Vibrational Partition Functions from Bond Order and Populations Relationships

A novel method is presented that computes harmonic vibrational partition functions from bond orders and population relationships (QBOP). The QBOP model first computes zero-point energies (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 calculate the harmonic vibrational partition function. Combined with traditional rotational, translational, and electronic partition function approximations, the 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+1 d data for first-row elements: H, Li, Be, B, C, N, O, and F. The model is benchmarked to traditional semiempirical models (i.e., AM1, PM6, PM7, and XTB-2) and it is found that 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 bottlenecks in computational chemistry applications.