It consists of both kinetic (describing motion) and potential energy parts. At very high temperatures, the Debye Hukel classical plasma methods can be used. ThomasFermi Approximation and Basics of the Density Functional Theory As stated at the beginning of section 2.7 the total energy is a key function describ-ing the basic physical and chemical properties of materials: the ground state. Such electron fluids can be used to model dense, finite-temperature plasmas. If the temperature is greater than 12 eV, the electron liquid becomes partially degenerate, since the states above the Fermi energy begin to get occupied. For a metal like Aluminum, E F is of the order of 12 electron Volts. (b) Integral Equation methods, e.g., the CHNC, an acronym for the classical-map hyper-netted-chain method, or the Fermi hyper-netted-chain method.īecause of Fermi statistics, the electrons in the electron liquid fill up to an energy level known as the Fermi energy E F. A proper discussion of strongly interacting regimes require the use of methods like: At high temperatures, this becomes the Debye-Hukel length. The simplest approximation to the screening of the Coulomb interaction 1 / r by the other electrons is given by the form e x p( − r / r T F) / r, where r T F is known as the Thomas-Fermi screening length. Using atomically resolved scanning tunneling microscopy and spectroscopy, the screening length is. However, because of the screening of the Coulomb interaction by other electrons (thus weakening it), a free-electron-like model known as the Landau Fermi-Liquid theory works to some extent. band bending and explain it by ThomasFermi screening. Most common metals are in the regime 2 < r s < 6 and hence the metallic regime is poorly described by perturbation theory. This is known as the Coupling constant of the problem. The Coulomb energy goes as 1 / r s, and hence we see that the ratio (potential Energy) / (Kinetic Energy) = r s. The kinetic energy goes as, in atomic units, at T=0. It is clear that at high density r s tends to zero. This radius is denoted by r s, and is known as the Wigner-Seitz radius.
If the number of particles per unit volume (in 3D, or per unit area in 2D) is n, then it is customary to define the radius of the sphere (or disc in 2D) which contains one particle. In principle, however, the Thomas-Fermi screening length depends on the valence electron density VASP determines this parameter from the number of valence electrons (read from the POTCAR file) and the volume and writes the corresponding. At zero temperature, this happens if the density is very high. For typical semiconductors, a Thomas-Fermi screening length of about 1.8 Å-1 yields reasonable band gaps.
The weakly interacting regime of densities is known as the electron gas.