Chapter 3
Localization-Delocalization Matrices
and Electron Density-Weighted
Adjacency/Connectivity Matrices:
A Bridge Between the Quantum Theory
of Atoms in Molecules and Chemical
Graph Theory
Chérif F. Matta, Ismat Sumar, Ronald Cook and Paul W. Ayers
The development of chemistry has both led to, and been made
possible by, the evolution of certain primary concepts. These
concepts, without which there would be neither correlation nor
prediction of the observations of descriptive chemistry, are:
(1) the existence of atoms of functional groupings of atoms in
molecules as evidenced by characteristic sets of properties;
(2) the concept of bonding; and (3) the associated concepts of
molecular structure and molecular shape. These concepts
logically (but not historically) are consequences of fundamental
topological properties of the charge distribution (electronic and
nuclear) in a molecular system. In terms of the
Born-Oppenheimer approximation the electronic distribution
ρ(r) is the scalar field defined in the real three-dimensional space
with Euclidean metric. The universal topological properties of
ρ(r) are characterized by its gradient field ∇ρ(r) [1].
I.S. Dmitriev (1981)
C.F. Matta (&) Á I. Sumar
Department of Chemistry and Physics, Mount Saint Vincent University,
Halifax, NS B3M 2J6, Canada
e-mail: cherif.matta@msvu.ca
C.F. Matta
Department of Chemistry, Dalhousie University, Halifax, NS B3H 4J3, Canada
C.F. Matta Á I. Sumar
Department of Chemistry, Saint Mary’s University, Halifax, NS B3H 3C3, Canada
I. Sumar Á P.W. Ayers (&)
Department of Chemistry, McMaster University, Hamilton, ON L8S 4L8, Canada
e-mail: ayers@mcmaster.ca
R. Cook (&)
TDA Research, Inc, 12345 W. 52nd Ave, Wheat Ridge, CO 80033, USA
e-mail: rnldcook@gmail.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_3
53
Localization-Delocalization Matrices
and Electron Density-Weighted
Adjacency/Connectivity Matrices:
A Bridge Between the Quantum Theory
of Atoms in Molecules and Chemical
Graph Theory
Chérif F. Matta, Ismat Sumar, Ronald Cook and Paul W. Ayers
The development of chemistry has both led to, and been made
possible by, the evolution of certain primary concepts. These
concepts, without which there would be neither correlation nor
prediction of the observations of descriptive chemistry, are:
(1) the existence of atoms of functional groupings of atoms in
molecules as evidenced by characteristic sets of properties;
(2) the concept of bonding; and (3) the associated concepts of
molecular structure and molecular shape. These concepts
logically (but not historically) are consequences of fundamental
topological properties of the charge distribution (electronic and
nuclear) in a molecular system. In terms of the
Born-Oppenheimer approximation the electronic distribution
ρ(r) is the scalar field defined in the real three-dimensional space
with Euclidean metric. The universal topological properties of
ρ(r) are characterized by its gradient field ∇ρ(r) [1].
I.S. Dmitriev (1981)
C.F. Matta (&) Á I. Sumar
Department of Chemistry and Physics, Mount Saint Vincent University,
Halifax, NS B3M 2J6, Canada
e-mail: cherif.matta@msvu.ca
C.F. Matta
Department of Chemistry, Dalhousie University, Halifax, NS B3H 4J3, Canada
C.F. Matta Á I. Sumar
Department of Chemistry, Saint Mary’s University, Halifax, NS B3H 3C3, Canada
I. Sumar Á P.W. Ayers (&)
Department of Chemistry, McMaster University, Hamilton, ON L8S 4L8, Canada
e-mail: ayers@mcmaster.ca
R. Cook (&)
TDA Research, Inc, 12345 W. 52nd Ave, Wheat Ridge, CO 80033, USA
e-mail: rnldcook@gmail.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_3
53