Cellular Augmentation Methods

This is the simplified, two-region potential, on which the augmented-plane wave (APW) method by Slater [226,227] is essentially based. It stands for the rigorous approach which correctly describes both the spherical, atomic-like region close to the nucleus and also the flat region between the nuclei, by treating the two regions differently, in the spirit of the above muffin-tin idea. 

To do so, a hybrid wave function (the augmented plane wave) is constructed, composed of atomic functions (called partial waves, with spherical harmonics Yii ) inside the atomic, muffin-tin sphere Tmt and a single plane wave outside the atomic sphere, that is 

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This monograph is based almost entirely on the work of O.K. Andersen. It is therefore appropriate to reveal the sources of the material presented, and at the same time give a brief history of the development of linear methods. At present several types of such methods are used, e.g. the linear muffin-tin orbitals (LMTO) method [1.19], the linear augmented plane-wave (LAPW) method [1.19], the augmented spherical-wave (ASW) method [1.20], and the linear rigorous cellular (LRC) method [1.15]. Of these the LMTO method, which was the earliest, will be our main concern. 

Other methods for detennining the energy band structure include cellular methods. Green fiinction approaches and augmented plane waves [2, 3]. The choice of which method to use is often dictated by die particular system of interest. Details in applying these methods to condensed matter phases can be found elsewhere (see section B3.2). 

The classical methods of chemical and fermentative synthesis and purification are augmented by the powerful genetically modified cellular systems of production, by transgenic animals and plants, as well as by sophisticated techniques of syntliesis, analysis, purification, such as chual catalysts, micro-reactors, and process intensification. 

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