Thomas R. Mattsson

Designing meaningful density functional theory calculations in materials science—a primer

Density functional theory (DFT) methods for calculating the quantum mechanical ground states of condensed matter systems are now a common and significant component of materials research. The growing importance of DFT reflects the development of sufficiently accurate functionals, efficient algorithms and continuing improvements in computing capabilities. As the materials problems to which DFT is applied have become large and complex, so have the sets of calculations necessary for investigating a given problem. Highly versatile, powerful codes exist to serve the practitioner, but designing useful simulations is a complicated task, involving intricate manipulation of many variables, with many pitfalls for the unwary and the inexperienced. We discuss several of the most important issues that go into designing a meaningful DFT calculation. We emphasize the necessity of investigating these issues and reporting the critical details.

The AM05 density functional applied to solids

We show that the AM05 functional [Armiento and Mattsson, Phys. Rev. B 72, 085108 (2005)] has the same excellent performance for solids as the hybrid density functionals tested in Paier et al. [J. Chem. Phys. 124, 154709 (2006); 125, 249901 (2006)]. This confirms the original finding that AM05 performs exceptionally well for solids and surfaces. Hartree-Fock hybrid calculations are typically an order of magnitude slower than local or semilocal density functionals such as AM05, which is of a regular semilocal generalized gradient approximation form. The performance of AM05 is on average found to be superior to selecting the best of local density approximation and PBE for each solid. By comparing data from several different electronic-structure codes, we have determined that the numerical errors in this study are equal to or smaller than the corresponding experimental uncertainties.

Direct observation of an abrupt insulator-to-metal transition in dense liquid deuterium

Driving liquid deuterium into metal Quick and powerful compression can force materials to change their properties dramatically. Knudson et al. compressed liquid deuterium to extreme temperatures and pressures using high-energy magnetic pulses at the Sandia Z-machine (see the Perspective by Ackland). Deuterium began to reflect like a mirror during compression, as the electrical conductivity sharply increased. The observed conditions for metallization of deuterium and hydrogen help us to build theoretical models for the universes most abundant element. This a our understanding of the internal layering of gas giant planets such as Jupiter and Saturn. Science, this issue p. 1455; see also p. 1429 Magnetic compression drives an insulator-to-metal transition in dense liquid deuterium. [Also see Perspective by Ackland] Eighty years ago, it was proposed that solid hydrogen would become metallic at sufficiently high density. Despite numerous investigations, this transition has not yet been experimentally observed. More recently, there has been much interest in the analog of this predicted metallic transition in the dense liquid, due to its relevance to planetary science. Here, we show direct observation of an abrupt insulator-to-metal transition in dense liquid deuterium. Experimental determination of the location of this transition provides a much-needed benchmark for theory and may constrain the region of hydrogen-helium immiscibility and the boundary-layer pressure in standard models of the internal structure of gas-giant planets.Eighty years ago, it was proposed that solid hydrogen would become metallic at sufficiently high density. Despite numerous investigations, this transition has not yet been experimentally observed. More recently, there has been much interest in the analog of this predicted metallic transition in the dense liquid, due to its relevance to planetary science. Here, we show direct observation of an abrupt insulator-to-metal transition in dense liquid deuterium. Experimental determination of the location of this transition provides a much-needed benchmark for theory and may constrain the region of hydrogen-helium immiscibility and the boundary-layer pressure in standard models of the internal structure of gas-giant planets.

Quantum molecular dynamics simulations for the nonmetal-to-metal transition in fluid helium.

We have performed quantum molecular dynamics simulations for dense helium to study the nonmetal-to-metal transition at high pressures. We present new results for the equation of state and the Hugoniot curve in the warm dense matter region. The optical conductivity is calculated via the Kubo-Greenwood formula from which the dc conductivity is derived. The nonmetal-to-metal transition is identified at about 1 g/cm(3). We compare with experimental results as well as with other theoretical approaches, especially with predictions of chemical models.

Quantum Monte Carlo applied to solids

We apply diffusion quantum Monte Carlo to a broad set of solids, benchmarking the method by comparing bulk structural properties (equilibrium volume and bulk modulus) to experiment and density functional theory (DFT) based theories. The test set includes materials with many different types of binding including ionic, metallic, covalent, and van der Waals. We show that, on average, the accuracy is comparable to or better than that of DFT when using the new generation of functionals, including one hybrid functional and two dispersion corrected functionals. The excellent performance of quantum Monte Carlo on solids is promising for its application to heterogeneous systems and high-pressure/high-density conditions. Important to the results here is the application of a consistent procedure with regards to the several approximations that are made, such as finite-size corrections and pseudopotential approximations. This test set allows for any improvements in these methods to be judged in a systematic way.

