Experimental Basicities of Superbasic Phosphonium Ylides and Phosphazenes

pKaH values and θH angles of phosphanes to predict their electronic and steric parameters

Phosphanes play an important role in various applications, serving as a class of organic bases with basicities spanning more than 30 orders of magnitude. Accessing comprehensive basicity data for phosphanes has been challenging due to scattered information across multiple sources and notable gaps in the existing data. In this report, we present basicities (pKaH values) of a diverse set of phosphanes, both newly measured or calculated and collected from the literature. We demonstrate that pKaH values can serve as an alternative to Tolman electronic parameters (TEP values) in evaluating the electronic properties of phosphanes. Additionally, we suggest parameters for assessing the steric properties of phosphanes without the need for preparation or calculation of metal-ligand complexes.

Water-Tolerant Superbase Polyoxometalate [H2(Nb6O19)]6- for Homogeneous Catalysis

Here, doubly protonated Lindqvist-type niobium oxide cluster [H2(Nb6O19)]6-, fabricated by microwave-assisted hydrothermal synthesis, exhibited superbase catalysis for Knoevenagel and crossed aldol condensation reactions accompanied by activating C-H bond with pKa >26 and proton abstraction from a base indicator with pKa=26.5. Surprisingly, [H2(Nb6O19)]6- exhibited water-tolerant superbase properties for Knoevenagel and crossed aldol condensation reactions in the presence of water, although it is well known that the strong basicity of metal oxides and organic superbase is typically lost by the adsorption of water. Density functional theory calculation revealed that the basic surface oxygens that share the corner of NbO6 units in [H2(Nb6O19)]8- maintained the negative charges even after proton adsorption. This proton capacity and the presence of un-protonated basic sites led to the water tolerance of the superbase catalysis.

Exploiting the (-C-H···C-) Interaction to Design Cage-Functionalized Organic Superbases and Hyperbases: A Computational Study

A set of carbon center-based P-ylidesubstituting bases have been exploited computationally with pentacyclo[5.4.0.02,6.03,10.05.9]undecane (PCU) and pentacyclo [6.4.0.02,7.03,11.06,10] dodecane (PCD) scaffolds using the B3LYP-D3/6-311+G(d,p) level of theory. The proton affinities calculated in the gas phase are in the range of superbases and hyperbases. The Atomsin-Molecules and Natural Bond Orbital calculations reveal that the -C-H···C- interaction plays a substantial role in improving the basicity, and tuning the -C-H···C- interaction can enhance the basicity of such systems. The free activation energy for proton exchange for PCD and PCU scaffolds substituted with P-ylide is substantially low. The computed results reveal the strength and nature of such - C-H···C- interactions compared to the -N-H···N- hydrogen bonds. The isodesmic reactions suggest that the superbasicity achieved using these frameworks arises from a combination of several factors, such as the ring strain of the bases in their unprotonated form, steric repulsion, and the intramolecular -C-H···C- interaction.

Base-catalyzed diastereodivergent thia-Michael addition to chiral β-trifluoromethyl-α,β-unsaturated N-acylated oxazolidin-2-ones

Base-catalyzed diastereodivergent thia-Michael addition of thiols to chiral β-trifluoromethyl-α,β-unsaturated N-acylated oxazolidin-2-ones is reported. By tuning the base-catalyst (i-Pr2NEt, DABCO, or P2-t-Bu), a range of chiral thia-Michael adducts was synthesized in good yields with high diastereoselectivities. A plausible mechanism was proposed on the basis of the experimental results. This work is complementary to the existing methods offering advantages, e.g., switchable diastereoselectivity using a readily synthesized chiral starting material, a cheap and readily available base catalyst, and a simple and practical operation, enabling synthetic application in organic synthesis.

