A Bond-Energy/Bond-Order and Populations Relationship.

We report an analytical bond energy from bond orders and populations (BEBOP) model that provides intramolecular bond energy decompositions for chemical insight into the thermochemistry of molecules. The implementation reported here employs a minimum basis set Mulliken population analysis on well-conditioned Hartree-Fock orbitals to decompose total electronic energies into physically interpretable contributions. The model's parametrization scheme is based on atom-specific parameters for hybridization and atom pair-specific parameters for short-range repulsion and extended Hückel-type bond energy term fitted to reproduce CBS-QB3 thermochemistry data. The current implementation is suitable for molecules involving H, Li, Be, B, C, N, O, and F atoms, and it can be used to analyze intramolecular bond energies of molecular structures at optimized stationary points found from other computational methods. This first-generation model brings the computational cost of a Hartree-Fock calculation using a large triple-ζ basis set, and its atomization energies are comparable to those from widely used hybrid Kohn-Sham density functional theory (DFT, as benchmarked to 109 species from the G2/97 test set and an additional 83 reference species). This model should be useful for the community by interpreting overall ab initio molecular energies in terms of physically insightful bond energy contributions, e.g., bond dissociation energies, resonance energies, molecular strain energies, and qualitative energetic contributions to the activation barrier in chemical reaction mechanisms. This work reports a critical benchmarking of this method as well as discussions of its strengths and weaknesses compared to hybrid DFT (i.e., B3LYP, M062X, PBE0, and APF methods), and other cost-effective approximate Hamiltonian semiempirical quantum methods (i.e., AM1, PM6, PM7, and DFTB3).

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 Re, De, and ωe, 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 Re, De, and ωe, 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.