In nature, heterometallic enzymes enable a variety of efficient catalytic transformations1,2, where the relative proximity of the substrates is a key feature and is controlled by the metals. Inspired by this, chemists have developed heterometallic complexes where two different metals held within the same molecular environment can work together to create a “cooperative” effect. Cooperative heterometallic complexes are often “greater than the sum of their parts”, outperforming the homometallic counterparts in terms of activity and selectivity, or enabling chemical transformations that are otherwise inaccessible3,4,5,6,7. This concept has been exploited across multiple reactions, including metal-halogen exchange8, C–H activation9 and asymmetric catalysis10. Heterometallic cooperativity has vast potential to improve catalyst activity, and the “Pairodic Table of Element Pairs” emphasises the extensive number of heterometallic combinations available6, each leading to unique reactivities3,6. However, this approach remains underexplored, with most organometallic catalyst design focused on ligand modification. Understanding the origins of heterometallic cooperativity is crucial to improve catalyst design and harness the full potential of this strategy.

Heterometallic complexes can operate via multisite interactions with each metal catalysing different reaction steps3, or with one metal acting as the primary catalytic site and the other metal(s) modulating its reactivity. This is often dictated by the structure. When bound to different heteroatoms in the ligand (Fig. 1a), the metal-metal’ distances (M–M′, where M ≠ M′) are often dependent on the ligand flexibility and multisite interactions may be favoured. Electronic communication can arise when two metals are connected through a heteroatom in dimeric and dinucleating systems (Fig. 1b, c), resulting in short M–M′ distances7. This electronic modulation can also occur in “ate” complexes (e.g. lithium magnesiate LiMgR3 or lithium zincate LiZnR3), where a hard metal M is paired with a softer, more carbophilic metal M′ (e.g. Li+ with MgR3/ZnR3)4,6,11. This anionic “ate” activation can increase the nucleophilicity and/or Brønsted basicity of the M′-R group, while concomitantly enhancing the Lewis acidity of the M+ cation. Heterometallic complexes may also feature direct polar M–M′ bonds12, providing access to unique reactivities3.

Fig. 1: Heterometallic structural motifs and polymerisation products highlighted in this review.
figure 1

L = ligand, X = bridging or exchangeable ligand (e.g. nitrogen, oxygen, halogen).

Whilst heterometallic cooperativity has been well-studied in a range of organic transformations, heterometallic catalysis is still gathering momentum in polymerisation processes7,13. With increased demand for sustainable plastics, research into ring-opening polymerisation (ROP) and ring-opening copolymerisation (ROCOP) to produce useful and degradable polymers has grown rapidly. Two of the most promising current strategies14 are the production of poly(lactic acid) (PLA) via ROP of bioderived lactide (LA)15, and carbon dioxide (CO2)/epoxide ROCOP to form polycarbonates and polyurethanes16. The material properties are dictated by the polymer microstructure (e.g. chain length, dispersity and tacticity) and organometallic RO(CO)P catalysts have generally outperformed organocatalysts and enzymes in combining activity with polymerisation control17.

Heterometallic catalysts have the potential to revolutionise RO(CO)P by providing multiple and inequivalent catalytic sites for monomer activation and nucleophilic attack, which are key steps during initiation and propagation. The catalyst performance is controlled by the metals, ligand architecture and the polymerisation conditions. Importantly, not all metal combinations are cooperative. While isolated studies have been reported, this review identifies key structural motifs and overarching heterometallic activity trends across cyclic ester/carbonate ROP, epoxide and CO2/cyclic anhydride ROCOP and aziridine/carbon monoxide (CO) ROCOP (Fig. 1), in order to guide future heterometallic catalyst development.

Ring-opening polymerisation

Cyclic ester ROP is an efficient route towards degradable aliphatic polyesters with engineering, packaging18 and biomedical applications17,19,20. Metal-catalysed ROP typically proceeds through a coordination-insertion mechanism with the catalysts comprising a Lewis acidic metal and a nucleophile (e.g. alkoxide/amide) supported by sterically-hindered ligands17,20,21. While many homometallic ROP catalysts have been reported21,22,23,24,25, some multimetallic complexes (e.g. bis-Al, Hf, In, Mg, Ti, Y, Zn and Zr) have shown significant activity and selectivity enhancements24,25,26,27,28, and some of which have been proposed to operate via a chain-shuttling mechanism29,30. There is a substantial opportunity to further improve catalyst performance through heterometallic cooperativity, and progress has already been made with heterocombinations from across the Periodic Table. While detailed mechanistic studies have not yet been reported for heterometallic complexes, experimental observations indicate that the larger and more electropositive metal acts as the monomer coordination site, and the more Lewis acidic metal acts as the source of the M-alkoxide nucleophile31. Complexes where alkali metals (K/Li/Na) are combined with divalent (Mg/Zn)31,32,33,34,35, trivalent (Al/In/Y)36,37,38,39,40 or tetravalent (Ge/Sn) elements have been most prevalent in ROP41. Combining non-toxic and earth abundant metals such as Al, Mg and Zn with alkali metals is particularly appealing from both economic and environmental perspectives42.

Alkali metal/divalent metal heterocombinations

In situ generated Li/Zn and Li/Mg complexes 1a-b (Fig. 2) both displayed good activities at ambient temperature, converting 62 equiv. and 88 equiv. rac-LA in 15 min, respectively (Đ = 1.18 (1a), 1.31 (1b)), with 1 equiv. neopentyl alcohol32. Interestingly, 1a exhibited higher activity and stereocontrol (Ps = 0.87–0.88) in 5:1 toluene:THF than in toluene (activity) or THF (stereocontrol). Solvent choice can significantly influence heterometallic solution-state structures, and the reduced stereocontrol in THF may arise from the in situ formation of less sterically hindered solvent separated Li+MR3 (M = Mg, Zn) ion pairs43. Solution-state structural analysis is therefore crucial for uncovering differences between solvent separated and contact ion pairs, and understanding how these changes influence catalyst activity within ROP5.

Fig. 2: Main group heterometallic catalysts for cyclic ester ROP.
figure 2

Structural representations of heterometallic complexes reported for cyclic ester ROP, where alkali metals are combined with di-, tri- and tetravalent heterometals and trivalent Al is combined with divalent metals. aIn 12c, one Ca bridges two (salen)AlCl complexes with each ligand retaining one phenolic OH group.

