The accurate computation of forces and other energy derivatives has been a long-standing challenge for quantum Monte Carlo methods. A number of technical obstacles contribute to this challenge. We discuss how these obstacles can be removed with the auxiliary-field quantum Monte Carlo (AFQMC) approach. AFQMC is a general, high-accuracy, many-body total-energy method for molecules and solids. The implementation of back-propagation for pure estimators allows direct calculation of gradients of the energy via the Hellmann-Feynman theorem. A planewave basis with norm-conserving pseudopotentials is used for the study of periodic bulk materials. Completeness of the planewave basis minimizes the effect of so-called Pulay terms. The ionic pseudopotentials, which can be incorporated in AFQMC in exactly the same manner as in standard independent-electron methods, regulate the force and stress estimators and eliminate any potential divergence of the Monte Carlo variances. The resulting approach allows applications of full geometry optimizations in bulk materials. It also paves the way for many-body computations of the phonon spectrum in solids.
Deformation, lattice instability, and metallization during solid-solid structural transformations under general applied stress tensor: example of Si I -> Si II
采用密度泛函理论（DFT）研究了半导体Si I（立方A4结构）和金属Si II（四方A5结构）在一般应力张量作用下的固-固相变（PT）过程中的应力-应变行为、弹性不稳定性和金属化.与正常的应力（$σ_1$，$σ_2$，$σ_3$）作用沿$\left<110 \right>$，$\left<1\bar{1}0 \right>$，和$\left<001\right>$，分别指示模拟单元，我们确定了6个独立的应力，驱动硅I $\rightarrow$硅II PT的晶格不稳定性的组合，和一个超导金属电子过渡。金属化先于结构PT，因此，应力Si I可以是金属。令人惊讶的是，无应力的Si II在DFT中是亚稳态的。值得注意的是，静水压力的PT为75.81 GPa，而在单轴应力下为11.03 GPa（或3.68 GPa平均压力）。我们的主要成果：Si I -> Si II PT由修正相变功的临界值描述，如用相场方法发现的，并且PT准则对于一般施加应力只有两个参数。更一般地说，我们的研究结果是至关重要的揭示新的（和更经济的）材料合成路线的新的或已知的高压阶段下控制和可预测的非流体静力学加载和塑性形变。
Space charge dynamics in solid electrolytes with steric effect and Vegard stresses: resistive switching and ferroelectric-like hysteresis of electromechanical response
Rational Mechanics of Material Strength in Brittle Solids
School of Civil and Environmental Engineering, Georgia Institute of Technology（佐治亚理工学院土木与环境工程学院）；The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology（佐治亚理工学院乔治·W·伍德鲁夫机械工程学院）
