tions. One may mention ferro- (or ferri-) magnetic lattices, commutable
spin-cross-over systems, single molecule magnets or spintronic devices. In these
systems the metal ions are connected by closed-shell ligands which mediate the
interactions between the localized spins. Theoreticians have made great efforts in
understanding the mechanisms of the magnetic interactions between magnetic sites
and have developed appropriate computational tools for their study, either based on
wave-function based methods or on density functional theory (DFT) [10–13].
The magnetism of organic compounds receives more and more attention, and the
idea that one might conceive the organic counterpart of the magnetic devices
developed by coordination chemists attracts more and more attention from
researchers [14–17]. Several works deal with famous stable radicals such as
nitroxydes and parent compounds [18]. Nevertheless purely carbon-based magnetic
polyradical architectures, using for instance the meta-xylylene unit as a building
block, have been conceived and even synthesized [19]. These architectures are
conjugated hydrocarbons and the present contribution focuses on these systems.
Conjugated hydrocarbons have the advantage of presenting a high homogeneity
(same sp
2 carbons, similar CC bond lengths) and their description may take benefit
from the topological models developed in the early days of Quantum Chemistry
[20]. We shall concentrate here our attention on open-shell hydrocarbons. In contrast to what happens in coordination chemistry, the unpaired electrons may be
strongly delocalized, as manifest from the shapes of the singly occupied molecular
orbitals (SOMOs). Actually when one branches a (CH 2 )
. group on a closed-shell
moiety, such as a benzene ring or a fuzzed polycyclic hydrocarbon, the spin density
is no longer concentrated on the added methylene group, it spreads over the whole π
systems. This phenomenon is the spin delocalization, and Sect. 14.2 focuses on its
study in free radicals. The topological rules governing its extension are derived
from the Hückel Hamiltonian and confirmed by DFT calculations. In Sect. 14.3,
fully conjugated di- or poly-radicals are considered. They are frequently seen as
resulting from the attachment of two (or more) radical groups on a closed-shell
moiety. It is shown that spin delocalization can also be easily predicted from the
Hückel model and that the topology governs the ground state spin multiplicity
(singlet or triplet) owing to the Ovchinnikov’s rule [21]. This rule has been originally established from a magnetic model Hamiltonian, which is in principle valid
for strongly-correlated systems, while the π electronic population is usually considered as weakly correlated. The same rule is here derived from a mixed
Hückel-Hubbard picture, which simply considers the effect of on-site bi-electronic
repulsion as a first-order perturbation to the energies. This procedure avoids any
self-consistent mean-field calculation of the Hubbard Hamiltonian. On a series of
examples, it is shown that the energy gaps between the lowest triplet and singlet
states estimated from elementary analytical calculations compare well with the
quantitative DFT predictions reported in Sect. 14.4.
Often confused with spin delocalization, spin polarization, discussed in
Sect. 14.5, is a different phenomenon. It introduces spin densities in orbitals of
different symmetries than the SOMOs, for instance in the σ system of π radicals.
While spin delocalization is well described by restricted open-shell formalisms, spin
362
J.-P. Malrieu et al.
spin-cross-over systems, single molecule magnets or spintronic devices. In these
systems the metal ions are connected by closed-shell ligands which mediate the
interactions between the localized spins. Theoreticians have made great efforts in
understanding the mechanisms of the magnetic interactions between magnetic sites
and have developed appropriate computational tools for their study, either based on
wave-function based methods or on density functional theory (DFT) [10–13].
The magnetism of organic compounds receives more and more attention, and the
idea that one might conceive the organic counterpart of the magnetic devices
developed by coordination chemists attracts more and more attention from
researchers [14–17]. Several works deal with famous stable radicals such as
nitroxydes and parent compounds [18]. Nevertheless purely carbon-based magnetic
polyradical architectures, using for instance the meta-xylylene unit as a building
block, have been conceived and even synthesized [19]. These architectures are
conjugated hydrocarbons and the present contribution focuses on these systems.
Conjugated hydrocarbons have the advantage of presenting a high homogeneity
(same sp
2 carbons, similar CC bond lengths) and their description may take benefit
from the topological models developed in the early days of Quantum Chemistry
[20]. We shall concentrate here our attention on open-shell hydrocarbons. In contrast to what happens in coordination chemistry, the unpaired electrons may be
strongly delocalized, as manifest from the shapes of the singly occupied molecular
orbitals (SOMOs). Actually when one branches a (CH 2 )
. group on a closed-shell
moiety, such as a benzene ring or a fuzzed polycyclic hydrocarbon, the spin density
is no longer concentrated on the added methylene group, it spreads over the whole π
systems. This phenomenon is the spin delocalization, and Sect. 14.2 focuses on its
study in free radicals. The topological rules governing its extension are derived
from the Hückel Hamiltonian and confirmed by DFT calculations. In Sect. 14.3,
fully conjugated di- or poly-radicals are considered. They are frequently seen as
resulting from the attachment of two (or more) radical groups on a closed-shell
moiety. It is shown that spin delocalization can also be easily predicted from the
Hückel model and that the topology governs the ground state spin multiplicity
(singlet or triplet) owing to the Ovchinnikov’s rule [21]. This rule has been originally established from a magnetic model Hamiltonian, which is in principle valid
for strongly-correlated systems, while the π electronic population is usually considered as weakly correlated. The same rule is here derived from a mixed
Hückel-Hubbard picture, which simply considers the effect of on-site bi-electronic
repulsion as a first-order perturbation to the energies. This procedure avoids any
self-consistent mean-field calculation of the Hubbard Hamiltonian. On a series of
examples, it is shown that the energy gaps between the lowest triplet and singlet
states estimated from elementary analytical calculations compare well with the
quantitative DFT predictions reported in Sect. 14.4.
Often confused with spin delocalization, spin polarization, discussed in
Sect. 14.5, is a different phenomenon. It introduces spin densities in orbitals of
different symmetries than the SOMOs, for instance in the σ system of π radicals.
While spin delocalization is well described by restricted open-shell formalisms, spin
362
J.-P. Malrieu et al.