Morphological Control of Heteroleptic cis- and trans-Pd2L2L′2 Cages

Control over the integrative self-sorting of metallo-supramolecular assemblies opens up possibilities for introducing increased complexity and function into a single self-assembled architecture. Herein, the relationship between the geometry of three ligand components and morphology of three self-sorted heteroleptic [Pd₂ L ₂ L ′₂]⁴⁺ cages is examined. Pd-mediated assembly of two bis-monodentate pyridyl ligands with native bite angles of 75° and 120° affords a cis-[Pd₂ L ₂ L ′₂]⁴⁺ cage while the same reaction with two ligands with bite angles of 75° and 60° gives an unprecedented, self-penetrating structural motif; a trans-[Pd₂(anti- L )₂ L ′₂]⁴⁺ heteroleptic cage with a “doubly bridged figure eight” topology. Each heteroleptic assembly can be formed by cage-to-cage conversion of the homoleptic precursors and morphological control of [Pd₂ L ₂ L ′₂] cages is achieved by selective ligand displacement transformations in a system of three ligands and at least six possible cage products.     

Solvent‐Dependent Self‐Assembly Behaviour and Speciation Control of Pd6L8 Metallo‐supramolecular Cages

The C₃‐symmetric chiral propylated host‐type ligands (±)‐tris(isonicotinoyl)‐tris(propyl)‐cyclotricatechylene ( L1 ) and (±)‐tris(4‐pyridyl‐4‐benzoxy)‐tris(propyl)‐cyclotricatechylene ( L2 ) self‐assemble with Pd^II into [Pd₆L₈]¹²⁺ metallo‐cages that resemble a stella octangula. The self‐assembly of the [Pd₆( L1 )₈]¹²⁺ cage is solvent‐dependent; broad NMR resonances and a disordered crystal structure indicate no chiral self‐sorting of the ligand enantiomers in DMSO solution, but sharp NMR resonances occur in MeCN or MeNO₂. The [Pd₆( L1 )₈]¹²⁺ cage is observed to be less favourable in the presence of additional ligand, than is its counterpart, where L=(±)‐tris(isonicotinoyl)cyclotriguaiacylene ( L1 a ). The stoichiometry of reactant mixtures and chemical triggers can be used to control formation of mixtures of homoleptic or heteroleptic [Pd₆L₈]¹²⁺ metallo‐cages where L= L1 and L1 a .     

Conformational control of Pd2L4 assemblies with unsymmetrical ligands

With increasing interest in the potential utility of metallo-supramolecular architectures for applications as diverse as catalysis and drug delivery, the ability to develop more complex assemblies is keenly sought after. Despite this, symmetrical ligands have been utilised almost exclusively to simplify the self-assembly process as without a significant driving foa mixture of isomeric products will be obtained. Although a small number of unsymmetrical ligands have been shown to serendipitously form well-defined metallo-supramolecular assemblies, a more systematic study could provide generally applicable information to assist in the design of lower symmetry architectures. Pd₂L₄ cages are a popular class of metallo-supramolecular assembly; research seeking to introduce added complexity into their structure to further their functionality has resulted in a handful of examples of heteroleptic structures, whilst the use of unsymmetrical ligands remains underexplored. Herein we show that it is possible to design unsymmetrical ligands in which either steric or geometric constraints, or both, can be incorporated into ligand frameworks to ensure exclusive formation of single isomers of three-dimensional Pd₂L₄ metallo-supramolecular assemblies with high fidelity. In this manner it is possible to access Pd₂L₄ cage architectures of reduced symmetry, a concept that could allow for the controlled spatial segregation of different functionalities within these systems. The introduction of steric directing groups was also seen to have a profound effect on the cage structures, suggesting that simple ligand modifications could be used to engineer structural properties.

Steric and geometric constraints were used to design unsymmetrical ditopic ligands that form single Pd₂L₄ cage isomers with high fidelity.     

