Page 25 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

10 J. TOMASI

The concept of atom, for example, must be accompanied by a definition of "valence
states", based on the definition of hybrid orbitals, which play a prominent role in the
definition of VB structures and also constitute an important component in models based on
localized orbitals (LO). Localized orbitals represent a bridge between partitions of a
molecule based on molecular orbitals and partitions based on a dissection of the charge
distribution into local subunits. LO give an alternative view of electron correlation holes,
and in a different context offer a good starting point for semiclassical segmental partitions
of the charge distribution. The alternative concept of charge partitioning according to the
values of some physical quantities (e.g. the Bader's approach) challenge the traditional
partition into atoms or into LOs, offering new views of some concepts and permitting new
admixtures of tools.

I have selected few examples taken from the theory of molecular bonding, but this aspect
of competition and transference of concepts is present in all the fields of chemistry -and
they are quite numerous- in which quantum theory has given contributions.
Another important point is the connection with in-depth calculations. We have already
remarked that this connection is extremely important for the elaboration of interpretations.
There are two main lines, in my opinion.

The first could be called a constructive (synthetic) approach. Pragmatic and theoretical
reasons suggest to start computations appropriate for the model one has selected at a low
level of the theory; the goal is not to obtain the most complete report on the problem under
scrutiny but to reach a satisfactory degree of confidence in the interpretation obtained by
analyzing the results, and a set of reports at increasing levels of the mathematical model
may be of noticeable help in assessing the quality of the description. The constructive
approach may be also employed with the aim of getting accurate reports. In this case an
interpretative model is (tentatively) adopted, and the mathematical model is formulated
accordingly. The goal now is to get accurate results at a lower computational cost than
using brute force methods. Many formulations of this strategy have been elaborated, some
addressed to specific problems, others of more general character. The quotation of an
example always make more clear what a general statement means; to this end we recall the
recent generalized multi-structural wavefunction method (GMS) [21]. This approach
remind me the suggestion expressed by Dirac in the last lines of the above reported
quotation. It is worth to remark that the modern reformulations of the VB theory play an
important role in this field [22-23]. On the whole, the constructive approach is the most
potent and versatile method to connect chemical concepts to in-depth calculations,

The second approach is addressed to elaborate methods able to derive from accurate
calculations the points of interest for the interpretation The strategy, in general, consists in
the adoption of a simpler model (the mathematical aspects of the model are again
concerned) and the task consists in reducing the information coming from the full in-depth
calculation (not the the numerical values of observables and other statutory quantities
alone) to the level of the simpler model. For example accurate calculations may be reduced
at the level of a simple VB theory (Robb, Hiberty) or of a simple MO perturbation scheme
(Bernardi) making more transparent the interpretation.
Both approaches are subjected to criticisms and to errors. The stipulation of the model
constitutes a bias in favour of one among several possible alternatives, and the conclusions
will suffer if the choice was not appropriate. All the models, by definition, are subjected to
failures of this kind, and it rests with the users to exert their acumen to decide if the model
is applicable to the case under examination.