Vibrational Partition Functions from Bond Order and Populations Relationships

We present a novel method that computes harmonic vibrational partition functions from bond orders and popu- lation relationships (QBOP). The QBOP model first computes ZPEs and net vibrational bond energies from our earlier zero-point energies from bond orders and populations (ZPE-BOP) model and then maps these variables to calcu- late the harmonic vibrational partition function. Combined with traditional rotational, translational, and electronic partition function approximations, our method allows the approximate calculation of finite temperature thermal effects without a Hessian calculation. The method uses a total of 12 parameters that have been fitted to B3LYP/cc-pVTZ+1d data for first-row elements: H, Li, Be, B, C, N, O, and F. We benchmark our model to traditional SQM models (i.e., AM1, PM6, PM7, and XTB-2) and found QBOP-1 provides similar results. This work shows a novel way to obtain useful thermal energy calculations without a costly Hessian calculation, and thereby shifting standard bottle-necks in computational chemistry applications.