A Simple Method for Incorporating Madelung Field Effects into ab Initio Embedded Cluster Calculations of Crystals and Macromolecules

Density functional theory calculations of copper-doped rutile crystals: Local structural, electronic, optical, and electron paramagnetic resonance properties

The local structural, electronic, optical, and electron paramagnetic resonance (EPR) properties are uniformly studied for Cu²⁺ -doped rutile (TiO₂ ) crystals by using the density functional theory (DFT) calculations. The local cation-oxygen bond lengths and planar bond angle, band gap, Mulliken charge and overlapping population, density of state (DOS), and UV-Vis absorption spectra are calculated for pure and copper-doped rutile. The smaller overlapping population of Cu-O bonds in the doped system than Ti-O bonds in pure rutile reflects weaker orbital admixtures or covalency of the former. Compared with pure rutile, Cu²⁺ doping leads to significant redshift of the UV-Vis absorption band and the narrow impurity band in visible and near-infrared regions arising from the Cu²⁺ d-d transitions and narrowing of the band gap by about 0.636 eV, possibly suggesting enhancement of visible light activity. The Cu dopant induces a spin magnetic moment of 0.74 μB for the doped rutile. The calculated UV-Vis absorption spectra and spin Hamiltonian parameters for copper-doped rutile show reasonable agreement with the experimental data and some improvement related to the previous perturbation formula calculations. Present systematic studies would be helpful to understand the mechanisms of the enhancement in the optical and magnetic properties of this material with transition-metal (especially Cu²⁺ ) dopants.

Polarizable continuum models provide an effective electrostatic embedding model for fragment-based chemical shift prediction in challenging systems

Ab initio nuclear magnetic resonance chemical shift prediction provides an important tool for interpreting and assigning experimental spectra, but it becomes computationally prohibitive in large systems. The computational costs can be reduced considerably by fragmentation of the large system into a series of contributions from many smaller subsystems. However, the presence of charged functional groups and the need to partition the system across covalent bonds create complications in biomolecules that typically require the use of large fragments and careful descriptions of the electrostatic environment. The present work shows how a model that combines chemical shielding contributions from non-overlapping monomer and dimer fragments embedded in a polarizable continuum model provides a simple, easy-to-implement, and computationally inexpensive approach for predicting chemical shifts in complex systems. The model's performance proves rather insensitive to the continuum dielectric constant, making the selection of the optimal embedding dielectric less critical. The PCM-embedded fragment model is demonstrated to perform well across systems ranging from molecular crystals to proteins.

Effect of surface vacancies on the adsorption of Pd and Pb on MgO(100)

Abstract

Theoretical quantum mechanical calculations have been carried out to establish the effect of surface vacancies on the adsorption of Pd and Pb atoms on the defective MgO(100) surface. The investigated defects included neutral, singly and doubly charged O and Mg vacancies on the (100) surface of MgO. These vacancies played the role of F_sⁿ⁺ and V_sⁿ⁻ (n = 0, 1, 2) adsorption centers for a single Pd or Pb atom. From the results of calculations, it is clear that the Pd- and Pb-atom adsorption at the F_sⁿ⁺ and V_sⁿ⁻ centers shows different characteristics than at the regular O²⁻ and Mg²⁺ centers. Drastic changes in geometric, energetic, and electronic parameters are evident in Pd/V_sⁿ⁻ and Pb/V_sⁿ⁻. The effect of F_s⁰ and F_s⁺, which in practice are the most important vacancies, is smaller, yet the adsorption of Pd and Pb at these centers is more energetically favorable than at the regular O²⁻ center. Of the two metals studied, the atom of Pd is bound by the F_s⁰ and F_s⁺ centers with higher adsorption energies.