Heterometallic Li/Mg complex 2 (Fig. 2, Li–Mg distance = 2.67 Å), converted 55 equiv. rac-LA in 1 h with 1 equiv. MeOH in DCM at 20 °C (Đ = 1.22)33. The experimental Mn values were almost double those calculated, which was attributed to slow initiation via in situ generated Mg–Cl species (by reaction of Mg-nBu with DCM). The mono-Mg complex displayed similar control (Đ = 1.12), however this catalyst required 2 h to convert 55 equiv. rac-LA under otherwise identical conditions.

Lithium and sodium zincates 3a-b (Fig. 2) exhibited similar activity, polymerising 182 equiv. and 190 equiv. l-LA, respectively (toluene, 48 h, 90 °C)34, with relatively good control (Đ = 1.42 and 1.26, respectively) and generating OH-terminated PLA chains. 3b was also active and controlled under non-anhydrous conditions, converting 87 equiv. l-LA in 48 h at 90 °C (Đ = 1.33). This was attributed to the partial dissociation of 3b to form the mono-Na aryloxide complex in situ, with the latter shown to be more active in l-LA ROP (138 equiv. l-LA converted in 24 h, anhydrous conditions, Đ = 1.33), however the solution-state structures of 3a-b were not investigated. 3a generated only trace PLA under non-anhydrous conditions, which suggested that complete hydrolysis occurred. A trisphenol ligand was used to synthesise tetrametallic M2/Zn2 and M2/Mg2 (M = Li or Na) complexes 4a-d (Fig. 2)35. The additional Zn centre in 4b may enhance the activity vs. 3b (238 equiv. l-LA converted in 36 h at 110 °C, Đ = 1.31)34, albeit direct comparison could not be made due to the different reaction conditions.

We recently reported Na/Zn2 and K/Zn2 complexes 5a-b (Fig. 2) for LA, ε-caprolactone (ε-CL) and δ-valerolactone (δ-VL) ROP31, which outperformed the homometallic counterparts by combining high activities (Na/K) with good control (Zn2). In the presence of 2 equiv. benzyl alcohol (BnOH), 5b (K/Zn2) converted 60 equiv. rac-LA in just 20 s (THF, room temperature, Đ = 1.40, kobs = 1.7 × 10−2 s−1); to date, this is the fastest heterometallic catalyst system reported for LA ROP. NMR spectroscopy (including DOSY) and density-functional theory calculations suggested that 5a-b retain their heterometallic structures in the solution-state. 5a-b display improved activities in Lewis donor THF (vs. the analogous bis-Zn complex), and the fivefold activity increase in LA ROP upon switching Na (5a) for the larger K centre (5b) highlighted the key role of Na/K in LA coordination and activation. In both cases, incorporating Na/K also labilised the Zn-Et bonds (vs. the bis-Zn complex), as evidenced by NMR spectroscopy, accelerating the nucleophilic attack and LA ring-opening.

Alkali metal/trivalent metal heterocombinations

Sterically-hindered mono-alkoxide Li/Al complexes 6a-b (Fig. 2) were inactive, however the bis-alkoxide 6c-d analogues polymerised LA at room temperature36, which is uncommon for Al-based catalysts23,26. 6c-d were still relatively slow, converting 189 equiv. rac-LA in 16 h in DCM, albeit with good control (Đ = 1.03)36 compared to other Group 1 catalysts23. The enhanced activity of 6c-d vs. Al-based catalysts was tentatively attributed to their in situ dissociation to [(RN-o-C6H4)2O)Al(OBn)] (R = C5H9 or Cy) and LiOBn. However, these monometallic counterparts were inactive under the conditions employed with 6c-d, providing evidence for cooperative Li/Al operation in 6c-d.

Preliminary results with M/Al complexes 7a-c (M = Li, Na, K respectively, Fig. 2) indicated that 7a and the analogous bis-Al complex were more active than 7b-c in ROP37. 7a and the bis-Al analogue converted 78 and 75 equiv. l-LA, respectively, whereas 7b-c polymerised 48 and 20 equiv. l-LA, respectively (1 equiv. BnOH, 5 h, 125 °C, toluene). The higher activity of 7a vs. 7b-c was not specifically addressed but deviates from the activity trend commonly observed for Group 1 ROP catalysts (Li+ < Na+ < K+), where larger metals typically enhance monomer coordination thus polymerisation activity44. NMR analysis indicates the (L)Al-Me2 groups are more nucleophilic in 7a-c than in the bis-Al species. The activity differences observed suggest a combination of multiple factors are important, including the metals, ligand and solution-state structures.

The Li/In complex 8 (Fig. 2) converted 98 equiv. rac-LA in 30 min with 1 equiv. isopropanol (iPrOH), and 96 equiv. rac-LA in 1 h without iPrOH (toluene, 80 °C)38. Polymerisation control was poor in both cases, albeit slightly improved without iPrOH (Đ = 2.16 vs. 2.56 with OiPr). The reduced control with 8/iPrOH may arise from competitive “activated monomer” and coordination-insertion mechanisms, as evidenced by both OiPr and Me PLA end groups. As the synthesis of [{ONCyNO}In(Me)] proved challenging, the activity of 8 was compared to homometallic [{ONCyNO}In(CH2SiMe3)], which was significantly slower converting 93 equiv. rac-LA in 15 h (no iPrOH, toluene, 80 °C); the reduced activity was attributed to slower initiation by the less nucleophilic In-CH2SiMe3.

In comparison to 8, the Li/Y complex 9 (Fig. 2) exhibited higher activity in ROP without an alcohol (BnOH), converting 225 equiv. rac-LA to form heterotactic PLA (Ps = 0.99) in 5 h at 30 °C in THF (vs. 68 equiv. in 7 h at 70 °C with 1 equiv. BnOH)39. DOSY NMR analysis confirmed the heterometallic structure of 9 in THF solvent. Initiation was proposed to occur via nucleophilic attack from the ligand of 9 based on SEC, 1H NMR spectroscopy and MALDI-ToF analysis.

Alkali metal/tetravalent metal heterocombinations

The Li/Ge complex 10a (Fig. 2) was almost twice as active as the mono-Ge analogue in l-LA ROP (57% vs. 35% PLA yield, respectively; 500 equiv. l-LA, 10 equiv. iPrOH, 6 h, 100 °C), which may arise from Li+ enhancing l-LA coordination41. In contrast, the Li/Sn complex, 10b, was slower than the homometallic mono-Sn analogue, which was attributed to the higher moisture- and air-sensitivity of the former and possible catalyst decomposition during ROP.

