Sukurma Zoran, Schlipf Martin, Kresse Georg
University of Vienna, Faculty of Physics, Kolingasse 14-16, A-1090 Vienna, Austria.
VASP Software GmbH, Berggasse 21/14, 1090 Vienna, Austria.
J Chem Theory Comput. 2025 May 13;21(9):4481-4493. doi: 10.1021/acs.jctc.5c00127. Epub 2025 Apr 28.
For optimal accuracy, auxiliary-field quantum Monte Carlo (AFQMC) requires trial states consisting of multiple Slater determinants. We develop an efficient algorithm to select the determinants from an AFQMC random walk eliminating the need for other methods. When determinants contribute significantly to the nonorthogonal configuration interaction energy, we include them in the trial state. These refined trial wave functions significantly reduce the phaseless bias and sampling variance of the local energy estimator. With 100 to 200 determinants, we lower the error of AFQMC by up to a factor of 10 for second-row elements that are not accurately described with a Hartree-Fock trial wave function. For the HEAT set, we improve the average error to within chemical accuracy. For benzene, the largest studied system, we reduce AFQMC error by 80% with 214 Slater determinants and find a 10-fold increase of the time to solution. We show that phaseless errors prevail in systems with static correlation or strong spin contamination. For such systems, improved trial states enable stable free-projection AFQMC calculations, achieving chemical accuracy even in the strongly correlated regime.
为了实现最佳精度，辅助场量子蒙特卡罗（AFQMC）需要由多个斯莱特行列式组成的试探态。我们开发了一种高效算法，从AFQMC随机游走中选择行列式，从而无需其他方法。当行列式对非正交组态相互作用能有显著贡献时，我们将它们包含在试探态中。这些经过优化的试探波函数显著降低了局部能量估计器的无相偏置和采样方差。对于那些用哈特里 - 福克试探波函数无法准确描述的第二周期元素，使用100到200个行列式，我们将AFQMC的误差降低了高达10倍。对于HEAT数据集，我们将平均误差提高到了化学精度范围内。对于所研究的最大体系苯，使用214个斯莱特行列式，我们将AFQMC误差降低了80%，同时发现求解时间增加了10倍。我们表明，无相误差在具有静态关联或强自旋污染的体系中普遍存在。对于此类体系，改进的试探态能够实现稳定的自由投影AFQMC计算，即使在强关联区域也能达到化学精度。
