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 order to address this issue, in this work, we proposed a general linear correction method (LCM) 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 was demonstrated and validated within the framework of DFT+U, an important member of the DFT+X family. It was then applied to important nuclear materials of uranium-based binaries U-M (M=Al, Ga, In) alloys. With this thorough investigation, we resolved the long-standing discrepancy between theoretical predictions and experimental observations of phase stability with unprecedented accuracy, and predicted several previously unknown stable intermetallic compounds under high pressure. The broad applicability of the method was 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. Since LCM allows the parameter U to be self-consistently determined by linear response approach so that restoring the exact xc functional behavior of piecewise straight line in the ground state energy as a function of fractional number of electrons from the pure DFT’s piecewise convexity, this work establishes LCM-DFT+U as a fully first-principles approach (i.e., do not requires any experimental input) and validates the linear correction method as a robust and general scheme that can be readily extended to other DFT+X methods.

电子强关联体系；Hubbard模型；DFT+U；线性修正方法；铀合金