Orbital Transformers for Predicting Wavefunctions in Time-Dependent Density Functional Theory
arXiv:2603.03511v1 Announce Type: new Abstract: 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
arXiv:2603.03511v1 Announce Type: new Abstract: 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.
Executive Summary
This article proposes OrbEvo, a novel equivariant graph transformer architecture for predicting wavefunctions in time-dependent density functional theory (TDDFT). The model learns to evolve electronic wavefunction coefficients across time steps, efficiently representing them as linear combinations of atomic orbitals. The authors design two OrbEvo models, OrbEvo-WF and OrbEvo-DM, using wavefunction pooling and density matrix as interaction methods, respectively. The study demonstrates the accuracy of OrbEvo in capturing quantum dynamics of excited states under external fields, including time-dependent wavefunctions, dipole moments, and optical absorption spectra. The model's performance is evaluated on two datasets, QM9 and MD17, consisting of 5,000 and 1,500 molecular configurations, respectively. The results show that OrbEvo accurately predicts quantum dynamics of excited states, outperforming conventional real-time TDDFT methods.
Key Points
- ▸ OrbEvo proposes a novel equivariant graph transformer architecture for predicting wavefunctions in TDDFT.
- ▸ The model learns to evolve electronic wavefunction coefficients across time steps, efficiently representing them as linear combinations of atomic orbitals.
- ▸ Two OrbEvo models, OrbEvo-WF and OrbEvo-DM, are designed using wavefunction pooling and density matrix as interaction methods, respectively.
Merits
Strength
OrbEvo efficiently represents electronic wavefunction coefficients as linear combinations of atomic orbitals, significantly reducing computational complexity compared to conventional real-time TDDFT methods.
Strength
The model's equivariant conditioning encodes both strength and direction of external electric fields, enabling accurate predictions of quantum dynamics under external fields.
Strength
OrbEvo's performance is evaluated on two large datasets, QM9 and MD17, demonstrating its feasibility for real-world applications.
Demerits
Limitation
The model's performance is limited to a specific range of molecular configurations and external fields, and further research is required to generalize it to more complex systems.
Limitation
The authors rely on autoregressive rollout to limit error accumulation, but this approach may not be suitable for all molecular configurations and external fields.
Expert Commentary
The development of OrbEvo represents a significant breakthrough in the field of quantum chemistry, as it provides an efficient and accurate method for simulating quantum dynamics. While the model's performance is limited to a specific range of molecular configurations and external fields, it has the potential to be generalized to more complex systems through further research. The authors' reliance on autoregressive rollout to limit error accumulation is a reasonable approach, but further investigation is required to determine its suitability for all molecular configurations and external fields. Overall, OrbEvo is a promising development that may have significant implications for the field of quantum chemistry and beyond.
Recommendations
- ✓ Further research is required to generalize OrbEvo to more complex molecular configurations and external fields.
- ✓ Investigation into the suitability of autoregressive rollout for all molecular configurations and external fields is necessary.
