An Ghysels

First Principle Kinetic Studies of Zeolite-Catalyzed Methylation Reactions

Methylations of ethene, propene, and butene by methanol over the acidic microporous H-ZSM-5 catalyst are studied by means of state of the art computational techniques, to derive Arrhenius plots and rate constants from first principles that can directly be compared with the experimental data. For these key elementary reactions in the methanol to hydrocarbons (MTH) process, direct kinetic data became available only recently [J. Catal.2005, 224, 115-123; J. Catal.2005, 234, 385-400]. At 350 °C, apparent activation energies of 103, 69, and 45 kJ/mol and rate constants of 2.6 × 10(-4), 4.5 × 10(-3), and 1.3 × 10(-2) mol/(g h mbar) for ethene, propene, and butene were derived, giving following relative ratios for methylation k(ethene)/k(propene)/k(butene) = 1:17:50. In this work, rate constants including pre-exponential factors are calculated which give very good agreement with the experimental data: apparent activation energies of 94, 62, and 37 kJ/mol for ethene, propene, and butene are found, and relative ratios of methylation k(ethene)/k(propene)/k(butene) = 1:23:763. The entropies of gas phase alkenes are underestimated in the harmonic oscillator approximation due to the occurrence of internal rotations. These low vibrational modes were substituted by manually constructed partition functions. Overall, the absolute reaction rates can be calculated with near chemical accuracy, and qualitative trends are very well reproduced. In addition, the proposed scheme is computationally very efficient and constitutes significant progress in kinetic modeling of reactions in heterogeneous catalysis.

TAMkin: A Versatile Package for Vibrational Analysis and Chemical Kinetics

TAMkin is a program for the calculation and analysis of normal modes, thermochemical properties and chemical reaction rates. At present, the output from the frequently applied software programs ADF, CHARMM, CPMD, CP2K, Gaussian, Q-Chem, and VASP can be analyzed. The normal-mode analysis can be performed using a broad variety of advanced models, including the standard full Hessian, the Mobile Block Hessian, the Partial Hessian Vibrational approach, the Vibrational Subsystem Analysis with or without mass matrix correction, the Elastic Network Model, and other combinations. TAMkin is readily extensible because of its modular structure. Chemical kinetics of unimolecular and bimolecular reactions can be analyzed in a straightforward way using conventional transition state theory, including tunneling corrections and internal rotor refinements. A sensitivity analysis can also be performed, providing important insight into the theoretical error margins on the kinetic parameters. Two extensive examples demonstrate the capabilities of TAMkin: the conformational change of the biological system adenylate kinase is studied, as well as the reaction kinetics of the addition of ethene to the ethyl radical. The important feature of batch processing large amounts of data is highlighted by performing an extended level of theory study, which TAMkin can automate significantly.

Vibrational modes in partially optimized molecular systems

In this paper the authors develop a method to accurately calculate localized vibrational modes for partially optimized molecular structures or for structures containing link atoms. The method avoids artificially introduced imaginary frequencies and keeps track of the invariance under global translations and rotations. Only a subblock of the Hessian matrix has to be constructed and diagonalized, leading to a serious reduction of the computational time for the frequency analysis. The mobile block Hessian approach (MBH) proposed in this work can be regarded as an extension of the partial Hessian vibrational analysis approach proposed by Head [Int. J. Quantum Chem. 65, 827 (1997)]. Instead of giving the nonoptimized region of the system an infinite mass, it is allowed to move as a rigid body with respect to the optimized region of the system. The MBH approach is then extended to the case where several parts of the molecule can move as independent multiple rigid blocks in combination with single atoms. The merits of both models are extensively tested on ethanol and di-n-octyl-ether.

