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 one-parameter double hybrids based on the adiabatic connection, the exact dependence of the basis-set correction functional on the coupling-constant parameter λ involves a uniform coordinate scaling by a factor 1/λ of the density and of the basis functions. Neglecting this uniform coordinate scaling corresponds essentially to the recent work of Mester and Kállay, 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.