Chapter 14
Magnetic Properties of Conjugated
Hydrocarbons from Topological
Hamiltonians
Jean-Paul Malrieu, Nicolas Ferré and Nathalie Guihéry
Abstract The present chapter shows first that the topological Hückel Hamiltonian
provides an analytical expression of both the singly occupied Molecular Orbitals
and the spin density distribution of mono- and poly-radical conjugated hydrocarbons. It permits a new derivation of the Ovchinnikov’s rule (first established from a
magnetic model Hamiltonian), which predicts the preferred ground state spin
multiplicity from the topology of the molecule. From the Hubbard simplified representation of the bi-electronic Hamiltonian one obtains directly, without any matrix
diagonalization, a reasonable evaluation of the singlet-triplet energy difference. For
singlet di-radicals the method enables one to predict whether the Ms = 0
single-determinant solution is subject to a spin-symmetry breaking. The spin
polarization of the closed shells, which is a different phenomenon, of bi-electronic
origin, increases the value of the magnetic coupling in these systems, contrasts the
spin densities between negative and positive values and spatially extends the spin
distribution. Numerical Unrestricted Density Functional Theory calculations illustrate the relevance of the predictions of the topological model.
14.1 Introduction
The occurrence of open shells (or singly occupied MOs) is more common in
coordination chemistry than in organic chemistry. The metal ions which usually
bear the unpaired electrons exhibit a local spin momentum responsible for magnetic
properties. The field of molecular magnetism [1–9] and its extension to periodic
lattices are key areas of coordination chemistry because of their potential applicaJ.-P. Malrieu (&) Á N. Guihéry
Laboratoire de Chimie et Physique Quantiques, UMR 5626 (CNRS), IRSAMC,
Université P. Sabatier, 118 Rte de Narbonne, 31062 Toulouse Cedex, France
e-mail: jean-paul.malrieu@irsamc.ups-tlse.fr
N. Ferré
Aix-Marseille Université, CNRS, Institut de Chimie Radicalaire,
13397 Marseille Cedex 20, France
© 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_14
361
Magnetic Properties of Conjugated
Hydrocarbons from Topological
Hamiltonians
Jean-Paul Malrieu, Nicolas Ferré and Nathalie Guihéry
Abstract The present chapter shows first that the topological Hückel Hamiltonian
provides an analytical expression of both the singly occupied Molecular Orbitals
and the spin density distribution of mono- and poly-radical conjugated hydrocarbons. It permits a new derivation of the Ovchinnikov’s rule (first established from a
magnetic model Hamiltonian), which predicts the preferred ground state spin
multiplicity from the topology of the molecule. From the Hubbard simplified representation of the bi-electronic Hamiltonian one obtains directly, without any matrix
diagonalization, a reasonable evaluation of the singlet-triplet energy difference. For
singlet di-radicals the method enables one to predict whether the Ms = 0
single-determinant solution is subject to a spin-symmetry breaking. The spin
polarization of the closed shells, which is a different phenomenon, of bi-electronic
origin, increases the value of the magnetic coupling in these systems, contrasts the
spin densities between negative and positive values and spatially extends the spin
distribution. Numerical Unrestricted Density Functional Theory calculations illustrate the relevance of the predictions of the topological model.
14.1 Introduction
The occurrence of open shells (or singly occupied MOs) is more common in
coordination chemistry than in organic chemistry. The metal ions which usually
bear the unpaired electrons exhibit a local spin momentum responsible for magnetic
properties. The field of molecular magnetism [1–9] and its extension to periodic
lattices are key areas of coordination chemistry because of their potential applicaJ.-P. Malrieu (&) Á N. Guihéry
Laboratoire de Chimie et Physique Quantiques, UMR 5626 (CNRS), IRSAMC,
Université P. Sabatier, 118 Rte de Narbonne, 31062 Toulouse Cedex, France
e-mail: jean-paul.malrieu@irsamc.ups-tlse.fr
N. Ferré
Aix-Marseille Université, CNRS, Institut de Chimie Radicalaire,
13397 Marseille Cedex 20, France
© 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_14
361