Coulomb integral computation

ZlNDO/S is differen t from ZINDO/1 because th ey use differen t algorithms in computing the Coulomb integrals. Hence the two et uation s used in th e rn ixed m odel in ZINDO/1 are also employed... 

The sum A is over all the atoms in the quantum region and B is over all the atoms in the classical region. The two-electron and two-center Coulomb integral, Y b, is computed in MINDO/3 by... 

While in principle all of the methods discussed here are Hartree-Fock, that name is commonly reserved for specific techniques that are based on quantum-chemical approaches and involve a finite cluster of atoms. Typically one uses a standard technique such as GAUSSIAN-82 (Binkley et al., 1982). In its simplest form GAUSSIAN-82 utilizes single Slater determinants. A basis set of LCAO-MOs is used, which for computational purposes is expanded in Gaussian orbitals about each atom. Exchange and Coulomb integrals are treated exactly. In practice the quality of the atomic basis sets may be varied, in some cases even including d-type orbitals. Core states are included explicitly in these calculations. 

Alternatively, these one-center coulomb integrals can be computed from first principles using Slater or Gaussian type orbitals. 

Most modern Hiickel programs will accept the molecular structure as the input. In older programs, the input requires the kind of atoms present in the molecule (characterized by their Coulomb integrals a) and the way in which they are connected (described by the resonance integrals. ). These are fed into the computer in the form of a secular determinant. Remember that the Coulomb and resonance integrals cannot be calculated (the mathematical expression of the Hiickel Hamiltonian being unknown) and must be treated as empirical parameters. 

Due to the problems discussed at the end of section 7.2.2., the integration in the two center case has been done using the methodology outlined by O-Ohata and Ruedenberg [26b]. The integral to be computed now is a reduced Coulomb integral written as ... 

The first of these methods was developed by Hoffmann in 1963 (1) and is known as extended Hiickel theory (EHT). Briefly, the method uses Hiickel formalism however, explicit consideration of non-bonded interactions and all overlap integrals are a refinement. Slater orbitals are used, and the computations require only one parameter, the valence state ionization potential for the Coulomb integral and indirectly for the reso-... 

Several authors " have attempted to use density functional type approaches for only the correlation energy. If the Hartree-Fock expression for exchange is kept, this of course ensures that the self-Coulomb integrals are properly cancelled by self-exchange one goes back (for better or worse) to the HF level as the point of reference. The computational demands are of the same order as those of the HF calculation itself Results of early attempts of this nature have been summarized by Stoll et al If the local density approximation to correlation. 

Of course, this is chiefly due to the availability of efficient SCF programs which can be used by anyone as soon as computer time is available. Work of that sort had the merit of showing that certain disagreements between experiment and precomputational theory which were attributed to correlation may in fact have little to do with it. For instance, the reduction of Coulomb integrals in the Parr-Pariser-Pople theory of 7t-electron systems was considered in the past as produced by a- and a -electron correlation. The determination of optimized basis orbitals in atomic valence states (2) and in simple polyatomic molecules... 

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