Chapter 6
Emergent Scalar and Vector Fields
in Quantum Chemical Topology
A. Martín Pendás, E. Francisco, A. Gallo Bueno, J.M. Guevara Vela
and A. Costales
Abstract Several potentially useful scalar and vector fields that have been scarcely
or even never used to date in Quantum Chemical Topology are defined, computed,
and analyzed for a few small molecules. The fields include the Ehrenfest force
derived from the second order density matrix, which does not show many of the
spurious features encountered when it is computed from the electronic stress tensor,
the exchange-correlation (xc) potential, the potential acting on one electron in a
molecule, and the additive and effective energy densities. The basic features of the
topology of some of these fields are also explored and discussed, paying attention to
their possible future interest.
6.1 Introduction
The use of topological approaches in the theory of chemical bonding has become a
standard procedure to gain insight on the nature of quantum mechanical binding in all
sort of systems, from small molecules to biomolecules or even materials [16, 28, 29].
An outstanding advantage of these techniques over other procedures lies in their
invariance under orbital transformations. Being based on quantities derived from real
or momentum space density matrices, their physical or chemical interpretation exists
A. Martín Pendás (&) Á E. Francisco Á A. Gallo Bueno Á J.M. Guevara Vela Á A. Costales
University of Oviedo, 33006 Oviedo, Spain
e-mail: angel@fluor.quimica.uniovi.es
E. Francisco
e-mail: evelio@uniovi.es
A. Gallo Bueno
e-mail: gelbehahn@gmail.com
J.M. Guevara Vela
e-mail: jmguevarav@gmail.com
A. Costales
e-mail: costalesmaria@uniovi.es
© 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_6
131
Emergent Scalar and Vector Fields
in Quantum Chemical Topology
A. Martín Pendás, E. Francisco, A. Gallo Bueno, J.M. Guevara Vela
and A. Costales
Abstract Several potentially useful scalar and vector fields that have been scarcely
or even never used to date in Quantum Chemical Topology are defined, computed,
and analyzed for a few small molecules. The fields include the Ehrenfest force
derived from the second order density matrix, which does not show many of the
spurious features encountered when it is computed from the electronic stress tensor,
the exchange-correlation (xc) potential, the potential acting on one electron in a
molecule, and the additive and effective energy densities. The basic features of the
topology of some of these fields are also explored and discussed, paying attention to
their possible future interest.
6.1 Introduction
The use of topological approaches in the theory of chemical bonding has become a
standard procedure to gain insight on the nature of quantum mechanical binding in all
sort of systems, from small molecules to biomolecules or even materials [16, 28, 29].
An outstanding advantage of these techniques over other procedures lies in their
invariance under orbital transformations. Being based on quantities derived from real
or momentum space density matrices, their physical or chemical interpretation exists
A. Martín Pendás (&) Á E. Francisco Á A. Gallo Bueno Á J.M. Guevara Vela Á A. Costales
University of Oviedo, 33006 Oviedo, Spain
e-mail: angel@fluor.quimica.uniovi.es
E. Francisco
e-mail: evelio@uniovi.es
A. Gallo Bueno
e-mail: gelbehahn@gmail.com
J.M. Guevara Vela
e-mail: jmguevarav@gmail.com
A. Costales
e-mail: costalesmaria@uniovi.es
© 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_6
131