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!

Delocalization error in approximate DFT clearly manifests itself in homodimer cation systems (like H₂⁺ or (H₂O)₂⁺), with GGA functionals typically leading to large energy errors and qualitatively incorrect structures. It also causes problems in a variety of other chemically important contexts.

Spurious delocalization of spin density in a small radical-cation water cluster.

We have found that the delocalization error in densities can cause major errors in WF-in-DFT embedding – these errors are not particular to the projector-based scheme we use,but simple expose a limitation of partitioning systems based on the electron density when that electron density is qualitatively flawed.

Following work from Kieron Burke, we have found the simple expedient of using Hartree-Fock densities in WF-in-DFT calculations really improves reliability in cases where there is a serious delocalization error, and doesn’t cause major problems (in the examples we have studied) when there is not a big delocalization error.

You can read about this work in a paper that has just appeared online: Pennifold et al., ‘Correcting density-driven errors in projection-based embedding’, J. Chem. Phys. 146, 084113 (2017); DOI: 10.1063/1.4974929.

Clem’s paper on the interpretation of pump-probe experiments on the purple-bacteria light-harvesting complex LHII is now in print in J Phys Chem B.

Through careful and extensive calculations involving molecular dynamics, time-dependent density functional theory, and quantum dynamics we have shown that the interpretation of anisotropy decay rates in terms of strength of coupling to a dissipative bath is not so easily justified. The reason is that static (or inhomogeneous) disorder itself produces anisotropy decay at about the experimentally observed rate.

The paper also contains an epic, paper-length appendix on how to compute such quantities for the circularly degenerate oscillator model.

Congratulations Clem!

C. Stross, M. W. Van der Kamp, T. A. A. Oliver, J. N. Harvey, N. Linden and F. R. Manby, “How Static Disorder Mimics Decoherence in Anisotropy Pump–Probe Experiments on Purple-Bacteria Light Harvesting Complexes”, J. Phys. Chem. B, 120, 11449-11463 (2016), DOI: 10.1021/acs.jpcb.6b09916