Nonspherical model density matrices for Rung 3.5 exchange-correlation functionals

Kohn-Sham (KS) density functional theory models electrons' complicated many-body interactions using exchange-correlation density functionals. Semilocal functionals, rungs 1-3 on the ``Jacob's Ladder'' of approximate exchange-correlation functionals, model the XC energy density at each point r using information from an infinitesimal region about r. Nonlocal fourth-rung exchange functionals incorporate a dependence on the entire one-particle density matrix of the noninteracting KS reference system. Nonlocal functionals provide improved accuracy for many properties, but have higher computational costs, particularly in extended systems. ``Rung 3.5'' exchange functionals incorporate the product of the KS density matrix with a semilocal model density matrix, balancing the strengths and limitations of semilocal and nonlocal approximations. This work proposes new semilocal model density matrices for Rung 3.5 functionals. Semilocal density matrices containing 1-3 parameters improve upon previous work for both molecular thermochemistry and kinetics, and show promise for development of future non-empirical Rung 3.5 Density Functionals.