Ab initio Hartree-Fock-Roothaan

The fundamental tool for the generation of an approximately transferable fuzzy electron density fragment is the additive fragment density matrix, denoted by Pf for an AFDF of serial index k. Within the framework of the usual SCF LCAO ab initio Hartree-Fock-Roothaan-Hall approach, this matrix P can be derived from a complete molecular density matrix P as follows. 

Theoretical quantum-chemical study of pyridine adsorption at Hg electrode (including its charged surface) has been described by Man ko et al. [137,138]. An ab initio Hartree-Fock-Roothaan method has been employed. The electrode was modeled as a planar seven-atomic Hg-7 cluster. The deepest minimum of the total energy of the adsorption system was found for positive charge density and Py interacting with the metal through the lone electron... 

Semi-empirical calculations for the simple vinyl cation C2H3+ have been reported by Hoffmann (1964) and by Yonezawa et ad., (1968). More rigorous calculations by Sustmann et ad. (1969) are based on a semi-empirical method based on the neglect of diatomic differential overlap (NDDO) calibrated to results of ab initio Hartree-Fock-Roothaan SCF calculations. Recent work by Hopkinson et al. (1971) is entirely based on a non-empirical LCAO-MO-SCF method. 

Table 4.1. Comparison of orbital ionization potentials (in eV) for SiO observed experimentally from uv photoelectron spectroscopy with those calculated by the MS-SCF-Ya method, ab initio Hartree-Fock-Roothaan method, incorporating the ASCF approach (HFR ASCF), and with perturbation theory (HFR + PT)...

Table 4.3. Experimental properties of SiO and Si Oj compared to those calculated by Snyder and Raghavachari (1984) using ab initio Hartree-Fock-Roothaan SCF calculations...

Reasonable results have also been obtained for Zn Mdssbauer isomer shifts in zinc chalcogenides from LMTO band calculations (Svane and Antoncik, 1986) and for Sb compounds (Ravenak et al., 1983) using the DYM-Aot method. The overall conclusion must be that the time is ripe for the systematic calculation of Fe isomer shift and electric-field-gradient values in Fe-0, Fe-S, and other polyhedra using ab initio Hartree-Fock-Roothaan or DVM-Aa methods. 

Table 5.11. Electronic structure of the COj cluster molecular-orbital compositions in terms of atomic-orbital components based on ab initio Hartree-Fock-Roothaan SCF calculations"...

Usually, the parent molecules M are confined to some limited size that allows rapid determination of the parent molecule density matrices within a conventional ab initio Hartree-Fock-Roothaan-Hall scheme, followed by the determination of the fragment density matrices and the assembly of the macro-molecular density matrix using the method described above. The entire iterative procedure depends linearly on the number of fragments, that is, on the size of the target macromolecule M. When compared to the conventional ab initio type methods of computer time requirements growing with the third or fourth power of the number of electrons, the linear scaling property of the ADMA method is advantageous. 

The principal differences between ab initio and semiempirical calculations is that ab initio methods evaluate all of the integrals numerically instead of relying on experimental information to assign values to integrals. The term ab initio means from the beginning. If a large enough set of well-chosen basis functions is used, the results of ab initio Hartree-Fock-Roothaan calculations can nearly replicate the Hartree-Fock... 

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