Polymer Chemistry

Polymer Chemistry PAPER

Cite this: Polym. Chem., 2013, 4, 3077

Ring-opening polymerization of racemic b-butyrolactone promoted by rare earth trisborohydride complexes towards a PHB-diol: an experimental and DFT study† Sophie M. Guillaume,*a Liana Annunziata,a Iker del Rosal,b Christophe Iftner,b Laurent Maron,*b Peter W. Roesky*c and Matthias Schmidc The ring-opening polymerization (ROP) of racemic b-butyrolactone (BL), catalyzed by the homoleptic

Received 13th January 2013 Accepted 5th February 2013

lanthanide trisborohydride complexes, [Ln(BH4)3(THF)3] with Ln ¼ La, Nd, and Sm, is reported, together with a DFT study of the polymerization mechanism. Well-defined atactic a,u-dihydroxytelechelic poly(3hydroxybutyrate)s (PHBs), PHB diols, are thus synthesized (Mn up to 8000 g mol1, 1.02 # Ð # 1.10) as

DOI: 10.1039/c3py00056g

evidenced both experimentally and computationally. DFT investigations also emphasize the lack of

www.rsc.org/polymers

stereoselectivity of the catalyst although a high activity is energetically evidenced.

Introduction Poly(b-hydroxyalkanoate)s (PHAs) are biocompatible and biodegradable aliphatic polyesters that are naturally produced by many bacteria as an intracellular carbon and energy compound. PHAs have attracted many academic and industrial interests as they are suitable for environmental and biomedical applications such as ne chemicals, biofuels, bulk commodity bioplastics, implant biomaterials or nanocarriers for drug delivery.1 Poly(3-hydroxybutyrate) (PHB), the most common biological PHA produced by various microorganisms, is a perfectly isotactic (structure with only the (R)-conguration), highly crystalline thermoplastic polymer. Alternatively, PHAs can be chemically synthesized by ring-opening polymerization (ROP) of four-membered ring b-lactones.2 Recent efforts have been especially aimed at the controlled stereoselective synthesis of well-dened PHBs from the coordination–insertion ROP of b-butyrolactone (BL) promoted by discrete metal complexes. a Institut des Sciences Chimiques de Rennes, CNRS – Université de Rennes 1 (UMR 6226), Organometallics: Materials and Catalysis, Campus de Beaulieu, 35042 Rennes Cedex, France. E-mail: [email protected] b

Laboratoire de Physique et Chimie de Nano-Objets, Université de Toulouse, INSA and CNRS, UMR5626 (IRSAMC), 135 Avenue de Rangueil, F-31077 Toulouse, France. E-mail: [email protected]

c Institut f¨ ur Anorganische Chemie and Helmholtz Research School: Energy-Related Catalysis, Karlsruher Institut f¨ ur Technologie (KIT), Engesserstr. 15, 76128 Karlsruhe, Germany. E-mail: [email protected]

† Electronic supplementary information (ESI) available: Additional 13C DEPT NMR spectrum of a H–PHB–H produced from [La(BH4)3(THF)3], a view of the different transition states and intermediates as well as the key geometrical parameters corresponding to Fig. 9, are available in Fig. S2 and S3 and Table S1, respectively, along with all Cartesian coordinates. See DOI: 10.1039/c3py00056g

This journal is ª The Royal Society of Chemistry 2013

This approach allows ne tuning of the PHB microstructure and macromolecular architecture. End-group delity, predictable w/M n) values are molar mass and narrow dispersity (ÐM ¼ M highly desirable, as well as a living process, enabling access to block copolymers.2 In particular, a,u-dihydroxytelechelic PHBs, PHB-diols, have been targeted as precursors to triblock polyester,3 polymethylmethacrylate4 or polyurethane5 copolymers. Such PHB-diols were initially synthesized by anionic ROP of BL using a 4-hydroxybutanoic acid sodium salt/18-crown-6 complex as an initiator followed by termination with a bromo-alcohol, or by a tin catalyzed transesterication procedure from high molar mass polymers with ethylene glycol.6 The end-groups observed were primary hydroxyl groups, secondary hydroxyl groups or crotonic esters, as evidenced from 1H NMR and electrospray ionization tandem mass spectrometry analyses. The rare earth borohydride catalyzed ROP of cyclic esters pioneered by Guillaume et al. has been quite developed over the past decade.7 Such complexes feature BH4 ligand(s) in which hydrogen atoms are bridging the metal center and the boron atom(s). The signicant advantage of such a borohydride-based route was demonstrated, by combined extensive experimental and computational evidences, to directly afford, without any post-polymerization chemical modication, a,udihydroxytelechelic polyesters.7,8 Given the high potential of such polyester diols in macromolecular engineering,9 several cyclic esters including in particular larger-size more easily polymerizable cyclic monomers such as lactones (3-caprolactone,8,10 d-valerolactone,11 u-pentadecalactone),12 diester (lactides),9e,11b,13 or carbonate (trimethylene carbonate)14 have been studied.7 Only recently, the related isospecic ROP of the smaller and less prone to polymerize racemic b-butyrolactone (rac-BL), was reported using silica-supported rare earth

Polym. Chem., 2013, 4, 3077–3087 | 3077

Polymer Chemistry

Paper

trisborohydride complexes, SiO2@[Ln(BH4)3(THF)3] with Ln ¼ La and Nd.15 The latter were shown to be more stereoselective than the homogeneous parent (unsupported) catalysts, [Ln(BH4)3(THF)3]. Atactic PHB was also briey reported from linked bis(amide) yttrium borohydride complexes.13c However, the data remained limited and the nature of the PHB chainends was not addressed.13c,15 In the present contribution, we report the controlled ROP of rac-BL promoted by the homoleptic complexes, [Ln(BH4)3(THF)3] with Ln ¼ La (1), Nd (2), and Sm (3) (Fig. 1). Formation of atactic PHB-diols is evidenced through detailed spectroscopic analyses of the recovered PHBs and further supported by DFT investigations of the reaction mechanism.

