We provide a rigorous derivation of a class of double-hybrid approximations, combining Hartree-Fock exchange and second-order Møller-Plesset correlation with a semilocal exchange-correlation density functional. These double-hybrid approximations contain only one empirical parameter and use a density-scaled correlation energy functional. Neglecting density scaling leads to a one-parameter version of the standard double-hybrid approximations. We assess the performance of these double-hybrid schemes on representative test sets of atomization energies and reaction barrier heights, and we compare to other hybrid approximations, including range-separated hybrids. Our best one-parameter double-hybrid approximation, called 1DH-BLYP, roughly reproduces the two parameters of the standard B2-PLYP or B2GP-PLYP double-hybrid approximations, which shows that these methods are not only empirically close to an optimum for general chemical applications but are also theoretically supported.
Bibliographical noteFunding Information:
K.S. thanks Professor I. Othman (Atomic Energy Commission of Syria) for his support. J.T. and A.S. acknowledge support from Agence Nationale de la Recherche (contract Wademecom 07-BLAN-0272). We also thank J. G. Ángyán for discussions.