Divalent/trivalent metal heterocombinations

The Al/Zn complex 11 (Fig. 2) was more active than the analogous mono-Al and bis-Al complexes in ε-CL ROP45, resulting in 95% PCL yield in 6 min at 70 °C (2:1:100 BnOH:catalyst:ε-CL)46. It was, however, slower than the bis-Zn analogue45, which produced 98% PCL in 1 min under the same conditions suggesting that Zn is more catalytically active than Al in 1146. The higher activity of Zn was attributed to the lower bond dissociation energy of Zn-O (284 kJ mol−1) vs. Al-O (512 kJ mol−1); M-OR bond cleavage is a key step in ROP.

Our group reported Al/Zn and Mg/Al complexes 12a-b40, which displayed good catalyst activities in rac-LA ROP, outperforming the mono-Al analogue by respective factors of two and 11 under identical conditions (12a, kobs = 1.8 × 10−3 s−1; 12b, kobs = 8.8 × 10−3 s−1; mono-Al kobs = 0.8 × 10−3 s−1; toluene, 120 °C, 1:50:100 catalyst:propylene oxide (PO):rac-LA. The mono-Zn and mono-Mg analogues were completely inactive under the same conditions, while Ca/Al and Li/Al complexes 12c-d displayed lower activities than the mono-Al complex. Based on kinetic and computational studies (including ab initio molecular dynamics calculations), the high activity of 12a-b was attributed to close intermetallic proximity, increased ligand strain and the rigid square pyramidal geometry around the Al centre (highest with 12b), leading to improved monomer coordination. In addition, the Lewis acidity of Mg and Zn led to bridging Mg- or Zn-Cl-Al moieties thus longer and weaker Al–Cl bonds in 12a-b (vs. mono-Al), which correlated with faster initiation (induction periods were 1, 3 and 4 min for 12a,b and mono-Al, respectively).

Transition metal/main group heterocombinations

Main group/transition metal heterometallic ROP catalysts have so far focused on titanium, an attractive, non-toxic, inexpensive and abundant metal47,48. The development of heterometallic zirconium and hafnium catalysts offers an interesting area for future development, as both metals have excellent precedent in ROP49,50. The M/Ti(IV) complexes 13a-d (M = Li, Na, Zn, Mg; Fig. 3) are efficient initiators for l-LA ROP in toluene at 30 °C47. The alkali metal-containing 13a-b exhibited similar activity to the mono-Ti(IV) complex (76 equiv. l-LA converted in 94 h at 30 °C), despite X-ray crystallography of 13a indicating increased Ti Lewis acidity, with longer and weaker (more nucleophilic) Ti-(OiPr)2 bonds. Significant rate enhancements were however observed with 13c-d, with 13c (Zn/Ti) polymerising 91 equiv. l-LA within 30 min and 13d (Mg/Ti) converting 89 equiv. l-LA in 3.5 h with good control (Đ = 1.27 (13c), 1.28 (13d)). The higher activity of 13c vs. 13d was originally attributed to the lower charge density of Zn than Mg resulting in weaker Zn-OR bonds than Mg-OR. However, due to the similarity in the ionic radii and charge (Zn2+ = 74 pm, Mg2+ = 72 pm)51, other factors such as the higher Lewis acidity and oxophilicity of Mg (Ɵ = 0.6) vs. Zn (Ɵ = 0.2) are likely to be key factors in explaining the metal-alkoxide bond strengths52.

Fig. 3: Heterometallic main group/Ti ROP catalysts.
figure 3

Structural representations of cyclic ester ROP catalysts combining Ti with alkali metals or divalent metals.

Complex 14 bears a tetradentate ligand framework, and incorporation of Na was shown to increase the Ti Lewis acidity and weaken the Ti-OiPr bonds (Fig. 3)48. Whilst only trace PCL was formed with the mono-Ti(III) and Ti(IV) analogues, 14 converted 182 equiv. ε-CL in 1 h (toluene, 60 °C), albeit with low polymerisation control (Đ = 2.5).

F-block metal-based heterometallic complexes

ROP catalysts featuring f-block metals have also been developed to take advantage of their oxophilicity, Lewis acidity and large coordination spheres. Evidencing the role of lanthanide (Ln) metals in monomer activation, the activity of Na/Ln clusters ([Ln2Na8(OCH2CF3)14(THF)6], Ln = Sm, Y, Yb; 15a-c, respectively)53 in ROP directly reflects the Ln ionic radius: 15a > 15b ≈ 15c for ε-CL and 15a > 15b > 15c for trimethylene carbonate (TMC) ROP. Notably, 15a converted 3840 equiv. ε-CL in 30 min whereas only trace PCL formed with 15b-c at [ε-CL]:[catalyst] loading of 4000:1. 15a showed extraordinary activity for TMC ROP, converting 4000 equiv. in 1 min at 25 °C (Đ = 1.44). Heterometallic 15a-c exhibited higher activity than the homometallic Ln phenoxide clusters and Na(OCH2CF3)54. The enhanced activity of 15a-c was attributed to Na/Ln cooperativity via concurrent monomer activation and rapid ligand exchange. Moderate polymerisation control (Đ = 1.4-1.7) and shorter than expected Mn values were linked to initiation via multiple Ln-OCH2CF3 bonds and transesterification. 15a-c were more active in toluene than in THF, which may suggest modification of the cluster structure in THF.

Similar trends were observed with Li2Ln2 (Ln = Y, Er, Eu and Sm) complexes 16a-d (Fig. 4)55, with an activity decrease in l-LA ROP with decreasing Ln radius (16d > 16c > 16b ≈ 16a). Complexes 16a and 16d were more active than the mono-Y and Sm analogues, which was tentatively attributed to reduced steric hindrance around Ln in 16a,d. NMR analysis also suggested 16a is more flexible than mono-Y, with the piperazidine ring in a chair conformation rather than a boat conformation. Similarly to clusters 15a-c, 16a-d showed higher activity and control in toluene than THF, which may indicate structural differences in Lewis donor solvents. Indeed, 16c generated 98% PLA in toluene and 83% PLA in THF (30 min, 60 °C, [LA]:[Ln] = 1000:2), producing PLA with shorter than expected Mn in THF. It is plausible that 16a-d dissociate in coordinating solvents to generate multiple initiating species, and/or that THF coordination to Li/Ln may inhibit monomer coordination56. The Li/Th(IV) complex 17 (Fig. 4) is the only actinide-based heterometallic ROP catalyst reported to date57. It displayed relatively low activity and polymerisation control, converting 48 equiv. l-LA in 2 h (toluene, 30 °C) with a bimodal Mn dispersity (Đ = 1.63).

