Zero-Point Energies from Bond Orders and Populations Relationships

We report two analytical models for calculating quantum mechanical zero point energies (ZPEs) based on data from just a single-point quantum chemistry energy calculation. Fol- lowing our earlier model that partitioned molecular atomization energies and bond ener- gies using bond orders and orbital population analyses (i.e. the BEBOP method), the ZPE- BOPn methods reported here partition molecular zero-point energies from bond orders and orbital populations. As a starting point, the ZPE-BOP1 model employs a Mulliken orbital populations via a minimal population localization from a B3LYP/6-311+G(3d2f,2df,2p) calculation and leverages an extended Hückel-type vibrational bond energy term with two atom-pairwise parameters that are fit to reproduce scaled ZPEs from B3LYP calculations. For improved accuracy, the ZPE-BOP2 model employs Mulliken orbital populations via a minimal population localization from an ROHF/6-311+G(3d2f,2df,2p) calculation and employs an extended Hückel-type vibrational bond energy term, a short-range anharmonic energy term, and a coupled three-body oscillator energy term with seven atom-pairwise parameters. Both methods efficiently predict ZPEs in molecules without the need for a costly Hessian calculation, but ZPE-BOP2 outperforms ZPE-BOP1 in strained and long- chain molecules and provides reasonable predictions of ZPEs from Hessian calculations using semiempirical quantum chemistry methods (e.g., AM1, PM6, and PM7). This work shows progress toward computational approximations to predict useful chemical physical properties from orbital populations without intensive Hessian calculations.