866 research outputs found
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
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
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
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
Holonomic constraints : an analytical result
Systems subjected to holonomic constraints follow quite complicated dynamics
that could not be described easily with Hamiltonian or Lagrangian dynamics. The
influence of holonomic constraints in equations of motions is taken into
account by using Lagrange multipliers. Finding the value of the Lagrange
multipliers allows to compute the forces induced by the constraints and
therefore, to integrate the equations of motions of the system. Computing
analytically the Lagrange multipliers for a constrained system may be a
difficult task that is depending on the complexity of systems. For complex
systems, it is most of the time impossible to achieve. In computer simulations,
some algorithms using iterative procedures estimate numerically Lagrange
multipliers or constraint forces by correcting the unconstrained trajectory. In
this work, we provide an analytical computation of the Lagrange multipliers for
a set of linear holonomic constraints with an arbitrary number of bonds of
constant length. In the appendix of the paper, one would find explicit formulas
for Lagrange multipliers for systems having 1, 2, 3, 4 and 5 bonds of constant
length, linearly connected.Comment: 13 pages, no figures. To appear in J. Phys. A : Math. The
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
On the Geometry and Entropy of Non-Hamiltonian Phase Space
We analyze the equilibrium statistical mechanics of canonical, non-canonical
and non-Hamiltonian equations of motion by throwing light into the peculiar
geometric structure of phase space. Some fundamental issues regarding time
translation and phase space measure are clarified. In particular, we emphasize
that a phase space measure should be defined by means of the Jacobian of the
transformation between different types of coordinates since such a determinant
is different from zero in the non-canonical case even if the phase space
compressibility is null. Instead, the Jacobian determinant associated with
phase space flows is unity whenever non-canonical coordinates lead to a
vanishing compressibility, so that its use in order to define a measure may not
be always correct. To better illustrate this point, we derive a mathematical
condition for defining non-Hamiltonian phase space flows with zero
compressibility. The Jacobian determinant associated with time evolution in
phase space is altogether useful for analyzing time translation invariance. The
proper definition of a phase space measure is particularly important when
defining the entropy functional in the canonical, non-canonical, and
non-Hamiltonian cases. We show how the use of relative entropies can circumvent
some subtle problems that are encountered when dealing with continuous
probability distributions and phase space measures. Finally, a maximum
(relative) entropy principle is formulated for non-canonical and
non-Hamiltonian phase space flows.Comment: revised introductio
Hydrogen and muonium in diamond: A path-integral molecular dynamics simulation
Isolated hydrogen, deuterium, and muonium in diamond have been studied by
path-integral molecular dynamics simulations in the canonical ensemble.
Finite-temperature properties of these point defects were analyzed in the range
from 100 to 800 K. Interatomic interactions were modeled by a tight-binding
potential fitted to density-functional calculations. The most stable position
for these hydrogenic impurities is found at the C-C bond center. Vibrational
frequencies have been obtained from a linear-response approach, based on
correlations of atom displacements at finite temperatures. The results show a
large anharmonic effect in impurity vibrations at the bond center site, which
hardens the vibrational modes with respect to a harmonic approximation.
Zero-point motion causes an appreciable shift of the defect level in the
electronic gap, as a consequence of electron-phonon interaction. This defect
level goes down by 70 meV when replacing hydrogen by muonium.Comment: 11 pages, 8 figure
Alchemical normal modes unify chemical space
In silico design of new molecules and materials with desirable quantum
properties by high-throughput screening is a major challenge due to the high
dimensionality of chemical space. To facilitate its navigation, we present a
unification of coordinate and composition space in terms of alchemical normal
modes (ANMs) which result from second order perturbation theory. ANMs assume a
predominantly smooth nature of chemical space and form a basis in which new
compounds can be expanded and identified. We showcase the use of ANMs for the
energetics of the iso-electronic series of diatomics with 14 electrons, BN
doped benzene derivatives (C(BN)H with ),
predictions for over 1.8 million BN doped coronene derivatives, and genetic
energy optimizations in the entire BN doped coronene space. Using Ge lattice
scans as reference, the applicability ANMs across the periodic table is
demonstrated for III-V and IV-IV-semiconductors Si, Sn, SiGe, SnGe, SiSn, as
well as AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, and InSb. Analysis of our
results indicates simple qualitative structure property rules for estimating
energetic rankings among isomers. Useful quantitative estimates can also be
obtained when few atoms are changed to neighboring or lower lying elements in
the periodic table. The quality of the predictions often increases with the
symmetry of system chosen as reference due to cancellation of odd order terms.
Rooted in perturbation theory the ANM approach promises to generally enable
unbiased compound exploration campaigns at reduced computational cost
Isotopic equilibria in aqueous clusters at low temperatures: Insights from the MB-pol many-body potential
By combining path-integrals molecular dynamics simulations with the accurate MB-pol potential energy surface, we investigate the role of alternative potential models on isotopic fractionation ratios between H and D atoms at dangling positions in water clusters at low temperatures. Our results show clear stabilizations of the lighter isotope at dangling sites, characterized by free energy differences ΔG that become comparable to or larger than kBT for temperatures below ∼75 K. The comparison between these results to those previously reported using the empirical q-TIP4P/F water model [P. E. Videla et al., J. Phys. Chem. Lett. 5, 2375 (2014)] reveals that the latter Hamiltonian overestimates the H stabilization by ∼25%. Moreover, predictions from the MB-pol model are in much better agreement with measured results reported for similar isotope equilibria at ice surfaces. The dissection of the quantum kinetic energies into orthogonal directions shows that the dominant differences between the two models are to be found in the anharmonic characteristics of the potential energy surfaces along OH bond directions involved in hydrogen bonds.Fil: Videla, Pablo Ernesto. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química, Física de los Materiales, Medioambiente y Energía. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química, Física de los Materiales, Medioambiente y Energía; ArgentinaFil: Rossky, Peter J.. Rice University; Estados UnidosFil: Laria, Daniel Hector. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química, Física de los Materiales, Medioambiente y Energía. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química, Física de los Materiales, Medioambiente y Energía; Argentina. Comisión Nacional de Energía Atómica; Argentin
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