Computational Chemistry

Diwas obtained fromD 1 by promoting an electron from spin orbitalc 2 ato the
spin orbitalc 3 a. Another possibility is

Dj¼

1

ffiffiffiffi

4!

p

c 1 ð 1 Það 1 Þ c 1 ð 1 Þbð 1 Þ c 3 ð 1 Það 1 Þ c 3 ð 1 Þbð 1 Þ

c 1 ð 2 Það 2 Þ c 1 ð 2 Þbð 2 Þ c 3 ð 2 Það 2 Þ c 3 ð 2 Þbð 2 Þ

c 1 ð 3 Það 3 Þ c 1 ð 3 Þbð 3 Þ c 3 ð 3 Það 3 Þ c 3 ð 3 Þbð 3 Þ

c 1 ð 4 Það 4 Þ c 1 ð 4 Þbð 4 Þ c 3 ð 4 Það 4 Þ c 3 ð 4 Þbð 4 Þ

ð 5 : 167 Þ

Here two electrons have been promoted, from the spin orbitalsc 2 aandc 2 bto
c 3 aandc 3 b.DiandDjrepresent promotion into virtual orbitals of one and two
electrons, respectively, starting with the HF electronic configuration (Fig.5.22).
Equation5.165is analogous to Eq.5.164¼5.52: in Eq.5.164¼5.52“compo-
nent” MOscare expanded in terms of basis functionsf, and in Eq.5.165a total
MOCis expanded in terms of determinants, each of which represents a particular
electronic configuration. We know that thembasis functions of Eq.5.164¼5.52
generatemcomponent MOsc(Section 5.2.3.6.1), so theideterminants of Eq.5.165
must generateitotal wavefunctionsC, and Eq.5.165should really be written

D 1 Di Dj

The HF determinant A single-excited determinant A doubly-excited determinant

a spin MOs b spin MOs

y 4

y 3

y 2

y 1

y 4

y 3

y 2

y 1

y 4

y 3

y 2

y 1

Fig. 5.22 Configuration interaction (CI): promotion of electrons from the occupied MOs
(corresponding to the Hartree–Fock determinant) gives determinants corresponding to excited
states. A weighted sum of determinantsD 1 ,D 2 ,...,Di,..., corresponds to a molecule in which the
electrons partly populate virtual MOs and are not strictly confined to the lowest-energy MOs, thus
giving them a better chance to avoid one another and decreasing electron–electron repulsion. The
method generates a series of wavefunctions and energies; the lowest-energy wavefunction and
energy corresponds to the ground electronic state, the others to excited states

5.4 Post-Hartree–Fock Calculations: Electron Correlation 271