Angular dependence of Gaussian‐Lobe orbitals. II. Set of axial Gaussian‐Lobe orbitals

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Abstract
The topological properties of real spherical harmonic representations on the unit sphere have been found to provide a convenient tool to infer the lobe edifices which mimic these orbitals. The prohibitive number of lobes required in such an approach for l > 2, can be avoided in using only axial Gaussian‐lobe orbitals (AGLO). It is proved that 2l + 1 independent Ylo‐like functions correctly span the relevant Ylm (m = −l,l) subspace. The multipolar component analysis of any spatial arrangement of lobes is derived, and allows the optimization of the angular dependence of AGLOS. The cases of d‐ and f‐orbitals are studied in detail and accurate optimized functions are proposed. This method can be easily extended to obtain the atomic orbitals of any azimuthal quantum number l‐subspace.

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