Three-Body Dispersion Corrections to the Spherical Atom Model: The PFD-3B Density Functional

The performance of the isotropic spherical atom model can be significantly enhanced through combination with anisotropic three-body dispersion interactions to give the new PFD-3B density functional, which reduces the mean absolute deviation (MAD) relative to CCSD(T)/CBS benchmark energies from 0.78 to 0.19 kcal/mol for the S22 test set. Comparison with the extended S22 × 5 test set in the figure indicates that this accuracy is maintained through large variations in geometry. The performance of the PFD-3B functional over the S22 × 5 test set is superior to any of the functionals previously applied to this set. Over the S22 set of examples, the MADs from the CCSD(T)/CBS values for R_e, D_e, and ω_e, are 0.032 Å, 0.21 kcal/mol, and 6 cm^-1, respectively. Over a comparable set of 26 examples containing second and third row atoms, the MADs from the CCSD(T)/CBS values for R_e, D_e, and ω_e, are 0.033 Å, 0.19 kcal/mol, and 5 cm^-1, respectively. If used to optimize the geometry of the 48 examples, on average the PFD-3B functional introduces an error of only 0.042 kcal/mol in CCSD(T) single-point energies. This small error combines with the reported analytical first and second derivatives to makes the PFD-3B functional an attractive model for geometry optimization and zero-point energy calculations.