A quantitative determination of reaction mechanisms from density functional theory calculations: Fischer-Tropsch synthesis on flat and stepped cobalt surfaces

We systematically investigated the mechanism of the C-1 + C-1 coupling reactions using density functional theory. The activation energies of C-1 + C-1 coupling and carbon hydrogenation reactions on both flat and stepped surfaces were calculated and analyzed. Moreover, the coverages of adsorbed C-1 species were estimated, and the reaction rates of all possible C-1 + C-1 coupling pathways were quantitatively evaluated. The results suggest that the reactions of CH2 + CH2 and CH3 + C at steps are most likely to be the key C-1 + C-1 coupling steps in FT synthesis on Co catalysts. The reactions of C-2 + C-1 and C-3 + C-1 coupling also were studied; the results demonstrate that in addition to the pathways of RCH + CH2 and RCH2 + C, the coupling of RC + C and RC + CH also may contribute to the chain growth after C-1. (C) 2008 Elsevier Inc. All rights reserved.

CHx hydrogenation on Co(0001): A density functional theory study

Hydrogenation is an important process in the Fischer-Tropsch synthesis. In this work, all the elementary steps of the hydrogenation from C to CH4 are studied on both flat and stepped Co(0001) using density functional theory (DFT). We found that (i) CH3 hydrogenation (CH3+H-->CH4) is the most difficult one among all the elementary reactions on both surfaces, possessing barriers of around 1.0 eV; (ii) the other elementary reactions have the barriers below 0.9 eV on the flat and stepped surfaces; (iii) CH2 is the least stable species among all the CHx(x=1-3) species on both surfaces; and (iv) surface restructuring may have little effect on the CHx(x=0-3) hydrogenation. The barriers of each elementary step on both flat and stepped surfaces are similar and energy profiles are also similar. The reason as to why CHx hydrogenation is not structure-sensitive is also discussed. (C) 2005 American Institute of Physics.

General insight into CO oxidation: A density functional theory study of the reaction mechanism on platinum oxides

CO oxidation on PtO2(110) has been studied using density functional theory calculations. Four possible reaction mechanisms were investigated and the most feasible one is the following: (i) the O at the bridge site of PtO2(110) reacts with CO on the coordinatively unsaturated site (CUS) with a negligible barrier; (ii) O-2 adsorbs on the bridge site and then interacts with CO on the CUS to form an OO-CO complex; (iii) the bond of O-OCO breaks to produce CO2 with a small barrier (0.01 eV). The CO oxidation mechanisms on metals and metal oxides are rationalized by a simple model: The O-surface bonding determines the reactivity on surfaces; it also determines whether the atomic or molecular mechanism is preferred. The reactivity on metal oxides is further found to be related to the 3rd ionization energy of the metal atom.

A density functional theory study on the water formation at high coverages and the water effect in the Fischer-Tropsch synthesis

The O removal through water formation is an important process in the Fischer-Tropsch synthesis. In this study, both steps in water formation (O + H --> OH, OH + H --> H2O) are studied on the stepped Co(0001) at high coverages using density functional theory. We find the following. (i) In both O-O and O-OH co-adsorption systems, two transition states (TSs) were located for the O hydrogenation: in one TS, both O and H are on the same terrace, and in the other they are at the interface between the step edge and the terrace below. (ii) In both the O-O and O-OH co-adsorption systems, the O hydrogenation at the interface is easier (E-a = 0.32 eV in the O-O system, E-a = 1.10 eV in the O-OH system) than that on the same terrace (E-a = 1.49 eV in the O-O system, E-a = 1.80 eV in the O-OH system). (iii) In both the O-O and O-OH co-adsorption systems, only one TS for the OH hydrogenation was located, in which both OH and H are on the same terrace. (iv) Compared to the OH hydrogenation in the O-OH system (E-a = 1.46 eV), the reaction in the OH-OH system (E-a = 0.64 eV) is much easier. The barrier differences and the water effect on the Fischer-Tropsch synthesis are discussed. A possible route with low barriers for water formation is proposed.