Palladium(II)-Based Self-Assembled Heteroleptic Coordination Architectures: A Growing Family

Metal-driven self-assembly is one of the most effective approaches to lucidly design a large range of discrete 2D and 3D coordination architectures/complexes. Palladium(II)-based self-assembled coordination architectures are usually prepared by using suitable metal components, in either a partially protected form (PdL′) or typical form (Pd; charges are not shown), and designed ligand components. The self-assembled molecules prepared by using a metal component and only one type of bi- or polydentate ligand (L) can be classified in the homoleptic series of complexes. On the other hand, the less explored heteroleptic series of complexes are obtained by using a metal component and at least two different types of non-chelating bi- or polydentate ligands (such as L^a and L^b). Methods that allow the controlled generation of single, discrete heteroleptic complexes are less understood. A survey of palladium(II)-based self-assembled coordination cages that are heteroleptic has been made. This review article illustrates a systematic collection of such architectures and credible justification of their formation, along with reported functional aspects of the complexes. The collected heteroleptic assemblies are classified here into three sections: 1) [(PdL′)_m(L^a)_x(L^b)_y]-type complexes, in which the denticity of L^a and L^b is equal; 2) [(PdL′)_m(L^a)_x(L^b)_y]-type complexes, in which the denticity of L^a and L^b is different; and 3) [Pd_m(L^a)_x(L^b)_y]-type complexes, in which the denticity of L^a and L^b is equal. Representative examples of some important homoleptic architectures are also provided, wherever possible, to set a background for a better understanding of the related heteroleptic versions. The purpose of this review is to pave the way for the construction of several unique heteroleptic coordination assemblies that might exhibit emergent supramolecular functions.     

Supramolecular Coordination Cages Based on N-Heterocyclic Carbene-Gold(I) Ligands and Their Precursors: Self-Assembly,Structural Transformation and Guest-Binding Properties

The incorporation of functional groups into the cavity of discrete supramolecular coordination cages (SCCs) will bring unique functions and applications. Here, three dicarboxylate ligands (H₂ L1 Cl, H₂ L2 Cl and H₂ L3 Cl) containing N-heterocyclic carbene (NHC) precursors as linkers were introduced to construct SCCs by combining with two C₃-symmertic (CpZr)₃(μ₃-O)(μ₂-OH)₃ clusters as three-connect vertices, resulted in a series of rugby-like V₂E₃ (V=vertex, E=edge) type homoleptic cages ( SCC-1 , SCC-2 and SCC-3 ). However, V₄E₆-type tetrahedral cages ( SCC-4 and SCC-5 ), incorporating six Au-NHC moieties, were obtained when the corresponding NHC-gold(I) functionalized ligands (H₂ L1 ^Au, H₂ L2 ^Au) were applied. For the first time, we present a trackable CpZr-involved cage to cage conversion to generate a heteroleptic V₂E₃ cage ( SCC-6 ) from two homoleptic cages ( SCC-2 and SCC-5 ) with different geometries of V₂E₃ and V₄E₆. The heteroleptic assembly SCC-6 can also be formed upon a subcomponent displacement strategy. The structural transformation and reassembly processes were detected and monitored by ¹H NMR spectroscopy and electrospray-ionization mass spectrometry. The formation of heteroleptic assembly was further supported by single crystal X-ray diffraction analysis. Moreover, homoleptic cage SCC-2 possesses a trigonal bipyramidal cationic cavity allowing the encapsulation of a series of sulfonate anionic guests.     

Controlled Construction of Heteroleptic [Pd2(LA)2(LB)(LC)]4+ Cages: A Facile Approach for Site-Selective endo-Functionalization of Supramolecular Cavities

Construction of supramolecular structures with internal functionalities is a promising approach to build enzyme-like cavities. The endo-functionalized [Pd₁₂L₂₄] and [Pd₂L₄] coordination cages represent the most successful systems in this regard. However, these systems mainly contain one type of endo-moiety. We herein provide a solution for the controlled endo-functionalization of [Pd₂L₄] cages. Site-selective introduction of the endo-functional group was achieved through the formation of heteroleptic [Pd₂( L^A )₂( L^B )( L^C )] cages. Using two orthogonal steric control elements is the key for the selective formation of the hetero-assemblies. We demonstrated the construction of two hetero-cages with a single internal functional group as well as a hetero-cage with two distinct endohedral functionalities. The endo-functionalized hetero-cages bound sulfonate guests with fast-exchange dynamics. This strategy provides a new solution for the controlled endo-functionalization of supramolecular cavities.     

