Introduction

Polycaprolactone (PCL) is a biodegradable, biocompatible and bioresorbable polymer that belongs to the family of aliphatic polyesters1,2. In past years, PCLs attract great attentions as well-known biomaterials with a plenty of applications in the fields of pharmacy, medicine, and biomedical engineering, including controlled-release drug delivery systems, absorbable surgical sutures, nerve guides, and three-dimensional (3-D) scaffolds3,4,5,6,7. PCLs are currently using as a promising target towards functionalized polymers8,9. PCLs are prepared by ring-opening polymerization of the cyclic monomer ɛ-caprolactone (CL) (Fig. 1), which can be obtained via cationic, anionic, or coordination mechanisms, depending on the catalytic system and the nature of active species6,10,11.

Figure 1
figure 1

Ring-opening polymerization (ROP) of the cyclic monomer ɛ-caprolactone (CL).

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A wide range of catalysts/initiators have currently been used to promote the ring-opening polymerization of cyclic esters, including metal alkoxide complexes12,13,14, organometallic complexes15,16,17,18,19, and even enzymes20 (see a number of comprehensive reviews6,10,11,21,22 for more details). Among them, Group 4 metallocenes are gaining great attention in the synthesis of functionalized polymers via block-copolymerization23,24,25,26, besides their industrial use for olefin polymerization21. Because of the fact that Group 4 metallocene catalysts have long been used in olefin polymerizations, current research aims to expand their potential use for the production of the biomaterial PCL, using a rational design27,28,29 or a new synthesis route such as cationic ring-opening polymerization (CROP)30.

Zirconocene/borate catalytic systems30 have previously been used as effective catalysts for CROP of cyclic monomers (e.g., oxazolines23,31, lactones24,25, cyclic carbonates26) and linear monomers (e.g., vinyl ethers32 and methyl methacrylate24). The main limitation of these catalytic systems for polymer synthesis is their practical use, as controlling polymer molecular weight distribution during cationic polymerization is challenging30. Further studies to understand these catalytic processes at the atomic scale could help design and improve the polymerization catalyst of cyclic esters.

Tuning ligand framework on the catalyst structure with a combination of different catalytic systems17,19,24,33 has been reported as a strategy to improve the CROP activity with controlled molecular weight. The first cationic zirconocene complex system for the CROP of cyclic esters was reported by Hayakawa et al.25,26. The quantitative polymerization of CL in toluene at room temperature or 60 °C was obtained with afforded monodisperse PCLs (Mw/Mn = 1.06–1.3). The best catalytic system was found for the methyl substituted ligand, (Me5Cp)CpZrMe2, as it polymerized CL with good control (Mw/Mn < 1.13, Mn,calcd ≈ Mn,GPC), and the molecular weight of the resulting PCLs increased with monomer conversion. They also suggested the higher catalyst efficiency as (Me5Cp)2ZrMe2 > (Me5Cp)CpZrMe2 > Cp2ZrMe2. Ten years later, a research group of Pitsikalis et al.24 reported the CROP of CL and δ-valerolactone using zirconocene catalytic systems with three different borate cocatalysts, B(C6F5)3, [B(C6F5)4]–[Ph3C]+ and [B(C6F5)4]–[Me2NHPh]+. In this work, three zirconocenes were introduced in the reaction, namely the bis(cyclopentadiene) ligand (Cp2ZrMe2), bis(indene) ligand (Ind2ZrMe2), and tertiary butyl substituted ligand ((tBuCp)2ZrMe2) and the high molecular weights PCL and narrow molecular weight distributions (Mn = 10,000–38,000 g/mol and Mw/Mn < 1.1) were obtained in a well-controlled manner. The catalyst performance was also reported as Cp2ZrMe2 < Ind2ZrMe2, and (tBuCp)2ZrMe2. The same research group also applied their catalytic systems for copolymerizations of other monomers such as methacrylate24, vinyl ether32 and 2-oxazoline23,31. The first mixed cyclopentadienyl-indenyl zirconocene, CpIndZrMe2, was used as a sole catalyst for the polymerizations of CL without adding any cocatalyst33. The resulting polymers yielded high quantitative outcome in terms of medium molecular weight polymers and moderate to broad polydispersities (Mn = 25,000–128,000 g/mol and Mw/Mn = 1.11–1.98). These experimental studies open the way to enhance catalyst activities, polymer yields and molecular weights of the zirconocene polymerization by ligand modifications.

