Lee Joonho, Malone Fionn D, Morales Miguel A, Reichman David R
Department of Chemistry, Columbia University, New York, New York 10027, United States.
Quantum Simulations Group, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, United States.
J Chem Theory Comput. 2021 Jun 8;17(6):3372-3387. doi: 10.1021/acs.jctc.1c00100. Epub 2021 May 13.
We explore the extended Koopmans' theorem (EKT) within the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method. The EKT allows for the direct calculation of electron addition and removal spectral functions using reduced density matrices of the -particle system and avoids the need for analytic continuation. The lowest level of EKT with AFQMC, called EKT1-AFQMC, is benchmarked using atoms, small molecules, 14-electron and 54-electron uniform electron gas supercells, and a minimal unit cell model of diamond at the Γ-point. Via comparison with numerically exact results (when possible) and coupled-cluster methods, we find that EKT1-AFQMC can reproduce the qualitative features of spectral functions for Koopmans-like charge excitations with errors in peak locations of less than 0.25 eV in a finite basis. We also note the numerical difficulties that arise in the EKT1-AFQMC eigenvalue problem, especially when back-propagated quantities are very noisy. We show how a systematic higher-order EKT approach can correct errors in EKT1-based theories with respect to the satellite region of the spectral function. Our work will be of use for the study of low-energy charge excitations and spectral functions in correlated molecules and solids where AFQMC can be reliably performed for both energy and back propagation.
我们在无相辅助场量子蒙特卡罗（AFQMC）方法中探究扩展的库普曼斯定理（EKT）。EKT允许使用N粒子系统的约化密度矩阵直接计算电子添加和移除谱函数，并且无需进行解析延拓。AFQMC的最低级EKT，即EKT1 - AFQMC，通过原子、小分子、14电子和54电子均匀电子气超胞以及Γ点处金刚石的最小单胞模型进行基准测试。通过与数值精确结果（可能的话）和耦合簇方法进行比较，我们发现EKT1 - AFQMC能够在有限基组下重现类似库普曼斯电荷激发的谱函数的定性特征，峰位置误差小于0.25 eV。我们还指出了EKT1 - AFQMC本征值问题中出现的数值困难，特别是当反向传播量非常嘈杂时。我们展示了一种系统的高阶EKT方法如何能够校正基于EKT1的理论在谱函数卫星区域方面的误差。我们的工作将有助于研究关联分子和固体中的低能电荷激发和谱函数，在这些研究中，AFQMC对于能量和反向传播都能够可靠地执行。
