Usually, density functional models are considered approximations to density functional theory, However, there is no systematic connection between the two, and this can make us doubt about a linkage. This attitude can be further enforced by the vagueness of the argumentation for using spin densities. Questioning the foundations of density functional models leads to a search for alternative explanations. Seeing them as using models for pair densities is one of them. Another is considering density functional approximations as a way to extrapolate results obtained in a model system to those of a corresponding physical one.
Using the local density approximation and the LYP, BLYP, and B3LYP functionals within Reference--State One--Particle Density--Matrix Theory
For closed-shell systems, the local density approximation (LDA) and the LYP, BLYP, and B3LYP functionals are shown to be compatible with reference-state one-particle density-matrix theory, where this recently introduced formalism is based on Brueckner-orbital theory and an energy functional that includes exact exchange and a non-universal correlation-energy functional. The method is demonstrated to reduce to a density functional theory when the exchange-correlation energy-functional has a simplified form, i.e., its integrand contains only the coordinates of two electron, say r1 and r2, and it …
Force Balance Approach for Advanced Approximations in Density Functional Theories
我们提出了一个系统的和建设性的方法来确定交换相关势的密度泛函理论，包括矢量势。该方法不依赖于能量或作用泛函。相反，它是基于电流量的运动方程（力平衡方程），是可行的，在基态和时间相关的设置。除了可微性和因果关系问题外，这避免了轨道相关泛函的优化有效势过程。我们为不同的密度泛函理论提供了简单的交换型近似，对于均匀系统和没有外部矢量势的交换仅局部密度和Slater X $α$近似。
