An ?E matrix? for the L�wdin ? function, expanded in a Taylor series: An analytic treatment of molecular charge density near the origin

A displaced STO can be expanded in spherical harmonics with the coefficient functions or Löwdin a functions characterized by a C matrix. These α functions themselves may be expanded in a Taylor series that is characterized by its own E matrix. This expansion is necessary for the representation of the α function by a power series and for its evaluation about the origin. As an application, we find the power series for the molecular charge density in the vicinity of the center of a model diatomic molecule. Our analytic approach is general and yields excellent results.