M. J. Gillan

Calculation of the vacancy formation energy in aluminium

This paper addresses the problem of calculating the vacancy formation energy in simple metals and presents results for aluminium. The calculations are based on the pseudopotential method, the local-density approximation for exchange and correlation, and periodically repeating geometry. The approach used is similar to that proposed by Car and Parrinello, and allows the simultaneous relaxation of the electrons and the ionic positions. Problems peculiar to metals in this approach are discussed and a way of overcoming them is presented. The calculated vacancy energy (0.56 eV) in aluminium is in quite good agreement with experiment (0.66 eV). Comparisons with perturbation theory show that the calculated value is subject to a technical error of only approximately 0.03 eV and that corrections due to periodic boundary conditions are also of this order. The contribution to the vacancy energy from non-linear effects is similar to the jellium estimate of Evans and Finnis.

The melting curve of iron at the pressures of the Earth's core from ab initio calculations

The solid inner core of the Earth and the liquid outer core consist mainly of iron so that knowledge of the high-pressure thermodynamic properties of iron is important for understanding the Earths deep interior. An accurate knowledge of the melting properties of iron is particularly important, as the temperature distribution in the core is relatively uncertain and a reliable estimate of the melting temperature of iron at the pressure of the inner-core boundary would put a much-needed constraint on core temperatures. Here we used ab initio methods to compute the free energies of both solid and liquid iron, and we argue that the resulting theoretical melting curve competes in accuracy with those obtained from high-pressure experiments. Our results give a melting temperature of iron of ∼6,700 ± 600u2009K at the pressure of the inner-core boundary, consistent with some of the experimental measurements. Our entirely ab initio methods should also be applicable to many other materials and problems.

The adsorption of H2O on TiO2 and SnO2(110) studied by first-principles calculations

First-principles calculations based on density functional theory and the pseudopotential method have been used to investigate the energetics of H2O adsorption on the (110) surface of TiO2 and SnO2. Full relaxation of all atomic positions is performed on slab systems with periodic boundary conditions, and cases of full and half coverage are studied. Both molecular and dissociative (H2O→OH−+H−) adsorption are treated, and allowance is made for relaxation of the adsorbed species to unsymmetrica configurations. It is found that for both TiO2 and SnO2 an unsymmetrical dissociated configuration is the most stable. The symmetrical molecularly adsorbed configuration is unstable with respect to lowering of symmetry, and is separated from the fully dissociated configuration by at most a very small energy barrier. The calculated dissociative adsorption energies for TiO2 and SnO2 are in reasonable agreement with the results of thermal desorption experiments. Calculated total and local electronic densities of states for dissociatively and molecularly adsorbed configurations are presented, and their relation with experimental UPS spectra is discussed.

A systematic study of the surface energetics and structure of TiO2(110) by first-principles calculations

First-principles calculations based on density functional theory and the pseudopotential method have been used to study the surface energetics and structure of the TiO2(110) surface. Periodically repeating slab geometry is used, and we have investigated the effect of variable vacuum width and slab thickness on the predicted surface energy and surface atomic displacements. We find that vacuum widths of only 4 A are sufficient to converge the surface energy to within 0.01 J m−2. Slab thicknesses of at least 6 layers are necessary to achieve similar convergence of the surface energy. Predicted surface atomic displacements are found to differ significantly for slab thicknesses of four layers or less. The displacements are in semi-quantitative agreement with those from other calculations and a recent experimental study. However, in common with all other calculations, the displacement of the bridging oxygen is significantly underestimated when compared to the experimental value.

