Stabilization of Ab Initio Molecular Dynamics Simulations at Large Time Steps

The Verlet method is still widely used to integrate the equations of motion in ab initio molecular dynamics simulations. We show that the stability limit of the Verlet method may be significantly increased by setting an upper limit on the kinetic energy of each atom with only a small loss in accuracy. The validity of this approach is demonstrated for molten lithium fluoride.Comment: 9 pages, 3 figure

Path-integral molecular dynamics simulation of 3C-SiC

Molecular dynamics simulations of 3C-SiC have been performed as a function of pressure and temperature. These simulations treat both electrons and atomic nuclei by quantum mechanical methods. While the electronic structure of the solid is described by an efficient tight-binding Hamiltonian, the nuclei dynamics is treated by the path integral formulation of statistical mechanics. To assess the relevance of nuclear quantum effects, the results of quantum simulations are compared to others where either the Si nuclei, the C nuclei or both atomic nuclei are treated as classical particles. We find that the experimental thermal expansion of 3C-SiC is realistically reproduced by our simulations. The calculated bulk modulus of 3C-SiC and its pressure derivative at room temperature show also good agreement with the available experimental data. The effect of the electron-phonon interaction on the direct electronic gap of 3C-SiC has been calculated as a function of temperature and related to results obtained for bulk diamond and Si. Comparison to available experimental data shows satisfactory agreement, although we observe that the employed tight-binding model tends to overestimate the magnitude of the electron-phonon interaction. The effect of treating the atomic nuclei as classical particles on the direct gap of 3C-SiC has been assessed. We find that non-linear quantum effects related to the atomic masses are particularly relevant at temperatures below 250 K.Comment: 14 pages, 15 figure

Neural network based path collective variables for enhanced sampling of phase transformations

We propose a rigorous construction of a 1D path collective variable to sample structural phase transformations in condensed matter. The path collective variable is defined in a space spanned by global collective variables that serve as classifiers derived from local structural units. A reliable identification of local structural environments is achieved by employing a neural network based classification. The 1D path collective variable is subsequently used together with enhanced sampling techniques to explore the complex migration of a phase boundary during a solid-solid phase transformation in molybdenum

Kinetic energy of protons in ice Ih and water: a path integral study

The kinetic energy of H and O nuclei has been studied by path integral molecular dynamics simulations of ice Ih and water at ambient pressure. The simulations were performed by using the q-TIP4P/F model, a point charge empirical potential that includes molecular flexibility and anharmonicity in the OH stretch of the water molecule. Ice Ih was studied in a temperature range between 210-290 K, and water between 230-320 K. Simulations of an isolated water molecule were performed in the range 210-320 K to estimate the contribution of the intramolecular vibrational modes to the kinetic energy. Our results for the proton kinetic energy, K_H, in water and ice Ih show both agreement and discrepancies with different published data based on deep inelastic neutron scattering experiments. Agreement is found for water at the experimental melting point and in the range 290-300 K. Discrepancies arise because data derived from the scattering experiments predict in water two maxima of K_H around 270 K and 277 K, and that K_H is lower in ice than in water at 269 K. As a check of the validity of the employed water potential, we show that our simulations are consistent with other experimental thermodynamic properties related to K_H, as the temperature dependence of the liquid density, the heat capacity of water and ice at constant pressure, and the isotopic shift in the melting temperature of ice upon isotopic substitution of either H or O atoms. Moreover, the temperature dependence of K_H predicted by the q-TIP4P/F model for ice Ih is found to be in good agreement to results of path integral simulations using ab initio density functional theory.Comment: 11 pages, 6 figures, 2 table

From Classical to Quantum and Back: Hamiltonian Adaptive Resolution Path Integral, Ring Polymer, and Centroid Molecular Dynamics

Path integral-based simulation methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical simulations. To reduce this numerical effort, we recently proposed a method, based on a rigorous Hamiltonian formulation, which restricts the quantum modeling to a small but relevant spatial region within a larger reservoir where particles are treated classically. In this work, we extend this idea and show how it can be implemented along with state-of-the-art path integral simulation techniques, such as ring polymer and centroid molecular dynamics, which allow the approximate calculation of both quantum statistical and quantum dynamical properties. To this end, we derive a new integration algorithm which also makes use of multiple time-stepping. The scheme is validated via adaptive classical--path-integral simulations of liquid water. Potential applications of the proposed multiresolution method are diverse and include efficient quantum simulations of interfaces as well as complex biomolecular systems such as membranes and proteins

Classical-path integral adaptive resolution in molecular simulation: towards a smooth quantum-classical coupling

Simulations that couple different classical molecular models in an adaptive way by changing the number of degrees of freedom on the fly, are available within reasonably consistent theoretical frameworks. The same does not occur when it comes to classical-quantum adaptivity. The main reason for this is the difficulty in describing a continuous transition between the two different kind of physical principles: probabilistic for the quantum and deterministic for the classical. Here we report the basic principles of an algorithm that allows for a continuous and smooth transition by employing the path integral description of atoms.Comment: 8 pages 4 figure

Path Integral Molecular Dynamics within the Grand Canonical-like Adaptive Resolution Technique: Simulation of Liquid Water

Quantum effects due to the spatial delocalization of light atoms are treated in molecular simulation via the path integral technique. Among several methods, Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to investigate properties induced by spatial delocalization of atoms; however computationally this technique is very demanding. The abovementioned limitation implies the restriction of PIMD applications to relatively small systems and short time scales. One possible solution to overcome size and time limitation is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme (AdResS). AdResS requires a relatively small region treated at path integral level and embeds it into a large molecular reservoir consisting of generic spherical coarse grained molecules. It was previously shown that the realization of the idea above, at a simple level, produced reasonable results for toy systems or simple/test systems like liquid parahydrogen. Encouraged by previous results, in this paper we show the simulation of liquid water at room conditions where AdResS, in its latest and more accurate Grand-Canonical-like version (GC-AdResS), is merged with two of the most relevant PIMD techniques available in literature. The comparison of our results with those reported in literature and/or with those obtained from full PIMD simulations shows a highly satisfactory agreement

Extreme multiplicity in cylindrical Rayleigh-Benard convection: II. Bifurcation diagram and symmetry classification

A large number of flows with distinctive patterns have been observed in experiments and simulations of Rayleigh-Benard convection in a water-filled cylinder whose radius is twice the height. We have adapted a time-dependent pseudospectral code, first, to carry out Newton's method and branch continuation and, second, to carry out the exponential power method and Arnoldi iteration to calculate leading eigenpairs and determine the stability of the steady states. The resulting bifurcation diagram represents a compromise between the tendency in the bulk towards parallel rolls, and the requirement imposed by the boundary conditions that primary bifurcations be towards states whose azimuthal dependence is trigonometric. The diagram contains 17 branches of stable and unstable steady states. These can be classified geometrically as roll states containing two, three, and four rolls; axisymmetric patterns with one or two tori; three-fold symmetric patterns called mercedes, mitubishi, marigold and cloverleaf; trigonometric patterns called dipole and pizza; and less symmetric patterns called CO and asymmetric three-rolls. The convective branches are connected to the conductive state and to each other by 16 primary and secondary pitchfork bifurcations and turning points. In order to better understand this complicated bifurcation diagram, we have partitioned it according to azimuthal symmetry. We have been able to determine the bifurcation-theoretic origin from the conductive state of all the branches observed at high Rayleigh number