A standard local coordinate system for multipole refinements of the estrogen core structure

A comparative charge density study on a series of estrogen derivatives has been initiated. The study utilizes the Hansen-Coppens atom-centred multipole model to describe the valence electron density distribution. Direct comparison of the population parameters for each estrogen after the respective multipole refinements requires standardization of the atom-centred local coordinate systems. Such a standard coordinate system for the common estrogen core is reported, taking advantage of the shape of those multipoles which have the spatial characteristics of sp² and sp³ hybrid orbitals. Additionally, populating these principal multipoles at the beginning stage of the refinements improves the stability of these large highly correlated calculations.