## Introduction

The finding of fresh monomers1,2 and the development of active catalysts3,4 are the central topics in synthetic polymer chemistry. Carbonyl sulfide (COS), a key intermediate of the atmospheric sulfur cycle and the most abundant sulfur-containing gas in the troposphere, causes haze, acid rain, and ozonosphere damage5, and is also a one-carbon (C1) heterocumulene and structural analog of carbon dioxide (CO2). Utilizing COS to copolymerize with epoxides is a emerging atom-economic and versatile approach to produce functional sulfur-containing polymers6,7,8,9,10,11. In contrast, traditional synthesis of sulfur-containing polymers often involves the condensation of thiols with phosgene and ring-opening polymerization (ROP) of cyclic thiocarbonates that are generally derived from thiols and phosgene6.

Recent synthetic advances6,7,8,9,10,11 provide metal catalytic strategies for making a variety of COS-derived poly(monothiocarbonate)s that have good solubility in organic solvents, superior optical properties, and excellent chemical resistance6,7. Zinc-cobalt(III) double-metal cyanide complexes8 and (salen)CrX/onium salts (Lewis bases, LBs, Fig. 1a)9,10,11 have been discovered to catalyze the COS/epoxide copolymerization. Unfortunately, metal-contaminated or colored copolymers are resulted and severely impede their applications in optical, optoelectronic, photochemical, or biomedical materials12,13,14. Organic Lewis pairs composed of triethylborane (TEB) and LBs, including amidine, quinidine, quaternary onium salts could generate poly(monothiocarbonate)s from COS and epoxides15 (Fig. 1b). However, the TEB/LB pairs often led to relative broad polydispersity (PDI) and higher molecular weights than the calculated one. Meanwhile, only TEB, which is toxic and spontaneous combustion in air, was effective to COS/epoxide copolymerization.

The above-mentioned catalysts have the coordination bonds that are responsible to the activation of the monomers. Whereas very few of reports suggested an anionic copolymerization process involved C1 monomers. For example, Nozaki et al., disclosed that [PPN]Cl could solely catalyze the carbon-disulfide (CS2)/propylene sulfide copolymerization16. Feng and Gnanou et al. presented that alkoxide/benzyl alcohol (BnOH) could effectively initiate the CO2/epoxide copolymerization17,18. However, anionic copolymerization of COS with epoxides remains unexplored. In contrast with the CO2/epoxide copolymerization that is often expected to attain fully alternating structure and no production of side cyclic carbonate (i.e., 100% polycarbonate)19,20,21,22,23,24, the chemistry of COS/epoxide copolymerization is more complicated6. One is the possible occurrence of oxygen/sulfur exchange reactions (O/S ERs), which cause the production of CO2, and thiirane intermediate, will produce randomly distributed dithiocarbonate and carbonate units in the final copolymer8,25,26,27. The other is that the copolymerization of structurally asymmetric COS with a terminated epoxide, will generate four consecutive monothiocarbonate diads, i.e.,: head-to-tail (H–T), tail-to-head (T–H), tail-to-tail (T–T), and head-to-head (H−H) diads6. As a result, metal-free catalyst for anionic COS/ epoxide copolymerization should avoid O/S ER, attain highly regioselectivity involved two asymmetric monomers and be precisely controlled by varying the monomer to initiator ratios under mild condition.

Herein, we have developed a living copolymerization of COS with various epoxides with high activity, using commonly available thioureas (TUs) and organic LBs (DBU, MTBD, P4, P2, and P1, Fig. 1c). This catalyst system was developed based on the hypothesis that the cooperative catalytic process of Lewis pairs composed of TU and base, undergoing a non-covalent mode to activate and stabilize the alcohol initiator/chain end for controlling the anionic copolymerization28,29,30,31. The resulting poly(monothiocarbonate)s have perfectly alternating structure with regioregularity, controlled molecular weights and narrow PDIs, and are colorless (Supplementary Fig. 1).

