Local molecular descriptors

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. 

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... 

Based on the experience with tertiary phosphines, the importance of the steric properties of NHC hgands in determining chemical behaviour has been immediately recognised. The main practical problem, however, is that NHC hgands substantiaUy present a local symmetry axis, whereas phosphines present a local symmetry axis. This imphes that the well-accepted molecular descriptor used to quantify steric properties in phosphines, the Tohnan cone angle [78], cannot be applied to NHC ligands. 

Figure 4.1 Ligand-based virtual screening methods. The figure shows different computational methods for screening compound databases that take either a local or a global view on molecular structure. Molecular similarity methods that operate on molecular descriptors, histogram representations, superposition or (reduced) molecular graphs evaluate molecular structure globally. By contrast, local structural features are explored by substructure and pharmacophore searching or QSAR modeling.

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. 

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. 

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] ... 

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

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. 

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. 

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. 

Other topological molecular descriptors can be obtained by using suitable functions applied to - local vertex invariants, the most common functions are atom and/or bond additives, resulting in descriptors which give correlation of physico-chemical properties that are atom and/or bond additives themselves. - Zagreb indices and -> ID numbers are derived according to this approach. 

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]. 

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 ... 

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

Schultz-type indices based on eigenvectors were recently proposed [Medeleanu and Balaban, 1998] as - local vertex invariants and molecular descriptors, on the basis of the eigenvector of adjacency and distance matrices associated with the lowest (largest negative) eigenvalue. The LOVIs are derived from the following A-dimensional column vectors ... 

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] ... 

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

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). 

In the present article, we report a study concerning the reaction mechanism of a prototype reaction using both static and dynamic approaches to explore a DFT potential surface. The static approach is the standard IRC model, while the dynamic one is based on a Carr-Parrinello method performed with localized (Gaussian) orbitals, the so-called atom-centered density matrix propagation (ADMP) model.25 Our aim is to elucidate the differences, and the common aspects, between the two approaches in the analysis of bond breaking/formation. To this end, we have chosen topological quantities as probe molecular descriptors. 

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. 

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. 

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