An adaptation of the full configuration interaction quantum Monte Carlo (FCIQMC) method is presented, for correlated electron problems containing heavy elements and the presence of significant relativistic effects. The modified algorithm allows for the sampling of the four-component spinors of the Dirac--Coulomb(--Breit) Hamiltonian within the relativistic no-pair approximation. The loss of spin symmetry and the general requirement for complex-valued Hamiltonian matrix elements are the most immediate considerations in expanding the scope of FCIQMC into the relativistic domain, and the alternatives for their efficient implementation are motivated and demonstrated. For the canonical correlated four-component chemical benchmark application of Thallium Hydride, we show that the necessary modifications do not particularly adversely affect the convergence of the systematic (initiator) error to the exact correlation energy for FCIQMC calculations, which is primarily dictated by the sparsity of the wave function, allowing the computational effort to somewhat bypass the formal increases in Hilbert space dimension for these problems. We apply the method to the larger problem of the spectroscopic constants of Tin Oxide, correlating 28 electrons in 122 Kramers-paired spinors, finding good agreement with experimental and prior theoretical relativistic studies.
Enabling ab initio geometry optimization of strongly correlated systems with transferable deep quantum Monte Carlo
FU Berlin, Department of Mathematics and Computer Science（柏林自由大学数学与计算机科学系）；Microsoft Research AI4Science（微软研究院AI4Science）；FU Berlin, Department of Physics（柏林自由大学物理系）；Rice University, Department of Chemistry（莱斯大学化学系）
Predicting highly correlated hydride-ion diffusion in SrTiO$_3$ crystals based on the fragment kinetic Monte Carlo method with machine-learning potential
氧化物由于其快速的离子传导性和强的还原性而引起人们的关注。最近，氢化物离子在SrTiO $_{3-x}$ H $_{x}$氢氧化物晶体中的迁移已被研究，表明氢离子的迁移被缓慢的氧扩散阻断。在这项研究中，我们调查的氢化物离子迁移机制，使用动力学蒙特卡罗方法来了解氢化物和氧离子之间的关系。将该方法应用于氢化物和氧离子迁移的困难涉及离子迁移势垒的复杂变化，其动态地根据周围氢化物和氧离子的特性而变化。我们可以使用机器学习神经网络模型来预测这些复杂的变化。然后可以使用该模型进行模拟，以预测温度依赖的离子迁移行为。我们发现我们对氢化物离子扩散激活势垒的模拟结果与实验结果符合得很好。我们还发现，氢离子迁移的影响，缓慢的氧扩散和氧扩散的离子迁移障碍的变化加速。对于1,000 CPU的实现，该方法的并行处理效率为84.92%，表明该方法可以以合理的计算成本广泛应用于晶体中离子迁移的模拟。
Accounting for correlations with core electrons by means of the generalized relativistic effective core potentials: Atoms Hg and Pb and their compounds