Fig. 4: Heterometallic ROP catalysts featuring f-block elements.
figure 4

Structural representations of cyclic ester ROP catalysts combining lanthanides or actinides with alkali metals, divalent metals, trivalent metals or transition metals.

Ln-based heterometallic ROP complexes have also been extended beyond alkali metals to Al58, Mg59 and Ni60. Heterometallic Ln/Al (Ln = Y, Sm) complexes 18a-d (Fig. 4) were studied in rac-LA ROP58. While 18a showed activity and control enhancements compared to the mono-Al and Y counterparts, converting 123 equiv. rac-LA in 5 h at 20 °C in toluene (Đ = 1.95), the reactivity of 18a was further improved by addition of 5 equiv. hexamethyldisilazane (as a chain-transfer agent) or by alcoholysis with iPrOH. The alkoxide analogues 18c-d were highly active and both converted 495 equiv. rac-LA in 30 min with moderate control (Đ = 2.32 and 1.70, respectively). Strikingly, 18d polymerised 1820 equiv. rac-LA in 1 h at 20 °C in toluene (Đ = 1.72), generating high Mn PLA (69 100 g/mol). The Al centre in 18a-d was proposed not to be directly involved in ROP due to the low activity of mono-Al species (vs. 18c-d), however Al may modulate the activity of Ln through electronic communication via the bridging O atom.

The activity of Ln/Mg allyl complexes 19a-b (Ln = La or Y, respectively, Fig. 4) was explored in ε-CL and rac-LA ROP59. 19a outperformed 19b, converting 198 equiv. ε-CL in 20 s at 20 °C and 85 equiv. rac-LA in 2 h at 40 °C with good control (Đ < 1.4). While 19b converted 122 equiv. ε-CL in 1.3 min at 20 °C, it was inactive for rac-LA ROP. The lower activity of 19b was attributed to the smaller size of Y3+ (90 pm, vs. La3+, 103 pm). Both complexes initiated ROP via nucleophilic attack of the allyl moiety on the coordinated monomer, as evidenced by 1H NMR spectroscopy.

Heterometallic Ln/Ni(II) complexes 20a-g (Fig. 4, Ln = Ce, Nd, Sm, Eu, Tb, Ho and Tm) were tested for l-LA ROP60, however despite the improved control, all were less active than mono-Ni species. This was attributed to the Ln(NO3)3 moiety occupying the outer O2O2 salen cavity thus sterically hindering the monomer approach to Ni in the N2O2 core. Indeed, 20b displayed the longest Ln-Ni distance (3.48 Å) and showed the highest activity, converting 730 equiv. l-LA in 24 h at 130 °C (Đ = 1.12).

Key activity trends in ROP

Across heterometallic ROP studies, enhanced activity with larger and more Lewis acidic metals featuring more open coordination geometries emerges as one of the most prevalent trends. The highest activities are generally observed with medium/large metals, e.g. alkali metals and lanthanides, attributed to larger coordination spheres enhancing monomer coordination and activation. Combining Lewis acidic metals with more electronegative metals with weaker M-OR bonds may accelerate coordination and nucleophilic attack. Heterometallic complexes based on Al/Zn46, K/Zn31, La/Mg59, Li/In38, Li/Mg and Li/Zn32, Li/Sm55, Mg/Al40, Na/Sm53, Na/Zn31, Sm/Al58 and Ti/Zn47 have all displayed superior activities compared to the homometallic analogues. Most of these complexes feature a M-O-M′ framework, enabling intermetallic electronic communication and/or “ate”-type activation (vide supra), which can lead to enhanced nucleophilicity of the M-R bond (e.g. R = alkoxide)38,47,48,58. Despite these promising results, future ROP studies should explore the solution-state structure of heterometallic catalysts to confirm that the enhanced activities can be accredited to heterometallic cooperativity. Heterometallic catalysts should also be benchmarked against all homometallic counterparts to fully understand when heterometallic cooperativity leads to an activity enhancement.

While ROP provides a convenient route to access aliphatic polyesters and polycarbonates, these materials can also be accessed via epoxide ROCOP with cyclic anhydrides or CO2, respectively. ROCOP provides access to a broader scope of material properties due to the greater monomer structural diversity, and there is a growing interest in heterometallic ROCOP catalyst design. Owing to the mechanistic similarities between ROP and ROCOP, both of which include monomer coordination, nucleophilic attack and ring-opening, catalysts employed for these processes are often structurally-alike; some catalyst systems have demonstrated impressive activities in both56,61,62,63,64,65,66. Advances in heterometallic ROP catalysis may therefore inform future understanding and design of heterometallic ROCOP catalysts and vice versa.

Ring-opening copolymerisation

Epoxide ROCOP with CO2 or cyclic anhydrides displays sustainability benefits, as CO2 may be sourced from industrial waste streams16,67,68, and some epoxides and anhydrides can be derived from biomass (e.g. limonene/α-pinene oxide, succinic/citraconic anhydrides)69,70. Life cycle analysis has suggested that incorporating CO2 into polyol production (for subsequent polyurethane synthesis) can reduce petrochemical consumption by 20% and CO2 emissions by 19% compared to conventional polyol synthesis71.

Catalyst design has enabled the generation of nearly perfect polycarbonates (>99% carbonate linkages) through ROCOP, by overcoming the undesired formation of polyether linkages and cyclic carbonates70,72. Most catalyst systems reported are homometallic and often multimetallic64,70,73, including bis-Co(II)74, Co(III)75,76, Fe(III)77, Mg(II)67 and Zn(II) complexes78,79,80,81,82,83. Studies have pointed towards a bimetallic mechanism, which limits the use of dimeric catalysts with high monomer loadings or at high dilutions. Intermetallic proximity in the range of 3–5 Å is generally optimal for improved catalyst performance, which has directed ligand design towards dinucleating scaffolds77,84. Mechanistic studies on homobimetallic complexes suggest that both metals are involved in ROCOP, and hint that heterometallic catalysts could further improve activities by enhancing both epoxide coordination (Lewis acidic/electrophilic metals) and the nucleophilicity of the metal-carbonate bond. Examples of heterobimetallic catalysts that combine main group, transition and Ln metals have recently been reported.

