PPP-type Hamiltonians

It must be emphasized that in fact a very similar situation characterizes experimental investigations, since very different experimental techniques are employed, and different questions are asked, when investigating simple diatomics on the one hand and complex systems, such as chlorophyl, proteins, fullerenes, etc. on the other. Even if one could resolve and measure, for instance, all the individual ro-vibrational lines in the electronic spectra of large systems involving, say, more than 50 carbon atoms, the usefulness of such information is debatable. Likewise, our theoretical inquiries call for different models, approximations and techniques when handling different types of problems. 

Successful model building is at the very heart of modern science. It has been most successful in physics but, with the advent of quantum mechanics, great inroads have been made in the modelling of various chemical properties and phenomena as well, even though it may be difficult, if not impossible, to provide a precise definition of certain qualitative chemical concepts, often very useful ones, such as electronegativity, aromaticity and the like. Nonetheless, all successful models are invariably based on the atomic hypothesis and quantum mechanics. The majority, be they of the ah initio or semiempirical type, is defined via an appropriate non-relativistic, Born-Oppenheimer electronic Hamiltonian on some finite-dimensional subspace of the pertinent Hilbert or Fock space. Consequently, they are most appropriately expressed in terms of the second quantization formalism, or even unitary group formalism (see, e.g. [33]). 

In the ah initio case, the relevant finite-dimensional one-electron space is spanned by a minimum, double-zeta, double-zeta plus polarization, etc., basis set and further approxi- 

We can thus conveniently express the standard PPP Hamiltonian in a modified (particle number preserving) second quantized form 

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