## Results

### Anionic COS/propylene oxide (PO) copolymerization

Previous studies have shown that the organic bases, e.g.: amidine and guanidine widely employed as the cocatalysts for metal complex for catalyzing CO2(COS) /epoxide copolymerization6,32,33,34. In this scenario, the organic bases often exhibited no activity towards CO2/epoxide copolymerizations19,20,21,22,23,24,32,33,34. Since COS is more reactive than CO2 and the expected thiocarbonate anion [OC(=O)S] is more nucleophilic than carbonate anion [OC(=O)O]6, we performed the sole catalysis of LBs (DBU, MTBD, P4, P2, and P1) for COS/PO copolymerization as controls (entries 1–5 in Table 1) for comparatively studying the catalytic performance of the designed Lewis pairs of TU/LB (entries 9–18 in Table 1). Unexpectedly, we observed that DBU could solely catalyze COS/PO copolymerization in a high PO/DBU feed ratio of 250/1 at ambient temperature (25 °C) for a long time of 24 h (entry 1, Table 1). Poly(propylene monothiocarbonate)s (PPMTCs) were obtained with a number-average molecular weight (Mn) of 38.3 kg/mol with production of 7% of cyclic monothiocarbonate. P4, a phosphazene with the strongest basicity35, was active for the anionic ROP of epoxides, cyclic esters, and caprolactam36,37,38,39, was also effective to the COS/PO copolymerization with a TOF of 23 h−1 even under a PO/P4 feed ratio (1000/1). However, the copolymer selectivity was only 60%, and 8% polyether was detected (entry 2 in Table 1, Supplementary Fig. 2). The sole catalysis of P2, P1, and MTBD for the copolymerization exhibited high copolymer selectivity (≥96%), but low TOFs (1–4 h−1, entries 3–5 in Table 1). Concurrently, high reaction temperatures (≥70 °C) or the use of TBD (at 20 °C) only afforded cyclic products (entry 6 in Supplementary Table 2; entry 10 in Supplementary Table 1). PPMTCs obtained by these organic bases had Mns of 29.4–46.0 kg/mol and PDIs of 1.20–1.58. This result exclusively suggested that the COS/PO copolymerization could be performed in an anionic manner.

The activity and selectivity of the above LB-catalyzed COS/PO copolymerization were clearly enhanced by introducing TU-1 (entries 9–12 in Table 1), while TU-1 did not catalyze the reaction alone (entry 11 in Supplementary Table 1). For example, P4/TU-1 and P2/TU-1 pairs afforded improved TOFs (41 and 24 h−1), copolymer selectivity (97/3 and >99%) even in high monomer/pair feed ratios of 2000/1/1 and 1000/1/1, respectively, (entries 9–10, Table 1). Concurrently, COS/PO copolymerization via the catalysis of DBU/TU-1 or MTBD/TU-1 pairs led to a slight improvement of TOF (4–7 h−1) and the copolymer selectivity (93/7 and 95/5) while the P1/TU-1 pair had low TOF (1 h−1), but perfect copolymer selectivity (>99%) (entry 5, Supplementary Table 1). Of note, the use of TU-1 caused a slight decrease of Mn (30.2–36.1 kg/mol) and narrower PDIs of 1.13–1.16, suggesting the generation of larger amounts of active centers when TU-1 was introduced. Of special interest, MTBD/TU-1 pair catalysis provided a copolymer with a remarkably high Mn of 98.4 kg/mol with PDI of 1.14 after 72 h reaction (entry 13, Table 1), which can be ascribed to a longer lifespan of the active species.

The addition of benzyl alcohol (BnOH) to the COS/PO copolymerization catalyzed by either single LB (entries 6–8 in Table 1, entries 3, 6, and 8 in Supplementary Table 1) or TU-1/LB pairs (entries 14–18 in Table 1, entries 2, 4, 7, and 9 in Supplementary Table 1) led to a dramatic improvement of TOF without the sacrifice of the copolymer selectivity, even in a rather low catalyst loading. For example, adding equimolar BnOH to P4 and P4/TU-1-catalyzed copolymerizations presented improved TOFs of 55 and 75 h−1, respectively, (entries 7 and 14 in Table 1). In addition, high loading of TU-1 and BnOH (P4/TU-1/BnOH = 1/5/5) led to a dramatic increase of TOF to 112 h−1 (entry 15 in Table 1). Introducing equimolar BnOH to the DBU/TU-1 pair led to a clear promotion of TOF (22 h−1) even in a low PO/DBU/TU-1 feed ratio of 2000/1/1(entry 17 in Table 1). In contrast, no copolymers were afforded in the absence of BnOH in PO/DBU feed ratio of 2000/1 under the same reaction conditions (entry 12 in Supplementary Table 1). Actually, LB could activate BnOH rapidly through H-bond interaction to form alkoxide anion, which initiate the copolymerization28,29,30,31. Hence, the stronger the basicity of the LB, the higher TOFs of the COS/PO copolymerization. This was evident by the TOF deceasing with the basicity orders of P4 > P2 > DBU ≥ MTBD > P1. Being totally different from the (salen)CrCl complexes and TEB/LB pairs9,15, the TU-1/LB pairs could catalyze COS/PO copolymerization in a low COS/PO feed ratio of 1.2/1, even in a feed ratio of 1.05/1 (entries 1–2, Supplementary Table 1). Since COS did not homopolymerize, the copolymerization stopped once PO was nearly completely consumed. The resultant copolymers had 100% of alternating degree (Supplementary Figs. 311), indicative of much faster COS activation than successive PO enchainment. O/S ER was also effectively suppressed for all samples in Table 1 and Supplementary Table 1. Moreover, the control experiment ruled out the possible route of ROP of the cyclic monothiocarbonate formed (Supplementary Fig. 12).

