Somoyai function

The Somoyai parameter s has the physical dimension of bohr". Since a notable part of the electronic density is mimicked by the composite nuclear potential, it can be assumed that only their difference provides a description of the chemical bonding. Then, for any fixed value of s, the Somoyai function gives information about the role of the electronic density in the chemical bonding. 

Somoyai function - quantum-chemical descriptors SP indices ( subgraph property indices)... 

The Somoyaiparameter s has the physical dimensions ofbohr. For any fixed choice ofv, the Somoyai function 5(r,v) is an almost everywhere continuous and differentiable function of the position variable r. 

It is convenient to consider the shape description of all three functions within a common framework. For any molecular property P that is described by a 3D function P(r) which is continuous in r, such as the electronic density p(r), and the composite nuclearpotential Vn(r). or the Somoyai function 5(r,v) with a constant v parameter, the level sets F a) for any constant value a of function P(r) are defined as the following collection of points ... 

Parameter s in the Somoyai function can be chosen so that G(r,v) becomes small within a given part of the space. For example, one may select an envelope (01,02) of... 

One may require that parameters is chosen so that the absolute value 5(r,s) of the Somoyai function 5(r,s) is minimized within the envelope ( 1,02) of the given 3D property P(r) ... 

The shape of the Somoyai function Sfr, ) given for a suitably chosen parameter value s provides a 3D description of the bonding pattern within the molecule. 

The Somoyai function is defined in terms of the electronic density function and the composite nuclear potential, providing a 3D shape representation of the bonding pattern within the molecule under study. Some of the topological techniques of molecular shape analysis have been reviewed, with special emphasis on applications to the Somoyai function. A combination of a family of recently introduced ab initio quality macromolecular electronic density computation methods with the electrostatic Hellmann-Feynman theorem provides a new technique for the computation of forces acting on the nuclei of large molecules. This method of force computation offers a new approach to macromolecular geometry optimization. 

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