Machine-learning interatomic potentials (MLIPs) have enabled molecular dynamics at near ab initio accuracy, yet remain limited to energies and forces by construction, leaving electronic observables such as dipole moments and polarizabilities inaccessible. We introduce DenSNet, a density-first approach to machine-learned electronic structure that learns the Hohenberg--Kohn map from nuclear configurations to the ground-state electron density. Our approach employs an SE(3)-equivariant neural network to predict density coefficients of a flexible atom-centered Gaussian basis, combined with a $Δ$-learning strategy that uses superposed atomic densities as a prior to accelerate training. A second equivariant network then maps the predicted density to the total energy, providing a unified framework for molecular dynamics and electronic structure. We validate DenSNet on ethanol, ethanethiol, and resorcinol, where infrared spectra from machine-learned trajectories show excellent agreement with experimental gas-phase measurements. To test scalability, we train on polythiophene oligomers with 1--6 monomers and extrapolate to chains of up to 12 monomers, generating stable long-time trajectories whose infrared spectra agree with reference density functional theory calculations. Here, we show that reinstating the electron density as the central learned quantity opens a practical route to transferable prediction of spectroscopic and electronic observables in large-scale molecular simulations.

翻译：机器学习原子间势能（MLIPs）已能以接近从头计算的精度实现分子动力学模拟，但其本质构造使其仅限于能量与力的预测，无法获取偶极矩、极化率等电子可观测物理量。我们提出DenSNet——一种以电子密度为先导的机器学习电子结构方法，通过学习从核构型到基态电子密度的Hohenberg-Kohn映射。该方法采用SE(3)等变神经网络预测柔性原子中心高斯基组的密度系数，并结合Δ学习策略将叠加的原子密度作为先验知识以加速训练。随后，第二个等变网络将预测的密度映射到总能量，为分子动力学与电子结构提供统一框架。我们在乙醇、乙硫醇和间苯二酚上验证DenSNet，机器学习轨迹产生的红外光谱与实验气相测量结果高度吻合。为测试可扩展性，我们在含1-6个单体的聚噻吩低聚物上训练模型，并外推至含12个单体的链体系，生成长时稳定轨迹，其红外光谱与参考密度泛函理论计算结果一致。研究表明，将电子密度恢复为核心学习量，为大规模分子模拟中光谱与电子可观测物理量的可迁移预测开辟了实用途径。