低标度XYG3双杂化密度泛函的开发与测评

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.

Development and Benchmark of Lower Scaling Doubly Hybrid Density Functional XYG3

Doubly hybrid density functional XYG3 is one of the most accurate density functional approximations 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\left(N^{\mathrm{5}}\right)］， where N denotes the system size， and the memory consumption scales in the fourth power［O\left(N^{\mathrm{4}}\right)］， which significantly limit the applicability 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 efficiency 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 tremendous potential of applying lower scaling doubly hybrid density functionals to complex large systems.