Normal Mode Analysis in Zeolites: Toward an Efficient Calculation of Adsorption Entropies

An efficient procedure for normal-mode analysis of extended systems, such as zeolites, is developed and illustrated for the physisorption and chemisorption of n-octane and isobutene in H-ZSM-22 and H-FAU using periodic DFT calculations employing the Vienna Ab Initio Simulation Package. Physisorption and chemisorption entropies resulting from partial Hessian vibrational analysis (PHVA) differ at most 10 J mol(-1) K(-1) from those resulting from full Hessian vibrational analysis, even for PHVA schemes in which only a very limited number of atoms are considered free. To acquire a well-conditioned Hessian, much tighter optimization criteria than commonly used for electronic energy calculations in zeolites are required, i.e., at least an energy cutoff of 400 eV, maximum force of 0.02 eV/Å, and self-consistent field loop convergence criteria of 10(-8) eV. For loosely bonded complexes the mobile adsorbate method is applied, in which frequency contributions originating from translational or rotational motions of the adsorbate are removed from the total partition function and replaced by free translational and/or rotational contributions. The frequencies corresponding with these translational and rotational modes can be selected unambiguously based on a mobile block Hessian-PHVA calculation, allowing the prediction of physisorption entropies within an accuracy of 10-15 J mol(-1) K(-1) as compared to experimental values. The approach presented in this study is useful for studies on other extended catalytic systems.

Comparative Study of Various Normal Mode Analysis Techniques Based on Partial Hessians

Standard normal mode analysis becomes problematic for complex molecular systems, as a result of both the high computational cost and the excessive amount of information when the full Hessian matrix is used. Several partial Hessian methods have been proposed in the literature, yielding approximate normal modes. These methods aim at reducing the computational load and/or calculating only the relevant normal modes of interest in a specific application. Each method has its own (dis)advantages and application field but guidelines for the most suitable choice are lacking. We have investigated several partial Hessian methods, including the Partial Hessian Vibrational Analysis (PHVA), the Mobile Block Hessian (MBH), and the Vibrational Subsystem Analysis (VSA). In this article, we focus on the benefits and drawbacks of these methods, in terms of the reproduction of localized modes, collective modes, and the performance in partially optimized structures. We find that the PHVA is suitable for describing localized modes, that the MBH not only reproduces localized and global modes but also serves as an analysis tool of the spectrum, and that the VSA is mostly useful for the reproduction of the low frequency spectrum. These guidelines are illustrated with the reproduction of the localized amine‐stretch, the spectrum of quinine and a bis‐cinchona derivative, and the low frequency modes of the LAO binding protein.

Cartesian formulation of the mobile block Hessian approach to vibrational analysis in partially optimized systems

Partial optimization is a useful technique to reduce the computational load in simulations of extended systems. In such nonequilibrium structures, the accurate calculation of localized vibrational modes can be troublesome, since the standard normal mode analysis becomes inappropriate. In a previous paper [A. Ghysels et al., J. Chem. Phys. 126, 224102 (2007)], the mobile block Hessian (MBH) approach was presented to deal with the vibrational analysis in partially optimized systems. In the MBH model, the nonoptimized regions of the system are represented by one or several blocks, which can move as rigid bodies with respect to the atoms of the optimized region. In this way unphysical imaginary frequencies are avoided and the translational/rotational invariance of the potential energy surface is fully respected. In this paper we focus on issues concerning the practical numerical implementation of the MBH model. The MBH normal mode equations are worked out for several coordinate choices. The introduction of a consistent group-theoretical notation facilitates the treatment of both the case of a single block and the case of multiple blocks. Special attention is paid to the formulation in terms of Cartesian variables, in order to provide a link with the standard output of common molecular modeling programs.

Calculating Reaction Rates with Partial Hessians: Validation of the Mobile Block Hessian Approach.

In an earlier paper, the authors have developed a new method, the mobile block Hessian (MBH), to accurately calculate vibrational modes for partially optimized molecular structures [J. Chem. Phys. 2007, 126 (22), 224102]. The proposed procedure remedies the artifact of imaginary frequencies, occurring in standard frequency calculations, when parts of the molecular system are optimized at different levels of theory. Frequencies are an essential ingredient in predicting reaction rate coefficients due to their input in the vibrational partition functions. The question arises whether the MBH method is able to describe the chemical reaction kinetics in an accurate way in large molecular systems where a full quantum chemical treatment at a reasonably high level of theory is unfeasible due to computational constraints. In this work, such a validation is tested in depth. The MBH method opens a lot of perspectives in predicting accurate kinetic parameters in chemical reactions where the standard full Hessian procedure fails.

