Accurate Ab-initio Neural-network Solutions to Large-Scale Electronic Structure Problems (2504.06087v1)

Abstract: We present finite-range embeddings (FiRE), a novel wave function ansatz for accurate large-scale ab-initio electronic structure calculations. Compared to contemporary neural-network wave functions, FiRE reduces the asymptotic complexity of neural-network variational Monte Carlo (NN-VMC) by $\sim n_\text{el}$, the number of electrons. By restricting electron-electron interactions within the neural network, FiRE accelerates all key operations -- sampling, pseudopotentials, and Laplacian computations -- resulting in a real-world $10\times$ acceleration in now-feasible 180-electron calculations. We validate our method's accuracy on various challenging systems, including biochemical compounds, conjugated hydrocarbons, and organometallic compounds. On these systems, FiRE's energies are consistently within chemical accuracy of the most reliable data, including experiments, even in cases where high-accuracy methods such as CCSD(T), AFQMC, or contemporary NN-VMC fall short. With these improvements in both runtime and accuracy, FiRE represents a new `gold-standard' method for fast and accurate large-scale ab-initio calculations, potentially enabling new computational studies in fields like quantum chemistry, solid-state physics, and material design.

Analyzing the Efficiency and Accuracy Paradox in Large-Scale Electronic Structure Calculations with Finite-Range Embeddings

The authors present a compelling paper that explores the proficiency of a novel finite-range embedding technique, known as FiRE, for addressing large-scale ab-initio electronic structure problems. This paper is situated at the nexus of enhancing computational scaling while safeguarding the accuracy typically offered by neural-network variational Monte Carlo (NN-VMC) approaches. The research embraces domains such as quantum chemistry, solid-state physics, and materials science, promising significant implications for those fields.

The central thrust of the paper is the innovative wave function ansatz named FiRE, which surpasses conventional limitations by reducing the computational complexity of NN-VMC from $O(n^4)$ to $O(n^3)$. This significant reduction stems from implementing restricted electron-electron interactions within the neural network, thus enabling effective performance on larger scales without compromising the calculation speed. FiRE unlocks new potential in large-scale calculations with a demonstrated $10\times$ acceleration in 180-electron scenarios, a feat previously unattainable due to computational constraints.

Significant portions of the paper are dedicated to comparing FiRE's performance against other state-of-the-art neural wave function models, including LapNet, FermiNet, and Psiformer. The experimental results highlight FiRE's ability to reach the chemical accuracy for complex systems, including strong electron correlation scenarios frequently encountered in conjugated hydrocarbons and organometallic compounds. Notably, FiRE achieves these results while facilitating the derivation of relative energies at a fraction of the computational expense associated with existing approaches, positioning itself as a promising candidate for emerging as a new standard in quantum chemistry computations.

The methodology section elaborately describes the computational framework underpinning FiRE, including the locality assumption for electron correlation effects. Unlike fully connected architectures, FiRE operates with a strategically chosen cutoff distance, focusing computational efforts on pertinent electron interactions within this range. The authors also introduce a global attention-based Jastrow factor to handle long-range interactions, enabling FiRE to retain favorable scaling properties while enhancing neural wave function accuracy.

The numerical results underscore FiRE’s efficacy across various benchmarks, exhibiting superior performance in calculating non-covalent interactions, singlet-triplet energy gaps in acenes, and accurate ionization potentials for organometallic compounds. The efficiency is further underscored through comprehensive ablation studies and convergence analyses, revealing empirically derived error scaling laws which echo the theoretical predictions in recent works on VMC convergence rates. Remarkably, FiRE maintains robust performance in system sizes involving 500 valence electrons and above, a testament to its architectural advances.

The implications of this research extend towards reducing the gap between accessible quantum chemical methods and those requiring computationally intensive corrections or approximations. By mitigating the necessity for intricate configurations such as active spaces in multireference calculations, FiRE presents an automated pathway to achieving high precision in molecular energy calculations.

In the broader context of the field, this paper suggests promising avenues for future research. The scalability of FiRE in periodic or tightly packed structures presents enriching domains for further exploration. Additionally, the discussion highlights potential challenges in further refining FiRE's implementation complexity and optimization convergence rates for even larger systems, which are crucial for expanding its applicability.

In summary, this work on FiRE is a significant stride in reconciling the dichotomy of computational efficiency and accuracy in electronic structure calculations. As this framework paves the way for more extensive and intricate ab-initio studies, it raises fascinating prospects for advancing theoretical insights and practical applications in a multitude of scientific domains.