Constrained-Orbital Density Functional Theory. Computational Method and Applications to Surface Chemical Processes

We present a method for performing density-functional theory (DFT) calculations in which one or more Kohn–Sham orbitals are constrained to be localized on individual atoms. This constrained-orbital DFT (CO-DFT) approach can be used to tackle two prevalent shortcomings of DFT: the lack of transparency with regard to the governing electronic structure in large (planewave based) DFT calculations and the limitations of semilocal DFT in describing systems with localized electrons or a large degree of static correlation. CO-DFT helps to address the first of these issues by decomposing complex orbital transformations occurring during elementary chemical processes into simpler and more intuitive transformations. The second issue is addressed by using the CO-DFT method to generate configuration states for multiconfiguration Kohn–Sham calculations. We demonstrate both of these applications for elementary reaction steps involved in the oxygen evolution reaction

Carbon-Induced Surface Transformations of Cobalt

A reactive force field has been developed that is used in molecular dynamics (MD) studies of the surface transformation of the cobalt (0001) surface induced by an overlayer of adsorbed carbon atoms. Significant surface reconstruction is observed with movement of the Co atoms upward and part of the C atoms to positions below the surface. In a particular C ad atom coverage regime step edge type surface sites are formed, which can dissociate adsorbed CO with a low activation energy barrier. A driving force for the surface transformation is the preference of C adatoms to adsorb in 5- or 6-fold coordinated sites and the increasing strain in the surface because of the changes in surface metal atom–metal atom bond distances with the increasing surface overlayer concentration. The process is found to depend on the nanosize dimension of the surface covered with carbon. When this surface is an overlayer on top of a vacant Co surface, it can reduce stress by displacement of the Co atoms to unoccupied surface positions and the popping up process of Co atom does not occur. This explains why small nanoparticles will not reconstruct by popping up of Co atoms and do not create CO dissociation active sites even when covered with a substantial overlayer of C atoms

Molecular Simulation of Protein Encapsulation in Vesicle Formation

Liposomes composed of fatty acids and phospholipids are frequently used as model systems for biological cell membranes. In many applications, the encapsulation of proteins and other biomacromolecules in these liposomes is essential. Intriguingly, the concentration of entrapped material often deviates from that in the solution where the liposomes were formed. While some reports mention reduced concentrations inside the vesicles, concentrations are also reported to be enhanced in other cases. To elucidate possible drivers for efficient encapsulation, we here investigate the encapsulation of model proteins in spontaneously forming vesicles using molecular dynamics simulations with a coarse grained force field for fatty acids and phospholipids as well as water-soluble and transmembrane proteins. We show that, in this model system, the encapsulation efficiency is dominated by the interaction of the proteins with the membrane, while no significant dependence is observed on the size of the encapsulated proteins nor on the speed of the vesicle formation, whether reduced by incorporation of stiff transmembrane proteins or by the blocking of the bilayer bulging by the presence of another membrane

Molecular Simulation of Protein Encapsulation in Vesicle Formation

Liposomes composed of fatty acids and phospholipids are frequently used as model systems for biological cell membranes. In many applications, the encapsulation of proteins and other biomacromolecules in these liposomes is essential. Intriguingly, the concentration of entrapped material often deviates from that in the solution where the liposomes were formed. While some reports mention reduced concentrations inside the vesicles, concentrations are also reported to be enhanced in other cases. To elucidate possible drivers for efficient encapsulation, we here investigate the encapsulation of model proteins in spontaneously forming vesicles using molecular dynamics simulations with a coarse grained force field for fatty acids and phospholipids as well as water-soluble and transmembrane proteins. We show that, in this model system, the encapsulation efficiency is dominated by the interaction of the proteins with the membrane, while no significant dependence is observed on the size of the encapsulated proteins nor on the speed of the vesicle formation, whether reduced by incorporation of stiff transmembrane proteins or by the blocking of the bilayer bulging by the presence of another membrane

