Theoretical methods solid-state computational models

The remarkable situation in which we find ourselves in modem materials science is that physics has for some time been sufficiently developed, in terms of fundamental quantum mechanics and statistical mechanics, that complete and exact ab initio calculations of materials properties can, in principle, be performed for any property and any material. The term ab initio" in this context means without any adjustable or phenomenological or calibration parameters being required or provided. One simply puts the required nuclei and electrons in a box and one applies theory to obtain the outcome of a specified measurement. The recipe for doing this is known but the execution can be tedious to the point of being impossible. The name of the game, therefore, has been to devise approximations and methods that make the actual calculations doable with limited computer resources. Thanks to increased computer power, the various approximations can be tested and surpassed and more and more complex materials can be modelled. This section provides a brief overview of the theoretical methods of solid state magnetism and of nanomaterial magnetism in particular. 

The need to model this distribution means that it is difficult to theoretically study the electronic states of oxide glasses. There are several ways to theoretically study the electronic state of oxide materials, these include band calculations and molecular orbital methods. (9-13) The randomness is a problem for the band approach because it requires translational symmetry of the unit cell a large super-cell may be chosen, but this is at the cost of increased computer time and possible spurious interactions between cells. On the other hand, the molecular orbital (MO) approach is usually applied to isolated molecules, (14-16) and can not handle infinite numbers of atoms as in the solid state. The embedded potential method is one of the improvements in moleculeir orbited methods which have been introduced in order to study solid state materials. (17) Basically, the cluster Hamilto-... 

The attractive property of the compounds under discussion is the relative simplicity of their crystal structures. Therefore, with the development of algorithms, programs and methods of the computational solid-state physics, they were constantly the objects of theoretical calculations they were the test models which were used to verify newly proposed approaches. As a consequence, taking the evolution of ideas on the electronic structure of these compounds as an example, it is possible to follow the development of the theory of crystals, which broadens its field of application, and widens the range of problems solved. 

Apart from the theoretical approaches, electronic energy spectra of carbides and nitrides have been studied using a variety of experimental techniques X-ray emission and photoelectron spectrosopy, optical and Auger spectroscopy, electron energy loss and positron annihilation spectroscopy, etc. However, interpretation of the results obtained requires, as a rule, use of the computational methods of the band theory of solids and quantum chemistry. Moreover, the data provided by theoretical methods are important by themselves, because they give much more detailed information on the electron states and chemical bonding than any of the experimental methods. They also allow us to model theoretically... 

The development of the solid state theory has created strong theoretical basis for the description of interactions between atoms in a crystal. The electronic structure model, resulting from these interactions, allows identifying electrical, magnetic and optical properties of a compound. Today, the development of computational methods and the numerical capabilities of big computers allow calculating the interactions in quite big crystalline clusters, and thus to determine their properties. Nevertheless there is no data allowing detailed analysis of the properties of the oxides to be performed. 

The advent of high-speed computers, availability of sophisticated algorithms, and state-of-the-art computer graphics have made plausible the use of computationally intensive methods such as quantum mechanics, molecular mechanics, and molecular dynamics simulations to determine those physical and structural properties most commonly involved in molecular processes. The power of molecular modeling rests solidly on a variety of well-established scientific disciplines including computer science, theoretical chemistry, biochemistry, and biophysics. Molecular modeling has become an indispensable complementary tool for most experimental scientific research. 

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