(681i) A Combinatorial Approach for Developing Minimally-Parameterized and Highly-Transferable Density Functionals

Conventionally, the development of semi-empirical density functionals has involved selecting a handful of functional forms and optimizing the parameters via least-squares fits to accurate data. However, such a procedure does not ensure that the resulting functional will be transferable to systems outside of its training set. In addition, overfitting to training data can lead to both poor performance on independent test cases and unwanted unphysical characteristics.

Since semi-empirical density functionals utilize power series enhancement factors, the systematic optimization of a density functional can be imagined as a combinatorial search problem, with all possible combinations of the available power series variables serving as potential functional forms. This approach increases the number of candidate functional forms from just a handful to 2ⁿ-1, where n is the total number of available variables. With the significantly enlarged functional space, fits can be characterized not only based on their training set performance, but additionally with respect to their transferability to an independent test set as well as their physical characteristics.

This procedure has recently been used to partially explore a meta-GGA functional space of 10⁴¹Â possible functional forms, resulting in the development of Ï?B97M-V, a range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation. With only 12 linear parameters, the functional significantly outperforms methods in and below its class that have upwards of 50 linear parameters on non-covalent interactions, isomerization energies, thermochemistry, and barrier heights. The merits of Ï?B97M-V will be demonstrated by comparing it to leading density functionals (such as M06-2X and M11) across a database of nearly 5,000 data points.