Graphical abstract

Electronic supplementary material

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Theoretical study of absorption of 2,2,6,6-tetramethylpiperidine-1-oxoammonium cation (TEMPO) on TiO₂(110) rutile surface

We present a theoretical study of the adsorption of 2,2,6,6-tetramethylpiperidine-1-oxoammonium cation (TEMPO) onto the TiO₂(110) surface rutile, investigating its bonding nature, electron properties and structural stability. Based on the results obtained with the PBE0/def2-SVP method, natural bond orbital (NBO) analysis suggests a bond order for the O--O bond in complexes 5 and 6, of 0.25 and 0.88, respectively. We also described NBOs for the main interactions of the TiO₂-TEMPO complexes.

A theoretical investigation on photocatalytic oxidation on the TiO2 surface

The TiO(2) photocatalytic oxidation mechanism was theoretically investigated by using long-range corrected time-dependent density functional theory (LC-TDDFT) with a cluster model of the anatase TiO(2)(001) surface. We found that LC-TDDFT with the cluster model quantitatively reproduces the photoexcitations of the TiO(2) surface by calculating the electronic spectra of a clean TiO(2) surface and one with oxygen defects. We calculated the electronic spectra of a molecularly adsorbed TiO(2) surface for the adsorptions of phenol, methanol, and methane molecules as typical organic molecules. We obtained the surprising result that the main peak of the phenol-adsorbed TiO(2) surface, which overlaps with the main peak of the clean TiO(2) surface, corresponds to charge transfers from the phenol molecule to the TiO(2) surface. This indicates that the TiO(2) photocatalytic oxidation proceeds through direct charge transfer excitation from the substrate molecules to the TiO(2) surface. In contrast, we found slight and no charge transfer for methanol and methane adsorption, respectively, in agreement with the experimental findings for their reactivities. In light of these results, we propose a new mechanism for heterogeneous TiO(2) photocatalytic oxidations.

SLIDE AND ROLLING MECHANISMS OF Pt CLUSTERS OUT OF OXYGEN VACANCY REGION ON MgO(100) SURFACE

We present the theoretical DFT/B3LYP investigations on the cluster nucleation process and moving mechanism for the Pt n (n = 1, 2, 3, 4, 8, and 12) clusters deposited on MgO surface with an embedded cluster model. The structures and energies of the Pt n clusters adsorbed on the perfect and oxygen vacancy MgO surfaces have been calculated. Based on the nucleation of the Pt n clusters on the oxygen vacancy sites of MgO surfaces, the two moving mechanisms of slide and rolling out of the vacancy region have been energetically investigated. The results show that the needed energies per atom moving out of the vacancy region decrease as the cluster sizes increase. Consequently, the big clusters move likely out of the vacancy sites by either slide or rolling model under a certain temperature condition.

Structures and reaction mechanisms of glycerol dehydration over H-ZSM-5 zeolite: a density functional theory study

The initial stage of glycerol conversion over H-ZSM-5 zeolite has been investigated using density functional theory (DFT) calculations on an embedded cluster model consisting of 128 tetrahedrally coordinated atoms. It is found that glycerol dehydration to acrolein and acetol proceeds favourably via a stepwise mechanism. The formation of an alkoxide species upon the first dehydration requires the highest activation energy (42.5 kcal mol(-1)) and can be considered as the rate determining step of the reaction. The intrinsic activation energies for the first dehydration are virtually the same for both acrolein and acetol formation, respectively, suggesting the competitive removal of the primary and secondary OH groups. A high selectivity to acrolein at moderate temperatures can be attributed to the selective activation of the stronger adsorption mode of glycerol through the secondary OH group and the kinetically favoured subsequent consecutive steps. In addition, the less reactive nature of acrolein relative to acetol precludes it from being converted to other products upon conversion to glycerol. In accordance with typical endothermic reactions, the forward rate constant for glycerol dehydration significantly increases with increasing reaction temperature.

Molecular dynamics simulation of the aggregation of titanium dioxide nanocrystals: preferential alignment

We use classical molecular-dynamics simulations to study the aggregation of various titanium dioxide (anatase) nanocrystals in vacuum. In all cases, we observe a strong tendency for the nanocrystals to aggregate with certain preferred orientations in a "hinge" mechanism. Although some of the nanocrystals possess significant dipole moments, dipole-dipole interactions do not direct aggregation, implying that higher-order multipole moments are the driving force for preferential alignment. These high-order multipole moments originate from under-coordinated O and Ti surface atoms on the edges between nanocrystal facets, which create localized regions of positive and negative charge. The observed mechanism for preferential alignment may be a driving force for oriented attachment and the growth of anisotropic structures during crystallization.

