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

It is shown that a discretized version of Feynman’s path integral provides a convenient tool for the numerical investigation of the properties of an electron solvated in molten KC1. The binding energy and the pair correlation functions are calculated. The local structure around the solute electron appears to be different from that of an F center in the solid.

Study of an F center in molten KCl

Computer simulation by the molecular dynamics technique has been used to investigate a modification of the previously introduced ’’central force model’’ for liquid water. The simulation involved 216 molecules, with periodic boundary conditions and Ewald summation, at 29.5°C and 1 g/cm3. In all respects considered (pressure, energy, pair correlation functions, self‐diffusion rate) the revised set of interactions represents water more accurately than the earlier set.

Revised central force potentials for water

In order to clarify the nature of hydrophobic interactions in water, we have used the molecular dynamics simulation method to study a system comprising two Lennard‐Jones solute particles and 214 water molecules. Although the solutes were placed initially in contact, forces in the system drive them slightly apart to permit formation of vertex‐sharing solvent ’’cages.’’ Definite orientational preferences have been observed for water molecules in the first solvation layer around the Lennard‐Jones solutes; these preferences are loosely reminiscent of structure in clathrates. Nevertheless, substantial local disorder is obviously present. The dynamical data show that translational and rotational motions of solvation–sheath water molecules are perceptibly slower (by at least 20%) than those in pure bulk water.

Molecular dynamics study of the hydration of Lennard‐Jones solutes

Based on Van Hove's formalism, a general discussion of scattering in liquids has been given. The scattering cross section has been expressed in terms of velocity correlation functions; in particular, for the incoherent scattering cross section it is shown that in the Gaussian approximation for Van Hove's ${G}_{s}(\mathrm{r}, t)$ function, only a knowledge of the velocity autocorrelation function ${〈\mathrm{v}(0)\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{v}(t)〉}_{T}$ is necessary. The departure from the Gaussian approximation is expressed in terms of higher order velocity correlation functions. A derivation of an approximate formula for the width function of the Gaussian ${G}_{s}(\mathrm{r}, t)$, suggested earlier by the authors, has been given. The frequency spectrum of the velocity autocorrelation function has been introduced, and it has been shown that, as a consequence of the fluctuation-dissipation relations, the spectral representation of the width function is formally identical with that obtained earlier for a harmonic solid. The first few moments of the energy transfer have been discussed. Some of these moments have been shown to satisfy certain relations which involve only experimentally observable quantities; and hence, these relations can be used as a check on the internal consistency of the experimental data.

Theory of Slow Neutron Scattering by Liquids. I

For a system of 216 water molecules, molecular dynamics calculations have been carried out at two temperatures in addition to the one studied and reported previously. As before, the Ben‐Naim and Stillinger effective pair potential was used for these calculations. The results document the breakdown of hydrogen‐bond order and the rapid increase in the freedom of molecular motions that accompany temperature rise in real water. We find no evidence at any temperature to support those water models which partition molecules into two classes (bonded framework or cluster molecules vs unbonded molecules). Nevertheless the pair potential distribution function changes with temperature in such a way as to suggest a basic hydrogen‐bond rupture mechanism characterized by an excitation energy of about 2.5 kcal/mole. Some results indicate that the potential utilized is a bit too tetrahedrally directional to represent real water faithfully, so a possible modification is mentioned.

Aneesur Rahman

Papers

Study of an F center in molten KCl

Revised central force potentials for water

Molecular dynamics study of the hydration of Lennard‐Jones solutes

Theory of Slow Neutron Scattering by Liquids. I

Molecular Dynamics Study of Temperature Effects on Water Structure and Kinetics