Results and discussion Synthesis and characterization of a,u-dihydroxytelechelic poly(3-hydroxybutyrate) The homoleptic trisborohydride complexes [Ln(BH4)3(THF)3] with Ln ¼ La (1), Nd (2), and Sm (3), the simplest rare earth borohydride complexes, have been demonstrated to efficiently promote the ROP of polar monomers among which are cyclic esters.7–14 All three borohydrides 1–3 were screened for their ability to ring-open polymerize rac-BL at room temperature with [rac-BL]0 : [BH4]0 ratios of 100–300. The most signicant results are gathered in Table 1 (entries 3–21) in comparison to available literature data (entries 1–2).15 The three complexes 1–3 polymerized rac-BL in THF or toluene without any noticeable inuence of either the nature of the metal center or of the solvent. Note that in some cases, THF (polar) was found to somewhat slow down the ROP of a cyclic ester in comparison to a non-coordinating solvent such as toluene, as a result of its competing ability to coordinate to the metal center versus the polar monomer.7a At a [rac-BL]0 : [BH4]0 ratio of 100, the ROP of rac-BL promoted by 1–3 proceeds for 18–24 h (Table 1, entries 3–21). The ROP of BL is indeed known to proceed more slowly than that of larger lactones.2,7,8 Typically, the controlled ROP of 3-caprolactone (CL), a monomer with a favorable polymerization enthalpy,2a catalyzed by 3 gives, under similar operating conditions (CH2Cl2–toluene: 30/70 v/v, 21 C, [3]0 ¼ 2.4–3.5 mmol L1, [CL]0 : [BH4]0 ¼ 108–157), a quantitative conversion within 10 minutes.8c Attempts to foster the ROP of rac-BL initiated by 1–3 upon increasing the reaction temperature up to

Fig. 1 Rare earth trisborohydride complexes investigated [Ln(BH4)3(THF)3] with Ln ¼ La (1), Nd (2), and Sm (3).

Table 1

ROP of rac-BL promoted by [Ln(BH4)3(THF)3] with Ln ¼ La (1), Nd (2), and Sm (3)

Entry

[Ln]a

[rac-BL]0/ [BH4]0b

Solvent (mL)

Temp. ( C)

Timec (h)

Conv.d (%)

Mn,theoe (g mol1)

Mn,NMRf (g mol1)

Mn,SECg (g mol1)

ÐMg

1 (ref. 15) 2 (ref. 15) 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 2 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3 3

33 33 100 100 100 100 200 300 33 100 100 100 100 200 300 100 100 100 100 200 300

Toluene Toluene THF (0.5) THF (0.5) Toluene (0.5) Toluene (0.5) Toluene (1) Toluene (1) THF (0.5) THF (0.5) THF (0.5) Toluene (0.5) Toluene (0.5) Toluene (1) Toluene (1) THF (0.5) THF (0.5) Toluene (0.5) Toluene (0.5) Toluene (1) Toluene (1)

20 20 25 50 25 60 25 25 25 25 50 25 60 25 25 25 50 25 60 25 25

24 24 24 18 23 18 48 92 24 24 18 23 18 48 92 23 18 23 18 48 72

91 100 75 67 100 43 39 31 98 83 84 100 74 32 31 80 73 100 72 38 22

2600 2900 6450 5750 8600 3700 6700 8000 2850 7150 7200 8600 6350 5500 8000 6900 6300 8600 6200 6550 5700

nd nd 6100 4400 6400 3800 6400 6750 2300 5420 5800 6300 5300 6400 7900 4300 4600 5900 5300 6700 4200

2700 3100 8200 7100 9500 5500 9000 8540 3700 7700 7450 7200 6050 7100 9700 7050 8100 5250 7350 8200 8300

1.75 1.83 1.07 1.07 1.06 1.10 1.09 1.10 1.23 1.07 1.07 1.06 1.08 1.03 1.03 1.07 1.04 1.03 1.06 1.02 1.09

a [Ln] ¼ [Ln(BH4)3(THF)3]. b 3[BH4]0 ¼ [Ln(BH4)3(THF)3]0. c The reaction time was not necessarily optimized. d Determined by NMR analysis of the crude reaction mixture. e Calculated from the relation: [BL]0/[BH4]0 conv.BL MBL with MBL ¼ 86 g mol1. f Determined by NMR analysis of the isolated polymer, from 1H resonances of both terminal groups (refer to experimental section). g Determined by SEC in THF at 30 C vs. polystyrene standards (uncorrected values).

3078 | Polym. Chem., 2013, 4, 3077–3087


Paper

Fig. 2

Polymer Chemistry

1

H NMR (500 MHz; CDCl3, 298 K) spectrum of a PHB produced from [La(BH4)3(THF)3] (Table 1, entry 4; * stands for residual monomer).

60 C remained unsuccessful (Table 1, entries 5, 10, 12, 16, 18 vs. 6, 11, 13, 17, 19, respectively). The molar mass values, as determined by 1H NMR analysis of a crude reaction aliquot (Mn,NMR; refer to the Experimental section) and by size exclusion chromatography (SEC; Mn,SEC) of the precipitated PHBs, were in fair agreement with the ones calculated (Mn,theo) based on one growing polymer chain per active Ln–BH4 polymerization site, i.e. three growing chains per metal center. Although the preparation of high molar mass PHBs was not the main objective of the present work rather aimed at mechanistic investigations, higher molar mass PHBs (Mn up to 8000 g mol1) than previously reported from these same rare earth trisborohydrides (Mn up to 3100 g mol1)15 or from the other rare earth borohydride catalysts investigated in the ROP of BL (Mn up to 4600 g mol1) were obtained.7a,13c These were in the same range as those obtained for PHBs (Mn up to 10 000 g mol1) prepared from 1,4butanediol and distannoxane as the catalyst.3a The dispersity data measured by SEC were fairly narrow (ÐM ¼ Mw/Mn < 1.10, Table 1, entries 3–21) and much narrower than the ones previously reported (ÐM ¼ 1.75–1.83, Table 1, entries 1 and 2;15 ÐM ¼ 1.15–1.30).13c,16 This observation suggests an initiation step faster than the propagation and a limited extent of transesterication side reactions that are commonly observed in ROP of cyclic esters.7a The controlled character of the polymerization was further conrmed by a second-feed experiment resulting in a polymer chain extension. A PHB sample with Mn,SEC ¼ 2300 g mol1, ÐM ¼ 1.23 was rst prepared by complete ROP of 100 equiv. of rac-BL with 2 at 25 C over 8 h ([rac-BL]0/[BH4]0 ¼ 33; rac-BL conversion ¼ 98%; Mn,theo ¼ 2850 g mol1). The polymerization was next resumed by subsequent addition of 200 equiv. of rac-BL to give PHB with Mn,SEC ¼ 2700 g mol1, ÐM ¼ 1.20 ([rac-BL]0/[BH4]0 ¼ 67; rac-BL conversion ¼ 72%; Mn,theo ¼ 6900 g mol1). All these results indicate some “living” character of the ROP of rac-BL promoted by the rare earth trisborohydride complexes.


