Ohno formula

The structure polycyclic hydrocarbons (eg. Fig. 2) is taken with benzene bond lengths Rq = 1.397A and bond angles 27r/3. The Ohno formula[7] for V(Rpq) is... 

A rehnement can be found in the Ohno formula [33] for calculating the hardness kernels ... 

Apart from minor exceptions all other parameters are given the same values as in standard INDO (electroneguivities, Slater-Condon parameters, bonding parameters) or CNDO/S (one-centre repulsion integrals) methods. Two-centre repulsion integrals are usually evaluted by the Ohno-Klopman formula. 

One of the first such kinetic studies of a perovskite mixed conducting electrode was reported by Ohno and co-workers in 1981, who found Lai /la/IoOs-a to have better kinetic properties than Pt as an SOFC cathode at 1000—1100 °C. °° A number of other JiepomOKizeo of general formula Lai jSr rMOs a (M = Cr, Mn, Fe, Co) were later studied by Takeda et al. ° To avoid reaction of the perovskites with the YSZ... 

With B =-2.5 eV, R,=1.4 A and a=1.46 A 1 we obtain around R roughly the same (linearized) behaviour as in the SSH parametrization. The two electron integral y was as usually calculated using Ohno s formula. The on-site term is Y =11.08 eV and the ionization potential 1=11.5 eV. First of all we obtain a symmetry adapted RHF solution with a density matrix P =l. In this case the total energy is (including repulsion y of the ionic cores)... 

Now we need a formula to interpolate between these two cases. A very similar situation appears in semiempirical quantum chemical methods, where -y has a simple form, given by the Klopman-Ohno approximation ... 

A subsequent use of the Ohno interpolative formula [54] for the two-center electron repulsion integrals, Yij, generates a realistic semi-empirical AIM hardness tensor (a.u.) [33] ... 

An advantage of the Combination Rules is, that one is not restricted to only one definition for the calculation of the hardness kernels. Other, more refined approximations can be used (e.g. the Mataga-Nishimoto [34] formula or the formulas by Pariser and Ohno) which may enhance the accuracy. This is not the case in EEM, at least when we want to retain its internal consistency. For larger systems, EEM has the advantage that it enables the direct calculation of global and local properties while the Combination Rules have to be applied recursively. Also EEM is directly applicable to the solid state. 

A comparison between the three foregoing methods, together with the results of EEM calculations, is shown in Fig. 1, in which the global hardnesses for some homonuclear diatomic molecules are plotted against the experimentally observed values (1 — A) [36]. It must be stressed that in all cases the same parameterization has been used, namely the isolated-atom hardnesses r x [11]. The differences are only due to differences in the expressions. For the Combination Rules, the hardness kernels were obtained from Ohno s formula. 

Differing from conventional PPP formulation, the repulsive Coulumb interaction term Vpq, which is usually given by Ohno s empirical formula, is modified here to take into account the chain-length dependent screening effect. To be specific, we adopt for Vpq the following expression ... 

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