The implementation of technique for full structural optimizations of complex periodic systems in the DFT-PAW package VASP, including the volume and shape of the unit cell and the internal coordinates of the atoms, together with a correction that allows an appropriate modeling of London dispersion forces, as given by the DFT-D2 approach of Grimme [Grimme, S. J. Comp. Chem. 2006, 27, 1787], is reported. Dispersion corrections are calculated not only for the forces acting on the atoms, but also for the stresses on the unit cell. This permits a simultaneous optimization of all degrees of freedom. Benchmark results on a series of prototype systems are presented and compared to results obtained by other methods and experimental data. It is demonstrated that the computationally inexpensive DFT-D2 scheme yields reasonable predictions for the structure, bulk moduli, and cohesive energies of weakly bonded materials.

Improved description of the structure of molecular and layered crystals: ab initio DFT calculations with van der Waals corrections.

The influence of a simple semiempirical van der Waals (vdW) correction on the description of dispersive, covalent, and ionic bonds within density functional theory is studied. The correction is based on the asymptotic London form of dispersive forces and a damping function for each pair of atoms. It thus depends solely on the properties of the two atoms irrespective of their environment and is numerically very efficient. The correction is tested in comparison with results obtained using the generalized gradient approximation or the local density approximation for exchange and correlation. The results are also compared with reference values from experiment or quantum chemistry methods. In order to probe the universality and transferability of the semiempirical vdW correction, a range of solids and molecular systems with covalent, heteropolar, and vdW bonds are studied.

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Semiempirical van der Waals correction to the density functional description of solids and molecular structures

Studies of the thermal expansion of solids in the temperature range 1–100 K are reviewed. Effects due to thermal vibrations of the lattice, electrons, magnetic interactions and defects are fully discussed. The survey of experimental data is intended to be comprehensive. From the large volume of theoretical work in recent years the authors have aimed to select for discussion the most significant contributions.

Thermal expansion of solids at low temperatures

Predictions of observable properties by density-functional theory calculations (DFT) are used increasingly often by experimental condensed-matter physicists and materials engineers as data. These predictions are used to analyze recent measurements, or to plan future experiments in a rational way. Increasingly more experimental scientists in these fields therefore face the natural question: what is the expected error for such a first-principles prediction? Information and experience about this question is implicitly available in the computational community, scattered over two decades of literature. The present review aims to summarize and quantify this implicit knowledge. This eventually leads to a practical protocol that allows any scientist—experimental or theoretical—to determine justifiable error estimates for many basic property predictions, without having to perform additional DFT calculations. A central role is played by a large and diverse test set of crystalline solids, containing all ground-state...

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Error Estimates for Solid-State Density-Functional Theory Predictions: An Overview by Means of the Ground-State Elemental Crystals

The paper is a survey of experimental and theoretical results on exciton states in crystals of xenon, krypton, argon and neon. The absorption and luminescence spectra of the crystals and the band structure of electron and exciton states are analysed. Some features of the exciton-phonon interaction in pure and doped crystals are discussed. In contrast with other types of molecular crystal, those of rare gases can simultaneously support free and localized excitons. All features of the exciton spectra, in particular the hydrogen-like series of light absorption, the rich pattern of luminescence and the absorption and emission bands due to impurity centres, have been given a natural explanation in terms of the intermediate-radius exciton strongly bonded to the crystal lattice. These investigations of excitons in atomic cryocrystals have revealed a number of new effects and extended our knowledge of the cooperative excitation states of dielectrics.

Excitons in rare-gas crystals

Single crystals of 99.995% purity neon were grown by directional solidification from the liquid, and the x-ray lattice constant was measured by means of a rotating-camera method. The volume coefficient of thermal expansion was determined over the interval 2.5 to 23.9\ifmmode^\circ\else\textdegree\fi{}K with a precision ranging from 5 ppm \ifmmode^\circ\else\textdegree\fi{}${\mathrm{K}}^{\ensuremath{-}1}$ at low temperatures to 18 ppm \ifmmode^\circ\else\textdegree\fi{}${\mathrm{K}}^{\ensuremath{-}1}$ at the highest temperature. The lattice constant extrapolated to 0\ifmmode^\circ\else\textdegree\fi{}K is 4.46368\ifmmode\pm\else\textpm\fi{}0.00009 \AA{}*. Lattice-constant measurements of a crystal under hydrostatic helium pressure gave values of the isothermal compressibility over the temperature range 4.2 to 20.6\ifmmode^\circ\else\textdegree\fi{}K. The compressibility extrapolated to 0\ifmmode^\circ\else\textdegree\fi{}K is (0.89\ifmmode\pm\else\textpm\fi{}0.02) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}10}$ ${\mathrm{cm}}^{2}$${\mathrm{dyn}}^{\ensuremath{-}1}$. This result is compared with the predicted values of several theoretical models. The isothermal compressibility and the volume coefficient of thermal expansion are combined with the heat capacity at constant pressure to determine the temperature variation of the thermal Gr\"uneisen parameter and the caloric Debye characteristic temperature. Existing theoretical treatments of the lattice dynamics of neon appear to be inadequate at finite temperatures.

Measurements of Lattice Constant, Thermal Expansion, and Isothermal Compressibility of Neon Single Crystals

Simultaneous length and x-ray lattice-parameter expansion measurements have been made on 6-mm-diam cylindrical specimens of 99.99%-purity krypton. The specimens were prepared and held in a rigid-tail cryostat in which specimen temperatures could be precisely controlled. The data show a divergence between the bulk and x-ray expansions at the higher temperatures, which indicates an appreciable net concentration of thermally generated vacancy defects at temperatures above 75\ifmmode^\circ\else\textdegree\fi{}K. The equilibrium atomic-vacancy concentration inferred from these measurements may be represented by $\mathrm{exp}[({{2.0}_{\ensuremath{-}0.5}}^{+1.0})\ensuremath{-}(895\ifmmode\pm\else\textpm\fi{}100)\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}/T]$. The monovacancy formation enthalpy and entropy are discussed and compared with other existing theoretical and experimental information on argon and krypton. From the present direct measurements it appears that the enthalpy of formation for the monovacancy in krypton may not be entirely accounted for by two-body central-force interactions. However, existing calculations of the contribution of many-body interactions to the binding energy of the noble-gas solids appear to be of the correct order of magnitude and sign to improve agreement between theory and experiment for the vacancy. It is found that an empirical law of corresponding states which describes a number of the bulk thermal properties of the noble-gas solids may also describe some of the defect properties.

D. L. Losee

Papers

Measurements of Lattice Constant, Thermal Expansion, and Isothermal Compressibility of Neon Single Crystals

Equilibrium Vacancy Concentration Measurements on Solid Krypton

ISOTOPE EFFECTS IN THE LATTICE CONSTANT AND THERMAL EXPANSION OF $sup 20$Ne AND $sup 22$Ne SINGLE CRYSTALS.