CPMD/GULP QM/MM interface for modeling periodic solids: Implementation and its application in the study of Y‐zeolite supported Rhn clusters

We report here the development of hybrid quantum mechanics/molecular mechanics (QM/MM) interface between the plane‐wave density functional theory based CPMD code and the empirical force‐field based GULP code for modeling periodic solids and surfaces. The hybrid QM/MM interface is based on the electrostatic coupling between QM and MM regions. The interface is designed for carrying out full relaxation of all the QM and MM atoms during geometry optimizations and molecular dynamics simulations, including the boundary atoms. Both Born–Oppenheimer and Car–Parrinello molecular dynamics schemes are enabled for the QM part during the QM/MM calculations. This interface has the advantage of parallelization of both the programs such that the QM and MM force evaluations can be carried out in parallel to model large systems. The interface program is first validated for total energy conservation and parallel scaling performance is benchmarked. Oxygen vacancy in α‐cristobalite is then studied in detail and the results are compared with a fully QM calculation and experimental data. Subsequently, we use our implementation to investigate the structure of rhodium cluster (Rh_n; n = 2 to 6) formed from Rh(C₂H₄)₂ complex adsorbed within a cavity of Y‐zeolite in a reducible atmosphere of H₂ gas. © 2016 Wiley Periodicals, Inc.     

A New Practical Route to ZSM‐5 Nanoparticles and Optimization of Synthetic Parameters through D‐optimal Design of Experiments

A D‐optimal experimental design with three levels of SiO₂/Al₂O₃, template/SiO₂, H₂O/SiO₂, Na₂O/SiO₂ and TPABr/TPAOH ratio parameters has been used to optimize the experimental parameters by an analysis of variances (ANOVA). The effects of these ratios in the initial synthetic mixture on the size of the ZSM‐5 zeolite nanoparticles have been studied. XRD and FE‐SEM analyses were used to characterize synthetic samples. Fischer test results showed that H₂O/SiO₂ and TPABr/TPAOH ratios are the most and least effective parameters, respectively, in the range studied. The most important two‐way interaction variables were the interaction of template/SiO₂ and TPABr/TPAOH molar ratios. The average particle size was in the 34–79 nm range. Furthermore, a mathematical model for the synthesis of ZSM‐5 zeolite nanoparticles was derived using experimental results. The optimized gel composition is as follows: SiO₂/Al₂O₃₌91.20, template/SiO₂₌0.16, H₂O/SiO₂₌40.42, Na₂O/SiO₂₌0.0147 and TPABr/TPAOH=0.     

Vapor‐Phase Aldolization of n‐Butyraldehyde to 2‐Ethyl‐2‐Hexenal over Solid‐Base Catalysts

Vapor‐phase aldol condensation of n‐butyraldehyde to 2‐ethyl‐2‐hexenal was studied at 1 atm and 150～ 300°C in a fixed‐bed, integral‐flow reactor by using NaX, KX, γ‐Al₂O₃ and Na/NaOH/γ‐Al₂CO₃ catalysts. Ion exchange of NaX zeolite with potassium acetate solution results in a decrease of crystallinity and apparent lowering of surface area, whereas the basic strength is enhanced. Treatment of γ‐Al₂O₃ with NaOH and Na causes a large decrease of the surface area but strong enhancement of the catalyst basicity. The catalytic activity on the basis of unit surface area is in the order Na/NaOH/γ‐Al₂O₃ < KXU < KXW < NaX >γ‐Al₂O₃, in accordance with the relative catalyst basic strength. The molar ratio of trimeric to dimeric products increases with increasing the reaction temperature and the catalyst basic strength except for Na/NaOH/γ‐Al₂O₃. Very high selectivity of 2‐ethyl‐2‐hexenal (>98.5%) was observed for reactions over NaX zeolite at 150°C. Based on the FT‐IR and the catalytic results, the reaction paths are proposed as follows: self‐aldol condensation of n‐butyraldehyde, followed by dehydration produces 2‐ethyl‐2‐hexenal, which then reacts with n‐butyraldehyde and successively dehydrates to 2,4‐diethyl‐2,4‐octadienal and 1,3,5‐triethylbenzene. For the reaction over NaX, the calculated Arrhenius frequency factor and activation energy are 314 mol/g·h and 32.6 kJ/mol, respectively.     

