Bond valence parameters relations between

Still it should have become obvious from the above discussion that there is a close functional relationship between bond valence and electron density at the bond critical point (and in the same way between bond valence and the Laplacian of V Pbcp) and that this correlation involves a scaling based on the principal quantum number (row number) of the atoms involved or a closely correlated quantity, and at least for the case of the Laplacian to a measure of atomic polarizability (such as the atomic hardness or its inverse the atomic sofmess). This fundamental correlation should thus be taken into account when fine-tuning approaches to determine bond valence parameters and BV-related forcefields. 

This number applies only to unsymmetrical (Ci) molecules, how ever, since the existence of symmetry implies further relations between constants and hence a still smaller number of independent parameters. As an illustration, consider the water molecule (62,.). A convenient set of internal coordinates is formed from ri and r, the stretches of the two OH bonds, and a, the distortion of the valence angle. The potential energy can be w ritten as... 

Table 4.11 contains bond polar parameter values for carbon-halogen bonds determined from experimental infrared intensities in halomethanes and carbonyl halides. As emphasized before, bond polar parameters are not directly related to the equilibrium charge distribution and, therefore, any relationship between the magnitude or sign of diese quantities and the actual polarity of valence bonds may only be qualitative. It should also be pointed out that parameter values are dependent on the accuracy of experimental measurements and the force fields employed. 

A simple criterion, which has the same nature as Ath of the catalyst, was used to represent the electron donor power during reaction the absolute value of the potential ionization difference. A/ = /r — /p, weighed by the ratio p/ r of carbon in product and reactant molecules respectively. The linear correlations obtained between A/ and Ath show that their slope is related to the electron donor power of the reactant, positive when C-C (alkanes, alkyl-aromatics) or C-H (alcohols) bonds are to be transformed, and negative when C=C bonds are concerned. The intercept depends on the extent of oxidation, and its absolute value increases from mild to total oxidation, respectively. A main difficulty is the actual state of cations at the steady state, but each time accurate experiments allow determining the mean valence state, the calculated Ath fits well the correlations. These lines may be used as a predictive trend, and allow, for example, to precise that more basic catalysts are needed for alkane ODH than for its mild oxidation to oxygenated compound. As a variety of solids have been catalytically experienced in literature, it would be worthwhile to consider far more examples than what is proposed here to refine the relationships observed. Finally, theoretical considerations are proposed to tentatively account for these linear relationships. Optical basicity would be closely related to the free enthalpy, and, as an intensive thermodynamic parameter, it is normal that it could be related to several characteristic properties, including now catalytic properties. 

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