Electronic correlations and transport in iron at Earth's core conditions.

The transport properties of iron under Earth's inner core conditions are essential input for the geophysical modelling but are poorly constrained experimentally. Here we show that the thermal and electrical conductivity of iron at those conditions remains high even if the electron-electron-scattering (EES) is properly taken into account. This result is obtained by ab initio simulations taking into account consistently both thermal disorder and electronic correlations. Thermal disorder suppresses the non-Fermi-liquid behavior of the body-centered cubic iron phase, hence, reducing the EES; the total calculated thermal conductivity of this phase is 220 Wm-1 K-1 with the EES reduction not exceeding 20%. The EES and electron-lattice scattering are intertwined resulting in breaking of the Matthiessen's rule with increasing EES. In the hexagonal close-packed iron the EES is also not increased by thermal disorder and remains weak. Our main finding thus holds for the both likely iron phases in the inner core.

Energy benchmarks for methane-water systems from quantum Monte Carlo and second-order Møller-Plesset calculations.

The quantum Monte Carlo (QMC) technique is used to generate accurate energy benchmarks for methane-water clusters containing a single methane monomer and up to 20 water monomers. The benchmarks for each type of cluster are computed for a set of geometries drawn from molecular dynamics simulations. The accuracy of QMC is expected to be comparable with that of coupled-cluster calculations, and this is confirmed by comparisons for the CH4-H2O dimer. The benchmarks are used to assess the accuracy of the second-order Møller-Plesset (MP2) approximation close to the complete basis-set limit. A recently developed embedded many-body technique is shown to give an efficient procedure for computing basis-set converged MP2 energies for the large clusters. It is found that MP2 values for the methane binding energies and the cohesive energies of the water clusters without methane are in close agreement with the QMC benchmarks, but the agreement is aided by partial cancelation between 2-body and beyond-2-body errors of MP2. The embedding approach allows MP2 to be applied without loss of accuracy to the methane hydrate crystal, and it is shown that the resulting methane binding energy and the cohesive energy of the water lattice agree almost exactly with recently reported QMC values.

Communication: On the stability of ice 0, ice i, and I(h).

Using ab initio methods, we examine the stability of ice 0, a recently proposed tetragonal form of ice implicated in the homogeneous freezing of water [J. Russo, F. Romano, and H. Tanaka, Nat. Mater. 13, 670 (2014)]. Vibrational frequencies are computed across the complete Brillouin Zone using Density Functional Theory (DFT), to confirm mechanical stability and quantify the free energy of ice 0 relative to ice I(h). The robustness of this result is tested via dispersion corrected semi-local and hybrid DFT, and Quantum Monte-Carlo calculation of lattice energies. Results indicate that popular molecular models only slightly overestimate the stability of ice zero. In addition, we study all possible realisations of proton disorder within the ice zero unit cell, and identify the ground state as ferroelectric. Comparisons are made to other low density metastable forms of ice, suggesting that the ice i structure [C. J. Fennel and J. D. Gezelter, J. Chem. Theory Comput. 1, 662 (2005)] may be equally relevant to ice formation.

Analyzing the errors of DFT approximations for compressed water systems.

We report an extensive study of the errors of density functional theory (DFT) approximations for compressed water systems. The approximations studied are based on the widely used PBE and BLYP exchange-correlation functionals, and we characterize their errors before and after correction for 1- and 2-body errors, the corrections being performed using the methods of Gaussian approximation potentials. The errors of the uncorrected and corrected approximations are investigated for two related types of water system: first, the compressed liquid at temperature 420 K and density 1.245 g/cm(3) where the experimental pressure is 15 kilobars; second, thermal samples of compressed water clusters from the trimer to the 27-mer. For the liquid, we report four first-principles molecular dynamics simulations, two generated with the uncorrected PBE and BLYP approximations and a further two with their 1- and 2-body corrected counterparts. The errors of the simulations are characterized by comparing with experimental data for the pressure, with neutron-diffraction data for the three radial distribution functions, and with quantum Monte Carlo (QMC) benchmarks for the energies of sets of configurations of the liquid in periodic boundary conditions. The DFT errors of the configuration samples of compressed water clusters are computed using QMC benchmarks. We find that the 2-body and beyond-2-body errors in the liquid are closely related to similar errors exhibited by the clusters. For both the liquid and the clusters, beyond-2-body errors of DFT make a substantial contribution to the overall errors, so that correction for 1- and 2-body errors does not suffice to give a satisfactory description. For BLYP, a recent representation of 3-body energies due to Medders, Babin, and Paesani [J. Chem. Theory Comput. 9, 1103 (2013)] gives a reasonably good way of correcting for beyond-2-body errors, after which the remaining errors are typically 0.5 mE(h) ≃ 15 meV/monomer for the liquid and the clusters.

