标题： 解冻高斯波包动力学与基于$Δ$-机器学习势能的模拟 显示英文标题

标题： Thawed Gaussian wavepacket dynamics with $Δ$-machine learned potentials

摘要： 提出了一种在机器学习势能面上进行变宽度（解冻）高斯波包（GWP）变分动力学的方法。这种方法不是拟合势能面（PES），而是使用核岭回归拟合全局谐波近似（GHA）的非谐性校正——这是一种$\Delta$机器学习方法。训练集由从头算电子能量与GHA给出值之间的能量差组成。随后使用学习到的势能，利用时变变分原理传播单个解冻GWP，以计算自相关函数，通过其傅里叶变换可以直接访问振动光谱。我们将该方法应用于模拟氨的光电离谱，并发现理论谱和实验谱之间有很好的一致性。我们展示了相比于拟合总电子能量，拟合非谐性校正需要更小的训练集。我们还证明了我们的方法可以在构建训练集时减少用于扫描PES的核空间的维度。因此，只需要用$\Delta$机器学习处理与大振幅运动相关的自由度，这为可靠地模拟大型柔性分子的振动光谱铺平了道路。 显示英文摘要

摘要： A method for performing variable-width (thawed) Gaussian wavepacket (GWP) variational dynamics on machine-learned potentials is presented. Instead of fitting the potential energy surface (PES), the anharmonic correction to the global harmonic approximation (GHA) is fitted using kernel ridge regression -- this is a $\Delta$-machine learning approach. The training set consists of energy differences between ab initio electronic energies and values given by the GHA. The learned potential is subsequently used to propagate a single thawed GWP using the time-dependent variational principle to compute the autocorrelation function, which provides direct access to vibronic spectra via its Fourier transform. We applied the developed method to simulate the photoelectron spectrum of ammonia and found excellent agreement between theoretical and experimental spectra. We show that fitting the anharmonic corrections requires a smaller training set as compared to fitting total electronic energies. We also demonstrate that our approach allows to reduce the dimensionality of the nuclear space used to scan the PES when constructing the training set. Thus, only the degrees of freedom associated with large amplitude motions need to be treated with $\Delta$-machine learning, which paves a way for reliable simulations of vibronic spectra of large floppy molecules.