  We provide a rigorous derivation of a class of double-hybrid approximations,
combining Hartree-Fock exchange and second-order Moller-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.