Careful analysis of the polymer microstructure by 1H and 13C NMR revealed two hydroxyl end functionalities as illustrated in Fig. 2 and 3, respectively. Indeed, the hydrogen resonances typical of a CH2OH (d1H 4.12 ppm, d13C 62.09 ppm) and CH(CH3) OH (d1H 4.20, 1.24 ppm, d13C 64.5, 22.5 ppm, respectively) groups were clearly observed. Besides, the adjacent penultimate protons and carbons of these chain-end groups, OCH(CH3) CH2CH2OH and C(O)CH2CH(CH3)OH, were unambiguously identied. The 13C DEPT NMR spectrum of PHB-diol samples further conrmed the previous assignments of the polymer chain termini (Fig. S1 in ESI†). In addition to the most intense resonances of the polymer backbone, a series of lower intensity resonances were observed that were assigned to OCH(CH3)CH2 (d 64.1 ppm), CH2OH (d 61.5 ppm), OC(O)CH2 (d 43.3 ppm), CH2CH2OH (d 34.6 ppm), and OCH(CH3)CH2 (d 22.4 ppm) (labeled b, e, g, c, f, a, d, respectively). For all initiators, the Pm (probability of meso enchainment between monomer units) measured by NMR analysis of the recovered PHBs was within the same range (Pm 0.56 (1), 0.54 (2), and 0.52 (3)) suggesting the formation of atactic polyester in agreement with previous ndings (Pm 0.50).15 Formation of PHB diols was further conrmed by MALDIToF mass spectrometry analysis of a low molar mass PHB sample (Mn,SEC ¼ 3300 g mol1) prepared from [Nd(BH4)3(THF)3] (2), as it is obtained for example in Table 1, entry 9. The spectrum featured a major distribution of peaks unambiguously assignable to H–PHB–H molecules cationized by Na+ ions (H–PHB–OCHMeCH2OH$Na+) with a repeat unit of 86 g mol1 (i.e., the molar mass of rac-BL; Fig. 4). The most intense signal detected, m/z: 2351.0 g mol1, corresponds to the sodium species H–[BL]26–OCHMeCH2OH$Na+ containing 26 monomer units (calculated isotopic mass for 12 C1081H16623Na116O54: 2350 g mol1) and hydroxyl end-groups. This observation matches the molar mass value determined by NMR (Mn,NMR ¼ 2300 g mol1), as well as the calculated data. Polym. Chem., 2013, 4, 3077–3087 | 3079

Polymer Chemistry

Fig. 3

13

Paper

C{1H} NMR (125 MHz, CDCl3, 298 K) spectrum of a PHB produced from [La(BH4)3(THF)3] (Table 1, entry 4).

Fig. 4 MALDI-ToF mass spectrum of a PHB sample produced from [Nd(BH4)3(THF)3] (2) (see as example for low molar mass PHB, Table 1, entry 9) and a zoomed region with the corresponding simulated spectrum (bottom). The major population corresponds to macromolecules ionized by Na+.

This clearly demonstrated that 2 acted as an effective initiator in the ROP of rac-BL and that the BH4 group indeed reduced the adjacent carbonyl function, ultimately affording a,u-dihydroxytelechelic PHB. Based on these analytical evidences of PHB-diols, and in light of our previous extensive investigations (both analytical and computational) on the ROP of related cyclic esters promoted by such rare earth borohydride complexes,7a,8,9a the ROP mechanism of rac-BL involving two successive BH activations can be proposed as depicted in Scheme 1. The initiation step involves rst the displacement of THF upon coordination of rac-BL to give [Ln(BH4)3(BL)3], i, followed by the hydride transfer to the adjacent carbonyl carbon and the BH3 transfer to the oxygen to form ii (rst BH activation), and nally the ringopening of the BL unit via oxygen–acyl bond cleavage with a second hydride transfer onto the same carbon to afford species

3080 | Polym. Chem., 2013, 4, 3077–3087

iii. Subsequent propagation goes on from this active rare earth alkoxide species. Ultimately, upon hydrolytic termination/ deactivation, the ketone is reduced while the Ln–O bond is

Scheme 1 ROP of a rac-BL initiated by a rare earth metal trisborohydride complex [Ln(BH4)3(THF)3]: synthesis of a,u-hydroxy telechelic PHB.


Paper

Polymer Chemistry

hydrolyzed, thus affording a,u-dihydroxytelechelic PHB. This mechanism which is reminiscent to that of the ROP of 3-caprolactone by such borohydride complexes,7a,8,10 has been further supported by DFT investigations. DFT studies of the ROP of b-butyrolactone promoted by [La(BH4)3(THF)3] (1) In order to support further the analytical evidences and to gain a better understanding of the mechanism, the ROP of rac-BL promoted by [Ln(BH4)3(THF)3] has been computed at the Density Functional Theory (DFT) (B3PW91) level of theory using the lanthanum complex 1. Initiation step of the ROP of rac-BL mediated by [La(BH4)3(THF)3] (1). The b-substitution of one hydrogen atom by a methyl group in b-butyrolactone leads to two enantiomeric BL-R and BL-S compounds. For the sake of a tractable analysis, the study of the ROP of both enantiomers is separately considered, starting with the BL-R enantiomer. In the same way, the prochirality of the C atom of the C]O bond leads to two different enantiofaces, re and si, of the enolate bond of the BL-R and BL-S monomers, labeled hereaer BL-R(R), BL-R(S), BL-S(R) and BL-S(S), respectively (Fig. 5). In order to understand the ROP mechanism of rac-BL, we have theoretically studied the ROP initiation step of both enantiomers, involving the nucleophilic attack of BH4 on each enantioface of both enantiomers. As the mechanism is a classical coordination–insertion one involving borohydride complexes, the main focus is placed on the energetic of the reactions as well as on the selectivity.

Fig. 5 Representation of the re (R) and si (S) enantiofaces of BL-R and BL-S monomers.

