Biomedical Engineering Reference
In-Depth Information
18
Semiempirical Models
I have spent a good deal of time discussing the current state of the art in quantum chemical
calculations, and I have deliberately focused on techniques where we perform all of the
calculations as exactly as possible. Over the years, it has become fashionable to refer to
such models as
ab initio
. This Latin phrase translates into 'from the beginning'; it certainly
does not necessarily mean 'correct'. Once we have stated the Hamiltonian and if necessary
the atomic orbital basis set then all the integrals are evaluated exactly without any attempt
at calibrating them against experiment. Thus the atomic Hartree-Fock model is an
ab initio
model, and the calculations I described for the hydrogen molecule ion and dihydrogen are
ab initio
calculations.
These early calculations were done in the 1920s and the 1930s, and you probably noticed
that I then jumped to the 1970s to discuss modern HF-LCAO calculations with GTO.
Scientists first got their hands on computers in a meaningful way in the 1970s, and one
unfortunate characteristic of
ab initio
calculations is that they are compute-intensive. From
the early days, by necessity rather than choice, workers tried to develop simple HF-LCAO-
basedmodels that applied to certain classes of molecule, and a characteristic of thesemodels
is that they avoid all the difficult integrals. There is usually a price to pay, and the models
have to be calibrated against experiment; some workers regard this as a major advantage in
order to achieve meaningful chemical predictions from cheap calculations. We often refer
to such calibrated models as
semiempirical
. This is not a Latin phrase but it translates into
'based on a correct model but calibrated and/or parameterized'. We can of course argue
for ever about what constitutes a 'correct' model; Hartree-Fock theory is certainly not
absolutely 'correct' because it averages over the electron interactions and so it usually runs
into trouble when trying to describe bond breaking.
