Graph Theory versus Quantum

F. Chemical Graph Theory versus Quantum Chemistry... 

We started this review with a brief discussion of some apparent dilemmas that we face in chemistry qualitative versus quantitative approaches, observables versus non-observables, structural criteria versus properties as criteria for characterization of aromaticity, chemical graph theory versus quantum chemistry, Clar 6/j rule versus Huckel An+ 2 rule, and hydrocarbons versus heteroatomic systems. As we have seen, most of the mentioned dilemmas are man-made and reflect inbred biases of different circles of chemists. It is not uncommon to come across critics with strong opinions and weak arguments, and it would be a waste of time to try to point out to them the other side of the coin . Max Planck apparently experienced difficult times before his quantum constant was accepted, as is reflected in the following quotations ... 

For the most part, much of the debate in the past between MO and VB theories versus graph theory has illustrated misconceptions about chemical graph theory. The two theoretical methodologies, quantum chemical and graph theoretical, consider somewhat different questions or different aspects of the same problem and are thus complementary to one another rather than competitive. So while MO and VB theories are, and will remain, about the nature of the chemical bond , we can say that Clar s model and chemical graph theory are, and will remain, about the nature of the chemical structure . Clearly, we need both the quantum chemical tool and the graph theoretical ideas to be combined in order to advance our understanding of complex chemical systems. 

In general, no simple, consistent set of analytical expressions for the resonance condition of all intradoublet transitions and all possible rhombicities can be derived with the perturbation theory for these systems. Therefore, the rather different approach is taken to numerically compute all effective g-values using quantum mechanics and matrix diagonalization techniques (Chapters 7-9) and to tabulate the results in the form of graphs of geff,s versus the rhombicity r = E/D. This is a useful approach because it turns out that if the zero-field interaction is sufficiently dominant over... 

Provided k can be estimated, a graph of the LHS of the equation versus [M] yields a value for fcj i which may be compared with the rate coeflBcient for spontaneous decomposition or isomerisation derived from the classical HRRKM theory or the quantum mechanical theory. ... 

The VSEPR theory allows chemists to successfully predict the approximate shapes of molecules it does not, however, say why bonds exist. The quantum mechanical valence bond theory, with its overlap of atomic orbitals, overcomes this difficulty. The resulting hybrid orbitals predict the geometries of molecules. A quantum mechanical graph of radial electron density (the fraction of electron distribution found in each successive thin spherical shell from the nucleus out) versus the distance from the nucleus shows maxima at certain distances from the nucleus—distances at which there are higher probabilities of finding electrons. These maxima correspond to Lewis s idea of shells of electrons. 

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