Scaling Relations for Acidity and Reactivity of Zeolites

Zeolites are widely applied as solid acid catalysts in various technological processes. In this work we have computationally investigated how catalytic reactivity scales with acidity for a range of zeolites with different topologies and chemical compositions. We found that straightforward correlations are limited to zeolites with the same topology. The adsorption energies of bases such as carbon monoxide (CO), acetonitrile (CH₃CN), ammonia (NH₃), trimethylamine (N­(CH₃)₃), and pyridine (C₅H₅N) give the same trend of acid strength for FAU zeolites with varying composition. Crystal orbital Hamilton populations (COHP) analysis provides a detailed molecular orbital picture of adsorbed base molecules on the Brønsted acid sites (BAS). Bonding is dominated by strong σ donation from guest molecules to the BAS for the adsorbed CO and CH₃CN complexes. An electronic descriptor of acid strength is constructed based on the bond order calculations, which is an intrinsic parameter rather than adsorption energy that contains additional contributions due to secondary effects such as van der Waals interactions with the zeolite walls. The bond order parameter derived for the CH₃CN adsorption complex represents a useful descriptor for the intrinsic acid strength of FAU zeolites. For FAU zeolites the activation energy for the conversion of π-adsorbed isobutene into alkoxy species correlates well with the acid strength determined by the NH₃ adsorption energies. Other zeolites such as MFI and CHA do not follow the scaling relations obtained for FAU; we ascribe this to the different van der Waals interactions and steric effects induced by zeolite framework topology

Stability of Extraframework Iron-Containing Complexes in ZSM‑5 Zeolite

The stability of oxygenated and hydroxylated iron complexes in Fe/ZSM-5 is studied by periodic DFT calculations. The reaction paths for the interconversion of various potential iron-containing complexes confined in the zeolite matrix are discussed. It is demonstrated that the distribution of mononuclear [FeO]⁺ species depends only slightly on the specific local zeolite environment. For all binuclear complexes considered, a notable preference for the location at the larger eight-membered ring γ site in the sinusoidal channel is observed. Nevertheless, the formation of the mononuclear species [FeO]⁺ in realistic systems is very unlikely. Irrespective of their location inside the zeolite matrix, such species show a strong tendency toward self-organization into binuclear oxygen-bridged [Fe­(μ-O)₂Fe]²⁺ complexes. Using ab initio thermodynamic analysis of the stability of different Fe complexes in ZSM-5, it is demonstrated that two distinct extraframework cationic complexes can be present in the Fe/ZSM-5 catalyst, namely, [Fe^III(μ-O)₂Fe^III]²⁺ and [Fe^II(μ-O)­Fe^II]²⁺. The [Fe^II(μ-O)­Fe^II]²⁺ complexes containing bivalent iron centers are mainly present in the Fe/ZSM-5 catalyst activated at low oxygen chemical potential and H₂O-free conditions, whereas the formation of its Fe³⁺-containing counterpart [Fe^III(μ-O)₂Fe^III]²⁺ is favored upon the high-temperature calcination in an O₂-rich environment

Monomer Formation Model versus Chain Growth Model of the Fischer–Tropsch Reaction

One of the great challenges in molecular heterogeneous catalysis is to model selectivity of a heterogeneous catalytic reaction based on first principles. Molecular kinetics simulations of the Fischer–Tropsch reaction, which converts synthesis gas into linear hydrocarbons, demonstrate the need for microkinetics approaches that do not make a priori choices of rate controlling steps. A key question pertaining to this reaction, in which hydrocarbons are formed through consecutive insertion of adsorbed CH_<i>x</i> monomers into adsorbed growing hydrocarbon chains, is whether the CO consumption rate depends on the rate of the CH_<i>x</i> insertion polymerization process. Microkinetic theory of this heterogeneous catalytic reaction based on quantum-chemical data is used to deduce expressions for the CO consumption rate and chain growth parameter α in the two limiting cases where chain growth rate is fast compared to the formation of CH_<i>x</i> (monomer formation limit) or where the reverse relation holds (chain growth limit). The conventional assumptions that CH_<i>x</i> formation is rate controlling and that change in CO coverage due to reaction is negligible lead to substantial overestimation of the rate of CO consumption. It appears that intermediate reactivity of the catalytic reaction center, with neither too low nor too high activation energies for C–O bond cleavage, and low reagent gas pressure lead to such monomer formation limiting type behavior, whereas maximum rate of CO consumption is found when chain growth rate is limiting

