Error estimates in semi-empirical estimation methods of surface reactions

In this paper, we examine the theoretical and numerical error properties of three semi-empirical methods when used separately and in conjunction with each other using oxygenated hydrocarbons as sample species. These methods are group additivity (GA), the linear scaling relations (LSRs), and the Brønsted–Evans–Polanyi (BEP) correlations. GA estimated heat of formation has nearly zero mean error for all species. GA heats of reaction have no systematic error only when GA is used with C2 or larger species, and DFT is used for all smaller species. Aside from a constant offset, LSR-estimated binding energies and heats of reaction show adequate agreement with the corresponding DFT energies. BEP-estimated activation energies are shown to have systematic errors when the input heats of reaction have systematic errors. Each method produces estimates whose errors are normally distributed with a nonzero mean and which are uncorrelated. Combinations of techniques also possess normally distributed errors.