Biomedical Engineering Reference
In-Depth Information
A 6-311G** basis set was used. The top curve is the HF-LCAO calculation, and shows
the usual bad dissociation limit. The remaining three curves are (in descending order) MP2,
MP3 and MP4(SDQ). The first point to notice is that MP
n
calculations are size consistent.
The second point is that none of the curves appear to be approaching the correct dissociation
limit of
1
E
h
. It is reported in the literature that MP
n
calculations do not work particularly
well for geometries far from equilibrium. The MP
n
series has not been proved to converge
to the true energy, but calculations using very high orders (MP48) have suggested that
convergence will eventually occur.
Finally,MP
n
calculations need aHF-LCAOwavefunction to act as the zero-order approx-
imation. It follows thatMP
n
can only be used for thosemolecules and electronic stateswhere
it is possible to find such a wavefunction. This rules out most excited states.
−
19.5 Multiconfiguration SCF
One problemwith traditional CI calculations is that excitations are to the virtual orbitals; the
occupied orbitals are usually determined variationally by the HF-LCAO procedure whilst
the virtual orbitals give poor representations of excited states. One solution to the problem
is to write the ground-state wavefunction as a linear combination of Slater determinants
and then use the variation procedure to optimize both the linear expansion coefficients and
the HF-LCAO coefficients. That is, we write
c
j
Ψ
j
Ψ
HF
Ψ
=
+
where Ψ
HF
is the Hartree-Fock wavefunction and Ψ
j
an excited state, in the usual sense
of CI calculations. In certain cases the ratio of some of the
c
j
will be fixed by symmetry.
The MCSCF model is regarded as highly specialized, with a small number of adherents.
A literature search revealed an average of 50 papers per annum in primary journals over
the last 10 years.
References
Bartlett, R.J. (1989)
J. Phys. Chem.
,
93
, 1697.
Møller, Chr. and Plesset, M.S. (1934)
Phys. Rev.
,
46
, 618.
Pople, J.A., Head-Gordon, M. and Raghavachari, K. (1987)
J. Chem. Phys.
,
87
, 5968.
