Scaling limits of the electronic Schrödinger equation fordiatomic molecules: Asymptotic prediction of correlation structure,potential energy curves, and symmetry quantum numbers

双原子分子电子薛定谔方程的标度极限：相关结构、势能曲线和对称量子数的渐近预测

• 批准号: 234732874
• 负责人: Professor Dr. Gero Friesecke
• 金额: --
• 依托单位: Lehrstuhl für Analysis (M7)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2017-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/234732874?language=en
• 关键词: Scaling; limits; electronic; Schr; dinger

The electronic Schrödinger equation plays a central role in molecular physics and quantum chemistry as it provides a quantitative and chemically specific description of a molecule's electronic structure. However, rigorous mathematical work on this equation has hitherto focused on qualitative, universal aspects. Here we will develop methods for the rigorous extraction of quantitative and chemically specific predictions in natural scaling limits, (i) the limit of high nuclear charge at fixed electron number and (ii) the double-limit of high nuclear charge and large interatomic distance. Explicit asymptotic results on correlation structure, potential energy curves, and symmetry quantum numbers will be worked out for the homonuclear dimer series H_2, He_2, Li_2, Be_2, B_2, C_2, N_2, O_2, F_2, Ne_2. This will require generalizing the functional-analytic and symmetry-reduction methods of Friesecke and Goddard [1, 2] from atoms to dimers, careful use of the theory of the single-electron Schrödinger equation for diatomic molecules, and utilization of symbolic computer packages such as Mathematics to handle cases with six or more electrons.The asymptotic results will be compared to experimental data, to the semi-empirical picture of Hund-Mulliken molecular orbital theory (we expect, based on analogous findings for atoms [1, 2], that asymptotic ground states in regime (ii) are similar to this picture), and state-of-the-art computational methods (both of wave function and density functional type). The envisioned results will establish, for the first time, a rigorous link between the quantitative precision of the Schrödinger equation and semi-empirical concepts of chemical bonding, elucidate mathematically the mechanisms leading to the high chemical specificity of bond formation, and provide rare benchmark correlated many-electron data for the design and validation of computational methods.

电子薛定谔方程在分子物理和量子化学中起着核心作用，因为它提供了分子电子结构的定量和化学特定描述。然而，迄今为止，关于这个方程的严格的数学工作集中在定性的、普遍的方面。在这里，我们将开发的方法，严格提取定量和化学的具体预测在自然标度限制，（i）高核电荷的限制在固定的电子数和（ii）高核电荷和大原子间距离的双重限制。对H_2，He_2，Li_2，Be_2，B_2，C_2，N_2，O_2，F_2，Ne_2系列均二聚体，给出了关联结构、势能曲线和对称量子数的显式渐近结果。这就需要将Friesecke和戈达德[1，2]的泛函分析和量子化方法从原子推广到二聚体，仔细使用双原子分子的单电子薛定谔方程理论，并利用数学等符号计算机软件包来处理六个或更多电子的情况。渐近结果将与实验数据进行比较，Hund-Mulliken分子轨道理论的半经验图像（我们期望，基于原子的类似发现[1，2]，在制度（ii）中的渐近基态与此图像相似），以及最先进的计算方法（波函数和密度泛函类型）。设想的结果将首次建立薛定谔方程的定量精度与化学键合的半经验概念之间的严格联系，从数学上阐明导致键形成的高化学特异性的机制，并为计算方法的设计和验证提供罕见的基准相关多电子数据。

项目成果

Density-Functional Theory for Strongly Correlated Bosonic and Fermionic Ultracold Dipolar and Ionic Gases.

强相关玻色子和费米子超冷偶极和离子气体的密度泛函理论

• DOI: 10.1103/physrevlett.115.033006
• 发表时间: 2015
• 期刊: Physical review letters
• 影响因子: 8.6
• 作者: Francesc Malet;André Mirtschink;Christian B. Mendl;Johannes Bjerlin;Elife Ö. Karabulut;Stephanie M. Reimann;Paola Gori-Giorgi
• 通讯作者: Paola Gori-Giorgi

N-density representability and the optimal transport limit of the Hohenberg-Kohn functional.

Hohenberg-Kohn 泛函的 N 密度表示性和最佳输运极限

• DOI: 10.1063/1.4821351
• 发表时间: 2013
• 期刊: The Journal of chemical physics
• 作者: Gero Friesecke;Christian B. Mendl;Brendan Pass;Codina Cotar;Claudia Klüppelberg
• 通讯作者: Claudia Klüppelberg