Absolute hardness: companion parameter to absolute electronegativity
For neutral and charged species, atomic and molecular, a property called absolute hardness eta is defined. Let E(N) be a ground-state electronic energy as a function of the number of electrons N. As is well-known, the derivative of E(N) with respect to N, keeping nuclear charges Z fixed, is the chemical potential ..mu.. or the negative of the absolute electronegativity chi: ..mu.. = (deltaE/deltaN)/sub Z/ = /sup -/chi. The corresponding second derivative is hardness: 2eta = (delta..mu../deltaN)/sub Z/ = (deltachi/deltaN)/sub Z/ = (delta/sup 2/E/deltaN/sup 2/)/sub Z/. Operational definitions of chi and eta are provided by the finite difference formulas (the first due to Mulliken) chi = 1/2(I+A), eta = 1/2(I-A), where I and A are the ionization potential and electron affinity of the species in question. Softness is the opposite of hardness: a low value of eta means high softness. The principle of hard and soft acids and bases is derived theoretically by making use of the hypothesis that extra stability attends bonding of A to B when the ionization potentials of A and B in the molecule (after charge transfer) are the same. For bases B, hardness is identified as the hardness of the species B/sup +/. Tables of absolute hardness are given for a number of free atoms, Lewis acids, and Lewis bases, and the values are found to agree well with chemical facts. 1 figure, 3 tables.
- Research Organization:
- Univ. of North Carolina, Chapel Hill
- DOE Contract Number:
- AM03-76SF00034
- OSTI ID:
- 6972000
- Journal Information:
- J. Am. Chem. Soc.; (United States), Vol. 105:26
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
ORGANIC
PHYSICAL AND ANALYTICAL CHEMISTRY
ATOMS
ELECTRONEGATIVITY
HARDNESS
LEWIS ACIDS
LEWIS BASES
AFFINITY
CALCULATION METHODS
COMPARATIVE EVALUATIONS
ELECTRONIC STRUCTURE
IONIZATION POTENTIAL
MATHEMATICAL MODELS
REVIEWS
BASES
DOCUMENT TYPES
HYDROGEN COMPOUNDS
INORGANIC ACIDS
MECHANICAL PROPERTIES
400201* - Chemical & Physicochemical Properties