The Unified Redox Scale for All Solvents: Consistency and Gibbs Transfer Energies of Electrolytes from their Constituent Single Ions

We have devised the unified redox scale Eabs H2O , which is valid for all solvents. The necessary single ion Gibbs transfer energy between two different solvents, which only can be determined with extra-thermodynamic assumptions so far, must clearly satisfy two essential conditions: First, the sum of the independent cation and anion values must give the Gibbs transfer energy of the salt they form. The latter is an observable and measurable without extra-thermodynamic assumptions. Second, the values must be consistent for different solvent combinations. With this work, potentiometric measurements on silver ions and on chloride ions show that both conditions are fulfilled using a salt bridge filled with the ionic liquid [N2225 ][NTf2 ]: if compared to the values resulting from known pKL values, the silver and chloride single ion magnitudes combine within a uncertainty of 1.5 kJ mol-1 to the directly measurable transfer magnitudes of the salt AgCl from water to the solvents acetonitrile, propylene carbonate, dimethylformamide, ethanol, and methanol. The resulting values are used to further develop the consistent unified redox potential scale Eabs H2O that now allows to assess and compare redox potentials in and over six different solvents. We elaborate on its implications.

Large changes in hydricity as a function of charge and not metal in (PNP)M–H (de)hydrogenation catalysts that undergo metal–ligand cooperativity

Ligand pKa and metal hydricity scale with one another in (de)hydrogenation catalysts that undergo metal–ligand cooperativity, irrespective of metal or ligand identity. Anionic hydrides are significantly more hydridic than their neutral counterparts.

Phosphazene Base-Catalyzed Intramolecular Hydroamidation of Alkenes with Amides

A method for the synthesis of cyclic amides via phosphazene base-catalyzed intramolecular hydroamidation of amide alkenes was developed. The reaction using a catalytic amount of P4-base had a good functional group tolerance and a broad substrate scope and could also be used to synthesize lactam, cyclic urea, and oxazolidinone compounds. This catalytic system was expanded to a one-pot intramolecular hydroamidation and intermolecular hydroalkylation. Deuterium labeling and radical trapping experiments provided mechanistic insights into the catalytic cycle of the hydroamidation reaction.

Cyclopropenium Ions in Catalysis

Cyclopropenium ions are the smallest class of aromatic compounds, satisfying Hückel's rules of aromaticity with two π electrons within a three-membered ring. First prepared by Breslow in 1957, cyclopropenium ions have been found to possess extraordinary stability despite being both cationic and highly strained. In the 65 years since their first preparation, cyclopropenium ions have been the subject of innumerable studies concerning their synthesis, physical properties, and reactivity. However, prior to our work, the reactivity of these unique carbocations had not been exploited for reaction promotion or catalysis.Over the past 13 years, we have been exploring aromatic ions as unique and versatile building blocks for the development of catalysts for organic chemistry. A major portion of this work has been focused on leveraging the remarkable properties of the smallest of the aromatic ions─cyclopropeniums─as a design element in the invention of highly reactive catalysts. Indeed, because of its unique profile of hydrolytic stability, compact geometry, and relatively easy oxidizability, the cyclopropenium ring has proven to be a highly advantageous construction module for catalyst invention.In this Account, we describe some of our work using cyclopropenium ions as a key element in the design of novel catalysts. First, we discuss our early work aimed at promoting dehydrative reactions, starting with Appel-type chlorodehydrations of alcohols and carboxylic acids, cyclic ether formations, and Beckmann rearrangements and culminating in the realization of catalytic chlorodehydrations of alcohols and a catalytic Mitsunobu-type reaction. Next, we describe the development of cyclopropenimines as strong, neutral organic Brønsted bases and, in particular, the use of chiral cyclopropenimines for enantioselective Brønsted catalysis. We also describe the development of higher-order cyclopropenimine superbases. The use of tris(amino)cyclopropenium (TAC) ions as a novel class of phase-transfer catalysts is discussed for the reaction of epoxides with carbon dioxide. Next, we describe the formation of a cyclopropenone radical cation that has a portion of its spin density on the oxygen atom, leading to some peculiar metal ligand behavior. Finally, we discuss recent work that employs TAC electrophotocatalysts for oxidation reactions. The key intermediate for this chemistry is a TAC radical dication, which as an open-shell photocatalyst has remarkably strong excited-state oxidizing power. We describe the application of this strategy to transformations ranging from the oxidative functionalization of unactivated arenes to the regioselective derivatization of ethers, C-H aminations, vicinal C-H diaminations, and finally aryl olefin dioxygenations. Collectively, these catalytic platforms demonstrate the utility of charged aromatic rings, and cyclopropenium ions in particular, to enable unique advances in catalysis.

