用平行输运规范和自适应压缩交换公式的快速实时含时混合泛函计算
Fast real-time time-dependent hybrid functional calculations with the parallel transport gauge and the adaptively compressed exchange formulation
摘要：
提出了一种新的方法来加速实时相关的密度泛函理论（rt-TDDFT）计算与混合交换相关泛函。对于大基组，大规模计算的计算瓶颈是Fock交换算符在含时轨道上的应用。我们的主要目标是减少应用Fock交换算子的频率，而不损失精度。我们实现这一点，结合最近开发的并行传输（PT）规范形式主义和自适应压缩交换算子（ACE）形式主义。PT规在所有规的选择中产生最慢的可能动态。当与隐式时间积分器（如Crank-Nicolson（CN）方案）耦合时，所得到的PT-CN方案可以将时间步长从亚阿秒显著增加到10-100阿秒。在每个时间步$t_{n}$，PT-CN需要在时间$t_{n+1}$的轨道的自洽解。我们使用ACE延迟更新的Fock交换算子在这个非线性系统，同时保持相同的自洽解决方案。我们通过计算苯分子的吸收光谱和体硅系统对超快激光脉冲的响应，使用平面波基组和HSE泛函来验证所得到的PT-CN-ACE方法的性能。我们报告的PT-CN-ACE方法的硅系统的强和弱标度范围从32到1024个原子，高达2048计算核心。与四阶龙格-库塔方法（RK 4）等标准显式时间积分器相比，PT-CN-ACE可以将Fock交换算子的应用减少近70倍，从而将1024个原子系统的总挂钟时间减少46倍。因此，我们的工作使混合功能的rt-TDDFT计算进行常规的大基组的第一次。
英文摘要：
We present a new method to accelerate real time-time dependent density functional theory (rt-TDDFT) calculations with hybrid exchange-correlation functionals. For large basis set, the computational bottleneck for large scale calculations is the application of the Fock exchange operator to the time-dependent orbitals. Our main goal is to reduce the frequency of applying the Fock exchange operator, without loss of accuracy. We achieve this by combining the recently developed parallel transport (PT) gauge formalism and the adaptively compressed exchange operator (ACE) formalism. The PT gauge yields the slowest possible dynamics among all choices of gauge. When coupled with implicit time integrators such as the Crank-Nicolson (CN) scheme, the resulting PT-CN scheme can significantly increase the time step from sub-attoseconds to 10-100 attoseconds. At each time step $t_{n}$, PT-CN requires the self-consistent solution of the orbitals at time $t_{n+1}$. We use ACE to delay the update of the Fock exchange operator in this nonlinear system, while maintaining the same self-consistent solution. We verify the performance of the resulting PT-CN-ACE method by computing the absorption spectrum of a benzene molecule and the response of bulk silicon systems to an ultrafast laser pulse, using the planewave basis set and the HSE functional. We report the strong and weak scaling of the PT-CN-ACE method for silicon systems ranging from 32 to 1024 atoms, with up to 2048 computational cores. Compared to standard explicit time integrators such as the 4th order Runge-Kutta method (RK4), the PT-CN-ACE can reduce the Fock exchange operator application by nearly 70 times, thus reduce the overall wall clock time time by 46 times for the system with 1024 atoms. Hence our work enables hybrid functional rt-TDDFT calculations to be routinely performed with a large basis set for the first time.
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