Data driven inference for the repulsive exponent of the Lennard-Jones potential in molecular dynamics simulations

The Lennard-Jones (LJ) potential is a cornerstone of Molecular Dynamics (MD) simulations and among the most widely used computational kernels in science. The LJ potential models atomistic attraction and repulsion with century old prescribed parameters (q = 6, p = 12, respectively), originally related by a factor of two for simplicity of calculations. We propose the inference of the repulsion exponent through Hierarchical Bayesian uncertainty quantification We use experimental data of the radial distribution function and dimer interaction energies from quantum mechanics simulations. We find that the repulsion exponent p ≈ 6.5 provides an excellent fit for the experimental data of liquid argon, for a range of thermodynamic conditions, as well as for saturated argon vapour. Calibration using the quantum simulation data did not provide a good fit in these cases. However, values p ≈ 12.7 obtained by dimer quantum simulations are preferred for the argon gas while lower values are promoted by experimental data. These results show that the proposed LJ 6-p potential applies to a wider range of thermodynamic conditions, than the classical LJ 6-12 potential. We suggest that calibration of the repulsive exponent in the LJ potential widens the range of applicability and accuracy of MD simulations.

Locally adaptive method to define coordination shell

An algorithm is presented to define a particle's coordination shell for any collection of particles. It requires only the particles' positions and no pre-existing knowledge or parameters beyond those already in the force field. A particle's shell is taken to be all particles that are not blocked by any other particle and not further away than a blocked particle. Because blocking is based on two distances and an angle for triplets of particles, it is called the relative angular distance (RAD) algorithm. RAD is applied to Lennard-Jones particles in molecular dynamics simulations of crystalline, liquid, and gaseous phases at various temperatures and densities. RAD coordination shells agree well with those from a cut-off in the radial distribution function for the crystals and liquids and are slightly higher for the gas.

Water's dual nature and its continuously changing hydrogen bonds

A model is proposed for liquid water that is a continuum between the ordered state with predominantly tetrahedral coordination, linear hydrogen bonds and activated dynamics and a disordered state with a continuous distribution of multiple coordinations, multiple types of hydrogen bond, and diffusive dynamics, similar to that of normal liquids. Central to water's heterogeneous structure is the ability of hydrogen to donate to either one acceptor in a conventional linear hydrogen bond or to multiple acceptors as a furcated hydrogen. Linear hydrogen bonds are marked by slow, activated kinetics for hydrogen-bond switching to more crowded acceptors and sharp first peaks in the hydrogen-oxygen radial distribution function. Furcated hydrogens, equivalent to free, broken, dangling or distorted hydrogens, have barrierless, rapid kinetics and poorly defined first peaks in their hydrogen-oxygen radial distribution function. They involve the weakest donor in a local excess of donors, such that barrierless whole-molecule vibration rapidly swaps them between the linear and furcated forms. Despite the low number of furcated hydrogens and their transient existence, they are readily created in a single hydrogen-bond switch and free up the dynamics of numerous surrounding molecules, bringing about the disordered state. Hydrogens in the ordered state switch with activated dynamics to make the non-tetrahedral coordinations of the disordered state, which can also combine to make the ordered state. Consequently, the ordered and disordered states are both connected by diffusive dynamics and differentiated by activated dynamics, bringing about water's continuous heterogeneity.

Behavior of the dielectric constant of Ar near the critical point

The fundamental question of the behavior of the dielectric constant near the critical point is addressed using Ar as the probe system. The neighborhood of the liquid-vapor critical point of Ar is accessed by classical Monte Carlo simulation and then explicit quantum mechanics calculations are performed to study the behavior of the dielectric constant. The theoretical critical temperature is determined by calculating the position of the discontinuity of the specific heat and is found to be at T(c)Theor=148.7K, only 2 K below the experimental value. The large fluctuations and the inhomogeneity of the density that characterize the critical point rapidly disappear and are not seen at T=T(c)Theor+2K. The structure of Ar obtained by the radial distribution function is found to be in very good agreement with experiment both in the liquid phase and 2 K above the critical temperature. The behavior of the dielectric constant is then analyzed after calculating the static dipole polarizability and using a many-body Clausius-Mossotti equation. The dielectric constant shows a density-independent behavior around the critical density, 2 K above the critical temperature. At this point, the calculated value of the dielectric constant is 1.173±0.005 in excellent agreement with the experimental value of 1.179.