Convergence in the QM‐only and QM/MM modeling of enzymatic reactions: A case study for acetylene hydratase

We report systematic quantum mechanics‐only (QM‐only) and QM/molecular mechanics (MM) calculations on an enzyme‐catalyzed reaction to assess the convergence behavior of QM‐only and QM/MM energies with respect to the size of the chosen QM region. The QM and MM parts are described by density functional theory (typically B3LYP/def2‐SVP) and the CHARMM force field, respectively. Extending our previous work on acetylene hydratase with QM regions up to 157 atoms (Liao and Thiel, J. Chem. Theory Comput. 2012, 8, 3793), we performed QM/MM geometry optimizations with a QM region M4 composed of 408 atoms, as well as further QM/MM single‐point calculations with even larger QM regions up to 657 atoms. A charge deletion analysis was conducted for the previously used QM/MM model ( M3a , with a QM region of 157 atoms) to identify all MM residues with strong electrostatic contributions to the reaction energetics (typically more than 2 kcal/mol), which were then included in M4 . QM/MM calculations with this large QM region M4 lead to the same overall mechanism as the previous QM/MM calculations with M3a , but there are some variations in the relative energies of the stationary points, with a mean absolute deviation (MAD) of 2.7 kcal/mol. The energies of the two relevant transition states are close to each other at all levels applied (typically within 2 kcal/mol), with the first (second) one being rate‐limiting in the QM/MM calculations with M3a ( M4 ). QM‐only gas‐phase calculations give a very similar energy profile for QM region M4 (MAD of 1.7 kcal/mol), contrary to the situation for M3a where we had previously found significant discrepancies between the QM‐only and QM/MM results (MAD of 7.9 kcal/mol). Extension of the QM region beyond M4 up to M7 (657 atoms) leads to only rather small variations in the relative energies from single‐point QM‐only and QM/MM calculations (MAD typically about 1–2 kcal/mol). In the case of acetylene hydratase, a model with 408 QM atoms thus seems sufficient to achieve convergence in the computed relative energies to within 1–2 kcal/mol.Copyright © 2013 Wiley Periodicals, Inc.     

Using Taguchi Robust Design Method to Develop an Optimized Synthesis Procedure for Nanocrystals of ZSM‐5 Zeolite

The effects of TPAOH/SiO₂, H₂O/SiO₂, SiO₂/Na₂O and SiO₂/Al₂O₃ ratios in the initial synthetic mixture on the crystallization of nanoparticles of ZSM‐5 zeolite under atmospheric pressure were studied. A Taguchi orthogonal experimental design with three levels of the above‐mentioned parameters was used to optimize the experiment parameters by the analysis of variances (ANOVA). Applying the Taguchi method significantly reduced the time and cost for optimization. The obtained products were characterized by scanning electron microscopy, X‐ray diffraction and FT‐IR spectroscopy. As a result of the Taguchi analysis TPAOH/SiO₂ followed by SiO₂/Al₂O₃ was the most influencing parameters for the synthesis of nanosized ZSM‐5 crystals.     

Organic‐Free,ZnO‐Assisted Synthesis of Zeolite FAU with Tunable SiO2/Al2O3 Molar Ratio

Zeolite FAU with tunable SiO₂/Al₂O₃ molar ratio has been successfully synthesized in the absence of organic structure‐directing agents (OSDA). Specifically, the addition of zinc species contributes to the feasible and effective adjustment of the framework SiO₂/Al₂O₃ molar ratio between about 4 and 6 depending on the amount of zinc species added in the batch composition. In contrast, a typical OSDA such as tetramethylammonium hydroxide (TMAOH) has a limited effect on the SiO₂/Al₂O₃ molar ratio of the zeolite. The role of zinc species is essential for the crystallization of zeolite FAU with a higher SiO₂/Al₂O₃ molar ratio under the particular synthesis conditions. It is speculated that zinc species may suppress the incorporation of aluminum into the aluminosilicate framework, which is due to the Coulombic repulsive interaction. A higher SiO₂/Al₂O₃ molar ratio is also found to be accompanied by a lower CO₂ adsorption heat for CO₂/CH₄ separation.     