Hydrogen Atom Abstraction from an OsII(NH3)2 Complex Generates an OsIV(NH2)2 Complex: Experimental and Computational Analysis of the N-H Bond Dissociation Free Energies and Reactivity

Double hydrogen atom abstraction from (TMP)Os^II(NH₃)₂ (TMP = tetramesitylporphyrin) with phenoxyl or nitroxyl radicals leads to (TMP)Os^IV(NH₂)₂. This unusual bis(amide) complex is diamagnetic and displays an N-H resonance at 12.0 ppm in its ¹H NMR spectrum. ¹H-¹⁵N correlation experiments identified a ¹⁵N NMR spectroscopic resonance signal at -267 ppm. Experimental reactivity studies and density functional theory calculations support relatively weak N-H bonds of 73.3 kcal/mol for (TMP)Os^II(NH₃)₂ and 74.2 kcal/mol for (TMP)Os^III(NH₃)(NH₂). Cyclic voltammetry experiments provide an estimate of the pK_a of [(TMP)Os^III(NH₃)₂]⁺. In the presence of Barton's base, a current enhancement is observed at the Os(III/II) couple, consistent with an ECE event. Spectroscopic experiments confirmed (TMP)Os^IV(NH₂)₂ as the product of bulk electrolysis. Double hydrogen atom abstraction is influenced by π donation from the amides of (TMP)Os^IV(NH₂)₂ into the d orbitals of the Os center, favoring the formation of (TMP)Os^IV(NH₂)₂ over N-N coupling. This π donation leads to a Jahn-Teller distortion that splits the energy levels of the d_xz and d_yz orbitals of Os, results in a low-spin electron configuration, and leads to minimal aminyl character on the N atoms, rendering (TMP)Os^IV(NH₂)₂ unreactive toward amide-amide coupling.

Modeling pKa of the Brønsted Bases as an Approach to the Gibbs Energy of the Proton in Acetonitrile

A simple but efficient computational approach to calculate pK_a in acetonitrile for a set of phosphorus, nitrogen, and carbon bases was established. A linear function that describes relations between the calculated ΔG’_a.sol(BH⁺) and pK_a values was determined for each group of bases. The best model was obtained through the variations in the basis set, in the level of theory (density functionals or MP2), and in the continuum solvation model (IPCM, CPCM, or SMD). The combination of the IPCM/B3LYP/6-311+G(d,p) solvation approach with MP2/6-311+G(2df,p)//B3LYP/6-31G(d) gas-phase energies provided very good results for all three groups of bases with R² values close to or above 0.99. Interestingly, the slopes and the intercepts of the obtained linear functions showed significant deviations from the theoretical values. We made a linear plot utilizing all the conducted calculations and all the structural variations and employed methods to prove the systematic nature of the intercept/slope dependence. The interpolation of the intercept to the ideal slope value enabled us to determine the Gibbs energy of the proton in acetonitrile, which amounted to −258.8 kcal mol⁻¹. The obtained value was in excellent agreement with previously published results.

Measurements and Utilization of Consistent Gibbs Energies of Transfer of Single Ions: Towards a Unified Redox Potential Scale for All Solvents

Utilizing the “ideal” ionic liquid salt bridge to measure Gibbs energies of transfer of silver ions between the solvents water, acetonitrile, propylene carbonate and dimethylformamide results in a consistent data set with a precision of 0.6 kJ mol⁻¹ over 87 measurements in 10 half‐cells. This forms the basis for a coherent experimental thermodynamic framework of ion solvation chemistry. In addition, we define the solvent independent peabsH2O ‐ and the EabsH2O values that account for the electronating potential of any redox system similar to the pHabsH2O value of a medium that accounts for its protonating potential. This EabsH2O scale is thermodynamically well‐defined enabling a straightforward comparison of the redox potentials (reducities) of all media with respect to the aqueous redox potential scale, hence unifying all conventional solvents′ redox potential scales. Thus, using the Gibbs energy of transfer of the silver ion published herein, one can convert and unify all hitherto published redox potentials measured, for example, against ferrocene, to the EabsH2O scale.

Strong Bases Design: Predicted Limits of Basicity

Brønsted superbases have wide applications in organic chemistry due to their ability to activate C-H bonds. The strongest neutral bases to date are substituted aminophosphazenes developed in the late 1980s by Reinhard Schwesinger. Since then, much effort has been expended to create even stronger neutral bases. In this article, the reasons for the instability of very basic compounds are investigated by means of high-level quantum-chemical calculations. Theoretical basicity limits are suggested for solutions as well as for the gas phase. A record-breaking superbase most likely to be synthesizable and stable at ambient conditions is proposed. Hexamethylphosphoramide is considered a reliable ionizing solvent for superbases.

