量子蒙特卡罗中的多行列式波函数
Multi-Determinant Wave-functions in Quantum Monte Carlo
摘要：
量子蒙特卡罗（QMC）方法在电子系统中提供多体薛定谔方程的直接解方面有着巨大的潜力，因此在过去的几十年里受到了广泛的关注。由于它们的低尺度与粒子数，QMC方法提出了一个令人信服的竞争力的替代大分子系统和固态计算的准确研究。尽管有这样的前景，该方法还没有广泛渗透到量子化学界，主要是因为固定节点的错误，这可能是大的，其控制是困难的。在这个角度来看，我们提出了一个系统的应用大规模的多决定簇扩展QMC，并报告其令人印象深刻的性能与第一行二聚体和55个分子的G1测试集。我们证明了这种策略的潜力，系统地减少固定节点的波函数的错误，并实现化学准确性的能量预测。当与传统的量子化学方法如MP2、CCSD（T）和各种DFT近似相比时，QMC结果显示出对所有这些方法的显着改进。事实上，只有显式相关的CCSD（T）方法与一个大的基组产生更准确的结果。试验波函数和算法改进的进一步发展似乎有希望使QMC作为大型电子系统的基准标准。
英文摘要：
Quantum Monte Carlo (QMC) methods have received considerable attention over the last decades due to their great promise for providing a direct solution to the many-body Schrodinger equation in electronic systems. Thanks to their low scaling with number of particles, QMC methods present a compelling competitive alternative for the accurate study of large molecular systems and solid state calculations. In spite of such promise, the method has not permeated the quantum chemistry community broadly, mainly because of the fixed-node error, which can be large and whose control is difficult. In this Perspective, we present a systematic application of large scale multi-determinant expansions in QMC, and report on its impressive performance with first row dimers and the 55 molecules of the G1 test set. We demonstrate the potential of this strategy for systematically reducing the fixed-node error in the wave function and for achieving chemical accuracy in energy predictions. When compared to traditional quantum chemistry methods like MP2, CCSD(T), and various DFT approximations, the QMC results show a marked improvement over all of them. In fact, only the explicitly-correlated CCSD(T) method with a large basis set produces more accurate results. Further developments in trial wave functions and algorithmic improvements appear promising for rendering QMC as the benchmark standard in large electronic systems.
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