A number of density functional theory (DFT) studies on the metallocene-initiated CROP of cyclic esters and related monomers have also been reported (see references therein34,35), which provided valuable aspects of DFT modeling and visualization of cationic mechanisms and molecular structures in complement to experimental observations. For example, the electronic and geometric properties of dimethylzirconocene catalysts were greatly influenced by the presence of the silicon-bridge and ancillary ligands19. The effects of ligand structure, solvent, and metal on the dimerization of dinuclear zirconocene cations have also been investigated with DFT36. We also studied the influence of ligand structure on the initiation and propagation steps of the trimethylene carbonate polymerization using the naked model approach17. The CROP process follows an active chain end (ACE) mechanism where propagating species are tertiary oxonium ions located at the chain end (Fig. 2)37,38. In brief, a precatalyst Cp2ZrMe2 is activated by a borate cocatalyst (e.g., B(C6F5)3, [B(C6F5)4]–[Ph3C]+ and [B(C6F5)4]–[Me2NHPh]+), via a methide abstraction (known as catalyst activation) and yields the ion-pair [Cp2ZrMe]+[AMe]– that is further separated into a cationic species Cp2ZrMe+ (C+) and a counteranion ([MeB(C6F5)3]– (1) and [B(C6F5)4]– (2)). The Cp2ZrMe+ is the active species in the polymerization process and that the propagation occurs through the ACE mechanism, where each propagating chain is initiated by a molecule of monomer (e.g. CL), corresponding to the initiation (or complexation, Cation → Complex) and propagation steps (Complex → R1 → P1), depicted in Fig. 2.

Figure 2
figure 2

Mechanism of CROP of CL using zirconocene/borate systems. Important species involved in the initiation and propagation mechanism, including isolated Cp2ZrMe+ and CL, monomer-activated complex, reactant, transition state and product, are also shown and labeled as Cation, Complex, Rn, TSn and Pn, respectively.

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Here, we employed the DFT modeling approach to study the effects of ligand structure through a series of zirconocene complexes (varying in steric hindrance and electronic properties) on the initiation and propagation. Their interactions with the boron cocatalysts on the rate-limiting step are analyzed in terms of the relative complex stability and the activation energies of the process. The structure–property relationship was then performed for the 54 zirconocene structures and the results were interpreted in terms of ancillary ligand, ligand substituents and bridge units. This study provides a better understanding of the structural characteristics of zirconocene catalysts in CL polymerizations.

Computational methods

All geometries were optimized without restraints in gas-phase using density functional theory (DFT)39,40 at the B3LYP level. This B3LYP is chosen because of its success in DFT modeling studies on similar processes7,13,17,35,41 and its lower activation energy compared to other DFT functionals (Figure S1 of Supporting Information, SI). Zirconium atoms were treated with the effective core potential double-ζ basis set (LANL2DZ)42 whereas all non-metal atoms (C, H, O, B, and F) with a double-ζ basis set, 6–31G(d). The DFT/mixed basis set method has been largely applied for transition metal complexes12,13,18,19,43. Harmonic frequency calculations were performed to confirm the transition states and local minima obtained and to determine the Gibbs free energy (G) at standard temperature and pressure (298.15 K and 101.325 kPa). Accurate free energies and molecular electronic properties (Mulliken population analysis, HOMO–LUMO energies, and dipole moment) were obtained at the CPCM(toluene)-B3LYP-D3(BJ)/6–311++G(d,p) (LANL2DZ) level using single-point calculations on the optimized structures, incorporating implicit solvation and dispersion correction. All calculations were carried out using the Gaussian 09/16 software29,44.

Results and discussion

In this study, we evaluated the effects of zirconocene structures on the process by means of DFT calculations. Initially, we considered five catalysts that have been previously reported for their CROP activities24,25 and dimeric properties36, namely Cp2ZrMe2 (C1), (Me5Cp)CpZrMe2 (C3), (Me5Cp)2ZrMe2 (H1), (tBuCp)2ZrMe2 (C4) and Ind2ZrMe2 (H16) (Fig. 3). These catalysts were selected for comparison purpose, and their properties vary in steric hindrance (C1, C3, H1, and C4) and electronic properties (C1 and H16). Their interactions with the two borate cocatalysts, [MeB(C6F5)3]– and [B(C6F5)4]–, in the initiation and propagation were analyzed for the activity of the process. Detailed information on how to obtain the structures of zirconocene/borate systems can be found in SI.

