The Pariser-Parr-Pople Method

The HMO equations (17.9) have the same form as the Roothaan equations (14.34), where corresponds to F, and e, corresponds to s,. We showed the matrix form of the Roothaan equations to be FC = SCe [Eq. (14.56)]. Hence the HMO equations are 

Because of the simplicity of the method, carrying out HMO calculations became a favorite pastime of organic chemists, and the results of HMO calculations have been tabulated for hundreds of compounds. The HMO method was widely used to rationalize and predict the properties and reactivities of conjugated compounds. 

A semiempirical 7r-electron theory that takes electron repnlsion into acconnt and thereby improves on the Hiickel method is the Pariser-Parr-Pople (PPP) method, developed in 1953. Here, the 7r-electron Hamiltonian (17.1) inclnding electron repnlsions is nsed, and the 7r-electron wave fnnction is written as an antisymmetrized product of TT-electron spin-orbitals. A minimal basis set of one Iprr STO on each conjngated atom is used, and the spatial tt MOs are taken as linear combinations of these AOs 4 = 2r=i Crifr- The Roothaan eqnations are used to find SCE tt MOs within the TT-electron approximation. 

In addition to assuming o—tt separability, the PPP method makes further approximations. As in Hiickel theory, overlap is neglected  

The PPP method does not attempt to explicitly specifyH or to calculate the integrals theoretically. Rather, the integrals and y are calculated fi-om approximate semiempirical formulas, some of which contain empirical parameters. For example, when the AOs and are on atoms R and S that are bonded to each other, may be taken as where the value of the empirical parameter k is chosen 

To do a PPP calculation, one starts with the HMO coefficients as an initial guess for the Cjj s, calculates the initial density matrix elements calculates the initial matrix elements, solves the equations (16.70) for 77-electron orbital energies e, and an improved set of coefficients Cj/, calculates improved values, and so on until convergence is reached. To improve the results. Cl of the 77 electrons may be included. 

The PPP method gives a good account of the electronic spectra of many, but not all, aromatic hydrocarbons. For more on the PPP method, see Parr, Chapter III Murrell and Harget, Chapter 2 Offenhartz, Chapter 11. 

The PPP method is little used nowadays and has been largely superseded by more-general semiempirical methods (Section 16.5). However, the PPP method is of historical importance, since many of the PPP approximations used to evaluate integrals are used in current semiempirical theories. 

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The CNDO method has been modified by substitution of semiempirical Coulomb integrals similar to those used in the Pariser-Parr-Pople method, and by the introduction of a new empirical parameter to differentiate resonance integrals between a orbitals and tt orbitals. The CNDO method with this change in parameterization is extended to the calculation of electronic spectra and applied to the isoelectronic compounds benzene, pyridine, pyri-dazine, pyrimidine and pyrazine. The results obtained were refined by a limited Cl calculation, and compared with the best available experimental data. It was found that the agreement was quite satisfactory for both the n TT and n tt singlet transitions. The relative energies of the tt and the lone pair orbitals in pyridine and the diazines are compared and an explanation proposed for the observed orders. Also, the nature of the lone pairs in these compounds is discussed. 

A method which is similar to the Pariser-Parr-Pople method for the n electron system and is applicable to common, saturated molecules has been proposed by Pople 28>. This method is called the CNDO complete neglect of differential overlap) SCF calculation. Katagiri and Sandorfy 29> and Imamura et al. °) have used hybridized orbitals as basis of the Pariser-Parr-Pople type semiempirical SCF calculation. 

One example showing a serious discrepancy of the frontier electron method was reported by Dewar H8,ii9). This is 10,9-borazaphenanthrene, and the value of / -B) was reported to have been calculated by the Pople method, but the parameters usyd were not indicated. Fujimoto s calculation by the Pariser-Parr-Pople method 120>, in perfect disagreement with Dewar s, gives the most reactive position as 8, which parallels experiment. The ambiguity involved in the integral values adopted seems to be serious, so that the establishment of parametrization for boron heterocycles is desirable. 

The calculations were carried out by J. J. C. Mulder, Leiden, according to the Pariser-Parr Pople method and were rounded off by taking into account configuration-interaction of all singly excited states. See Ref. i 2) fQj- results. 

The symmetry of the quinolizinium ion is such that only four monosubstitution products are possible for any given substituent. On the basis of a computation using the Pariser-Parr-Pople method, including all singlet mono-excited electronic configurations, Galasso (68MI21000) concluded The carbon atoms at 3 and 7 are expected to be most reactive towards electrophilic substitution. ... 

Calculations by the Pariser-Parr-Pople method on the quinoneimine obtained by Fremy s salt oxidation of dibenz[6,/]azepine indicate that the carbon adjacent to the carbonyl group is the most nucleophilic center. This is confirmed by nitration [Cu(N03)2-Ac0H] and bromination [NBS-(PhC0)202] studies, in which the 1-substituted derivatives are obtained. However, acylation by Vilsmeier or Friedel-Crafts reaction fails, extensive decomposition of the ring system taking place. 