Energy benchmarks for water clusters and ice structures from an embedded many-body expansion.

We show how an embedded many-body expansion (EMBE) can be used to calculate accurate ab initio energies of water clusters and ice structures using wavefunction-based methods. We use the EMBE described recently by Bygrave et al. [J. Chem. Phys. 137, 164102 (2012)], in which the terms in the expansion are obtained from calculations on monomers, dimers, etc., acted on by an approximate representation of the embedding field due to all other molecules in the system, this field being a sum of Coulomb and exchange-repulsion fields. Our strategy is to separate the total energy of the system into Hartree-Fock and correlation parts, using the EMBE only for the correlation energy, with the Hartree-Fock energy calculated using standard molecular quantum chemistry for clusters and plane-wave methods for crystals. Our tests on a range of different water clusters up to the 16-mer show that for the second-order Møller-Plesset (MP2) method the EMBE truncated at 2-body level reproduces to better than 0.1 mE(h)/monomer the correlation energy from standard methods. The use of EMBE for computing coupled-cluster energies of clusters is also discussed. For the ice structures Ih, II, and VIII, we find that MP2 energies near the complete basis-set limit reproduce very well the experimental values of the absolute and relative binding energies, but that the use of coupled-cluster methods for many-body correlation (non-additive dispersion) is essential for a full description. Possible future applications of the EMBE approach are suggested.

Fine tuning of graphene-metal adhesion by surface alloying.

We show that bimetallic surface alloying provides a viable route for governing the interaction between graphene and metal through the selective choice of the elemental composition of the surface alloy. This concept is illustrated by an experimental and theoretical characterization of the properties of graphene on a model PtRu surface alloy on Ru(0001), with a concentration of Pt atoms in the first layer between 0 and 50%. The progressive increase of the Pt content determines the gradual detachment of graphene from the substrate, which results from the modification of the carbon orbital hybridization promoted by Pt. Alloying is also found to affect the morphology of graphene, which is strongly corrugated on bare Ru, but becomes flat at a Pt coverage of 50%. The method here proposed can be readily extended to several supports, thus opening the way to the conformal growth of graphene on metals and to a full tunability of the graphene-substrate interaction.

Communication: energy benchmarking with quantum Monte Carlo for water nano-droplets and bulk liquid water.

We show the feasibility of using quantum Monte Carlo (QMC) to compute benchmark energies for configuration samples of thermal-equilibrium water clusters and the bulk liquid containing up to 64 molecules. Evidence that the accuracy of these benchmarks approaches that of basis-set converged coupled-cluster calculations is noted. We illustrate the usefulness of the benchmarks by using them to analyze the errors of the popular BLYP approximation of density functional theory (DFT). The results indicate the possibility of using QMC as a routine tool for analyzing DFT errors for non-covalent bonding in many types of condensed-phase molecular system.

First-principles energetics of water clusters and ice: a many-body analysis.

Standard forms of density-functional theory (DFT) have good predictive power for many materials, but are not yet fully satisfactory for cluster, solid, and liquid forms of water. Recent work has stressed the importance of DFT errors in describing dispersion, but we note that errors in other parts of the energy may also contribute. We obtain information about the nature of DFT errors by using a many-body separation of the total energy into its 1-body, 2-body, and beyond-2-body components to analyze the deficiencies of the popular PBE and BLYP approximations for the energetics of water clusters and ice structures. The errors of these approximations are computed by using accurate benchmark energies from the coupled-cluster technique of molecular quantum chemistry and from quantum Monte Carlo calculations. The systems studied are isomers of the water hexamer cluster, the crystal structures Ih, II, XV, and VIII of ice, and two clusters extracted from ice VIII. For the binding energies of these systems, we use the machine-learning technique of Gaussian Approximation Potentials to correct successively for 1-body and 2-body errors of the DFT approximations. We find that even after correction for these errors, substantial beyond-2-body errors remain. The characteristics of the 2-body and beyond-2-body errors of PBE are completely different from those of BLYP, but the errors of both approximations disfavor the close approach of non-hydrogen-bonded monomers. We note the possible relevance of our findings to the understanding of liquid water.

Assessment of density functional theory for iron(II) molecules across the spin-crossover transition.