Figure 3
figure 3

Five zirconocenes included for the study of catalyst structure effect. Nomenclatures used for each catalyst (C1, C3, H1, C4 and H16) were assigned according to our recent DFT study on the zirconocene dimer properties36. The order of the dimer stability of these catalysts is C1 > C3 > H16 >  > H1 > C4.

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Catalyst structure influence on the process in the presence of cocatalyst

To evaluate the effects of zirconocene structures on the initiation and propagation using zirconocene/borate catalytic systems, five catalysts (C1, C3, H1, C4, and H16) that have been previously used in lactone polymerization24,25 were considered (see Fig. 3). Calculations of the initiation and propagation mechanisms were carried out using a similar procedure as previously reported in the literature17. Values of complexation energies for the Cation → Complex step (ΔGcom) and activation Gibbs energies for the first and second propagations (ΔGǂEa1 and ΔGǂEa2) using the five zirconocenes of three different catalytic systems (C+, 1 and 2) are also included in Table 1. The heatmap corresponding to the energy cross-correlation between the catalyst pair for the initiation, first and second propagations, as well as bar charts for the ΔGǂEa1 values are depicted in Figs. 4 and S4. The ion-pair interactions between the different catalyst cations and the cocatalyst anions, [MeB(C6F5)3]− and [B(C6F5)4]−, during the reaction were analyzed in terms of relative complex stabilities, activation free energies, and geometries, in comparison with the available experimental data.

Table 1 Values of complexation energies (ΔGcom, Cation → Complex) and the activation energies in the first and second propagations (ΔGǂEa1 and ΔGǂEa2), as calculated for the initiation and the first and second chain propagation steps for zirconocene cation, X (C+), X/MeB(C6F5)3ˉ (1) and X/B(C6F5)4– (2) systems (X = C1, C3, H1, C4 and H16).
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Figure 4
figure 4

Heatmap corresponding to the energy cross-correlation between the catalyst pair for the (a) initiation and (b) first propagation. (c) Bar chart showing activation free energies (ΔGǂEa1, kJ/mol) of the first propagation step using the selected catalysts (C1, C3, H1, C4 and H16) for the three catalytic systems (C+, 1, and 2).

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Relative complex stability and activation free energies

In the initiation step, a cationic complex is formed (Cation → Complex), which is hindered by the introduction of steric bulk, such as methyl and alkyl substituents, to the Cp ligands. This steric effect decreases the relative complex stability in the following order (Table 1; Fig. 4a): C1 > C4 > C3 > H1 for C+ (corresponding to the ∆Gcom values of − 98.0, − 95.7, − 93.5, and − 87.4 kJ/mol, respectively), C1 > C3 > C4 > H1 for 1 (− 158.5, − 145.0, − 140.0, and − 129.5 kJ/mol, respectively), and C1 > C4 > C3 > H1 for 2 (− 159.3, − 145.0, − 138.7, and − 126.0 kJ/mol, respectively). However, changing the ancillary ligand from Cp (C1) to Ind (H16) greatly increases the complex stability, with ∆Gcom values changing from − 98.0, − 158.5, and − 159.3 kJ/mol to − 122.3, − 183.6, and − 172.9 kJ/mol for C+, 1 and 2, respectively. Note that these ligand effects have previously been shown as dominant in the zirconocene-initiated CROP of trimethylene carbonate17. The green color shown in the heatmap (Fig. 4a) further indicates that both cocatalyst anions strongly stabilize the cationic complex species of this step.

For the chain propagation, the activation free energies generally follow a trend C+  > 1 ~ 2 (Table 1 and Fig. 4b): the calculated barriers, ΔGǂEa1, for C1, C3, H1, C4, and H16 ranged from 74.0–92.5 kJ/mol for C+ to 71.6–88.9 and 70.6–83.2 kJ/mol for 1 and 2, respectively. This effect is more profound for the second propagation (ΔGǂEa2: C+  > 1 > 2), which has lower barriers (ΔΔG =  ~ 4 to 22 kJ/mol) compared to the first propagation (ΔGǂEa1 > ΔGǂEa2 and positive ΔΔG, Table 1; Figure S4). The bar charts in Fig. 4c further show that the relative barrier heights, ΔGǂEa1, follow the order C1 < C3 < H1 for Cp2 ligand and C1 < H16 for Ind2 ligand, which account for the activity difference (e.g., Mn, Mw/Mn; Table S1) reported by Hayakawa et al.25 and Pitsikalis et al.24. These results emphasize the influence of steric hindrance and bulkiness of the catalyst structures, which can be used as an important factor for ligand modifications.

