X-ray Structural Laboratory, A. N. Nesmeyanov Institute of Organoelement Compounds RAS, 119991 Moscow, Russian Federation.
N. D. Zelinsky Institute of Organic Chemistry RAS, 119991 Moscow, Russian Federation.
Science. 2017 Jan 6;355(6320):49-52. doi: 10.1126/science.aah5975.
The theorems at the core of density functional theory (DFT) state that the energy of a many-electron system in its ground state is fully defined by its electron density distribution. This connection is made via the exact functional for the energy, which minimizes at the exact density. For years, DFT development focused on energies, implicitly assuming that functionals producing better energies become better approximations of the exact functional. We examined the other side of the coin: the energy-minimizing electron densities for atomic species, as produced by 128 historical and modern DFT functionals. We found that these densities became closer to the exact ones, reflecting theoretical advances, until the early 2000s, when this trend was reversed by unconstrained functionals sacrificing physical rigor for the flexibility of empirical fitting.
密度泛函理论（DFT）的核心定理表明，处于基态的多电子系统的能量完全由其电子密度分布决定。这种联系是通过能量的精确泛函建立的，该泛函在精确密度处最小化。多年来，DFT 的发展集中在能量上，隐含地假设产生更好能量的泛函会成为精确泛函的更好近似。我们研究了另一面：由 128 种历史上和现代的 DFT 泛函产生的原子物种的能量最小化电子密度。我们发现，这些密度越来越接近精确密度，反映了理论的进步，直到 21 世纪初，这种趋势被无约束泛函逆转，这些泛函为了经验拟合的灵活性而牺牲了物理严谨性。
