The harmonic trap model, containing non-interacting fermions or bosons, is considered as an example for the QTPOS analysis. The QTPOS analysis of the bosonic
systems is particularly quite unprecedented not attempted before.
Keywords Quantum theory of atoms in molecules Á Topological analysis Á
Non-Coulombic systems Á Homogeneous potentials Á Virial theorem
4.1 Introduction
The quantum theory of atoms in molecules (QTAIM) has gained a widespread
recognition in the last 20 years in chemistry, molecular and solid-state physics, and
even in molecular biology [1–3]. However, all applications of the QTAIM have been
confined to the Coulombic systems namely, systems containing electrons and
clamped nuclei interacting via the Coulombic potential. Even the recent extension of
the QTAIM, termed the multi-component QTAIM (MC-QTAIM) [4–16], which
goes beyond the clamped nucleus model and deals with the AIM analysis of certain
types of non-Born-Oppenheimer molecular wavefunctions, is also confined to the
Coulombic systems. Although it is understandable that the Coulombic systems are of
prime interest in most applications in chemistry and physics, there are many
non-Coulombic systems which are also interesting to be considered from the viewpoint of the AIM analysis. However, before discussing examples of such systems, it
must be emphasized that even for usual molecular systems the Coulombic interactions are just approximate potentials, albeit accurate enough for most practical
applications, which are used usually in quantum chemical calculations. For highly
accurate quantum description of an atomic or molecular system, various small but
non-negligible non-Coulombic terms must be added to the Coulombic potential that
weak internal magnetic interactions of electrons, originating from the L-S and the
S-S couplings, and modifications originating from the finite size of nuclei are just
examples. Accordingly, confining the QTAIM formalism to the Coulombic interactions is “artificial” and certainly against the basic idea that atoms in molecules are
“real” objects emerging independent from the details of the models used to describe
molecular systems [17].
On the other hand, in recent decades a wealth of experimental and theoretical
evidence has been accumulated demonstrating molecular-like structure for systems
not traditionally considered as molecular systems. One may include in this list the
“nuclear molecules” in nuclear physics [18, 19], various “exotic molecules” composed of fundamental particles other than electron, protons and neutrons [20–31],
“artificial molecules” in condensed-matter physics [32–35], and the “molecular
Bose-Einstein condensates” [36–39]. In considering such molecular-like systems
the question emerges whether any underlying AIM structure is derivable from the
wavefunctions of these systems. To answer this question one must apply the AIM
analysis to these systems however, all such systems are intrinsically non-Coulombic
in their nature and the formalism of the orthodox QTAIM must be modified to be
90
S. Shahbazian
systems is particularly quite unprecedented not attempted before.
Keywords Quantum theory of atoms in molecules Á Topological analysis Á
Non-Coulombic systems Á Homogeneous potentials Á Virial theorem
4.1 Introduction
The quantum theory of atoms in molecules (QTAIM) has gained a widespread
recognition in the last 20 years in chemistry, molecular and solid-state physics, and
even in molecular biology [1–3]. However, all applications of the QTAIM have been
confined to the Coulombic systems namely, systems containing electrons and
clamped nuclei interacting via the Coulombic potential. Even the recent extension of
the QTAIM, termed the multi-component QTAIM (MC-QTAIM) [4–16], which
goes beyond the clamped nucleus model and deals with the AIM analysis of certain
types of non-Born-Oppenheimer molecular wavefunctions, is also confined to the
Coulombic systems. Although it is understandable that the Coulombic systems are of
prime interest in most applications in chemistry and physics, there are many
non-Coulombic systems which are also interesting to be considered from the viewpoint of the AIM analysis. However, before discussing examples of such systems, it
must be emphasized that even for usual molecular systems the Coulombic interactions are just approximate potentials, albeit accurate enough for most practical
applications, which are used usually in quantum chemical calculations. For highly
accurate quantum description of an atomic or molecular system, various small but
non-negligible non-Coulombic terms must be added to the Coulombic potential that
weak internal magnetic interactions of electrons, originating from the L-S and the
S-S couplings, and modifications originating from the finite size of nuclei are just
examples. Accordingly, confining the QTAIM formalism to the Coulombic interactions is “artificial” and certainly against the basic idea that atoms in molecules are
“real” objects emerging independent from the details of the models used to describe
molecular systems [17].
On the other hand, in recent decades a wealth of experimental and theoretical
evidence has been accumulated demonstrating molecular-like structure for systems
not traditionally considered as molecular systems. One may include in this list the
“nuclear molecules” in nuclear physics [18, 19], various “exotic molecules” composed of fundamental particles other than electron, protons and neutrons [20–31],
“artificial molecules” in condensed-matter physics [32–35], and the “molecular
Bose-Einstein condensates” [36–39]. In considering such molecular-like systems
the question emerges whether any underlying AIM structure is derivable from the
wavefunctions of these systems. To answer this question one must apply the AIM
analysis to these systems however, all such systems are intrinsically non-Coulombic
in their nature and the formalism of the orthodox QTAIM must be modified to be
90
S. Shahbazian