy configuration is imposed on the stretched exponent, and theoretical developments and empirical correlations between the structural relaxation and configurational entropy are established. Further, an improved expression of β(T) was proposed to eliminate the deviation of the fit by using Vogel-Fulcher-Tammann equation from viscosity data at higher temperatures, which conforms well over 200 K temperature range. The improvement on β(T) is correspondent to the improvement on the difference in thermal capacities between isobaric and isochoric processes.     

Configurational probabilities for monomers, dimers and trimers in fluids

A new analytical approach is proposed to model aggregation of molecules with isotropic, nearest-neighbor, attractive interactions. By treating the clustering process as a chain reaction, equations with the exact high temperature limit are derived by evaluating the occupation probabilities of nearest neighbors based on the Ono-Kondo approach for a hexagonal lattice to calculate the configurational probabilities of i-mers (i = 1, 2, 3). Equilibrium constants for dimers and trimers are calculated based on the configurational probability data. The proposed model agrees well with Monte Carlo simulations at medium and high temperatures. At low temperatures, the model can be improved by considering the full set of site densities in the first shell of a central trimer. Approximate analytical solutions derived from exact calculations of the grand partition function for monomer adsorption on a 4 x N hexagonal lattice with cylindrical boundary conditions also are presented.     

A simple model for calorimeters with temperature programming

We present a theoretical study of an RC-model constituted only by one heat capacity and one coupling with the thermostat. It is assumed that the thermostat temperature varies as a function of time, and the heat capacity variation is due to its dependence either on temperature or on the mass exchange with the exterior.The results are parallel to the corresponding RC-models where the thermostat temperature is constant. The variations of sensibility are shown, as well as a criterion for the applicability of inverse filtering as a deconvolution technique in calorimeters with temperature programming.     

New observations regarding deterministic, time-reversible thermostats and Gauss's principle of least constraint

Deterministic thermostats are frequently employed in nonequilibrium molecular dynamics simulations in order to remove the heat produced irreversibly over the course of such simulations. The simplest thermostat is the Gaussian thermostat, which satisfies Gauss's principle of least constraint and fixes the peculiar kinetic energy. There are of course infinitely many ways to thermostat systems, e.g., by fixing sigma(i)/p(i)/mu+l. In the present paper we provide, for the first time, convincing arguments as to why the conventional Gaussian isokinetic thermostat (mu = 1) is unique in this class. We show that this thermostat minimizes the phase space compression and is the only thermostat for which the conjugate pairing rule holds. Moreover, it is shown that for finite sized systems in the absence of an applied dissipative field, all other thermostats (mu not = 1) perform work on the system in the same manner as a dissipative field while simultaneously removing the dissipative heat so generated. All other thermostats (mu not = 1) are thus autodissipative. Among all mu, thermostats, only the mu = 1 Gaussian thermostat permits an equilibrium state.     

On the molecular origin of cold denaturation of globular proteins

A polypeptide chain can adopt very different conformations, a fundamental distinguishing feature of which is the water accessible surface area, WASA, that is a measure of the layer around the polypeptide chain where the center of water molecules cannot physically enter, generating a solvent-excluded volume effect. The large WASA decrease associated with the folding of a globular protein leads to a large decrease in the solvent-excluded volume, and so to a large increase in the configurational/translational freedom of water molecules. The latter is a quantity that depends upon temperature. Simple calculations over the -30 to 150 °C temperature range, where liquid water can exist at 1 atm, show that such a gain decreases significantly on lowering the temperature below 0 °C, paralleling the decrease in liquid water density. There will be a temperature where the destabilizing contribution of the polypeptide chain conformational entropy exactly matches the stabilizing contribution of the water configurational/translational entropy, leading to cold denaturation.     

From molecular dynamics to hydrodynamics: a novel Galilean invariant thermostat

This paper proposes a novel thermostat applicable to any particle-based dynamic simulation. Each pair of particles is thermostated either (with probability P) with a pairwise Lowe-Andersen thermostat [C. P. Lowe, Europhys. Lett. 47, 145 (1999)] or (with probability 1-P) with a thermostat that is introduced here, which is based on a pairwise interaction similar to the Nosé-Hoover thermostat. When the pairwise Nosé-Hoover thermostat dominates (low P), the liquid has a high diffusion coefficient and low viscosity, but when the Lowe-Andersen thermostat dominates, the diffusion coefficient is low and viscosity is high. This novel Nosé-Hoover-Lowe-Andersen thermostat is Galilean invariant and preserves both total linear and angular momentum of the system, due to the fact that the thermostatic forces between each pair of the particles are pairwise additive and central. We show by simulation that this thermostat also preserves hydrodynamics. For the (noninteracting) ideal gas at P = 0, the diffusion coefficient diverges and viscosity is zero, while for P > 0 it has a finite value. By adjusting probability P, the Schmidt number can be varied by orders of magnitude. The temperature deviation from the required value is at least an order of magnitude smaller than in dissipative particle dynamics (DPD), while the equilibrium properties of the system are very well reproduced. The thermostat is easy to implement and offers a computational efficiency better than (DPD), with better temperature control and greater flexibility in terms of adjusting the diffusion coefficient and viscosity of the simulated system. Applications of this thermostat include all standard molecular dynamic simulations of dense liquids and solids with any type of force field, as well as hydrodynamic simulation of multiphase systems with largely different bulk viscosities, including surface viscosity, and of dilute gases and plasmas.     

