Pariser-Parr-Pople theories, semiempirical

The next, short, chapter reviews different semiempirical crystal-orbital theories [tt-electron CO theories, namely Huckel and Pariser-Parr-Pople theory, as well as all valence electron CO theories with different degrees of neglect of the so-called differential overlap (CNDO, INDO, MINDO, etc.)]. Applications to highly conducting polymers and to periodic biopolymers are also presented. 

A more sophisticated semiempirical 7l-electron theory that takes electron repulsion into account is the Pariser-Parr-Pople (PPP) method . 

PPP (Pariser-Parr-Pople) [14-16] is an SCF (self-consistent field) Jt-electron theory, assuming o — jt separability. Only a single (2pz) atom orbital is considered on each atom and the Ji-electron Hamiltonian includes electron-electron interactions with ZDO (zero differential overlap) approximation. All integrals are determined by semiempirical parameters. The PPP method can only be used to calculate those physical properties for which jt electrons are mainly responsible. 

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. 

In this review we summarized our experience with the development and applications of semiempirical Pariser-Parr-Pople (PPP)-type and all-valence-electron methods to electronic spectra of radicals. After the era of PPP calculations on closed-shell molecules and the advent of semiempirical all-valence-electron methods, the electronic spectra of radicals represented a new challenge for molecular orbital (MO) theory. It was a time when progress in experimental techniques resulted in accumulation of a vast amount of data on the electronic spectra of radicals of various structural types. Compared to closed-shell molecules, the electronic spectra of some radicals exhibited peculiar features bands in the near infrared, many transitions in the whole UV/vis region, and some bands of extraordinary intensity. Clearly, without the help of MO theory, their interpretation seemed even harder than with closed-shell molecules. 

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. 

The earliest place where the quantity (/ - A) has made its appearance and played the role of a prominent character is the semiempirical electronic structure theory, which is known for its richness in scientific content, particularly for the physical basis in choosing the parameters and using the approximations. This theory provides one of the simplest and transparent models through the smiiempirical Hamiltonian as proposed by the Pariser-Parr-Pople (PPP) theory to approximate the total energy of a molecular system. In one of its simplest forms, the PPP Hamiltonian can be expressed as... 

A third approach, the one most important for the current discussions, is to treat the electric-field as a source of perturbation of the total molecular energy using real and virtual excited state transitions. This approach uses electronic wave functions either for all of the electrons of the molecule (ab initio calculations) or for only the valence electrons (so-called semiempirical theories). Semiempirical Hamiltonians may ignore electron interactions completely (Huckel theory). They may assume one jt-orbital per carbon and assume no overlap between adjacent electron orbitals (Pariser-Parr-Pople or PPP). Or, they may include both the a and... 

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. 

The VAEs of bases were also predicted using theoretical methods such as semiempirical Pariser-Parr-Pople (PPP) (Gompton et al. 1980 Younkin et al. 1976) and ab initio methods (Sevilla et al. 1995). Since these anion states are metastable with respect to the autodetachment of the electron, special care was taken in the aforementioned theoretical approaches to handle these anion states by employing confined basis set, Koopmans theorem approximation, and empirical determination of parameters to scale the theoretical results to the experimentally measured anion state energies for other compounds. Sevilla et al. (1995) used calculated values for VAEs of benzene, naphthalene, pyridine, pyrimidines, and uracil, which have experimentally known values to scale theoretically calculated VAEs for the DNA bases. A comparison of the experimental VAEs of the bases to those predicted theoretically is presented in O Table 34-1. From O Table 34-1, we see that the calculated VAE values are in excellent agreement with experimental VAEs and the difference between theory and experiment lies in the range... 

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