Molecular dipole moment in liquid water is an intriguing property, partly due to the fact that there is no unique way to partition the total electron density into individual molecular contributions. The prevailing method to circumvent this problem is to use maximally localized Wannier functions, which perform a unitary transformation of the occupied molecular orbitals by minimizing the spread function of Boys. Here we revisit this problem using a data-driven approach satisfying two physical constraints, namely: (a) The displacement of the atomic charges is proportional to the Berry phase polarization; (b) Each water molecule has a formal charge of zero. It turns out that the distribution of molecular dipole moments in liquid water inferred from latent variables is surprisingly similar to that obtained from maximally localized Wannier functions. Apart from putting a maximum-likelihood footnote to the established method, this work highlights the capability of graph convolution based charge models and the importance of physical constraints on improving the model interpretability.

液态水中的分子偶极矩是一个有趣的特性，部分原因是没有独特的方法将总电子密度划分为单个分子贡献。规避这个问题的主流方法是使用最大局部化万尼尔函数，该函数通过最小化男孩的扩散函数来对占据的分子轨道进行幺正变换。在这里，我们使用满足两个物理约束的数据驱动方法重新审视这个问题，即： (a) 原子电荷的位移与 Berry 相极化成正比；(b) 每个水分子的形式电荷为零。事实证明，从潜变量推断出的液态水中分子偶极矩的分布与从最大局部化万尼尔函数获得的分布惊人地相似。