The Hartree-Fock approximation

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The Hartree-Fock approximation
Assume that the wavefunction can be approximated
by a Slater-determinant.
Vary the orbitals and use the variation
principle to minimize the energy.
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The Hartree-Fock approximation (continued)
Fock-equation
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The Hartree-Fock approximation (continued)
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The Hartree-Fock approximation (continued)
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The Hartree-Fock approximation (continued)
Which MOs should we choose to construct the
Slater-determinant?
Hunds first rule The Slater-determinant has the
lowest energy if its constructed from the
MOs with the lowest MO-energy.
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The Hartree-Fock approximation (continued)
Koopmans-theorem
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The Hartree-Fock approximation (continued)
The Fock-operators effect depends on the
solution of the Fock-equation.
An iterative procedure is needed to solve the
Fock-equation, hence the name Self-Consisten
Field (SCF) for the Hartree- Fock approximation.
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The Hartree-Fock approximation (continued)
Linear combination of atomic orbitals (LCAO)
approximation
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The Hartree-Fock approximation (continued)

• The Hartree-Fock procedure
• choose basis functions ci
• calculate the overlap matrix S
• calculate the contribution of the one-electron
  operator to F
• calculate two-electron integrals
• make an initial guess for the MOs
• calculate the total energy

• calculate the Coulomb-integrals
• calculate the exchange-integrals
• compute the Fock-matrix F
• solve the Roothaan-equation
• compare the old an new MOs
• if old an new MOs are different then repeat this
  block