CO dissociation and O removal on Co(0001): a density functional theory study

CO dissociation and O removal (water formation) are two important processes in the Fischer-Tropsch synthesis. In this study, both processes are studied on the flat and stepped Co(0 0 0 1) using density functional theory. It is found that (i) it is difficult for CO to dissociate on the flat Co(0 0 0 1) due to the high barrier of 1.04 eV relative to the CO molecule in the gas phase; (ii) the stepped Co(0 0 0 1) is much more favoured for CO dissociation; (iii) the first step in water formation, O + H --> OH, is unlikely to occur on the flat Co(0 0 0 1) due to the high barrier of 1.72 eV, however, this reaction can become feasible on steps where the barrier is reduced to 0.73 eV; and (iv) the barrier in the second step, OH + H --> H2O, on steps is higher than that on the flat surface. (C) 2004 Elsevier B.V. All rights reserved.

The catalytic role of water in CO oxidation

Water, one of the most popular species in our planet, can play a catalytic role in many reactions, including reactions in heterogeneous catalysis. In a recent experimental work, Bergeld, Kasemo, and Chakarov demonstrated that water is able to promote CO oxidation under low temperatures (similar to200 K). In this study, we choose CO oxidation on Pt(111) in the presence of water as a model system to address the catalytic role of water for surface reactions in general using density functional theory. Many elementary steps possibly involved in the CO oxidation on Pt(111) at low temperatures have been investigated. We find the following. First, in the presence of water, the CO oxidation barrier is reduced to 0.33 eV (without water the barrier is 0.80 eV). This barrier reduction is mainly due to the H-bonding between the H in the H2O and the O at the transition state (TS), which stabilizes the TS. Second, CO can readily react with OH with a barrier of 0.44 eV, while COOH dissociation to produce CO2 is not easy (the barrier is 1.02 eV). Third, in the H2O+OH mixed phase, CO can be easily converted into CO2. It occurs through two steps: CO reacts with OH, forming COOH; and COOH transfers the H to a nearby H2O and, at the same time, an H in the H2O transfers to a OH, leading to CO2 formation. The reaction barrier of this process is 0.60 eV under CO coverage of 1/6 ML and 0.33 eV under CO coverage of 1/3 ML. The mechanism of CO oxidation at low temperatures is discussed. On the basis of our calculations, we propose that the water promotion effect can in general be divided into two classes: (i) By H-bonding between the H of H2O and an electron negative species such as the O in the reaction of CO+O+H2O-->CO2+H2O, H2O can stabilize the TS of the reaction and hence reduce the barrier. (ii) H2O first dissociates into H and OH and then OH or H participates directly in the reaction to induce new reaction mechanism with more favorable routes, in which OH or H can act as an intermediate. (C) 2003 American Institute of Physics.

Optimum decision delay of the finite-length DFE

This letter investigates the optimum decision delay and tap-length of the finite-length decision feedback equalizer. First we show that, if the feedback filter (FBF) length N-b is equal to or larger than the channel memory upsilon and the decision delay Delta is smaller than the feedforward filter (FFF) length N-f, then only the first Delta + 1 elements of the FFF can be nonzero. Based on this result we prove that the maximum effective FBF length is equal to the channel memory upsilon, and if N-b greater than or equal to upsilon and N-f is long enough, the optimum decision delay that minimizes the MMSE is N-f - 1.

A self-structured adaptive decision feedback equalizer

In a decision feedback equalizer (DFE), the structural parameters, including the decision delay, the feedforward filter (FFF), and feedback filter (FBF) lengths, must be carefully chosen, as they greatly influence the performance. Although the FBF length can be set as the channel memory, there is no closed-form expression for the FFF length and decision delay. In this letter, first we analytically show that the two-dimensional search for the optimum FFF length and decision delay can be simplified to a one-dimensional search and then describe a new adaptive DFE where the optimum structural parameters can he self-adapted.