Materials Theory

We construct a class of periodic tilings of the plane, which corresponds to toroidal arrangements of trivalent atoms, with pentagonal, hexagonal and heptagonal rings. Each tiling is characterized by a set of four integers and determines a toroidal molecule. The tiling rules are motivated by geometric considerations and the tiling patterns are rich enough to describe a wide class of toroidal carbon molecules, with a broad range of shapes and numbers of atoms. The molecular dimensions are simply related to the integers that determine the tiling. The configurational energy and the delocalisation energy of several molecules obtained in this way were computed for Tersoff and Hückel models. The results indicate that many of these molecules are not strained, and may be expected to be stable. We studied the influence of size on the Hückel spectrum: it bears both similarities and differences as compared with the case of tubules.

We present a new model to describe the unusual elastic properties of compressed emulsions. The response of a single droplet under compression is investigated numerically for different Wigner-Seitz cells. The response is softer than harmonic, and depends on the coordination number of the droplet. Using these results, we propose a new effective inter-droplet potential which is used to determine the elastic response of a monodisperse collection of disordered droplets as a function of volume fraction. Our results are in excellent agreement with recent experiments. This suggests that anharmonicity, together with disorder, are responsible for the quasi-linear increase of G and Π observed at φ c .

We develop a model to study the thermal expansion of surfaces, wherein phonon frequencies are obtained from ab initio total energy calculations. Anharmonic effects are treated exactly in the direction normal to the surface, and within a quasiharmonic approximation in the plane of the surface. We apply this model to the Ag(111) and Al(111) surfaces, and find that our calculations reproduce the experimental observation of a large and anomalous increase in the surface thermal expansion of Ag(111) at high temperatures [P. Statiris, H.C. Lu and T. Gustafsson, Phys. Rev. Lett. 72, 3574 (1994)]. Surprisingly, we find that this increase can be attributed to a rapid softening of the in-plane phonon frequencies, rather than due to the anharmonicity of the out-of-plane surface phonon modes. This provides evidence for a new mechanism for the enhancement of surface anharmonicity. A comparison with Al(111) shows that the two surfaces behave quite differently, with no evidence for such anomalous behavior on Al(111).

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.

The energetics of H 2 interacting with the Si(100) surface is studied by means of {\em ab initio} total energy calculations within the framework of density functional theory. We find a direct desorption pathway from the mono-hydride phase which is compatible with experimental activation energies and demonstrate the importance of substrate relaxation for this process. Both the transition state configuration and barrier height depend crucially on the degree of buckling of the Si dimers on the Si(100) surface. The adsorption barrier height on the clean surface is governed by the buckling via its influence on the surface electronic structure. We discuss the consequences of this coupling for adsorption experiments and the relation between adsorption and desorption.

We propose a lattice gas model to account for linear chain structures adsorbed on (112) faces of W and Mo. The model includes a dipole-dipole interaction as well as a long-ranged indirect interaction. We have explicitly demonstrated that the periodic ground states depend on a competition between dipole-dipole and indirect interaction. The effect of temperature is studied within the molecular-field approximation. The numerical results show that for dipole-dipole interaction only, all long periodic linear chain phases are suppressed to low temperatures. However, when the long-range indirect interaction becomes important, the long-periodic linear chain phases start to fill up the phase diagram and develop a high thermal stability. Model parameters are chosen to reconstruct a sequence of long-periodic phases as observed experimentally for Li/Mo(112) and Li/W(112).

We present a new technique aimed at preventing plane-wave based total energy and stress calculations from the effect of abrupt changes in basis set size. This s cheme relies on the interpolation of energy as a function of the number of plane waves, and on a scaling hypothesis that allows to perform the interpolation for a unique reference volume. From a theoretical point of view, the new method is compared to those already pr oposed in the literature, and its more rigorous derivation is emphasized. From a practical point of view, we illustrate the importance of the correction o n different materials (Si, BaTiO3, and He) corresponding to different types of b onding, and to different k-point samplings and cut-off energies. Then, we compare the different approaches for the calculation of the lattice par ameter, the bulk modulus, and its derivative versus pressure in bulk silicon.

Ab initio molecular dynamics calculations of deuterium desorbing from Si(100) have been performed in order to monitor the energy redistribution among the hydrogen and silicon degrees of freedom during the desorption process. The calculations show that part of the potential energy at the transition state to desorption is transferred to the silicon lattice. The deuterium molecules leave the surface vibrationally hot and rotationally cold, in agreement with experiments; the mean kinetic energy, however, is larger than found in experiments.

We present a new formulation of ab initio molecular dynamics which exploits the efficiency of plane waves in adaptive curvilinear coordinates, and thus provides an accurate treatment of first-row elements. The method is used to perform a molecular dynamics simulation of the CO_2 molecule, and allows to reproduce detailed features of its vibrational spectrum such as the splitting of the Raman sigma+_g mode caused by Fermi resonance. This new approach opens the way to highly accurate ab initio simulations of organic compounds.

Ab initio molecular dynamics calculations of deuterium desorbing from Si(100) have been performed in order to monitor the energy redistribution among the various D 2 and silicon degrees of freedom during the desorption process. The calculations show that a considerable part of the potential energy at the transition state to desorption is transferred to the silicon lattice. The deuterium molecules leave the surface vibrationally hot and rotationally cold, in agreement with thermal desorption experiments; the mean kinetic energy, however, is larger than found in a laser-induced desorption experiment. We discuss possible reasons for this discrepancy.