Cooperativity of steric bulk and H-bonding in coordination sphere engineering: heteroleptic PdII cages and bowls by design

Recently developed self-assembly strategies allow to rationally reduce the symmetry of metallosupramolecular architectures. In addition, the combination of multiple ligand types without creating compound mixtures has become possible. Among several approaches to realize non-statistical heteroleptic assembly, Coordination Sphere Engineering (CSE) makes use of secondary repulsive or attractive interactions in direct vicinity of the metal nodes. Previously, we used steric congestion to turn dinuclear [Pd₂L₄] cages with fourfold symmetry into [Pd₂L₃X₂] (X = solvent, halide) bowl structures. Here, we introduce a new subtype of this strategy based on balancing hydrogen bonding and repulsive interactions between ligands carrying quinoline (L^Qu) and 1,8-naphthyridine (L^Na) donors to generate trans-[Pd₂L₂] and [Pd₂L₃L′] cages, assisted by templation of encapsulated fullerenes. Combined with steric congestion caused by acridine (L^Ac) donors, we further report the first example of a heteroleptic [Pd₂L₂L′X₂] bowl. Formation, structure and fullerene binding ability of these metallo-supramolecular hosts were studied by NMR, mass spectrometry and single crystal X-ray diffraction.

Coordination Sphere Engineering (CSE) allows non-statistical assembly of heteroleptic supramolecular architectures by fine adjustment of steric and electronic features around square-planar Pd(ii) cations with naphthyridine donors.     

Chiral Self‐Discrimination and Guest Recognition in Helicene‐Based Coordination Cages

Chiral nanosized confinements play a major role for enantioselective recognition and reaction control in biological systems. Supramolecular self‐assembly gives access to artificial mimics with tunable sizes and properties. Herein, a new family of [Pd₂L₄] coordination cages based on a chiral [6]helicene backbone is introduced. A racemic mixture of the bis‐monodentate pyridyl ligand L¹ selectively assembles with Pd^II cations under chiral self‐discrimination to an achiral meso cage, cis‐[Pd₂ L^1P ₂ L^1M ₂]. Enantiopure L¹ forms homochiral cages [Pd₂ L^1P/M ₄]. A longer derivative L² forms chiral cages [Pd₂ L^2P/M ₄] with larger cavities, which bind optical isomers of chiral guests with different affinities. Owing to its distinct chiroptical properties, this cage can distinguish non‐chiral guests of different lengths, as they were found to squeeze or elongate the cavity under modulation of the helical pitch of the helicenes. The CD spectroscopic results were supported by ion mobility mass spectrometry.     

Tuning the Size and Geometry of Heteroleptic Coordination Cages by Varying the Ligand Bent Angle

Spherical assemblies of the type [Pd_nL_2n]²ⁿ⁺ can be obtained from Pd^II salts and curved N-donor ligands, L. It is well established that the bent angle, α, of the ligand is a decisive factor in the self-assembly process, with larger angles leading to complexes with a higher nuclearity, n. Herein, we report heteroleptic coordination cages of the type [Pd_nL_nL′_n]²ⁿ⁺, for which a similar correlation between the ligand bent angle and the nuclearity is observed. Tetranuclear cages were obtained by combining [Pd(CH₃CN)₄](BF₄)₂ with 1,3-di(pyridin-3-yl)benzene and ligands featuring a bent angle of α=120°. The use of a dipyridyl ligand with α=149° led to the formation of a hexanuclear complex with a trigonal prismatic geometry; for linear ligands, octanuclear assemblies of the type [Pd₈L₈L′₈]¹⁶⁺ were obtained. The predictable formation of heteroleptic Pd^II cages from 1,3-di(pyridin-3-yl)benzene and different dipyridyl ligands is evidence that there are entire classes of heteroleptic cage structures that are privileged from a thermodynamic point of view.     

An atropisomeric M2L4 cage mixture displaying guest-induced convergence and strong guest emission in water

Introduction of atropisomeric axes into a bent bispyridine ligand leads to the quantitative formation of a complex mixture of atropisomeric M₂L₄ cages upon treatment with metal ions. Whereas the isomer ratio of the obtained cage mixture, consisting of up to 42 isomers, is insensitive to temperature and solvent, the quantitative convergence from the mixture to a single isomer is accomplished upon encapsulation of a large spherical guest, namely fullerene C₆₀. The observed isomerization with other guests depends largely on their size and shape (e.g., <10 and 82% convergence with planar triphenylene and bowl-shaped corannulene guests, respectively). Besides the unusual guest-induced convergence, the present cage mixture displays the strongest guest emission (Φ_F = 68%) among previously reported M_nL_m cages and capsules, upon encapsulation of a BODIPY dye in water.

