An Improved Penalty-Based Excited-State Variational Monte Carlo Approach with Deep-Learning Ansatzes,Journal of Chemical Theory and Computation

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An Improved Penalty-Based Excited-State Variational Monte Carlo Approach with Deep-Learning Ansatzes
Journal of Chemical Theory and Computation ( IF 5.7 ) Pub Date : 2024-08-30 , DOI: 10.1021/acs.jctc.4c00678
P Bernát Szabó ₁ , Zeno Schätzle ₁ , Michael T Entwistle ₁ , Frank Noé _{1,

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Affiliation

We introduce several improvements to the penalty-based variational quantum Monte Carlo (VMC) algorithm for computing electronic excited states of Entwistle et al. [Nat. Commun. 14, 274 (2023)] and demonstrate that the accuracy of the updated method is competitive with other available excited-state VMC approaches. A theoretical comparison of the computational aspects of these algorithms is presented, where several benefits of the penalty-based method are identified. Our main contributions include an automatic mechanism for tuning the scale of the penalty terms, an updated form of the overlap penalty with proven convergence properties, and a new term that penalizes the spin of the wave function, enabling the selective computation of states with a given spin. With these improvements, along with the use of the latest self-attention-based ansatz, the penalty-based method achieves a mean absolute error below 1 kcal/mol for the vertical excitation energies of a set of 26 atoms and molecules, without relying on variance matching schemes. Considering excited states along the dissociation of the carbon dimer, the accuracy of the penalty-based method is on par with that of natural-excited-state (NES) VMC, while also providing results for additional sections of the potential energy surface, which were inaccessible with the NES method. Additionally, the accuracy of the penalty-based method is improved for a conical intersection of ethylene, with the predicted angle of the intersection agreeing well with both NES-VMC and multireference configuration interaction.

中文翻译：

具有深度学习分析的改进的基于惩罚的激发态变分蒙特卡罗方法

我们介绍了对 Entwistle 等人用于计算电子激发态的基于惩罚的变分量子蒙特卡罗 (VMC) 算法的一些改进。 [纳特。交流。 14 , 274 (2023)] 并证明更新方法的准确性与其他可用的激发态 VMC 方法具有竞争力。对这些算法的计算方面进行了理论比较，其中确定了基于惩罚的方法的几个优点。我们的主要贡献包括用于调整惩罚项大小的自动机制、具有经过验证的收敛特性的重叠惩罚的更新形式，以及惩罚波函数自旋的新项，从而能够选择性地计算给定的状态旋转。通过这些改进，再加上最新的基于自注意力的 ansatz 的使用，基于惩罚的方法对于一组 26 个原子和分子的垂直激发能实现了低于 1 kcal/mol 的平均绝对误差，而无需依赖方差匹配方案。考虑到碳二聚体解离过程中的激发态，基于惩罚的方法的准确性与自然激发态 (NES) VMC 的准确度相当，同时还提供了势能表面的其他部分的结果，这些部分是使用 NES 方法无法访问。此外，对于乙烯的圆锥形相交，基于惩罚的方法的准确性得到了提高，预测的相交角度与 NES-VMC 和多参考构型相互作用都非常吻合。

更新日期：2024-08-30

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