The effective atomic orbitals have been realized in the framework of Bader's atoms in molecules theory for a general wavefunction. This formalism can be used to retrieve from any type of calculation a proper set of orthonormalized numerical atomic orbitals, with occupation numbers that sum up to the respective Quantum Theory of Atoms in Molecules (QTAIM) atomic populations. Experience shows that only a limited number of effective atomic orbitals exhibit significant occupation numbers. These correspond to atomic hybrids that closely resemble the core and valence shells of the atom. The occupation numbers of the remaining effective orbitals are almost negligible, except for atoms with hypervalent character. In addition, the molecular orbitals of a calculation can be exactly expressed as a linear combination of this orthonormalized set of numerical atomic orbitals, and the Mulliken population analysis carried out on this basis set exactly reproduces the original QTAIM atomic populations of the atoms. Approximate expansion of the molecular orbitals over a much reduced set of orthogonal atomic basis functions can also be accomplished to a very good accuracy with a singular value decomposition procedure.
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7 June 2013
Research Article|
June 05 2013
The atomic orbitals of the topological atom
Eloy Ramos-Cordoba;
Eloy Ramos-Cordoba
1Institute of Computational Chemistry and Catalysis and Department of Chemistry,
University of Girona
, 17071 Girona, Spain
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Pedro Salvador;
Pedro Salvador
a)
1Institute of Computational Chemistry and Catalysis and Department of Chemistry,
University of Girona
, 17071 Girona, Spain
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István Mayer
István Mayer
2Institute of Organic Chemistry, Research Centre for Natural Sciences,
Hungarian Academy of Sciences
, P.O. Box 17, H-1525 Budapest, Hungary
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a)
E-mail: pedro.salvador@udg.edu
J. Chem. Phys. 138, 214107 (2013)
Article history
Received:
March 22 2013
Accepted:
May 13 2013
Citation
Eloy Ramos-Cordoba, Pedro Salvador, István Mayer; The atomic orbitals of the topological atom. J. Chem. Phys. 7 June 2013; 138 (21): 214107. https://doi.org/10.1063/1.4807775
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