Theoretical study of modes of adsorption of water dimer on H-ZSM-5 and H-Faujasite zeolites

Modes of adsorption of water dimer on H-ZSM-5 and H-Faujasite (H-FAU) zeolites have been investigated by a quantum embedded cluster approach, using the hybrid B3LYP density functional theory. The results indicate that there are two possible adsorption pathways, namely the stepwise process where only one water binds strongly to the (-O)3-Al-O(H) tetrahedral unit while the other weakly binds to the zeolite framework and the concerted process where both water molecules form a large ring of hydrogen-bonding network with the Brønsted proton and an oxygen framework. With inclusion of the effects of the Madelung potential from the extended zeolite framework, for adsorption on H-ZSM-5 zeolite, both the neutral and ion-pair complexes exist with adsorption energies of -15.13 and -14.73 kcal/mol, respectively. For adsorption on the H-FAU, only the ion-pair complex exists with the adsorption energy of -14.63 kcal/mol. Our results indicate that adsorption properties depend not only on the acidity of the Brønsted acidic site but also on the topology of the zeolite framework, such as on the spatial confinement effects which lead to very different adsorption structures for the ion-pair complexes in H-ZSM-5 and H-FAU, even though their adsorption energies are quite similar. Our calculated vibrational spectra for these ion-pair complexes support previous experimental IR interpretations.

Thermodynamics of reversible gas adsorption on alkali-metal exchanged zeolites—the interplay of infrared spectroscopy and theoretical calculations

Detailed understanding of weak solid-gas interactions giving rise to reversible gas adsorption on zeolites and related materials is relevant to both, fundamental studies on gas adsorption and potential improvement on a number of (adsorption based) technological processes. Combination of variable-temperature infrared spectroscopy with theoretical calculations constitutes a fruitful approach towards both of these aims. Such an approach is demonstrated here (mainly) by reviewing recent studies on hydrogen and carbon monoxide adsorption (at a low temperature) on alkali-metal exchanged ferrierite. However, the methodology discussed, which involves the interplay of experimental measurements and theoretical calculations at the periodic DFT level, should be equally valid for many other gas-solid systems. Specific aspects considered are the identification of gas adsorption complexes and thermodynamic studies related to standard adsorption enthalpy and entropy.

Vapor-Phase Beckmann Rearrangement of Oxime Molecules over H-Faujasite Zeolite

The Beckmann rearrangement (BR) plays an important role in a variety of industries. The mechanism of this reaction rearrangement of oximes with different molecular sizes, specifically, the oximes of formaldehyde (H(2)C=NOH), Z-acetaldehyde (CH(3)HC=NOH), E-acetaldehyde (CH(3)HC=NOH) and acetone (CH(3))(2)C=NOH, catalyzed by the Faujasite zeolite is investigated by both the quantum cluster and embedded cluster approaches at the B3LYP level of theory using the 6-31G (d,p) basis set. To enhance the energetic properties, single point calculations are undertaken at MP2/6-311G(d,p). The rearrangement step, using the bare cluster model, is the rate determining step of the entire reaction of these oxime molecules of which the energy barrier is between 50-70 kcal mol(-1). The more accurate embedded cluster model, in which the effect of the zeolitic framework is included, yields as the rate determining step, the formaldehyde oxime reaction rearrangement with an energy barrier of 50.4 kcal mol(-1). With the inclusion of the methyl substitution at the carbon-end of formaldehyde oxime, the rate determining step of the reaction becomes the 1,2 H-shift step for Z-acetaldehyde oxime (30.5 kcal mol(-1)) and acetone oxime (31.2 kcal mol(-1)), while, in the E-acetaldehyde oxime, the rate determining step is either the 1,2 H-shift (26.2 kcal mol(-1)) or the rearrangement step (26.6 kcal mol(-1)). These results signify the important role that the effect of the zeolite framework plays in lowering the activation energy by stabilizing all of the ionic species in the process. It should, however, be noted that the sizeable turnover of a reaction catalyzed by the Brønsted acid site might be delayed by the quantitatively high desorption energy of the product and readsorption of the reactant at the active center.

