H+H $_2$及几种氢键分子的无相位量子Monte Carlo研究
A study of H+H$_2$ and several H-bonded molecules by phaseless auxiliary-field quantum Monte Carlo with planewave and Gaussian basis sets
摘要：
本文采用无相量子场（AF）量子蒙特卡罗（QMC）方法对几种氢键体系的基态进行了计算。这些系统被选择来测试和基准新的无相位AF QMC方法的不同方面。它们包括H+H $_2$在平衡几何结构附近和范德华极限的过渡态，以及H $_2$ O、OH和H $_2$ O $_2$分子。这些系统中的大多数对传统的独立粒子电子结构方法提出了重大挑战，并且许多系统也有精确的结果。无相位AF QMC方法使用赝势平面波基或全电子高斯基组。对于某些系统，计算都做了比较和表征的性能AF QMC在不同的基组和不同的Hubbard-Stratonovich分解。作为输入单斯莱特行列式波函数从独立粒子计算得到了很好的结果。与精确全位形的高斯基AF QMC结果的比较表明，无相近似控制相位问题的误差很小。在大的基础尺寸的限制，AF QMC结果使用两种类型的基组是在良好的协议彼此和实验值。
英文摘要：
We present phaseless auxiliary-field (AF) quantum Monte Carlo (QMC) calculations of the ground states of some hydrogen-bonded systems. These systems were selected to test and benchmark different aspects of the new phaseless AF QMC method. They include the transition state of H+H$_2$ near the equilibrium geometry and in the van der Walls limit, as well as H$_2$O, OH, and H$_2$O$_2$ molecules. Most of these systems present significant challenges for traditional independent-particle electronic structure approaches, and many also have exact results available. The phaseless AF QMC method is used either with a planewave basis with pseudopotentials or with all-electron Gaussian basis sets. For some systems, calculations are done with both to compare and characterize the performance of AF QMC under different basis sets and different Hubbard-Stratonovich decompositions. Excellent results are obtained using as input single Slater determinant wave functions taken from independent-particle calculations. Comparisons of the Gaussian based AF QMC results with exact full configuration show that the errors from controlling the phase problem with the phaseless approximation are small. At the large basis-size limit, the AF QMC results using both types of basis sets are in good agreement with each other and with experimental values.
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