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On the Method of the Determination of the Global Hardness of Atoms and Molecules measures the resistance to elastic shape changes, and dislocation mobility which determine rates of plastic shape changes. Thus, annealed brass in which dislocations are mobile is said to be soft, but in the same brass, the dislocation can be im- mobilized by cold-rolling until it is hard enough to be used for springs. refractive index and which is largely determined by the HOMO-LUMO gap. However, it seems that Pearson (1999) differs from engineers and material scientists in the conceptual structure of physical hardness. Whether Electronegativity and Hardness are Quantum Observables: Notwithstanding the erudite discussion of Putz (2009) on the problem of observability of the electronegativity and chemical hardness, the hard- ness and the electronegativity are fundamentally hypothesis and conceptual structures and are not physical observables and, therefore, cannot be evaluated experimentally. As they are no observ- ables, the possibility of their quantum mechanical evaluation is completely ruled out (Ghosh et al., 2009, 2010; Islam et al., 2010, 2011). The chemical hardness, the atomic radius and THE HOMO-LUMO GAP Happily the HOMO-LUMO gap is the one and the same unique concept applies for the rational- ization of both chemical and physical hardness in chemistry and physics as well. The HOMO and the LUMO are the two frontier orbitals in the eigen value spectrum of atoms, molecules and the condensed matter. For molecules, the gap between the highest occupied MO and the lowest unoccupied MO in the bonding energy