Models Pariser-Parr-Pople model

We often speak of the PPP (Pariser-Parr-Pople) model in honour of these three authors. Thinking of the pyridine example above, we still divide the 42 electrons into two groups, the 6 7r-electrons and the 36 o--electrons. The spirit of the PPP model is that the cr-electrons and the atomic nuclei provide a potential for the TT-electrons. Attention focuses on the 7r-electrons. 

Monte Carlo simulations [17, 18], the valence bond approach [19, 20], and g-ology [21-24] indicate that the Peierls instability in half-filled chains survives the presence of electron-electron interactions (at least, for some range of interaction parameters). This holds for a variety of different models, such as the Peierls-Hubbard model with the onsite Coulomb repulsion, or the Pariser-Parr-Pople model, where also long-range Coulomb interactions are taken into account ]2]. As the dimerization persists in the presence of electron-electron interactions, also the soliton concept survives. An important difference with the SSH model is that neu-... 

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... 

Raghu, C., Anusooya Pati, Y., Ramasesha, S. Density-matrix renormalization-group study of low-lying excitations of polyacene within a Pariser-Parr-Pople model. Phys. Rev. B 2002, 66(3), 035116. 

Table 3. One and two-photon thresholds (in eV) of trans-polyenes, CnHn+2, in alkane matrices[58] and in the Pariser-Parr-Pople model[21]. The solid-state shift of 0.40eV of the ionic 1 1B state yields gas-phase values up to n = 12 covalent 2M+ shifts of 0.05eV are neglected.

Figure 5 Diamagnetic rings currents, Nx z), of half-filled Pariser-Parr-Pople models for regular polygons with D h symmetry. The dashed line at 2 = U/4 t0 = 1.17 corresponds to standard parameters z = 0 is the Hiickel limit of free electrons, while z 1 is the strong-correlation limit of antiferromagnetic Heisenberg spin chain with vanishing ring currents [50].

J. l.inderberg. Chon. Phys. Lett., 1,39 (I 967). Consistency Requirement in the Pariser-Parr-Pople Model. J. Linderberg and L. Seamans, Int. J. Quantum (.hem., 8, 925 (1974). Matrix Elements in All Valance Electron Models. 

From the high extinction values and the Pariser-Parr-Pople model... 

U-V and Pariser-Parr-Pople Model Studies on the Ordering of Lowest Excited States... 

Figure 25 Evolution of E lBu) — E 2Ag), as a function of polyene chain length, in the Pariser-Parr-Pople model.

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... 

Huckel theory for the even alternant hydrocarbons leads to the Coulson-Rushbrooke theorem and some other characteristic results shown by McLach-lan to be valid also in the Pariser-Parr-Pople model. These are the well-known pairing relations between electronic states of alternant hydrocarbon cat-and anions. This particle-hole symmetry is analogous to the situation discussed in Chapter 4 for electrons and holes in atomic subshells. 

Ma, H.B., et al. 2005. Spin distribution in neutral polyene radicals Pariser-Parr-Pople model studied with the density matrix renormalization group method. 7 Chem Phys 122. 

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