A new model approach for the near-critical point region: 1. Construction of the generalized van der Waals equation of state

To date, it has been considered that all classical equations of state (EOS) have failed to describe the properties of fluids near the critical region, where the density fluctuations have a significant influence on fluid properties. In this paper, we suggest a newly constructed equation for fluid states, the generalized van der Waals (GvdW) EOS with the highly simplified Dieterici's form P = [RT/(V - b)] - a(b/V)c by a new model potential construction describing intermolecular interactions. On the basis of the model potential construction, it is shown that the a, b, and c parameters have physical interpretations as an internal pressure, a void volume, and a dimensionless value that represents an inharmonic intermolecular cell potential, respectively. As an illustration of our model approach, we initially apply it to near the critical point (cp) region, where all classical EOS descriptions have been incorporated with experimental thermodynamic data, and we obtain a table of three parameters for 12 pure normal fluids, which precisely describes thermodynamic critical values. On the basis of the basic relations between pressure and volume at the critical point, we express the corresponding EOS in terms of the c parameter, and by this means, we also obtain a theoretical vapor-liquid equilibrium (VLE) line, which closely coincides with the experimental data for several pure normal fluids near the critical region. As a result, we show that thermodynamic properties near the critical region can be described analytically by only three parameters. In addition, to validate our EOS for the temperature-differential derivatives, we show that the calculated isochoric heat capacity (Cv) of saturated argon closely coincides with the experimental data. Moreover, the possibility of a precise description with respect to the entire fluid region is also argued, in terms of the physical cases from the triple point to the ideal gas region.

Molecular dynamics simulation of a pressure-driven liquid transport process in a cylindrical nanopore using two self-adjusting plates

Fluid transport through a nanopore in a membrane was investigated by using a novel molecular dynamics approach proposed in this study. The advantages of this method, relative to dual-control-volume grand-canonical molecular dynamics method, are that it eliminates disruptions to the system dynamics that are normally created by inserting or deleting particles from control volumes, and that it functions well for dense systems due to the number of particles being fixed in the system. Using the proposed method, we examined liquid argon transport through a nanopore by performing nonequilibrium molecular dynamics (NEMD) simulations under different back pressures. Validation of the code was performed by comparing simulation results to published experimental data obtained under equilibrium conditions. NEMD results show that constant pressure difference across the membrane was readily achieved.

Water structure theory and some implications for drug design

The development of theories of water structure has been hindered in the past by the difficulty of experimental measurement. Both measurement and computer modelling studies have now reached the stage where theoretical treatments of water structure are converging to a broadly acceptable model. In current understanding, water is a mixture of randomly hydrogen-bonded molecules and larger structures comprised of tetrahedral oxygen centres which, when hydrogen-bonded to each other, lead to five-membered and other rings which can aggregate to form three-dimensional structures. Evidence is taken from studies of the ices, from clathrates and other solid solutions, as well as from liquid solutions, that certain motifs occur very frequently and have relatively high stability, such as the (H2O)20 cavity-forming structure known from studies on clathrates. The implications of recent models of water structure for an understanding of biological events, including the interactions of drugs with receptors, are profound. It is becoming clear that modelling of aqueous solutions of any molecule must consider the explicit interactions with water molecules, which should not be regarded as a continuum: water itself is not a continuum. Solute molecules which possess hydrogen-bonding groups will provoke the formation of further hydrogen-bonding chains of water molecules: if these can form rings, such ringswilltend to persist longerthan chains, givingthesolute a secondary identity of associated water which may play a role in molecular recognition. Solutes that do not have hydrogen-bonding capability, or regions of solutes which are non-polar, may also produce partial cage-like water structures that are characteristic of the solute. The classification of many solutes as structure makers or structure breakers has relevance to the interactions between ligands and large biomolecules such as proteins. While it is generally accepted that sulfate and urea, respectively structure maker and breaker, may alter protein conformation through effects on water, it has not been recognised that bioactive ligands, which also change the conformation of proteins, may do so by a related, but more selective, mechanism. Very early studies of cell contents suggested that the associated water might be different from bulk water, a concept that lost support in the mid-20th century. Current theories of water structure may invite a reappraisal of this position, given the observation that structuring may extend for many molecular diameters from an ordered surface.

