PPP Method

Semiempirical methods, of whieh there are quite a few, differ in the proportion of caleulations from first prineiples and the relianee on empirieal substitutions. Different methods of parameterization also lead to different semiempirieal methods. Huekel and extended Huekel ealeulations are among the simplest of the semiempirieal methods. In the next two seetions, we shall treat a semiempirieal method, the self eonsistent field method, developed by Paiiser and Parr (1953) and by Pople (1953), whieh usually goes under the name of the PPP method. 

In the PPP method, only the n- orbitals and the eorresponding 7i-eleetrons are eonsidered. The parameters ineluded in the F matrix... 

The Pariser-Parr-Pople (PPP) method is an extension of the Huckel method that allows heteroatoms other than hydrogen. It is still occasionally used when... 

The ground-state electronic diagrams of some thiazolo dyes have been calculated with the use of theoretical model of fractional core charge model applied to PPP method (659). 

For commonly encountered conjugated systems like butadiene and benzene, the ad hoc assignment of new parameters is usually preferred as it is simpler than the computationaly more demanding PPP method. For less common conjugated systems the PPP approach is more elegant and has the definite advantage that the common user does not need to worry about assigning new parameters. If the system of interest contains... 

The integrals are again parameterized as in eq. (3.79). The approximations for the one-electron integrals in CNDO are the same as for INDO. The Pariser-Pople-Parr (PPP) method can be considered as a CNDO approximation where only 7r-electrons are treated. 

Theoretical studies of the relative stabilities of tautomers 14a and 14b were carried out mostly at the semiempirical level. AMI and PM3 calculations [98JST(T)249] of the relative stabilities carried out for a series of 4(5)-substituted imidazoles 14 (R = H, R = H, CH3, OH, F, NO2, Ph) are mostly in accord with the conclusion based on the Charton s equation. From the comparison of the electronic spectra of 4(5)-phenylimidazole 14 (R2 = Ph, R = R3 = H) and 2,4(5)-diphenylimidazole 14 (R = R = Ph, R = H) in ethanol with those calculated by using ir-electron PPP method for each of the tautomeric forms, it follows that calculations for type 14a tautomers match the experimentally observed spectra better (86ZC378). The AMI calculations [92JCS(P1)2779] of enthalpies of formation of 4(5)-aminoimidazole 14 (R = NH2, R = R = H) and 4(5)-nitroimidazole 14 (R = NO2, R = R = H) point to tautomers 14a and 14b respectively as being energetically preferred in the gas phase. Both predictions are in disagreement with expectations based on Charton s equation and the data related to basicity measurements (Table III). These inconsistencies may be... 

The absorption bands for both quinoid and dipolar structures have been calculated by the PPP method.2,12 The calculations for a more simplified model of the colored form of some spirobenzopyrans using the normal parameters are shown in Table 2.12 In this case, the spiro carbon in the indoline moiety is ignored in the 7i-electron system, and the quinoid structure is assumed. 

French workers have studied the 1H- and 13C-NMR parameters of disubstituted selenophenes.37 38 The proton chemical shifts are discussed in terms of magnetic anisotropy and electric field effects of the substituents in order to study the conformational equilibrium of the carbonyl group. The relationship between the H- and 13C-chemical shifts and 7t-electron distribution calculated by the PPP method are examined. Shifts and coupling constants are discussed in additivity terms. 

Ellis, Squire, and Jaffe have carried out a detailed study of the spin-orbit coupling in formaldehyde and azulene. The wave functions were calculated using the CNDO/S method, which is more general than the PPP method discussed earlier and also allows ff-orbitals to be included. Let us review their findings on formaldehyde ... 

Finally, the S - Sq and Tm -Ti absorption spectra of 15 conjugated hydrocarbons were calculated by Pancir and Zahradnik 45,4C) using a modified semiempirical parameter set. Their description of the singlet-triplet and triolet-triplet spectra achieves about the same accuracy as the PPP method for singlet-singlet spectra. 

There have been discussions whether the amide addition at C-6 is charge-controlled or orbital-controlled. Charge density calculations in 4-phenylpyrimidine (MNDO method) predict that the addition of the amide ion would preferably take place at position 2 (95UP1) this, however, does not agree with the experimental results. Therefore, the conclusion seems justified that the addition is not charge-controlled. Frontier orbital calculations, using the SCF-PPP method, show that the frontier orbital densities in the LUMO of pyrimidine are zero at C-2 and C-5, making these positions... 

