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 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

Thermodynamics of hexagonal-close-packed iron under Earth’s core conditions

The free energy and other thermodynamic properties of hexagonal-close-packed iron are calculated by direct ab initio methods over a wide range of pressures and temperatures relevant to the Earth’s core. The ab initio calculations are based on density-functional theory in the generalized-gradient approximation, and are performed using the projector augmented wave approach. Thermal excitation of electrons is fully included. The Helmholtz free energy consists of three parts, associated with the rigid perfect lattice, harmonic lattice vibrations, and anharmonic contributions, and the technical problems of calculating these parts to high precision are investigated. The harmonic part is obtained by computing the phonon frequencies over the entire Brillouin zone, and by summation of the free-energy contributions associated with the phonon modes. The anharmonic part is computed by the technique of thermodynamic integration using carefully designed reference systems. Detailed results are presented for the pressure, specific heat, bulk modulus, expansion coefficient and Grüneisen parameter, and comparisons are made with values obtained from diamond-anvil-cell and shock experiments

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

Melting curve of MgO from first-principles simulations

First-principles calculations based on density functional theory, both with the local density approximation (LDA) and with generalized gradient corrections (GGA), have been used to simulate solid and liquid MgO in direct coexistence in the range of pressure 0 <= p <= 135 GPa. The calculated LDA zero pressure melting temperature is T-m(LDA)=3110 +/- 50 K, in good agreement with the experimental data. The GGA zero pressure melting temperature T-m(GGA)=2575 +/- 100 K is significantly lower than the LDA one, but the difference between the GGA and the LDA is greatly reduced at high pressure. The LDA zero pressure melting slope is dT/dp similar to 100 K/GPa, which is more than 3 times higher than the currently available experimental one from Zerr and Boehler [Nature (London) 371, 506 (1994)]. At the core mantle boundary pressure of 135 GPa MgO melts at T-m=8140 +/- 150 K

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

Schottky defect formation energy in MgO calculated by diffusion Monte Carlo

The energetics of point defects in oxide materials plays a major role in determining their high-temperature properties, but experimental measurements are difficult, and calculations based on density functional theory (DFT) are not necessarily reliable. We report quantum Monte Carlo calculations of the formation energy E-S of Schottky defects in MgO, which demonstrate the feasibility of using this approach to overcome the deficiencies of DFT. In order to investigate system-size errors, we also report DFT calculations of E-S on repeating cells of up to similar to 1000 atoms, which indicate that QMC calculations on systems of only 54 atoms should yield high precision. The DFT calculations also provide the relaxed structures used in the variational and diffusion Monte Carlo calculations. For MgO, we find E-S to be in close agreement with results from DFT and from model interaction potentials, and consistent with the scattered experimental values. The prospects for applying the same approach to transition metal oxides such as FeO are indicated

Compositional instability of Earth's solid inner core

[1] All models that invoke convection to explain the observed seismic variations in Earth's inner core require unstable inner core stratification. Previous work has assumed that chemical effects are stabilizing and focused on thermal convection, but recent calculations indicate that the thermal conductivity at core temperatures and pressures is so large that the inner core must cool entirely by conduction. We examine partitioning of oxygen, sulfur, and silicon in binary iron alloys and show that inner core growth results in a variable light element concentration with time: oxygen concentration decreases, sulfur concentration decreases initially and increases later, and silicon produces a negligible effect to within the model errors. The result is a net destabilizing concentration gradient. Convective stability is measured by a Rayleigh number, which exceeds the critical value for reasonable estimates of the viscosity and diffusivity. Our results suggest that inner core convection models, including the recently proposed translational mode, can be viable candidates for explaining seismic results if the driving force is compositional

America\u27s Newest Boogeyman for Deviant Teen Behavior: Violent Video Games and the First Amendment

Are violent video games harming America’s youth? Is it possible a series of interconnected circuit boards can influence children (or even adults) to become, themselves, violent? If so, how should our society-- and government-- respond? To properly answer this last query, violent video games must be viewed through the lens of the First Amendment. Simply put: do games depicting grotesque acts of depravity so profound as to negatively influence the psyche warrant the full constitutional protections ordinarily guaranteed under the mantle of free speech and expression? Are these guarantees without limit? If not, how far may the government go in regulating the content or restricting the availability of these games? This paper first examines the history of video game development and its economic significance. Next, similar “societal boogeymen” are examined, compared, and contrasted to video games. Their impact on society and law is also examined. What, if any, First Amendment protections this class of video games should receive as well as possible regulatory schemes and limitations are then examined. Finally, after weighing public policy interests, a new regulatory framework is proposed