The Four Potential Parameters

The first parameter u (-) in Table 4.1 is defined by (3.45), and according to (3.51) it represents the second-order estimate of the position of the band centre relative to E n, i.e. 

The choice D = - i - 1 leads to a similar estimate of the intrinsic mass defined in (3.39)  

To see the significance of (+)/ (-) we must first derive several relations connecting the potential parameters. With the boundary conditions D = i and D = - l - 1, we find from (3.44) the equations 

The Wronskian relation (3.17) combined with (4.13,14) gives the final relation needed  

The final parameter j 2 determines the width of the energy window, i.e. the energy range over which the variational estimate (3.50) is valid, cf. the discussion following equation (3.53). We shall return to j 2 in Sect.4.3 where we consider the case of the Cr 3d band. 

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As an example of a set of standard parameters, Table 4.1 lists all the potential-dependent information needed to perform an energy-band calculation for (non-magnetic) chromium metal. In the following, chromium is used as an example when we discuss the physical significance of each of the four potential parameters (4.1). At the end of the chapter we derive free-electron potential parameters, give expressions for the volume derivatives of some se-... 

To give expressions for the Hamiltonian and overlap matrices which are written in terms of the four potential parameters coin, w j, > n, and j 9 we need the following two relations... 

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