Three-dimensional moments of molecular property fields

Descriptors that capture certain three-dimensional molecular features and d o not require molecular superposition or alignment for the assignment of mo lecular similarity have recently been proposed and investigated. Among thes e, moments of molecular features have been utilized in the QSAR of several molecular series. The present-work examines certain formal aspects of the u se of moment expansions for which the zero-order moment of a property field is nonvanishing. The first-order term of such moment expansion is then dep endent upon the origin of expansion, and it is pointed out that expansion a bout the molecular centroid is descriptive of first-order differences about the property-field mean. For a hydrophobic property field, this first-orde r termis just the Eisenberg hydrophobic moment. Second-order moments about the centroid can be written as components of the WHIM covariant matrix. Mom ent expansions are also performed about the property-field center-in analog y with expansions about the center of mass. For such expansion, a set of de scriptors consisting of moments of the molecular density and of a molecular hydrophobic property field as well as of related quantities are used in a QSAR:of the binding of 74 polyhalogenated aromatic molecules to; the Ah cys tolic receptor. This QSAR has been named CoMMA2 to distinguish it from CoMM A; for which the zero-order moment of the expansion vanishes.