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arXiv 1604.02183physics.chem-ph
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量子蒙特卡罗中固定节点误差的改进控制:水分子的情况

Toward an improved control of the fixed-node error in quantum Monte Carlo: The case of the water molecule

Michel Caffarel, Thomas Applencourt, Emmanuel Giner, Anthony Scemama

摘要:

采用全电子固定结点扩散蒙特卡罗(FN-DMC)方法计算了水分子在平衡几何条件下的非相对论基态能量。试验波函数的行列式部分是从微扰选择组态相互作用计算(CIPSI方法),包括高达约140万的决定因素。使用cc-pCV $n$ Z系列基组进行计算,其中$n$ =2至5。与大多数QMC作品相比,在Jastrow存在的情况下,没有对行列式部分进行重新优化。对于最大的cc-pCV 5 Z基组,获得了迄今为止报道的基态能量的最低上限-76.43744(18)。固定节点的能量被发现定期减少的基数$n$的函数和完整的基集限制(CBS)与{ \it精确节点}很容易提取。得到的能量为-76.43894(12)--与实验得出的最佳值完全一致--是迄今为止报道的最准确的理论估计。我们强调,采用选定的CI节点的质量不断提高,在一个给定的家庭的基组可能代表一个简单的,确定性的,可重复的,和系统的方式来控制DMC中的固定节点误差。

英文摘要:

All-electron Fixed-node Diffusion Monte Carlo (FN-DMC) calculations for the nonrelativistic ground-state energy of the water molecule at equilibrium geometry are presented. The determinantal part of the trial wavefunction is obtained from a perturbatively selected Configuration Interaction calculation (CIPSI method) including up to about 1.4 million of determinants. Calculations are made using the cc-pCV$n$Z family of basis sets, with $n$=2 to 5. In contrast with most QMC works no re-optimization of the determinantal part in presence of a Jastrow is performed. For the largest cc-pCV5Z basis set the lowest upper bound for the ground-state energy reported so far of -76.43744(18) is obtained. The fixed-node energy is found to decrease regularly as a function of the cardinal number $n$ and the Complete Basis Set limit (CBS) associated with {\it exact nodes} is easily extracted. The resulting energy of -76.43894(12) -in perfect agreement with the best experimentally derived value- is the most accurate theoretical estimate reported so far. We emphasize that employing selected CI nodes of increasing quality in a given family of basis sets may represent a simple, deterministic, reproducible, and systematic way of controlling the fixed-node error in DMC.

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