Geometric impact

The optimized transition-state structures (1-TS1 and 2-TS1) in the first propagation step of [X][MeB(C6F5)3]ˉ (1) and [X][B(C6F5)4]– (2) systems (X = C1, C3, H1, C4, and H16) are depicted in Figs. 5 and 6, respectively. Important geometric parameters for the first and second transition-state structures (TS1 and TS2) for the three catalytic systems (C+, 1, and 2) are included in Table 2. As expected, the ligand structure affects mainly the geometries around the catalytic center of the propagating chain end, with small changes in the Cα–Oα distance among the C+, 1, and 2 systems. The presence of the counteranion results in the elongation of the Cα–Oα bond by 0.02 Å, compared to that in the C+ system, and this bond becomes longer at TS1, with increasing of the methyl group on the Cp ligand (e.g., 2.049 Å at 1-TS1C1, 2.078 Å at 1-TS1C3, and 2.082 Å at 1-TS1H1). Similar trend was also found in the system 2 (Fig. 6). This is in agreement with the observed difference in the catalyst activity25.

Figure 5
figure 5

Optimized transition-state structures (1-TS1) in the first propagation step for different [X][MeB(C6F5)3]ˉ (1) systems (X = C1, C3, H1, C4 and H16). Atoms in the top view are shown in the ball-and-stick model. All distances are in Å. Imaginary frequencies for each TS are also indicated. Atomic definitions discussed in the text are also given in the figure.

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Figure 6
figure 6

Optimized transition-state structures (2-TS1) in the first propagation step for different [X][B(C6F5)4]– (2) systems (X = C1, C3, H1, C4 and H16). Atoms in the top view are shown in the ball-and-stick model. All distances are in units of Å. Imaginary frequencies for each TS are also indicated. Atomic definitions discussed in the text are also given in the figure.

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Table 2 Selected geometric parameters (Å) from the transition-state structures (TS1 and TS2) for the naked cation (C+), [C+][MeB(C6F5)3]– (1) and [C+][B(C6F5)4]– (2) systems for different catalyst structures.
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The steric effect on the ligand structure is greater in C4, which has steric crowding on its Cp ligand. This limits a cocatalyst access near the Cα atom of the propagating chain end, as evidenced by the longest Cα-B distance of 7.2 Å (see 1-TS1C4 in Fig. 5), compared to that in other systems.

There is a clear trend between the Zr-B distances and the steric degree on the Cp′ ligand, with Zr-B being significantly increased in the TS2 for bulkier Cp′ ligands, i.e., H1, C4, and H16. For example, the catalyst H1, bearing a highly steric congestion on both Cp′ rings, yields the highest Zr-B distances of ~ 8.5 to 9.5 Å for both 1 and 2 (see Zr-B in Table 2). At 1-TS1, Zr-B and B-Cα distances decrease in the order C1 > H1 > H16 > C3. Overall, the results show that the size and shape of the Cp′ ligand could complicate the interactions between the boron cocatalyst and the catalyst.

Structure–properties relationship

To find any factors that could account for the activation barriers of those five catalysts shown in Fig. 4c, we analyzed several electronic and geometric parameters, including HOMO–LUMO energies, atomic charge, and distances (M-Cen and Cα–Oα) involved in the catalytic center and the results are collected in Table 3. The Mulliken charges (q) of the metal center were analyzed at the Complex species and we found that the positive charge on the Zr atom correlates well with the observed activity difference of the Cp′ catalysts (C1, C3, and H1), i.e. the higher the charge on the Zr metal (q, C1 < C3 < H1), the higher the activation energies (Ea1, C1 < C3 < H1). Similar trends have been reported previously for styrene polymerization by a rare-earth-metal catalyst45. This is related to the donor–acceptor interaction between the ligand and the metal46 as can be seen from the longer distances between the Zr atom and the centroid of the Cp ring (Zr-Cen = 2.246, 2.274, and 2.289 Å in 2-C1, 2-C3, and 2-H1, respectively, Table 3). There are significant trends between the energy gaps and the number of the methyl group on the Cp ring of the catalyst (ΔE values in Table 3) as well as those between the activation energies (Ea1) and the Zr-Cen distances, atomic charge, and ΔE values (Figure S5).

