Population and bond order constrained Hartree-Fock:
electronegativity equalization, valence bond theory and bond resonance energies
Ph. Bultinck,
Department of Inorganic and Physical Chemistry, Ghent University,
Krijgslaan 281, 9000 Gent, Belgium.
Mail
Lundi, 15 octobre 2012, 14 h 00, Bibliothèque du LCT, tour 12-13,
4e étage
By including one electron or two electron constraints as potentials in the molecular
Hamiltonian, one can formulate a constrained Hartree-Fock theory, directing the
solutions towards wave functions that yield specific desired values for some observables
or desired values for chemical concepts such as atomic populations or bond orders.
The corresponding Euler-Lagrange equations lead to a modified Fock matrix, where
the contribution from the constraints only depends on the overlap matrix, when using
the Mulliken or Hirshfeld atoms-in-molecules method or the overlap matrix and the density
matrix in a way similar to regular Hartree-Fock theory.
Imposing a set of atomic population constraints in the Mulliken sense, reveals that the
energy shows a quadratic dependence on the fixed charges, thereby linking it closely to
the electronegativity equalization method. This behavior provides a procedure to obtain
the atomic electronegativity and hardness parameters in the
electronegativity equalization method.
Going further, one can impose constraints on bond orders in such a way that a specific
resonance structure can be imposed. Results will be shown for benzene, showing the
impressive flexibility of the molecule to lead to a very low energy wave function, away
from the RHF solution, but fulfilling the contraints of a Kekulé or Dewar structure. Finally,
by providing a framework for switching on or off a specific delocalization path, we can
reach an ab initio equivalent of the bond resonance energy; an often used concept in graph
theory of delocalized systems such as e.g., anthracene.