Biomedical Engineering Reference
In-Depth Information
by pseudo-potentials that have the same scattering properties of the
real ones outside the ion core region but are much weaker inside it
to decrease the computational cost [5, 44, 53, 104, 105].
8.3.2
Hartree-Fock Based Quantum Chemistry
ab initio
Techniques
In the Hartree-Fock (HF) theory, a set of self-consistent one-electron
equations is solved where the electron-electron interaction is treated
as an average static electric field that contains the exchange term
but does not include the electron correlation. Thus the predictions
concerning energetic, geometric, and electronic properties of
realistic systems are affected by large errors.
The reader could refer to textbooks on quantum chemistry or
electronic structure calculations for a general discussion on the
technicalities and the limits of validity of the HF theory [24, 49,
100, 120].
The electron correlation can be included into the theory
by replacing the HF ground state wave function with a linear
combination of multiple determinants where the ground state HF
Slater determinant
y
HF
is the first term:
+
...
y
y
y
1
y
=
c
+
c
+
c
(8.6)
0
HF
1
2
2
The additional terms of the linear combination are “excited”
determinants representing different excited molecular states with at
least one occupied molecular orbital (MO) replaced by a virtual MO.
This assumption is the basis of the CI schemes that are very accurate
and typically fulfill the chemical accuracy requirement. However,
due to its variational nature, a particularly heavy computational
workload is required to perform the calculations that are practically
affordable only for very small systems, even using a small basis set
for the MOs expansion.
Depending on the rules used to include the excited states into
the determinants, different CI schemes have been proposed and
used such as the CI singles (CIS), where only single excitations are
considered, the CI singles doubles (CISD) that includes single and
double excitations, the spin-flip CISD (SF-CISD), where spin flips
with respect to the HF solution are allowed for the excited states.
For a detailed review on the foundations and the technical aspects
