Title: Graph-based Quantum Response Theory and Shadow Born-Oppenheimer Molecular Dynamics Show Chinese title

Title: 基于图的量子响应理论和影子 Born-Oppenheimer 分子动力学

Abstract: Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations is adapted to the most recent shadow potential formulations of extended Lagrangian Born-Oppenheimer molecular dynamics, including fractional molecular-orbital occupation numbers, which enables stable simulations of sensitive complex chemical systems with unsteady charge solutions. The proposed formulation includes a preconditioned Krylov subspace approximation for the integration of the extended electronic degrees of freedom, which requires quantum response calculations for electronic states with fractional occupation numbers. For the response calculations we introduce a graph-based canonical quantum perturbation theory that can be performed with the same natural parallelism and linear scaling complexity as the graph-based electronic structure calculations for the unperturbed ground state. The proposed techniques are particularly well-suited for semi-empirical electronic structure theory and the methods are demonstrated using self-consistent charge density-functional tight-binding (SCC-DFTB) theory, both for the acceleration of self-consistent field calculations and for quantum molecular dynamics simulations. The graph-based techniques combined with the semi-empirical theory enable stable simulations of large, complex chemical systems, including tens-of-thousands of atoms. Show Chinese abstract

Abstract: 基于图的线性尺度电子结构理论用于量子力学分子动力学模拟，被适应于扩展拉格朗日玻恩-奥本海默分子动力学的最新影子势能公式，包括分数分子轨道占据数，这使得对敏感复杂化学系统进行不稳定电荷解的稳定模拟成为可能。 所提出的公式包括对扩展电子自由度积分的预条件Krylov子空间近似，这需要对具有分数占据数的电子态进行量子响应计算。 对于响应计算，我们引入了一种基于图的规范量子微扰理论，该理论可以以与无扰基态的基于图的电子结构计算相同的自然并行性和线性尺度复杂度进行。 所提出的技巧特别适合半经验电子结构理论，这些方法通过自洽电荷密度泛函紧束缚（SCC-DFTB）理论进行了演示，既用于自洽场计算的加速，也用于量子分子动力学模拟。 基于图的技术结合半经验理论能够对大型复杂化学系统进行稳定模拟，包括数以万计的原子。