Computational Physics

78 The Hartree–Fock method

Table 4.2.Bond angles in degrees forH 2 OandNH 3.

The angles are those of theH–O–HandH–N–H

chains respectively. Hartree–Fock (HF) and

experimental results are shown.

Molecule HF Expt.

H 2 O 107.1 104.5

NH 3 108.9 106.7

DatatakenfromRef.[17].

Table 4.3.Dissociation energies in atomic units for

LiFandNaBr. Hartree–Fock (HF) and experimental

results are shown.

Molecule HF Expt

LiF 0.2938 0.2934

NaBr 0.1978 0.2069

DatatakenfromRef.[17].

energies needed to dissociate diatomic molecules (seeTable 4.3) and again good
agreement is found with experiment.
Koopman’s theorem can be used to calculate ionisation potentials, that is, the
minimum energy needed to remove an electron from the molecule. Comparing the
results inTable 4.4for the ionisation potentials calculated via Koopman’s theorem
with those of the previous tables, it is seen that the approximations involved in
this ‘theorem’ are more severe than those of the Hartree–Fock theory, although
agreement with experiment is still reasonable.

*4.10 Improving upon the Hartree–Fock approximation

The Hartree–Fock approximation sometimes yields unsatisfactory results. This is
of course due to Coulomb correlations not taken into account in the Hartree–Fock
formalism. There exists a systematic way to improve on Hartree–Fock by construct-
ing a many-electron state as a linear combination of Slater determinants (remember
the Slater determinants span theN-electron Hilbert space of many-electron wave