Quantum chemical methods suffer from a common disadvantage because their results lack the generality and simplicity which would enable chemists to apply them in practice to a variety of chemical phenomena.
Some results obtained from the topological considerations may not be always derived from purely numerical calculations, because the sheer wealth of numerical data which has to be examined may often obscure a simple concept for the understanding or the rationalization of a particular chemical result.
In addition, a number of results may be obtained by just a pencil and a paper, without any use of computers. This is of importance for experimental chemists who are sometimes hampered in applying current computational theories because of the necessity of carrying out on computers using the specialized programs (not to mention the cost of some of these computations).
Finally, in developing the topological (mathematical) theory of chemistry our intention is not to compete with quantum-mechanical calculations, but rather to develop a symbolism that permits chemists to think in terms of graphical structures (since this is a natural way of chemical thinking about molecules and reactions); i.e., to learn as much as possible about the eventual chemical behaviour of the molecule by examining the properties of its molecular graph. Furthermore, we also suggest this procedure to those chemists who intend to use quantum-mechanical methods as the preliminary step which could be helpful in guiding and directing their calculations.