Local hybrid functionals based on density matrix products.

We present a novel similarity metric comparing exact and semilocal density functional theory (DFT) exchange holes in real space. This metric is obtained from the product of the one-particle density matrix and the uniform electron gas model density matrix. The metric is bound between 0 and 1, 1 in the uniform electron gas, 0 in regions asymptotically far from finite systems, and can detect delocalization of the exact exchange hole and effective fractional occupations. We also present a parameter-free local hybrid functional that uses this similarity metric to locally mix exact and semilocal DFT exchange energy densities. The resulting functional gives better thermochemistry and reaction barrier heights than our original local hybrids [Jaramillo et al., J. Chem. Phys. 118, 1068 (2003)], while retaining moderate accuracy for symmetric radical cation dimers.