(98c) Semi-Empirical Rate Constants for Complex Chemical Kinetics: First-Principles Assessment and Rational Refinement

An accurate description of the elementary steps involved in a catalytic process is the basis for a reliable microkinetic modeling of the surface chemistry. Though desirable, a first-principles calculation of the reaction parameters is presently unfeasible but for models involving a small number of reactions. For complex catalytic systems, semi-empirical approaches are therefore often employed to estimate reaction barriers and coverage effects. Here, we assess the semi-empirical unity bond index quadratic exponential potential (UBI-QEP) scheme, frequently used to estimate activation energies of elementary surface reactions from thermo-chemical data. Benchmarked against an extensive DFT data set for a range of surface catalytic reactions, the prevalent formulation is found to exhibit large errors with individual barriers deviating by more than 100% from their reference value. Our analysis traces this back to the blindness of UBI-QEP with respect to the nature of the involved transition states and to an intrinsic inconsistency in the established parameterization procedure. A simple modification of this procedure that maintains the dependence on bond distances underlying the UBI-QEP idea, but simultaneously recovers the consistency with the reference thermo-chemistry leads to a significant improvement in the accuracy of the predicted barriers. Insight into the nature of the transition state enters the scheme through one remaining empirical parameter. Such insight is established for many classes of reactions, but can alternatively come from selected first-principles calculations. For the present data set the UBI-QEP barriers provided by the modified scheme fall consistently within a window of +-10% around the DFT reference data. At a corresponding uncertainty the semi-empirical estimates provide invaluable data for the analysis of complex reaction schemes otherwise not easy to obtain. In particular in conjunction with systematic sensitivity analyses, they might even be the enabling tool for detailed microkinetic modeling approaches to technological systems, most of which are presently outside the capabilities of an exhaustive first-principles treatment. Much beyond the specific UBI-QEP framework our study thus nicely demonstrates the necessity and virtue of a first-principles assessment of prevalent semi-empirical approaches in practical catalysis research ? in terms of both a reliability assessment and rational refinement.