Structure and adsorption of a basic probe molecule on H-ZSM-5 nanostructured zeolite: An embedded ONIOM study

The adsorption properties of pyridine on H-ZSM-5 zeolites have been investigated by cluster calculations with the ONIOM scheme and with an embedded-ONIOM scheme. The active site has been modeled with cluster sizes of up to 46 tetrahedra. Two different types of pyridine adsorption complexes on the zeolite models are found. If Zeolite is modeled by a small 3T quantum cluster, the adsorption energy of the hydrogen-bonded pyridine complex (Py-Hz), is found to be -18.5kcal/mol. When a larger cluster or the ONIOM models are employed, the optimized geometries show the formation of pyrdinium cation [PyH(+)] bound as an ion-pair complex [PyH(+)][Z(-)]. The calculated energy of formation for this ion-pair complex is -36.8kcal/mol in the ONIOM (B3LYP/6-31G(d,p):UFF) model. Both values are considerably lower than the experimentally estimated heat of adsorption of pyridine in ZSM-5 zeolite of -47.6kcal/mol. Inclusion of the electrostatic effects of the zeolite crystal lattice via the embedded ONIOM model increases the adsorption energy to -44.4kcal/mol. Performing the quantum-chemical treatment at the MP2/6-31G(d,p) level instead of the B3LYP/6-31G(d,p) leads to a slightly lower adsorption energy to -45.9kcal/mol. These data suggest that the embedded ONIOM scheme provides an accurate method of studying the interaction of small organic molecules with zeolites.

Comparison of all sites for Ti substitution in zeolite TS-1 by an accurate embedded-cluster method

We studied the preferential location of Ti centers in the framework of the Ti-containing MFI zeolite TS-1 using a hybrid DFT/MM embedding method developed recently. This "covalent elastic polarizable environment" (covEPE) cluster embedding allows a complete and self-consistent treatment of solid covalent systems such as zeolites. For the present study, we used a gradient-corrected density functional approach. The resulting structural features of both Si- and Ti-substituted forms of the zeolite framework fit well with available experimental information. The calculated substitution energy of Ti at the 12 crystallographically different tetrahedral sites of the MFI structure vary within 19 kJ/mol with T12 and T2 as most and least preferred sites, respectively. On the basis of these computational results and the preferential sites for Ti substitution reported from different experimental investigations, we concluded that the Ti distribution in the TS-1 framework is not governed by the thermodynamic stability of the pure material.

Mechanisms of and Effect of Coadsorption on Water Dissociation on an Oxygen Vacancy of the MgO(100) Surface

The dissociation mechanism of a water molecule at an oxygen vacancy on the MgO(100) surface was studied by using the embedded cluster method at the DFT/B3 LYP level, while the energetic information was refined by using the IMOMO method at the CCSD level. We found that a water molecule initially adsorbs on one of the magnesium ions surrounding the vacancy site with a binding energy of 15.98 kcal mol(-1). It then can dissociate on the MgO(100) surface along two possible dissociation pathways. One pathway produces a hydroxyl group bonded to the original magnesium with a proton filling the vacancy via a transition state with a barrier of 4.67 kcal mol(-1) relative to the adsorbed water configuration. The other pathway yields two hydroxy groups; the hydroxy group originally belonging to the water molecule fills the vacancy, while the hydrogen atom binds with the surface oxygen to form the other hydroxy group. Hydrogen atoms of these hydroxy groups can recombine to form a hydrogen molecule and the surface is healed. Although the barrier (14.09 kcal mol(-1)) of the rate-controlling step of the latter pathway is higher than that of the former one, the energies of all of its stationary points are lower than that of the separated reactants (H(2)O+cluster). The effects of water coadsorption are modeled by placing an additional water molecule near the active center, which suggests that the more coadsorbed water molecules further stabilize the hydroxy species and prevent the hydrogen molecule formation through the latter pathway. The results support the photoemission spectral evidence of water dissociation on the defective MgO(100) surface at low water coverage.

