Chapter 4
Extending the Topological Analysis
and Seeking the Real-Space Subsystems
in Non-Coulombic Systems
with Homogeneous Potential Energy
Functions
Shant Shahbazian
Abstract It is customary to conceive the interactions of all the constituents of a
molecular system, i.e. electrons and nuclei, as Coulombic. However, in a more
detailed analysis one may always find small but non-negligible non-Coulombic
interactions in molecular systems originating from the finite size of nuclei, magnetic
interactions, etc. While such small modifications of the Coulombic interactions do not
seem to alter the nature of a molecular system in real world seriously, they are a serious
obstacle for quantum chemical theories and methodologies which their formalism is
strictly confined to the Coulombic interactions. Although the quantum theory of atoms
in molecules (QTAIM) has been formulated originally for the Coulombic systems,
some recent studies have demonstrated that most of its theoretical ingredients are not
sensitive to the explicit form of the potential energy operator. However, the
Coulombic interactions have been explicitly assumed in the mathematical procedure
that is used to introduce the basin energy of an atom in a molecule. In this study it is
demonstrated that the mathematical procedure may be extended to encompass the set
of the homogeneous potential energy functions thus relegating adherence to the
Coulombic interactions to introduce the energy of a real-space subsystem. On the
other hand, this extension opens the door for seeking novel real-space subsystems,
apart from atoms in molecules, in non-Coulombic systems. These novel real-space
subsystems, quite different from the atoms in molecules, call for an extended formalism that goes beyond the orthodox QTAIM. Accordingly, based on a previous
proposal the new formalism, which is not confined to the Coulombic systems nor to
the atoms in molecules as the sole real-space subsystems, is termed the quantum
theory of proper open subsystems (QTPOS) and its potential applications are detailed.
S. Shahbazian (&)
Faculty of Chemistry, Shahid Beheshti University, G. C., Evin,
P.O. Box 19395-4716, 19839 Tehran, Iran
e-mail: chemist_shant@yahoo.com
© Springer International Publishing Switzerland 2016
R. Chauvin et al. (eds.), Applications of Topological Methods
in Molecular Chemistry, Challenges and Advances in Computational
Chemistry and Physics 22, DOI 10.1007/978-3-319-29022-5_4
89
Extending the Topological Analysis
and Seeking the Real-Space Subsystems
in Non-Coulombic Systems
with Homogeneous Potential Energy
Functions
Shant Shahbazian
Abstract It is customary to conceive the interactions of all the constituents of a
molecular system, i.e. electrons and nuclei, as Coulombic. However, in a more
detailed analysis one may always find small but non-negligible non-Coulombic
interactions in molecular systems originating from the finite size of nuclei, magnetic
interactions, etc. While such small modifications of the Coulombic interactions do not
seem to alter the nature of a molecular system in real world seriously, they are a serious
obstacle for quantum chemical theories and methodologies which their formalism is
strictly confined to the Coulombic interactions. Although the quantum theory of atoms
in molecules (QTAIM) has been formulated originally for the Coulombic systems,
some recent studies have demonstrated that most of its theoretical ingredients are not
sensitive to the explicit form of the potential energy operator. However, the
Coulombic interactions have been explicitly assumed in the mathematical procedure
that is used to introduce the basin energy of an atom in a molecule. In this study it is
demonstrated that the mathematical procedure may be extended to encompass the set
of the homogeneous potential energy functions thus relegating adherence to the
Coulombic interactions to introduce the energy of a real-space subsystem. On the
other hand, this extension opens the door for seeking novel real-space subsystems,
apart from atoms in molecules, in non-Coulombic systems. These novel real-space
subsystems, quite different from the atoms in molecules, call for an extended formalism that goes beyond the orthodox QTAIM. Accordingly, based on a previous
proposal the new formalism, which is not confined to the Coulombic systems nor to
the atoms in molecules as the sole real-space subsystems, is termed the quantum
theory of proper open subsystems (QTPOS) and its potential applications are detailed.
S. Shahbazian (&)
Faculty of Chemistry, Shahid Beheshti University, G. C., Evin,
P.O. Box 19395-4716, 19839 Tehran, Iran
e-mail: chemist_shant@yahoo.com
© Springer International Publishing Switzerland 2016
R. Chauvin et al. (eds.), Applications of Topological Methods
in Molecular Chemistry, Challenges and Advances in Computational
Chemistry and Physics 22, DOI 10.1007/978-3-319-29022-5_4
89