Fig. 6

The free Gibbs energy prole of the initiation step of the ROP of BL-R is depicted in Fig. 6. A view of the different transition states and intermediates is available in Fig. 7 and 8. The key geometrical parameters are summarized in Table 2. The rst stage of the process, as already mentioned in the literature, involves the displacement of THF upon coordination of BL-R. This displacement is exoergic by 2.4 kcal mol1 and produces the complex [La(BH4)3(THF)2(BL-R)] (AR). Subsequently, starting from AR, the nucleophilic attack of borohydride to the carbonyl carbon CCO of BL-R can take place either on the re (TS(AR / BRR)) or the si (TS(AR / BSR)) enantiofaces. These attacks yield a second intermediate (BRR and BSR, respectively, for the nucleophilic attack on the re and si enantiofaces of BL-R) with an energy barrier of 14.5 and 14.0 kcal mol1 with respect to the entrance channel. The formation of BRR and BSR are found to be endergonic with respect to the separated reactants (+12.9 and +12.4 kcal mol1 respectively). The geometrical similarity between BRR and BSR is in good agreement with the small energy difference of these two intermediates. In both cases, the La–OCO distance is shortened compared to AR, and the CCO–OCO distance is elongated, which is consistent with the presence of a single bond between CCO and OCO. At TS(AR / BRR) and TS(AR / BSR), a pyramidalization of the CCO carbon is observed, i.e., a rehybridization from sp2 to sp3 of CCO, so that the resulting sp3 acceptor orbital points towards the migrating hydrogen atom of the borohydride leading to the formation of a CCO–Ht single bond in BRR and BSR. For BRR and BSR, it is also noteworthy that, compared to AR, the La–Ointra distance is shortened. The second-order perturbation NBO analysis reveals the presence of a stabilizing interaction between the endocyclic oxygen atom Ointra and the metal center (donation from a lone pair of the oxygen atom towards an empty d orbital of lanthanum). As we can see in Fig. 6, the free-energy prole of the initiation step of the ROP is similar, independently of the enantioface involved on the nucleophilic attack step. The geometrical parameters of the intermediates and transition states are also similar. In this case, for the sake of clarity, only the energy prole concerning the nucleophilic attack on the re enantioface is discussed for the remainder of this contribution. From BRR, the reaction continues via TS(BRR / CRR) that corresponds to the trapping of BH3 by the exocyclic oxygen

Calculated free-energy profile of the initiation step of the ROP of BL-R mediated by [La(BH4)3(THF)3] (1).


Polym. Chem., 2013, 4, 3077–3087 | 3081

Polymer Chemistry

Fig. 7

Paper

Optimized structures of complexes involved in the nucleophilic attack step of the ROP of BL-R mediated by [La(BH4)3(THF)3] (1).

(OCO) of the BL-R. The trapping occurs at long distances (H3B/ ˚ and 2.514 A, ˚ respectively) OCO and H3B/Ht distances of 3.709 A and is driven by electrostatic interactions (natural charges of

0 on BH3 and 0.84 on OCO). The trapping of BH3 proceeds with an energy barrier of 0.9 kcal mol1 with respect to BRR and leads to the formation of a borane complex CRR, calculated to be

Fig. 8 Optimized structures of complexes involved in the BH3 trapping, ring-opening, aldehyde reduction and arm-decoordination ROP of BL-R mediated by [La(BH4)3(THF)3] (1).

3082 | Polym. Chem., 2013, 4, 3077–3087


Paper

Polymer Chemistry

˚ of the stationary points calculated for the initiation step of the ROP of BL-R mediated by [La(BH4)3(THF)3] (1). The labels refer to the Table 2 Selected bond lengths (A) intermediates and transition states depicted in Fig. 7 and 8

Enantioface

Ln–OCO

Ln–Ointra

CCO–OCO

CCO–Ointra

CCO–Ht

B–Ht

OCO–B

B–Ht2

CCO–Ht2

BL-R — Nucleophilic attack AR re TS(AR / BRR) BRR re TS(AR / BSR) si BSR si

—

—

1.190

1.369

—

—

—

—

—

2.664 2.275 2.361 2.405 2.384

— — 2.624 — 2.748

1.210 1.316 1.309 1.271 1.305

1.344 1.432 1.500 1.395 1.487

— 1.175 1.147 1.365 1.161

1.24 1.504 1.610 1.323 1.567

— — 3.477 — 3.530

— — — — —

— — — — —

BH3 trapping TS(BRR / CRR) CRR TS(BSR / CSR) CSR

2.329 2.578 2.348 2.593

2.609 2.668 2.690 2.797

1.329 1.367 1.326 1.368

1.530 1.484 1.524 1.473

1.107 1.097 1.110 1.099

2.514 — 2.501 —

3.709 1.533 3.638 1.539

— 1.205 — 1.205

— — — —

Ring-opening + hydrogen transfer TS(CRR / DRR) re DRR re TS(DRR / ERR) re re ERR TS(CRR / ERR) re TS(CSR / DSR) si DSR si si TS(DSR / ESR) ESR si TS(CSR / ESR) si

3.707 2.907 2.749 2.778 2.593 3.894 4.847 4.460 2.863 2.561

2.260 2.256 2.240 2.186 2.385 2.251 2.198 2.193 2.206 2.336

1.238 1.249 1.271 1.455 1.336 1.238 1.234 1.257 1.447 1.325

2.546 2.815 2.846 2.861 1.972 2.416 2.867 2.843 2.877 1.986

1.098 1.097 1.097 1.094 1.089 1.099 1.100 1.102 1.096 1.091

— — — — — — — — — —

1.582 1.585 1.699 1.355 1.565 1.586 1.603 1.682 1.356 1.585

1.21 1.21 1.228 — 1.266 1.22 1.21 1.234 — 1.254

— — — 1.094 1.756 — — 2.090 1.095 1.857

Arm decoordination TS(ERR / ER) re ER si TS(ESR / FR)

3.801 — 4.359

2.171 2.171 2.170

1.435 1.432 1.435

2.925 2.996 2.934

1.095 1.095 1.095

— — —

1.344 1.34 1.343

— — —

1.097 1.096 1.096

re re si si

exergonic by 11.1 kcal mol1 with respect to the entrance channel. Starting from this last intermediate CRR, the formation of an alkoxyborane product ERR (with a terminal –CH2OBH2) that would lead to an hydroxyl termination aer hydrolysis, can take place through two different pathways, either a one-step concerted pathway in which the reduction of the aldehyde by the trapped BH3 group takes place simultaneously with the ringopening of the BL-R ring, or a second multistep pathway in which both reactions take place consecutively. The one step pathway involves the transition state TS(CRR / ERR) which lies 23.0 kcal mol1 above CRR. This step corresponds to the ratelimiting step of the ROP initiation of the BL-R. In TS(CRR / ERR), the interaction between the metal center and the intracyclic oxygen atom increases, whereas that with the exocyclic oxygen atom decreases as evidenced by the respective shortening and lengthening of these bonds with respect to CRR. This transition state leads to the formation of complex ERR. The formation of this complex is exoergic by 25.4 kcal mol1 with respect to CRR leading to an overall exoergic rst insertion of 36.5 kcal mol1 with respect to the separated reactants. The increase of the Ointra–CCO distance suggests a complete cleavage of the acyl– oxygen bond. In ERR, the intracyclic oxygen atom ensures the coordination of the alkoxyborane arm to the metal center. The NBO analysis reveals the presence of a residual interaction between the metal center and the exocyclic oxygen atom located


