Hamiltonian Pariser-Parr-Pople

The Pariser-Parr-Pople Hamiltonian for the description of the 7i-electrons in trans-polyacetylene is reparametrized using ab initio Coupled Cluster Doubles calculations based on a Restricted Hartree Fock reference on trans-butadiene. To avoid the spin contaminations inherent in Unrestricted Hartree Fock (UHF) type calculations on polymethine chains in the doublet state the Annihilated Unrestricted Hartree Fock (AUHF) model is applied in our PPP calculations (tPA (CH) , polyenes H-(CH)2N-H, polymethines H-(CH)2N+1-H). In geometry optimizations on polymethine chains it is shown that in contrast to results from Hiickel type models the width of neutral solitons is strongly... 

The Green s function method applied to the Pariser-Parr-Pople hamiltonian going beyond the Hartree-Fock approximation follows closely the work presented by the authors in 1967 Chem. Phys. Lett. 1, 295) and in 1968 (J. Chem. Phys. 49, 716). 

CCSD calculations of the polarizabilities and hyperpolarizabilities of increasingly large polyenes and substituted polyenes have been carried out using a Pariser-Parr-Pople Hamiltonian. It is found that electron correlation, as estimated at the CCSD level, always reduces the nonlinear optical responses, as a result of electron localization. On the other hand, the MP2 scheme fails because it provides a too small reduction of the polarizability or it predicts an enhancement of the first and second hyperpolarizabilities with respect to the HF results. 

JJ and Vij are the on-site and intersite Coulomb interactions (note that unlike tij, is not restricted to nearest neighbors and is long range). We use the same % as in Equation 7.20. For the we have chosen a parametrization similar to the Ohno parametrization of the Pariser-Parr-Pople Hamiltonian,... 

If the basis set is restricted to one pn basis function on each sp2 carbon, if the two-electron integrals ignore all three-center or four-center ones, and if we exclude exchange components, one has the Pariser-Parr-Pople model. If, further, all two-electron integrals are set to zero except for the repulsion between opposite spins on the same site and the one-electron tunneling terms are restricted to nearest neighbors, the result is the Hubbard Hamiltonian... 

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. 

The eigenvalues of the Hamiltonian matrix obtained by the Pariser-Parr-Pople (PPP) method. 

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...

It has been mentioned in the introduction that many authors [4] believed that the model-Hamiltonian Hg = OH would give a better basis for the semi-empirical quantum theory than the derivations starting from e.g. the Hartree-Fock Hamiltonian. One has previously had the dilemma that the parameters in the semi-empirical approach determined fi om selected experiments were usually rather different from those calculated by means of the ab-initio methods. This applied e.g. to Slater s F- and G-integrals in the theory of atomic spectra, to Hiickel s parameters a and P in the theory of conjugated systems, or to the y parameter in the Pariser-Parr-Pople scheme. Careful studies by Karl Freed and his group [9] in Chicago have shown that the discrepancy between the two sets of parameters disappears, if one bases the semi-... 

In the Pariser-Parr-Pople scheme, the so-called zero differential overlap approximation is used, and the u-electron system is treated as a nonpolarizable core. The interelectronic repulsions are explicitly taken into account in the total Hamiltonian. Resonance integrals, core integrals, and electronic repulsion integrals are given empirically, and Coulomb penetration integrals are neglected. ... 

PPP (Pariser-Parr-Pople) [14-16] is an SCF (self-consistent field) Jt-electron theory, assuming o — jt separability. Only a single (2pz) atom orbital is considered on each atom and the Ji-electron Hamiltonian includes electron-electron interactions with ZDO (zero differential overlap) approximation. All integrals are determined by semiempirical parameters. The PPP method can only be used to calculate those physical properties for which jt electrons are mainly responsible. 

The orbital expansions Eq. (11.10) and Eq. (11.12) are inserted in the hamil-tonian in Eq. (11-7), resulting in the Pariser-Parr-Pople model hamiltonian... 

Semiempirical MO theories fall into two categories those using a Hamiltonian that is the sum of one-electron terms, and those using a Hamiltonian that includes two-electron repulsion terms, as well as one-electron terms. The Hiickel method is a one-electron theory, whereas the Pariser-Parr-Pople method is a two-electron theory. 

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