### Chain microstructures of COS/PO copolymers

The perfectly alternating structure and regioregularity of the PPMTCs were also revealed by MALDI-TOF MS spectroscopy (Fig. 2). Figure 2a showed one distribution of α-OH, ω-OH-terminated [H + (PO + COS)m + n + (PS + COS) + PO + OH + K+] copolymer, i.e., a single PPTMC with two –OH end groups and one dithiocarbonate unit (Mn: 6.5 kg/mol; PDI: 1.15). Furthermore, high-resolution 1H(13C) NMR spectra (Supplementary Fig. 13a, b) revealed that the copolymer contained two secondary –OH end groups with minimal regio-defect (one dithiocarbonate unit)40. These results were indicative of inclusively regioselective attack of the sulfur anion to the CH2 site of PO, and thus the sole production of the T–H diad via the organocatalysis40. In the presence of BnOH, only one distribution of α-OBn, ω-OH copolymer-terminated [BnO + (PO + COS)n + H + K+] (Fig. 2b) with >99% T–H diad content (Supplementary Fig. 13c, d) was obtained without dithiocarbonate unit (Mn: 4.4 kg/mol; PDI: 1.14), meant that BnOH was a very efficient initiator and depressed the production of the dithiocarbonate unit.

### Living COS/PO copolymerization catalyzed by Lewis pairs

Remarkably, the TU/LB pair catalysis allowed for the copolymerization exhibiting the living features. Take the TU-1/DBU pair-catalyzed COS/PO copolymerization with or without using BnOH (Fig. 3a, b) as instances: linear increase of Mn with PO conversion, narrow PDIs (1.11–1.12, 1.16–1.19) to high PO conversion (89% and 83%, respectively). Simultaneously, the decay in monomer concentration follows zero-order kinetics under various loading of the TU-1/DBU pair in the presence or absence of BnOH or using TU-1/P2 pair without adding BnOH (Supplementary Fig. 15). In addition, the determined molecular weights by GPC and NMR (i.e.: MnGPC and MnNMR) were in well agreement with the calculated MnTheo that increased with the increase of the [PO]/[BnOH] molar ratio in a good linear fashion (Fig. 3c, Supplementary Table 3, and Figs. 17 and 18) while keeping narrow PDIs (1.17–1.19). This result confirmed that Mns of the resultant copolymers could be tuned by changing the [PO]/[BnOH] feeding ratio in the presence of TU-1/DBU pair. Of interest, further investigation showed that the use of exogenous water (even relatively large amounts, no BnOH added) could also effectively initiate the copolymerization and control the molecular weights of the resultant copolymers without changing the chain microstructure (Supplementary Table 4 and Figs. 2022). As a result, such TU/LB pairs are robust for the copolymerization under mild conditions.

We further explored the chain extension reaction via tandem synthesis (Fig. 3d and Supplementary Fig. 23). PO and COS were copolymerized firstly using TU-1/DBU pair without using BnOH ([PO]: [COS]: [TU-1]: [DBU] = 50: 60: 1: 1) at 25 °C for 10 h. After slowly venting the unreacted COS, PO was totally consumed according to the 1H NMR spectra, and the resultant PPTMC exhibited unimodal peak with a Mn of 8.6 kg/mol and a PDI of 1.19. Then, 1.0 ml PO and 1.18 g COS (COS: PO = 1.2: 1) were added into the reactor and sealed for another 20 h reaction at 25 °C. PO conversion was 88% according to 1H NMR spectra. The resultant copolymer had a Mn of 22.3 kg/mol with a PDI of 1.26, as revealed by that GPC curve shifted overall to high molecular weight. The result of the chain extension reaction also confirmed the living mode of TU-1/DBU pair-catalyzed COS/PO copolymerization.

