Cobalt–Bis(imino)pyridine-Catalyzed Asymmetric Hydrogenation

Article pubs.acs.org/Organometallics

Cobalt−Bis(imino)pyridine-Catalyzed Asymmetric Hydrogenation: Electronic Structure, Mechanism, and Stereoselectivity Kathrin H. Hopmann* Centre for Theoretical and Computational Chemistry (CTCC) and Department of Chemistry, University of Tromsø, N-9037 Tromsø, Norway S Supporting Information *

ABSTRACT: Academic and industrial efforts aim at replacing precious metal catalysts with cheaper and more environmentally friendly base metal variants. Two cobalt−bis(imino)pyridine (CoBIP) complexes were recently reported as promising candidates for asymmetric hydrogenation [Monfette, S.; et al. J. Am. Chem. Soc. 2012, 134, 4561−4564]. A comprehensive quantum mechanical analysis of these complexes is reported here, including electronic structures, preferred conformations, and mechanisms of activation. The full asymmetric hydrogenation mechanism is analyzed, and the origin of the observed enantioselectivities with both CoBIP catalysts is evaluated. A key finding is that CoBIP complexes catalyze a competing alkene isomerization reaction, which can have crucial implications for the yield and the stereochemical outcome of alkene hydrogenation.

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INTRODUCTION Enantiopure alkanes are important intermediates in synthetic, industrial, and pharmaceutical applications.1,2 Asymmetric hydrogenation of prochiral olefins is the most atom-efficient route to formation of enantiopure alkanes. Established catalytic systems for asymmetric hydrogenation are typically based on precious metals such as iridium or rhodium.1,3 Replacement of these with base metal variants is an ongoing quest in academia and industry.4 Base metals such as cobalt and iron are cheaper, more abundant, and of less environmental concern than their precious metal counterparts.4 The number of cobalt-based hydrogenation catalysts reported to date is small. Budzelaar and co-workers established that C2v-symmetric bis(imino)pyridine (BIP) cobalt complexes are able to catalyze hydrogenation of mono- and disubstituted olefins.5 These complexes formally contain Co(I), but can be viewed as Co(II), magnetically coupled to radical BIP.6 Hanson and co-workers reported that a bis[2-(dicyclohexylphosphine)ethyl]amine Co(II) complex catalyzes mild hydrogenation of CC, CO, and CN bonds.7,8 Chiral cobalt-based hydrogenation catalysts are particularly scarce; one example is a C2-symmetric semicorrin-Co(II) complex by Pfaltz and coworkers, which hydrogenates α,β-unsaturated carboxylic esters with enantiomeric excess (ee) values of up to 96%.9 On the basis of a ligand design originally reported by Bianchini et al.,10 Chirik and co-workers recently developed two C1-symmetric cobalt hydrogenation catalysts with chiral BIP ligands (Figure 1).11 With (S)-1-Me, hydrogenation of a series of unfunctionalized terminal olefins based on styrene showed good yields and enantiomeric excess values of up to 96% (Table 1). The (S)-2-CM catalyst was unreactive toward substituted styrenes, but showed an unprecedented ee of 96% for formation of 1-methylindane (Table 1).11 © XXXX American Chemical Society

Figure 1. Chiral CoBIP catalysts (S)-1-Me and (S)-2-CM reported by Chirik and co-workers.11

The chiral CoBIP complexes represent promising hydrogenation catalysts; however, some limitations can become detrimental for productive applications. These include low activity or selectivity with several substrates and, in at least one case, accumulation of an undesired side product (Table 1).11 Rational improvement of chiral CoBIP catalysts requires detailed knowledge about their catalytic and selective properties. Computational studies of a highly truncated model of an achiral CoBIP complex indicated that hydrogenation occurs through stepwise hydride transfer, H2 coordination, and a σbond metathesis type proton transfer;5 however, not all steps were computed explicitly. The very small computational model employed cannot describe the steric and electronic properties of a full CoBIP system correctly, nor can any insight on the mechanism for asymmetric alkene conversion be extracted from the results. Although there have been various theoretical studies providing insight into the mechanisms and enantioselectivities of precious-metal catalyzed hydrogenation reactions,12 to our knowledge there are no such studies on cobalt systems. Received: July 30, 2013

A

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Table 1. Selected Experimental Results for Asymmetric Hydrogenationa with Chiral CoBIP (all data adapted from ref 11, except absolute configuration of SubA13)bcde

Figure 2. Evaluated electronic states of CoBIP (BIP drawn simplified, L = 2,6-diisopropylaryl). CS = closed shell, AF-S = antiferromagnetic singlet, F-T = ferromagnetic triplet, AF-T = AF triplet. S indicates pure spin states, MS indicates BS states.

a

Reaction conditions: 5 mol % CoBIP, 4 atm H2, benzene 0.1 M, 22 °C, 24 h. bReported as (R),11 but appears to be (S).13 cAssignment in analogy to SubA.11 dReaction time 1 h. eIn addition, 56% 3-methyl1H-indene.

with eq 1 was added to the Gibbs free energies (GBS) computed for the BS geometry in order to obtain approximate spin-projected Gibbs free energies, Gpro:

In this paper, broken-symmetry density functional theory (BS-DFT) and full quantum chemical models are employed to study the electronic structures and preferred conformations of precatalytic and active chiral CoBIP complexes, the catalyst activation process, the full asymmetric hydrogenation mechanism, and the factors determining the stereoselectivity of hydrogenation for both reported catalysts.

