使用归一化流（normalizing flows）计算分子激发态
Computing excited states of molecules using normalizing flows
AI总结：
针对高激发离域分子振动态计算依赖坐标选择的难题，提出基于归一化流学习最优振动坐标的新方法，提升了能谱精度与基组收敛性，且坐标可跨基组截断迁移，适用于高维系统振动光谱计算。
摘要：
高激发和离域的分子振动态计算是一项具有计算挑战性的任务，其效果强烈依赖于描述振动运动的坐标选择。我们提出了一种新方法，利用归一化流（normalizing flows，即参数化可逆函数）来学习满足变分原理的最优振动坐标。该方法生成的坐标可适配当前的振动问题，显著提升了计算能谱的精度，并加快了基组收敛速度。我们通过计算H₂S、H₂CO以及HCN/HNC的100个最低振动激发态，验证了该方法的效率。该方法通过提升哈密顿量的可分离性，有效捕捉了分子的基本振动行为，因此能够对近似量子数进行有效指认。我们还证明，优化后的坐标在不同基组截断水平下具有可迁移性，为高维系统的振动光谱计算提供了一种低成本的高效方案。
英文摘要：
Calculations of highly excited and delocalized molecular vibrational states are computationally challenging tasks, which strongly depends on the choice of coordinates for describing vibrational motions. We introduce a new method that leverages normalizing flows -- parametrized invertible functions -- to learn optimal vibrational coordinates that satisfy the variational principle. This approach produces coordinates tailored to the vibrational problem at hand, significantly increasing the accuracy and enhancing basis-set convergence of the calculated energy spectrum. The efficiency of the method is demonstrated in calculations of the 100 lowest excited vibrational states of H$_2$S, H$_2$CO, and HCN/HNC. The method effectively captures the essential vibrational behavior of molecules by enhancing the separability of the Hamiltonian and hence allows for an effective assignment of approximate quantum numbers. We demonstrate that the optimized coordinates are transferable across different levels of basis-set truncation, enabling a cost-efficient protocol for computing vibrational spectra of high-dimensional systems.
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