精确固定节面量子Monte Carlo方法

A New Algorithm of the Fixed-Node Quantum Monte Carlo

提出了固定节面量子MonteCarlo的一个新方法 ,与传统的固定节面法相比 ,这个新方法能更准确地计算分子的能量 .导出了系统能量本征值的一个展开式 ,证明传统固定节面法所求出的能量值仅仅是能量本征值的零级近似 ;而新方法可以在只增加很少计算量 (小于 1% )的情况下 ,方便地求出一级近似、二级近似……给出了该方法的具体计算公式和步骤 ,并用它处理了H2 ,LiH ,Li2 和H2 O分子的基态能 .计算结果表明 ,对这些分子的基态只需要二级近似即可获得 97%以上的电子相关能 .

A new algorithm of the Fixed-node quantum Monte Carlo is reported in this paper. It is more accurate for the calculation of the molecule energies than the conventional Fixed - node quantun Monte Carlo processes. A develop formula of the energy eigenvalue of the system is deduced in the text. It is proved that the conventional Fixed - node energy is only the zeroth-order-approximation of the energy eigenvalue of the system. the first(or second......) order-approximation of the energy eigenvalue can be conveniently calculated by this new algorithm, with but very little increase in computational cost(under 1%). The computation formulas and concrete procedures of this algorithm are presented in this paper. This new algorithm is used to compute the energies of the ground states for molecules H2, LiH, Li2 and H2O. The calculated results show that the energy values of the molecules after only the third-order-approximation can achieve over 98% of the correlation energy, indicating that the new algorithm is very superior in both accuracy and computational cost.