Pople’s model

More recently there have been some modifications in the model, and the mathematical treatments have been considerably improved. Kirkwood (1111) used the Bernal-Fowler model and devised a statistical method to Eillow for near neighbors. Pople (1659) allowed for bending H bonds of the type shown in Fig. 8-1. Harris and Alder applied to Pople s model a statistical mechanical treatment which attempts a precise evaluation of distortion polarization (877). The calculated results are shown in Table 2-III, and in Fig. 2-1 they are compared with experimental values. These changes correct for failures of the simplest dipole picture, and as more of them are added the principal appeal of the electrostatic model—simplicity—tends to be lost. 

CH2 this is counter to Pople s model. The ease for w-electron transfer in CH3—CH=0 is greater than for CH3—CH=CH2, and the C—C bond separation energy for the former is higher than for the latter, according to their calculations. In this connection, an attempt... 

The local diamagnetic term i.e., shielding restricted only to the electrons of the N atom, and the difference Aafoc with respect to N2 were calculated semiempirically for small N-containing molecules including N2F4 using Pople s model [15] and the atom-dipole model... 

In the 20—25 years after the proposal of Pople s models " for estimating the effect of r-electron ring currents on H NMR chemical shifts in conjugated molecules, many investigations confirmed that the simple ring-current models, based on semiempirical " or even just classical theories, could yield (i yi benzene) ratios that would satisfactorily rationalize experimental trends when they were confronted with H NMR chemical shifts that had been obtained under consistent experimental conditions for a large number of protons in a wide range of planar, condensed, benzenoid hydrocarbons this is perhaps the one class of molecules over which... 

Interestingly, the protons are in the shielding region, with the vortexes in close proximity. In contrast, the n orbital contribution to B shows the typical response of an aromatic system as expected from Pople s model (see Figure 10.4) ... 

As suggested by Pople s model, the hydrogen atoms are in the paratropic (deshielding) region of B . 

It should be noted that our computed field lines correspond even closer to the refinement of Pople s model suggested, for example, in the textbook of Gunther [12]. In this model, two ring current loops are considered, and two induced circular fields are superposed. The field lines of the tr contributions in Figure 10.4 show such topology. The graphical representation of the B field lines, calculated from first principles, supports Pople s model, and allows the direct comparison of external magnetic field with the response of the molecule. 

In order to obtain more specific qualitative information for above acid attack dealu-mination in USY zeolite, the pople s CNDO/2 calculations were made on a model of the six ring cluster with a TtO,(OH)i structure unit (T represents A1 atom or Si atom) in Fig, 1 (ref. 4, ref. 7) which simu-lates the Sr and Si sites of faujasite zeolite. 

Pople s CNDO/2 method and a hexagonal cluster model used in calculations to simulate charge densities Wiberg bond orders of Al - O and Si - O in the six - ring sites and the total energies of the zeolite clusters. 

A simple model for associated water was needed in which oxygen-oxygen repulsions in water could be equated to those in H20-H30+, which required examination of the energy and associated structural changes on the addition of an unsolvated proton to a liquid water superdipole. Pople s modification103 of Kirkwood s72 static water... 

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. 

More sophisticated examples of such expressions are used in Pople s Gl, G2 and G3 theories.162-164 In the onion approaches, the calculated structure of the lower level is used as a constraint upon the higher level of theory. The breaking of covalent bonds between the model and the real system is treated by replacing the corresponding atom in the real system with a hydrogen atom in the model system, much like the link atom method. The coordinates of the new... 

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. 

Fig. 10.4. The staggered, normalized bond dimerization, S , (defined in eqn (4.27)) as a function of bond index from the centre of the chain of various states of trans-polyacetylene calculated from the Pariser-Parr-Pople-Peierls model. 1 A+ (crosses), (squares), 1 5 (triangles), 2 (diamonds) andpolaron (circles).

Development of model sciences to obtain consistent results without unnecessary computation This approach is illustrated by the Gaussian-2 (G2) model chemistry developed by Pople s group. ... 

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