Liquid Water from First Principles:  Investigation of Different Sampling Approaches

Abstract

A series of first principles molecular dynamics and Monte Carlo simulations were carried out for liquid water to investigate the reproducibility of different sampling approaches. These simulations include Car−Parrinello molecular dynamics simulations using the program cpmd with different values of the fictitious electron mass in the microcanonical and canonical ensembles, Born−Oppenheimer molecular dynamics using the programs cpmd and cp2k in the microcanonical ensemble, and Metropolis Monte Carlo using cp2k in the canonical ensemble. With the exception of one simulation for 128 water molecules, all other simulations were carried out for systems consisting of 64 molecules. Although the simulations yield somewhat fortuitous agreement in structural properties, analysis of other properties demonstrate that one should exercise caution when assuming the reproducibility of Car−Parrinello and Born−Oppenheimer molecular dynamics simulations for small system sizes in the microcanonical ensemble. In contrast, the molecular dynamics and Monte Carlo simulations in the canonical ensemble appear to be more reliable. Furthermore, in the case of canonical Car−Parrinello molecular dynamics simulations the application of Nosé−Hoover chain thermostats allows the use of larger fictitious electron masses. For the Becke−Lee−Yang−Parr exchange and correlation energy functionals and norm-conserving Troullier−Martins or Goedecker−Teter−Hutter pseudopotentials, these simulations at a fixed density of 1.0 g/cm3 and a temperature close to 315 K point to an overstructured liquid with a height of the first peak in the oxygen−oxygen radial distribution function of about 3.0, an underestimated value of the classical constant-volume heat capacity of about 70 J/(mol K), and an underestimated self-diffusion constant of about 0.04 Å2/ps.

Quantum diffusion in liquid water from ring polymer molecular dynamics

“…The present results are also relevant to those of a very recent ab initio molecular-dynamics study of liquid water at 315 K. 55 This study employed the Becke-Lee-Yang-Parr 56,57 ͑BLYP͒ density functional in a number of independent simulations of systems of 64 and 128 water molecules. The resulting self-diffusion coefficient was found to be 0.04± 0.02 Å 2 / ps-nearly an order of magnitude smaller than the experimental value of 0.35 Å 2 /ps at 315 K. 58 Insofar as we can tell from the present results, quantummechanical effects in the nuclear motion and finite-size effects are unlikely to be the only causes of such a large discrepancy.…”

Microscopic properties of liquid water from combined ab initio molecular dynamics and energy decomposition studies

“…Therefore, various physical effects such as van der Waals interactions between molecules and the quantum behaviour of nuclei have to been reproduced only approximately or even completely neglected. In addition, the high computational cost of AIMD imposes severe restrictions on the size of a model system and time length of the simulations thus introducing additional finite-size errors and statistical uncertainties into the properties calculated [99][100][101][102][103][104][105][106][107] .…”

Fluxionality of gold nanoparticles investigated by Born-Oppenheimer molecular dynamics

“…For the solution of the SCF equations, we used an optimizer based on orbital transformations, which scales linearly in the number of basis functions [55]. It has been already demonstrated that this optimization algorithm, in combination with the GPW linear scaling calculation of the Kohn-Sham matrix, can be used for applications with several thousands of basis functions [56]. Geometry optimizations have been carried out using the Broyden-Fletcher-Goldfarb-Shanno minimization algorithm 5 (BFGS) [57][58][59][60][61], and the structures have been optimized until the atomic displacements were lower than 3 · 10 −3 Bohr and the forces lower than 4.…”