Phenomenological kinetics (PK) is widely used in the study of the reaction rates in heterogeneous catalysis, and it is an important aid in reactor design. PK makes simplifying assumptions: It neglects the role of fluctuations, assumes that there is no correlation between the locations of the reactants on the surface, and considers the reacting mixture to be an ideal solution. In this article we test to what extent these assumptions damage the theory. In practice the PK rate equations are used by adjusting the rate constants to fit the results of the experiments. However, there are numerous examples where a mechanism fitted the data and was shown later to be erroneous or where two mutually exclusive mechanisms fitted well the same set of data. Because of this, we compare the PK equations to "computer experiments" that use kinetic Monte Carlo (kMC) simulations. Unlike in real experiments, in kMC the structure of the surface, the reaction mechanism, and the rate constants are known. Therefore, any discrepancy between PK and kMC must be attributed to an intrinsic failure of PK. We find that the results obtained by solving the PK equations and those obtained from kMC, while using the same rate constants and the same reactions, do not agree. Moreover, when we vary the rate constants in the PK model to fit the turnover frequencies produced by kMC, we find that the fit is not adequate and that the rate constants that give the best fit are very different from the rate constants used in kMC. The discrepancy between PK and kMC for the model of CO oxidation used here is surprising since the kMC model contains no lateral interactions that would make the coverage of the reactants spatially inhomogeneous. Nevertheless, such inhomogeneities are created by the interplay between the rate of adsorption, of desorption, and of vacancy creation by the chemical reactions.

The conceptual idea of degree of rate control (DRC) approaches is to identify the “rate limiting step” in a complex reaction network by evaluating how the overall rate of product formation changes when a small change is made in one of the kinetic parameters. We examine two definitions of this concept by applying it to first-principles kinetic Monte Carlo simulations of the CO oxidation at RuO₂(110). Instead of studying experimental data we examine simulations, because in them we know the surface structure, reaction mechanism, the rate constants, the coverage of the surface and the turn-over frequency at steady state. We can test whether the insights provided by the DRC are in agreement with the results of the simulations thus avoiding the uncertainties inherent in a comparison with experiment. We find that the information provided by using the DRC is non-trivial: It could not have been obtained from the knowledge of the reaction mechanism and of the magnitude of the rate constants alone. For the simulations the DRC provides furthermore guidance as to which aspects of the reaction mechanism should be treated accurately and which can be studied by less accurate and more efficient methods. We therefore conclude that a sensitivity analysis based on the DRC is a useful tool for understanding the propagation of errors from the electronic structure calculations to the statistical simulations in first-principles kinetic Monte Carlo simulations

Microkinetic modeling of surface chemical reactions still relies heavily on the mean-field based rate equation approach. This approach is expected to be most accurate for systems without appreciable lateral interactions among the adsorbed chemicals, and there in particular for the uniform adlayers resulting in poisoned regimes with predominant coverage of one species. Using first-principles kinetic Monte Carlo simulations and the CO oxidation at RuO(2)(110) as a showcase, we demonstrate that even in this limit mean-field rate equations fail to predict the catalytic activity by orders of magnitude. This deficiency is traced back to the inability to account for the vacancy pair formation that is kinetically driven by the ongoing reactions.

We show from ab initio density-functional calculations and model studies that, in the electron-doped manganite La x Ca 1ÿx MnO 3 (x 1), unbound electrons are introduced into the conduction band, which then trap themselves in the exchange-induced magnetic potential wells forming the self-trapped magnetic polarons (STMP). Hopping beyond the nearest neighbors drastically reduces the binding energy, while the Jahn-Teller coupling increases it somewhat, resulting in a net binding of about 100 20 meV. The electron is self-trapped in a seven-site ferromagnetic region, beyond which the lattice is essentially antiferromagnetic. In light of the recent experiments of Neumeier and Cohn, our results suggest that the STMP may be present in the lightly electron-doped manganites. consists of an electron bound to an impurity center, with the electron distorting the moments of the neighboring magnetic ions via exchange interaction. In contrast, the existence of the simpler and perhaps the more elegant counterpart, viz. the self-trapped magnetic polaron (STMP) [2-4], has not been conclusively established. In this case, the electron is bound, not by the impurity potential, but rather by the magnetic potential well, exchange induced by the electron itself ( Fig. 1). Even though several materials, notably EuSe and EuTe, have been studied in the past as prime candidates for the STMP, it continues to remain an elusive entity [5][6][7][8].In light of this, the recent experiments by Neumeier and Cohn [9], suggesting the existence of the magnetic polarons in the lightly electron-doped CaMnO 3 , are of considerable interest. These systems do satisfy several criteria conducive to the formation of the STMP, viz. On the other hand, the formation of the STMP in the electron-doped CaMnO 3 is contrary to the idea of de Gennes that doped electrons in the manganites are delocalized over the entire lattice producing a canted magnetic state [2]. However, the canted state is now well known to be unstable with respect to phase separation [11] or by correlation effects [12]. Also, using a onedimensional model, Batista et al. [13] have argued that in the limit of low doping the system is inhomogeneous, containing magnetic polarons, again in disagreement with the de Gennes result. Recently, Chen and Allen [14] developed a theoretical model for the STMP in CaMnO 3 . However, it lacked a realistic treatment of the energetics and also neglected electron hopping beyond the first nearest neighbor (1NN), which turns out to be an important destabilizing factor.Model Hamiltonian and the Mott polaron.-The basic physics of the formation of the STMP is contained in the Hamiltonian, describing the double-exchange interaction between the Mne g electrons and the Mnt 2g core spins:where c y ia creates an electron at site i with orbital index a (z 2 ÿ 1 or x 2 ÿ y 2 ), ij is the angle between the (classical) Mnt 2g core spins (denoted by S), arranged on a cubic lattice for CaMnO 3 , J denotes the AF superexchange, t ab ij is the hopping integral, and prime over the summ...

In Fig. 10, the labels ''J ab '' and ''J c '' were interchanged. The correct figure along with the original caption appears below. FIG. 10. Exchange interaction in LaMnO 3 with the full Hamiltonian, i.e., with J H ϭ1 eV and with t 2g hopping included. The intraplane and interplane exchanges, J ab and J c , correspond to the e g -e g Ј and e g Ј-e g Ј orbital orientations, respectively. PHYSICAL REVIEW B 68, 029901͑E͒ ͑2003͒