Absolute hardness, definition

An absolutely scientific definition of the term essential cr volatile oils is hardly possible, but for all practical purposes they may be defined as odoriferous bodies of an oily nature obtained almost exclusively from vegetable sources, generally liquid (sometimes semi-solid or solid) at ordinary temperatures, and volatile without decomposition. This definition must be accepted within the ordinary limitations which are laid down by the common acceptation of the words, which will make themselves apparent in the sequel, and show that no more restricted definition is either advantageous or possible. Many essential oils, for example, are partially decomposed when distilled by themselves, and some even when steam distilled. 

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 ... 

The second approach to defining the absolute hardness rj has a companion parameter taken from density functional theory, called the electronic chemical potential p. The value of /i is essentially the same as the negative of X, as defined in Equation 3.1, and the value of 77 is essentially the same as in the more approximate definition in Equation 3.2. Tables 3.1-3.5 record some useful values for radicals, molecules and ions based on this definition. 

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. 

For periodic systems, an ad hoc partitioning of their absolute hardnesses into atomic contributions results in the definition of reactivity indices for such extended compounds [205] which proves useful in order to understand the chemical behavior of solid-state materials [206]. For example, the differing reactivities of various polymorphs of lithium aluminate may be rationalized in terms of their acid-base behavior [207], and the quantum-chemical explanation is in accordance with the principle of Le Chatelier. 

Usually, the hardness is seen only as a companion to electronegativity, i.e., associated with the second order effects, as its Parr-Pearson basic (3.3) and (4.251) definitions reflect. This is also the case when the absolute actual picture is employed, a statement supported also by the close quantitative atomic rff and r p scales as the representations from the Figure 4.13 indicate. Instead, when the absolute approach is performed the situation regarding both qualitative and quantitative absolute hardness scale completely changes. Actually, the //J/ values predict a smooth increase of the hardness effects paralleling those of compare the Figures 4.13 and 4.12, respectively. Remarkably, the linked behavior of with is achieved even their basic definitions, Eqs. (4.254) and (4.256), respectively, are not directly related, as there are, for instance, the definitions of... 

Parr and al. gave in 1988 atheoretical support to the absolute hardness. In the density functional theory two basic parameters were introduced. Any chemical system can be characterized by its chemical potential, p, and its absolute hardness, T]. The chemical potential measures the escaping tendency of an electronic cloud, while absolute hardness determines the resistance of the species to lose electrons. The exact definitions of these quantities are ... 

Another definition of aromaticity that does not depend explicitly on either experimental results or on comparison with reference compounds is derived from the concept of absolute hardness, 17, which is defined as one-half of the energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of a system (equation 4.70). According to Koopmans theorem, Ehomo is related to the ionization potential of the species, while Elumo is related to its electron affinity. A large gap between these two orbitals implies resistance to both oxidation and reduction, and low chemical reactivity is one of the defining characteristics of aromaticity. 

The absolute hardness is not to be confused with the Mulliken-Jaffe definition of electronegativity, given by Equation (14.25), where the electronegativity / is defined as the average of the IE and EA (for the valence electrons). The absolute hardness and... 

In the beginning when the HSAB principle was Just introduced, the meaning of hardness was not easy to understand. Certainly, it is not the hardness that measures the resistance against deformation. Then, what is it It was not un il the last several years that the real definition of absolute hardness received a quantitative and theoretical backing. ... 

Discussions about molecular diversity involve the concepts of similarity and dissimilarity and may be confusing as their meanings are content related. Similarity is in the eye of the beholder. Chemists may find similarity hard to define, but they generally are quick to identity it when they see it and at times are willing to debate the similarity of one structure to another. Similarity is not absolute, but relative to the space in which it is defined. In chemistry, this means the definitions must always be held in context to the property space used to define the structures. 

This definition of hardness is related to Mulliken s definition of electronegativity, called absolute electronegativity by Pearson ... 

GAP is an important stability index, a large GAP being related to the high stability of a molecule with its low reactivity in chemical reactions. It is an approximation of the lowest excitation energy of the molecule and can be used for the definition of absolute and activation hardness. 

The quantity 77 is called the absolute, or chemical, hardness. From the method of finite differences we obtain the operational definition of 77 ... 

This situation was rectified in 1954 when by international agreement the definition of the temperature scale was changed so that now the triple point of water is fixed by definition at 273.16 on the Kelvin scale. The Kelvin scale now has therefore one labeled fixed point instead of two unlabeled fixed points with 100 divisions in between. (Alternatively you could think of the new scale as having two fixed points, one at absolute zero and the other at the triple point of water, with 273.16 divisions in between, but since absolute zero is unattainable it is hardly a fixed point in the usual sense.)... 

---