Main group heterometallic complexes in epoxide/CO2 ROCOP

Initial studies on homogeneous heterometallic catalyst systems investigated a mixture of LZn2(OAc)2:LZnMg(OAc)2:LMg2(OAc)2 in an assumed 1:2:1 ratio (L = macrocyclic diphenolate tetramine ligand of 21-26, Fig. 5). This mixed system was twice as active (TOF = 79 h−1) as a 1:1 mixture of LZn2(OAc)2:LMg2(OAc)2 in CHO/CO2 ROCOP (0.1 mol% catalyst loading, neat epoxide, 1 bar CO2, 80 °C)85. The first pure homogeneous heterometallic ROCOP catalyst reported was LZnMgBr2 (21, Fig. 5)86, which displayed TOF = 34 h−1 in CHO/CO2 ROCOP. 21 was twice as active as LMg2Br2 and five times faster than the 1:1 LMg2Br2:LZn2Br2 mixture, whereas LZn2Br2 was inactive (0.1 mol% catalyst loading, neat epoxide, 1 bar CO2, 80 °C). 21 displayed relatively good polymerisation control, generating >99% carbonate linkages with only trace cyclic carbonate, albeit with a bimodal dispersity (Đ = 1.14), which is common in the field and is often attributed to the presence of diol impurities acting as chain-transfer agents to produce telechelic polymers87.

Fig. 5: Main group and transition metal heterometallic complexes for epoxide ROCOP with CO2 or cyclic anhydrides.
figure 5

Structural representations of ROCOP catalysts that feature heterometal combinations from across the s, p and d-block.

Metathesis of 21 with potassium carboxylates generated Mg/Zn complexes 22a-h with acetate/benzoate co-ligands (Fig. 5)88. Kinetic studies showed that switching the co-ligand from Br to para-NO2 benzoate reduced the induction period from 160 min (21) to 20 min (22d) and enhanced the propagation rate from 3.0 × 10−5 s−1 to 3.8 × 10−5 s−1, respectively. 22a-h displayed excellent selectivities (>99% carbonate linkages) and retained their heterometallic structure in THF-d8, suggesting that the structures are likely to be retained during polymerisation (neat epoxide). The high activities of 21 and 22a-h were attributed to cooperative Mg/Zn catalysis via a chain-shuttling mechanism (Fig. 6), with Lewis acidic Mg enhancing epoxide coordination and the labile Zn-carbonate bond accelerating the nucleophilic attack. Recently, 22i catalysed the one-pot RO(CO)P of bio-based ε-decalactone with CHO/CO2 in the presence of 4 equiv. 1,2-cyclohexane diol, giving >90% monomer conversions89. The resultant degradable poly(cyclohexene carbonate-b-decalactone-b-cyclohexene carbonate) terpolymers displayed >99% CO2 selectivity and molar masses ranging from 38–71 kg/mol (Đ < 1.16), with improved material properties compared to poly(cyclohexene carbonate).

Fig. 6: Heterometallic chain-shuttling mechanism.
figure 6

Proposed mechanism for CHO/CO2 ROCOP with heterometallic complexes 22a-h88.

LMZnX2 complexes 23a-f90 and 24a-c91, combining Zn with s- and p-block heterometals, were also tested in ROCOP (Fig. 5). With 23e-f, epoxide activation on Mg or Ca (respectively) was proposed as X-ray crystallographic studies showed THF coordination to these metals. Heterometallic 23e (Mg/Zn) displayed a TOF of 72 h−1 and was six times more active than LZn2I2 (0.1 mol% catalyst loading, neat epoxide, 1 bar CO2, 80 °C). However, all other heterocombinations investigated were less active than LZn2I2. As well as the heterometal selected, the ligand conformation and the intermetallic separation may also play a role, as these differed with Li (23b, “crown-shape”; Zn–Li = 2.86 Å), Mg (23e, “bowl-shape”; Zn–Mg = 3.06 Å) and Ca (23f, “S-shaped”; Zn–Ca = 3.35 Å). Interestingly, only 23b,d-e were selective for polycarbonate formation (>96%), with 23a,c,f generating cis-cyclic carbonates (>99%). Cyclic carbonate formation was linked to the iodide lability and potential dissociation of the growing polymer chain from the metal due to the increased ionic character of the metal carbonate bond92.

The importance of the metal combination in CHO/CO2 ROCOP was also evident with complexes 24a-c91, where L adopts a “bowl” conformation with three chloride co-ligands. Heterometallic 24a-c were less active and selective than LZn2Cl2 (TOF = 9 h−1, 0.1 mol% catalyst loading, neat epoxide, 1 bar CO2, 80 °C), with significant polyether formation (up to 32%). Increasing the CO2 pressure to 20 bar led to a perfectly alternating polycarbonate with 24c, suggesting that CO2 insertion may be implicated in the rate-limiting step, unlike L-based bis-Zn and Mg/Zn complexes, which are generally zero-order in CO282,88. The CO2 uptake (Al < Ga < In) increased with the decrease in the Lewis acidity of the Group 13 metal91. This observation, along with the increased lability of the metal-alkoxide intermediates, was used to explain the activity increase from Al (TOF = 1 h−1) to In (TOF = 9 h−1). These features also outweighed the influence of intermetallic proximity on the activity of 24a-c, with both the distance and activity increasing on descending Group 13 (Zn–Al = 3.02 Å, Zn–Ga = 3.12 Å, Zn–In = 3.15 Å).

Main group and transition metal heterometallic complexes in epoxide/CO2 ROCOP

Heterometallic main group/transition metal complexes based on L have also been synthesised (25a-b63 and 2693, Fig. 5). Both 25a-b (Ti/Zn) showed low to moderate activity, selectivity and polymerisation control in CHO/CO2 ROCOP with TOF = 3 h−1, ~94% carbonate linkages and bimodal dispersity (Đ = 1.35 and 1.37, respectively; 1 mol% catalyst loading, 1 bar CO2, 80 °C)63. Notably, the analogous mono-Ti and mono-Zn complexes were inactive in CHO/CO2 ROCOP, highlighting the benefit of heterometallic Ti/Zn86. 25a-b were also moderately active in ROP, converting up to 89 equiv. l-LA in 40 min (Đ = 1.13) and 94 equiv. ε-CL in 90 min (Đ = 1.21-1.33) at 70 °C in THF63.