Transition Metal Carbide Complexes

Carbide complexes remain a rare class of molecules. Their paucity does not reflect exceptional instability but is rather due to the generally narrow scope of synthetic procedures for constructing carbide complexes. The preparation of carbide complexes typically revolves around generating L_nM-CE_x fragments, followed by cleavage of the C-E bonds of the coordinated carbon-based ligands (the alternative being direct C atom transfer). Prime examples involve deoxygenation of carbonyl ligands and deprotonation of methyl ligands, but several other p-block fragments can be cleaved off to afford carbide ligands. This Review outlines synthetic strategies toward terminal carbide complexes, bridging carbide complexes, as well as carbide-carbonyl cluster complexes. It then surveys the reactivity of carbide complexes, covering stoichiometric reactions where the carbide ligands act as C₁ reagents, engage in cross-coupling reactions, and enact Fischer-Tropsch-like chemistry; in addition, we discuss carbide complexes in the context of catalysis. Finally, we examine spectroscopic features of carbide complexes, which helps to establish the presence of the carbide functionality and address its electronic structure.

Tris(tetramethylguanidinyl)phosphine: The Simplest Non-ionic Phosphorus Superbase and Strongly Donating Phosphine Ligand

We report the synthesis and properties of the much sought‐after tris(1,1,3,3‐tetramethylguanidinyl) phosphine P(tmg)₃, a crystalline, superbasic phosphine accessible through a short and scalable procedure from the cheap and commercially available bulk chemicals 1,1,3,3‐tetramethylguanidine, tris(dimethylamino)‐phosphine and phosphorus trichloride. The new phosphine exhibits exceptional electron donor properties and readily forms transition metal complexes with gold(I), palladium(II) and rhodium(I) precursors. The formation of zwitterionic Lewis base adducts with carbon dioxide and sulfur dioxide was explored. In addition, the complete series of phosphine chalcogenides was prepared from the reaction of P(tmg)₃ with N₂O and the elemental chalcogens.

Stable Singlet Carbenes as Organic Superbases

A simple experimental procedure for scaling carbene Brønsted basicity is described. The results highlight the strong basicity of pyrazol-4-ylidenes, a type of mesoionic carbene, also named cyclic-bentallenes (CBA). They are more basic (pK_aH >42.7 in acetonitrile) than the popular proazaphosphatrane Verkade bases, and even the Schwesinger phosphazene superbase P₄ (^t Bu). The basicity of these compounds can readily be tuned, and they are accessible in multigram quantities. These results open new avenues for carbon centered superbases.

High Spin Cobalt Complexes Supported by a Trigonal Tris(Phosphinimide) Ligand

Terminal, π-basic moieties occupy a prominent position in the stabilization of unusual or reactive inorganic species. The electron-releasing, π-basic properties of phosphinimides (PN) have been employed to stabilize electron-deficient early transition metals and lanthanides. In principle, a ligand field comprised of terminal PN groups should enable access to high-valent states of late first row transition metals. Herein, we report a new class of multidentate phosphinimide ligands to logically explore this hypothesis. Access to such ligands is made possible by a new procedure for the electrophilic amination of rigid, sterically encumbering, multidentate phosphines. Such frameworks facilitate terminal PN coordination to cobalt as demonstrated by the synthesis of a trinuclear Co^II₃ complex and a homoleptic, three-coordinate Co^III complex. Interestingly, the Co^III complex exhibits an exceedingly rare S = 2 ground state. Combined XRD, magnetic susceptibility, and DFT studies highlight that terminally bound PNs engage in strong dπ-pπ interactions that present a weak ligand field appropriate to stabilize high-spin states of late transition metals.

