Electronic chemical potential states

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 electronic chemical potential is constant for a system in its electronic ground state, which led Parr et al. to associate the chemical potential with minus one times the electronegativity, since the electronegativity is also equalized in the ground state [7]. This equalization of the chemical potential also suggests that electronic structure theory can be expressed in a way that resembles classical thermodynamics. Ergo, Parr et al. wrote the total differential of the energy as... 

The paper of Parr and Bartolotti is prescient in many ways [1], It defines the shape function and describes its meaning. It notes the previously stated link to Levy s constrained search. It establishes the importance of the shape function in resolving ambiguous functional derivatives in the DFT approach to chemical reactivity—the subdiscipline of DFT that Parr has recently begun to call chemical DFT [6-9]. Indeed, until the recent resurgence of interest in the shape function, the Parr-Bartolotti paper was usually cited because of its elegant and incisive analysis of the electronic chemical potential [10],... 

To conclude, in a BF mixture model of superconductivity we have extracted an analytic relation between a BEC Tc and the electron chemical potential that varies with the degree of CP formation. The BEC Tc formula contains contributions from both varying electron number as well as from the redistribution of ffee-electron states caused by boson formation. As a result Tc vs X exhibits non-monotonic behavior, so that superconductivity emerges only for a limited range of coupling-parameter and doping-concentration values. 

From the theoretical point of view, the electrophilicity concept has been recently discussed in terms of global reactivity indexes defined for the ground states of atoms and molecules by Roy et al.18 19. In the context of the conceptual density functional theory (DFT), a global electrophilicity index defined in terms of the electronic chemical potential and the global hardness was proposed by Maynard et al.20 in their study of reactivity of the HIV-1 nucleocapsid protein p7 zinc finger domains. Recently, Parr, Szentp ly and Liu proposed a formal derivation of the electrophilicity, co, from a second-order energy expression developed in terms of the variation in the number of electrons.21... 

At zero pressure and temperature, we also have pt = (dE/dN). In this case N is the number of molecules in the system, and pr is the ordinary chemical potential of thermodynamics. The electronic chemical potential of a single molecule plays somewhat the same role. At equilibrium p must be constant everywhere, and p will be the correct electron density for the ground state. The quantity x is called the absolute electronegativity, for reasons that will become clear. ... 

There is no change in the electronic chemical potential, but the hardness of the excited state is less than that of the ground state. 

Finally, it turns out that the new definitions of electronic chemical potential, //, and hardness, rj, in DFT are actually old concepts in both solid-state physics and electrochemistry. In these fields it is often convenient to think of solids as havng electrons which are relatively free to move about, and which are independent components rather than appendages of the atoms. 

Which fundamental properties X could we be interested in Realizing that the electron density distribution function contains all the information about the system in the ground state (Hohenberg and Kohn theorems), its response to several perturbations is certainly of fundamental importance. Other properties also provide valuable information, such as the energy and the electronic chemical potential of the system. We will consider all of these and try to find analytical expressions for their response to, or resistance against, changes in N or v(r). 

This definition introduces electronegativity as an electronic chemical potential similar to a thermodynamic chemical potential in any system of atoms in a nonequilibrium state, there must be a flux of electronic density from the regions of high potential to the regions of lower potential. 

Figure 5.18. Schematic representation of the density of states N(E) in the conduction band and of the definitions of work function d>, chemical potential of electrons p, electrochemical potential of electrons or Fermi level p, surface potential x> Galvani (or inner) potential

Though we and others (27-29) have demonstrated the utility and the improved sensitivity of the peroxyoxalate chemiluminescence method for analyte detection in RP-HPLC separations for appropriate substrates, a substantial area for Improvement and refinement of the technique remains. We have shown that the reactions of hydrogen peroxide and oxalate esters yield a very complex array of reactive intermediates, some of which activate the fluorophor to its fluorescent state. The mechanism for the ester reaction as well as the process for conversion of the chemical potential energy into electronic (excited state) energy remain to be detailed. Finally, the refinement of the technique for routine application of this sensitive method, including the optimization of the effi-ciencies for each of the contributing factors, is currently a major effort in the Center for Bioanalytical Research. 

---