Double-hybrid density-functional theory with density-based basis-set correction

We develop the theory justifying the application of the density-based basis-set correction (DBBSC) method to double-hybrid approximations in order to accelerate their basis convergence. We show that, for the oneparameter double hybrids based on the adiabatic connection, the exact dependence of the basis-set correction functional on the coupling-constant parameter $\lambda$ involves a uniform coordinate scaling by a factor 1/$\lambda$ of the density and of the basis functions. Neglecting this uniform coordinate scaling corresponds essentially to the recent work of Mester and K{\'a}llay [J. Phys. Chem. Lett. 16, 2136 (2025)] on the application of the DBBSC method to double-hybrid approximations. Test calculations on molecular atomization energies and reaction barrier heights confirm that the DBBSC method efficiently accelerates the basis convergence of double-hybrid approximations, and also show that neglecting the uniform coordinate scaling is a reasonable approximation.