Chemical Sub-Structural Cluster Expansions For Molecular Properties

Abstract

The correlation of different molecular sub-structures with various molecular properties has a long history, of over a century. And currently such structural characterizations still remain of central interest in chemistry. Thus a general formalism to analyze a property or activity in terms of sub-structural contributions is of interest, and is pursued here. The approach may indeed be viewed as a formalization and extension of standard bond-energy ideas as arise even in introductory chemistry courses. The present formalism allows for:

• a more complete and comprehensive formulation, with higher-order corrections to achieve greater accuracy;

• a more general form for the class of sub-structures appearing in the expansion, thereby allowing more general (e.g., “multiplicative”) properties to be expanded; and

• a more general form for the expansion functions, thereby allowing more rapid convergence rates for the expansions.

An illustrative example for the structure/property correlation of conjugated-hydrocarbon π-energy is made. Some comments on the use for describing bio-activities, and in particular toxicities, are made.

Key Words:

• Cluster expansions
• structure/property correlations
• Möbius inversion
• chemical graph theory
• topological indices
• acyclic conjugated hydrocarbons