Localized pairs, method

Further comparative calculations by both VB and MO methods on BeEfe have been reported, using a minimal STO basis, with exponents optimized for various r zsz With choice of particular VB configurations, it is shown that a model based on the resonance valence state, including ionic configurations, is particularly useful. Both methods show a localized-pair bond description to be useful. 

There is no room here to collect together all important achievements in quantum chemistry which are strongly or loosely connected to geminals or at least, their development was perhaps motivated by the successes or failures of geminal theories (cf. e.g. the self-consistent electron pair method by Meyer and its reformulations [69,70,71], or the connections to valence bond theory [72]). We have to mention an important book by Hurley [73] in which significant attention was paid to geminals and their localization. 

The description of such molecules as He2+, 02 and NO is more satisfactory by the molecular orbital method than by the Heitler-London since in the latter an additional concept, that of the three electron bond, must be introduced in order to explain the molecule and its properties. The conception of directional valency is perhaps more easily conceived by the method of localized pairs, but as already pointed out, the molecular orbital treatment of delocalized electrons also leads to the tetrahedral model of methane. 

Frequencies and intensities of bands in the IR spectra of 1,2,4-triazines have been calculated by the 4-31G method50 and by ab initio Hartree-Fock level with 6-31G, 6-31G, U-9 and 3-21G methods.51 The shifts for the protons in the parent 1,2,4-triazine have been predicted and are in reasonable agreement with the observed values.52 The shifts of the 13C NMR signals for 3,5,6-trichloro-l, 2,4-triazine have been calculated by the first and second order SCS method and compared with the experimental values.53 The nature of lone pair effects of heteroatoms on direct 13C — H spin coupling constants has been calculated by the AMI method54 and the nuclear shielding tensors of 15N and 1 C nuclei by the SOLO (second-order corrected localized orbital-local origin method) ab initio method.55 14N Shifts have been predicted.75 The electron distribution of 1,2,4-triazines has been estimated from the observed NMR shifts.76... 

The separate runs have found a number of different solutions, although not necessarily local minima. For instance, population 5 has the correct values for the first two parameters and has values that differ from the correct values for the other two parameters by a single bit flip. A pair of correlated mutations would take this solution to the true minimum. In situations such as this, it is often useful to take the best solutions produced by the GA and apply a local minimization method to drive them to the bottom of the neatest local minimum. Population 2 is probably also in the basin of attraction of the solution and would drop in with the aid a local minimizer. 

The exploitation of localized orbitals for dispersion energy calculations has already been proposed since the early works on local correlation methods [41 5]. In classical and semiclassical models most often the atoms are selected as force centers only a few works exploit the advantages related to the use of two-center localized orbitals and lone pairs. A notable exception is the recent work of Silvestrelh and coworkers [46-50], who adapted the Tkatchenko-Scheffler model [16] for maximally localized Wannier functions (MLWF), which are essentially Boys localized orbitals for solids. It is worthwhile to mention that one of the very first use of the bond polarizabilities as interacting units for the description of London dispersion forces has been suggested as early as in 1969 by Claverie and Rein [51] see also [52],... 

---