密度泛函理论中紧致定域轨道的鲁棒线性标度优化
Robust linear-scaling optimization of compact localized orbitals in density functional theory
摘要：
在密度泛函理论（DFT）中，严格按照基函数的局部子集展开的紧凑单电子轨道的局部性可以用来实现计算时间随系统大小的线性增长，这在大规模模拟中至关重要。然而，尽管紧凑轨道的优点，实际的基于轨道的线性标度DFT方法的发展一直受到阻碍，因为一个紧凑的表示的电子基态是很难找到的变分优化程序。在这项工作中，我们表明，紧凑轨道的缓慢和不稳定的优化源于紧凑轨道的几乎不变的混合，大部分但不完全本地化在相同的基函数的子集。我们还构造了一个近似的海森函数，可以用来识别有问题的近不变模式，并沿着它们进行变分优化，而不会在计算的能量中引入显著的误差。这使我们能够创建一个线性标度的DFT方法与低的计算开销，被证明是有效的和准确的固定核计算和半导体和绝缘体的分子动力学模拟。
英文摘要：
Locality of compact one-electron orbitals expanded strictly in terms of local subsets of basis functions can be exploited in density functional theory (DFT) to achieve linear growth of computation time with systems size, crucial in large-scale simulations. However, despite advantages of compact orbitals the development of practical orbital-based linear-scaling DFT methods has long been hindered because a compact representation of the electronic ground state is difficult to find in a variational optimization procedure. In this work, we show that the slow and unstable optimization of compact orbitals originates from the nearly-invariant mixing of compact orbitals that are mostly but not completely localized within the same subsets of basis functions. We also construct an approximate Hessian that can be used to identify the problematic nearly-invariant modes and obviate the variational optimization along them without introducing significant errors into the computed energies. This enables us to create a linear-scaling DFT method with a low computational overhead that is demonstrated to be efficient and accurate in fixed-nuclei calculations and molecular dynamics simulations of semiconductors and insulators.
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