at the growing chain end. The increase of the CCO–OCO bond distance also indicates a single bond character between these two atoms. The formation of the nal alkoxyborane product ERR from CRR can also occur following a multistep pathway, i.e. the cleavage of the acyl–oxygen bond followed by the reduction of the aldehyde group by BH3. In this case, the hydrogen transfer is the rate-limiting step. The ring-opening step leads, via an accessible transition state TS(CRR / DRR) which lies only 10.2 kcal mol1 above CRR, to an endergonic DRR complex located at 4.0 kcal mol1 with respect to the separated reactants. In DRR, the BL-R ring is already opened and a double bond remains between CCO and OCO as evidenced by the decrease of the CCO– OCO bond length (Table 2). From DRR, the complex ERR is formed through the reduction of the aldehyde function by the trapped BH3 group that involves TS(DRR / ERR). The energy barrier for this step is 18.8 kcal mol1 relative to CRR (7.7 kcal mol1 with respect to the entrance channel). The transition state TS(DRR / ERR) corresponding to this reduction is kinetically accessible and presents some similarities with the concerted transition state TS(CRR / ERR). One B–H bond is slightly elongated with the hydrogen atom pointing toward CCO. The CCO–OCO–B angle is close to 90 , indicating an interaction between the hydrogen atom and CCO. Finally, the decoordination of the alkoxyborane arm leads to the nal FR product located at 38.7 kcal mol1 with respect to the entrance channel. This decoordination requires a low

Polym. Chem., 2013, 4, 3077–3087 | 3083

Polymer Chemistry

Paper

Table 3 Comparison of the relative Gibbs-free energies (kcal mol1) of the intermediates and transition states in the initiation reaction of the ROP of BL-R(R) and BL-S(S). The labels A to F refer to the intermediate and transition states shown in Fig. 7 and 8

Monomer

BL-R

BL-S

BL-R

BL-S

Considered enantioface

re

re

re

re

Nucleophilic attack A 2.4 TS(A / B) 14.5 B 12.9 Trapping of BH3 TS(B / C) 13.8 C 11.1

2.7 13.8 11.5 13.9 12.0

Ring-opening TS(C / D) 0.9 D 4.0 TS(D / E) 7.7 E 36.5 TS(C / E) 11.9 Arm-decoordination TS(E / F) 34.7 F 38.7

2.7 3.6 8.8 37.3 11.3 35.1 39.3

activation barrier (+1.8 kcal mol1 with respect to ERR). In FR, the exocyclic oxygen is no longer interacting with the metal center and the coordination of the alkoxyborane arm to the metal center is ensured by the endocyclic oxygen. Therefore, the reduction of the aldehyde function is, as observed above, the rate-determining step of an overall facile reaction. Interestingly, the second pathway is the most kinetically accessible although the differences in energy are within the precision of the method. The relative Gibbs-free energies of the intermediates and the activation barriers involved in the initiation reaction of BL-R and BL-S ROP are almost identical (Table 3). In particular, from AS, the formation of the nal alkoxyborane product FS takes place through a kinetically accessible and thermodynamically favorable mechanism. In the same way, for the rst propagation step, the activation barriers and the energies of the products obtained from FS and FR are also very close, indicating no stereoselectivity of the catalyst. This is in good agreement with the atactic polymer formation experimentally observed above. Thus, only FR and the insertion of a second BL-R monomer have been considered. Insertion of a second BL-R monomer: propagation step. From FR, the insertion of a second BL-R monomer step can proceed either through (i) nucleophilic attack of the oxygen atom of the alkoxyborane arm to the carbonyl carbon of the

Fig. 9

BL-R monomer, or through (ii) nucleophilic attack of a second borohydride to the carbonyl carbon of the BL-R monomer. Both nucleophilic attacks have been investigated. The energy prole computed for the rst propagation step is depicted in Fig. 9. A view of the different transition states and intermediates is reported, for the sake of manuscript length limitations, in Fig. S2 and S3, and the key geometrical parameters are summarized in Table S1 (refer to ESI†). The reaction involving the nucleophilic attack of the alkoxyborane arm begins with the formation of an endergonic GRR with a Gibbs-free energy of 5.4 kcal mol1 with respect to the entrance channel, which corresponds to the loss of entropy upon coordination of free BL-R. Subsequently from GRR, the nucleophilic attack of the alkoxyborane group to the carbonyl carbon CCO of BL-R takes place via the transition state TS(GRR / HRR), yielding a second intermediate, HRR. The activation energy for this nucleophilic attack is 14.9 kcal mol1 with respect to GRR. This kinetically accessible process corresponds to the rate-limiting step of the ROP propagation of BL-R. From a geometrical point of view, it is very similar to the TS described for the initiation step. Subsequently from HRR, the formation of the IRR, involves the transition state TS(HRR / IRR) which lies 3.6 kcal mol1 above HRR (15.8 kcal mol1 above to the separated reactants). This transition state corresponds to the cleavage of the acyl–Ointra bond, i.e. a spontaneous ring-opening, of the BL-R cycle. For this intermediate, ˚ The CCO– the BL-R ring is completely opened (CCO–O2 ¼ 2.9 A). OCO distance is also shortened, thereby highlighting the relocalization of a double bond between these two atoms. The last step concerns the relaxation of the growing polymer chain that essentially consists in the decoordination of the alkoxyborane arm. This process takes place through the transition state TS(IRR / JRR), leading to the JRR product, with a Gibbsfree energy of 0.5 kcal mol1 with respect to the entrance channel. Unlike the initiation step, the decoordination of the alkoxyborane arm is an exergonic process and may not occur. As aforementioned, from FR, it is also possible to form a second alkoxyborane arm by the nucleophilic attack of a second borohydride to the carbonyl carbon of BL-R. The energy data for this alternative pathway and the structure of the intermediates and transition states are similar to those obtained for the initiation reaction. The reaction begins with the formation of an endergonic FRAR, with a Gibbs-free energy of 2.8 kcal mol1

Calculated free-energy profile of the propagation step of the ROP of BL-R mediated by [La(BH4)2(THF)2(O(C(H)(CH3)(CH2)2)OBH2)].