### Kinetic and mechanistic study

The cooperative catalysis of TU-1/LB pair for the COS/PO copolymerization was firmly supported by the kinetic studies (Fig. 4a). The apparent rate constant (kapp) obtained from the slopes of the best-fit lines to the plots of PO conversion vs. time, is well proportional to [TU-1] + [DBU] in the absence or presence of BnOH, suggesting that the TU-1/DBU pair behaved as a discreet catalyst species [(a) in Fig. 6]. As expected, kapp of the TU-1/P2 pair was 13.6 ± 0.3*10−2 h−1 and higher than that of TU-1/DBU pair (5.7 ± 0.8*10−2 h−1) for the copolymerization under the same conditions due to the stronger basicity of P2. This result is in agreement with the binding constant via 1H NMR dilution (see Methods, Supplementary Fig. 24) that was 10.3 ± 2.5 for TU-1/DBU pair and 21.2 ± 2.2 for TU-1/P2 pair in equilibrium in CDCl3 at 25 °C (Fig. 4b). Because the H-bond interaction could be weakened by elevating the temperature30, the TU-1/DBU pair catalysis for COS/PO copolymerization at high temperatures (≥55 °C) produced considerable amounts of the cyclic products (Supplementary Table 2), which is consistent with the catalysis involving only the bases for the coupling reaction of COS with PO41.

We have further studied the combining capabilities of TU-1, DBU, COS, and PO in CDCl3 using 1H NMR spectra (Fig. 5 and Supplementary Fig. 25). In a high concentration of TU-1 and DBU (0.5 M), the H-bond interaction was clearly revealed by the proton signal of NH group (5.65 ppm) of TU-1 disappearing while the six protons (NCH2) of DBU became chemically equivalent (Supplementary Fig. 25). Of interest, TU-1 was shown to solely activate PO and did not interact with COS in CDCl3 (Fig. 5a). Conversely, DBU could only activate COS owing to a clear deshielding effect of protons of NCH2 of DBU (from 2.38 to 2.77 ppm) and appearance of chemical equivalent protons of NCH2 of DBU rather than activate PO (Fig. 5b). Such supramolecular specific recognition of TU-1 to PO and DBU to COS in TU-1/DBU pair promoted the copolymerization cooperatively.

The introduction of BnOH into the polymerization system led to the prior formation of the BnOC(=O)S…DBUH+ owing to the deprotonation of BnOH by DBU, generated species (b) and (c) in Fig. 6, as revealed by 1H NMR spectra (Supplementary Fig. 26)42. Since PO was activated by TU-1 through H-bond [species (d) in Fig. 6, revealed by Fig. 5b], the chain growth could be accelerated (Table 1). On the other hand, in the absence of BnOH, trace water (i.e., R=H, Fig. 6) could also initiate the copolymerization via the similar activation route of BnOH by TU/LB pair. Such H2O initiation led to the formation of the end –S(O=C)–OH group, which was thermodynamically unstable and thus converted to –SH group via decarboxylation process6,40. Since the end –SH group has the stronger acidity than –OH group, it was rapidly deprotonated, generating bifunctional initiator for further chain growth, a copolymer with two end secondary –OH groups and one dithiocarbonate unit (f) was produced, which was clearly revealed by Fig. 2a (Supplementary Figs. 13 and 22).

### The impact of Lewis pairs on COS/epoxides copolymerizations

Different Lewis pairs including other thioureas were also investigated for the copolymerization of COS with several epoxides. Two other thioureas, TU-2 and TU-3 were synthesized43 and successfully utilized for the COS/PO copolymerization (entries 1–4 in Table 2). H-bond interactions of both TU-2 and TU-3 with DBU are similar to that of the DBU/TU-1 pair (Supplementary Fig. 28). The TU-3/DBU pair was more active than TU-1 (TU-2)/DBU pairs for the copolymerization, but with a slightly lower copolymer selectivity of 93%. Both TU-2 and TU-3 paired with P2 showed the same TOFs (29 h−1, entries 3–4, Table 2) for the COS/PO copolymerization. Totally, TU-3 with more electron-withdrawing group resulted in the production of slightly more amounts of cyclic products. In addition, two epoxides, glycidyl phenyl ether (PGE) and cyclohexene oxide (CHO) were copolymerized with COS by using P2/TU-1, P4/TU-1 pairs, affording fully alternating copolymers (entries 5–8, Table 2). Thereof, the COS/PGE copolymerization were fully regioselective with T–H diad content of >99% (Supplementary Fig. 29), while COS/CHO copolymerization could proceed at 40 °C, afforded well-defined copolymer with perfect alternating degree and >99% copolymer selectivity (Supplementary Fig. 30). These results illustrate the use of several low-cost thioureas for the copolymerization of COS and epoxides with different structures.