Fig. 8. Absorption spectra (AB upper curves) and circular dichroism (CD lower curves) of calycanthine (formula in the inset of the figure). The solid lines refer to the experimental spectra and the broken lines to the theoretical curves for the configuration illustrated, calculated by the Pariser-Parr-Pople method using the dipole velocity procedure21,22)...

The electronic spectra of quinoxaline and its 2-chloro, 2-methoxy, and 2-amino derivatives have been calculated by the Pariser-Parr-Pople method. The calculated and the observed spectra agree well.247... 

Ten unsaturated carbonyl compounds representing a variety of structural types were selected for study. These are given in Table II, together with their pKa values and dipole moments, where available the non-alternant systems are indicated in italics. The fourth column contains the it dipole moments of the neutral molecules as obtained by the Pariser-Parr-Pople method using the parameters of Table I. 

We begin our examination of specific SCF-type semiempirical methods with the simplest, the Pariser-Parr-Pople method. 

The third fundamental hypothesis of the CNDO approximation concerns the core matrix elements H. These correspond to the and parameters of the Pariser-Parr-Pople method, the core including here only the Is electrons and the nuclei. 

Aminothiazoie absorbs near 270 nm (e = 14,000) corresponding to the ir4 — tt electronic transition calculated by the Pariser-Parr-Pople method at 199 nm (63). The amino group in the 2-position introduces a bathochromic shift (90,91). Localization of the transition is shown in Fig. VI-2. This figure suggests that, in the tt4— excited state, protonation... 

K. Ohno, Theor. Chim. Acta, 2, 219 (1964). Some Remarks on the Pariser-Parr-Pople Method. 

The Pariser-Parr-Pople method provides a satisfactory interpretation of the absorptions in the UV and visible regions. ° Transition... 

The Pariser-Parr-Pople Method and Roothaan s Equations... 

The pyrido[l,2-a]pyrazinium cation has been compared with the quinolizinium ion and the other monoazaquinolizinium cations, using the Pariser-Parr-Pople method to calculate electronic structures and absorption spectra. The ultraviolet spectrum of pyrido[l,2-a]pyrazinium bromide in water shows maxima at 232, 276, 287, 322, and 336 nm. Ultraviolet spectra have been recorded for various substituted compounds and their iV-oxides. The bands at 1685 and 1655 cm in the infrared spectrum (KBr disc) of the oxo compound 5 (R = H) confirm its formulation as the 0X0 form rather than as the corresponding hydroxy tautomer. Similarly the dioxo derivative 6 exists as such, in preference to the hydroxy form 5 (R = OH). The presence of a two-proton singlet at 6 6.1 in the PMR spectrum (in trifluoroacetic acid) of compound 6 is strong evidence in favor of this formulation. Ultraviolet spectral data are consistent with structures 6 and 5 (R = H). ... 

The Pariser-Parr-Pople method, self-consistent molecular orbital calculations, and the Huckel approach have been applied to the theoretical calculation of transition energies and intensities in the ultraviolet spectra of pyrido[2,3-ft]pyrazine and other azanaphthalenes. Good agreement with experimental data was obtained. The infrared spectra of the parent heterocycle" and its 8-hydroxy derivative have been discussed the 0X0 form is preferred to the hydroxy form both in chloroform solution and in the solid state. As with other a-hydroxyazines, the oxo form is also favored in the 2-, 3-, and 6-hydroxy compounds. Ultraviolet spectra have been measured for the parent heterocycle and various substituted compounds. The spectrum of the parent is substantially similar to other azanaphthalenes. In ethanol the principal bands are at ca. 260,300, and 350 nm. Both the infrared and ultraviolet spectra of about 60 derivatives of the ring system have been assembled. ... 

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. 

The 1998 Nobel prize in chemistry was shared by Walter Kohn, one of the developers of density-functional theory, and John A. Pople, one of the developers of the Gaussian series of programs and widely used Gaussian basis sets, the Pariser-Parr-Pople method, the CNDO and INDO methods, and one of the first to apply the MP and CC methods to molecular calculations. The Nobel committee noted that computational quantum chemistry is revolutionising the whole of chemistry. ... 

Today we know that the HF method gives a very precise description of the electronic structure for most closed-shell molecules in their ground electronic state. The molecular structure and physical properties can be computed with only small errors. The electron density is well described. The HF wave function is also used as a reference in treatments of electron correlation, such as perturbation theory (MP2), configuration interaction (Cl), coupled-cluster (CC) theory, etc. Many semi-empirical procedures, such as CNDO, INDO, the Pariser-Parr-Pople method for rr-eleetron systems, ete. are based on the HF method. Density functional theory (DFT) can be considered as HF theory that includes a semiempirical estimate of the correlation error. The HF theory is the basie building block in modern quantum chemistry, and the basic entity in HF theory is the moleeular orbital. 

Restricted to 7t-electrons. These methods exist for the calculation of electronically excited states of polyenes, both cycHc and linear. These methods, such as the Pariser-Parr-Pople method (PPP), can provide good estimates of the 7t-electronic excited states, when parameterized well. Indeed, for many years, the PPP method outperformed ah initio excited state calculations [6]. 

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