Linear free-energy-related estimation methods

The extraction ability of neutral organophosphorus compounds closely related to the charge density of phosphoryl oxygen (qo) and phosphorus atom(qp). It was found that the distribution ratio of cerium enhanced as the qo and qp values was increased. Meanwhile a linear free energy relationship exists between the 2A.i values and the Kabachnik constant for substituents of phosphorus compounds. As estimated by least squares method, an empirical equation v° =-3.84+0.1682Ai was deduced... 

Since the linear and related expansion formulas depend on fits to regions of the curve that are statistically less and less reliable, it makes sense to find a measure for extrapolation that depends on the relative accuracy of the relative free energy estimate for all points along the curve. The cumulative integral extrapolation method is one approach to this idea. 

The most appropriate parameter seems to be the chemical shift of the carbon atom — the carbocation centre (SC ). Its main advantage is its close relationship with the value of -electron deficiency in the carbocation centre which can be estimated by the MO method. For the series of structurally related arenonium ions - a linear correlation is found between the free activation energy of the... 

Calculated absorption spectra for magnesium and free-base porphine [13], obtained using the methods described above, are compared with experimental spectra in Fig. 5. The transition energies used are estimates, AE obtained from a least-squares fit of calculated and gas-phase experimental transition energies for the two molecules [45]. The resultant linear relation... 

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