Novel Flower‐Like Ag‐SiO2‐MgO‐Al2O3 Material: Preparation,Characterization and Catalytic Application in Methanol Dehydrogenation

Catalytic direct dehydrogenation of methanol to formaldehyde was carried out over Ag‐SiO₂‐MgO‐Al₂O₃ catalysts prepared by sol‐gel method. The optimal preparation mass fractions were determined as 8.3% MgO, 16.5% Al₂O₃ and 20% silver loading. Using this optimum catalyst, excellent activity and selectivity were obtained. The conversion of methanol and the selectivity to formaldehyde both reached 100%, which were much higher than other previously reported silver supported catalysts. Based on combined characterizations, such as X‐ray diffraction (XRD), scanning electronic microscopy (SEM), diffuse reflectance ultraviolet‐visible spectroscopy (UV‐Vis, DRS), nitrogen adsorption at low temperature, temperature programmed desorption of ammonia (NH₃‐TPD), desorption of CO₂ (CO₂‐TPD), etc., the correlation of the catalytic performance to the structural properties of the Ag‐SiO₂‐ MgO‐Al₂O₃ catalyst was discussed in detail. This perfect catalytic performance in the direct dehydrogenation of methanol to formaldehyde without any side‐products is attributed to its unique flower‐like structure with a surface area less than 1 m²/g, and the strong interactions between neutralized support and the nano‐sized Ag particles as active centers.     

Ab initio simulations of two‐dimensional electronic spectra: The SOS//QM/MM approach

Two‐dimensional electronic spectroscopy (2DES) is a cutting‐edge technique for investigating with high temporal resolution energy transfer, structure, and dynamics in a wide range of systems in physical chemistry, energy sciences, biophysics, and biocatalysis. However, the interpretation of 2DES is challenging and requires computational modeling. This perspective provides a roadmap for the development of computational tools that could be routinely applied to simulate 2DES spectra of multichromophoric systems active in the UV region (2DUV) using state‐of‐the‐art ab initio electronic structure methods within a quatum mechanics/molecular mechanics (QM/MM) scheme and the sum‐over‐states (SOS) approach (here called SOS//QM/MM). Multiconfigurational and multireference perturbative methods, such as the complete active space self‐consistent field and second‐order multireference perturbation theory (CASPT2) techniques, can be applied to reliably calculate the electronic properties of multichromophoric systems. Hybrid QM/MM method and molecular dynamics techniques can be used to assess environmental and conformational effects, respectively, that shape the 2D electronic spectra. DNA and proteins are important biological targets containing UV chromophores. We report ab initio simulation of 2DUV spectra of a cyclic tetrapeptide containing two interacting aromatic side chains, a model system for the study of protein structure and dynamics by means of 2DUV spectroscopy. © 2013 Wiley Periodicals, Inc.     

First principles study of gallium‐cleaning for hydrogen‐contaminated α‐Al2O3(0001) surfaces

The use of gallium for cleaning hydrogen‐contaminated Al₂O₃ surfaces is explored by performing first principles density functional calculations of gallium adsorption on a hydrogen‐contaminated Al‐terminated α‐Al₂O₃(0001) surface. Both physisorbed and chemisorbed H‐contaminated α‐Al₂O₃(0001) surfaces with one monolayer (ML) gallium coverage are investigated. The thermodynamics of gallium cleaning are considered for a variety of different asymptotic products, and are found to be favorable in all cases. Physisorbed H atoms have very weak interactions with the Al₂O₃ surface and can be removed easily by the Ga ML. Chemisorbed H atoms form stronger interactions with the surface Al atoms. Bonding energy analysis and departure simulations indicate, however, that chemisorbed H atoms can be effectively removed by the Ga ML. © 2013 Wiley Periodicals, Inc.     