Octahedral Fe(2+) molecules are particularly interesting as they often exhibit a spin-crossover transition. In spite of the many efforts aimed at assessing the performances of density functional theory for such systems, an exchange-correlation functional able to account accurately for the energetic of the various possible spin-states has not been identified yet. Here, we critically discuss the issues related to the theoretical description of this class of molecules from first principles. In particular, we present a comparison between different density functionals for four ions, namely, [Fe(H(2)O)(6)](2+), [Fe(NH(3))(6)](2+), [Fe(NCH)(6)](2+), and [Fe(CO)(6)](2+). These are characterized by different ligand-field splittings and ground state spin multiplicities. Since no experimental data are available for the gas phase, the density functional theory results are benchmarked against those obtained with diffusion Monte Carlo, one of the most accurate methods available to compute ground state total energies of quantum systems. On the one hand, we show that most of the functionals considered provide a good description of the geometry and of the shape of the potential energy surfaces. On the other hand, the same functionals fail badly in predicting the energy differences between the various spin states. In the case of [Fe(H(2)O)(6)](2+), [Fe(NH(3))(6)](2+), [Fe(NCH)(6)](2+), this failure is related to the drastic underestimation of the exchange energy. Therefore, quite accurate results can be achieved with hybrid functionals including about 50% of Hartree-Fock exchange. In contrast, in the case of [Fe(CO)(6)](2+), the failure is likely to be caused by the multiconfigurational character of the ground state wave-function and no suitable exchange and correlation functional has been identified.

Assessing the accuracy of quantum Monte Carlo and density functional theory for energetics of small water clusters.

We present a detailed study of the energetics of water clusters (H(2)O)(n) with n ≤ 6, comparing diffusion Monte Carlo (DMC) and approximate density functional theory (DFT) with well converged coupled-cluster benchmarks. We use the many-body decomposition of the total energy to classify the errors of DMC and DFT into 1-body, 2-body and beyond-2-body components. Using both equilibrium cluster configurations and thermal ensembles of configurations, we find DMC to be uniformly much more accurate than DFT, partly because some of the approximate functionals give poor 1-body distortion energies. Even when these are corrected, DFT remains considerably less accurate than DMC. When both 1- and 2-body errors of DFT are corrected, some functionals compete in accuracy with DMC; however, other functionals remain worse, showing that they suffer from significant beyond-2-body errors. Combining the evidence presented here with the recently demonstrated high accuracy of DMC for ice structures, we suggest how DMC can now be used to provide benchmarks for larger clusters and for bulk liquid water.

The kinetics of homogeneous melting beyond the limit of superheating.

Molecular dynamics simulation is used to study the time-scales involved in the homogeneous melting of a superheated crystal. The interaction model used is an embedded-atom model for Fe developed in previous work, and the melting process is simulated in the microcanonical (N, V, E) ensemble. We study periodically repeated systems containing from 96 to 7776 atoms, and the initial system is always the perfect crystal without free surfaces or other defects. For each chosen total energy E and number of atoms N, we perform several hundred statistically independent simulations, with each simulation lasting for between 500 ps and 10 ns, in order to gather statistics for the waiting time τ(w) before melting occurs. We find that the probability distribution of τ(w) is roughly exponential, and that the mean value <τ(w)> depends strongly on the excess of the initial steady temperature of the crystal above the superheating limit identified by other researchers. The mean <τ(w)> also depends strongly on system size in a way that we have quantified. For very small systems of ~100 atoms, we observe a persistent alternation between the solid and liquid states, and we explain why this happens. Our results allow us to draw conclusions about the reliability of the recently proposed Z method for determining the melting properties of simulated materials and to suggest ways of correcting for the errors of the method.

Thermal stability of corrugated epitaxial graphene grown on Re(0001).

We report on a novel approach to determine the relationship between the corrugation and the thermal stability of epitaxial graphene grown on a strongly interacting substrate. According to our density functional theory calculations, the C single layer grown on Re(0001) is strongly corrugated, with a buckling of 1.6 Å, yielding a simulated C 1s core level spectrum which is in excellent agreement with the experimental one. We found that corrugation is closely knit with the thermal stability of the C network: C-C bond breaking is favored in the strongly buckled regions of the moiré cell, though it requires the presence of diffusing graphene layer vacancies.

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 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 generalize the techniques developed recently for classical nuclei. We present practical calculations based on density functional theory with a generalized-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.

First-principles simulations of lithium melting: stability of the bcc phase close to melting.

We report large-scale first-principles simulations of melting of four different phases of Li at pressures ranging from 0 to 50 GPa. We find excellent agreement with existing experimental data at low pressures, and confirm that above 10 GPa the melting line develops a negative slope, in parallel to what occurs for Na at 30 GPa. Surprisingly, our results indicate that the melting temperature of the bcc phase is always higher than that of fcc Li, suggesting the intriguing possibility of the existence of a narrow field of bcc stability separating the fcc and liquid phases, as predicted by Alexander and McTague [Phys. Rev. Lett. 41, 702 (1978)].