## Discussion

We have described the synthesis of perfectly alternating and regioregular poly(monothiocarbonate)s from COS and epoxides by employing thioureas and organic bases under mild conditions. Of importance, the use of thioureas and BnOH led to living/controlled COS/epoxide copolymerization, improved catalytic activity and copolymer selectivity than previous systems. One of the key features of such metal-free catalyst systems is that it can be applied to a variety of epoxides. Due to the ease of tailoring the molecular structures of these organic thioureas and bases, this strategy is a promising alternative to get metal-free well-defined sulfur-containing polymers with high activity and selectivity. Our ongoing efforts are to seek a better understanding of the mechanistic aspects of such catalytic processes, and to develop chiral TU/LB pairs for the copolymerization.

## Methods

### Materials

Propylene oxide (PO), glycidyl phenyl ether (PGE), and cyclohexene oxide (CHO) were purified by distillation after stirring with calcium hydride for 3 days. 1,3-Diisopropyl-2-thiourea (TU-1) was purchased from Sigma Aldrich and sublimeed before use. 1-cyclohexyl-3-phenylthiourea (TU-2) and 1-[3,5-bis(trifluoromethyl) phenyl]-3-cyclohexylthiourea (TU-3) were synthesized according to literature43. 1H NMR spectra of TU-2 and TU-3 are shown in Supplementary Fig. 27. Tert-butylimino-tris(dimethylamino) phosphorene (tBu-P1, P1, 97%), 1-tert-Butyl-2,2,4,4,4-pentakis(dimethylamino)-2λ5, 4λ5-catenadi (phosphazene)(tBu-P2, P2, ~2.0 M in THF) and 1-tert-butyl-4,4,4-tris(dimethylamino)-2,2-bis [tris(dimethylamino)- phosphoranylidenamino]-2λ5, 4λ5-catenadi(phosphazene) (tBu-P4, P4, ~0.8 M in hexane) were purchased from Sigma and used directly. 1,5,7-Triazabicyclo[4,4,0]dec-5-ene (TBD) was purchased from Aldrich Chemical Co, which were purified by dissolving in toluene over CaH2, filtering after stirring overnight, and removing the solvent. Benzyl alcohol (BnOH), N-methyl-1,5,7-triazabicyclododecene (MTBD) and 1,8-diazabicyclo[5,4,0]undec-7-ene (DBU) were purchased from Alfa Aesar Chemical Co. and Aldrich Chemical Co., respectively, which were purified by distillation over distillation over CaH2 and stored in an inert gas (N2)-filled glove box. Sodium hydride (95%) was purchased from Sigma and used directly. Carbonyl sulfide (COS) (99.9%) was purchased from the APK (shanghai) Gas Company LTD and used as received.

### Representative procedure for copolymerization reactions

All polymerizations were carried out in glove box under N2 atmosphere unless otherwise specified. A 10-ml autoclave with magnetic stirrer was first dried in an oven at 110 °C overnight, then immediately placed into the glove box chamber. After keeping under vacuum for 1–2 h, the reaction vessel was put into the glove box under nitrogen atmosphere. The copolymerization of COS with PO described below is taken from entry 17 in Table 1 as an example. TU-1 (1.4 mg, 0.007 mmol) was added to the reactor firstly. PO (1.0 ml, 14 mmol) was then carefully added into the vessel. Afterwards, DBU (1.05 μl, 0.007 mmol) and BnOH (0.75 μl, 0.007 mmol) were added into the reactor, respectively. The reactor was sealed and then taken out for charging with the set amounts of COS. The copolymerization was performed at 25 °C for 24 h. Then, the reactor was cooled in ice-water bath, and the unreacted COS was slowly vented. An aliquot was taken from the resulting crude product for the determination of the PO conversion and the molar ratio of copolymer/cyclic products by 1H NMR spectrum. Traces of acetic acid were then added for 1H NMR spectrum, in order to prevent degradation of the crude product. Next, the crude product was quenched with HCl in ethanol (1 mol/l). The crude product was dissolved with CH2Cl2 and then precipitated in cold methanol. The product was collected by centrifugation and dried in vacuum at 40 °C until a constant weight.

