Pariser-Parr approximation

These are the main features of the Pariser-Parr approximation. There remains the choice of the Hpp integrals, the classical expression for which is... 

There are, of course, certain circumstances in which the SCF equations can easily be shown to reduce to Hiickel-type equations. Thus in the standard excited-state equations of Hall for 7r-electron aromatic hydrocarbons, it can be shown that the LCAO coefficients are often precisely the same as in the Hiickel scheme. However, this particular state is not of direct value for our purposes. Further, Pople has shown that if the Pariser-Parr approximation of zero differential overlap is accepted, then, apart from some (usually) small terms in inverse internuclear distances, the total w-electron energy is given by an expression identical in form to that of Hiickel theory. Both writers adopt the approximation of neglecting all overlap integrals. This is particularly serious with overlap integral may be as large as... 

Electronic transitions of Z-methylthiothiazole and A-4-thiazoline-2-thione were calculated using Pariser-Parr-Poplc and Complete Neglect of Differential Overlap approximations (61. 72). The major improvements afforded by the CNDO model are the calculation of the n cr transition and the interpretation of the 2.34-nm band as an n transition. 

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... 

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. 

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

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. 

More explicit molecular orbital methods including the electronic repulsion terms are called advanced molecular orbital methods. In such methods, F matrix elements of the Fock equation are calculated by Eqs. (6.6) and (6.7), and the iterative procedure, or self-consistent field (SCF) procedure must be used. The most convenient advanced molecular orbital method for the polycyclic aromatic compounds is the semiempirical method suggested by Pariser, Parr, and Pople (the PPP method). In this PPP method, the required integral values are empirically determined using the following approximations. 

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