The PPP-SCF

In PPP-SCF calculations, we make the Bom-Oppenheimer, a-rr separation, and single-electron approximations just as we did in Huckel theor y (see section on approximate solutions in Chapter 6) but we take into account mutual electrostatic repulsion of n electrons, which was not done in Huckel theory. We write the modified Schroedinger equation in a form similar to Eq. 6.2.6 

In the Huckel theory of simple hydrocarbons, one assumes that the election density on a carbon atom and the order of bonds connected to it (which is an election density between atoms) are uninfluenced by election densities and bond orders elsewhere in the molecule. In PPP-SCF theory, exchange and electrostatic repulsion among electrons are specifically built into the method by including exchange and electrostatic terms in the elements of the F matrix. A simple example is the 1,3 element of the matrix for the allyl anion, which is zero in the Huckel method but is 1.44 eV due to election repulsion between the 1 and 3 carbon atoms in one implementation of the PPP-SCF method. 

The elements of the F matr ix depend on either the charge densities q or the bond orders p, which in turn depend on the elements of the F matrix. This circular dependence means that we must start with some initial F matrix, calculate eigenvectors, use the eigenvectors to calculate q and p, which lead to new elements in the F matr ix, calculate new eigenvectors leading to a new F matrix, and so on, until repeated iteration brings about no change in the results. The job now is to fill in the elements of the F matr ix. 

The diagonal matrix element F is broken up into three parts 

Let us illustrate the meaning of F by the example of carbon atom 1 in the linear, three-carbon allyl anion C3Hg. There are two carbon atoms other than Ci, one adjacent and the other nonadjacent. Equation (8-44) has three temis, one for each carbon atom 

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Once the format of the Fock matrix is known, the semiempirical molecular problem (and it is a considerable one) is finding a way to make valid approximations to the elements in the Fock matrix so as to avoid the many integrations necessary in ab initio evaluation of equations like Fij = J 4>,F4> dx. After this has been done, the matrix equation (9-62) is solved by self-consistent methods not unlike the PPP-SCF methods we have already used. Results from a semiempirical... 

Electronic energy levels can be satisfactorily calculated using the PPP-SCF-MO method and the results used to assign bands in the observed UV spectra. Comparison of results for... 

The off-diagonal elements Hi2 = H2 calculated by the PPP SCF method are substantial, T/i2 = 0.8eV. The resulting split between the two formerly degenerate configurations is sufficient to move the lower Cl state below the energy of the configuration xi i- The result of a full PPP SCF SCI calculation (Figure 4.27) is essentially the same. 

Since the establishment of necessary basis for accurate computation, simpler approaches with appropriate parameterization have been developed. In particular, parameterization of the PPP-SCF-CI (Pariser, Parr, Pople-self-consistent-field-configuration interaction) method has enabled /8-values (of sufficient accuracy to provide a basis for molecular design) to be obtained with much less powerful computers. Routines are now available for microcomputers that run in reasonable time with adequate accuracy [20]. 

Pomerantz and coworkers reported in 1989 [83] that very simple perturbational molecular orbital (PMO) methods could be applied to a number of hydrocarbon aromatic oligomers and conducting polymers. These calculations provided band gaps and UV-vis absorption maxima that were in excellent agreement with both observed data, where available, and data calculated by more sophisticated procedures. Thus for polymer 49 the PMO method gave a value of 0.54 eV [83], while the VEH calculations mentioned above gave a band gap of 0.44 eV [81] and the PPP-SCF band gap calculations gave 0.73 eV [84]. 

The investigation by Mustroph et al. (1981) was made using SCF-CI with the PPP approximation to calculate the influence of substituents on the longest wavelength band. This study is interesting because the authors come to the conclusion that 591 nm is the theoretical limit that can be obtained with substituted benzenediazo-nium ions. As far as we are aware, that limit had not been reached by the early 1990s. 

A thiepin is formally isoelectronic with the 8ic-electron 1,3,5,7-cyclooctatetraene and 1,3,5-cycloheptatrienide ion and, if planar, may actually be antiaromatic. Recently, the question of the antiaromaticity of thiepin has been the subject of interest for both synthetic and theoretical chemists. The apparent instability of the thiepin ring system is in good agreement with theoretical calculations. Dewar and Trinajstic 68) have reported that the thiepin is considered to be weakly antiaromatic (RE = — 1.45 kcal mol-1) based on PPP SCF MO calculations. On the other hand, Hess Jr. and Schaad 69) have found it to be substantially antiaromatic (RE = —0.232 J) by using the Huckel MO method. This result was also supported by a graph-theoretical treatment by Aihara 70). 

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... 

We now consider the PPP, CNDO, INDO, and MINDO two-electron semiempirical methods. These are all SCF methods which iteratively solve the Hartree-Fock-Roothaan equations (1.296) and (1.298) until self-consistent MOs are obtained. However, instead of the true Hartree-Fock operator (1.291), they use a Hartree-Fock operator in which the sum in (1.291) goes over only the valence MOs. Thus, besides the terms in (1.292), f/corc(l) m these methods also includes the potential energy of interaction of valence electron 1 with the field of the inner-shell electrons rather than attempting a direct calculation of this interaction, the integrals of //corc(/) are given by various semiempirical schemes that make use of experimental data furthermore, many of the electron repulsion integrals are neglected, so as to simplify the calculation. 

The structure of the reaction product of 2-aminopyridine and diethyl malonate, described by Chichibabin as 2,4-dioxo-3,4-dihydro-2//-pyrido-[l,2-<7]pyrimidine,96 was first questioned by Snyder and Robison253 on the basis of the high melting point and poor solubility of the compound. They suggested the tautomeric 2-hydroxy-4-oxo-4H-pyrido[l,2-a]pyrimidine structure. The problem was solved by Katritzky and Waring273 who compared the UV spectrum of the product with that of fixed tautomers and found that the product may best be described as anhydro- 2-hydroxy-4-oxo-4/f-pyrido[l,2- ]pyrimidinium)hydroxide (63). Because of the chemical behavior of these compounds, however, the contribution of other mesomeric forms to the structure has also been considered.122 Thus, PPP-SCF quantum chemical calculations suggest that 1,4-dipolar cycloadditions to the C-3 and C-9a atoms are to be expected.352 This type of reaction does in fact occur (see Section III,C,10). Katritzky and Waring273 estimated the ratio of the mesomeric betaine (63 R = H) and the 2-hydroxy-4-oxo tautomers to be about 20 1. 

The suggested structure of the photoinduced form of naphtoquinone methide was confirmed by identification of this compound at 77 K, the coincidence of experimental and calculated Pariser-Parr-Pople self-consistent field chemical ionization (PPP SCF Cl) spectral characteristics, and the sharp change in the rate of the dark relaxation from the photoinduced state to the initial form (by four orders of magnitude) upon passage from hydrocarbon to aprotic hydrogen-bond acceptor solvents.11... 

The larger values calculated by the PPP method <1966JA4804> when the sulfur 3d- or the 4p-orbitals are included are not surprising, since inclusion of the sulfur 3d-orbitals in the calculations leads to a drift of the G- and Jt-electrons toward the sulfur atom. With the diffusely polarized 6-31G (+sd+sp) basis set, a better correlation is obtained with MP2 values than with SCF values 1992JPC7301>. 

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