On the Gaussian-Lobe Representation of Atomic Orbitals

The reliability of angularly dependent properties calculated from wavefunctions constructed over a nonnuclear-centered Gaussian basis has been explored by examining the spherical harmonic expansion of the Gaussian-lobe function representation of a p_z function. It is found that the component of p_z in the Y₁⁰ subspace is similar to a double-zeta function while the component in the Y₃⁰ subspace is several orders of magnitude less than the Y₁⁰ component.

Expectation values for several angularly dependent operators are evaluated over the Gaussian-lobe function representation of a p_z orbital and compared with the expectation value calculated over the corresponding double-zeta function. The small angular asymmetry in the Gaussian-lobe function representation of the atomic p_z orbitals is reflected in the similarity between the two expectation values.