Density functional theory electronic chemical potential

Within density functional theory, the chemical potential and the hardness t] become partial derivatives of the system s energy E expressed as a functional of an external potential V(r), i.e., the nuclear conformation, and a function of the number of electrons N ... 

Besides the already mentioned Fukui function, there are a couple of other commonly used concepts which can be connected with Density Functional Theory (Chapter 6). The electronic chemical potential p is given as the first derivative of the energy with respect to the number of electrons, which in a finite difference version is given as half the sum of the ionization potential and the electron affinity. Except for a difference in sign, this is exactly the Mulliken definition of electronegativity. ... 

Experimental data as well as density functional theory show that the ground-state properties of solids depend primarily on the densities of the valence electrons. Therefore, pE may be considered to be the electronic chemical potential (Pearson, 1997). Since pE denotes the energy per mole of... 

The inherent problems associated with the computation of the properties of solids have been reduced by a computational technique called Density Functional Theory. This approach to the calculation of the properties of solids again stems from solid-state physics. In Hartree-Fock equations the N electrons need to be specified by 3/V variables, indicating the position of each electron in space. The density functional theory replaces these with just the electron density at a point, specified by just three variables. In the commonest formalism of the theory, due to Kohn and Sham, called the local density approximation (LDA), noninteracting electrons move in an effective potential that is described in terms of a uniform electron gas. Density functional theory is now widely used for many chemical calculations, including the stabilities and bulk properties of solids, as well as defect formation energies and configurations in materials such as silicon, GaN, and Agl. At present, the excited states of solids are not well treated in this way. 

It is however possible to obtain a physically meaningful representation of 0(r) for cations, in the context of density functional theory. The basic expression here is the fundamental stationary principle of DFT, which relates the electronic chemical potential ju, with the electrostatic potential and the functional derivatives of the kinetic and exchange-correlation contributions [20] ... 

In the last three decades, density functional theory (DFT) has been extensively used to generate what may be considered as a general approach to the description of chemical reactivity [1-5]. The concepts that emerge from this theory are response functions expressed basically in terms of derivatives of the total energy and of the electronic density with respect to the number of electrons and to the external potential. As such, they correspond to conceptually simple, but at the same time, chemically meaningful quantities. 

Global hardness. The partial charge concept helps the chemist to visualize within a molecule or a network, how the electronic density changes as a function of the spatial location of the various atomic constituents. Another useful information for chemical reactivity would be to visualize where the electronic chemical potential variation should be the largest or the lowest. Such a parameter is called a frontier index and may be defined in density-functional theory as f = dQHOMO/LUMO N (16). Point-charge approximation of this relation shows that each atom of a chemical compound should have a frontier index fj such that (17) ... 

E. J. Baerends, O. V. Gritsenko, and R. van Leeuwen, in Chemical Applications of Density Functional Theory, B. B. Laird, R. B. Ross, and T. Ziegler, Eds., American Chemical Society, Washington, DC, 1996, pp. 20-41. Effective One-Electron Potential in the Kohn-Sham Molecular Orbital Theory. 

The electron-transfer reactivities are defined as derivatives of the electron-density p(r) with respect to total electron number Jf, Ufr), or chemical potential p, s r). The treatment of JT as a continuous variable [8-12] is justified by reference to the ensemble formulation of density-functional theory [8,18] and, in consequence, of the Kohn-Sham theory. We show in Sect. 4, in previously unpublished work [42], that this ensemble formulation yields either vanishing or infinite local and global softnesses for localized systems with... 

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