I shall discuss the design of a family of next generation of density functional theories. In contrast to most approaches to functional design, we have adopted a combinatorial approach, in which we have trained a huge number of functionals (over 10<sup>10</sup> in the case of meta-GGA based functionals). The functional from each class that performs best on independent test data (survival of the most transferable) is self-consistently trained to yield new generation functionals that are very promising for application purposes. A key component of these functionals is the non-local VV10 density-density correlation functional for dispersion. VV10 enables highly accurate treatment of non-bonded interactions, if the entire functional is self-consistently trained.<br/>This approach has been applied to the development of 4 different functionals, spanning the top 3 rungs of Perdew’s Jacob’s Ladder classification scheme. At Rung 3, a meta-GGA functional, B97M-V, produces more accurate chemical results (on a statistical basis) than any other reported to date. At Rung 4, a combinatorially designed hybrid GGA, ωB97X-V, significantly improves over B97M-V for thermochemistry and kinetics. Extending the GGA treatment of the semi-local contribution to meta-GGA yielded the ωB97M-V functional, which is a further significant improvement in overall accuracy. These functionals have been included in a large-scale comparison of 200 different density functionals from Rungs 1-4 across 5000 pieces of reliable ab initio reference data. The first part of the talk will be a concise review of these results.<br/>The major part of the talk will focus on unpublished work on extending the combinatorial design paradigm to double hybrid density functionals (DHDFs), which comprise Rung 5 of Jacob’s Ladder. DHDFs include non-local correlation via the virtual Kohn-Sham orbitals, typically via a second order perturbation theory expression. I will report on the extent to which a combinatorially designed Rung 5 functional can surpass the performance of the best Rung 4 functionals (and existing DHDFs). Answering this question also provides a partial answer to the question of what is the highest level of accuracy attainable from DFT today.

Combinatorial design and assessment of density functionals up to the top of Jacob's ladder

256th National Meeting (2018)

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