framework called Quantum Theory of Proper Open Subsystems (QTPOS) was
developed to deal with all types, rather than just the topological atoms, of the
real-space subsystems [47]. While in that paper only the Coulombic systems were
conceived as targets, the present contribution demonstrates that the QTPOS may be
conceived as a general theory that deals with both the Coulombic and non-Coulombic
systems composed of a single type of quantum particles interacting with each other
and external fields through the homogeneous potentials. Apart from the previously
considered examples [41], and those considered in this chapter, a large number of
interesting systems, some indicated in the first section, remain to be considered within
context of the QTPOS. However, a completely comprehensive theory must encompass also quantum systems containing particles that their interaction potentials are
inhomogeneous functions. This is also important in the case of extending the QTAIM
analysis further since upon adding new, albeit small, terms to the Coulombic potentials the resulting potential energy operator is inevitably inhomogeneous.
The comparative analysis of the real-space subsystems emerging in fermionic
and bosonic systems is another novel aspect of the present study. This is an
interesting area for future studies since it may reveal the “local” role of the Pauli
Exclusion Principle in molecular systems. Pauli “repulsions” and associated steric
interactions are usually invoked in both qualitative and quantitative analysis to
rationalize conformational selections, tracing molecular stresses and instabilities.
However, most of such analyzes are based on indirect methods and one may hope
that a direct comparative QTAIM analysis on a fermionic system and associated
bosonic counterpart may reveal a more detailed picture of the role of the statistics
on the local interactions in molecular systems.
Acknowledgments The author is grateful to Masume Gharabaghi and Ángel Martín-Pendás for
their detailed reading of a previous draft of this paper and helpful suggestions.
References
1. Bader RFW (1990) Atoms in molecules: a quantum theory. Oxford University Press, Oxford
2. Popelier PLA (2000) Atoms in molecules an introduction. Pearson, London
3. Matta C, Boyd RJ (2007) Quantum theory of atoms in molecules: from solid state to DNA and
drug design. Wiley, Weinheim
4. Nasertayoob P, Goli M, Shahbazian S (2011) Int J Quantum Chem 111:1970–1981
5. Goli M, Shahbazian S (2011) Int J Quantum Chem 111:1982–1998
6. Heidar Zadeh F, Shahbazian S (2011) Int J Quantum Chem 111:1999–2013
7. Goli M, Shahbazian S (2011) Theoret Chem Acc 129:235–245
8. Goli M, Shahbazian S (2012) Theoret Chem Acc 131, 1208:1–19
9. Goli M, Shahbazian S (2013) Theoret Chem Acc 132, 1362:1–14
10. Goli M, Shahbazian S (2013) Theoret Chem Acc 132, 1365:1–17
11. Goli M, Shahbazian S (2013) Theoret Chem Acc 132, 1410:1–22
12. Shahbazian S (2013) Found Chem 15:287–302
13. Goli M, Shahbazian S (2014) Phys Chem Chem Phys 16:6602–6613
14. Goli M, Shahbazian S (2015) Comput Theoret Chem 1053:96–105
15. Goli M, Shahbazian S (2015) Phys Chem Chem Phys 17:245–255
98
S. Shahbazian
developed to deal with all types, rather than just the topological atoms, of the
real-space subsystems [47]. While in that paper only the Coulombic systems were
conceived as targets, the present contribution demonstrates that the QTPOS may be
conceived as a general theory that deals with both the Coulombic and non-Coulombic
systems composed of a single type of quantum particles interacting with each other
and external fields through the homogeneous potentials. Apart from the previously
considered examples [41], and those considered in this chapter, a large number of
interesting systems, some indicated in the first section, remain to be considered within
context of the QTPOS. However, a completely comprehensive theory must encompass also quantum systems containing particles that their interaction potentials are
inhomogeneous functions. This is also important in the case of extending the QTAIM
analysis further since upon adding new, albeit small, terms to the Coulombic potentials the resulting potential energy operator is inevitably inhomogeneous.
The comparative analysis of the real-space subsystems emerging in fermionic
and bosonic systems is another novel aspect of the present study. This is an
interesting area for future studies since it may reveal the “local” role of the Pauli
Exclusion Principle in molecular systems. Pauli “repulsions” and associated steric
interactions are usually invoked in both qualitative and quantitative analysis to
rationalize conformational selections, tracing molecular stresses and instabilities.
However, most of such analyzes are based on indirect methods and one may hope
that a direct comparative QTAIM analysis on a fermionic system and associated
bosonic counterpart may reveal a more detailed picture of the role of the statistics
on the local interactions in molecular systems.
Acknowledgments The author is grateful to Masume Gharabaghi and Ángel Martín-Pendás for
their detailed reading of a previous draft of this paper and helpful suggestions.
References
1. Bader RFW (1990) Atoms in molecules: a quantum theory. Oxford University Press, Oxford
2. Popelier PLA (2000) Atoms in molecules an introduction. Pearson, London
3. Matta C, Boyd RJ (2007) Quantum theory of atoms in molecules: from solid state to DNA and
drug design. Wiley, Weinheim
4. Nasertayoob P, Goli M, Shahbazian S (2011) Int J Quantum Chem 111:1970–1981
5. Goli M, Shahbazian S (2011) Int J Quantum Chem 111:1982–1998
6. Heidar Zadeh F, Shahbazian S (2011) Int J Quantum Chem 111:1999–2013
7. Goli M, Shahbazian S (2011) Theoret Chem Acc 129:235–245
8. Goli M, Shahbazian S (2012) Theoret Chem Acc 131, 1208:1–19
9. Goli M, Shahbazian S (2013) Theoret Chem Acc 132, 1362:1–14
10. Goli M, Shahbazian S (2013) Theoret Chem Acc 132, 1365:1–17
11. Goli M, Shahbazian S (2013) Theoret Chem Acc 132, 1410:1–22
12. Shahbazian S (2013) Found Chem 15:287–302
13. Goli M, Shahbazian S (2014) Phys Chem Chem Phys 16:6602–6613
14. Goli M, Shahbazian S (2015) Comput Theoret Chem 1053:96–105
15. Goli M, Shahbazian S (2015) Phys Chem Chem Phys 17:245–255
98
S. Shahbazian