Doubly Hybrid Meta DFT:  New Multi-Coefficient Correlation and Density Functional Methods for Thermochemistry and Thermochemical Kinetics

This paper presents two new multi-coefficient correlation and density functional methods based on mixing scaling-all-correlation (SAC) theory and hybrid meta density functional theory with empirical parameters. Both methods were optimized against a database of 109 atomization energies and 42 barrier heights. The resulting methods, called MC3BB and MC3MPW, were tested against a database of saddle point geometries, and scaling factors were optimized for calculating vibrational frequencies. The two new methods were compared to the methods that we have previously determined to be most efficient for thermochemistry and thermochemical kinetics, where the criterion is the average of the mean unsigned errors for bond energies and barrier heights. These comparisons show that MC3BB is more accurate than any other method that has comparable cost. Both new methods are well suited for direct dynamics calculations that require Hessians. The new approach is called doubly hybrid density functional theory if kinetic energy density is not included in the functional and doubly hybrid meta density functional theory if it is.