Melting properties of a simple tight-binding model of transition metals. I. The region of half-filled d-band.

We present calculations of the free energy, and hence the melting properties, of a simple tight-binding model for transition metals in the region of d-band filling near the middle of a d-series, the parameters of the model being designed to mimic molybdenum. The melting properties are calculated for pressures ranging from ambient to several megabars. The model is intended to be the simplest possible tight-binding representation of the two basic parts of the energy: first, the pairwise repulsion due to Fermi exclusion; and second, the d-band bonding energy described in terms of an electronic density of states that depends on structure. In addition to the number of d-electrons, the model contains four parameters, which are adjusted to fit the pressure dependent d-band-width and the zero-temperature pressure-volume relation of Mo. We show that the resulting model reproduces well the phonon dispersion relations of Mo in the body-centered-cubic structure, as well as the radial distribution function of the high-temperature solid and liquid given by earlier first-principles simulations. Our free energy calculations start from the free energy of the liquid and solid phases of the purely repulsive pair potential model, without d-band bonding. The free energy of the full tight-binding model is obtained from this by thermodynamic integration. The resulting melting properties of the model are quite close to those given by earlier first-principles work on Mo. An interpretation of these melting properties is provided by showing how they are related to those of the purely repulsive model.

The role of steps in the dissociation of H(2) on Mg(0001).

The role of steps in the dissociation of molecules on metal surfaces has been extensively investigated in the past. In particular, both theoretical calculations and experimental results for H(2) dissociation on transition metal (TM) surfaces show that steps can significantly increase the reactivity, leading to higher metal-H binding energies and lower activation energies. Here we have used density functional theory (DFT) with the generalized gradient approximation (GGA) to investigate the role of steps on the Mg(0001) surface in the dissociation of H(2) and the binding of H to the metal surface. Our results follow those found for TM surfaces as far as H adsorption energies are concerned, namely that adsorption energies are higher near the steps. However, we find that the activation energy for the dissociation of hydrogen is hardly affected by the presence of steps, with a DFT-GGA value of 0.85 eV, only marginally lower than the value 0.87 eV found on the flat Mg(0001) surface.

High-precision calculation of Hartree-Fock energy of crystals.

When using quantum chemistry techniques to calculate the energetics of bulk crystals, there is a need to calculate the Hartree-Fock (HF) energy of the crystal at the basis-set limit. We describe a strategy for achieving this, which exploits the fact that the HF energy of crystals can now be calculated using pseudopotentials and plane-wave basis sets, an approach that permits basis-set convergence to arbitrary precision. The errors due to the use of pseudopotentials are then computed from the difference of all-electron and pseudopotential total energies of atomic clusters, extrapolated to the bulk-crystal limit. The strategy is tested for the case of the LiH crystal, and it is shown that the HF cohesive energy can be converged with respect to all technical parameters to a precision approaching 0.1 mE(h) per atom. This cohesive energy and the resulting HF value of the equilibrium lattice parameter are compared with literature values obtained using Gaussian basis sets.

Hydrogen dissociation and diffusion on Ni- and Ti-doped Mg(0001) surfaces.

It is well-known, both theoretically and experimentally, that alloying MgH(2) with transition elements can significantly improve the thermodynamic and kinetic properties for H(2) desorption, as well as the H(2) intake by Mg bulk. Here, we present a density functional theory investigation of hydrogen dissociation and surface diffusion over a Ni-doped surface and compare the findings to previously investigated Ti-doped Mg(0001) and pure Mg(0001) surfaces. Our results show that the energy barrier for hydrogen dissociation on the pure Mg(0001) surface is high, while it is small/null when NiTi are added to the surface as dopants. We find that the binding energy of the two H atoms near the dissociation site is high on Ti, effectively impeding diffusion away from the Ti site. By contrast, we find that on Ni, the energy barrier for diffusion is much reduced. Therefore, although both Ti and Ni promote H(2) dissociation, only Ni appears to be a good catalyst for Mg hydrogenation, allowing diffusion away from the catalytic sites. Experimental results corroborate these theoretical findings, i.e., faster hydrogenation of the Ni-doped Mg sample as opposed to the reference Mg- or Ti-doped Mg.

Ab initio statistical mechanics of surface adsorption and desorption. I. H2O on MgO (001) at low coverage.

We present a general computational scheme based on molecular dynamics (MD) 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 MD 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 that the equilibration rate on the surface is faster than the desorption rate. We apply the theory by ab initio MD simulation to the case of H2O on MgO (001) in the low-coverage limit, using the Perdew-Burke-Ernzerhof (PBE) form of exchange correlation. The calculations yield an 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.