Hindered Translator and Hindered Rotor Models for Adsorbates: Partition Functions and Entropies

Sprowl, Lynza H.; Campbell, Charles T.; Árnadóttir, Líney

doi:10.1021/acs.jpcc.5b11616

Cited by 127 publications

(203 citation statements)

References 41 publications

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“…The next step is to estimate values of binding energies for adsorption of all species on the surface, for example using experimental results from the literature, results from DFT calculations, or scaling relations (20)(21)(22)(23)(24). In addition, it is necessary to estimate values for the entropies of the adsorbed species, for example using results from experimental studies (25), correlations in the literature (26), results from DFT calculations of vibrational frequencies (27)(28)(29)(30)(31)(32)(33)(34), combined with hindered translator and hindered rotor models for the three modes associated with motion parallel to the surface (35,36), or by assuming models for the extent of mobility on the surface. It is now possible to estimate values for lumped equilibrium constants, K ads,i , to form the adsorbed species from the reactants and/or products, followed by calculation of θ p .…”

Section: Analytical Strategy For Analysis Of Reaction Schemesmentioning

confidence: 99%

Analysis of reaction schemes using maximum rates of constituent steps

Motagamwala

Dumesic

2016

Proc. Natl. Acad. Sci. U.S.A.

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We show that the steady-state kinetics of a chemical reaction can be analyzed analytically in terms of proposed reaction schemes composed of series of steps with stoichiometric numbers equal to unity by calculating the maximum rates of the constituent steps, r max,i , assuming that all of the remaining steps are quasi-equilibrated. Analytical expressions can be derived in terms of r max,i to calculate degrees of rate control for each step to determine the extent to which each step controls the rate of the overall stoichiometric reaction. The values of r max,i can be used to predict the rate of the overall stoichiometric reaction, making it possible to estimate the observed reaction kinetics. This approach can be used for catalytic reactions to identify transition states and adsorbed species that are important in controlling catalyst performance, such that detailed calculations using electronic structure calculations (e.g., density functional theory) can be carried out for these species, whereas more approximate methods (e.g., scaling relations) are used for the remaining species. This approach to assess the feasibility of proposed reaction schemes is exact for reaction schemes where the stoichiometric coefficients of the constituent steps are equal to unity and the most abundant adsorbed species are in quasi-equilibrium with the gas phase and can be used in an approximate manner to probe the performance of more general reaction schemes, followed by more detailed analyses using full microkinetic models to determine the surface coverages by adsorbed species and the degrees of rate control of the elementary steps.chemical kinetics | catalysis | microkinetics C hemical reactions take place through sequences of elementary steps, and the dynamics of the overall stoichiometric reaction are typically controlled by key steps in this sequence of steps. For example, in the case of a catalytic reaction, the reaction kinetics are controlled by the energetics of the transition states for the rate-controlling steps and by the energetics of species that are abundant on the active sites (i.e., the Gibbs free energies of these transition states and adsorbed species relative to the reactants and products of the overall stoichiometric reaction). However, whereas the observed reaction kinetics are controlled by a limited number of transition states and adsorbed species, it is typically required to carry out detailed microkinetic analyses to identify the nature of these key transition states and adsorbed species. Thus, a general strategy to elucidate how the reaction kinetics are controlled by a proposed reaction mechanism is first to carry out density functional theory (DFT) calculations to determine the thermodynamic properties of all adsorbed species and transition states, and then to build a microkinetic model to determine the surface coverages by all adsorbed species and the forward and reverse rates of all elementary steps for a range of reaction conditions (1-5). Sensitivity analyses are then carried out using this microkineti...

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Section: Analytical Strategy For Analysis Of Reaction Schemesmentioning

confidence: 99%

Analysis of reaction schemes using maximum rates of constituent steps

Motagamwala

Dumesic

2016

Proc. Natl. Acad. Sci. U.S.A.