The adsorption and dissociation of ROH molecules on TiO2(110)

Abstract First-principles calculations based on density-functional theory and the pseudopotential method are used to investigate the energetics of adsorption of the series of molecules H 2 O, CH 3 OH, H 2 O 2 and HCO 2 H on the TiO 2 (110) surface. The aim of the work is to elucidate the factors that determine whether the adsorption is molecular or dissociative, including the acidity of the molecule, the geometry and electrostatic properties of the surface, and the interaction between adsorbed species. It is shown that the theoretical methods reproduce experimental values of the gas-phase heterolytic and homolytic dissociation energies to reasonable accuracy (within ∼20xa0kJxa0mol −1 for all four molecules). We find that the adsorption energy for the most favourable molecular mode of adsorption is extremely close to that for dissociative adsorption in the cases of H 2 O, CH 3 OH and H 2 O 2 . For HCO 2 H, dissociative adsorption is favoured by a substantial margin, provided the dissociated geometry preserves the equivalence of the two oxygens in the formate ion. It is also shown that the geometry of the TiO 2 (110) surface plays a crucial role in determining the conformations of the most stable geometries, and that hydrogen bonding between adsorbed species is also important.

The Structure of the Stoichiometric and Reduced SnO2 (110) Surface

First-principles calculations based on density functional theory (DFT) and the pseudopotential method have been used to study the stoichiometric and reduced SnO2(110) surface. The ionic relaxations are found to be moderate for both the stoichiometric and reduced surfaces, and are very similar to those found in recent DFT-pseudopotential work on TiO2. Removal of neutral oxygen leaves two electrons per oxygen on the surface, which are distributed in channels passing through bridging oxygen sites. The associated electron density can be attributed to reduction of tin from Sn4+ to Sn2+, but only if the charge distribution on Sn2+ is recognized to be highly asymmetric. Reduction of the surface gives rise to a broad distribution of gap states, in qualitative agreement with spectroscopic measurements.

First-principles molecular dynamics simulation of water dissociation on TiO2 (110)

Abstract We have performed first-principles molecular dynamics calculations of water adsorption on TiO2 (110). We find that dissociative adsorption occurs at the fivefold-coordinated Ti site resulting in the formation of two types of hydroxyl group. The vibrational spectra calculated from this hydroxylated surface show that a clear stretch frequency is present for only one of these groups, with vibrations from the other hydroxyl broadened due to hydrogen bonding between the two hydroxyl groups.

Self-consistent first-principles technique with linear scaling

An algorithm for first-principles electronic structure calculations having a computational cost which scales linearly with the system size is presented. Our method exploits the real-space localization of the density matrix, and in this respect it is related to the technique of Li, Nunes and Vanderbilt. The density matrix is expressed in terms of localized support functions, and a matrix of variational parameters, L, having a finite spatial range. The total energy is minimized with respect to both the support functions and the elements of the L matrix. The method is variational, and becomes exact as the ranges of the support functions and the L matrix are increased. We have tested the method on crystalline silicon systems containing up to 216 atoms, and we discuss some of these results.

Linear-scaling density-functional-theory technique: The density-matrix approach

A recently proposed linear-scaling scheme for density-functional pseudopoten-tial calculations is described in detail. The method is based on a formulation of density functional theory in which the ground state energy is determined by minimization with respect to the density matrix, subject to the condition that the eigenvalues of the latter lie in the range [0,1]. Linear-scaling behavior is achieved by requiring that the density matrix should vanish when the separation of its arguments exceeds a chosen cutoff. The limitation on the eigenvalue range is imposed by the method of Li, Nunes and Vanderbilt. The scheme is implemented by calculating all terms in the energy on a uniform real-space grid, and minimization is performed using the conjugate-gradient method. Tests on a 512-atom Si system show that the total energy converges rapidly as the range of the density matrix is increased. A discussion of the relation between the present method and other linear-scaling methods is given, and some problems that still require solution are indicated.

Structure of the (0001) surface of α-Al2O3 from first principles calculations

Fully self-consistent ab initio calculations based on pseudopotentials are used to study the structure and energetics of the basal-plane surface of α-Al2O3. The calculated forces on the atoms are used to relax the atomic positions to equilibrium. It is shown that surface relaxations are very large and lead to a reduction of the surface energy by over a factor of two. The results support the validity of earlier work based on pair-interaction models.