Design of Novel Uncharged Organic Superbases: Merging Basicity and Functionality

ConspectusOne of the constant challenges of synthetic chemistry is the molecular design and synthesis of nonionic, metal-free superbases as chemically stable neutral organic compounds of moderate molecular weight, intrinsically high thermodynamic basicity, adaptable kinetic basicity, and weak or tunable nucleophilicity at their nitrogen, phosphorus, or carbon basicity centers. Such superbases can catalyze numerous reactions, ranging from C-C bond formation to cycloadditions and polymerization, to name just a few. Additional benefits of organic superbases, as opposed to their inorganic counterparts, are their solubility in organic reaction media, mild reaction conditions, and higher selectivity. Approaching such superbasic compounds remains a continuous challenge. However, recent advances in synthetic methodology and theoretical understanding have resulted in new design principles and synthetic strategies toward superbases. Our computational contributions have demonstrated that the gas-phase basicity region of 350 kcal mol^-1 and even beyond is easily reachable by organosuperbases. However, despite record-high basicities, the physical limitations of many of these compounds become quickly evident. The typically large molecular weight of these molecules and their sensitivity to ordinary reaction conditions prevent them from being practical, even though their preparation is often not too difficult. Thus, obviously structural limitations with respect to molecular weight and structural complexity must be imposed on the design of new synthetically useful organic superbases, but strategies for increasing their basicity remain important.The contemporary design of novel organic superbases is illustrated by phosphazenyl phosphanes displaying gas-phase basicities (GB) above 300 kcal mol^-1 but having molecular weights well below 1000 g·mol^-1. This approach is based on a reconsideration of phosphorus(III) compounds, which goes along with increasing their stability in solution. Another example is the preparation of carbodiphosphoranes incorporating pyrrolidine, tetramethylguanidine, or hexamethylphosphazene as a substituent. With gas-phase proton affinities of up to 300 kcal mol^-1, they are among the top nonionic carbon bases on the basicity scale. Remarkably, the high basicity of these compounds is achieved at molecular weights of around 600 g·mol^-1. Another approach to achieving high basicity through the cooperative effect of multiple intramolecular hydrogen bonding, which increases the stabilization of conjugate acids, has recently been confirmed.This Account focuses on our efforts to produce superbasic molecules that embody many desirable traits, but other groups' approaches will also be discussed. We reveal the crucial structural features of superbases and place them on known basicity scales. We discuss the emerging potential and current limits of their application and give a general outlook into the future.

Phosphorus-Containing Superbases: Recent Progress in the Chemistry of Electron-Abundant Phosphines and Phosphazenes

The renaissance of Brønsted superbases is primarily based on their pronounced capacity for a large variety of chemical transformations under mild reaction conditions. Four major set screws are available for the selective tuning of the basicity: the nature of the basic center (N, P, …), the degree of electron donation by substituents to the central atom, the possibility of charge delocalization, and the energy gain by hydrogen bonding. Within the past decades, a plethora of neutral electron-rich phosphine and phosphazene bases have appeared in the literature. Their outstanding properties and advantages over inorganic or charged bases have now made them indispensable as auxiliary bases in deprotonation processes. Herein, an update of the chemistry of basic phosphines and phosphazenes is given. In addition, due to widespread interest, their use in catalysis or as ligands in coordination chemistry is highlighted.

Design of non-ionic carbon superbases: second generation carbodiphosphoranes

The edge-cutting design, synthesis and characterization of the so far strongest non-ionic carbon superbases is presented.

A new generation of carbodiphosphoranes (CDPs), incorporating pyrrolidine, tetramethylguanidine, or tris(dimethylamino)phosphazene as substituents is introduced as the most powerful class of non-ionic carbon superbases on the basicity scale to date. The synthetic approach as well as NMR spectroscopic and structural characteristics in the free and protonated form are described. Investigation of basicity in solution and in the gas phase by experimental and theoretical means provides the to our knowledge first reported pK_BH⁺ values for CDPs in the literature and suggest them as upper tier superbases.

Acid-base properties of phosphoric and acetic acid in aprotic organic solvents - A complete thermodynamic characterisation

Knowledge regarding the acid-base behaviour in non-aqueous media has remained relatively scarce in spite of its importance for many aspects of chemistry. The research presented in this work fills some of particularly important gaps in the corresponding thermodynamic data. We report on a detailed study of acid-base properties of dihydrogen phosphate and acetate in aprotic organic solvents (acetonitrile, dimethyl sulfoxide, and dimethylformamide). It was found that several processes, i.e. protonation, homoassociation, and dimerisation play important roles in defining the basicity of these widely important anions. In the case of dihydrogen phosphate, formation of higher homoassociates (two anions, one acid molecule and vice versa) was detected, whereas acetate formed only simple homoassociates of 1:1 stoichiometry. The dimerisation of dihydrogen phosphate and acetic acid were confirmed to be important processes as well. The thermodynamics of the above mentioned reactions was characterised in detail by means of various experimental methods: ITC, spectrophotometry, NMR-spectroscopy, and conductometry. Reliable equilibrium constants and other thermodynamic reaction functions were determined. The obtained results were discussed in terms of hydrogen bonding potential of the anions and their conjugated acids, as well as solvent properties, i.e. their ability to solvate the species involved in the studied processes.