3084 | Polym. Chem., 2013, 4, 3077–3087


Paper with respect to the separated reactants. For FRAR (as for AR), the BL-R monomer is coordinated to the lanthanum atom by its exocyclic oxygen atom. The nucleophilic attack of the borohydride onto the carbonyl carbon of BL-R proceeds through an accessible transition state TS(FRAR / FRBRR) located at 21.7 kcal mol1 with respect to the entrance channel (+18.9 kcal mol1 with respect to FRAR). This transition state leads to an adduct (FRBRR) calculated to be endergonic by 19.3 kcal mol1 with respect to the separated reactants. For FRBRR, as for BRR, the La– OCO distance is shortened compared to FRAR and the CCO–OCO distance is elongated, which is consistent with the presence of a single bond between CCO and OCO. Subsequently, from FRBRR, the BH3 trapping step takes place through an accessible transition state TS(FRBRR / FRCRR), which lies +22.1 kcal mol1 above the entrance channel and +2.8 kcal mol1 with respect to FRBRR. This transition state leads to the formation of an exergonic intermediate (FRCRR) located at 5.7 kcal mol1 with respect to the separated reactants. From a geometrical point of view, for FRCRR, BH3 is trapped by the exocyclic oxygen atom (OCO) of the BL-R, as shown by a short OCO–BH3 distance and the boron pyramidalization (sum of angles around B ¼ 330 ). From FRCRR, the bisalkoxyborane arm complex FRERR formation can take place via a concerted pathway (hydrogen transfer and simultaneous ring-opening) as well as via a multistep pathway (ringopening and then hydrogen transfer). As for the ROP initiation step, the most favorable pathway relies on the multistep pathway. The rst stage of the process involves the cleavage of the acyl–oxygen bond of BL-R, via an accessible transition state TS(FRCRR / FRDRR), which lies 10.4 kcal mol1 above FRCRR, leading to an endergonic FRDRR complex, located at 3.5 kcal mol1 with respect to the entrance channel. From FRDRR, the complex FRERR, which lies 27.3 kcal mol1 below the entrance channel, is obtained by the reduction of the aldehyde function by the trapped BH3 group characterized by TS(FRDRR / FRERR). This transition state corresponds to the rate-limiting step of the formation reaction of the second alkoxyborane arm. Finally, the system evolves to the nal FRFRR product. The formation of FRFRR is predicted to be exergonic (28.7 kcal mol1 with respect to the separated reactants) leading, from a thermodynamic point of view, to an overall favorable reaction. From a geometrical point of view, for FRFRR, as for FR, the exocyclic oxygen is no longer interacting with the metal center and the coordination of the alkoxyborane arm to the metal center is ensured by the endocyclic oxygen. Thus, the two considered pathways for this second insertion leading to either the polymerization on two arms or a one armonly growing of the polymer chain, are competitive from a thermodynamic and kinetic point of view. This demonstrates once again the lack of selectivity of the complex but in both cases, the insertion sequence would randomize, in line with a formation of an atactic polymer, as observed experimentally.

Conclusion In this contribution, we have shown that the synthetically easily accessible trisborohydride complexes, [Ln(BH4)3(THF)3] with Ln ¼ La, Nd, and Sm, were efficient catalysts in the controlled ROP This journal is ª The Royal Society of Chemistry 2013

Polymer Chemistry of rac-BL. Under mild operating conditions, especially at room temperature, well-dened atactic a,u-hydroxy telechelic PHBs are thus formed. DFT calculations on, in particular, the initiation step conrmed the formation of such PHB-diols. Such PHB diols are highly valuable, in particular as synthetic building blocks towards more sophisticated unique tailor-made polymer materials.

Experimental section All manipulations were performed under inert atmosphere (argon, 95%, TCI Chemicals) was distilled twice from CaH2 prior to use. ˚ molecular sieves. Toluene was CDCl3 was dried over 3–4 A distilled under argon from melted sodium prior to use. THF was rst pre-dried over sodium hydroxide and distilled under argon over CaH2, and then freshly distilled a second time under argon from Na/benzophenone prior to use. [Ln(BH4)3(THF)3] with Ln ¼ La (1), Nd (2), and Sm (3) were synthesized according to the reported literature procedure.17 All other reagents were used as received (Aldrich).

Instrumentation and measurements 1

H (500 and 400 MHz) and 13C{1H} (125, 100 MHz) NMR spectra were recorded on Bruker Avance AM 500 and Ascend 400 spectrometers at 23 C. Chemical shis (d) are reported in ppm and were referenced internally relative to tetramethylsilane (d 0 ppm) using the residual 1H and 13C solvent resonances. Monomer conversions were calculated from 1H NMR spectra of the crude polymer samples by using the integration (Int.) ratio Int.PHB/[Int.PHB + Int.BL] of the methine hydrogen (d 5.25 ppm for polymer, d 4.66 ppm for monomer). Average molar mass (Mn,SEC) and dispersity (ÐM ¼ Mw/Mn) values of the PHBs were determined by size-exclusion chromatography (SEC) in THF at 30 C (ow rate 1.0 mL min1) on a Polymer Laboratories PL50 apparatus equipped with a refractive index detector and a set of two ResiPore 300 7.5 mm columns. The polymer samples were dissolved in THF (2 mg mL1). All elution curves were calibrated with polystyrene standards and Mn,SEC values of the PHBs were uncorrected for the difference in hydrodynamic radius vs. polystyrene. The SEC traces of the polymers all exhibited a monomodal and symmetrical peak. The molar masses of short-chain PHB samples were determined by 1H NMR analysis in CDCl3 from the relative intensities of the signals of the PHB main-chain methine protons (–OCH(CH3)CH2, d 5.25 ppm) and those of the chain-end methylene protons (–CH2CH2OH, d 4.12 ppm). MALDI-MS spectra were recorded at the CESAMO (Bordeaux, France) on a Voyager mass spectrometer (Applied Biosystems). The instrument is equipped with a pulsed N2 laser source (337 nm) and a time-delayed extracted ion source. Spectra were recorded in the positive-ion mode using the reectron mode and with an accelerating voltage of 20 kV. The polymer samples were dissolved in THF at 10 mg mL1. A THF solution (1 mL) of the matrix (Indole Acrylic Acid, IAA – Aldrich, 99%, 10 mg mL1) Polym. Chem., 2013, 4, 3077–3087 | 3085

