Ricci Matteo, Silvestrelli Pier Luigi, Dobson John F, Ambrosetti Alberto
Dipartimento di Fisica e Astronomia, Università degli Studi di Padova, Via Francesco Marzolo 8, 35131 Padova, Italy.
Nanoscale Science and Technology Centre, Griffith University, Nathan, Queensland 4111, Australia.
J Phys Chem Lett. 2022 Sep 8;13(35):8298-8304. doi: 10.1021/acs.jpclett.2c02197. Epub 2022 Aug 29.
Using a sum-rule approach, we develop an exact theoretical framework for polarizability and asymptotic van der Waals correlation energy functionals of small isolated objects. The functionals require only monomer ground-state properties as input. Functional evaluation proceeds via solution of a single position-space differential equation, without the usual summations over excited states or frequency integrations. Explicit functional forms are reported for reference physical systems, including atomic hydrogen and single electrons subject to harmonic confinement, and immersed in a spherical-well potential. A direct comparison to the popular Vydrov-van Voorhis density functional shows that the best performance is obtained when density decay occurs at atomic scales. The adopted sum-rule approach implies general validity of our theory, enabling exact benchmarking of van der Waals density functionals and direct inspection of the subtle long-range correlation effects that constitute a major challenge for approximate (semi)local density functionals.
采用求和规则方法，我们为小的孤立物体的极化率和渐近范德瓦尔斯相关能量泛函建立了一个精确的理论框架。这些泛函仅需要单体基态性质作为输入。泛函评估通过求解单个位置空间微分方程进行，无需对激发态进行通常的求和或频率积分。报告了参考物理系统的显式泛函形式，包括处于谐波限制下并沉浸在球形阱势中的氢原子和单电子。与流行的Vydrov-van Voorhis密度泛函的直接比较表明，当密度在原子尺度上衰减时可获得最佳性能。所采用的求和规则方法意味着我们理论的普遍有效性，能够对范德瓦尔斯密度泛函进行精确基准测试，并直接检查构成近似（半）局域密度泛函主要挑战的微妙长程相关效应。
