We investigate the use of optimized correlation-consistent Gaussian basis sets for the study of insulating solids with auxiliary-field quantum Monte Carlo (AFQMC). The exponents of the basis set are optimized through the minimization of the second-order Møller–Plesset perturbation theory (MP2) energy in a small unit cell of the solid. We compare against other alternative basis sets proposed in the literature, namely, calculations in the Kohn–Sham basis and in the natural orbitals of an MP2 calculation. We find that our optimized basis sets accelerate the convergence of the AFQMC correlation energy compared to a Kohn–Sham basis and offer similar convergence to MP2 natural orbitals at a fraction of the cost needed to generate them. We also suggest the use of an improved, method independent, MP2-based basis set correction that significantly reduces the required basis set sizes needed to converge the correlation energy. With these developments, we study the relative performance of these basis sets in LiH, Si, and MgO and determine that our optimized basis sets yield the most consistent results as a function of volume. Using these optimized basis sets, we systematically converge the AFQMC calculations to the complete basis set and thermodynamic limit and find excellent agreement with experiment for the systems studied. Although we focus on AFQMC, our basis set generation procedure is independent of the subsequent correlated wavefunction method used.

中文翻译：

---

优化高斯基集加速固体中辅助场量子蒙特卡罗的收敛

我们研究使用优化的相关一致高斯基集来研究带有辅助场量子蒙特卡洛（AFQMC）的绝缘固体。通过最小化固体小晶胞中的二阶Møller-Plesset微扰理论（MP2）能量来优化基集的指数。我们与文献中提出的其他替代基础集进行了比较，即以Kohn-Sham基础和MP2计算的自然轨道进行计算。我们发现，与Kohn–Sham基础相比，我们优化的基础集可加快AFQMC相关能量的收敛，并以产生MP2自然轨道所需成本的一小部分提供与MP2自然轨道相似的收敛。我们还建议使用独立于方法的改进型，基于MP2的基集校正，可显着减小收敛相关能量所需的基集大小。随着这些发展，我们研究了这些基集在LiH，Si和MgO中的相对性能，并确定了我们优化的基集产生的体积函数最一致。使用这些优化的基础集，我们系统地将AFQMC计算收敛到完整的基础集和热力学极限，并找到与实验研究的系统极好的一致性。尽管我们专注于AFQMC，但我们的基集生成过程与随后使用的相关波函数方法无关。和MgO，并确定我们优化的基集可产生最一致的结果，即体积的函数。使用这些优化的基础集，我们系统地将AFQMC计算收敛到完整的基础集和热力学极限，并找到与实验研究的系统极好的一致性。尽管我们专注于AFQMC，但我们的基集生成过程与随后使用的相关波函数方法无关。和MgO，并确定我们优化的基集可产生最一致的结果，即体积的函数。使用这些优化的基础集，我们系统地将AFQMC计算收敛到完整的基础集和热力学极限，并找到与实验研究的系统极好的一致性。尽管我们专注于AFQMC，但我们的基集生成过程与随后使用的相关波函数方法无关。