单决定性固定节点扩散蒙特卡罗中的偏差抵消：费米占据数的启示
Bias Cancellation in One-Determinant Fixed-Node Diffusion Monte Carlo: Insights from Fermionic Occupation Numbers
摘要：
固定节点扩散蒙特卡罗（FN-DMC）的精度取决于最佳可用试验状态$Ψ_T$的节点位置。可用于大系统的实用FN-DMC方法依赖于包含显式相关的单个Slater行列式（SD）的紧凑而有效的$Ψ_T$。然而，SD节点可能更适合于一个系统而不是另一个系统，这可能导致不准确的FN-DMC能量差。如何估计标准差的不对等性或适当性仍然是一个挑战。在这里，我们使用的测量之间的自然轨道占有数（NOON）的斯莱特行列式（SD）的矢量从精确的解决方案在NOON矢量空间，这可以被看作是SD不等价的措施和FN-DMC能量差异的非动态相关相关的偏差的预期程度的措施的基础上的欧几里德距离的差异。这是探讨一组小的非共价复合物和共价键断裂的Si $_2$与N $_2$。事实证明，基于NOON的措施很好地反映了现有数据中存在的偏差的幅度和符号，从而为SD FN-DMC能量差异中偏差消除的性质提供了新的见解。
英文摘要：
Accuracy of the fixed-node diffusion Monte Carlo (FN-DMC) depends on the node location of the best available trial state $Ψ_T$. The practical FN-DMC approaches available for large systems rely on compact yet effective $Ψ_T$s containing explicitly correlated single Slater determinant (SD). However, SD nodes may be better suited to one system than to another, which may possibly lead to inaccurate FN-DMC energy differences. It remains a challenge, how to estimate inequivalency or appropriateness of SDs. Here we use the differences of a measure based on Euclidean distance between the natural orbital occupation number (NOON) vector of the Slater determinant (SD) from the exact solution in the NOON vector space, that can be viewed as a measure of SD inequivalency and a measure of the expected degree of nondynamic-correlation-related bias in FN-DMC energy differences. This is explored on a set of small noncovalent complexes and covalent bond breaking of Si$_2$ vs. N$_2$. It turns out that NOON-based measures well reflect the magnitude and sign of the bias present in the data available, thus providing new insights to the nature of bias cancellation in SD FN-DMC energy differences.
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