Hardness and the Electronic Energy

Written in this way is called the information, or uncertainty, entropy. But in fact, using the results of Table 4.6, and calculating suitable average quantum numbers, the ordinary thermodynamic entropy can be obtained from Equation (4.30). 

Thus as the temperature increases, the energy, the entropy, the uncertainty and the softness all increase. There is other evidence showing a relation between softness and entropy. For example, in Table 4.2 we found that the softness always decreased as molecules were formed from atoms or radicals. But the entropy also decreases, as translational motion is converted to rotational and vibrational. Also, if we examine a series of related molecules, we will find that the entropy increases as the softness increases (Table 4.7). 

In spite of all this, there is an important counter-example. The transition state for a chemical reaction is very soft, as we have seen, and is higher in energy than the reactants. Nevertheless, the entropy of activation,, is negative more often 

It would be very useful if a quantitative relationship could be found between 

The preceding sections have shown that it is rj, and not p, which is more closely related to energy. Also, the relationship is an inverse one in that means —A77. An annoying restriction is that p should be constant, or change very little. Also it is the electronic energy, which appears in DFT-based equations such as (4.5) and (4.21), where N is the number of electrons. Changes in nuclear-nuclear repulsion are usually easy to calculate, however. 

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