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

A molecular-dynamcis study of silver diffusion in superionic conductor $\ensuremath{\alpha}$-AgI is performed. Interionic potentials are constructed using Pauling's ideas of ionic radii. The diffusion constant for silver and its temperature dependence are in good agreement with experiment. Good agreement is also obtained for the silver density map with the experiment of Cava, Reidinger, and Wuensch.

Ionic Motion in α -AgI

Sets of configurations selected from three molecular dynamics simulations for liquid water have been analyzed for the distribution of hydrogen‐bond clusters. Two simulations correspond to water at 1 g cm−3, while the third corresponds to highly compressed water at 1.346 g cm−3. An energy criterion was adopted for existence of a hydrogen‐bond between two molecules. As the cutoff value for bonding increases (becomes more permissive), a bond percolation threshold is encountered at which initially disconnected clusters suddenly produce a large space‐filling random network. At least for the model studied, any chemically reasonable definition of ’’hydrogen‐bond’’ leads to this globally connected structure though a few disconnected fragments inhabit its interior. Although some polygonal closures can exist, the critical percolation threshold is apparently well predicted by Flory’s theory of the gel point for dendritic polymerization.

Aspects of the percolation process for hydrogen‐bond networks in water

We present a general discussion of the isoenthalpic–isostress molecular dynamics theories of Andersen and Parrinello–Rahman. The Parrinello–Rahman theory is shown to be applicable to the case of nonlinear elasticity if the reference state of zero strain is taken to be the state under zero stress; this brings the theory into accord with the thermodynamics of anisotropic solids for arbitrary values of the strain. For the isoenthalpic–isostress ensemble there is a microcanonical counterpart for which we present fluctuation formulas involving the constant strain specific heat, temperature coefficients of thermodynamic tension, and stiffness coefficients. The use of these various ensembles for the molecular dynamic study of polymorphic transitions in crystals is discussed.

Statistical ensembles and molecular dynamics studies of anisotropic solids. II

The $\ensuremath{\alpha}\ensuremath{\rightleftarrows}\ensuremath{\beta}$ phase transition in AgI is studied with use of the new molecular-dynamics technique which allows for a dynamical variation of the shape and size of the cell. In the present model, upon heating of $\ensuremath{\beta}$-AgI, the iodine ions undergo a hep \ensuremath{\rightarrow} bee transformation and silver ions become mobile, whereas the reverse transformation is observed on cooling of $\ensuremath{\alpha}$-AgI. The calculated $\ensuremath{\alpha}\ensuremath{\rightleftarrows}\ensuremath{\beta}$ transition temperature and structural and dynamical properties are in good agreement with experiments.

Structural Transitions in Superionic Conductors

The simulation technique of molecular dynamics has been used to investigate a central‐force model for liquid water at 22 °C and 1 g/cm3. In this model, the same atomic pair potentials are used both for intramolecular and intermolecular interactions. Atomic pair correlation functions and velocity autocorrelation functions have been computed. The results demonstrate that stable, nonlinear, vibrating molecules are present, and that they form a random hydrogen‐bond network of the type usually attributed to water. These exploratory calculations suggest that small modifications in the central potentials VHH, VOH, and VOO would produce a more faithful representation of real water.

Aneesur Rahman

Papers

Ionic Motion in α -AgI

Aspects of the percolation process for hydrogen‐bond networks in water

Statistical ensembles and molecular dynamics studies of anisotropic solids. II

Structural Transitions in Superionic Conductors

Study of a central force model for liquid water by molecular dynamics