Scaling Laws for Geometry and Macromolecules in Solution: An Interdisciplinary Approach to Statistical and Thermal Physics

An interdisciplinary program, dealing with statistics within basic geometry, is presented and discussed across some modern physics. Its fundamentals are of general interest in physical chemistry, but specially suit investigating conformational statistics and universal scaling of polymer chains in solution. We pointed out an equivalence principle for shape and statistics that can straightforwardly link probability distributions to geometrical quantities at smaller length scales. The average polymer size is thus expected following analytically from the energy surface of its dimeric unit. This would finally suggest extending molecular mechanics to a geometrical setting that reaches the limit of vanishing scales.

Alternative optical equation for dielectric liquids

A "statistically permanent" pair of molecules interacting by dispersion forces, as a unit element of a simple cubic "crystal" modeling a nonpolar liquid dielectric at a given thermal state, has been used to explain low and high pressure refractive index n measurements. It has been shown that the equation (epsilon-1)2epsilon+1 / 9epsilon=c(lambda)r exp r(2) / 1-T/T(l)[where epsilon identical withn(2), c(lambda)>or=1 close to a unity liquid constant for wavelength lambda, r =4pirhoalpha/3, rho is the number density, alpha is the mean polarizability of a free molecule, T(l) is the internal temperature = a/RV, a is the van der Waals constant identical with(27/64)(RT(c))(2)/p(c), and R is the universal gas constant] is more accurate than any already known optical equation of liquids. The small changes in Lorentz-Lorenz refraction L identical with(epsilon-1)V/(epsilon+2) according to ( partial differentialL/ partial differentialp)(T)<0 and ( partial differentialL/ partial differentialT)(p)>( partial differentialL/ partial differentialT)(V)>0 are expected and observed in all pressure ranges. The translational fluctuation parameter <x(-6)> of the right order of magnitude is obtained from n.

Ion-ion oscillatory potentials in liquid metals

Radial distribution functions obtained by X-ray and neutron measurements have been analyzed for eight liquid metals, Li, Na, K, Rb, Cs, Hg, A1 and Pb, and for the liquid insulator Ar. It is shown that pair potentials between the ions in liquid metals can be obtained from the data, and that the general features of these curves are similar on the basis of various approximate theories of liquids. In particular, the Born-Green theory and the method of Percus & Yevick have been used in all cases. For the eight liquid metals, and for two different temperatures in each case, long-range oscillatory interactions are always found in the ion-ion potentials. While these general features of the pair potentials are the same in Born-Green and Percus-Yevick theories, in the important region round the first minimum and the following maximum the results are quantitatively different. The potentials, however, are only weakly temperature-dependent in the Born-Green approach, and the approximate validity of this method for liquid metals appears to receive further confirmation from calculations of viscosity and surface tension, which are in quite surprisingly good agreement with experiment. The Percus-Yevick approach seems distinctly less good for metals, but may perhaps be more appropriate to deal with liquid insulators. However, many body forces may also be important in argon. The long-range oscillations are interpreted as conduction electron screening of the ions, though the amplitude of the oscillations is substantially greater than a Hartree point-ion model predicts. It is pointed out that core sizes and/or electron interactions will have to be incorporated carefully into the screening theory in order to understand the present findings in a fully quantitative way. The long-range oscillations afford striking evidence that the Fermi surface is quite sharp even in a liquid metal like mercury, where the mean free path is short. Some evidence of the damping of the oscillations is found, and rough values thereby obtained for the blurring of the Fermi distribution. Sodium remains a somewhat puzzling case, as the oscillations appear to fall off rather more slowly than theory would predict. By means of the Ornstein-Zernike direct correlation function f , it is pointed out that, solely from radial distribution function data which appears at first sight rather similar for insulating and conducting liquids, the two types may be distinguished. For insulators, f has no nodes, whereas for metals it has marked oscillations. This suggests that f is closely connected with the pair interaction ϕ(r) , and by analysis of the equations of the Born-Green, Percus-Yevick and hyperchain methods, it is shown that they all yield f(r) = - ϕ(r)/kT for sufficiently large r . It is inferred therefore that this is a general result, and does not depend on the use of approximate theories.