Equilibrium Acidities of Nitroalkanes in an Ionic Liquid

The acidity ladder scale in [BMPY][NTf₂] was successfully expanded toward the weak acidity region for about five more p K units compared to the previously established one. This allows the acidities of a series of 13 aliphatic and aromatic nitroalkanes to be determined accurately by the UV-vis spectroscopic method. The acidity of nitroalkane in [BMPY][NTf₂] covers ∼8 p K units and is significantly weaker than those in DMSO and water. The Hammett plot for 4-substituted phenylnitromethanes shows an excellent linearity with a slope of 2.06, which is rather close to that in DMSO but significantly larger than that in water (0.80). The regression analyses reveal that the solvation behavior of [BMPY][NTf₂] on the acidic dissociations of C-H acids is similar to that of DMSO.

Polymerization of Polar Monomers Mediated by Main-Group Lewis Acid-Base Pairs

The development of new or more sustainable, active, efficient, controlled, and selective polymerization reactions or processes continues to be crucial for the synthesis of important polymers or materials with specific structures or functions. In this context, the newly emerged polymerization technique enabled by main-group Lewis pairs (LPs), termed as Lewis pair polymerization (LPP), exploits the synergy and cooperativity between the Lewis acid (LA) and Lewis base (LB) sites of LPs, which can be employed as frustrated Lewis pairs (FLPs), interacting LPs (ILPs), or classical Lewis adducts (CLAs), to effect cooperative monomer activation as well as chain initiation, propagation, termination, and transfer events. Through balancing the Lewis acidity, Lewis basicity, and steric effects of LPs, LPP has shown several unique advantages or intriguing opportunities compared to other polymerization techniques and demonstrated its broad polar monomer scope, high activity, control or livingness, and complete chemo- or regioselectivity, as well as its unique application in materials chemistry. These advances made in LPP are comprehensively reviewed, with the scope of monomers focusing on heteroatom-containing polar monomers, while the polymerizations mediated by main-group LAs and LBs separately that are most relevant to the LPP are also highlighted or updated. Examples of applying the principles of the LPP and LP chemistry as a new platform for advancing materials chemistry are highlighted, and currently unmet challenges in the field of the LPP, and thus the suggested corresponding future research directions, are also presented.

Method development for the analysis of resinous materials with MALDI-FT-ICR-MS: novel internal standards and a new matrix material for negative ion mode

Matrix-assisted laser desorption/ionization (MALDI) is a mass spectrometry (MS) ionization technique suitable for a wide variety of sample types including highly complex ones such as natural resinous materials. Coupled with Fourier transform ion cyclotron resonance (FT-ICR) mass analyser, which provides mass spectra with high resolution and accuracy, the method gives a wealth of information about the composition of the sample. One of the key aspects in MALDI-MS is the right choice of matrix compound. We have previously demonstrated that 2,5-dihydroxybenzoic acid is suitable for the positive ion mode analysis of resinous samples. However, 2,5-dihydroxybenzoic acid was found to be unsuitable for the analysis of these samples in the negative ion mode. The second problem addressed was the limited choice of calibration standards offering a flexible selection of m/z values under m/z 1000. This study presents a modified MALDI-FT-ICR-MS method for the analysis of resinous materials, which incorporates a novel matrix compound, 2-aminoacridine for the negative ion mode analysis and extends the selection of internal standards with m/z <1000 for both positive (15 different phosphazenium cations) and negative (anions of four fluorine-rich sulpho-compounds) ion mode. The novel internal calibration compounds and matrix material were tested for the analysis of various natural resins and real-life varnish samples taken from cultural heritage objects. Copyright © 2017 John Wiley & Sons, Ltd.