1,325 research outputs found

### Ab initio statistical mechanics of surface adsorption and desorption: II. Nuclear quantum effects

We show how the path-integral formulation of quantum statistical mechanics
can be used to construct practical {\em ab initio} techniques for computing the
chemical potential of molecules adsorbed on surfaces, with full inclusion of
quantum nuclear effects. The techniques we describe are based on the
computation of the potential of mean force on a chosen molecule, and generalise
the techniques developed recently for classical nuclei. We present practical
calculations based on density functional theory with a generalised-gradient
exchange-correlation functional for the case of H$_2$O on the MgO~(001) surface
at low coverage. We note that the very high vibrational frequencies of the
H$_2$O molecule would normally require very large numbers of time slices
(beads) in path-integral calculations, but we show that this requirement can be
dramatically reduced by employing the idea of thermodynamic integration with
respect to the number of beads. The validity and correctness of our
path-integral calculations on the H$_2$O/MgO~(001) system are demonstrated by
supporting calculations on a set of simple model systems for which quantum
contributions to the free energy are known exactly from analytic arguments.Comment: 11 pages, including 2 figure

### The energetics of water on oxide surfaces by quantum Monte Carlo

Density functional theory (DFT) is widely used in surface science, but gives
poor accuracy for oxide surface processes, while high-level quantum chemistry
methods are hard to apply without losing basis-set quality. We argue that
quantum Monte Carlo techniques allow these difficulties to be overcome, and we
present diffusion Monte Carlo results for the formation energy of the MgO(001)
surface and the adsorption energy of H$_2$O on this surface, using periodic
slab geometry. The results agree well with experiment. We note other oxide
surface problems where these techniques could yield immediate progress.Comment: 5 pages, 2 figure

### Comment on 'Molybdenum at High Pressure and Temperature: Melting from Another Solid Phase'

There has been a major controversy over the past seven years about the
high-pressure melting curves of transition metals. Static compression
(diamond-anvil cell: DAC) experiments up to the Mbar region give very low
melting slopes dT_m/dP, but shock-wave (SW) data reveal transitions indicating
much larger dT_m/dP values. Ab initio calculations support the correctness of
the shock data. In a very recent letter, Belonoshko et al. propose a simple and
elegant resolution of this conflict for molybdenum. Using ab initio
calculations based on density functional theory (DFT), they show that the
high-P/high-T phase diagram of Mo must be more complex than was hitherto
thought. Their calculations give convincing evidence that there is a transition
boundary between the normal bcc structure of Mo and a high-T phase, which they
suggest could be fcc. They propose that this transition was misinterpreted as
melting in DAC experiments. In confirmation, they note that their boundary also
explains a transition seen in the SW data. We regard Belonoshko et al.'s Letter
as extremely important, but we note that it raises some puzzling questions, and
we believe that their proposed phase diagram cannot be completely correct. We
have calculated the Helmholtz and Gibbs free energies of the bcc, fcc and hcp
phases of Mo, using essentially the same quasiharmonic methods as used by
Belonoshko et al.; we find that at high-P and T Mo in the hcp structure is more
stable than in bcc or fcc.Comment: 1 page, 1 figure. submitted to Phys. Rev. Let

### Complementary approaches to the ab initio calculation of melting properties

Several research groups have recently reported {\em ab initio} calculations
of the melting properties of metals based on density functional theory, but
there have been unexpectedly large disagreements between results obtained by
different approaches. We analyze the relations between the two main approaches,
based on calculation of the free energies of solid and liquid and on direct
simulation of the two coexisting phases. Although both approaches rely on the
use of classical reference systems consisting of parameterized empirical
interaction models, we point out that in the free energy approach the final
results are independent of the reference system, whereas in the current form of
the coexistence approach they depend on it. We present a scheme for correcting
the predictions of the coexistence approach for differences between the
reference and {\em ab initio} systems. To illustrate the practical operation of
the scheme, we present calculations of the high-pressure melting properties of
iron using the corrected coexistence approach, which agree closely with earlier
results from the free energy approach. A quantitative assessment is also given
of finite-size errors, which we show can be reduced to a negligible size.Comment: 14 pages, two figure

### Ab initio statistical mechanics of surface adsorption and desorption: I. H$_2$O on MgO (001) at low coverage

We present a general computational scheme based on molecular dynamics (m.d.)
simulation for calculating the chemical potential of adsorbed molecules in
thermal equilibrium on the surface of a material. The scheme is based on the
calculation of the mean force in m.d. simulations in which the height of a
chosen molecule above the surface is constrained, and subsequent integration of
the mean force to obtain the potential of mean force and hence the chemical
potential. The scheme is valid at any coverage and temperature, so that in
principle it allows the calculation of the chemical potential as a function of
coverage and temperature. It avoids all statistical mechanical approximations,
except for the use of classical statistical mechanics for the nuclei, and
assumes nothing in advance about the adsorption sites. From the chemical
potential, the absolute desorption rate of the molecules can be computed,
provided the equilibration rate on the surface is faster than the desorption
rate. We apply the theory by {\em ab initio} m.d. simulation to the case of
H$_2$O on MgO (001) in the low-coverage limit, using the Perdew-Burke-Ernzerhof
(PBE) form of exchange-correlation. The calculations yield an {\em ab initio}
value of the Polanyi-Wigner frequency prefactor, which is more than two orders
of magnitude greater than the value of $10^{13}$ s$^{-1}$ often assumed in the
past. Provisional comparison with experiment suggests that the PBE adsorption
energy may be too low, but the extension of the calculations to higher
coverages is needed before firm conclusions can be drawn. The possibility of
including quantum nuclear effects by using path-integral simulations is noted.Comment: 11 pages + 10 figure

### Ab-initio chemical potentials of solid and liquid solutions and the chemistry of the Earth's core

A general set of methods is presented for calculating chemical potentials in
solid and liquid mixtures using {\em ab initio} techniques based on density
functional theory (DFT). The methods are designed to give an {\em ab initio}
approach to treating chemical equilibrium between coexisting solid and liquid
solutions, and particularly the partitioning ratio of solutes between such
solutions. For the liquid phase, the methods are based on the general technique
of thermodynamic integration, applied to calculate the change of free energy
associated with the continuous interconversion of solvent and solute atoms, the
required thermal averages being computed by DFT molecular dynamics simulation.
For the solid phase, free energies and hence chemical potentials are obtained
using DFT calculation of vibrational frequencies of systems containing
substitutional solute atoms, with anharmonic contributions calculated, where
needed, by thermodynamic integration. The practical use of the methods is
illustrated by applying them to study chemical equilibrium between the outer
liquid and inner solid parts of the Earth's core, modelled as solutions of S,
Si and O in Fe. The calculations place strong constraints on the chemical
composition of the core, and allow an estimate of the temperature at the
inner-core/outer-core boundary.Comment: 19 pages, two figure

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