Page 19 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

4 J. TOMASI
3. Models and interpretation in quantum chemistry

To put things in a clearer perspective it is convenient to introduce - in a compendious form
- few methodological concepts.
Theoretical chemistry works on models. My point of view on models in chemistry - and
quantum chemistry in particular - has been expressed elsewhere [6]; this view closely
corresponds to that expressed by other colleagues [7-11]. I suggested a partition of a
quantum chemical model into three components, and in my scientific practice I have always
taken into consideration the presence and interplay of these three components. The
consideration of the evolution of the whole quantum chemistry suggests me now the
introduction of a fourth component of the models. My revised partition of quantum
chemical models may be put in the following form.

1) The material composition of the model (material model) which states what portion of
matter is explicitly considered in the model. This portion of matter may be described
in a "realistic" way, or reduced to a simplified description (e.g. a set of coupled
oscillators).
2) The physical aspects of the model (physical model) which collects the selection of
physical interactions considered in the model. It may be convenient to introduce a
distinction between interactions involving the components of the material model
alone and interactions involving the exterior.
3) The mathematical aspects of the model (mathematical model). Methods and
approximations used to study the selected physical interactions in the given material
model.
4) The interpretative aspects of the model (interpretative model). The collection of
chemical "concepts" (according to the definition given by Coulson) or other
interpretative tools selected to "understand" the output of a model.

The introduction of the last components in quantum chemical models makes easier the
analysis of the second methodological point I will consider here.

What is the ultimate goal of theoretical investigation in chemistry? There could be a
difference of opinions on this point and I will not express here my point of view. There
will be however unanimity on the statement that this ultimate goal - whatever its nature is -
will be achieved in a safer way if there is a good understanding of the results obtained with
the model.
Scientific inquiry, which requires the definition of a model, the examination of the results,
then, if necessary, the elaboration of another model, in a sequence of steps, is a complex
taste in which interpretation (or description) plays a crucial role. I hope that the
introduction of three levels, or steps, in the process of interpretation will be of some help
for our task.

1) Report. The outcome of the model must be collected, and selected, to put in evidence
the results of interest for the desired scope. The first step collects the relevant
empirical evidence provided by the model. In many cases the report is sufficient to
reject a given model (e.g. for reasons due to its mathematical component) but usually
it provides the material for the following steps.
2) Interpretation (or description). The aspects of the phenomenon brought in evidence by
the report are related to a set of "chemical concepts" which introduces a rationale in
the empirical evidence. This is the realm of chemical (or structural) "theories" which