利用基本对称性破缺进行辅助场量子蒙特卡罗：C $_{36}$富勒烯和铁卟啉模型配合物的自旋能隙
Utilizing Essential Symmetry Breaking in Auxiliary-Field Quantum Monte Carlo: Application to the Spin Gaps of the C$_{36}$ Fullerene and an Iron Porphyrin Model Complex
摘要：
我们提出了三个不同的例子，其中无相位的空间场量子蒙特卡罗（ph-AFQMC）可以可靠地进行与基本对称性破缺的单行列式试验波函数。我们首先利用ph-AFQMC的基本时间反演对称性破缺来计算TS 12集合中的三重态-单重态能隙。我们发现统计学上更好的性能ph-AFQMC与复杂的限制轨道比自旋非限制轨道。然后，我们展示了利用必要的自旋对称性破缺时计算的单三重态间隙的一个已知的双自由基，C $_{36}$。ph-AFQMC与自旋不受限制的Hartree-Fock（ph-AFQMC+UHF）失败灾难性的，即使与自旋投影和预测没有biradicaloid字符。利用从正则化轨道优化的二阶Møller-Plesset微扰理论（$κ$ -OOMP 2）获得的近似Brueckner轨道，ph-AFQMC定量地捕获了C $_{36}$的强双自由基特征。最后，我们将ph-AFQMC应用于模型铁卟啉复合物中的五重态-三重态能隙的计算，其中具有小活性空间的蛮力方法无法捕获三重态基态。我们使用UHF、$κ$ -OOMP 2和在UHF和$κ$ -OOMP 2轨道上进行的单双耦合簇（CCSD）明确地表明，三重态和五重态都没有强相关性。在这个问题中没有本质的对称破缺。凭借这一点，我们能够可靠地执行UHF+ph-AFQMC与cc-pVTZ基组，并预测该模型几何结构的三重基态。在这项工作中，最大的ph-AFQMC在956个轨道中关联了186个电子。我们的工作突出了实用性，可扩展性和准确性的ph-AFQMC与一个单一的决定性的审判波函数与基本对称性破缺系统主要由动态相关与静态相关。
英文摘要：
We present three distinct examples where phaseless auxiliary-field Quantum Monte Carlo (ph-AFQMC) can be reliably performed with a single-determinant trial wavefunction with essential symmetry breaking. We first utilized essential time-reversal symmetry breaking with ph-AFQMC to compute the triplet-singlet energy gap in the TS12 set. We found statistically better performance of ph-AFQMC with complex-restricted orbitals than with spin-unrestricted orbitals. We then showed the utilization of essential spin symmetry breaking when computing the single-triplet gap of a known biradicaloid, C$_{36}$. ph-AFQMC with spin-unrestricted Hartree-Fock (ph-AFQMC+UHF) fails catastrophically even with spin-projection and predicts no biradicaloid character. With approximate Brueckner orbitals obtained from regularized orbital-optimized second-order Møller-Plesset perturbation theory ($κ$-OOMP2), ph-AFQMC quantitatively captures strong biradicaloid character of C$_{36}$. Lastly, we applied ph-AFQMC to the computation of the quintet-triplet gap in a model iron porphyrin complex where brute-force methods with a small active space fail to capture the triplet ground state. We show unambiguously that neither triplet nor quintet is strongly correlated using UHF, $κ$-OOMP2, and coupled-cluster with singles and doubles (CCSD) performed on UHF and $κ$-OOMP2 orbitals. There is no essential symmetry breaking in this problem. By virtue of this, we were able to perform UHF+ph-AFQMC reliably with a cc-pVTZ basis set and predicted a triplet ground state for this model geometry. The largest ph-AFQMC in this work correlated 186 electrons in 956 orbitals. Our work highlights the utility, scalability, and accuracy of ph-AFQMC with a single determinant trial wavefunction with essential symmetry breaking for systems mainly dominated by dynamical correlation with little static correlation.
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