A complex mixture of atropisomeric M₂L₄ cages is shown to undergo perfect convergence to a single isomer upon encapsulation of spherical C₆₀ in water. Moreover, the cage mixture displays very strong guest emission upon encapsulation of a BODIPY dye.     

“Eggs in egg cartons”: co-crystallization to embed molecular cages into crystalline lattices

Discrete (M₃L₂)_n cages assembled from a tripodal ligand (L) and metal ions (M: Cu(i) or Ag(i)) are embedded in networked coordination hosts formed by partial dissociation of the same discrete cages during the crystallization process. The resulting “eggs-in-an-egg-carton” structures provide unique examples of the co-crystallization of discrete and infinite coordination frameworks.

Discrete coordination cages were connected into the infinite lattices via shape-complementary co-crystallization with networked coordination hosts in the “eggs-in-an-egg-carton” styles.     

A Highly Fluorescent Metallosalalen‐Based Chiral Cage for Enantioselective Recognition and Sensing

A highly fluorescent coordination cage [Zn₈L₄I₈] has been constructed by treating enantiopure pyridyl‐functionalized metallosalalen units (L) with zinc(II) iodide and characterized by a variety of techniques including microanalysis, thermogravimetric analysis (TGA), circular dichroism (CD) spectroscopy, and single‐crystal and powder X‐ray diffraction. Strong intermolecular π–π, CH???π, and CH???I interactions direct packing of the cage molecules to generate a 3D polycage network interconnected by pentahedral cages formed by adjacent pentamers. The cage has an amphiphilic helical cavity decorated with chiral NH functionalities capable of interactions with guest species such as saccharides. The fluorescence of the cage was greatly enhanced by five enantiomeric saccharides in solution, with enantioselectivity factors of 2.480–4.943, and by five enantiomeric amines in the solid state, with enantioselective fluorescence enhancement ratios of 1.30–3.60. This remarkable chiral sensing of both saccharides and amines with impressive enantioselectivity may result from the steric confinement of the cavity as well as its conformational rigidity. It holds great promise for the development of novel chiral cage materials for sensing applications.     

How to not build a cage: endohedral functionalization of polyoxometalate-based metal–organic polyhedra

Introducing functionalities into the interior of metal–organic cage complexes can confer properties and utilities (e.g. catalysis, separation, drug delivery, and guest recognition) that are distinct from those of unfunctionalized cages. Endohedral functionalization of such cage molecules, for decades, has largely relied on modifying their organic linkers to covalently append targeted functional groups to the interior surface. We herein introduce an effective coordination method to bring in functionalities at the metal sites instead, for a set of polyhedral cages where the nodes are in situ formed polyoxovanadate clusters, [V^IV₆O₆(OCH₃)₉(μ₆-SO₄)(COO)₃]²⁻. Replacing the central sulfates of these hexavanadate clusters with more strongly coordinating phosphonate groups allows the installation of functionalities within the cage cavities. Organophosphonates with phenyl, biphenyl, and terphenyl tails were examined for internalization. Depending on the size/shape of the cavities, small phosphonates can fit into the molecular containers whereas larger ones inhibit or transform the framework architecture, whereby the first non-cage complex was isolated from a reaction that otherwise would lead to entropically favored regular polyhedra cages. The results highlight the complex and dynamic nature of the self-assembly process involving polyoxometalates and the scope of molecular variety accessible by the introduction of endo functional groups.

Installation of oversized functions within a metal–organic cage may “burst” or even transform the molecular cage itself.     

Tunable Fullerene Affinity of Cages,Bowls and Rings Assembled by PdII Coordination Sphere Engineering

For metal-mediated host compounds, the development of strategies to reduce symmetry and introduce multiple functionalities in a non-statistical way is a challenging task. We show that the introduction of steric stress around the coordination environment of square-planar Pd^II cations and bis-monodentate nitrogen donor ligands allows to control the size and shape of the assembled product, from [Pd₂L₄] cages over [Pd₂L₃] bowl-shaped structures to [Pd₂L₂] rings. Therefore, banana-shaped ligand backbones were equipped with pyridines, two different quinoline isomers and acridine, the latter three introducing steric congestion through hydrogen substituents on annelated benzene rings. Differing behavior of the four resulting hosts towards the binding of C₆₀ and C₇₀ fullerenes was studied and related to structural differences by NMR spectroscopy, mass spectrometry and single crystal X-ray diffraction. The three cages based on pyridine, 6-quinoline or 3-quinoline donors were found to either bind C₆₀, C₇₀ or no fullerene at all.     

