Absolute softness, definition

The equations 7, 8 and 9 fail to operate when the HOMO - LUMO energy gap becomes too small and do not consider the influence on chemical properties of other orbitals, besides the HOMO and LUMO s. Moreover, it is not possible to study the site selectivity of a chemical species considering only absolute hardness other than space-dependent (local) versions of hardness/softness concepts [5]. Thus in addition to the global definition of r) and S, the local hardness [4] and local softness [5] have been introduced as follows ... 

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. 

---