The molecular dipole moment ($\boldsymbol{\mu}$) is a central quantity in
chemistry. It is essential in predicting infrared and sum-frequency generation
spectra, as well as induction and long-range electrostatic interactions.
Furthermore, it can be extracted directly from high-level quantum mechanical
calculations, making it an ideal target for machine learning (ML). In this
work, we choose to represent this quantity with a physically inspired ML model
that captures two distinct physical effects: local atomic polarization is
captured within the symmetry-adapted Gaussian process regression (SA-GPR)
framework, which assigns a (vector) dipole moment to each atom, while movement
of charge across the entire molecule is captured by assigning a partial
(scalar) charge to each atom. The resulting "MuML" models are fitted together
to reproduce molecular $\boldsymbol{\mu}$ computed using high-level
coupled-cluster theory (CCSD) and density functional theory (DFT) on the QM7b
dataset. The combined model shows excellent transferability when applied to a
showcase dataset of larger and more complex molecules, approaching the accuracy
of DFT at a small fraction of the computational cost. We also demonstrate that
the uncertainty in the predictions can be estimated reliably using a calibrated
committee model. The ultimate performance of the models depends, however, on
the details of the system at hand, with the scalar model being clearly superior
when describing large molecules whose dipole is almost entirely generated by
charge separation. These observations point to the importance of simultaneously
accounting for the local and non-local effects that contribute to
$\boldsymbol{\mu}$; further, they define a challenging task to benchmark future
models, particularly those aimed at the description of condensed phases.

本论文提出使用物理启发式的机器学习模型来描述分子偶极矩，利用局部原子极化和原子间电荷转移来进行建模，并且该模型展现出较好的可迁移性和预测效果。

结合原子部分电荷和原子偶极矩预测分子偶极矩

Predicting molecular dipole moments by combining atomic partial charges  and atomic dipoles

Machine learning has emerged as an invaluable tool in many research areas. In
the present work, we harness this power to predict highly accurate molecular
infrared spectra with unprecedented computational efficiency. To account for
vibrational anharmonic and dynamical effects -- typically neglected by
conventional quantum chemistry approaches -- we base our machine learning
strategy on ab initio molecular dynamics simulations. While these simulations
are usually extremely time consuming even for small molecules, we overcome
these limitations by leveraging the power of a variety of machine learning
techniques, not only accelerating simulations by several orders of magnitude,
but also greatly extending the size of systems that can be treated. To this
end, we develop a molecular dipole moment model based on environment dependent
neural network charges and combine it with the neural network potentials of
Behler and Parrinello. Contrary to the prevalent big data philosophy, we are
able to obtain very accurate machine learning models for the prediction of
infrared spectra based on only a few hundreds of electronic structure reference
points. This is made possible through the introduction of a fully automated
sampling scheme and the use of molecular forces during neural network potential
training. We demonstrate the power of our machine learning approach by applying
it to model the infrared spectra of a methanol molecule, n-alkanes containing
up to 200 atoms and the protonated alanine tripeptide, which at the same time
represents the first application of machine learning techniques to simulate the
dynamics of a peptide. In all these case studies we find excellent agreement
between the infrared spectra predicted via machine learning models and the
respective theoretical and experimental spectra.

本文提出了一种基于机器学习的策略来预测分子红外光谱的方法，建立在从头分子动力学模拟的基础上，利用各种机器学习技术加速模拟并扩展可处理的系统大小，其中包括环境依赖性神经网络电荷的分子偶极矩模型和 Behler 和 Parrinello 的神经网络势能。通过引入完全自动化的采样方案和神经网络势能训练期间的分子力，我们能够仅基于少量的电子结构参考点来获得非常精确的机器学习模型，同时在甲醇分子，含有多达 200 个原子的正构烷和质子化的丙氨酸三肽的情况下，将其应用于模拟红外光谱，并发现与理论和实验光谱具有出色的一致性。