A new advancement in computational materials science is poised to accelerate the discovery of novel materials, particularly those containing heavier elements. Researchers have successfully extended the phaseless auxiliary-field quantum Monte Carlo (pw-AFQMC) method to accurately incorporate spin-orbit coupling (SOC), a relativistic effect crucial for understanding the behavior of materials with heavier atoms.
The breakthrough, detailed in research led by Zheng Liu and Shiwei Zhang, in collaboration with Fengjie Ma, addresses a longstanding challenge in the field. Traditionally, accurately modelling materials where SOC plays a significant role has been computationally prohibitive. This new method allows for the concurrent treatment of both electronic correlation and SOC effects, opening doors to more reliable predictions of material behavior under extreme conditions.
Spin-orbit coupling arises from the interaction between an electron’s spin and its orbital motion. Its influence grows with atomic number, impacting a material’s magnetic, electronic, and topological characteristics. The team achieved this integration by employing fully-relativistic pseudopotentials derived from Dirac-like equations – a cornerstone of relativistic quantum mechanics. These pseudopotentials effectively simplify the complex interactions within the material, making calculations more manageable without sacrificing accuracy.
The modified pw-AFQMC method utilizes a two-component Hamiltonian in the spinor basis, effectively doubling the computational space to account for electron spin. This increase in computational demand is offset by the phaseless approximation, a key methodological innovation that avoids the “sign problem” – a common obstacle in quantum Monte Carlo simulations. By restricting the trial wave function to be non-negative, the phaseless approximation enhances the efficiency and stability of the calculations.
To demonstrate the accuracy of their approach, the researchers performed calculations on iodine molecules (I2) and bulk lead (Pb). The calculations for I2 yielded a dissociation energy of 7.637 eV, a substantial improvement over previous scalar-relativistic calculations which produced 7.513 eV. The discrepancy of 0.124 eV underscores the significant impact of SOC on accurately describing diatomic molecular dissociation.
Similarly, the cohesive energy of lead was calculated to be 2.341 eV, closely aligning with both density functional theory (DFT) results (2.378 eV) and experimental data (2.365 eV). This close agreement, within 0.037 eV, validates the method’s ability to capture subtle energetic details influenced by SOC.
Beyond validating the method, the team applied it to predict the transition pressure of indium phosphide (InP), a compound semiconductor. By constructing and analyzing equations of state for both the zinc-blende and rock-salt crystal structures, they accurately determined the transition pressure to be 14.2 GPa – the pressure at which InP undergoes a structural phase change.
The implications of this advancement extend to several key areas of materials science. The ability to accurately model SOC is paramount for the development of materials for spintronics, topological quantum computing, and advanced magnetic storage. These fields rely on precisely understanding and controlling the interplay between electron spin and orbital motion.
The optimized multiple-projector norm-conserving pseudopotentials used in this work are derived from fully-relativistic (FR) all-electron Dirac-like equations. These pseudopotentials replace the complex interactions between valence electrons and atomic cores with a smoother, computationally tractable potential, while still accurately capturing relativistic effects. The non-local component of these pseudopotentials is crucial for incorporating SOC and was carefully formulated and implemented within the phaseless pw-AFQMC framework.
The researchers emphasize that this work bridges the gap between fundamental quantum physics and the practical design of next-generation materials. By providing a more accurate and efficient method for modelling materials with heavy elements, this advancement promises to accelerate the pace of materials discovery and innovation. The ability to accurately predict material properties under extreme conditions will be particularly valuable for designing materials for demanding applications.
The development, detailed in a paper published on (as evidenced by a preprint available on arXiv), represents a significant step forward in computational materials science, offering a powerful new tool for researchers seeking to unlock the potential of advanced materials.