The reactivities of isomeric thienothiophenes calculated in n -electron approximation by the PPP method, and those calculated considering all valence electrons, show reasonable agreement. It should be noted, however, that the choice of parameters in PPP calculations is somewhat arbitrary, especially for heavy atoms (e.g., sulfur). This may lead to a discrepancy between theoretical (in 7r-electron approximation) and experimental estimation of reactivities. For example, Clark applied the semiempirical method PPP SCF MO to calculate the reactivities of different positions in thienothiophenes 1—3, thiophene, and naphthalene from the localization energy values and found the following order of decreasing reactivity for electrophilic substitution thieno[3,4-b]-thiophene (3) > thieno[2,3-Z>]thiophene (I) > thieno [3,2-b]thiophene... 

Related research has been reported by Elder and Worley (39), in which MNDO was used to examine the structure of coniferyl alcohol, and its corresponding phenolate anion and free radical. This method represents an improvement over the PPP method, in that MNDO is an all-electron technique, and performs geometry optimizations. It was found that the calculated spin densities and charge values for the reactive sites did not correlate quantitatively with observed bond frequency, but it was observed that positions with partial negative charge and positive spin densities are the positions through which the polymerization has been found to occur. 

Considering the proliferation of MO calculations in recent years, it is remarkable how few calculations have been reported for these heterocycles. Frontier orbitals of several betaines have been calculated using the Hiickel method and electroselectivity correctly predicted on the basis of the orbital symmetry.Similar results have been obtained for pyridinium-3-olates (427) using the Pariser- Parr Pople (PPP) method. The CNDO... 

Much work has been reported on type B azapentalenes, and this can be classified according to the degree of sophistication of the calculations. Simple Hiickel linear combination of atomic orbitals (LCAO) methods have been widely used, though more recently more sophisticated Pariser-Parr-Pople (PPP) methods (using only re-electrons) and all-electron CNDO calculations have been reported. 

The work of Taddei et al.230 on imidazol2,1 -6]thiazole 337 and derivatives has interesting implications on the structure of azapen-talenes, and an important aspect of this study is that the molecular geometry used for calculations on 6-phenylimidazo[2,l-6]thiazole 417 was obtained from X-ray structure determinations130b (Section V,A). The reactivity of this system (Scheme 18, Section IV,C,4,b) is better correlated with Tr-electron densities than with total charges, and 7r-bond orders (by the PPP method) show that the thiazole part of the molecule is more localized than the imidazole part (Section VII). Proton chemical shifts, except that of the H2 proton a to sulfur (Section V,G,2), vary linearly with the total charge carried by the ring carbon atoms. 

Chia and Simmons388 calculated the resonance energies (ER)20 of four mono- and dibenzotetraazapentalenes (Scheme 24). Values are comparable with those of o-condensed aromatic systems (naphthacene, ER = 110 kcal mol-1 chrysene, ER = 116.5 kcal mol-1), and, like these carbocyclic systems, angularly-shaped molecules are more stable than linear ones. HMO calculations of delocalization energies (DE) show that the tetraazapentalene structure 15 is more stable than the tetra-azacyclooctatetraene valence isomer 324 (Scheme 14, Section IV,B,2) whether 324 is planar or tub-shaped. Calculations of electrophilic reactivity (Section IV,C,4,d), electronic spectra (by the PPP method employing all singly excited configurations), and bond orders have been carried out, and they confirm the aromatic nature of these systems. 

A semi-empirical ir-electron theory that takes electron repulsion into account is the Pariser-Parr-Pople (PPP) method (R.G. Parr. Quantum Theory of Molecular Electronic Structure, Benjamin, N.Y., 1963). 

The simple, or Hiickel based, molecular orbital theory (HMO and PPP methods) frequently provides useful qualitative insights but cannot be used reliably in a quantitative manner. For this purpose it is necessary to use a method which takes account of all the electrons as well as their mutual repulsions. A major bottleneck in such calculations is in the computation and storage of the enormous number of electron-repulsion integrals involved. Early efforts to reduce this problem led Hoffmann to the EH approximation (I.N. Levine, Quantum Chemistry, 4-th ed., 1991, Prentice-Hall, Inc., Ch. 16, 17), and Pople and co-workers to the CNDO, INDO and NDDO-approximations (B-70MI40100). 

The FE MO, HMO, and PPP methods are restricted to planar conjugated molecules (e.g., butadiene, benzene, pyridine), and make the pi-electron approximation of treating only those valence electrons that are in pi MOs (those that have eigenvalue — 1 for reflection in the molecular plane) they assume the existence of a pi-electron Hamiltonian Hm of the form... 

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