Local molecular descriptors

Molecular descriptors calculated as - information content of molecules. Different criteria are used for defining - equivalence classes, i.e. equivalency of atoms in a molecule such as chemical identity, ways of bonding through space, molecular topology and symmetry, - local vertex invariants [Bonchev, 1983]. 

Local or global molecular descriptors related to the electronic distribution in the molecule they are fundamental to many chemical reactions, physico-chemical properties, and ligand-macromolecule interactions. The theory of electronic density is based on a quantum-mechanical approach however, - electronegativity and charges, which are not physical observables, are also important quantities for the definition of several electronic descriptors. 

Some molecular descriptors and local vertex invariants proposed as a generalization or modification of the original connectivity indices are reported below. 

Based on these local invariants, the ordered structural code (OSC) is a molecular descriptor defined as the ascending ordered sequence of SC, in the molecule [Barysz and IHnajstic, 1984]  

These are global molecular descriptors derived from an H-depleted molecular graph where each vertex is weighted by a local vertex invariant called Atom-in-Structure Invariant Index (ASII) defined as [Bangov, 1988]  

Ehresmann B, de Groot MJ, Alex A, Clark T. New molecular descriptors based on local properties at the molecular surface and a boiling-point model derived from them. I Chem Inf Comput Sci 2004 44 658-68. 

Based on the length of the paths in the molecular graph, other local vertex invariants and molecular descriptors have been proposed. 

The sums of the local vertex invariants X, and c, over all of the atoms give the corresponding molecular descriptors, called centrocomplexity topological index X and centric topological index C, respectively  

To obtain spatial autocorrelation molecular descriptors, function /(x,) is any physico-chemical property calculated for each atom of the molecule, such as atomic mass, polarizability, etc., and - local vertex invariants such as - vertex degree. Therefore, the molecule atoms represent the set of discrete points in space and the atomic property the function evaluated at those points. 

Appropriate combinations of Mi, M2 and M3 give various unsymmetric walk matrices and hence various local and molecular descriptors. 

The resulting descriptor can be regarded as isolated from the molecular RDF that contains the sum of N possible descriptors. Thus, every Af-atomic molecule can have N local RDF descriptors. However, local descriptors can cover the entire molecule, depending on the predehned maximum distance of the function their center is just localized on a single atom. 

In many chemical problems the comparisons of local molecular regions are more important than global comparisons. The presence of functional groups or other molecular moieties with specified shape properties often imply similar chemical behavior even if the molecules compared have very different global shapes. For this reason, local molecular shape descriptors and local shape codes are of major importance. 

Electric polarization, dipole moments and other related physical quantities, such as multipole moments and polarizabilities, constitute another group of both local and molecular descriptors, which can be defined either in terms of classical physics or quantum mechanics. They encode information about the charge distribution in molecules [Bbttcher et al, 1973]. They are particularly important in modelling solvation properties of compounds which depend on solute/solvent interactions and in fact are frequently used to represent the -> dipolarity/polarizability term in - linear solvation energy relationships. Moreover, they can be used to model the polar interactions which contribute to the determination of the -> lipophilicity of compounds. 

In the approach proposed by G. Menon and A. Cammarata a series of congeneric structures is classified by the activity type using the principal components of a set of local molecular descriptors based on a superstructure constructed by the simplest chemically consistent superposition of the structures. 

Bond multiplicity is taken into account by augmenting the edge distance matrix with a supplementary column and row where the elements are conventional bond orders, therefore obtaining an edge distance matrix for multigraphs [Bonchev, 1983]. All the local vertex invariants and molecular descriptors defined above can also be calculated on this matrix. 

In these cases, the chlorobenzenes act as electron acceptors while the benzidine molecule behaves as an electron donor. The effect of chlorine substitution on the aromaticity of the planar benzene ring of the chlorobenzene derivatives is assessed from the nucleus independent chemical shift (NICS) criterion proposed by Schleyer et al. [338]. Among the various global and local molecular descriptors, electrophilicity (m) is found to be the most appropriate reactivity parameter regarding toxicity 

Several earlier review articles are relevant to our subject. Slichter reviews the work done in his laboratory [16], most of it concerned with atoms or molecules adsorbed on the metal clusters, and the experimental techniques used in such studies [17]. Duncan s review [9] pays special attention to the C NMR of adsorbed CO. Most recently, one of us has given a rather detailed review of the held, in particular on metal NMR of supported metal catalysts [18]. While the topics and examples discussed in this chapter will inevitably have some overlap with these previous reviews, particular emphasis is directed toward highlighting the ability of metal NMR to access the iff-LDOS at both metal surfaces and molecular adsorbates. The iff-LDOS is an attractive concept, in that it contains information on both a spatial (local) and energy (electronic excitations) scale. It can bridge the conceptual gap between localized chemical descriptors (e.g., the active site or the surface bond) and the delocalized descriptors of condensed matter physics (e.g., the band structure of the metal surfaces). 

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