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.     

Reversible measure-preserving integrators for non-Hamiltonian systems

We present a systematic method for deriving reversible measure-preserving integrators for non-Hamiltonian systems such as the Nosé-Hoover thermostat and generalized Gaussian moment thermostat (GGMT). Our approach exploits the (non-Poisson) bracket structure underlying the thermostat equations of motion. Numerical implementation for the GGMT system shows that our algorithm accurately conserves the thermostat energy function. We also study position and momentum distribution functions obtained using our integrator.     

Effects of Configurational Fluctuation on Electronic Coupling for Charge Transfer Dynamics

We advance a theory for the effects of bridge configurational fluctuations on the electronic coupling for electron transfer reactions in donor-bridge-acceptor systems. The theory of radiationless transitions was applied for activationless electron transfer, where the nuclear Franck–Condon constraints are minimized, with the initial vibronic state interacting directly with the final vibronic manifold, without the need for thermal activation. Invoking the assumption of energy-independent coupling, the time-dependent initial state population probability was analyzed in terms of a cumulant expansion. Two limiting situations were distinguished, i.e. the fast configurational fluctuation limit, where the electron transfer rate is given in terms of the configurational average of me squared electronic coupling, and the slow configurational fluctuation limit, where the dynamics is determined by a configurational averaging over a static distribution of electron transfer probability densities. The correlation times for configurational fluctuations of the electronic coupling will be obtained from the analysis of molecular dynamics, in conjunction with quantum mechanical calculations of the electronic coupling, to establish the appropriate limit for electron transfer dynamics.     

Enhanced sampling of particular degrees of freedom in molecular systems based on adiabatic decoupling and temperature or force scaling

A method to enhance sampling of a small subset of N(h) particular degrees of freedom of a system of N(h) + N(l) degrees of freedom is presented. It makes use of adiabatically decoupling these degrees of freedom by increasing their mass followed by either increasing their temperature or reducing their interaction or the force acting on them. The appropriate statistical-mechanical expressions for use of these methods in simulation studies are derived. As long as the subset of mass-increased degrees of freedom is small compared to the total number of degrees of freedom of the system, sampling of this subset of degrees of freedom can be much enhanced at the cost of a slight perturbation of the configurational distribution. This is illustrated for a test system of 1000 SPC, simple point charge, water molecules at 300 K and a density of 997 kg m(-3). Various fractions N(h)/(N(h) + N(l)) of water molecules were adiabatically decoupled to different degrees. The size of the diffusion coefficient of these decoupled water molecules was used as a measure for how much the sampling was enhanced and the average potential energy per water molecule was used as a measure of how much the configurational distribution of the system gets distorted. A variety of parameter values was investigated and it was found that for N(h)/(N(h) + N(l)) ≤ 0.1 the diffusion of the N(h) molecules could be enhanced by factors up to 35 depending on the method, the ratio N(h)/(N(h) + N(l)), the extent of adiabatic decoupling, and the temperature or force scaling factors, at the cost of a slight perturbation of the configurational distribution.     

Theoretical advances in the dissolution studies of mineral–water interfaces

This article presents theoretical advances in computational modeling of dissolution at mineral–water interfaces with specific emphasis on silicates. Two different Monte Carlo methods have been developed that target equilibrium properties and kinetics in silicate–water dissolution. The equilibrium properties are explored using the combined reactive Monte Carlo and configurational bias Monte Carlo (RxMC-CBMC) method. The new RxMC-CBMC method is designed to affordably simulate the three-dimensional structure of the mineral with explicit water molecules. The kinetics of the overall dissolution process is studied using a stochastic kinetic Monte Carlo method that utilizes rate constants obtained from accurate ab initio calculations. Both these methods provide important complementary perspective of the complex dynamics involving chemical and physical interactions at the mineral–water interface. The results are compared to experimental and previous computational data available in the literature.     

Density functional theory study on the bridge structure in dimeric aluminum (III) water complexes

Density-functional theory methods were used to investigate the structure of dimeric aluminum (III) water complexes as a function of bridging group. The possibilities of oxygen, water, and hydroxyl bridge ligands and a variety of structural arrangements, such as cis/trans, with respect to the relative position of hydroxyl ligands, were considered. Within the limit of our computational level, we found that electrostatic repulsion between hydroxyls is important in deciding the polyaluminum structure. Although the structures of aluminum-hexaaquo predominate, species with small number of charges or a large number of hydroxyl ligands have a tendency toward a five-coordinate trigonal bipyramidal configuration. Because water is electronically neutral, it cannot provide enough negative charges as a bridge ligand to stabilize two Al(III) molecules. The energy differences among many configurational isomers of hydroxyl Al are so small that they may coexist and convert into each other easily at room temperature.