Table 3 Calculated Mulliken atomic charge (q, in unit of e) on Zr atom and HOMO and LUMO energies (EHOMO and ELUMO, au)a of Complex and energy gaps (ΔE, au)a between the HOMO of CL and the LUMO of Complex for the naked cation (C+) and [X][A¯] systems (X = C1, C3, H1, H16, C4; A−  = [MeB(C6F5)3]− (1) and [B(C6F5)4]− (2)). Values of Zr-Cen and Cα-Oα distances were also included.
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To evaluate further whether the naked cation model could be a representative of the metallocene/borate system, we compared the two activation Gibbs energies of the rate-limiting step among the three catalytic systems (Fig. 7). We observed significant correlations between the activation energies, Ea1, from the naked model and the full models of [B(C6F5)4]– and [MeB(C6F5)3]– containing systems, with R2 of 0.6468 and 0.6905, respectively. These relationship analyses further suggest us that it is possible to use the naked cation approach as a pre-screening strategy for catalyst design for CROP of cyclic ester.

Figure 7
figure 7

Relationship between the two activation Gibbs energies (ΔGǂEa1) obtained from different catalytic model systems: (a) naked model vs B(C6F5)4; (b) naked model vs MeB(C6F5)3 and (c) MeB(C6F5)3 vs B(C6F5)4. Values are in units of kJ/mol. C1 is an outliner, which does not include in the equation.

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Catalyst design with the naked model

Previous structure–activity relationship studies have proven that structural and electronic properties of metallocene catalyst can be tunable by quantum chemistry calculations for CROP17,18,19,36 and olefin polymerization27,28,47,48. As the results shown above for a small set of zirconocenes, the naked cation approach could be used as a simple strategy in pre-screening a large data set of compounds for candidate catalysts (Fig. 8). To expand the data set, we employed a larger data set of 54 zirconocene structures and used them for in silico pre-screening calculations with the naked model. We also used the same energetic parameters previously described for the CROP activity, i.e., ΔGcom for the relative complex stability (Cation → Complex) and Ea1 for the activation energy in the first propagation step (R1 → TS1). From this data set, 29 optimized structures were taken from our previous study16 and additional 25 structures were built and optimized, leading to a total of 54 catalyst structures. Nomenclature of each catalyst structures (Cn and Hn) was assigned in a similar fashion as previously reported by Karttunen et al.48 where Cn and Hn represent the available crystallographic structures and in silico design, respectively. The resulting structures and energetics as well as electronic properties for the 54 zirconocenes are collected in Tables S2 and S3. Bar charts showing the ∆Gcom and Ea1 values are plotted in Fig. 9. Using the C1 energies as a reference, it is clear that both ancillary Cp′ ligand and ligand/fluorine substitutions significantly alter the ∆Gcom and Ea1 values, and the latter has a strong effect. Other structural and electronic characteristics of zirconocene catalysts in CL polymerizations were described as ancillary ligand, ligand substituent and bridge below.

Figure 8
figure 8

Schematic ligand structures of the studied zirconocenes.

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Figure 9
figure 9

Bar chart showing (a) complexation energies, ∆Gcom, and (b) activation free energies of the first propagation (Ea1) for different catalyst ligands. The energies of C1 (∆Gcom = − 98.0 kJ/mol and Ea1 = 74.5 kJ/mol) are indicated with dashed lines.

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Effect of ancillary Cp′ ligand

The effect of Cp′ ligands on electronic and steric properties of the complexes can be seen by considering the three Cp′ ligands (Cp, Ind, Flu). Given the data in Tables S2 and S3 and Fig. 9, it is seen that changing Cp into more electron-rich ligand Ind or Flu clearly affects both electronic and steric nature of the catalyst in the process. This type of modification has a greater effect on the complex formation (up to 29 kJ/mol) as it increases the complex stability with a trend C1 ≈ C15 < H16 < H22 (corresponding to the ∆G values of − 98.0, − 97.9, − 122.3 and − 127.3 kJ/mol, respectively, Table S2). However, this effect yields a slight increase in the Ea1 values in the order: C1 (74.5 kJ/mol) < C15 (77.4 kJ/mol) < H16 (80.7 kJ/mol) < H22 (80.8 kJ/mol). These results are in-line with our previous study17 and support the slower kinetics observed for larger ancillary ligands24.

