Atomic environment concept

An experimental way to find the smallest primitive cell is the atomic environment concept. The distances of all lattice points around a central lattice are put into a histogram. In the histogram the largest gap between different lattice points is used as the guiding rule to define the coordination polyhedron (Figures 2.38a and b). 

M. C. Desjonqueres and D. Spanjaard, Concepts in Surface Physics, Second Edition, Springer Verlag, Berlin (1996) and references therein R. Haydock, V. Heine and M. J. Kelly, Electronic Structure Based on the Local Atomic Environment for Tight-Binding Bands,. Phys. C 5 2845 (1972)... 

The concept of electronegativity is easy to visualize but difficult to apply quantitatively. Muffiken s definition, based on free-atomic properties, does not account for the influence of the local atomic environment on the ionic state that is reflected, for example, in the fact that the degree of ionicity... 

Two partly complementary, partly overlapping concepts, namely free volume and liquid-like (LL) atomic environments, have been used over the years to explain the increased fluidity or ease of local plastic accommodations of imposed shape changes in glassy solids. They were first discussed in Sections 1.5 and 1.14. The concept of free volume, which was introduced by Fox and Flory (1950) and has been further elaborated by many others since, is based on a local excess of... 

However, one of the most successfiil approaches to systematically encoding substructures for NMR spectrum prediction was introduced quite some time ago by Bremser [9]. He used the so-called HOSE (Hierarchical Organization of Spherical Environments) code to describe structures. As mentioned above, the chemical shift value of a carbon atom is basically influenced by the chemical environment of the atom. The HOSE code describes the environment of an atom in several virtual spheres - see Figure 10.2-1. It uses spherical layers (or levels) around the atom to define the chemical environment. The first layer is defined by all the atoms that are one bond away from the central atom, the second layer includes the atoms within the two-bond distance, and so on. This idea can be described as an atom center fragment (ACF) concept, which has been addressed by several other authors in different approaches [19-21]. 

The chemical environment foran atom m a molecule is probably niiit iie to th at molecule. Chem istry tries to find unify in g concepts an d the atom type Is on e of those unifying con cepts. For example, the AMBER force field defines five atom types for oxygens ... 

The concept of natural orbitals may be used for distributing electrons into atomic and molecular orbitals, and thereby for deriving atomic charges and molecular bonds. The idea in the Natural Atomic Orbital (NAO) and Natural Bond Orbital (NBO) analysis developed by F. Weinholt and co-workers " is to use the one-electron density matrix for defining the shape of the atomic orbitals in the molecular environment, and derive molecular bonds from electron density between atoms. 

The naive concept that a fixed set of valence AOs suffices for all charge states and bonding environments is equivalent to the use of a minimum basis set (e.g., STO-3G), which is known to be quite inadequate for quantitative purposes. Nevertheless, if the AOs are properly allowed to adjust dynamically in the molecular environment, one recovers a minimal-basis description that is surprisingly accurate the natural minimal basis. In the NBO framework the effective natural atomic orbitals are continually optimized in the molecular environment, and the number of important NAOs therefore remains close to minimal, greatly simplifying the description of bonding. 

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