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

/pdf/molecular-dynamics-with-coupling-to-an-external-bath-3i7yfm75rd.pdf

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.

/pdf/quantum-espresso-a-modular-and-open-source-software-project-4t6vlupbeh.pdf

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

In any system, the effective exclusion of an atom from the immediate neighborhood of another atom can be used to derive a necessary (but not sufficient) condition which the diffraction pattern of the system has to satisfy. This condition provides a new method of scaling the observed diffraction data from liquids. The currently available x‐ray and neutron‐diffraction data on liquid argon at 84°K are found to differ in a systematic manner, and this discrepancy appears to be beyond the experimental uncertainties of the data. It is demonstrated that the above‐mentioned condition can be used as a reliability criterion as well. Using this criterion, it is found that the neutron‐diffraction data are much more reliable.

Normalization of diffraction data from liquids

Triplet correlations in liquids

Liquid ${\mathrm{Rb}}^{+}$${\mathrm{Br}}^{\ensuremath{-}}$ has been investigated by molecular dynamics for comparison with neutron inelastic scattering results. The properties of ${\mathrm{Rb}}^{+}$ and ${\mathrm{Br}}^{\ensuremath{-}}$ on the one hand and those of the nuclei of Rb and Br on the other offer rather special features for such a parallel investigation. The results reported here use the Born-Mayer type of interaction between nonpolarizable ions. Based on a molecular dynamics study of a rather small, 122-ion system, our conclusion is that such a force model is probably inadequate for a satisfactory explanation of the neutron scattering data; we also conclude that allowing for ion polarization will impove the situation. Thus detailed studies of the equation of state have to be complemented with dynamical studies of molten salts before one can draw conclusions about the dependability of the Hamiltonian used for the system. Our results for ${g}_{++}$ and ${g}_{\ensuremath{-}\ensuremath{-}}$ show a shoulder to the right of the first maximum. This feature has also been observed in neutron experiments on NaCl and in Monte Carlo calculations on "hard sphere" molten salts. As has already been reported, the calculated and observed static structure factors are in fair agreement. However, a detailed comparison shows more marked features in the calculated results than have been found experimentally. From the density fluctuations a velocity of sound has been deduced which is considerably larger than the only available experimental value. A comparison of the frequency characteristics of the density fluctuations at various wavelengths with neutron scattering data shows that at certain wavelengths there are large discrepancies which are, at least in part, related to the inadequacy of the rigid-ion model Hamiltonian used for these calculations.

Density fluctuations in molten salts. II. Molecular dynamics study of liquid RbBr

Longitudinal and Transverse Excitations in a Glass

Stillinger and Weber have introduced a model potential to study the solid and liquid forms of silicon. This potential has been used in a number of computer simulation studies of silicon. We have calculated the elastic constants of silicon using the Stillinger–Weber potential at three different temperatures T=888, 1164, and 1477 K. The adiabatic elastic constants are calculated using fluctuation formula appropriate for the microcanonical ensemble. We find that the calculated shear modulus C44 is smaller than the experimental values by ∼30% at T=888 K, ∼40% at the two higher temperatures, and the modulus C12 is larger than the experimental value by 25%–30%. Simulations with N=216 and 1728 particles were carried out to check on the number dependence of the results. These two particle numbers give equivalent results for the elastic constants. The calculated elastic constants show the same softening with rising temperature as shown by the experimental values.

Aneesur Rahman

Papers

Normalization of diffraction data from liquids

Triplet correlations in liquids

Density fluctuations in molten salts. II. Molecular dynamics study of liquid RbBr

Longitudinal and Transverse Excitations in a Glass

Molecular dynamic calculation of elastic constants of silicon