The changes in electronic properties due to the larger ancillary ligands can be seen from the atomic charge and HOMO–LUMO energies. The positive charges of Zr atoms become higher as the reaction proceeds from Cation to Complex (Cation/Complex): C1 (1.537e−/1.861e−), C15 (1.807e−/1.893e−), H16 (1.672e−/2.007e−), and H22 (1.647e−/1.886e−). The HOMO energies are strongly perturbed, with the Cation species being most affected (Figure S6a). This ancillary effect also shows a trend with ∆EHOMO-LUMO values at Complex and R1 (Figure S6b). The electronic origin of this modification is evident in the complexation energies of H16 and H17 (− 122.3 vs − 85.1 kJ/mol, respectively). The loss of a benzene ring in H16 into a cyclohexane in H17 creates a steric clash between the cyclohexane ring and the methylene carbon of the CL monomer (Figure S7). However, this effect is insignificant to the activation barrier of the first propagation (80.7 vs 79.9 kJ/mol for H16 and H17).

Effect of ligand substituent

The substituent effects were analyzed by considering three different ligands (Cp2, Ind2, or CpInd) substituted by methyl, alkyl, or phenyl groups. The methyl substituents significantly decreased the relative stability of the complex, with C1 (− 98.0 kJ/mol) compared to C3 (− 93.5 kJ/mol) and H1 (− 87.4 kJ/mol). The effect also raises the activation free energies up to ~ 15 kJ/mol when comparing C3 to H1 and C7 to C10 (Fig. 9b; Table S3). This can be explained by the electron-donating ability of the methyl substituent. The alkyl substituents also had the same effect, i.e., destabilized the complex and increased the activation energies. The effects of the alkyl group, however, are more complicated than those of methyl groups, as steric crowding might limit monomer access depending on their location on the Cp′ ring. This can be seen in C2, H2, and C4 (Figures S8, S9). For example, C2 has four possible conformations (namely, C2[1,2′], C2[1,3′], C2[1,4′], and C2[1,5′]), and their relative stabilities slightly differ upon steric repulsion with respect to the monomer (Figures S10–S13). The relative stability of the complex follows the trend C2[1,3′] < C2[1,2′] < C2[1,5′] < C2[1,4′] (Figure S10), while this trend is C2[1,5′] < C2[1,3′] < C2[1,4′] < C2[1,2′] for activation energies of the first propagation (Figure S13). A longer linear alkyl chain leads to a more stable complex, while the effect becomes stronger for the branch alkyl group (C2, H2 vs C4, Figure S8). The complexation and activation energies are higher, up to ~ 25 and ~ 20 kJ/mol (C4 vs H2, Figs. 9 and Figs. S8, S9), respectively. Overall, the alkyl substituents containing longer or steric ligands would lower the stability of the complex and raise the activation energies of the propagation.

The phenyl substituent destabilizes the complex and increases the activation energy, which varies depending on the position of the phenyl group. It is expected that the electron-donating ability of the phenyl group would make the cation less reactive towards the coordination of the monomer. This effect is observed in H16, C20, H19, and H20 (Figures S14, S15), with relative complex stability decreasing as 4-phenyl (H20; − 114.4 kJ/mol) > 3-phenyl (H19; − 95.3 kJ/mol) > 2-phenyl (C20; − 92.8 kJ/mol), and activation energies increasing as 3-phenyl (H19; 70.1 kJ/mol) < 2-phenyl (C20; 78.9 kJ/mol) < 4-phenyl (H20; 89.4 kJ/mol). Similar effects can be found for the CpInd ligand (see H9, H10, and H14 in Figures S16, S17): the complex stability decreases as 4-phenyl (H14) > 3-phenyl (H10) > 2-phenyl (H9), whereas activation energy increases as 2-phenyl (H9) < 3-phenyl (H10) < 4-phenyl (H14). When electron-withdrawing fluorine (F) is introduced into the phenyl substituent, it significantly affects the activation energies when comparing C20 and C21: their relative energies of ∆Gcom and Ea1 differ by ~ 5 and ~ 12 kJ/mol, respectively. The data in Fig. 9b also indicates that H19 and H21, bearing 3-phenyl (indene) and 3-(3,5-di(trifluoromethyl)phenyl)indene ligands, exhibited the lower Ea1 values (70.1 and 69.4 kJ/mol) compared to that for C1.

