Pariser-Pople-Parr theory

Basic Assumptions of the Pariser-Parr-Pople Theory... 

The localized many-body perturbation theory (LMBPT) applies localized HF orbitals which are unitary transforms of the canonical ones in the diagrammatic many-body perturbation theory. The method was elaborated on models of cyclic polyenes in the Pariser-Parr-Pople (PPP) approximation. These systems are considered as not well localized so they are suitable to study the importance of non local effects. The description of LMBPT follows the main points as it was first published in 1984 (Kapuy etal, 1983). 

A semi-empirical ir-electron theory that takes electron repulsion into account is the Pariser-Parr-Pople (PPP) method (R.G. Parr. Quantum Theory of Molecular Electronic Structure, Benjamin, N.Y., 1963). 

Murrell, J. N., The Theory of the Electronic Spectra of Organic Molecules, Wiley, New York, 1963. Good discussions of the applications of HMO, FE MO, and Pariser-Parr-Pople theory to organic compounds. 

The theoretical difficulty of making this separation derives from the indistinguish-ability of electrons and the requirement that the total wavefunction be antisymmetric with respect to permutations of the electronic co-ordinates. One approach has been to abandon a full quantum mechanical description in favour of a simplified model hamiltonian which can be conveniently parameterized in terms of experimental quantities. This is the rationale behind Huckel theory, CNDO, and other more sophisticated methods such as MINDO. These techniques have been well documented and reviewed elsewhere (Dewar,1 Pariser, Parr, and Pople,2 Murrell and Hargett,3 etc.) and will not be pursued further here. 

O-H bond. Among such properties a prominent one is the ultraviolet absorption spectrum and the theory may therefore be used for the examination of some of the spectroscopic shifts which accompany the lactam-lactim tautomerization. Much caution must, however, be exercised in this respect. Thus, in a recent paper Kwiatkowski135,137 performed Pariser-Parr-Pople-type calculations on the electronic structure of hydroxypurines, essentially to interpret their ultraviolet spectra. In these calculations he assumed that these compounds exist predominantly in their lactim form, and the results of his calculations, at least for 6- and 8-hydroxypurine, did not seem to contradict this assumption. It is only in the case of the 2-hydroxy isomer that a particularly striking disagreement between theory and experiment led him to admit that this last compound may exist in the lactam form. Calculations carried out for this form gave, in fact, a more satisfactory agreement with experiment.138 As we have seen, unambiguous infrared spectroscopy evidence clearly show s that all three isomers exist essentially in the lactam form. This shows that ultraviolet absorption may provide only very uncertain evidence about the lactam-lactim tautomerism in hydroxypurines and related compounds. 

The two-electron integrals pq kl] are < p(l)0fc(2) e2/ri2 0,(l)0j(2) > and may involve as many as four orbitals. The models of interest are restricted to one and two-center terms. Two electrons in the same orbital, [pp pp], is 7 in Pariser-Parr-Pople (PPP) theory[4] or U in Hubbard models[5], while pp qq are the two-center integrals kept in PPP. The zero-differential-overlap (ZDO) approximation[3] can be invoked to rationalize such simplification. In modern applications, however, and especially in the solid state, models are introduced phenomenologically. Particularly successful models are apt to be derived subsequently and their parameters computed separately. 

Even if some interesting applications of the GHF-method had been found in solid-state theory [23,24], the applications to molecular systems were comparativlely few [40]. One major application to molecular systems had been worked out by Fukutome [40], and it was a study of the properties of the polyacetylene by means of the Pariser-Parr-Pople (PPP) approximation. It seemed hence desirable to make a molecular study based on ab-inttU) calculations to verify that one would get similar results and to get some experience in handling general Hartree-Fock orbitals of a complex nature, and for this purpose we started with some simple applications to atoms and to the BH molecule. 

M. Hida, unpublished results. b HMO, Hiickel molecular orbital theory. PPP, Pariser-Parr-Pople method. 

A long period elapsed before significant extensions were made to Huckel s 1931 molecular orbital theory. In the 1950s mutual repulsion energies were taken into account by Pariser, Parr, (1953) and Pople (1953) in calculating matrix elements. Hoffmann (1963) devised a scheme whereby the important off diagonal matrix elements for a bonds as well as n bonds were calculated as the arithmetic mean of the adjacent diagonal elements... 

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