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!