Cu-Au intermetallic alloys are classic paradigms in the history of alloy theory for studying order-disorder transition, phase stability, and so on. However, density functional theory with a generalized gradient approximation (GGA) fails to describe their formation energies and Au-rich ground states, e.g., calculated formation energies are nearly 40% smaller than experimental values. In this work, we found that these discrepancies, which are also common in other Cu-transition metal (TM) intermetallic alloys, are actually caused by the fact that GGA produces Cu-3d bands with a shallower energy level than the experimental results, leading to incorrect d-d hybridizations. By using the Hubbard U correction to adjust the d-bands to the correct position, the discrepancies in GGA calculations are eliminated. Our finding that the correct d-bands position is the key to characterize Cu-TMs, which can be achieved efficiently by applying the Hubbard U correction.

Cu-Au金属间合金是合金理论史上研究有序-无序转变、相稳定性等的经典范例。然而，采用广义梯度近似（GGA）的密度泛函理论无法描述它们的形成能和富Au基态，例如，计算的形成能比实验值小近40%。在这项工作中，我们发现这些差异在其他 Cu-过渡金属 (TM) 金属间合金中也很常见，实际上是由于 GGA 产生的 Cu-3 d带的能级比实验结果更浅，导致错误的dd杂交。通过使用 Hubbard U校正将d带调整到正确的位置，可以消除 GGA 计算中的差异。我们发现正确的d带位置是表征 Cu-TM 的关键，这可以通过应用 Hubbard U校正来有效实现。