Effect of bridge

The effect of bridge can be seen by comparing C1 to C5, C6, H4, H6 and C14, C3 to C7 and C8, H1 to C10, C11, C12, and C13, H16 to H18, C22, and C18, H22 to C24 and H23, and others (H2 vs H3, C15 vs C16, H7 vs H8, H10 vs H13, and H24 vs H25). As in other ligand effects, the bridge ligands generally destabilize all intermediates, leading to the lower stabilization to the complex and the higher activation energies to the first propagation. Longer bridge ligands also show similar effects, as can be seen in C1, C5, and C14 for Cp2 ligand or H16, C22, C18 for Ind2 ligand (Figure S18). This can be explained from the structural constraint found along the reaction intermediates, which can be justified from the Cen–Zr–Cen (α) and Cen–Cen (β) angles where Cen is the centroid of the Cp′ ring. We analyzed these angles for all 54 catalysts and found three different clusters (Fig. 10): carbon bridge ligands (8 catalysts; cluster I), non-carbon bridge ligand (Si, Ge, P; 21 catalysts; cluster II) and unbridged ligands (25 catalysts; cluster III). All these data can be found in Tables S2 and S3. The cluster I show more open structures of catalyst, which was characterized by the highest β values of around 69°–75°. This can be rationalized from the smallest atomic radius of bridging carbon compared with the other atoms (Si, Ge, P). Cluster II also shows similar characteristics of the bridged ligand but to a lesser extent (β ~ 55° to 65° and α ~ 122° to 132°). The cluster III is the largest members representing the unbridged ligands, with a narrow Cp–Cp structure (β ~ 34° to 55° and α ~ 131° to 142°). Excellent linear correlation (R2 = 0.91668) is found when plotting between the α and β angles at Cation and the values are significantly reduced when going to Complex and R1 (Fig. 10).

Figure 10
figure 10

Correlation between the Cen-M-Cen (α) and Cen–Cen (β) angles in all catalyst structures at different intermediate species: (a) Cation, (b) Complex, and (c) R1. Three clusters I–III of zirconocenes can be classified, according to the α/β angles, and are shown in black, red and blue, respectively.

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Furthermore, bridge ligands can be used for selective coordination of monomers, particularly for CpInd ligands. They can be used for selective insertion from either a five-membered or a six-membered ring. Comparing C15 (unbridged) with C16 (bridged), the unbridged case shows similar energetics for both insertions C15(5) and C15(6) (− 98.0 vs − 97.9 kJ/mol for ∆Gcom and 76.1 vs 77.4 kJ/mol for Ea1, respectively). However, due to the bridge, complex formations with the five-membered insertion of C16(5) are 26 kJ/mol more stable than those with the six-membered insertion of C16(6), while the activation energy remains unchanged (76.0 vs 74.1 kJ/mol for C16(5) and C16(6), Figure S19).

Despite the destabilizing effect by the bridge, there is an exception when the Cp′ ligand substituted by the electron-donating group. This can be seen in H3, which possess butyl substituent on the Cp ring and a silicon bridged atom, is found to exhibit the lower activation energy (69.9 kJ/mol) compared to that of C1 (Fig. 9b). Overall, the results indicate that the catalytic performance relies not only on the catalyst structure but also on the electronic nature of the ligand, which has a profound effect on the reaction performance.

Conclusion

We present a structure–property relationship in the CL CROP reaction on the 54 zirconocene structures using DFT calculations. Catalyst structure effect is then investigated as an important factor for tuning the CROP activity, which is analyzed in terms of ancillary ligands, ligand substituents, and bridging units. The polymerization was confirmed to proceed via a cationic mechanism where the ring opening taking place via alkyl-bond cleavage. The activation free energies calculated for the insertion of the first monomer into the Cα–Oα bond within the CL ring for C1, C3, and H1 does correlate with the observed difference in the catalyst activity reported experimentally. The calculations also show that ligand substituent has a dominant effect to the reaction, especially the electron-donating groups of alkyl and phenyl substituents. The ancillary ligands showed a direct effect on electronic energies, while the bridges are mainly responsible for the catalyst geometry leading to a decrease in the complex stability and an increase in the activation energy of the propagating step. From the structure–property analysis, we demonstrate that the naked model approach can be applied to prescreen catalyst candidate for the CROP process. Overall, this study contributes to a better understanding of the structural characteristics of metallocene catalysts in CL polymerizations, paving the way for further investigations and advancements in this field.