From Lewis to quantum mechanical models

In the description of nature afforded by quantum mechanics, one classifies and characterizes the state of a total system in terms of the eigenvalues of a set of commuting observables acting on an element of the Hilbert space, the state vector. Molecular orbital theory in its canonical representation as originally 

One might imagine that, with the advent of quantum mechanics and its application to chemistry, Dalton s atomic theory would have been reinforced. This has not happened. Quantum mechanics has been shown to account for the properties of isolated atoms and for the total properties of a molecular system. The increased understanding that would result from the discovery of a firm theoretical basis for Dalton s theory has not been obtained because of the lack of a quantum definition of an atom in a molecule. This is not to say that the concepts of atoms,and bonds do not appear in the quantum mechanical treatments of chemical systems. They do, but in the reverse manner to that described above. Rather than finding its quantum basis, the 

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