Density Functional Theory for Quantum Freezing: The Wigner Crystallization in A2d Electron System: Exploring the Thermodynamics and Crystal Structures of A2d Electron Systems using Density Functional Theory (Journal of Advances and Scholarly Researches in Allied Education, 2019)
The density functional theory (DFT) is based on an exact correspondence between equilibrium one-particle densities and external potentials [10]. If we denote by n(r) the one-particle density of the system, the system can be characterized by an appropriate thermodynamic potential which attains its minimum [11] value for the correct (equilibrium) density n0(r). For the study of crystallization, the relevant thermodynamic potentials are the grand potential Ω and the intrinsic Helmholtz free energy F, the latter being a unique functional of the one–particle density.