Complex Reaction Environments and Competing Reaction Mechanisms in Zeolite Catalysis: Insights from Advanced Molecular Dynamics

The methanol-to-olefin process is a showcase example of complex zeolite-catalyzed chemistry. At real operating conditions, many factors affect the reactivity, such as framework flexibility, adsorption of various guest molecules, and competitive reaction pathways. In this study, the strength of first principle molecular dynamics techniques to capture this complexity is shown by means of two case studies. Firstly, the adsorption behavior of methanol and water in H-SAPO-34 at 350 °C is investigated. Hereby an important degree of framework flexibility and proton mobility was observed. Secondly, the methylation of benzene by methanol through a competitive direct and stepwise pathway in the AFI topology was studied. Both case studies clearly show that a first-principle molecular dynamics approach enables unprecedented insights into zeolite-catalyzed reactions at the nanometer scale to be obtained.

Mobile Block Hessian Approach with Adjoined Blocks: An Efficient Approach for the Calculation of Frequencies in Macromolecules.

In an earlier work, the authors developed a new method, the mobile block Hessian (MBH) approach, to accurately calculate vibrational modes for partially optimized molecular structures [ J. Chem. Phys. 2007 , 126 ( 22 ), 224102. ]. It is based on the introduction of blocks, consisting of groups of atoms, that can move as rigid bodies. The internal geometry of the blocks need not correspond to an overall optimization state of the total molecular structure. The standard MBH approach considers free blocks with six degrees of freedom. In the extended MBH approach introduced herein, the blocks can be connected by one or two adjoining atoms, which further reduces the number of degrees of freedom. The new approach paves the way for the normal-mode analysis of biomolecules such as proteins. It rests on the hypothesis that low-frequency modes of proteins can be described as pure rigid-body motions of blocks of consecutive amino acid residues. The method is validated for a series of small molecules and further applied to alanine dipeptide as a prototype to describe vibrational interactions between two peptide units; to crambin, a small protein with 46 amino acid residues; and to ICE/caspase-1, which contains 518 amino acid residues.

Water coordination and dehydration processes in defective UiO-66 type metal organic frameworks

The UiO-66 metal organic framework is one of the most thermally and chemically stable hybrid materials reported to date. However, it is also accepted that the material contains structurally embedded defects, which may be engineered to enhance properties towards specific applications such as catalysis, sensing, etc. The synthesis conditions determine to a large extent the level of perfection of the material and additionally the catalytic activity may be enhanced by post-synthesis activation at high temperature under vacuum, in which defect coordinating species (H2O, HCl, monocarboxylic modulators, etc.) evaporate. The molecular level characterization of defects is extremely challenging from both theoretical and experimental points of view. Such experimental endeavor was recently proposed via experimental SXRD measurements, also unraveling the coordination of water on the Zr–O–Zr defect sites [Angew. Chem., Int. Ed., 2015, 54, 11162–11167]. The present work provides a theoretical understanding of defect structures in UiO-66(Zr) by means of periodic density functional theory calculations and ab initio molecular dynamics simulations. A range of defect structures are generated with different numbers of missing linkers. For each of the defects, the free energetic and mechanical stability is discussed and the coordination of water and charge balancing hydroxide ions is studied. For catalysis applications, the material is mostly pretreated to remove water by dehydration reactions. For each of the proposed defect structures, mechanistic pathways for dehydration reactions of the Zr-bricks are determined employing nudged elastic band (NEB) calculations. During the dehydroxylation trajectory, loose hydroxyl groups and terephthalate decoordinations are observed. Furthermore, dehydration reactions are lower activated if terephthalate linkers are missing in the immediate environment of the inorganic brick. The creation of defects and the dehydration processes have a large impact on the mechanical properties of the material, which is evidenced by lower bulk moduli and elastic constants for structures with more defects.