标题： 球面傅里叶变换中的信息编码 显示英文标题

标题： Information encoding in spherical DFT

摘要： 球形密度泛函理论（DFT）[Theophilou, J. Chem. Phys. 149, 074104 (2018)] 是经典DFT定理的一种重新表述，其中多电子系统的总密度的作用被一组球形化密度所取代，这些球形化密度是通过在每个原子核周围对总电子密度进行球面对平均而构建的。在Hohenberg-Kohn DFT及其约束搜索推广中，电子密度足以重建组成原子的空间位置和原子序数，从而确定外部势。然而，球形DFT的原始证明需要知道每个球形化密度的起源原子位置，除了球形化密度集合本身之外。在本工作中，我们利用几何代数中的形式结果——特别是距离几何学这一子领域——来证明，这种空间信息已经编码在球形化密度的集合中，不需要独立指定。因此，球形化密度集合唯一地确定了系统的总外部势，正如Hohenberg-Kohn DFT中那样。这一理论结果通过LiF和甘氨酸（最简单的氨基酸）的数值例子进行了说明。除了为球形DFT建立坚实的实践基础外，扩展定理还为在设计原子模拟的经典或机器学习势能时使用球形化原子基态密度——而不是取向依赖的基函数——提供了依据。 显示英文摘要

摘要： Spherical density functional theory (DFT) [Theophilou, J. Chem. Phys. 149, 074104 (2018)] is a reformulation of the classic theorems of DFT, in which the role of the total density of a many-electron system is replaced by a set of sphericalized densities, constructed by spherically-averaging the total electron density about each atomic nucleus. In Hohenberg-Kohn DFT and its constrained-search generalization, the electron density suffices to reconstruct the spatial locations and atomic numbers of the constituent atoms, and thus the external potential. However, the original proofs of spherical DFT require knowledge of the atomic locations at which each sphericalized density originates, in addition to the set of sphericalized densities themselves. In the present work, we utilize formal results from geometric algebra -- in particular, the subfield of distance geometry -- to show that this spatial information is encoded within the ensemble of sphericalized densities themselves, and does not require independent specification. Consequently, the set of sphericalized densities uniquely determines the total external potential of the system, exactly as in Hohenberg-Kohn DFT. This theoretical result is illustrated through numerical examples for LiF and for glycine, the simplest amino acid. In addition to establishing a sound practical foundation for spherical DFT, the extended theorem provides a rationale for the use of sphericalized atomic basis densities -- rather than orientation-dependent basis functions -- when designing classical or machine-learned potentials for atomistic simulation.