Efficient periodic resolution-of-the-identity Hartree-Fock exchange method with k-point sampling and Gaussian basis sets

Simulations of condensed matter systems at the hybrid density functional theory (DFT) level pose significant computational challenges. The elevated costs arise from the non-local nature of the Hartree-Fock exchange (HFX) in conjunction with the necessity to approach the thermodynamic limit (TDL). In this work, we address these issues with the development of a new efficient method for the calculation of HFX in periodic systems, employing k-point sampling. We rely on a local atom-specific resolution-of-the-identity scheme, the use of atom-centered Gaussian type orbitals (GTOs), and the truncation of the Coulomb interaction to limit computational complexity. Our real-space approach exhibits a scaling that is at worst linear with the number of k-points. Issues related to basis set diffuseness are effectively addressed through the auxiliary density matrix method (ADMM). We report the implementation in the CP2K software package, as well as accuracy and performance benchmarks. The method demonstrates excellent agreement with equivalent Gamma-point supercell calculations in terms of relative energies and nuclear gradients. Good strong and weak scaling performances, as well as GPU acceleration, make this implementation a promising candidate for high-performance computing.

对凝聚态物质系统在混合密度泛函理论（DFT）水平上的模拟，对计算提出了重大挑战。这种高成本的产生源于哈特里-福克交换（HFX）的非局域特性以及逼近热力学极限（TDL）的必要性。在本研究中，我们通过开发一种针对周期性系统中HFX计算的新高效方法来应对这些问题，该方法采用k点采样。我们依赖局部原子特异的解算身份方案，使用原子中心的高斯型轨道（GTOs），以及对库仑相互作用的截断以限制计算复杂性。我们的空间方法展现出在最坏情况下与k点数量成线性关系的扩展性。通过辅助密度矩阵法（ADMM）有效解决了基组扩散相关的问题。我们报告了在CP2K软件包中的实现，以及准确性和性能基准。该方法在相对能量和核梯度方面与等效的伽马点超单元计算表现出极佳的一致性。良好的强、弱扩展性能以及GPU加速，使得这一实现成为高性能计算的潜在优秀候选。