Convenient implementation of rung-3.5 density functionals in standard Gaussian-basis codes

Developing more broadly accurate density functional approximations can be accomplished not only by new parameterizations with existing ingredients but also by using new ingredients encoding new physics, such as rung-3.5 energy densities that allow a better balance of static correlation and electron delocalization and also allow an explicit treatment of static correlation. Here, we introduce a convenient implementation of rung-3.5 energy densities as ingredients for new density functionals. With this implementation, overlap-projected rung-3.5 functionals can be implemented in any code that uses Gaussian basis functions by computing a set of auxiliary basis functions with the same form as Gaussian basis functions but having modified orbital exponents. We illustrate the method with M11po, a density functional constructed from the broadly accurate M11plus density functional by replacing all Coulomb-projected rung-3.5 ingredients with overlap-projected rung-3.5 ingredients, without reparameterization. M11po gives performance approaching that of the harder-to-implement M11plus functional, and it is freely available as an extension to the PySCF electronic structure package.