Creating Coordination‐Based Cavities in a Multiresponsive Supramolecular Gel

Creating cavities in varying levels, from molecular containers to macroscopic materials of porosity, have long been motivated for biomimetic or practical applications. Herein, we report an assembly approach to multiresponsive supramolecular gels by integrating photochromic metal–organic cages as predefined building units into the supramolecular gel skeleton, providing a new approach to create cavities in gels. Formation of discrete O‐Pd₂L₄ cages is driven by coordination between Pd²⁺ and a photochromic dithienylethene bispyridine ligand (O‐PyFDTE). In the presence of suitable solvents (DMSO or MeCN/DMSO), the O‐Pd₂L₄ cage molecules aggregate to form nanoparticles, which are further interconnected through supramolecular interactions to form a three‐dimensional (3D) gel matrix to trap a large amount of solvent molecules. Light‐induced phase and structural transformations readily occur owing to the reversible photochromic open‐ring/closed‐ring isomeric conversion of the cage units upon UV/visible light radiation. Furthermore, such Pd₂L₄ cage‐based gels show multiple reversible gel–solution transitions when thermal‐, photo‐, or mechanical stimuli are applied. Such supramolecular gels consisting of porous molecules may be developed as a new type of porous materials with different features from porous solids.     

Supramolecular Catalysis of the oxa-Pictet–Spengler Reaction with an Endohedrally Functionalized Self-Assembled Cage Complex

An endohedrally functionalized self-assembled Fe₄L₆ cage complex can catalyze oxa-Pictet—Spengler cyclizations of tryptophols and various aldehyde derivatives, showing strong rate accelerations and size-selectivity. Selective molecular recognition of substrates controls the reactivity, and the cage is capable of binding and activating multiple different species along the multistep reaction pathway. The combination of a functionalized active site, size-selective reactivity, and multistep activation, all from a single host molecule, illustrates the biomimetic nature of the catalysis.     

A Rotaxane‐like Cage‐in‐Ring Structural Motif for a Metallosupramolecular Pd6L12 Aggregate

A BODIPY‐based bis(3‐pyridyl) ligand undergoes self‐assembly upon coordination to tetravalent palladium(II) cations to form a Pd₆L₁₂ metallosupramolecular assembly with an unprecedented structural motif that resembles a rotaxane‐like cage‐in‐ring arrangement. In this assembly the ligand adopts two different conformations—a C‐shaped one to form a Pd₂L₄ cage which is located in the center of a Pd₄L₈ ring consisting of ligands in a W‐shaped conformation. This assembly is not mechanically interlocked in the sense of catenation but it is stabilized only by attractive π‐stacking between the peripheral BODIPY chromophores and the ligands’ skeleton as well as attractive van der Waals interactions between the long alkoxy chains. As a result, the co‐arrangement of the two components leads to a very efficient space filling. The overall structure can be described as a rotaxane‐like assembly with a metallosupramolecular cage forming the axle in a metallosupramolecular ring. This unique structural motif could be characterized via ESI mass spectrometry, NMR spectroscopy, and X‐ray crystallography.     

Guest Exchange Mechanisms in Mono‐Metallic PdII/PtII‐Cages Based on a Tetra‐Pyridyl Calix[4]pyrrole Ligand

Planar pyridyl N‐oxides are encapsulated in mono‐metallic Pd^II/Pt^II‐cages based on a tetra‐pyridyl calix[4]pyrrole ligand. The exchange dynamics of the cage complexes are slow on both the NMR chemical shift and EXSY timescales, but encapsulation of the guests by the cages is fast on the human timescale. A “French doors” mechanism, involving the rotation of the meso‐phenyl walls of the cages, allows the passage of the planar guests. The encapsulation of quinuclidine N‐oxide, a sterically more demanding guest, is slower than pyridyl N‐oxides in the Pd^II‐cage, and does not take place in the Pt^II counterpart. A modification of the encapsulation mechanism for the quinuclidine N‐oxide is postulated that requires the partial dissociation of the Pd^II‐cage. The substrate binding selectivity featured by the cages is related to their different guest uptake/release mechanisms.     

