Chapter 6, Harder Questions, Answers
Q1
Why are even very carefully-parameterized SE methods like AM1 and PM3 not
as accurate and reliable as high-level (e.g. MP2, CI, coupled-cluster) ab initio
calculations?
One reason is that an attempt to get the best fit of program parameters to a number
(say, a training set of 50 molecules) of a variety (like heat of formation, geometric
parameters, dipole moments) of parameters results in a significant unavoidable error
in the accuracy of the fit. Imagine fitting a least-squares line to a collection of data
points (x,y); unless the underlying relationship is genuinely linear, the fit will be
imperfect and predictions ofyfromxwill be subject to error. Nevertheless, geometries
of “normal’ molecules from AM1 and PM3 are generally quite good, although heats
of formation and relative energies are less accurate.
A more fundamental reason is that predictions for molecules very different from
those outside the training set should be less reliable than those for molecules similar
to the ones used for parameterization. Therefore for investigating exotic species
like, say, planar carbon or nitrogen pentafluoride AM1 and PM3 are considered
unreliable, and even noncorrelated ab initio calculations would be considered well
short of definitive nowadays [1].
Reference
- Lewars E (2008) Modeling marvels. Computational anticipation of novel molecules. Springer,
The Netherlands
Chapter 6, Harder Questions, Answers
Q2
Molecular mechanics is essentially empirical, while methods like PPP, CNDO, and
AM1 are semiempirical. What are the analogies in PPP etc. to MM procedures of
developing and parameterizing a forcefield? Why are PPP etc. onlysemiempirical?
The analogies in semiempirical (SE) methods to MM procedures for developing
a forcefield arise from the need to fit experimental values to parameters in equa-
tions. In SE parameterization heats of formation, geometric parameters, etc. are
used to adjust the values of integrals in the Hamiltonian of quantum-mechanical
equations. In MM vibrational frequencies, geometric parameters, etc. are used to
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