The Mg/Co complex 26 (Fig. 5) recently outperformed all L-supported heterometallic complexes in CHO/CO2 ROCOP, with TOF of 455 h−1 at 1 bar CO2 pressure (0.1 mol% catalyst loading, neat epoxide, 80 °C), > 99% carbonate linkages and good polymerisation control (Đ = 1.13)93. Under identical conditions, 26 was almost five times more active than 22h (Mg/Zn), suggesting that Co is more active than Zn in ROCOP. 26 was also twice as active as LCo2(OAc)2, and three times faster than LMg2(OAc)2 (0.1 mol% catalyst loading, neat epoxide, 1 bar CO2, 120 °C). These observations were supported by kinetic studies, as the transition state Gibbs free energy (ΔG‡) and enthalpy barriers (ΔH‡) were lowest for 26 (ΔG‡ = 94.5 ± 1.2 kJ mol−1, ΔH‡ = 77.3 ± 1.2 kJ mol−1) and highest for LMg2(OAc)2 (ΔG‡ = 100.2 ± 1.3 kJ mol−1, ΔH‡ = 83.3 ± 1.3 kJ mol−1), implying that Co accelerates nucleophilic attack by lowering the ΔH‡. Conversely, the entropy ΔS‡ values were reduced for 26 and LMg2(OAc)2 (ΔS‡ = −46.1 ± 3.4 J mol−1 and −45.4 ± 3.7 J mol−1, respectively) vs. LCo2(OAc)2 (ΔS = −60.2 ± 4.2 J mol−1)93. This was attributed to the lower bond directionality of Mg, possibly resulting in increased degrees of freedom during epoxide coordination. 26 was therefore proposed to catalyse ROCOP via a chain-shuttling mechanism (Fig. 6) with CHO coordination to Mg, followed by ring-opening via the Co-carbonate bond.

The M/Co complexes 27a-d (M = Na, K, Rb or Cs, respectively) were recently reported as the first heterometallic catalysts to exhibit good turnover numbers for PO/CO2 ROCOP94. 27b (K/Co) was most active, displaying TOF of 340 h−1 vs. 27a (TOF = 120 h−1), 27c (TOF = 54 h−1) and 27d (TOF = 47 h−1) in neat PO (0.025 mol% catalyst loading, 50 °C, 20 bar CO2 pressure). Monomodal SEC traces were obtained in the presence of >50 equiv. of 1,2-cyclohexane diol as a chain-transfer agent, with controllable Mn values between 1.3 and 79.6 kg/mol. 27b also displayed an outstanding TOF of 800 h−1 (0.025 mol%, 70 °C, 30 bar CO2 pressure), with narrow dispersity (Đ = 1.07), >99% CO2 uptake and 93% polycarbonate selectivity. The highest activity of 27b was attributed to the optimal combination of metal sizes and binding affinities. While smaller Na may be coordinatively saturated by the crown ether, preventing PO coordination, the larger Rb and Cs in 27c-d prevent coplanar incorporation into the macrocycle and form aggregate structures. From the kinetic data, the rate-determining step was proposed to involve ring-opening of K-coordinated PO by a Co(III)-carbonate intermediate via a chain-shuttling mechanism akin to other heterometallic catalysts (Fig. 6). Notably, 27b was also more than twice as active as Mg/Co complex 26 in CHO/CO2 ROCOP (kp = 31.7 mM−1 s−1 at 50 °C for 27b and kp = 15.1 mM−1 s−1 for 26 at 60 °C).

The Ln/Co3 complexes 28a-f (Ln = La, Ce, Pr, Nd, Eu or Gd, respectively, Fig. 5) were recently studied in CHO/CO2 ROCOP95. Both Ln and Co were proposed to act as Lewis acids, based on MeOH and H2O coordination in the solid-state structures. 28a-f significantly outperformed their monometallic counterparts (monometallic Co(II) complex and La(OAc)3), which yielded only trace polycarbonate, either alone or in combination, whereas 28a displayed a TOF of 1375 h−1 with >99% carbonate linkages and narrow (bimodal) dispersity (Đ = 1.04/1.04; 8.0 × 10−4 mmol% catalyst loading, neat epoxide, 20 bar CO2, 130 °C). 28d with medium-sized Nd displayed the highest activity (TOF = 1625 h−1; Đ = 1.05/1.04). 28a-f were proposed to promote ROCOP by CHO coordination to the oxophilic Ln, followed by epoxide ring-opening by the Co-acetate/-carbonate bond. The resulting Ln-alkoxide was then proposed to form carbonate species with Co-bound CO2, leading to chain propagation.

Heterometallic complexes containing lanthanide elements in epoxide/CO2 ROCOP

Epoxide activation is a key ROCOP step, and Ln metals have displayed good monomer coordination in ROP53,55,58,59. A range of Ln/Zn complexes have also been developed for CHO/CO2 ROCOP, including complexes 29a-b (Ln = Nd, Y)96, 30b-c (Ln = Y, Nd or Sm)97 and 31a-j (Ln = Y, Lu, Dy, Sm or La)98 (Fig. 7). 29a (Nd2/Zn) showed good activity with maximum TOF = 273 h−1 (ref. 96), 99% carbonate linkages and moderate polymerisation control (Đ = 1.81; 0.1 mol% catalyst loading, [epoxide] = 4.92 M in toluene, 7 bar CO2, 70 °C). Conversely, 29b (Y2/Zn) was significantly slower and less selective with TOF of 33 h−1 and 63% carbonate linkages, likely linked to the smaller size of Y3+ (90 pm) vs. Nd3+ (99 pm) giving poorer epoxide coordination. While ROCOP catalysts typically require elevated temperatures, 29a also displayed good activity at ambient temperature with TOF = 82 h−1 (Đ = 1.65) under otherwise identical conditions. The analogous mono-Nd complex and ZnEt2/BnOH mixture failed to initiate ROCOP (7 bar CO2, 70 °C), highlighting the cooperativity of the Nd/Zn system.

Fig. 7: Heterometallic Ln/Zn complexes for epoxide ROCOP with CO2 or cyclic anhydrides.
figure 7

Structural representation of zinc-based ROCOP catalysts featuring lanthanide heterometals from across the f-block.

