用图变压器预测分子激发态量子动力学，比传统方法快得多。
Orbital Transformers for Predicting Wavefunctions in Time-Dependent Density Functional Theory
- 用等变图变压器建模轨道系数随时间演化
- 在QM9和MD17数据集上准确预测波函数与吸收光谱
- 适合需要快速模拟电子动态的量子化学研究者
我们旨在学习时变密度泛函理论（TDDFT）模拟的波函数，这些波函数可高效表示为原子轨道的线性组合系数。在实时光学激发下，分子电子波函数随时间演化，可用于第一性原理预测光学吸收、电子动力学和高阶响应。但传统实时光学TDDFT需对所有占据态进行精细时间步长传播，计算耗时。本文提出OrbEvo模型，基于等变图变压器架构，学习全电子波函数系数在时间步间的演化。为考虑外场影响，设计了等变条件编码，将SO(3)对称性破缺至SO(2)，以同时编码电场强度与方向。提出两种模型：OrbEvo-WF使用波函数池化，OrbEvo-DM则通过张量收缩将所有占据态的密度矩阵聚合为特征向量，更直观地学习时间演化算符。采用专为限制自回归滚动中误差累积而设计的训练策略。在包含5,000种不同分子的QM9数据集和1,500个丙二醛分子构型的MD17数据集上评估，结果表明OrbEvo能准确捕捉外场下的激发态量子动力学，包括时间依赖波函数、时间依赖偶极矩和光学吸收光谱。
原文摘要 · Abstract (English)
We aim to learn wavefunctions simulated by time-dependent density functional theory (TDDFT), which can be efficiently represented as linear combination coefficients of atomic orbitals. In real-time TDDFT, the electronic wavefunctions of a molecule evolve over time in response to an external excitation, enabling first-principles predictions of physical properties such as optical absorption, electron dynamics, and high-order response. However, conventional real-time TDDFT relies on time-consuming propagation of all occupied states with fine time steps. In this work, we propose OrbEvo, which is based on an equivariant graph transformer architecture and learns to evolve the full electronic wavefunction coefficients across time steps. First, to account for external field, we design an equivariant conditioning to encode both strength and direction of external electric field and break the symmetry from SO(3) to SO(2). Furthermore, we design two OrbEvo models, OrbEvo-WF and OrbEvo-DM, using wavefunction pooling and density matrix as interaction method, respectively. Motivated by the central role of the density functional in TDDFT, OrbEvo-DM encodes the density matrix aggregated from all occupied electronic states into feature vectors via tensor contraction, providing a more intuitive approach to learn the time evolution operator. We adopt a training strategy specifically tailored to limit the error accumulation of time-dependent wavefunctions over autoregressive rollout. To evaluate our approach, we generate TDDFT datasets consisting of 5,000 different molecules in the QM9 dataset and 1,500 molecular configurations of the malonaldehyde molecule in the MD17 dataset. Results show that our OrbEvo model accurately captures quantum dynamics of excited states under external field, including time-dependent wavefunctions, time-dependent dipole moment, and optical absorption spectra.
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