Page 29 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

14 J. TOMASI

The number of detailed studies on these last systems is nowadays sufficiently large to
generalize the results, and to project the conclusion to more complex (o "perverse",
according to Coulson) systems. The traditional view of a reaction occurring on a well
defined surface, with a flux of representative points passing the transition state region is
untenable. The separation between static and dynamic aspects of a problem, so often
exploited for studies an isolated molecule must be reconsidered.

There is a deluge of papers, as well as of methods and of approaches, addressed to these
problems. It is significant that in this blossoming of studies there is space for very simple
models (as regards the material composition of the model) as well as for very complex
models with a high degree of realism in the chemical composition.

A combination of different approaches is at present the most convenient strategy. Most of
the work done an complex material models adopts a classical formalism, disregarding for
the moment quantum aspects, while there are significant progresses in quantum description
of simple models [26].
I have briefly touched here two examples, structure of large molecules and reactions in
condensed media. The number of examples could be by far larger, from isolated molecules
again (the dynamics of excited polyatomic molecules, the study of their roto-vibrational
levels) to man-made materials with their specific properties (ceramics, polymers,
incommensurable phase systems, dispersed mesosystems) to materials of natural origin
(mainly, but not exclusively, of biological nature).
Numerous additions to our collection of methodological remarks could derive from the
consideration of other examples. The picture drawn here is extremely incomplete, but
sufficient to express some remarks and to draw some conclusions.
The various attempts, in the different fields, can be viewed as an effort to combine
methods and experience of two disciplines which have reached since longtime their
maturity: quantum mechanics for isolated systems and statistical mechanics. This effort of
combination produces important results, and the progress in this area is indisputable.
There is however the need of a qualitative jump. The resulting theory should not be called
quantum chemistry again: this now is an old and glorious name, corresponding to a very
active research domain, promising new progresses and important results; the more generic
name of theoretical chemistry is more suitable. Specific suggestions for the elaboration of
this theory, not supported by detailed analysis and discussion, could be considered with
scepticism or criticized for many reasons (partiality, inconsistency, errors, etc.). For this
reason I will refrain from suggestions, but I am unable to resist temptation of adding a few
concise remarks. Temperature is not a statutory quantity in quantum mechanics of isolated
systems and it is introduced here via a classical picture. A quantum definition of T, e.g. via
the fluctuations theory, could be an important supplement to a reformulated and generalized
theory. Time has a special status in quantum mechanics [27] but it should be reconsidered
when passing to complex systems arranged in hierarchical order [28,29]. We have thus far
assumed that all the activities in this domain are "covered" by the usual quantum theory.
The proviso expressed by Dirac just before the sentence we have quoted has been until
now superfluous. There are no convincing evidences of limits of the quantum theory in the
fields covered by groups I to IV. There is however a widespread dissatisfaction with some
basic aspects of the theory. If there will be something to change (and a change at this level
means the formulation of a new theory, encompassing the old one) the clue should come
from the realm of complexity, rather than from a reconsideration of simple gedanken