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“…We note that dispersion corrections can influence both the vibrational frequencies and the adsorption entropy to a significant extent. For instance, Sprowl et al reported differences of as high as 3.0R in the calculated entropy using their hindered translator/rotor approach, depending on whether or not dispersion corrections were included.…”

Section: Discussionmentioning

confidence: 66%

“…The specific contributions of different entropic terms are given in (d) with two standard deviation error. The θ std for ethane was taken from Sprowl et al [Color figure can be viewed at wileyonlinelibrary.com]…”

Section: Resultsmentioning

confidence: 91%

“…The molar translational entropy is given by

S_{trans} = R ((), \ln Q_{trans}^{FT} + 1 + \ln α + \frac{\partial italiclnα}{\partial italiclnT})

which reduces to the 2D translational entropy as α → 1. In addition, there is a configuration entropy term that corresponds to converting the entropy calculated above from ideal saturation conditions (one adsorbate per site) to a standard state concentration . This equals

S_{config} = italicRln ((), e / θ_{std})

where θ std is the standard state concentration of the adsorbate.…”

Section: Methodsmentioning

confidence: 99%

“…Further, arguments based on a “statistical” cancellation of errors in computing the entropy change in a reaction have sometimes been used to neglect small modes (say less than 100 cm −1 ) completely. Approximations to the nonvibrational modes include invoking the “free” 1D or 2D translator approximation or an “intermediate” level of approximation such as employing the hindered translator/rotor model or the classical anharmonic model (or the complete sampling of the potential energy surface) to treat the low frequency modes; the quantum harmonic oscillator model is then used to treat the other (vibrational) modes. It should be noted here that when a prediction is made using approximations, estimating the associated uncertainties allows for assessing the reliability of the method.…”

Section: Introductionmentioning

confidence: 99%

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Estimating vibrational and thermodynamic properties of adsorbates with uncertainty using data driven surrogates

et al. 2019

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In this work, we propose a strategy to develop data driven local surrogate models of ab initio potential energy functions describing the interaction of adsorbates on heterogeneous catalytic materials. We show that these multivariable surrogate models, based on orthogonal polynomial expansion and trained on sampled ab-initio energies/forces, can be used to compute harmonic vibrational frequencies and the entropy of adsorbates. Further, we show that the errors in our surrogate model can be estimated and propagated to calculate the uncertainty in the computed properties. We show proof-of-concept illustrations of our method to calculate the vibrational frequencies of ethene on 1D edges of molybdenum sulfide (MoS 2 ), (b) 2D surfaces of Pt(111), and (c) 3D micropores of a HZSM-5 zeolite; the entropy of ethane adsorbed on Pt(111); and the associated uncertainties in all the cases. K E Y W O R D S data driven models, DFT, entropy, heterogeneous catalysis, orthogonal polynomial expansions, uncertainty quantification, vibrational frequencies

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Progress in Computational and Machine‐Learning Methods for Heterogeneous Small‐Molecule Activation

Choi

Lee

et al. 2020

Advanced Materials

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The chemical conversion of small molecules such as H2, H2O, O2, N2, CO2, and CH4 to energy and chemicals is critical for a sustainable energy future. However, the high chemical stability of these molecules poses grand challenges to the practical implementation of these processes. In this regard, computational approaches such as density functional theory, microkinetic modeling, data science, and machine learning have guided the rational design of catalysts by elucidating mechanistic insights, identifying active sites, and predicting catalytic activity. Here, the theory and methodologies for heterogeneous catalysis and their applications for small‐molecule activation are reviewed. An overview of fundamental theory and key computational methods for designing catalysts, including the emerging data science techniques in particular, is given. Applications of these methods for finding efficient heterogeneous catalysts for the activation of the aforementioned small molecules are then surveyed. Finally, promising directions of the computational catalysis field for further outlooks are discussed, focusing on the challenges and opportunities for new methods.

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Hindered Translator and Hindered Rotor Models for Adsorbates: Partition Functions and Entropies

Cited by 127 publications

References 41 publications

Analysis of reaction schemes using maximum rates of constituent steps

Analysis of reaction schemes using maximum rates of constituent steps

Estimating vibrational and thermodynamic properties of adsorbates with uncertainty using data driven surrogates

Progress in Computational and Machine‐Learning Methods for Heterogeneous Small‐Molecule Activation

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