用解析能量导数优化量子蒙特卡罗波函数
Optimization of Quantum Monte Carlo Wave Functions Using Analytical Energy Derivatives
摘要：
基于Newton方法和变分能量一阶、二阶导数的解析计算，提出了一种优化量子蒙特卡罗（QMC）波函数的算法。这种直接应用的变分原理产生显着较低的能量比方差最小化方法时，适用于相同的试验波函数。变分参数的局部极小值的二次收敛。本文提出了一个一般定理，它大大简化了波函数优化情况下导数的解析表达式。为了演示该方法，计算了第一行元素的基态能量。
英文摘要：
An algorithm is proposed to optimize quantum Monte Carlo (QMC) wave functions based on New ton's method and analytical computation of the first and second derivatives of the variati onal energy. This direct application of the variational principle yields significantly low er energy than variance minimization methods when applied to the same trial wave function. Quadratic convergence to the local minimum of the variational parameters is achieved. A g eneral theorem is presented, which substantially simplifies the analytic expressions of de rivatives in the case of wave function optimization. To demonstrate the method, the ground state energies of the first-row elements are calculated.
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