Chapter 2
On Quantum Chemical Topology
Paul L.A. Popelier
Abstract Quantum Chemical Topology (QCT) is a branch of theoretical chemistry
that uses the language of dynamical systems (e.g. attractor, basin, homeomorphism,
gradient path/phase curve, separatrix, critical points) to partition chemical systems
and characterise them via associated quantitative properties. This methodology can
be applied to a variety of quantum mechanical functions, the oldest and most
documented one being the electron density. We define and discuss the topological
atom, and justify the name topology. Then we define the quantum atom without
reference to the topological atom. Subsequently, it turns out that each topological
atom is a quantum atom, a property that enables the construction of a topologically
inspired force field called QCTFF. We briefly discuss the four primary energy
contributions governing this force field under development, and how the machine
learning method kriging captures the variation in these energies due to geometrical
change. Finally, in a more philosophical style, we advocate falsification in the area
of chemical interpretation by means of quantum mechanical tools, introducing the
concept of a non-question.
2.1 Introduction
Recently a chapter on the “Quantum Theory of Atoms in Molecules (QTAIM)” [1]
was commissioned by editors Frenking and Shaik for their book on fundamental
aspects of chemical bonding. This detailed and lengthy chapter has meanwhile been
published [2], and features alongside authoritative chapters on alternative approaches such as EDA, NBO, Valence Bond, conceptual DFT, Block-localised
P.L.A. Popelier (&)
Manchester Institute of Biotechnology (MIB), 131 Princess Street,
Manchester M1 7DN, UK
e-mail: pla@manchester.ac.uk
P.L.A. Popelier
School of Chemistry, University of Manchester, Oxford Road,
Manchester M13 9PL, UK
© 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_2
23
On Quantum Chemical Topology
Paul L.A. Popelier
Abstract Quantum Chemical Topology (QCT) is a branch of theoretical chemistry
that uses the language of dynamical systems (e.g. attractor, basin, homeomorphism,
gradient path/phase curve, separatrix, critical points) to partition chemical systems
and characterise them via associated quantitative properties. This methodology can
be applied to a variety of quantum mechanical functions, the oldest and most
documented one being the electron density. We define and discuss the topological
atom, and justify the name topology. Then we define the quantum atom without
reference to the topological atom. Subsequently, it turns out that each topological
atom is a quantum atom, a property that enables the construction of a topologically
inspired force field called QCTFF. We briefly discuss the four primary energy
contributions governing this force field under development, and how the machine
learning method kriging captures the variation in these energies due to geometrical
change. Finally, in a more philosophical style, we advocate falsification in the area
of chemical interpretation by means of quantum mechanical tools, introducing the
concept of a non-question.
2.1 Introduction
Recently a chapter on the “Quantum Theory of Atoms in Molecules (QTAIM)” [1]
was commissioned by editors Frenking and Shaik for their book on fundamental
aspects of chemical bonding. This detailed and lengthy chapter has meanwhile been
published [2], and features alongside authoritative chapters on alternative approaches such as EDA, NBO, Valence Bond, conceptual DFT, Block-localised
P.L.A. Popelier (&)
Manchester Institute of Biotechnology (MIB), 131 Princess Street,
Manchester M1 7DN, UK
e-mail: pla@manchester.ac.uk
P.L.A. Popelier
School of Chemistry, University of Manchester, Oxford Road,
Manchester M13 9PL, UK
© 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_2
23