Pariser-Parr-Pople approximation

Qualitatively, similar relationships are ascertained in heteroaromatic systems where the same conclusion is derived by a numerical calculation. In more elaborate calculations than the Hiickel method, such as the Pariser-Parr-Pople approximation 21>23>, similar distinct parallelisms are recognized 59> (Table 4.1). Essentially the same circumstances exist also... 

D. The Parametrization of the Pariser-Parr-Pople Approximation for it Electrons. 93... 

In order to make up for these defects of the self-consistent field method some empirical or semi-empirical corrections must be introduced, the calibration of which are obtained by a close comparison of the theoretical results with experimental data for some fundamental compounds. The resulting procedure in its current form is the so-called Pariser-Parr-Pople approximation of the SCF method. The results obtained can still be improved by configuration mixing correcting for the residual correlation error. 

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). 

Many such expressions have been suggested, most of them in the context of the Pariser-Parr-Pople calculations for n conjugated species. We describe below most of the approximations which were found suitable even though some of them have not been used in the methods designed for a bonded molecules. 

In the first place the Hiickel approximation for the tt electrons has been replaced by a self-consistent field (SCF) procedure, generally in a semiempirical approximation of the Pariser-Parr-Pople type completed with some limited configuration interaction (PPP-CI method).59 00 Second, the a skeleton of the molecules has been treated by the Del Re procedure61 for saturated systems (which is the counterpart for the a electrons of the Hiickel method for 77 electrons) as refined for the a skeletons of conjugated heterocycles by... 

The third fundamental hypothesis of the CNDO approximation concerns the core matrix elements H. These correspond to the and parameters of the Pariser-Parr-Pople method, the core including here only the Is electrons and the nuclei. 

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. 

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