### Characterization

1H and 13C NMR spectra were performed on a Bruker Advance DMX 400 MHz or 600 MHz spectrometer. And chemical shift values were referenced to TMS at 0 ppm for 1H NMR and 13C NMR. The number-average molecular weight (Mn) and molecular weight distribution (Ð = Mw/Mn) of the resultant copolymers were determined with a PL-GPC220 chromatograph (Polymer Laboratories) equipped with an HP 1100 pump from Agilent Technologies. The GPC columns were eluted with THF with 1.0 ml/min at 40 °C. The sample concentration was 0.4 wt. %, and the injection volume was 50 μl. Calibration was performed using monodisperse polystyrene standards. Matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) mass spectrometric measurements were performed on a Waters MALDI Micro MX mass spectrometer, equipped with a nitrogen laser delivering 3 ns laser pulses at 337 nm. Dithranol (97%, Alfa), was used as the matrix. CH3COOK ( ≥ 98%, Aladdin) was added for ion formation.

### Binding constant studies

Equations used for binding studies44:

$${\mathrm{For}}\,{\mathrm{dilution}}:\frac{{\delta _0 - \delta _i}}{{[A]_0}} = - 2K_{{\mathrm e}{\mathrm q}}(\delta _0 - \delta _i) + K_{{\mathrm e}{\mathrm q}}(\delta _0 - \delta _\infty )$$
(1)

where: δ0 is the chemical shift of the ortho-protons of pure TU-1; [A]0 is concentration of TU-1 or a base; δi is the chemical shift of the ortho-protons of TU-1 in the solution when [TU-1] = [base] = [A]0; δ is the chemical shift ortho-protons of the “pure complex” TU-1 with a base, (δ0 – δ) is a constant; Keq is the binding constant between TU-1 and a Base.

Following a similar procedure reported by Matthew K. Kiesewetter29, NMR dilution experiments were carried in CDCl3 with the concentration of [TU-1] = [base] varied from 0.01 M to 0.06 M in CDCl3. DBU and P2 were employed as bases respectively. The 1H NMR spectra was shown in Supplementary Fig. 24. The binding constants (Keq) were determined from the slope of the linear forms of the binding equation (above). And the error in Keq is exactly the error in the slope of the line, which can be determined from linear regression.

### Calculation of copolymer selectivity, PO conversion and TOF

Copolymer selectivity and PO conversion were calculated based on the 1H NMR spectrum of the crude product. Taking entry 11 in Table 1 as an example, spectrum of the crude product was showed in Supplementary Fig. 35. Protons with chemical shifts at 4.80, 3.52, 3.26 and 1.51 ppm belong to the methenyl (d), methene (e), and methyl (f) groups, respectively, the peaks in 5.16, 3.08, and 1.36 ppm [also seen in Supplementary Fig. 5, a purified PPTMC] belong to the methenyl (a), methene (b), and methyl (c) groups in the copolymer. And the area ratio of these two parts was taken as the copolymer selectivity. The corresponding peaks in 3.02, 2.77, and 2.46, 1.32 ppm belong to methenyl (h), methene (g) and methyl (i) in PO which was not consumed. On the base of 1H NMR spectra, we have:

$${\mathrm{Copolymer}}\,{\mathrm{selectivity}} = \frac{{A_{5.16}}}{{A_{5.16} + A_{4.82}}}\times 100\%$$
(2)
$${\mathrm{PO}}\,{\mathrm{conversion}} = \left( {1 - \frac{{A_{2.77}}}{{A_{5.16} + A_{4.82} + A_{2.77}}}} \right)\times 100\%$$
(3)

Thus,

$${\mathrm{TOF}}\,({\mathrm h}^{ - 1}) = {\mathrm{PO}}\,{\mathrm{conversion}}\times \frac{{[{\mathrm P}{\mathrm O}]/[{\mathrm L}{\mathrm B}]}}{t}$$
(4)

### Data availability

The authors declare that the data supporting this study are available within the paper and its Supplementary Information File. All other data is available from the authors upon reasonable request.