Molecular electronic density fitting using elementary Jacobi rotations under atomic shell approximation

Fitted electron density functions constitute an important step in quantum s imilarity studies. This fact not only is presented in the published papers concerning quantum similarity measures (QSM), but also can be associated wi th the success of the developed fitting algorithms. As has been demonstrate d in previous work, electronic density can be accurately fitted using the a tomic shell approximation (ASA). This methodology expresses electron densit y functions as a linear combination of spherical functions, with the constr aint that expansion coefficients must be positive definite, to preserve the statistical meaning of the density function as a probability distribution. Recently, an algorithm based on the elementary Jacobi rotations (EJR) tech nique was proven as an efficient electron density fitting procedure. In the preceding studies, the EJR algorithm was employed to fit atomic density fu nctions, and subsequently molecular electron density was built in a promole cular way as a simple sum of atomic densities. Following previously establi shed computational developments, in this paper the fitting methodology is a pplied to molecular systems. Although the promolecular approach is sufficie ntly accurate for quantum QSPR studies, some molecular properties, such as electrostatic potentials, cannot be described using such a level of approxi mation. The purpose of the present contribution is to demonstrate that usin g the promolecular ASA density function as the starting point, it is possib le to fit ASA-type functions easily to the nb initio molecular electron den sity. A comparative study of promolecular and molecular ASA density functio ns for a large set of molecules using a fitted 6-311G atomic basis set is p resented, and some application examples are also discussed.