13.2 Two Different Hückel-Lewis Schemes to Define
a Configuration Interaction in the Hückel
Framework
The Hückel framework defines the reference wave function, W ref and its energy,
E ref . It is possible to extract information from this structure in the same way it is
done at high level of calculations. The Hückel solution should be seen as a quantum
chemistry calculation done in a minimal basis. If one tries to write the reference
wave function on a set of localized structures, many approaches can be defined.
These approaches are a posteriori analysis of the reference wave function and help
to understand the nature of its electronic structure. We defined the following
schemes:
HL-CI: The Hückel Lewis Configuration Interaction (CI) is formally equivalent to
the Hückel method for the interaction between several localized structures: one can
diagonalize a Hamiltonian in the basis of localized Lewis structures. In the following, this will be referred to as the energy based scheme.
HL-P: The Hückel Lewis Projection is a CI expansion based on the overlap
between W ref and each of the chosen localized structures W i . This will be referred to
as the space based scheme.
13.2.1 Energy Based Scheme
The HL-CI method is an analog of the Hückel method in the multiconfigurational
framework [17–20]. It is based on the assumption that the delocalized wave
function, which has the lowest possible energy, results from the interaction of all
local structures of higher energy. Let W ref be a delocalized wave function of energy
E ref to be written on the basis of N local structures W i
f g i¼1;N of energy E i . One
searches ~
W, of energy ~
E:
~
W ¼
X N
i
c i W i
ð13:16Þ
such that:
~
E ¼ E ref :
ð13:17Þ
In Hückel theory, atomic basis functions are assumed to be orthonormal. The
interaction between neighbouring functions is included in the off-diagonal term of
the Hamiltonian. In the HL-CI framework, these two approximations are done
among the local structures.
13 Localized Structures at the Hückel Level …
345
a Configuration Interaction in the Hückel
Framework
The Hückel framework defines the reference wave function, W ref and its energy,
E ref . It is possible to extract information from this structure in the same way it is
done at high level of calculations. The Hückel solution should be seen as a quantum
chemistry calculation done in a minimal basis. If one tries to write the reference
wave function on a set of localized structures, many approaches can be defined.
These approaches are a posteriori analysis of the reference wave function and help
to understand the nature of its electronic structure. We defined the following
schemes:
HL-CI: The Hückel Lewis Configuration Interaction (CI) is formally equivalent to
the Hückel method for the interaction between several localized structures: one can
diagonalize a Hamiltonian in the basis of localized Lewis structures. In the following, this will be referred to as the energy based scheme.
HL-P: The Hückel Lewis Projection is a CI expansion based on the overlap
between W ref and each of the chosen localized structures W i . This will be referred to
as the space based scheme.
13.2.1 Energy Based Scheme
The HL-CI method is an analog of the Hückel method in the multiconfigurational
framework [17–20]. It is based on the assumption that the delocalized wave
function, which has the lowest possible energy, results from the interaction of all
local structures of higher energy. Let W ref be a delocalized wave function of energy
E ref to be written on the basis of N local structures W i
f g i¼1;N of energy E i . One
searches ~
W, of energy ~
E:
~
W ¼
X N
i
c i W i
ð13:16Þ
such that:
~
E ¼ E ref :
ð13:17Þ
In Hückel theory, atomic basis functions are assumed to be orthonormal. The
interaction between neighbouring functions is included in the off-diagonal term of
the Hamiltonian. In the HL-CI framework, these two approximations are done
among the local structures.
13 Localized Structures at the Hückel Level …
345