General linear correction method for DFT+X energy: application to U-M (M=Al, Ga, In) alloys under high pressure

TL;DR

This paper introduces a linear correction method for DFT+X approaches, notably DFT+U, to eliminate ambiguity in energy calculations, enabling accurate phase stability predictions and discovery of new compounds under high pressure.

Contribution

It proposes a general linear correction scheme that removes model parameter ambiguity in DFT+X methods, validated within DFT+U and applied to uranium alloys and other systems.

Findings

Resolved discrepancies between theory and experiment for U-M alloys under high pressure.

Predicted several new stable intermetallic compounds at high pressure.

Validated the correction method across diverse materials systems.

Abstract

DFT+X methods, such as DFT+U and DFT+DMFT, are important supplements to standard density functional theory when strong on-site Coulomb interactions are present. However, the involvement of external parameters in the underlying model Hamiltonian introduces intrinsic ambiguity when comparing the total energies obtained with different model parameters. This renders DFT+X approaches semi-empirical and severely hinders their capability to describe phase ordering and phase stability, especially when reliable experimental benchmarks are unavailable, such as under high pressure. In this work, we resolve this longstanding problem by proposing a general linear correction method that eliminates the ambiguous energy contributions introduced by the model Hamiltonian in DFT+X approaches, thereby enabling direct comparison of their energies calculated with different interaction parameters. The method is demonstrated and validated within the framework of DFT+U, an important member of the DFT+X family. It is then applied to important nuclear materials of uranium-based binaries U-M (M=Al, Ga, In) alloys. With this approach, we resolve the long-standing discrepancy between theoretical predictions and experimental observations of phase stability with unprecedented accuracy, and predict several previously unknown stable intermetallic compounds under high pressure. The broad applicability of the method is further confirmed by accurate predictions of formation enthalpies for diverse systems, including Np-Al, U-Si, and Cu-O binaries, the ternary MnSnAu compound, and oxygen adsorption on the Cu(111) surface. This work establishes linear-corrected DFT+U as a fully first-principles approach and validates the linear correction method as a robust and general scheme that can be readily extended to other DFT+X methods.