Molecular geometry basis

Whereas correlation energies can be included, in practice it is even more time-consuming to use them in the determination of molecular geometries (ie, n P and determining the correct basis set to use can be difficult. 

The shapes of the monomeric molecules of the Group 2 halides (gas phase or matrix isolation) pose some interesting problems for those who are content with simple theories of bonding and molecular geometry. Thus, as expected on the basis of either sp hybridization or the... 

Heats of formation, molecular geometries, ionization potentials and dipole moments are calculated by the MNDO method for a large number of molecules. The MNDO results are compared with the corresponding MINDO/3 results on a statistical basis. For the properties investigated, the mean absolute errors in MNDO are uniformly smaller than those in MINDO/3 by a factor of about 2. Major improvements of MNDO over MINDO/3 are found for the heats of formation of unsaturated systems and molecules with NN bonds, for bond angles, for higher ionization potentials, and for dipole moments of compounds with heteroatoms. 

It became apparent that these STO-hG minimal basis sets were not particularly adequate for the accurate prediction of molecular geometries, and this failing was attributed to their lack of flexibility in the valence region. The next step was to give a little more flexibility to the STO- Gbasis sets, whilst retaining their computational attractiveness. The classic paper is that by Ditchfield, Hehre and Pople. 

The major features of molecular geometry can be predicted on the basis of a quite simple principle—electron-pair repulsion. This principle is the essence of the valence-shell electron-pair repulsion (VSEPR) model, first suggested by N. V. Sidgwick and H. M. Powell in 1940. It was developed and expanded later by R. J. Gillespie and R. S. Nyholm. According to the VSEPR model, the valence electron pairs surrounding an atom repel one another. Consequently, the orbitals containing those electron pairs are oriented to be as far apart as possible. 

Andzelm and Wimmer, 1992, published one of the first comprehensive studies on the performance of approximate density functional theory in which optimized molecular geometries were reported. These authors computed the geometries of several organic species containing the atoms C, N, O, H, and F at the local SVWN level, using a polarized double-zeta basis set optimized for LDA computations. Some trends have been discerned... 

Molecular geometries, which were not reported in this study, have been obtained using the 6-31 G(d,p) and cc-pVDZ basis sets. Thus, the 6-31 lG(d,p) and cc-pVTZ results refer to single point energy calculations only. 

The GHO basis can therefore provide a localised, directional set of orbitals (hybrids) which do not have the principal qualitative disadvantage of the usual hybrid sets they can be mutually orientated in any directions. What is more the directions taken up by the GHOs can be decided variationally and not by the unitary properties of a hybridisation matrix . This conclusion means that the use of a GHO basis provides both a localised bonding picture and simultaneously a theoretical validation of the VSEPR rules. Thus, it is not necessary, for example, to contrast the hybrid method and the VSEPR method for molecular geometries (30) they are complementary. 

The Lewis symbols will be used in the discussion of bonding, especially covalent bonding, and will form the basis of the discussion of molecular geometry. 

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