There are about four or five distinct ingredients used in modern density functionals:

• integrals of functions of the density and its gradients (GGAs, etc)
• inclusion of the kinetic energy density in such expressions (meta-GGAs)
• a fraction of exact Hartree–Fock exchange (or a length-scale-screened variant)
• a contribution from a wavefunction-based correlation method like MP2 or RPA

Now there is another:

Tim Wiles and F R Manby, ‘Wavefunction-like Correlation Model for Use in Hybrid Density Functionals’, J. Chem. Theory Comput., Article ASAP, DOI: 10.1021/acs.jctc.8b00337.

In this paper we introduce the UW12 correlation functional:

• an explicit functional of occupied orbitals (i.e. a functional  of the 1-RDM)
• an F12-like model of dynamic electron correlation
• can be self-consistently optimized in a straightforward way
• most of the complicated stuff handled through familiar DFT quadrature
• no double-summation over virtual orbitals, so fast basis-set convergence

This functional can be used as a viable (and hybrid) alternative to use of MP2 in double-hybrid functionals, as we demonstrate in this paper. Our hybrid XCH-BLYP-UW12 functional has only one parameter, and is competitive with more highly parameterised  double hybrids for reaction barrier test sets.

If you don’t have access and want to read the paper, just email Fred.

Congratulations to Tim for publishing this work!