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| Home > JCE Print > Journal of Chemical Education > Issues >
1999
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February
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Research: Science and Education
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Maximum Chemical and Physical Hardness
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Ralph G. Pearson
University of California at Santa Barbara, Department of Chemistry, Santa Barbara, CA 93106
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February 1999
Vol. 76 No. 2
p. 267
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| Abstract |
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Density functional theory (DFT) is briefly reviewed, especially concepts such as the electronic chemical potential and the hardness of the electron density function. There is much evidence, and a mathematical proof, that this chemical hardness is a maximum for an equilibrium system. The proof is based on a combination of statistical mechanics, the fluctuation-dissipation theorem, and correlation functions. In MO theory the principle of maximum hardness (PMH) corresponds to a maximum difference in the orbital energies of the HOMO and the LUMO, in most cases. Other kinds of evidence for the PMH are presented, along with some of the consequences.
Physical hardness concerns changes in shape and volume of a solid sample. Changes in shape are most important in engineering and materials applications. Changes in volume, however, are more fundamental and easier to visualize. The physical hardness, with respect to volume, is given by BV0, where B is the bulk modulus and V0 is the equilibrium molar volume per atom. A table of hardness values for various solids is given.
Applying the same proof as for chemical hardness, it is shown that BV0 is a maximum for the equilibrium system. This principle of maximum physical hardness (PMPH) enables us to calculate the Gruneisen constant and the rate of change of the compressibility with pressure for certain simple solids.
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| More Information |
 Citation |
Pearson, Ralph G. J. Chem. Educ. 1999 76 267.
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Keywords |
Physical Chemistry; Theoretical Chemistry; Statistical Mechanics; Solid-State Chemistry; compressibility; fluctuation-dissipation
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History |
Created:
Last Updated: |
June 15, 1999
June 22, 2005
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| Home > JCE Print > Journal of Chemical Education > Issues >
1999
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February
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267
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