The Ln/Zn complexes 30a-c (Fig. 7, Ln = Y, Nd or Sm, respectively) displayed moderate activity and selectivity in CHO/CO2 ROCOP97. The most active complex, 30a, required 24 h to generate 71% polycarbonate (toluene, 30 bar CO2, 70 °C) but outperformed the homometallic Y complex, which showed negligible activity. High CO2 pressures were required for polycarbonate synthesis; only 16% polycarbonate was formed with 30a at ambient pressure, and the poor polymerisation control of 30a-c (Đ = 8.42–9.50) was attributed to polymer degradation and cyclic carbonate/polyether formation.

The Ln ionic radii in zincate complexes 31a-j (Fig. 7) significantly influenced their activity in CHO/CO2 ROCOP99; 31c-d,h-i featuring medium-sized Dy and Sm were most active (TOF = 124 h−1), generating perfectly alternating polycarbonates with moderate control (Đ = 1.52–1.62, 1500:1 [CHO]:[catalyst], 30 bar CO2, 70 °C). Structural analysis of 31d indicated close Sm-Zn proximity (3.47 Å) and elongated Zn-phenoxide bonds, suggesting 31d might be more nucleophilic than both mono-Sm and mono-Zn complexes. Indeed, the homometallic counterparts of 31c-d,h-i showed low or no activity under the same conditions. Low to moderate activities were observed with 31a-b,f-g (larger Ln) and no polymer was formed with 31e,j (smallest Ln).

Studies of Ln/Zn complexes 32a-j (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Dy, Fig. 7) in CHO/CO2 ROCOP highlight the importance of the anionic co-ligand, as well as the Ln size98. While acetate complex 32a exhibited TOF = 230 h−1 and generated polymers with >99% carbonate linkages, the nitrate analogue 32b formed trace polymer and trifluoroacetate complex 32c favoured polyether formation (neat epoxide, 10 bar CO2, 100 °C). The higher activity of 32a was attributed to the rapid exchange of the coordinated and outer-sphere acetate anions. The highest catalyst activities and selectivities were observed with 32a-f, which featured larger Ln metal centres than 32g-j. 32d (Ce/Zn) showed the highest activity with TOF = 370 h−1 (Đ = 1.3).

All Ln/Zn complexes reported for CHO/CO2 ROCOP were proposed to operate via a chain-shuttling mechanism (Fig. 6), with the Lewis acidic Ln metal activating CHO for nucleophilic attack by the labile Zn-carbonate, formed via CO2 insertion into the Zn-alkoxide bonds. Due to mechanistic similarities, it is plausible that the heterometallic cooperativity of catalysts reported for epoxide/CO2 ROCOP could be extended to epoxide/cyclic anhydride ROCOP, to form a series of polyesters by switching the carbonyl source70.

Heterometallic complexes in epoxide/cyclic anhydride ROCOP

To date only two heterometallic complexes, 2186 (Mg/Zn, Fig. 5) and 33100 (Yb/Zn, Fig. 7), have been explored in epoxide/anhydride ROCOP. 21 displayed promising activity in CHO/phthalic anhydride ROCOP, likely operating via a similar chain-shuttling mechanism proposed for CHO/CO2 ROCOP (Fig. 6), with TOF = 188 h−1 (ref. 86), which was 40 times higher than the 1:1 LMg2Br2:LZn2Br2 mixture (1 mol% catalyst loading, neat epoxide, 100 °C). 21 also showed excellent selectivity for polyester formation (>99%) and good polymerisation control with Mn values up to 10 900 g/mol (bimodal Đ = 1.04, 1.09). 33 was tested in CHO/maleic anhydride (MA) ROCOP with and without a co-catalyst (4-dimethylaminopyridine (DMAP) or triphenylphosphine (TPP))100. In the absence of a co-catalyst, 33 converted 17% CHO in 2.5 h at 110 °C (250:250:1 CHO:MA:33), giving high polyether content (61%). With TPP, 33 converted 73% CHO in 6 h at 110 °C, yielding a perfectly alternating polyester with Mn up to 12 830 g/mol (Đ = 1.13; 250:250:1:1 CHO:MA:33:TPP). Using the more nucleophilic DMAP co-catalyst, 33 converted 90% CHO under the same conditions but gave lower polyester selectivity (31% polyether linkages).

Aziridine/CO ROCOP

Aziridine/CO ROCOP is an underexplored route towards poly-β-peptides and polypeptoids (N-alkylated polymer) with potential applications in catalysis, materials and biomedicine101,102,103,104. Suitable catalysis is required to produce poly-β-peptides/polypeptoids and to overcome the formation of side-products such as β-lactams and polyamines (Fig. 8)105,106,107. Mono-Co systems have been most explored but have generally displayed poor polymerisation control (Đ ≈ 11.5)108 and low selectivity for alternating aziridine/CO enchainment, requiring high CO pressures (<69 bar)105.

Fig. 8: Proposed aziridine/CO ROCOP mechanism for Co/Pd catalyst systems.
figure 8

Proposed heterometallic mechanism for complexes 34a-g along with targeted poly(β-peptide) product and potential side-products from aziridine/CO ROCOP109.

Co/Pd complexes 34a-g (Fig. 8, Co-Pd distances ≈ 2.6 Å) are the only heterometallic catalysts reported for aziridine/CO ROCOP109. 34a exhibited the highest activity for both substituted and non-substituted aziridines, yielding 69% copolymer from 2-methylaziridine in 6 h at 100 °C and 50 bar CO pressure (Đ = 1.5; 1 mol% catalyst). Unfortunately, the catalyst selectivity for copolymer production was not assessed. However, 34a-g were significantly more active than monometallic [Co(C(=O)Me)(CO)3(PPh3)], [Co(C(=O)CH2Ph)(CO)4]105,108 and [PdMe(NCMe)(bpy)]+[BF4] complexes, which was attributed to Co/Pd cooperativity. 34a-g were proposed to operate via reversible aziridine coordination to Pd, generating the [PdC(=O)R(aziridine)(L)]+[Co(CO)4] (R = Me, Ph; L = dppe, bpy, tmeda or phen) ion pair, followed by aziridine ring-opening via nucleophilic attack of Co upon the methylene carbon of the aziridine and subsequent CO insertion (Fig. 8).

