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Angular dependence of Gaussian‐Lobe orbitals. II. Set of axial Gaussian‐Lobe orbitals
Author(s) -
Le Rouzo H.,
Silvi B.
Publication year - 1978
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560130305
Subject(s) - cubic harmonic , atomic orbital , subspace topology , physics , gaussian , sto ng basis sets , slater type orbital , basis set , molecular orbital theory , azimuth , quantum number , linear combination of atomic orbitals , quantum mechanics , mathematics , mathematical analysis , optics , molecule , electron
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.