Ein neuer Aluminium/Nickel/Oxo‐Cluster: [Ni(acac)OAl(OtBu)2]4

A New Aluminum/Nickel/Oxo‐Cluster: [Ni(acac)OAl(OtBu)₂]₄ When bis(tert‐butoxy)alane (tBu‐O)₂AlH is allowed to react with nickeldiacetylacetonate at elevated temperature a new nickel/aluminum/oxo cluster [Ni(acac)OAl(OtBu)₂]₄ is formed together with aluminum acetylacetonate Al(acac)₃ and some other products. The metal/oxo cluster is isolated by crystallization and structurally fully characterized by X‐ray diffraction analysis. The molecule [Ni(acac)OAl(OtBu)₂]₄ contains an eight membered Al₄O₄ cycle, to which eight mutually edge sharing NiO₂Al cycles are fused. The overall point symmetry of the metal/oxo cluster is almost S₄. While the aluminum atoms are tetrahedrally surrounded by oxygen ligands (mean distances Al‐O in‐between 1, 730(6) and 1, 789(6) Å)), the nickel atoms are in a square pyramidal coordination sphere of oxygen atoms (Ni‐O_axial = 1.938(6) Å, Ni‐O_basal = 2.056(9) Å; all polyhedra are distorted). The nickel atoms have a d⁸ high spin electron configuration (μ_eff = 3.32 B.M.).     

Seed‐Assisted,One‐Pot Synthesis of Hollow Zeolite Beta without Using Organic Structure‐Directing Agents

Hollow aluminosilicate zeolite beta was successfully synthesized by adding CIT‐6, that is, zincosilicate zeolite, which has the same topology as beta, as seeds to the Na‐aluminosilicate gel without the need for organic structure‐directing agents. One important factor in the successful organic structure‐directing agent (OSDA)‐free synthesis of hollow beta crystals is the solubility of the seed crystals in alkaline media. CIT‐6 was less stable than aluminosilicate zeolite beta in alkaline media and the solubility changed depending on whether the crystals were calcined or not. The hollow beta could be obtained by using the uncalcined CIT‐6 seed crystals. The volumes of intra‐crystalline voids were tuned by changing the reaction time and the initial gel compositions, such as the SiO₂/Al₂O₃ and Na₂O/SiO₂ ratios. We estimated that the intra‐crystalline voids were formed through the dissolution of the seed crystals, just after the crystal growth of new beta on the outer surface of the seeds. In addition, new crystal growth toward inside of the void was also observed by TEM. On the basis of the characterization data, such as chemical analysis, N₂‐adsorption/desorption measurements, and TEM observation, a formation mechanism of the intra‐crystalline voids is proposed and discussed.     

Synthesis of Aluminum‐Rich Analcime Using an Ethylene Diamine Derivative as Template

The hydrothermal synthesis of analcime (ANA) with N,N′‐dibenzyl‐N,N,N′,N′‐tetramethylethylenediamine (DBTMED) as template was systematically studied. The various parameters that affect the crystallization of analcime, such as temperature, time, Al source, and Si/Al ratio were investigated. Systematic variations of these parameters revealed that ANA was obtained from the reaction mixture with the optimized ratios of SiO₂/Al₂O₃ = 5–9.5 in presence of DBTMED, whereas template‐free clear solution methods require SiO₂/Al₂O₃ ratio of greater than 25. When experiments were conducted at 130 and 150 °C for 4 days, a mixture of analcime and zeolite P was present in the samples, and a pure analcime sample could be obtained with heating in the temperature range 160–180 °C. When microwave and conventional heating were used, analcime could be obtained after 2 days. The obtained products were characterized by XRD, SEM, and IR spectroscopy.     

Substrate‐Guided Front‐Face Reaction Revealed by Combined Structural Snapshots and Metadynamics for the Polypeptide N‐Acetylgalactosaminyltransferase 2

The retaining glycosyltransferase GalNAc‐T2 is a member of a large family of human polypeptide GalNAc‐transferases that is responsible for the post‐translational modification of many cell‐surface proteins. By the use of combined structural and computational approaches, we provide the first set of structural snapshots of the enzyme during the catalytic cycle and combine these with quantum‐mechanics/molecular‐mechanics (QM/MM) metadynamics to unravel the catalytic mechanism of this retaining enzyme at the atomic‐electronic level of detail. Our study provides a detailed structural rationale for an ordered bi–bi kinetic mechanism and reveals critical aspects of substrate recognition, which dictate the specificity for acceptor Thr versus Ser residues and enforce a front‐face S_Ni‐type reaction in which the substrate N‐acetyl sugar substituent coordinates efficient glycosyl transfer.     

