Softness Indices

In DFT, the most important descriptors are hardness and softness indices (Parr and Yang 1989, Geerlings et al. 1996a, Geerlings et al. 1996b). 

The second derivative of energy with respect to the number of electrons is called absolute hardness (q) or chemical hardness (Parr and Pearson 1983). For a molecule with N electrons, the absolute hardness is defined by 

Based on molecular orbital energies, especially the frontier orbital energies (Clare 1994 Huang et al. 1996), some main descriptors can be defined and information can be obtained about reactivity/stability of specific regions of the molecule. 

Highest occupied molecular energy (Ehomo) is related to the El and is a measure of nucleophilicity. 

Lowest unoccupied orbital energy (Elumo) is related to the EA and it is a measure of electrophilicity. 

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The Society of Forensic Toxicology (SOFT) indicated in their consensus evaluation of the scientific status of hair analysis that they considered it a useful forensic tool for the investigation of drug use. At least 12 forensic laboratories in Europe and in the U.S., including those of the FBI, have used hair analysis in hundreds of forensic investigations. There have been 12 challenges to hair analysis to date in the U.S. courts. Hair analysis was successfully defended in all instances. An extensive review of these cases has been published. ... 

Because of their orderly arrangements, the chains of the tactic polymers (syndiotactic and isotactic) can lie closer together and the polymers are partially crystalline, whereas atactic polymers are amorphous and soft indicating the absence of all crystalline order. Isotactic pol q)ropy-lene is highly crystalline with a melting point of 160°C, whereas the atactic isomer is an amorphous (noncrystalline) soft polymer with a melting... 

DFT-based descriptors are those derived from the Density Functional Theory and the most important are chemical potential, molecular electronegativity, hardness and softness indices, and Fukui functions. 

In terms of local softness, three local softness indices centered on the ath atom (s +, s , and s°) were defined as [Roy, 2004b]... 

For the social criteria, two methods are applied in this study. A more detailed safety-related discussion of the bioethanol process can be found in the open Hterature [45]. In the first method, safety during operation, operability of the plant, safe startup and shutdown, and location-specific demands are selected as four soft indicators for sustainability assessment. The evaluation and justification of each indicator are provided in Table 6.13, where standard definition and scaling system can be found in Othman et al. [1]. In this approach, the process with the higher score is more desirable. Again the dry grind process is found to be superior. 

This representation is referred to the open representation since the electrons and spin number can vary freely over a series of molecules at a well-defined chemical potential. In analogy to the previously written perturbation expansions, one can now perform a Taylor series expansion of H p.j, is,v,vs around changes in these four variables. In this expansion, the global and local softness indices will emerge in a natural way. These global softnessess can again be expressed in a matrix-vector notation as... 

Hardness indicates how much force is required to bring about a rather small deformation, while softness indicates that a larger deformation is obtainable with a somewhat smaller force. However, in scientific studies it is necessary to be more precise about these quantities. 

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