Symmetry Constraints in the Ionization Potentials and on the Formulation of the Hohenberg-Kohn-Sham Theory

摘要: Density functional-theory was given a formal structure with the Hohenberg-Kohn1 (HK) theorems and succesful practical procedure Kohn-Sham2 (KS) scheme to construct density function as linear combinations of squares auxiliary functions ψi symmetry i weight ci. The obey Schrodinger like wave equation eigenvalue ei. overall system has be consistent “occupation” i-th “states”. In principle set {i} should complete total energy E[ρ;{ci,N}] minimized respect parameters {ci,N}, then HK-KS equations really written δE[ρ;{ci,N}] = 0 \( \int {\rho d\tau =} {\sum\nolimits_i {{c_i}{{\left({{\psi_i}} \right)}^2}}} \) dτ N, allowing for fractional Also ionization potential μi, (with δci (i) ≈ 1) is by $$- \mu _i \sum\nolimits_{\rm{i}} {\frac{{\partial E}}{{\partial c_i }}} {\rm{ }}\partial c_i^{\left( \right)} + }}\sum\nolimits_{{\rm{n > 1}}} {\frac{1}{{{\rm{n!}}}}} \sum\nolimits_{j,k, \cdots } {\left( {\partial ^n E/\left( \partial c_k \right)\left( c_k^{\left( \right)}$$ with \(\sum\nolimits_j c_j^{(i)} 1}\). this way μi − ei Δμi there will μk ≤ μi≠k, corresponding least removal one electron. Examples results are discussed shown. internal an important (hidden or explicit) part theory when properly considered, have always compared reasonable well experiment (see Keller, Amador de Teresa3, also Trickey4).