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

X. L. Pan, H. L. Song+7 more|arXiv (Cornell University)|Feb 28, 2026

Nuclear Materials and Properties0 citations

TL;DR

Proposes a general linear correction to remove dependence on model parameters in DFT+X energies, enabling direct comparison across different interaction parameters, demonstrated within DFT+U and applied to U-M (M=Al, Ga, In) alloys under high pressure.

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.

Motivation & Objective

• Address ambiguity in DFT+X total energies caused by model Hamiltonian parameters.
• Introduce a general linear correction to remove energy contributions from the model, enabling direct energy comparisons across interaction parameters.
• Demonstrate the method within DFT+U and apply it to uranium-based binaries under high pressure.
• Evaluate the approach against experimental benchmarks and extend validation to other systems.

Proposed method

• Develop a linear-correction framework that eliminates ambiguous energy contributions from the model Hamiltonian in DFT+X energies.
• Demonstrate the method using DFT+U as the primary example.
• Apply the corrected energies to U-M (M=Al, Ga, In) alloys under high pressure to address phase stability.
• Validate the approach by comparing with experimental observations and known formation enthalpies across diverse systems.

Experimental results

Research questions

• RQ1 Can a general linear correction remove the intrinsic ambiguity introduced by model parameters in DFT+X energies?
• RQ2 Does the corrected DFT+U energy yield accurate phase stability predictions for U-M alloys under high pressure?
• RQ3 Is the linear correction approach robust across diverse systems beyond U-M, such as Np-Al, U-Si, Cu-O, MnSnAu, and surface adsorption scenarios?

Key findings

• The linear correction method eliminates ambiguous energy contributions from the model Hamiltonian in DFT+X energies.
• Corrected energies enable direct comparison across different interaction parameters within DFT+U.
• Applied to U-M (M=Al, Ga, In) under high pressure, the method resolves discrepancies with experimental observations of phase stability and predicts new stable intermetallics.
• The approach yields accurate formation enthalpies for diverse systems, validating broad applicability to other DFT+X methods.