Nature and Location of Cationic Lanthanum Species in High Alumina Containing Faujasite Type Zeolites

The nature, concentration, and location of cationic lanthanum species in faujasite-type zeolites (zeolite X, Y and ultrastabilized Y) have been studied in order to understand better their role in hydrocarbon activation. By combining detailed physicochemical characterization and DFT calculations, we demonstrated that lanthanum cations are predominantly stabilized within sodalite cages in the form of multinuclear OH-bridged lanthanum clusters or as monomeric La³⁺ at the SI sites. In high-silica faujasites (Si/Al = 4), monomeric [La(OH)]²⁺ and [La(OH)₂]⁺ species were only found in low concentrations at SII sites in the supercages, whereas the dominant part of La³⁺ is present as multinuclear OH-bridged cationic aggregates within the sodalite cages. Similarly, in the low-silica (Si/Al = 1.2) La–X zeolite, the SI′ sites were populated by hydroxylated La species in the form of OH-bridged bi- and trinuclear clusters. In this case, the substantial repulsion between the La³⁺ cations confined within the small sodalite cages induces the migration of La³⁺ cations into the supercage SII sites. The uniquely strong polarization of hydrocarbon molecules sorbed in La–X zeolites is caused solely by the interaction with the accessible isolated La³⁺ cations

First-Principles-Based Microkinetics Simulations of Synthesis Gas Conversion on a Stepped Rhodium Surface

The kinetics of synthesis gas conversion on the stepped Rh(211) surface were investigated by computational methods. DFT calculations were performed to determine the reaction energetics for all elementary reaction steps relevant to the conversion of CO into methane, ethylene, ethane, formaldehyde, methanol, acetaldehyde, and ethanol. Microkinetics simulations were carried out on the basis of these first-principles data to predict the CO consumption rate and the product distribution as a function of temperature. The elementary reaction steps that control the CO consumption rate and the selectivity were analyzed in detail. Ethanol formation can only occur on the stepped surface, because the barrier for CO dissociation on Rh terraces is too high; step-edges are also required for the coupling reactions. The model predicts that formaldehyde is the dominant product at low temperature, ethanol at intermediate temperature, and methane at high temperature. The preference for ethanol over long hydrocarbon formation is due to the lower barrier for C­(H) + CO coupling as compared with the barriers for CH_<i>x</i> + CH_<i>y</i> coupling reactions. The C­(H)­CO surface intermediate is hydrogenated to ethanol via a sequence of hydrogenation and dehydrogenation reactions. The simulations show that ethanol formation competes with methane formation at intermediate temperatures. The rate-controlling steps are CO removal as CO₂ to create empty sites for the dehydrogenation steps in the reaction sequence leading to ethanol, CH_<i>x</i>CH_<i>y</i>O hydrogenation for ethanol formation, and CH₂ and CH₃ hydrogenation for methane formation. CO dissociation does not control the overall reaction rate on Rh. The most important reaction steps that control the selectivity of ethanol over methane are CH₂ and CH₃ hydrogenation as well as CHCH₃ dehydrogenation

Site Stability on Cobalt Nanoparticles: A Molecular Dynamics ReaxFF Reactive Force Field Study

The stability of step-edge-type surface sites on cobalt nanoparticles is investigated for particles of increasing size of 1.8, 2.2, and 2.9 nm, that contain 321, 603, and 1157 atoms, respectively. The stability of surface configurations is probed by analyzing the kinetics of the disappearance of step-edge sites as a function of temperature using ReaxFF reactive force field molecular dynamics (MD) simulations. The MD simulations are based on a newly designed reactive force field. Two different activation energy regimes are identified. A low activation barrier of the order of 7 kJ/mol corresponds to single atom movement, which is independent of Co nanoparticle size. Higher activation energies (28, 37, and 22 kJ/mol for the three clusters, respectively) correspond to the shift of overlayer terraces. These concerted shifts appear to be sensitive to particle size, terrace size, and the structure of the facet. Step edges are more stable on larger particles. Shifting of the (111) surface layers leads to transformation of a thin surface layer from the initially face-centered cubic structure to hexagonal close-packed structure