Polymer Chemistry

Paper

and a MeOH solution of the cationisation agent (NaI, 10 mg mL1) were prepared. The solutions were then combined in a 10 : 1 : 1 volume ratio of a matrix-to-sample-to-cationisation agent. One to two microliters of the resulting solution was deposited onto the sample target and vacuum-dried. 2 Typical ROP of rac-BL from [Ln(BH4)3(THF)3] with Ln ¼ La (1), Nd (2), and Sm (3) In a typical experiment (Table 1, entry 15), [Nd(BH4)3(THF)3] (2) (14.0 mg, 34.6 mmol, 1 equiv.) in THF (1.0 mL) was charged in a Schlenk ask in the glove, prior to the addition of rac-BL (893 mg, 10.4 mmol, 300 equiv.). The mixture was immediately stirred at 23 C and the polymerization was allowed to proceed over the appropriate reaction time (reaction times were not systematically optimized). The reaction was then quenched by adding an excess of an acetic acid solution (ca. 1 mL of a 1.6 mmol L1 solution in toluene). The resulting mixture was dried under vacuum and the conversion of rac-BL was determined by 1 H NMR analysis of the residue in CDCl3. The crude polymer was next dissolved in CH2Cl2 and puried upon precipitation in cold pentane, ltered and dried under vacuum. The nal polymer was then analyzed by NMR, SEC and MALDI-ToF mass spectrometry analyses (Table 1). DFT methodological details

3

4

5

6 18

All calculations were performed with Gaussian 03. Calculations were carried out at the Density Functional Theory (DFT) level using the hybrid functional B3PW91.19 Geometry optimizations were achieved without any symmetry restriction. Calculations of vibrational frequencies were systematically done in order to characterize the nature of stationary points. Stuttgart effective core potentials20 and their associated basis set were used for zinc. Silicon, nitrogen, hydrogen, carbon and oxygen atoms were treated with 6-31G(d,p) double-z basis sets.21 The electron density and partial charge distribution were examined in terms of localized electron-pair bonding units by using the NBO program implemented in Gaussian 03.22

7

8

Acknowledgements This research has been nancially supported in part by the CNRS, the R´ egion Bretagne (ACOMB research program) and Rennes M´ etropole. L. M. is a member of the Institut Universitaire de France. CINES and CALMIP are acknowledged for a generous grant of computing time. ANR, UPS, INSA and CNRS are also acknowledged for nancial support. The Humboldt Foundation is also acknowledged for a professorship grant (LM). M. S. thanks the Cusanuswerk for nancial support.

References 1 (a) G.-Q. Chen, Chem. Soc. Rev., 2009, 38, 2434–2446; (b) J. Lu, R. C. Tappel and C. T. Nomura, J. Macromol. Sci., Part C: Polym. Rev., 2009, 49, 226–248; (c) K. Sudesh, H. Abe and Y. Doi, Prog. Polym. Sci., 2000, 25, 1503–1555; (d) C. Errico, C. Bartoli, F. Chiellini and E. Chiellini, J. Biomed.

3086 | Polym. Chem., 2013, 4, 3077–3087

9

Biotechnol., 2009, ID 571702; (e) B. Hazer, Int. J. Polym. Sci., 2010, ID 423460; (f) X. Gao, J.-C. Chen, Q. Wu and G.-Q. Chen, Curr. Opin. Biotechnol., 2011, 22, 768–774; (g) S. Taguchi, T. Iwata, H. Abe, Y. Doi, Polymer Science: A comprehensive Reference, 2012, vol. 9, pp. 157–180. (a) O. Coulembier and P. Dubois, Handbook of Ring-Opening Polymerization, ed. P. Dubois, O. Coulembier and J.-M. Rasquez, Wiley, Weinheim, 2009, pp. 227–254; (b) J.-F. Carpentier, Macromol. Rapid Commun., 2010, 31, 1696– 1705; (c) C. M. Thomas, Chem. Soc. Rev., 2010, 39, 165–173. (a) S. Hiki, M. Miyamoto and Y. Kimura, Polymer, 2000, 41, 7369–7379; (b) S. Dai, L. Xue, M. Zinn and Z. Li, Biomacromolecules, 2009, 10, 3176–3181; (c) S. Dai and Z. Li, Biomacromolecules, 2008, 89, 1883–1893; (d) A. P. Andrade, B. Witholt, D. Chang and Z. Li, Macromolecules, 2003, 36, 9830–9835. (a) Arslan, B. Hazer and M. Kowalczuk, J. Appl. Polym. Sci., 2002, 85, 965–973; (b) H. Arslan, A. Mentes and B. Hazer, J. Appl. Polym. Sci., 2004, 94, 1789–1796. (a) Q. Zhao and G. Cheng, J. Mater. Sci., 2004, 39, 3829–3831; (b) G. Ciardelli, K. Kojima, A. Lendlein, P. Neuenschwander and U. W. Suter, Macromol. Chem. Phys., 1997, 198, 2667– 2688; (c) X. J. Loh, S. H. Goh and J. Li, Biomaterials, 2007, 28, 4113–4123; (d) J. Pan, G. Li, Z. Chen, X. Chen, W. Zhu and K. Xu, Biomaterials, 2009, 30, 2975–2984. (a) H. Arslan, G. Adamus, B. Hazer and M. Kowalczuk, Rapid Commun. Mass Spectrom., 1999, 13, 2433–2438; (b) T. D. Hirt, P. Neuenschwander and U. W. Suter, Macromol. Chem. Phys., 1996, 197, 1609–1614. (a) S. M. Guillaume, L. Maron and P. Roesky, Handbook on the Physics and Chemistry of Rare Earth, ed. J.-C. G. B¨ unzli and V. K. Pecharsky, Elsevier Science B.V., Amsterdam, 2013, vol. 44, ch. 259, in press; (b) M. Visseaux and F. Bonnet, Coord. Chem. Rev., 2010, 255, 374–420; and references therein. Illustrative references: (a) S. M. Guillaume, M. Schappacher and A. Soum, Macromolecules, 2003, 36, 54–60; (b) N. Barros, P. Mountford, S. M. Guillaume and L. Maron, Chem.–Eur. J., 2008, 14, 5507–5518; (c) I. Palard, A. Soum and S. Guillaume, Chem.–Eur. J., 2004, 10, 4054–4062; (d) I. Palard, A. Soum and S. M. Guillaume, Macromolecules, 2005, 38, 6888–6894; (e) I. Palard, M. Schappacher, A. Soum and S. M. Guillaume, Polym. Int., 2006, 55, 1132– 1137; (f) J. Jenter, P. W. Roesky, N. Ajellal, S. M. Guillaume, N. Susperregui and L. Maron, Chem.–Eur. J., 2010, 16, 4629–4638; (g) P. W. Roesky, S. Marks, M. Kuzdrowska, S. M. Guillaume, L. Anunziata and L. Maron, ChemPlusChem, 2012, 77, 350–353. Illustrative references: (a) S. M. Guillaume, Eur. Polym. J., 2013, 49, 768–779; (b) M. Le Hellaye, N. Fortin, J. Guilloteau, A. Soum, S. Lecommandoux and S. M. Guillaume, Biomacromolecules, 2008, 9, 1924–1933; (c) M. Schappacher, N. Fur and S. M. Guillaume, Macromolecules, 2007, 40, 8887–8896; (d) M. Schappacher, A. Soum and S. M. Guillaume, Biomacromolecules, 2006, 7, 1373–1379; (e) Y. Nakayama, S. Okuda, H. Yasuda and T. Shiono, React. Funct. Polym., 2007, 67, 798–806.