Density Functional Study of the Mechanism of the Beckmann Rearrangement Catalyzed by H-ZSM-5: A Cluster and Embedded Cluster Study

The mechanism of the Beckmann rearrangement (BR) catalyzed by the ZSM-5 zeolite has been investigated by both the quantum cluster and embedded cluster approaches at the B3LYP level of theory using the 6-31G(d,p) basis set. Single-point calculations were carried out at the MP2/6-311G(d,p) level of theory to improve energetic properties. The embedded cluster model suggests that the initial step of the Beckmann rearrangement is not the O-protonated oxime but the N-protonated oxime. The energy barriers derived from the proton shuttle of the N-bound to the O-bound isomer are determined to be approximately 99 and approximately 40 kJ/mol for the embedded cluster and quantum cluster approaches, respectively. The difference in the activation energy is due mainly to the effect of the Madelung potential from the zeolite framework. The next step is the rearrangement step, which is the transformation of the O-protonated oxime to be an enol-formed amide compound, formimidic acid. The activation energy, at the rearrangement step, is calculated to be approximately 125 and approximately 270 kJ/mol for the embedded cluster and quantum cluster approaches, respectively. The final step is the tautomerization step which transforms the enol-form to the keto-form, formamide compound. The energy barrier for tautomerization is calculated to be 123 and 151 kJ/mol for the embedded cluster and quantum cluster approaches, respectively. These calculated results suggest that the rate-determining step of the vapor phase of the Beckmann rearrangement on H-ZSM-5 is the rearrangement or tautomerization step.

Nature of the Metal−Support Interaction in Bifunctional Catalytic Pt/H-ZSM-5 Zeolite

The metal-support interaction of a dispersed Pt atom on H-ZSM-5 zeolite has been investigated by using an embedded cluster and cluster models with the density functional theory/B3LYP functional method. We found that the Pt atom interacts with a Brønsted proton and a nearby framework oxygen. Interaction with the framework oxygen causes electron transfer from the zeolite to the Pt atom. Concurrently, a Brønsted proton stabilizes the Pt atom on the zeolite surface by withdrawing excess electron density from the Pt atom. These charge transfers result in a zero net charge on the Pt atom while changing its orbital occupation. The binding energy of Pt on the Brønsted acid was 15 kcal/mol. Inclusion of the Madelung potential by Surface Charge Representation of the Electrostatic Embedded Potential method (SCREEP) had small effects on structure and charge density of Pt/H-ZSM-5 but it shifted the stretching mode of CO toward a higher frequency by almost 40 cm(-1). The frequency shift of absorbed CO calculated with embedded cluster models was from 8 to 11 cm(-1) red shift, compared to 20 cm(-1) red shift from experiment. This implies that not only the electronic state of the Pt atom but also the Madelung potential of the support is responsible for the observed small red shift of CO on the Pt-H-ZSM-5.

A combined molecular dynamics+quantum mechanics method for investigation of dynamic effects on local surface structures

A combined molecular dynamics (MD)+quantum mechanics (QM) method for studying processes on ionic surfaces is presented. Through the combination of classical MD and ab initio embedded-cluster calculations, this method allows the modeling of surface processes involving both the structural and dynamic features of the substrate, even for large-scale systems. The embedding approach used to link the information from the MD simulation to the cluster calculation is presented, and rigorous tests have been carried out to ensure the feasibility of the method. The electrostatic potential and electron density resulting from our embedded-cluster model have been compared with periodic slab results, and confirm the satisfying quality of our embedding scheme as well as the importance of applying embedding in our combined MD+QM approach. We show that a highly accurate representation of the Madelung potential becomes a prerequisite when the embedded-cluster approach is applied to temperature-distorted surface snapshots from the MD simulation.