Molecular shape quantum chemical concept

Well-defined products from the chaotic turmoil, which is a chemical reaction, result from a balance between external thermodynamic factors and the internal molecular parameters of chemical potential, electron density and angular momentum. Each of the molecular products, finally separated from the reaction mixture, is a new equilibrium system that balances these internal factors. The composition depends on the chemical potential, the connectivity is determined by electron-density distribution and the shape depends on the alignment of vectors that quenches the orbital angular momentum. The chemical, or quantum, potential at an equilibrium level over the entire molecule, is a measure of the electronegativity of the molecule. This is the parameter that contributes to the activation barrier, should this molecule engage in further chemical activity. Molecular cohesion is a holistic function of the molecular quantum potential that involves all sub-molecular constituents on an equal basis. The practically useful concept of a chemical bond is undefined in such a holistic molecule. 

Apparently, the concept of similarity plays an important role in the chemistry of functional groups. Motivated by the recent revival of interest in molecular similarity [7-39], we shall present a systematic approach towards a quantum chemical description of functional groups. There are two main components of the approach described in this report. The first component is shape-similarity, based on the topological shape groups and topological similarity measures of molecular electron densities[2,19-34], whereas the second component is the Density Domain approach to chemical bonding [4]. The topological Density Domain is a natural basis for a quantum... 

Some of the chemical concepts with little or no quantum-mechanical meaning outside the Bohmian formulation but, well explained in terms of the new interpretation, include electronegativity, the valence state, chemical potential, metallization, chemical bonding, isomerism, chemical equilibrium, orbital angular momentum, bond strength, molecular shape, phase transformation, chirality and barriers to rotation. In addition, atomic stability is explained in terms of a simple physical model. The central new concepts in Bohmian mechanics are quantum potential and quantum torque. 

Problems associated with the quantum-mechanical definition of molecular shape do not diminish the importance of molecular conformation as a chemically meaningful concept. To find the balanced perspective it is necessary to know that the same wave function that describes an isolated molecule, also describes the chemically equivalent molecule, closely confined. The distinction arises from different sets of boundary conditions. The spherically symmetrical solutions of the free molecule are no longer physically acceptable solutions for the confined molecule. 

A detailed review of the basic concepts of fuzzy sets can be found in other chapters of this volume. Here only the specific notations and the fuzzy set concepts most relevant to the molecular shape problem are reviewed, followed by a simple proof for a special fuzzy set generalization of the Hausdorff distance, motivated by the quantum chemical properties of fuzzy electronic densities of molecules. 

The characterization of the interrelations between chemical bonding and molecular shape requires a detailed analysis of the electronic density of molecules. Chemical bonding is a quantum mechanical phenomenon, and the shorthand notations of formal single, double, triple, and aromatic bonds used by chemists are a useful but rather severe oversimplification of reality. Similarly, the classical concepts of body and surface , the usual tools for the shape characterization of macroscopic objects, can be applied to molecules only indirectly. The quantum mechanical uncertainty of both electronic and nuclear positions within a molecule implies that valid descriptions of both chemical bonding and molecular shape must be based on the fuzzy, delocalize properties of electronic density distributions. These electron distributions are dominated by the nuclear arrangements and hence quantum mechanical uncertainly affects electrons on two levels by the lesser positional uncertainty of the more massive nuclei, and by the more prominent positional uncertainty of the electrons themselves. These two factors play important roles in chemistry and affect both chemical bonding and molecular shape. 

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