Zero-Point Energies from Bond Orders and Populations Relationship

Our group recently reported a bond energy from bond orders and populations (BEBOP) model that can quantitatively predict atomization energies and bond energies using well-conditioned orbital populations that are obtained from ab initio single point energy calculations. We now show that a similar procedure can be used to predict zero-point vibrational energies (ZPEs) of a molecule using just one ab initio single point energy calculation. Like the BEBOP model, our ZPE-BOP model is based on Mulliken orbital populations obtained from a minimum basis set projection of Hartree-Fock orbital populations using a well-conditioned basis set. Seven atom-pairwise parameters were fit to reproduce B3LYP-scaled ZPEs for molecules containing H, Li, Be, B, C, N, O, and F atoms using expressions that involve an extended Hückel-type bond energy term, a short-range anharmonic energy term, and a coupled three-body oscillator energy term. Notably, this first-generation model has better accuracies (as benchmarked to 109 species from the G2/97 test set and an additional 83 reference species) than other highly efficient and approximate quantum chemistry methods (e.g., AM1, PM6, and PM7 semiempirical methods). Moreover, this model appears to be able to extrapolate ZPEs for molecules that are not part of our training set, indicating that ZPE-BOP would be transferable across chemical space.