Kinetic Monte Carlo simulations of nucleation on a surface with periodic strain: Spatial ordering and island-size distribution

We use kinetic Monte Carlo simulations to study nucleation of adsorbate islands on a solid surface on which a periodic strain field has been imposed. We show that, in spite of its very small effect on the diffusion constant of the atoms, the field orders the ensemble of islands. Better ordering and a narrower size distribution are obtained when the ensemble of islands produced by nucleation is coarsened.

AM05 Density Functional Applied to the Water Molecule, Dimer, and Bulk Liquid.

We compare results for water obtained with the AM05 exchange-correlation density functional ( Armiento, R.; Mattsson, A. E. Phys. Rev. B 2005, 72, 085108 ) with those obtained with five other pure functionals: LDA, PBE, PBEsol, RPBE, and BLYP. For liquid water, AM05 yields an O-O pair correlation function that is more structured than the ones of PBE and BLYP, which, in turn, are more structured than the one of RPBE. However, LDA and PBEsol yields more structured water than AM05. We show that AM05 yields a H2O dimer binding energy of 4.9 kcal/mol. The result is thus within 0.15 kcal/mol of CCSD(T) level theory (5.02 ± 0.05 kcal/mol). We confirm that accuracy in the water dimer binding energy is not a strong indicator for the fidelity of the resulting structure of liquid water.

A new method for simulating the late stages of island coarsening in thin film growth: The role of island diffusion and evaporation

We have developed a method for simulating the evolution of an ensemble of one-atom-high islands from deposition and nucleation to coarsening. Using this method we have studied three regimes of coarsening; coarsening due to island coalescence, coarsening driven by evaporation, and the case in which both mechanisms act simultaneously. The parameters have been chosen to mimic coarsening of Ag on Ag(001); they are not meant to reproduce the experimental results for Ag quantitatively, but to provide simulations relevant to metal-on-metal homoepitaxy. We find that the scaling laws proposed by the mean-field theory for the time dependence of the number of islands and the island size distribution function work well in the limiting case when coarsening is dominated by island diffusion and coalescence. In the opposite limit, when coarsening is dominated by evaporation, the scaling predicted for the island size works well, but the island size distribution predicted by the mean-field theory is narrower than the one f...

Shock compression of hydrocarbon foam to 200 GPa: Experiments, atomistic simulations, and mesoscale hydrodynamic modeling

Hydrocarbon foams are versatile materials extensively used in high energy-density physics (HEDP) experiments. However, little data exist above 100 GPa, where knowledge of the behavior is particularly important for designing, analyzing, and optimizing HEDP experiments. The complex internal structure and properties of foam call for a multi-scale modeling effort validated by experimental data. We present results from experiments, classical molecular dynamics simulations, and mesoscale hydrodynamic modeling of poly(4-methyl-1-pentene) (PMP) foams under strong shock compression. Experiments conducted using the Z-machine at Sandia National Laboratories shock compress ∼0.300 g/cm3 density PMP foams to 185 GPa. Molecular dynamics (MD) simulations model shock compressed PMP foam and elucidate behavior of the heterogeneous foams at high pressures. The MD results show quantitative agreement with the experimental data, while providing additional information about local temperature and dissociation. Three-dimensional ...

Simulations of mobility and evaporation rate of adsorbate islands on solid surfaces

We perform kinetic Monte Carlo simulations to examine the kinetic properties of one-atom-high islands formed by atoms adsorbed on a single-crystal surface. At sufficiently high temperature, the atoms can leave the island to migrate on the substrate. We call this process evaporation. We find that most of the evaporation events are described by a Poisson process characterized by a rate constant k(N,T), where N is the number of atoms in the island and T is the temperature. We also observe correlated evaporation events, which tend to follow each other in rapid succession. This complicated situation can be described, however, by an effective Poisson process that is defined to generate the correct vapor pressure. The dependence of k(N,T) on N follows an equation proposed by Metiu and Rosenfeld, and not a power law observed in previous work. The random motion of the atoms around the border of the island causes its center of mass to move along the surface. This island motion is diffusional, except at the shortest...