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DataThe Schrödinger equation (SE) [1], a foundational pillar in quantum mechanics, provides a deep understanding of particle behavior at atomic and subatomic scales. It offers a mathematical description of the quantum scale, revealing insights into the probabilistic nature of particle dynamics and the quantized energy levels within these systems. Notably, the time-independent form of the SE, particularly in many-body systems [2], is pivotal for deciphering complex behaviors in atomic and molecular structures. Solving the many-body SE is a significant challenge in quantum chemistry and condensed matter physics, especially for large systems [3]. The Hamiltonian operator in the SE combines the Laplacian and potential energy terms, making the equation complex to solve analytically for intricate molecules.
DFT [4] is widely employed for analyzing the electronic structures of many-body systems, particularly in atoms, molecules, and condensed phases. DFT simplifies complex calculations by using electron density rather than wave functions, based on the foundational Hohenberg-Kohn theorem [5]. Despite its utility, DFT’s computational load increases exponentially with system size [6]. The method also grapples with accuracy issues due to approximations in electron interaction modeling [7] and challenges in calculating strong electron-electron correlations in materials like transition metal complexes [8, 9, 10]. Further complexities arise in time-dependent DFT applications for excited states and optical properties [11, 12, 13, 14], and electron repulsion adds to the intricacy in electronic structure calculations [15]. While beneficial, DFT faces scalability and precision issues in complex materials [16, 17].
In addressing existing challenges in materials science, this work introduces a novel physics-informed [18], vision-based deep learning model, QuantumShellNet, designed for swift and precise prediction of ground-state eigenvalues in materials. QuantumShellNet begins by approximating the system’s Hamiltonian for electronic structure derivation. This structure, transformed into a standardized image format, is then fed into an orbital encoder convolutional neural network (CNN). The model subsequently utilizes an atomic multilayer-perceptron (AMLP) block, integrating key material properties, for predictions. With approximately 235,000 parameters, QuantumShellNet excels in computational efficiency, surpassing traditional DFT and advanced ML models like FermiNet [19] and PsiFormer [20].
Key contributions of this work include: (i) the introduction of an orbital-to-vector approach that significantly improves computational efficiency by reducing from higher orders to O(1) [21] and decreasing training time; (ii) the development of the AMLP model for accurate predictions of total energies of elements and molecules using orbital vectors; and (iii) an enhanced capability for predicting unseen materials, providing new insights into various systems.
Cite this article (BibTeX – Soon):
@article{polat2025quantumshellnet,
title={QuantumShellNet: Ground-state eigenvalue prediction of materials using electronic shell structures and fermionic properties via convolutions},
author={Polat, Can and Kurban, Hasan and Kurban, Mustafa},
journal={Computational Materials Science},
volume={246},
pages={113366},
year={2025},
publisher={Elsevier}
}References
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