Quantitative Analysis of the Self‐Assembly Process of a Pd12L24 Coordination Sphere

The self‐assembly process of a Pd₁₂L₂₄ sphere was revealed by a quantitative approach (quantitative analysis of self‐assembly process: QASAP) quantifying all the substrates, the products, and the observable intermediates, indicating that the Pd₁₂L₂₄ sphere is produced through several pathways. Firstly, Pd_n L_2n (n= 6, 8, and 9), which are perfectly closed structures smaller than the Pd₁₂L₂₄ sphere, and a mixture of intermediates not observed by NMR ( Int ) were produced. Next, the sphere was assembled from intra‐/intermolecular reaction of a certain class of Int (path A) and from the coordination of free pyridyl groups in Int to the Pd^II center of Pd_n L_2n (n= 6, 8, and 9) (path B). While capping the free pyridyl groups in Int with Pd^II ions perfectly inhibited the sphere formation, the addition of free L to Int accelerated the formation of the sphere.     

On phase equilibria and crystal structures in the systems Ce-Pd-B and Yb-Pd-B. Physical properties of R2Pd13.6B5 (R=Yb, Lu)

Phase equilibria and crystal structures of ternary compounds were determined in the systems Ce-Pd-B and Yb-Pd-B at 850 °C in the concentration ranges up to 45 and 33 at% of Ce and Yb, respectively, employing X-ray single crystal and powder diffraction. Phase relations in the Ce-Pd-B system at 850 °C are governed by formation of extended homogeneity fields, τ₂-CePd₈B_2−x (0.10<x<0.48); τ₃-Ce₃Pd_25−xB_8−y (1.06<x<1.87; 2.20<y<0.05), and CePd₃B_x (0<x<0.65) the latter arising from binary CePd₃. Crystallographic parameters for the new structure type τ₂-CePd₈B_2−x (space group C2/c, a=1.78104(4) nm, b=1.03723(3) nm, c=1.16314(3), β=118.515(1)° for x=0.46) were established from X-ray single crystal diffraction. The crystal structures of τ₂-CePd₈B_2−x and τ₃-Ce₃Pd_25−xB_3−y are connected in a crystallographic group-subgroup relationship. Due to the lack of suitable single crystals, the novel structure of τ₁-Ce₆Pd_47−xB₆ (x=0.2, C2/m space group, a=1.03594(2) nm, b=1.80782(3) nm, c=1.01997(2) nm, β=108.321(1)°) was determined from Rietveld refinement of X-ray powder diffraction data applying the structural model obtained from single crystals of homologous La₆Pd_47−xB₆ (x=0.19) (X-ray single crystal diffraction, new structure type, space group C2/m, a=1.03988(2) nm, b=1.81941(5) nm, c=1.02418(2) nm, β=108.168(1)°).The Yb-Pd-B system is characterized by one ternary compound, τ₁-Yb₂Pd₁₄B₅, forming equilibria with extended solution YbPd₃B_x, YbB₆, Pd₅B₂ and Pd₃B. The crystal structures of both Yb₂Pd₁₄B₅ and isotypic Lu₂Pd₁₄B₅ were determined from X-ray Rietveld refinements and found to be closely related to the Y₂Pd₁₄B₅-type (I4₁/amd). The crystal structure of binary Yb₅Pd_2−x (Mn₅C₂-type) was confirmed from X-ray single crystal data and a slight defect on the Pd site (x=0.06) was established.The three structures τ₁-Ce₆Pd_47−xB₆, τ₂-CePd₈B_2−x and τ₃-Ce₃Pd_25−xB_8−y are related and can be considered as the packings of fragments observed in Nd₂Fe₁₄B structure with different stacking of common structural blocks.Physical properties for Yb₂Pd_13.6B₅ (temperature dependent specific heat, electrical resistivity and magnetization) yielded a predominantly Yb-4f¹³ electronic configuration, presumably related with a magnetic instability below 2 K. Kondo interaction and crystalline electric field effects control the paramagnetic temperature domain.