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Title: Revisiting the definition of the electronic chemical potential, chemical hardness, and softness at finite temperatures

We extend the definition of the electronic chemical potential (μ{sub e}) and chemical hardness (η{sub e}) to finite temperatures by considering a reactive chemical species as a true open system to the exchange of electrons, working exclusively within the framework of the grand canonical ensemble. As in the zero temperature derivation of these descriptors, the response of a chemical reagent to electron-transfer is determined by the response of the (average) electronic energy of the system, and not by intrinsic thermodynamic properties like the chemical potential of the electron-reservoir which is, in general, different from the electronic chemical potential, μ{sub e}. Although the dependence of the electronic energy on electron number qualitatively resembles the piecewise-continuous straight-line profile for low electronic temperatures (up to ca. 5000 K), the introduction of the temperature as a free variable smoothens this profile, so that derivatives (of all orders) of the average electronic energy with respect to the average electron number exist and can be evaluated analytically. Assuming a three-state ensemble, well-known results for the electronic chemical potential at negative (−I), positive (−A), and zero values of the fractional charge (−(I + A)/2) are recovered. Similarly, in the zero temperature limit, the chemical hardness is formallymore » expressed as a Dirac delta function in the particle number and satisfies the well-known reciprocity relation with the global softness.« less
Authors:
 [1] ;  [2] ;  [1] ;  [3] ;  [4]
  1. Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México D. F. 09340 (Mexico)
  2. (Canada)
  3. Department of Chemistry, McMaster University, Hamilton, Ontario L8S 4M1 (Canada)
  4. Departamento de Química, Centro de Investigación y de Estudios Avanzados (Cinvestav), Av. Instituto Politécnico Nacional 2508, México D. F. 07360 (Mexico)
Publication Date:
OSTI Identifier:
22493120
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 143; Journal Issue: 15; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; DELTA FUNCTION; ELECTRON TRANSFER; ELECTRONS; HARDNESS; PARTICLES; THERMODYNAMIC PROPERTIES