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

The method of molecular dynamics has been used to study the structure of a liquid and its relation with the process of self‐diffusion.The particles around a given particle are separated into shells of primary, secondary, etc., neighbors by a precise geometrical procedure. Each shell of neighbors of a particle generates a closed convex polyhedron surrounding the polyhedron of the previous shell. The faces of the polyhedra are the bisector planes of lines joining the particle to its neighbors. The primary polyhedron is the smallest closed convex polyhedron around the particle.The primary polyhedra of a random system of points, of a liquid, and of a solid are compared; the average number f of faces are found to be 15.67, 14.45, and 14.26, respectively. The average number p of sides to the polygons forming the faces is obtained through the relation p=6—(12/f).The pair correlation function g(r) is decomposed into a sum Σig(i)(r), where g(i)(r), arises out of neighbors forming the ith‐order polyhedra. The d...

Liquid Structure and Self‐Diffusion

Hydrogen-bond patterns in liquid water

4096 molecules of water forming an ice Ic structure and 2048 molecules forming an ice Ih structure, with standard periodic boundary conditions in each case, have been used to calculate the dipole correlations which arise from proton allocation to the oxygen nuclei according to the Bernal‐Fowler ice rules. The calculations reveal a substantial antiparallel correlation in the coordination shells at about twice the distance of the nearest neighbors in the lattice. The value of gK, the Kirkwood correlation factor, is found to be 2.07±0.02 for ice Ih. For ice Ic the value, determined with less precision, is 2.11±0.10. In connection with Kirkwood's dielectric formula the value of gK implies an effective dipole moment, μs, of the molecule in the solid ice Ih phase equal to 2.92 D.

Proton Distribution in Ice and the Kirkwood Correlation Factor

A new formulation of lattice gauge theory without explicit path integrals or sums is obtained by using the microcanonical ensemble of statistical mechanics. Expectation values in the new formalism are calculated by solving a large set of coupled, nonlinear, ordinary differential equations. The average plaquette for compact electrodynamics calculated in this fashion agrees with standard Monte Carlo results. Possible advantages of the microcanonical method in applications to fermionic systems are discussed.

Microcanonical Ensemble Formulation of Lattice Gauge Theory

The technique of computer simulation by molecular dynamics has been used to investigate highly compressed water at mass density 1.346 g/cm3. The calculations involve 216 rigid molecules, subject to an additive interaction (the ``ST2 potential'') whose strong anisotropic character has been shown to describe the hydrogen bond phenomenon. In the light of previous calculations on the same model at ordinary pressures, substantial restructuring of the liquid in response to compression is obvious. No evidence arises to support description of the liquid in terms of crystal structures of ices VI and VII, the solid forms that might be expected to be relevant at the chosen density. The calculations indicate that the initial effect of pressure increase (at 1 atm) leads to increased fluidity, as is known to be the case for real water.

Aneesur Rahman

Papers

Liquid Structure and Self‐Diffusion

Hydrogen-bond patterns in liquid water

Proton Distribution in Ice and the Kirkwood Correlation Factor

Microcanonical Ensemble Formulation of Lattice Gauge Theory

Molecular dynamics study of liquid water under high compression