Key activity trends in ROCOP

The nature of the metal combination and the initiating nucleophile are key in epoxide/CO2, epoxide/anhydride and aziridine/CO ROCOP. Generally, the different metals are proposed to adopt distinct roles, with the more Lewis acidic metal(s) activating the monomer(s) and the more labile metal-oxygen bonds accelerating nucleophilic attack63,86,88,90,91,93,95. While many heterometallic complexes have led to enhanced activities, selectivities and polymerisation control, not all heterocombinations give improved performance, and a careful balance of Lewis acidity and M-OR bond polarity is required. Similarly to the trend observed in ROP, the catalytic activity of Ln-based heterometallic catalysts in ROCOP is often linked to Ln size; Ln with medium/large ionic radii (e.g. Ce and Sm) generally increase epoxide coordination and catalyst activity96,97,98. Notably, most heterometallic ROCOP catalysts operate without a co-catalyst, enabling the synthesis of high molar mass polymers, albeit often with the aforementioned bimodal dispersity.

Summary and outlook

In both ROP and ROCOP, heterometallic catalysts have displayed reactivity enhancements by facilitating concurrent monomer activation and nucleophilic attack. However, not all heterometallic combinations improve catalyst performance. Whilst more studies are required to fully understand and predict cooperative heterocombinations, key RO(CO)P catalyst features have started to emerge, including the metal size and coordination number, M-OR bond strength, M–M′ proximity, and the solution-state catalyst structure under polymerisation conditions.

Pairing a hard metal (M, e.g. Group 1, 2 and Ln) with a softer, more carbophilic metal (M′, e.g. Co and Zn) can result in anionic “ate” activation, with the transfer of anionic ligands to the more carbophilic metal. For example, complexes 3a-b and 4a-d bear structures typically referred to as higher order zincates/magnesiates, where the central carbophilic Zn2+/Mg2+ is surrounded by four anionic ligands. While not all of the complexes discussed herein bear typical “ate” structures, almost all feature a bridging M-O-M′ unit that enables electronic communication between the two metal centres. This electronic communication has the potential to form complexes with at least a partial “ate” character, with the tug of war of electron density between M and M′ lying to the side of M′. This unequal sharing of the electron density may simultaneously increase the Lewis acidity of the M centre and also the nucleophilicity of the M′-R group (where R = e.g. an alkoxide); both are key catalyst features in ROP and ROCOP. The concept of heterometallic cooperativity has been relatively well-exploited with heterometallic complexes in epoxide/CO2 ROCOP, where the two metals typically adopt different roles of epoxide coordination and nucleophilic attack from a metal-carbonate group in the chain-shuttling mechanism. The larger Lewis acidic metal (e.g. K, Mg or Ln) usually enhances Lewis donor (e.g. monomer) coordination, as observed by the preferential coordination of THF to Mg in 23e (Mg/Zn)90 and MeOH/H2O to the Ln centre in 28a-f (Ln/Co)95 in the molecular structures. Studies with 26 (Mg/Co) and 27b (K/Co) suggest that the more Lewis acidic Mg/K enhances the role of epoxide coordination, whereas the more electronegative metals (e.g. Co and Zn) typically accelerate the nucleophilic attack and epoxide ring-opening93,94, lowering the transition state barriers vs. the homometallic counterparts. Many of the reported heterometallic ROCOP catalysts feature heterometals in close proximity, typically within the 3–5 Å range proposed to be crucial for effective bimetallic electronic communication and the chain-shuttling ROCOP mechanism77,84. Catalysts designed for cyclic ester/cyclic carbonate ROP and CO2/epoxide ROCOP share several key features, including the Lewis acidity of the metal and nucleophilicity of the M–O(polymer) bond. Studies on bimetallic ROP catalysts suggest that intermetallic proximity can also be important, however further mechanistic investigations are required. While the individual heterometal roles are less well understood in ROP, the highest activities have been observed with complexes where medium/large Group 1/Ln metals are combined with Zn. Complexes comprising larger Lewis acidic Group 1/2/Ln metals have generally displayed superior activities, attributed to the presence of additional monomer coordination sites. Based on the mechanistic similarities between ROP and ROCOP, it is plausible that in the presence of heterometallic complexes, ROP also proceeds via Lewis acidic activation of the monomer by the Group 1/Ln metals, followed by nucleophilic attack and monomer insertion at the more electronegative M′-OR bond. This hypothesis is supported by structural analysis showing THF coordinated to alkali metals in 2, 3a-b, 4a-d, 5a-b, 6a-d, 13a-b, 14 and 16a-d and to Ln metals in 18a-d.

Heterometallic catalyst performance is also influenced by the reaction conditions; the solvent (or monomer) may alter the complex aggregation state or promote the in situ formation of solvent separated ion pairs. Throughout heterometallic RO(CO)P, there are examples where THF solvent decreases the catalyst activity, and further studies are required to understand whether this stems from increased M–M′ distances (by in situ modification of solution-state heterometallic structures) and/or competitive THF metal coordination blocking the monomer approach. Understanding whether heterometallic complexes maintain their structure in the solution-state is therefore crucial.

Alkali and Ln-based heterometallic catalysts have typically led to high activities in RO(CO)P, and there is scope for catalyst development with di-, tri- and tetravalent metal heterocombinations. Many of the heterometallic systems reported thus far have also been investigated under different reaction conditions, which makes comparisons challenging. This is especially prominent in ROP, and thus systematic studies are required to identify superior and inferior heterocombinations.

Heterometallic cooperativity has the potential to shape future RO(CO)P catalyst design. At present, heterometallic catalyst performance often falls short of the homometallic frontrunners, however there has been far more extensive research into homometallic catalysts, with >100 homobimetallic examples reported for LA ROP (vs. 39 heterometallic catalysts). While heterometallic catalyst synthesis is sometimes regarded as challenging, different methodologies including sequential deprotonation, coordination and/or transmetalation reactions, and reactions with preformed “ate” complexes have been successfully employed to prepare heterometallic complexes. Promisingly, we are now reaching a turning point, with a recently reported Mg/Co system now amongst the most active epoxide/CO2 ROCOP catalysts at atmospheric CO2 pressure. More recently, DFT calculations have been used to understand which catalyst features lead to heterometallic cooperativity in RO(CO)P, and there are exciting opportunities to use computational approaches to both understand and predict cooperative heterometallic catalysis in the future. The studies described here signal clear directions for understanding and exploiting heterometallic cooperativity within RO(CO)P catalysis.