系列硅铝比纳米薄层ZSM-5分子筛的合成和表征

以自制不对称双子季铵盐表面活性剂为模板, 在水热合成体系中控制合成系列硅铝比纳米薄层ZSM-5分子筛.采用X射线衍射(XRD)、N₂吸附-脱附、X射线荧光光谱(XRF)、扫描电镜(SEM)和²⁷Al魔角旋转核磁共振(²⁷Al MAS-NMR)对合成的样品进行了表征. 详细研究了晶化温度、晶化时间、结构导向剂(SDA)用量、碱度等对合成的影响和纳米薄层ZSM-5分子筛的形成过程. 结果表明: 分子筛硅铝比越高, 结构导向剂用量越大, 所需的晶化时间越短; 晶化温度越高, 晶化时间越短; 且不同硅铝比纳米薄层ZSM-5分子筛的形貌规整度、比表面积和介孔/微孔孔容比例随着硅铝比而变化.     

Synthesis of Zeolite ZSM-2 Using Zeolite NaX as Seeds

Introduction Oxygen and nitrogen have been produced tradition-ally by cryogenic distillation of air. Methods for the non-cryogenic separation based on selective adsorption have been developed and commercialized since the 1970s and have led to a cost-effective process for this important separation.1 Low-silica zeolites are important materials for producing oxygen by selective adsorption of nitrogen. In 19891990, a new generation of lith-ium-based adsorbents was developed.2,3 Highly lithium exc…     

Effect of SiC/nano‐CeO2 on wear resistance and microstructures of Ti3Al/γ‐Ni matrix laser‐cladded composite coating on Ti–6Al–4V alloy

The Ti–6Al–4V alloy is an important aviation material, but has a poor resistance to slide wear. Laser cladding of the Al₃Ti + Ni/Cr/C + TiB₂/Al₂O₃ + SiC/nano‐CeO₂ preplaced powders on the Ti–6Al–4V alloy can form the Ti₃Al/γ‐Ni matrix composite coating, which improves the wear resistance of the substrate. In this study, the Al₃Ti + Ni/Cr/C + TiB₂/Al₂O₃ + SiC/nano‐CeO₂ laser‐cladded coating was researched by means of X‐ray diffraction, scanning electron microscopy, and energy dispersive spectrometry. The experimental results indicate that under the action of SiC/nano‐CeO₂, this composite coating exhibited a fine microstructure. Furthermore, the proper content of nano‐CeO₂ decreased the crack tendency. The results above indicated that, it is feasible to improve the tribological property of the Al₃Ti + Ni/Cr/C + TiB₂/Al₂O₃ laser‐cladded coating by adding of SiC/nano‐CeO₂. Copyright © 2011 John Wiley & Sons, Ltd.     

A QM/MM Investigation of the Catalytic Mechanism of Metal‐Ion‐Independent Core 2 β1,6‐N‐Acetylglucosaminyltransferase

β1,6‐GlcNAc‐transferase (C2GnT) is an important controlling factor of biological functions for many glycoproteins and its activity has been found to be altered in breast, colon, and lung cancer cells, in leukemia cells, in the lymhomonocytes of multiple sclerosis patients, leukocytes from diabetes patients, and in conditions causing an immune deficiency. The result of the action of C2GnT is the core 2 structure that is essential for the further elongation of the carbohydrate chains of O‐glycans. The catalytic mechanism of this metal‐ion‐independent glycosyltransferase is of paramount importance and is investigated here by using quantum mechanical (QM) (density functional theory (DFT))/molecular modeling (MM) methods with different levels of theory. The structural model of the reaction site used in this report is based on the crystal structures of C2GnT. The entire enzyme–substrate system was subdivided into two different subsystems: the QM subsystem containing 206 atoms and the MM region containing 5914 atoms. Three predefined reaction coordinates were employed to investigate the catalytic mechanism. The calculated potential energy surfaces discovered the existence of a concerted S_N2‐like mechanism. In this mechanism, a nucleophilic attack by O6 facilitated by proton transfer to the catalytic base and the separation of the leaving group all occur almost simultaneously. The transition state for the proposed reaction mechanism at the M06‐2X/6‐31G** (with diffuse functions on the O1′, O5′, O_Glu, and O6 atoms) level was located at C1? O6=1.74 Å and C1? O1=2.86 Å. The activation energy for this mechanism was estimated to be between 20 and 29 kcal mol^?1, depending on the method used. These calculations also identified a low‐barrier hydrogen bond between the nucleophile O6H and the catalytic base Glu320, and a hydrogen bond between the N‐acetamino group and the glycosidic oxygen of the donor in the TS. It is proposed that these interactions contribute to a stabilization of TS and participate in the catalytic mechanism.     

