Local-scaling density functional theory atoms

In Table VIII, we present the local-scaling- transformation-energy results for lithium and beryllium and compare them with results obtained with other methods. It is worth mentioning that the Hartree-Fock results for these atoms are a first instance of atxurate energy values obtained within the context of a formalism based on density functional theory. 

In order to properly assess the local-scaling transformation formulation of the density functional theory, we first consider the concept of local-scaling transformation and second, apply it to the topological features of atomic and molecular one-electron densities. 

Recent dramatic advances in computational techniques and computer power have enabled us to simulate crystalline structures from first-principles by means of the electronic structure calculation of the whole system within the density functional theory. Even liquid and vitreous silica have come to be studied by the ab initio MD method or so-called Car-Parrinello method [59]. Thus the application of the classical MD method is to be shifted to study of dynamics with a larger system size and longer simulation time. For example, the simulation of the oxygen diffusivity mentioned in the previous section needs accumulation of positions of five hundred atoms over 120 ps at each pressure, for which the ab initio MD is too inefficient. On the other hand, a local structural deformation relevant for the diffusion could be simulated with a smaller cell and a shorter time scale. It is obviously fruitful to make proper use ofthese approaches, i.e. the classical MD supported by first-principles cluster calculations and the ab initio MD, in each problem of materials science. 

ONETEP [1], the order-N electronic total energy package is a numerical implementation of Density Functional Theory. Unlike usual implementations of DFT, the computational resources required for the calculation of the energy of a particular atomic system scales linearly with the number of electrons, which makes it exceptionally efficient in investigations of large systems. However, in our work we exploited another feature of ONETEP, namely, that it uses local basis functions. 

Hence, in this chapter, we proceed further on our way from the fundamental theory to different representations of first-quantized relativistic quantum chemistry — now guided mostly by questions of algorithmic technique and feasibility. For the sake of compactness, the focus in this chapter must be on techniques that are specific to the relativistic realm. In nonrelativistic theory numerous approaches have been devised to reduce the computational effort of quantum chemical calculations. Apart from the just mentioned density-fitting approach, specific linear-scaling techniques have been devised [715-717] that ensure a linear increase in the computational effort with system size (measured by the atom or electron number or directly by the number of basis functions). These employ, for example, localized orbitals or sparse-matrix operations. All these techniques apply directly to the relativistic variants. 

In particular, the most powerful method for studing lattice defects, due to the high sensitivity of positrons to open volume defects such as vacancies, vacancy clusters, voids, dislocations, grain boundaries, etc., is positron annihilation spectroscopy (PAS). A diagram illustrating the applicability of PAS and other techniques as a function of defect size and density versus depth in material is shown in Figure 4.25. Thus, PAS represents a non-local experimental technique that is sensitive to microstructural defects at the atomic scale. A well-established theory of positron annihilation phenomena is currently available. Especially for metallic materials, it is possible to perform ab initio calculations of positron parameters for various defects and atomic arrangements [72,73]. 

When an atomic system is cooled below its glass temperature, it vitrifies, that is, it forms an amorphous solid [1]. Upon decreasing the temperature, the viscosity of the fluid increases dramatically, as well as the time scale for structural relaxation, until the solid forms concomitantly, the diffusion coefficient vanishes. This process is observed in atomic or molecular systems and is widely used in material processing. Several theories have been developed to rationalize this behavior, in particular, the mode coupling theory (MCT) that describes the fluid-to-glass transition kinetically, as the arrest of the local dynamics of particles. This becomes manifest in (metastable) nondecaying amplitudes in the correlation functions of density fluctuations, which are due to a feedback mechanism that has been called cage effect [2],... 

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