Zero-differential-overlap approximation, semiempirical

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 methods are widely used, based on zero differential overlap (ZDO) approximations which assume that the products of two different basis functions for the same electron, related to different atoms, are equal to zero [21]. The use of semiempirical methods, like MNDO, ZINDO, etc., reduces the calculations to about integrals. This approach, however, causes certain errors that should be compensated by assigning empirical parameters to the integrals. The limited sets of parameters available, in particular for transition metals, make the semiempirical methods of limited use. Moreover, for TM systems the self-consistent field (SCF) procedures are hardly convergent because atoms with partly filled d shells have many... 

Analogous to the PPP method for planar 7r-systems, semiempirical all-valence methods can be and were extended to include Cl, thus giving rise to a family of procedures based on the CNDO, INDO and NDDO variants of the zero-differential overlap (ZDO) approximation, many of which were applied also to the discussion of Cl effects in radical cations. Due to the parametric incorporation of dynamic correlation effects, such procedures often yield rather accurate predictions of excited-state energies and they continue to be the methods of choice for treating very large chromophores which are not amenable to ab initio calculations. 

By ab initio we refer to quantum chemical methods in which all the integrals of the theory, be it variational or perturbative, are exactly evaluated. The level of theory then refers to the type of theory employed. Common levels of theory would include Hartree-Fock, or molecular orbital theory, configuration interaction (Cl) theory, perturbation theory (PT), coupled-cluster theory (CC, or coupled-perturbed many-electron theory, CPMET), etc. - We will use the word model to designate approximations to the Hamiltonian. For example, the zero differential overlap models can be applied at any level of theory. The distinction between semiempirical and ab initio quantum chemistry is often not clean. Basis sets, for example, are empirical in nature, as are effective core potentials. The search for basis set parameters is not usually considered to render a model empirical, whereas the search for parameters in effective core potentials is so considered. 

If a zero differential overlap (ZDO) approximation (47) is invoked, as in semiempirical CNDO theories, the gross atomic population reduces to the electron density Paa (24). 

The two-electron integrals require the main computational effort in a HF calculation and their number is significantly reduced in semiempirical methods by the zero differential overlap (ZDO) approximation. This basic semiempirical assumption sets products of functions for one electron but located at different atoms equal to zero (i.e. /xa(1)vb(1) = 0, where and vb are two different orbitals loeated on centers A and B, respectively). The overlap matrix, S, is set equal to the unit matrix, S v = and the two-electron integrals (/xv Act) are zero, unless fx = v and k = a, that is,... 

In several semiempirical methods of quantum chemistry (e.g., in the Hiickel method) we assume the Zero Differential Overlap (ZDO) approximation, i.e. that XkXl (Xk) kl and hence the second terms in as weU as in are equal to zero, and therefore... 

As we have seen, EHT is a nonself-consistent method but the self-consistency over charge and configuration is included in the MR approximation. The Ab-initio HE SCF method requires the self-consistent calculation of the density matrix (see Chap. 4). This feature of the HE approach is maintained in the semiempirical methods, based on the zero differential overlap (ZDO) approximation. This approximation is used to reduce the number of multicenter integrals appearing in HE LCAO calculations. 

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