低标度XYG3双杂化密度泛函的开发与测评

Development and Benchmark of Lower Scaling Doubly Hybrid Density Functional XYG3

以XYG3为代表的双杂化泛函代表了目前密度泛函方法的最高精度,可以胜任复杂化学环境中不同类型的相互作用的精准描述.然而由于XYG3采用二级微扰相关能(PT2)的形式引入未占轨道信息,其计算标度随体系尺寸呈5次方增长,同时内存需求呈4次方增长,这极大削弱了XYG3方法在复杂大体系研究中的可用性.本文介绍了一种结合局域密度拟合方法(Local Resolution-of-Identity,RI-LVL)与拉普拉斯变换(Laplace Transformation,LT)的低标度算法.采用MPI与OpenMP的混合并行设计,实现了可兼顾计算精度、计算效率和数值稳定性的低标度XYG3(LT-XYG3)计算功能.在一系列水簇及ISOL22测试集的测评中,LT-XYG3有效地降低了双杂化泛函的计算成本与内存消耗,展示了良好的可靠性与应用前景.

Doubly hybrid density functional XYG3 is one of the most accurate density functional approxima⁃tions currently available.XYG3 introduces the unoccupied orbital information in the form of the second-order perturbation theory(PT2),and therefore suffers the same computational costs as the standard PT2 method.The formal computational scaling of the canonical XYG3 is N to the fifth power[O(N^(5))],where N denotes the system size,and the memory consumption scales in the fourth power[O(N4)],which significantly limit the ap⁃plicability of XYG3 to complex large systems.In this work,we introduce a local-scaling XYG3 method,LT-XYG3,which is based on the local variant of Resolution-of-Identity technique(RI-LVL)and the Laplace-Transformed PT2(LT-PT2).The use of an OpenMP/MPI hybrid parallel design guarantees the parallel efficien⁃cy of LT-XYG3 for different kinds of chemical environment.Systematic benchmark on a serial of water clusters with various system sizes and the ISOL22 test set demonstrates that LT-XYG3 holds the same accuracy as the canonical XYG3 and brings a great advantage in both time and memory consumptions,suggesting a tremen⁃dous potential of applying lower scaling doubly hybrid density functionals to complex large systems.