Delocalized and localized molecular orbitals

Delocalized and localized molecular orbitals

Delocalized and localized
molecular orbitals
Bởi:
Thanh Truong
Within the molecular orbital or Hartree-Fock theory, the multi-electron wavefunction is
approximated by a single Slater determinant. where

are molecular orbitals and are eigenfunctions of the Fock operator with the orbital
energies
as eigenvalues. The molecular orbitals are approximated as Linear Combination of
Atomic Orbitals (LCAO) as
and are delocalized over the entire molecule as shown in the case of ethylene below

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Delocalized and localized molecular orbitals

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Delocalized and localized molecular orbitals

Orbtial energies shown in the figure above obey the Koopman's theorem and thus can
be related to ionization potential and electron affinity of the molecule. Since the MO's
are delocalized, they are more difficult to provide much physical interpretation.
However, as a property of a determinant that a column can be added by another column
multiplied by a constant without changing the value of the determinant. That means
one can transform the delocalized MO into another set of MO and still does not change

the total wavefunction and thus all observables of the molecule. There are several
ways that one can transfer the delocalized MO's into localized MO's as shown below
for ethylene.

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Delocalized and localized molecular orbitals

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Delocalized and localized molecular orbitals

In this case, the localized MO's show the nature of each bond. For instance, C=C has
one sigma bond and one pi bond. Since localized MO's are not eigenfuctions of the
Fock operator, orbital energies no longer have any physical meaning.
Exercise: Use Basic QChem Edu or Basic QChem tool with PsiViewer in Avisto to
show the delocalized and localized MO's for BeH2. You can download these tools and
Avisto from Astonis.

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