Page 23 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

8 J. TOMASI

calculations. The names of Roothaan, Boys, Nesbet, McWeeny, Löwdin, Shavitt are few
examples randomly selected to make more clear what kind of activity I am considering
here. This activity has continued in the following years, and the formal framework of
quantum chemical theory has greatly changed from 1960 to now.
It is my impression, however, that the momentum has decreased, and not for the lack of
enthusiasm. Several interesting approaches have been formulated ten, or more, years ago
and still wait the final step necessary to pass from an exploratory stage to efficient tools to
be used for chemical applications. Formal quantum chemistry is a mature discipline and the
progresses occur now at a slower pace. The potentialities are not fully exploited, however,
and further efforts must be encouraged, the reward being now larger than 30 years ago,
because the larger impact quantum theory has now in chemistry. An example is given by
the density functional theories, which after many years of induction, are now amply paying
for the efforts of elaboration. The future of quantum chemistry is also in the hands of the
persons struggling with unconventional approaches.

4.2. GROUP II

The definition given by Coulson for this second branch of quantum chemistry has not been
a well selected choice. Coulson spoke of "non-electronic computers", when the use of
computers to examine "chemical concepts" and to elaborate new interpretation tools was
already initiated. Within few years from the Coulson analysis the computer become the
main instrument for interpretation (or description).
What is the main difference in the use of quantum calculations between group I and II ?

Group I relies, as said before, on the reductionistic ideal that everything, in the field of
chemistry, is amenable to the first principles and that a correct applications of the
principles, accompanied by the necessary computational effort, will give the answer one is
searching. It is a rigourous approach, based on quantum mechanical principles, in which
the elements of the computation have no cognitive status, unless when employed to get
numerical values of physical observables or of other quantities having a well defined status
in the theory.
Group II accepts the basic postulates of group I, performs molecular calculations as group
I but with a different philosophy which may be appreciated by contrasting two quotations.
The opening sentence of Quantum Chemistry by Eyring et al. I have already quoted is
often considered as a shortened re-formulation of another famous saying by Dirac [19]
which deserves to be reported here because its second part is often omitted: "The
underlying physical laws necessary for the mathematical theory of a large part of physics
and the whole of chemistry are thus completely known, and the difficulty is only that the
exact application of these laws leads to equations much too complicated to be soluble. It
therefore becomes desiderable that approximate practical methods of applying quantum
mechanics should be developed, which can lead to an explanation of the main features of
complex atomic systems without too much computation". The members of group II
address their attention to the last part of this sentence, with the emphasis put on the
"explanation". It is a quite different philosophy, in which the extreme variety of chemical
phenomena plays the essential role in assessing the strategy.

To achieve their objective the members of group II are compelled to complement the
quantities with a correct formal status in quantum mechanics (e.g the observables) with