Preparation of uniform and nano‐sized NaA zeolite using silatrane and alumatrane precursors

Nano‐sized Na A zeolite was successfully synthesized via the sol–gel process and microwave techniques. The synthesis parameters, such as hydroxide ion concentration, seed amount, as well as heating time and temperature, were studied to obtain the most uniform and very small sized NaA zeolite using the composition of SiO₂:Al₂O₃:xNa₂O:410H₂O; 3 ≤ x ≤ 6. It was found that hydroxide ion concentration affects the crystal size and heating time, whereas a higher amount of seed provides smaller sized NaA zeolite. The zeolite product can be synthesized using a higher temperature for a shorter time or lower temperature for a longer time. The best conditions for synthesizing the smallest size, 0.1–0.2 µm, and the most homogeneous NaA zeolite is to use the composition of SiO₂:Al₂O₃:3Na₂O:410H₂O and 3 wt% crystal seed at 80 °C microwave heating for 6 h. The synthesized NaA zeolite was characterized using XRD and SEM. Copyright © 2006 John Wiley & Sons, Ltd.     

Interface formation of Al2O3 on n‐GaN(0001): Photoelectron spectroscopy studies

Al₂O₃ insulator layers were deposited step by step by the physical vapor deposition (PVD) method onto gallium nitride in the wurtzite form, n‐type and (0001)‐oriented. The substrate surface and the early stages of Al₂O₃/n‐GaN(0001) interface formation were characterized in situ under ultra‐high vacuum conditions by X‐ray and ultraviolet photoelectron spectroscopy (XPS, UPS). The electron affinity (EA) of the substrate cleaned by annealing was 3.6 eV. Binding energies of the Al 2p (76.0 eV) and the O 1s (532.9 eV) confirmed the creation of the Al₂O₃ compound in the deposited film for which the EA was 1.6 eV. The Al₂O₃ film was found to be amorphous with a bandgap of 6.9 eV determined from the O 1s loss feature. As a result, the calculated Al₂O₃/n‐GaN(0001) valence band offset (VBO) is ?1.3 eV and the corresponding conduction band offset (CBO) 2.2 eV.     

Multi‐instrument characterization of the surfaces and materials in microfabricated,carbon nanotube‐templated thin layer chromatography plates. An analogy to ‘The Blind Men and the Elephant’

We apply a suite of analytical tools to characterize materials created in the production of microfabricated thin layer chromatography plates. Techniques used include X‐ray photoelectron spectroscopy (XPS), valence band spectroscopy, time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) in both positive and negative ion modes, Rutherford backscattering spectroscopy (RBS), and helium ion microscopy. Materials characterized include: the Si(100) substrate with native oxide: Si/SiO₂, alumina (35 nm) deposited as a diffusion barrier on the Si/SiO₂: Si/SiO₂/Al₂O₃, iron (6 nm) thermally evaporated on the Al₂O₃: Si/SiO₂/Al₂O₃/Fe, the iron film annealed in H₂ to make Fe catalyst nanoparticles: Si/SiO₂/Al₂O₃/Fe(NP), and carbon nanotubes (CNTs) grown from the Fe nanoparticles: Si/SiO₂/Al₂O₃/Fe(NP)/CNT. The Fe films and nanoparticles appear in an oxidized state. Some of the analyses of the CNTs/CNT forests appear to be unique: (i) the CNT forest appears to exhibit an interesting ‘channeling’ phenomenon by RBS, (ii) we observe an odd–even effect in the SIMS spectra of C_n^‐ species for n = 1 – 6, with the n ≥ 6 ions showing a steady decrease in intensity, and (iii) valence band characterization of CNTs using X‐radiation is reported. Initial analysis of the CNT forest by XPS shows that it is 100 at.% carbon. After one year, only ca. 0.25 at.% oxygen is observed. The information obtained from the combination of the different analytical tools provides a more complete understanding of our materials than a single technique, which is analogous to the story of ‘The Blind Men and the Elephant’. The raw XPS and ToF‐SIMS spectra from this study will be submitted to Surface Science Spectra for archiving. Copyright © 2013 John Wiley & Sons, Ltd.