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

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

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

Ab initio statistical mechanics of surface adsorption and desorption: I. H2_2O 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

The earth’s core: an approach from first principles

The Earth’s core is largely composed of iron (Fe), alloyed with less dense elements such as sulphur, silicon and/or oxygen. The phase relations and physical properties of both solid and liquid Fe-alloys are therefore of great geophysical importance. As a result, over the past fifty years the properties of Fe and its alloys have been extensively studied experimentally. However, achieving the extreme pressures (up to 360 GPa) and temperatures (~6000K) found in the core provide a major experimental challenge, and it is not surprising that there are still considerable discrepancies in the results obtained by using different experimental techniques. In the past fifteen years quantum mechanical techniques have been applied to predict the properties of Fe. Here we review the progress that has been made in the use of first principles methods to study Fe and its alloys, and as a result of these studies we conclude: (i) that pure Fe adopts an hexagonal close packed structure under core conditions and melts at ~6200 K at 360 GPa, (ii) that thermodynamic equilibrium and observed seismic data are satisfied by a liquid Fe alloy outer core with a composition of ~10 mole% S (or Si) and 8 mole% O crystallising at ~ 5500 K to give an Fe alloy inner core with ~8 mole% S (or Si) and 0.2 mole % O, and (iii) that with such concentrations of S (or Si), an Fe alloy might adopt a body centred cubic structure in all or part of the inner core. In the future the roles of Ni, C, H and K in the core need to be studied, and techniques to predict the transport and rheological properties of Fe alloys need to be developed