通过范围分离抑制扩散蒙特卡罗中的固定节点误差
Taming the fixed-node error in diffusion Monte Carlo via range separation
摘要：
将密度泛函理论（DFT）和波函数理论（WFT）通过电子间库仑算符的值域分离（RS）相结合，得到了具有紧致多行列式试探波函数的精确的固定节点扩散蒙特卡罗（FN-DMC）能量.特别是，我们在这里结合了短程交换相关泛函的味道的选择配置相互作用（SCI）称为\emph{configuration interaction using a perturbative selection made iteratively}（CIPSI），一个计划，我们的标签RS-DFT-CIPSI。本研究的带回家的信息之一是，RS-DFT-CIPSI试验波函数产生更低的固定节点能量与更紧凑的多行列式扩展比CIPSI，特别是对于小的基组。实际上，由于RS-DFT-CIPSI的CIPSI分量从描述电子-电子聚结点周围的相关空穴的短程部分中解脱出来，因此与传统的CIPSI计算相比，达到给定精度所需的试验波函数中的行列式的数量显著减少。重要的是，通过进行各种数值实验，我们的证据表明，RS-DFT计划基本上扮演了一个简单的Jastrow因子的作用，通过模仿短程相关效应，从而避免了执行随机优化的负担。考虑到55原子化能量的高斯-1基准组的分子，我们表明，使用一个固定的值的$μ=0.5$ ~玻尔$^{-1}$提供了有效的误差抵消以及紧凑的试验波函数，使本方法的一个很好的候选人的准确描述大型化学系统。
英文摘要：
By combining density-functional theory (DFT) and wave function theory (WFT) via the range separation (RS) of the interelectronic Coulomb operator, we obtain accurate fixed-node diffusion Monte Carlo (FN-DMC) energies with compact multi-determinant trial wave functions. In particular, we combine here short-range exchange-correlation functionals with a flavor of selected configuration interaction (SCI) known as \emph{configuration interaction using a perturbative selection made iteratively} (CIPSI), a scheme that we label RS-DFT-CIPSI. One of the take-home messages of the present study is that RS-DFT-CIPSI trial wave functions yield lower fixed-node energies with more compact multi-determinant expansions than CIPSI, especially for small basis sets. Indeed, as the CIPSI component of RS-DFT-CIPSI is relieved from describing the short-range part of the correlation hole around the electron-electron coalescence points, the number of determinants in the trial wave function required to reach a given accuracy is significantly reduced as compared to a conventional CIPSI calculation. Importantly, by performing various numerical experiments, we evidence that the RS-DFT scheme essentially plays the role of a simple Jastrow factor by mimicking short-range correlation effects, hence avoiding the burden of performing a stochastic optimization. Considering the 55 atomization energies of the Gaussian-1 benchmark set of molecules, we show that using a fixed value of $μ=0.5$~bohr$^{-1}$ provides effective error cancellations as well as compact trial wave functions, making the present method a good candidate for the accurate description of large chemical systems.
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