Pariser-Parr-Pople PPP Model

The PPP model introduced by Pariser and Parr (1953) and Pople (1953) can be considered as a generalization of the Hubbard model. In the PPP Hamiltonian not only on-site repulsion but two-center two-electron interactions are also considered  

The two-electron part of the PPP Hamiltonian can be expressed in terms of the particle number operators similarly to the Hubbard case. Applying the relevant anticommutation rules one may write as  

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Finally, for purposes of comparison, it is useful to have a pi electron model which makes neither the Hiickel nor the VB assumptions about the strength of the electron-electron interaction. Such a model can provide a smooth bridge between the Hiickel and Heisenberg models as the relative strength of the chemical bonding and electron repulsion interactions between electrons are changed. Such a role is played by the Pariser-Parr-Pople (PPP) model [21,22], and its close relative, die Hubbard model [23], The PPP model can be... 

We overview our valence bond (VB) approach to the ir-electron Pariser-Parr-Pople (PPP) model Hamiltonians referred to sis the PPP-VB method. It is based on the concept of overlap enhanced atomic orbitals (OEAOs) that characterizes modern ab initio VB methods and employs the techniques afforded by the Clifford algebra unitary group approach (CAUGA) to carry out actual computations. We present a sample of previous results, sis well sis some new ones, to illustrate the ability of the PPP-VB method to provide a highly correlated description of the ir-electron PPP model systems, while relying on conceptusilly very simple wave functions that involve only a few covalent structures. 

Two models are particularly well suited for the calculation of the electronic spectra of conjugated ir-electronic systems. Both are based on the principle of differential overlap and involve no multicenter repulsion integrals. The Pariser-Parr-Pople (PPP) model (7), whose basis set contains only atomic orbitals of it symmetry, is particularly good for irir transitions in hydrocarbons and other molecules with a limited number of heteroatoms. Because of the unreliability of the PPP method in the presence of heteroatoms, we chose a second model which is available in two versions (CNDO/S (8) and INDO/S (9) for the calculations on 1 and 2. This model utilizes a basis set which contains all valence shell orbitals and leads to less uncertainty in parameterization even when a large number of heteroatoms are present. This model works well for irir transitions but often fails when applied to nir, air and ira transitions. This should not be a serious limitation in the present application since the only transitions of sufficient intensity to be of interest are of the wir type. 

Despite these difficulties, Lasaga and Karplus have discussed the calculation of excitation energies based on an operator equation related to (3). Simons and Dalgaard have proposed a perturbation approach to a similar operator problem. To date, however, numerical applications have been limited to the analysis of the singlet excitation of ethylene in Pariser-Parr-Pople (PPP) model, a two-level problem. ... 

Propagator or Green s function methods are employed in this chapter to analyze the many-electron problem in planar unsaturated molecules as treated within the Pariser-Parr-Pople (PPP) model. A derivation of the model in many-electron theory serves to demonstrate the nature of the approximations involved. Applications are presented for the case of weakly interacting atoms. A decoupling procedure for Green s functions proposed by the authors is shown capable of yielding a correct description of this case. 

The a—71 separability was used in the Pariser— Parr—Pople (PPP) model Hamiltonian ° to calculate TT-electron energies. The theoretical basis and design of the PPP model Hamiltonian was recently reviewed. ... 

Initial experimental studies [32] [using UV-Vis-NIR and electron spin resonance (ESR) techniques] of highly doped polythiophene showed the bipolaron structure to be dominant. Later, this finding was supported by theoretical studies [33]. However, the majority of the early theoretical studies used the Su-Schrieffer-Heeger (SSH) Pariser-Parr-Pople (PPP) model Hamiltonians and or low-level ab initio calculations such as HF/STO-3G. Semiempirical calculations predicted that two polarons on the oligothio-phene chain would be more stable than a bipolaron for oligomers longer than the dodecamer [34], and many... 

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). 

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. 

Table II provides a survey of representative calculations of p and 7 of molecular aggregates with an eye toward determining the bulk susceptibilities or, at least, toward addressing the effect that crystal packing has on the NLO responses. Initial studies focused on the first hyperpolarizability, and this was a consequence of the earlier work by Chemla, Zyss, and collaborators and of the necessity to improve the oriented gas model (see Section II). Dirk et al. [47] studied dimers of urea and of (A)-(5-nitropyrid i)-2(i.)-prolinol (PNP) by adopting a Pariser Parr Pople (PPP) Hamiltonian. They showed the limits of...

Two major contributions to the 7t-energy change in the ring-cleavage reaction leading to a PAHTC need to be included in the model. In a simplified Pariser-Parr-Pople (PPP) method with Hiickel orbitals as the basis [33], the PAHTC is an arylmethyl cation, with resonance energy... 

The term model Hamiltonian is more general. From this point of view the effective Hamiltonians and pseudo-Hamiltonians could also be considered as model Hamiltonians . However, for clarity, we suggest that the term model Hamiltonian should be used when some simplified form of an approximate Hamiltonian has been guessed from a preliminary physical analysis. In contrast with the effective Hamiltonians and the pseudo-Hamiltonians that can be obtained by means of well defined mathematical procedures, the model Hamiltonians are generally parametrized from experiment. They would involve the semi-empirical Hamiltonians of quantum chemistry and solid-state physics (Hiickel, Hubbard, Pariser-Parr-Pople (PPP),...). 

The earliest place where the quantity (/ - A) has made its appearance and played the role of a prominent character is the semiempirical electronic structure theory, which is known for its richness in scientific content, particularly for the physical basis in choosing the parameters and using the approximations. This theory provides one of the simplest and transparent models through the smiiempirical Hamiltonian as proposed by the Pariser-Parr-Pople (PPP) theory to approximate the total energy of a molecular system. In one of its simplest forms, the PPP Hamiltonian can be expressed as... 

Because all the ab-initio methods mentioned above are quite time consuming, semi-empirical methods have been developed which replace certain integrals appearing in the Hartree Fock equations by parameters (or in some cases, functions) chosen so that the results fit the spectral properties of certain model compounds. Some of these methods are the Huckel model, Hubbard model, Pariser-Parr-Pople (PPP), CNDO, MNDO, (7), Since the first three of these methods are related and have played a significant role inthe work of the last few years, I will discuss them in more detail. 

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