Relativistic Fermionic Neural Networks Based on Zeroth-Order Regular Approximation: ZORANet.

Area of Science:

• Computational chemistry
• Quantum mechanics
• Artificial intelligence in science

Background:

• Relativistic effects are crucial for accurate electronic structure calculations, especially for heavy elements.
• Existing deep neural network methods face challenges in handling relativistic quantum chemistry problems.
• The scalar zeroth-order regular approximation (ZORA) is a common relativistic approximation but suffers from gauge-dependent errors.

Purpose of the Study:

• Introduce ZORANet, a novel Fermionic neural network framework for relativistic electronic structure calculations using scalar ZORA.
• Address numerical challenges in relativistic calculations, including electron-nucleus cusp correction and importance sampling.
• Develop variants (scaled ZORANet, atomic ZORANet) to mitigate ZORA's gauge-dependent errors.

Main Methods:

• Developed ZORANet, a Fermionic neural network framework based on scalar ZORA.
• Implemented electron-nucleus cusp correction and importance sampling for training stability and error reduction.
• Created scaled ZORANet and atomic ZORANet variants to address gauge dependence.

Main Results:

• ZORANet and scaled ZORANet energies show excellent agreement with exact ZORA and Dirac results for hydrogen-like systems.
• ZORANet achieves chemical accuracy for ionization potentials and electron affinities of first and second-row elements, outperforming FermiNet.
• Atomic ZORANet matches state-of-the-art accuracy for hydride dissociation energies, surpassing FermiNet.

Conclusions:

• ZORANet is a highly accurate all-electron method for relativistic quantum chemistry.
• It effectively treats electron correlation and relativistic effects with comparable computational cost to FermiNet.
• ZORANet shows promise for developing integral ab initio relativistic quantum chemistry methods.