Chapter 1, Harder Questions, Answers
Q6
Should calculations from first principles (ab initio) necessarily be preferred to those
which make some use of experimental data (semiempirical)?
There are two aspects to confronting this question: a practical and what might be
called a philosophical. On the practical aspect impinge questions of time, reliabil-
ity, and accuracy. The philosophical issue is subtler.
If planned ab initio calculations would take an unacceptably long time with the
software and hardware available, then one must simply either abandon the project or
resort to a semiempirical method; these are typically hundreds to many thousands of
times faster. Reliability and accuracy are not sharply distinct: one might not be able to
rely on a calculation if it is not sufficiently accurate. Reliability could, alternatively,
be equated with consistency (one usual meaning of the term): a method might be
sometimes very accurate, but might erratically lapse in this regard. Only comparison
with experiment for a carefully selected set of relevant cases can show how accurate
and reliable a method is. For some problems the extremely fast molecular mechanics
method is the most accurate and reliable: for reasonably normal monofunctional
compounds, and particularly hydrocarbons, geometries are commonly accurate to
within 0.01 A ̊for bond lengths and to within 2for bond angles, and to within
ca. 1 kJ mol#^1 for heats of formation [1].
An amusing polemical debate on the virtues of semiempirical versus ab initio
methods took place between Dewar, on the one hand, and Halgren, Kleier, and
Lipscomb, on the other [2]. The Dewar group pioneered the semiempirical AM1
method, which spawned the PM3 method, these two being the most popular
semiempirical quantum-mechanical methods today, and Lipscomb and coworkers
were early advocates of ab initio methods. Dewar argued that ab initio methods
were hopelessly inaccurate and expensive. Those were the days (1975) when own-
ing your own computer was a dream and one paid perhaps $500 an hour to use one;
it suffices to note that $500 was worth far more then and the fastest computer was
far slower than a cheap personal computer is today. Dewar concluded that a study of
the interconversion of benzene valence isomers by semiempirical versus ab initio
methods would cost $5,000 versus $1 billion! Lipscomb and coworkers argued that
whatever their practical virtues, semiempirical methods “obscure the physical bases
for success...and failure alike”. This controversy is dated by the enormous increase
in computer speed and the sophistication attained by ab initio methods since then,
but it captures the flavor of part of the philosophical divide between the two
approaches: the desire to get answers that might in principle, but less expediently,
have been obtained in the lab, versus the desire to understand the underlying
reasons for the phenomena being studied.
Nowadays chemists do not worry much about the virtues of semiempirical
versus ab initio methods. Ab initio methods, it must be conceded, dominate
computational chemistry studies in the leading journals, and indeed the study of
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