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

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 2 l + 1 independent Y lo ‐like functions correctly span the relevant Y lm ( 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 AGLO S. 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.