Density Functional Theory An Advanced Course
Density Functional Theory (DFT) has firmly established itself as the workhorse for the atomic-level simulation of condensed matter phases, pure or composite materials and quantum chemical systems. The present book is a rigorous and detailed introduction t
- PDF / 439,856 Bytes
- 9 Pages / 439.37 x 666.142 pts Page_size
- 75 Downloads / 528 Views
Introduction
One of the basic problems in theoretical physics and chemistry is the description of the structure and dynamics of many-electron systems. These systems comprise single atoms, the most elementary building blocks of ordinary matter, all kinds of molecules, ranging from dimers to proteins, as well as mesoscopic systems, for example clusters or quantum dots, and solids, including layered structures, surfaces and quasi-crystals. The following two paragraphs list the properties of such systems which are generally of interest, without, however, aiming at completeness. These properties can roughly be classified as either structural or dynamical. An important structural property is the electronic shell structure (or band structure in the case of crystals). The shell structure directly determines the stability of a system, but also shows up in a number of other properties—it is, for instance, a key factor in transport properties like the electrical conductivity. Stability manifests itself in various binding energies. These are either of electronic nature, such as the ionization potential and the work function, or they characterize the bonds between atoms, such as the atomization energy of molecules and the cohesive energy of solids. Other structural properties, which are related to shell structure, are electric or magnetic moments. The geometry of poly-atomic systems, that is bond lengths and bond angles as well as the symmetry of the atomic arrangement, constitutes yet another important structural property. Often several geometrical configurations which are almost degenerate (at least compared to typical thermal energies) are observed for such systems. In this case the relative stability of the various configurations is of obvious interest. All these properties have in common that they can be calculated if the relevant electronic ground states are known. Even if more than one ground state is involved, as in the comparison of energies of systems with different electron numbers or with different atomic configurations, there is no need to determine excited electronic states. The electronic excitation spectrum is the most notable dynamical property. Excitation energies are not only the quantities necessary for an understanding of optical properties, they also feature in all kinds of scattering processes. In addition to the excitation spectrum, a complete description of excitation or ionization requires the evaluation of the associated transition probabilities. In a poly-atomic system the E. Engel, R.M. Dreizler, Introduction. In: E. Engel, R.M. Dreizler, Density Functional Theory, Theoretical and Mathematical Physics, pp. 1–9 (2011) c Springer-Verlag Berlin Heidelberg 2011 DOI 10.1007/978-3-642-14090-7 1
2
1 Introduction
excitation of nuclear motion is also possible, the rotational-vibrational motion in molecules or lattice vibrations (phonons) in solids being the simplest examples. The discussion of these dynamical properties obviously requires knowledge of either excited stationary states of the system, or
Data Loading...
