Interatomic Potentials in Metals Sample Clauses

Interatomic Potentials in Metals. ‌ The dynamics of the ions in a metal are conventionally assumed to be classical [113] whereas a quantum mechanical description is necessary for the electrons [15–17]. In a QBIP representation, we make the assumption that the electrons move rigidly with the ions and, as a result, we only need to perform a single quantum mechanical calculation for the electrons. In this picture, the ions experience an effective screened Coulomb interaction, due to the quantum-mechanical electrons, which is not rescreened during ionic motion. This is the approximation of neutral pseudoatoms [114]. Pseudoatoms behave rather differently to normal atoms with the main distinction being that they cannot be polarised [13]. The central quantity in DFT quantum mechanics is the electron density n(r) [46] and, without approximation, the DFT total energy can be written as Etot ({R}) = 2 + Eion−el [n (r) , {R}] (1.1) 1 Σ′ ZiZje2 ij R ij where {R} denotes the set of all ionic positions, Zi is the atomic number of the atom i, Rij is the interatomic separation (where the prime over the summation refers to the exclusion of the i = j term) and Eion−el is an unknown energy functional describing the ion-electron and electron-electron interaction, dependent on both the electron den- sity and ionic positions. The ion-electron energy functional is an extremely complex many-body function of which only a small contribution will be pairwise. This contri- bution will act so as to screen the bare ionic Coulomb interaction. We may consider a general cluster expansion of Eion−el, in which case we get triplet v3, quadruplet v4 and higher order interaction terms, in addition to a many-body embedding contribu- tion and pairwise term. These interaction terms can either be derived as in the GPT [10, 99, 115, 116], or they can be assumed in a parameterised form as in empirical interatomic potentials [117–122]. The simplest representation of Eq.(1.1) is that of a pure pair potential v2, which was a viewpoint advocated in metals by early practitioners of empirical interatomic potentials [112, 123–126]. The cohesive energy in such a representation is taken with respect to the individual atomic total energies N tot ij Ecoh ({R}) = Etot ({R}) − E = Σ v2 (R ij