Fractional number of electrons transferred

Fig. 7. SCF, CISD and DFT charges versus Pauling electronegativities for fluorides of the first elements the electronegativity on the x axis is that of the central atom and the charge on the y axis is the net positive charge on it (i.e. the fractional number of electrons transferred to fluorine atoms), calculated with the 6-31G basis set (for SCF and CISD) or the DNP basis set (for DFT), see Table 2 (r is the correlation coefficient of the indicated fit).

This property of q is best seen in the equation Parr and I wrote for the equilibration of two systems, C and D. Electrons will flow from the one of lower electronegativity to that of higher electronegativity until a single chemical potential exists. The (fractional) number of electrons transferred is given by ... 

Global softness is just the inverse i). The quantities x and t) prove to be useful concepts for the discussion chemical bonding. Together x and t) provide an expression for charge transfer. 29.30 por instance, consider the equilibration of two systems A and B. The fractional number of electrons transferred can be written as... 

E vs. log(id-i)/f which should be linear with a slope of 59.1/n mV at 25 °C if the wave is reversible. This method relies however upon a prior knowledge of n, and if this is not known then the method is not completely reliable as theory predicts that when the electron transfer process itself is slow, so that equilibrium at the electrode between the oxidized and reduced forms of the couple is established slowly and the Nemst equation cannot be applied, then an irreversible wave is obtained and a similar plot will also yield a straight line but of slope 54.2/ana mV at 25 °C (a = transfer coefficient, i.e. the fraction of the applied potential that influences the rate of the electrochemical reaction, usually cu. 0.5 na = the number of electrons transferred in the rate-determining step). Thus a slope of 59.1 mV at 25 °C could be interpreted either as a reversible one-electron process or an irreversible two-electron process with a = 0.45. If the wave is irreversible in DC polarography then it is not possible to obtain the redox potential of the couple. 

A large number of electron transfer reactions have been reported, including some studies on cascade electron transfer processes (Adams et al., 1968). The data given in Table 7 represent only a small fraction of those reported in the literature. The last four values in Table 7 have been determined in conjunction with studies of radiation sensitization in which electron transfer processes are believed to play a major role. 

Hard and soft acid and base theory gives access to an early part of the slope in a reaction profile like that in Fig. 3.3, just as perturbation molecular orbital theory does. Using the definitions of absolute electronegativity and absolute hardness derived in Equations 3.5 and 3.6, the (fractional) number of electrons AN transferred is given by Equation 3.14. 

The electron transfer from a partially filled band is obtained by multiplying Nj.j by the fractional occupation of the T band. The purely ionic model is transformed by the latter two equations into a model containing a bonding charge that reproduces the essential features of the electronic structure of NaCl-type compounds when the hybridization is reasonably weak. Whereas the atom and angular-momentum projected densities of states in the unhybridized model arose simply from the T unhybridized bands, they now contain additional parts due to hybridization with the T bands. Dashed lines have been added to complete the hybridized density of states in fig. 58. The number of electrons transferred between the atoms by this interaction is estimated from eq. (68) to be, with UN as example,... 

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