Revisiting the variational nature of the quantum theory of atoms in molecules |
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| Affiliation: | 1. Karlsruhe Institute of Technology, Center for Functional Nanostructures, Haid-und-Neu-Straße 6, 76131 Karlsruhe, Germany;2. Karlsruhe Institute of Technology, Institute of Functional Interfaces, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany;3. Technische Universität Darmstadt, Clemens-Schöpf-Institut für Organische Chemie und Biochemie, Alarich-Weiss-Str. 8, 64287 Darmstadt, Germany;4. Max-Planck-Institute for Intelligent Systems, Heisenbergstr. 3, 70569 Stuttgart, Germany;5. Biophysical Chemistry, University of Heidelberg, Im Neuenheimer Feld 253, 69120 Heidelberg, Germany, Germany;6. Karlsruhe Institute of Technology, Institute of Toxicology and Genetics, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany;1. College of Chemistry and Life Science, Changchun University of Technology, Changchun 130012, PR China;2. School of Life Science and Technology, Changchun University of Science and Technology, Changchun 130022, PR China;3. State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, PR China;1. College of Chemistry, Chemical Engineering and Biotechnology, Donghua University, Shanghai 201620, PR China;2. UCL School of Pharmacy, 29-39 Brunswick Square, London WC1N 1AX, UK;3. Key Laboratory of Science & Technology of Eco-Textile, Donghua University, Ministry of Education, 201620, PR China |
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| Abstract: | A simplified derivation of the variational nature of the real space basins used in the quantum theory of atoms in molecules (QTAM) is presented. We focus on pointing out the non-standard characteristics of the variational problem that is solved, and on clarifying some points that tend to be misinterpreted. An explicit discussion of the meaning of the functional minimized is also presented and used to derive both a new form for the atomic virial theorem and to show how basin chemical potentials may be defined. |
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