Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density.
Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density.
复制标题
球形和系统平均对密度的零方差零偏差量子蒙特卡洛估计器。
DOI：
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发表时间：
2007
影响因子：
4.4
通讯作者：
Cyrus J. Umrigar
中科院分区：
文献类型：
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作者：
J. Toulouse;R. Assaraf;Cyrus J. Umrigar
我们构造了改进的量子蒙特卡罗估计的球平均和系统平均电子对密度（即，找到两个相隔相对距离u的电子的概率密度），也称为球平均电子位置胞内密度I（u），使用Assaraf和Caffarel介绍的可观测量的一般零方差零偏原理。通过将局部δ函数算子的平均值替换为方差小几个数量级的光滑非局部算子的平均值，可以大大提高I（u）的计算效率。这些新的估计也减少了由于近似试探波函数的系统误差（或偏差）的胞内密度。结合使用的试验Jastrow-Slater波函数中的参数的数量越来越多的优化，它们允许一个获得良好收敛的原子和分子的相关的胞内密度。这些思想可以应用于经典或量子蒙特卡罗计算中的任何对关联函数的计算。
We construct improved quantum Monte Carlo estimators for the spherically and system-averaged electron pair density (i.e., the probability density of finding two electrons separated by a relative distance u), also known as the spherically averaged electron position intracule density I(u), using the general zero-variance zero-bias principle for observables, introduced by Assaraf and Caffarel. The calculation of I(u) is made vastly more efficient by replacing the average of the local delta-function operator by the average of a smooth nonlocal operator that has several orders of magnitude smaller variance. These new estimators also reduce the systematic error (or bias) of the intracule density due to the approximate trial wave function. Used in combination with the optimization of an increasing number of parameters in trial Jastrow-Slater wave functions, they allow one to obtain well converged correlated intracule densities for atoms and molecules. These ideas can be applied to calculating any pair-correlation function in classical or quantum Monte Carlo calculations.