Classical Monte Carlo simulations have been carried out for liquid water in the NPT ensemble at 25 °C and 1 atm using six of the simpler intermolecular potential functions for the water dimer: Bernal–Fowler (BF), SPC, ST2, TIPS2, TIP3P, and TIP4P. Comparisons are made with experimental thermodynamic and structural data including the recent neutron diffraction results of Thiessen and Narten. The computed densities and potential energies are in reasonable accord with experiment except for the original BF model, which yields an 18% overestimate of the density and poor structural results. The TIPS2 and TIP4P potentials yield oxygen–oxygen partial structure functions in good agreement with the neutron diffraction results. The accord with the experimental OH and HH partial structure functions is poorer; however, the computed results for these functions are similar for all the potential functions. Consequently, the discrepancy may be due to the correction terms needed in processing the neutron data or to an effect uniformly neglected in the computations. Comparisons are also made for self‐diffusion coefficients obtained from molecular dynamics simulations. Overall, the SPC, ST2, TIPS2, and TIP4P models give reasonable structural and thermodynamic descriptions of liquid water and they should be useful in simulations of aqueous solutions. The simplicity of the SPC, TIPS2, and TIP4P functions is also attractive from a computational standpoint.

Comparison of simple potential functions for simulating liquid water

In molecular dynamics (MD) simulations the need often arises to maintain such parameters as temperature or pressure rather than energy and volume, or to impose gradients for studying transport properties in nonequilibrium MD A method is described to realize coupling to an external bath with constant temperature or pressure with adjustable time constants for the coupling The method is easily extendable to other variables and to gradients, and can be applied also to polyatomic molecules involving internal constraints The influence of coupling time constants on dynamical variables is evaluated A leap‐frog algorithm is presented for the general case involving constraints with coupling to both a constant temperature and a constant pressure bath

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Molecular dynamics with coupling to an external bath.

QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

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QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials

http://www2.stat.duke.edu/~scs/Courses/Stat376/Papers/Constraints/Shake1977.pdf

Numerical Integration of the Cartesian Equations of Motion of a System with Constraints: Molecular Dynamics of n-Alkanes

The previously developed particle mesh Ewald method is reformulated in terms of efficient B‐spline interpolation of the structure factors This reformulation allows a natural extension of the method to potentials of the form 1/rp with p≥1 Furthermore, efficient calculation of the virial tensor follows Use of B‐splines in place of Lagrange interpolation leads to analytic gradients as well as a significant improvement in the accuracy We demonstrate that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N) For biomolecular systems with many thousands of atoms this method permits the use of Ewald summation at a computational cost comparable to that of a simple truncation method of 10 A or less

A smooth particle mesh Ewald method

We investigate the existence of periodic nonuniform solutions of the first BBGKY equation under the assumption, first introduced by Kirkwood and Monroe, that the pair correlations in the solid can be described by the radial distribution function of a disordered metastable phase at the same temperature and density. The calculated one‐particle distribution function is used to obtain the equation of state of three systems, namely, hard spheres, rubidium, and Lennard‐Jones. The consequences of the central approximation are discussed in the light of our results.

A study of spatially nonuniform solutions of the first BBGKY equation

Molecular dynamic computer simulation methods have been employed to calculate the free energy difference between the fcc and hcp structures using a Morse potential parametrized to model Ni. The calculation is carried out for a temperature (∼1000 K) where anharmonic effects are important and also for a range of interactions about each particle. In addition, at the same temperature, another calculation using only nearest neighbor interactions was performed. Using lattice sums the potential energy for the two static lattices was calculated. For the Morse potential used, static lattice sums give a lower potential for the hcp structure. With only nearest neighbor interactions, the fcc–hcp free energy difference is determined only by the entropy difference. In this case the fcc structure has the lower free energy. When both anharmonic effects and longer range interactions are considered we find, at the temperature and density investigated, that the hcp structure is more stable.

Free energy difference calculations comparing fcc and hcp structures using molecular dynamics computer simulations

Molecular dynamics calculations were performed on two liquid ionic solutions, M3AX6 and MA3X10, containing a total of about 500 ions. Four different sets of radii for the M+, A3+, and X− ions were considered in a simplified Tosi–Fumi potential; the cation–anion distances were kept constant but the cation–anion radius ratios varied. These sets generated configurations in which the coordination of A3+ by X− ranged from octahedral to tetrahedral. Our goal was to investigate typical complexing molten salt solutions such as fluoroyttriates and chloroaluminates. In all the melts studied, A3+ tended to have preferential even coordination numbers, 4 or 6, and to form independent AX3−nn moieties in very dilute solutions. As the concentration of AX3 increased, these moieties became interconnected by close to linear A–X–A bridges to form larger species. In the octahedrally coordinated melts, this led to a three‐dimensional network with intermediate range order and to the formation of bridged species containing A3+ e...

Molecular dynamics studies of complexing in binary molten salts. II. Molten M3AX6 and MA3X10

The self-correlation function for the motion of an atom in a liquid was constructed in a manner which simulates the behavior of this function between the two extreme cases, viz, that in a solid and that in a simple diffusive model Using this function, the differential scattering cross section for cold neutrons was calculated for liquid lead and compared with available experimental results It appears that even in a simple liquid like lead the solidlike behavior of atomic motions persists for a considerable time (auth)

Dynamics of Atomic Motions in Liquids and Cold Neutron Scattering

An evaluation of the coefficient a (T,V) as defined in the equation for the excess Helmholtz free energy of mixing of binary solutions, ΔAmE=a (T,V)(λi−λj)2XiXj +..., derived from the conformal ionic solution theory is presented. This coefficient is shown to be negative and proportional to a fluctuation energy. The sign agrees with experimental calorimetric data of binary molten salt mixtures. A molecular dynamics computation of a (T,V) was made to compare theory and experiments. The calculated values are strongly dependent on the form of the repulsive contribution to the pair potentials (Tosi and Fumi model and Michielsen, Woerlee, Graaf, and Ketelaar model). Criteria for testing the repulsive part of proposed pair potentials are suggested as a result of this investigation.

Aneesur Rahman

Papers

A study of spatially nonuniform solutions of the first BBGKY equation

Free energy difference calculations comparing fcc and hcp structures using molecular dynamics computer simulations

Molecular dynamics studies of complexing in binary molten salts. II. Molten M3AX6 and MA3X10

Dynamics of Atomic Motions in Liquids and Cold Neutron Scattering

Erratum: Application of molecular dynamics computations to the conformal ionic solution theory: Thermodynamics of binary molten salt mixtures