On Quantitative Characterization of Molecular Structure

In order to get quantitative relationships between structures and their properties, one needs to And suitable numerical characterizations of structures. Numerical characterizations of the structure can then generate numerical descriptors of structures to be used for construction of structure-property correlations. Suitable structure descriptors could be tested to see if they correlate with molecular bioactivity in modeling effects and responses of such substances on living tissue or organisms. In this way, one can identify bioactive natural products or synthesized compounds, which can show novel therapeutic activities and be able to protect against diseases or combat diseases or harmful chemicals that have toxic or mutagenic effects, etc. 

The almost hidden but key word here is suitable. Chemical structures can be described in very many different ways using common chemical vocabulary and terminology. One can start by focusing on atoms and bonds the hybridization of atoms atomic charges the types of bonding, localized or delocalized and other quantum chemical parameters, describing local groups, stereochemistry and conformation, 

For structure-property and structure-activity studies, one should use solely structure invariants, and when structures are represented by molecular graphs, graph invariants could serve as structure descriptors. The mathematical term invariant means any quantity that is independent o/graphical representation of a molecule or adopted numbering of atoms. In other words, invariants represent intrinsic mathematical properties of molecular structure. They differ from the physicochemical molecular properties in that they are either obtained by counting or can be expressed with mathematical formulas and are always therefore numerically exact. The same can be said for quantum chemical molecular descriptors. In contrast, physicochemical molecular descriptors that are molecular properties are obtained by measuring, which may be sufficiently precise and thus numerically satisfactory nevertheless, with time, they may undergo some, even if minor, revisions. 

The structure-property correlations also represent property-property correlations with an important distinction they represent the correlation between structural (mathematical) property-physicochemical property or structural (mathematical) property-activity property, with which structural property encrypts the structure. 

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