We present a study of fixed- and partial-node approximations in Slater determinant basis sets, using full configuration interaction quantum Monte Carlo (FCIQMC) to perform sampling. Walker annihilation in the FCIQMC method allows partial-node simulations to be performed, relaxing the nodal constraint to converge to the FCI solution. This is applied to ab initio molecular systems, using symmetry-projected Jastrow mean-field wave functions for complete active space (CAS) problems. Convergence and the sign problem within the partial-node approximation are studied, which is shown to eventually be limited in its use due to the large walker populations required. However, the fixed-node approximation results in an accurate and practical method. We apply these approaches to various molecular systems and active spaces, including ferrocene and acenes. This also provides a test of symmetry-projected Jastrow mean-field wave functions in variational Monte Carlo for a new set of problems. For trans-polyacetylene molecules and acenes, we find that the time to perform a constant number of fixed-node FCIQMC iterations scales as and , respectively, resulting in an efficient method for CAS-based problems that can be applied accurately to large active spaces.

中文翻译：

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分子的 Slater 行列式空间中的固定和部分节点近似

我们介绍了 Slater 行列式基组中固定和部分节点近似的研究，使用全配置相互作用量子蒙特卡罗 (FCIQMC) 来执行采样。FCIQMC 方法中的沃克湮灭允许执行部分节点模拟，放宽节点约束以收敛到 FCI 解。这适用于 ab initio 分子系统，使用对称投影的 Jastrow 平均场波函数解决完整的活动空间 (CAS) 问题。研究了部分节点近似内的收敛和符号问题，由于需要大量的步行者种群，最终显示其使用受到限制。然而，固定节点近似导致了一种准确而实用的方法。我们将这些方法应用于各种分子系统和活性空间，包括二茂铁和并苯。这也为一组新问题提供了在变分蒙特卡罗中对称投影 Jastrow 平均场波函数的测试。为了在反式聚乙炔分子和并苯中，我们发现执行固定节点 FCIQMC 迭代次数恒定的时间分别为和，从而为基于 CAS 的问题提供了一种有效的方法，可以准确地应用于大型活动空间。