Ab-initio simulation of excited-state potential energy surfaces with transferable deep quantum Monte Carlo (2503.19847v1)

Abstract: The accurate quantum chemical calculation of excited states is a challenging task, often requiring computationally demanding methods. When entire ground and excited potential energy surfaces (PESs) are desired, e.g., to predict the interaction of light excitation and structural changes, one is often forced to use cheaper computational methods at the cost of reduced accuracy. Here we introduce a novel method for the geometrically transferable optimization of neural network wave functions that leverages weight sharing and dynamical ordering of electronic states. Our method enables the efficient prediction of ground and excited-state PESs and their intersections at the highest accuracy, demonstrating up to two orders of magnitude cost reduction compared to single-point calculations. We validate our approach on three challenging excited-state PESs, including ethylene, the carbon dimer, and the methylenimmonium cation, indicating that transferable deep-learning QMC can pave the way towards highly accurate simulation of excited-state dynamics.

Ab-initio Simulation of Excited-State Potential Energy Surfaces Using Transferable Deep Quantum Monte Carlo

The paper presents a method for the simulation of excited-state potential energy surfaces (PESs) with enhanced accuracy and computational efficiency through the use of transferable deep quantum Monte Carlo (QMC). This approach is particularly relevant when considering the simulation of quantum chemical systems where both ground and excited-state PES predictions are sought, especially in contexts such as photochemistry and light-matter interactions.

Methodology

Traditionally, quantum chemical calculations for excited states entail significant computational expense, limiting the practical application in dynamic simulations or where large numbers of molecular geometries are involved. This research addresses these challenges by leveraging neural network wave functions optimized across various geometries. The method innovatively combines weight sharing and dynamic ordering of electronic states within a neural network framework, increasing efficiency and computational feasibility.

Here, the authors introduce an advanced neural network architecture capable of representing similarities across different molecular configurations, lowering computational costs by two orders of magnitude compared to conventional single-point QMC simulations. Furthermore, by optimizing variational quantum Monte Carlo (VMC) methods across multiple geometries and electronic states simultaneously, the approach supports a coherent and accurate description of excited-state processes.

Key features of the methodology include:

• Weight Sharing & Dynamical State Ordering: Neural network parameters are shared across different electronic states, promoting error cancellation and optimization stability. Dynamic ordering adapts orthogonalization based on state energy, thereby accommodating level crossings and achieving continuous ansatzes.
• Application of Causal Self-Attention: The inclusion of both electronic and nuclear nodes in the ansatz enhances expressivity, allowing the model to incorporate explicit dependencies on the molecular geometries.

Results

The efficacy of the proposed method is demonstrated across three complex systems: ethylene, carbon dimer, and methylenimmonium cation.

1. Ethylene Relaxation PESs: The prediction of ethylene photochemical relaxation processes showed marked cost reduction while maintaining high accuracy. The dynamic state ordering skillfully managed continuity through conical intersections and model optimization.
2. Carbon Dimer Dissociation: The paper of multiple low-lying electronic states of the carbon dimer demonstrated effective handling of strong static and dynamic correlation, achieving computational savings and improved error cancellation.
3. Methylenimmonium Cation Multi-Dimensional PES: This example highlighted the significant computational gains achieved on higher-dimensional grids, where joint optimizations significantly cut down on resource requirements while preserving accuracy.

Implications and Future Directions

The research has profound implications for the simulation of electronic interactions in quantum chemistry and photodynamics, offering a scalable approach to simulating systems that traditionally demand substantial computational effort. It sets a precedent for quantum chemistry applications, where enhanced accuracy and efficiency will facilitate studies in areas such as material design and photo-controlled drug delivery.

Moreover, the transferable deep QMC framework provides a robust basis for further exploration of excited-state dynamics using machine learning techniques. Future developments could extend this approach to incorporate a broader range of molecular systems and integrate advanced machine learning models for improved predictive power.

In conclusion, the paper presents a significant advancement in the simulation of excited-state dynamics, reducing computational burdens while enriching the accessible accuracy in quantum chemical calculations. This development opens new avenues for practical applications and further research exploring the integration of neural networks with quantum chemistry.