Paper 10 Illustrative references: (a) S. M. Guillaume, M. Schappacher, N. M. Scott and R. Kempe, J. Polym. Sci., Part A: Polym. Chem., 2007, 45, 3611–3619; (b) A. Momin, F. Bonnet, M. Visseaux, L. Maron, J. Takats, M. J. Ferguson, X.-F. Le Goff and F. Nief, Chem. Commun., 2011, 47, 12203–12205; (c) C. Iner, F. Bonnet, F. Nief, M. Visseaux and L. Maron, Organometallics, 2011, 30, 4482–4485; (d) N. Susperregui, M. U. Kramer, J. Okuda and L. Maron, Organometallics, 2011, 30, 1326–1333; (e) G. Wu, W. Sun and Z. Shen, React. Funct. Polym., 2008, 68, 822–830. 11 (a) Y. Nakayama, K. Sasaki, N. Watanabe, Z. Cai and T. Shiono, Polymer, 2009, 50, 4788–4793; (b) Y. Nakayama, K. Sasaki, N. Watanabe, Z. Cai and T. Shiono, Polymer, 2009, 50, 4788–4793. 12 Y. Nakayama, N. Watanabe, K. Kusaba, K. Sasaki, Z. Cai, T. Shiono and C. Tsutsumi, J. Appl. Polym. Sci., 2011, 121, 2098–2103. 13 Illustrative references: (a) H. E. Dyer, S. Huijser, N. Susperregui, F. Bonnet, A. D. Schwarz, R. Duchateau, L. Maron and P. Mountford, Organometallics, 2010, 29, 3602–3621; (b) F. Bonnet, A. R. Cowley and P. Mountford, Inorg. Chem., 2005, 44, 9046–9055; (c) T. V. Mahrova, G. K. Fukin, A. V. Cherkasov, A. A. Trifonov, N. Ajellal and J.-F. Carpentier, Inorg. Chem., 2009, 48, 4258–4266; (d) J. Kratsch, M. Kuzdrowska, M. Schmid, N. Kazeminejad, C. Kaub, P. O~ na-Burgos, S. M. Guillaume and P. W. Roesky, Organometallics, 2013, 32, 1230–1238. 14 (a) I. Palard, M. Schappacher, B. Belloncle, A. Soum and S. M. Guillaume, Chem.–Eur. J., 2007, 13, 1511–1521; (b) S. M. Guillaume, P. Brignou, N. Susperregui, L. Maron, M. Kuzdrowska and P. W. Roesky, Polym. Chem., 2012, 3, 429–435. 15 N. Ajellal, G. Durieux, L. Delevoye, G. Tricot, C. Dujardin, C. M. Thomas and R. M. Gauvin, Chem. Commun., 2010, 46, 1032–1034. 16 This improved control in the present experiments may possibly arise from the better monomer purity; note that rac-BL used in the present study was carefully puried


Polymer Chemistry

17 18 19

20

21

22

(distillated twice) to avoid possible undesirable concomitant initiation by remaining impurities. S. M. Cendrowski-Guillaume, M. Nierlich, M. Lance and M. Ephritikhine, Organometallics, 1998, 17, 786–788. M. J. Frisch et al., Gaussian 03 (Revision B.05), 2003. (a) A. D. Becke, Phys. Rev. A, 1988, 38, 3098–3100; (b) J. P. Perdew, in Electronic structure of solids'91, ed. P. Ziesche and H. Eschrig, Akademie Verlag, Berlin, 1991; (c) P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh and C. Fiolhais, Phys. Rev. B: Condens. Matter Mater. Phys., 1992, 46, 6671–6687; (d) J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh and C. Fiolhais, Phys. Rev. B: Condens. Matter Mater. Phys., 1993, 48, 4978; (e) J. P. Perdew, K. Burke and Y. Wang, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 16533–16539; (f) K. Burke, J. P. Perdew and Y. Wang, in Electronic Density Functional Theory: Recent Progress and New Directions, ed. J. F. Dobson, G. Vignale and M. P. Das, (Plenum, 1998); Chapter Derivation of a Generalized Gradient Approximation: the PW91 Density Functional. (a) M. Dolg, H. Stoll, A. Savin and H. Preuss, Theor. Chim. Acta, 1989, 75, 173; (b) M. Dolg, H. Stoll and H. Preuss, Theor. Chim. Acta, 1989, 85, 441. (a) R. Ditcheld, W. J. Hehre and J. A. Pople, J. Chem. Phys., 1971, 54, 724; (b) W. J. Hehre, R. Ditcheld and J. A. Pople, J. Chem. Phys., 1972, 56, 2257; (c) P. C. Hariharan and J. A. Pople, Theor. Chem. Acc., 1973, 28, 213–222; (d) P. C. Hariharan and J. A. Pople, Mol. Phys., 1974, 27, 209– 214; (e) M. M. Francl, W. J. Pietro, W. J. Hehre, J. S. Binkley, D. J. DeFrees, J. A. Pople and M. S. Gordon, J. Chem. Phys., 1982, 77, 3654–3665; (f) T. Clark, J. Chandrasekhar, G. W. Spitznagel and P. v. R. Schleyer, J. Comput. Chem., 1983, 4, 294–301; (g) M. J. Frisch, J. A. Pople and J. S. Binkley, J. Chem. Phys., 1984, 80, 3265–3269. (a) A. E. Reed and F. Weinhold, J. Chem. Phys., 1983, 78, 4066–4074; (b) A. E. Reed, L. A. Curtiss and F. Weinhold, Chem. Rev., 1988, 88, 899–926.

Polym. Chem., 2013, 4, 3077–3087 | 3087