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Gpro = G BS + (ESmin − E BS)

Models. The starting geometries for free (S)-1-Cl, (S)-1-Me, and (S)-1-CM were modeled on the basis of the respective X-ray structures.11 For free (S)-2-CM, the (R)-2-CM structure was employed. Free (S)-1-H and (S)-2-H were modeled based on the (S)-1-Me and (R)-2-Cl structures, respectively.11 For (S)-1-Me and (R)-2-Cl, two conformers are seen in the X-ray structure,11 which here are referred to as a and b (vide inf ra). The reaction pathways were modeled with quantum chemical models comprising full CoBIP complexes (Figure 1) and full substrates.

COMPUTATIONAL DETAILS

Calculations. All calculations were performed with B3LYP14,15 and the triple-ζ basis set 6-311G(d,p) (on all atoms) as implemented in Gaussian 09,16 unless noted otherwise. The empirical dispersion correction (D2, S6 = 1.05 for B3LYP)17 was included in all calculations. Calculations were performed in vacuo, as an approximation to the low-polar benzene solvent employed in experiments.11 Additional geometry optimizations including IEFPCM provided similar results (see discussion). Thermochemical quantities (298.15 K) were computed at the same level of theory as geometry optimizations. All reported energies are Gibbs free energies, unless noted otherwise. To evaluate the effect of the functional, selected calculations were also performed with BHandHLYP, B3LYP*,18 and TPSSh.19 Geometry optimizations were performed with different pure and broken-symmetry (BS) spin states: closed-shell singlet (CS(S = 0)), antiferromagnetically coupled (AF) singlet, with the unpaired electron on the Co atom residing in a dxz (AF-S(MS = 0,dxz)) or dz2 orbital (AFS(MS = 0,dz2)), pure ferromagnetically coupled triplets F-T(S = 1,dxz) and F-T(S = 1,dz2), and AF-coupled triplet AF-T(MS = 1) (Figure 2). For selected species, the BS electronic energy was spin-projected to the true ground-state energy, ESmin:20

ESmin = E HS − (JAB /2)[Smax(Smax + 1) − Smin(Smin + 1)]

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RESULTS AND DISCUSSION Electronic Structure of Chiral CoBIP Complexes. Calculations by Budzelaar and co-workers indicate that the electronic state of symmetric N-aryl-substituted CoBIP complexes can be viewed as low-spin Co(II) (SCo = 1/2) antiferromagnetically (AF)-coupled to radical (SBIP = 1/2) BIP, resulting in an overall singlet.6 For monochloride CoBIP complexes with N-alkyl substituents, Wieghardt and co-workers reported a preferred overall triplet state, comprising high-spin Co(II) (SCo = 3/2) AF-coupled to radical (SBIP = 1/2) BIP.22 The preference for a triplet state was attributed to the nonplanarity of these complexes, induced by the alkyl ligands. At low temperature, the monochloride N-alkyl complexes exhibit a singlet state, implying these are temperaturedependent spin crossover complexes.22 The chiral CoBIP catalysts (Figure 1) have one N-aryl and one N-alkyl substituent. It is thus of interest to establish how this asymmetry affects the preferred electronic configuration. Various variants of the asymmetric CoBIP complexes are relevant here. The synthesis of (S)-1-Me involved (S)-1-Cl as a precursor (Scheme 1a).11 (S)-1-Me is a precatalyst, with the assumed active species comprising the monohydride (S)-1-H, formed upon exposure of (S)-1-Me to H2. If heated or if left standing at ambient temperature for several days, (S)-1-Me converts to the cyclometalated species (S)-1-CM.11 Also (S)-1CM reacts with H2 to give (S)-1-H (Scheme 1a). Here, (S)-1Cl, (S)-1-Me, (S)-1-CM, and (S)-1-H were geometryoptimized with various possible spin states: closed shell (CS),

(1)

where Smin is the total spin of the AF-coupled ground state (for two interacting sites A and B, Smin = SA − SB) and Smax the total spin of the corresponding high-spin (HS) state (SA + SB). EHS is the electronic energy of the HS state at the BS geometry. JAB was computed employing the Yamaguchi formalism:21

JAB = 2(E HS − E BS)/( S2

HS

− S2

BS

)

(3)

(2)

where EBS is the electronic energy of the geometry-optimized BS state, and ⟨S2⟩HS and ⟨S2⟩BS are the expectation values of the HS and BS S2 operators. The electronic energy difference (ESmin − EBS) obtained B

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Scheme 1. Variants of Complex 1a

Table 2. Relative Energiesa (kcal/mol) for GeometryOptimized Electronic States of (S)-1-Cl, (S)-1-Me, (S)-1CM, (S)-1-H, (S)-2-CM, and (S)-2-H complexb (statec) (S)-1-Cl, Conformer a CS(S = 0) AF-S(MS = 0,dxz) F-T(S = 1,dz2) AF-T(MS = 1) (S)-1-Me, Conformer a CS(S = 0) AF-S(MS = 0,dxz) F-T(S = 1,dz2) AF-T(MS = 1) (S)-1-Me, Conformer b CS(S = 0) AF-S(MS = 0,dxz) F-T(S = 1,dz2) AF-T(MS = 1) (S)-1-CM CS(S = 0) AF-S(MS = 0,dxz) F-T(S = 1,dz2) AF-T(MS = 1) (S)-1-H, Conformer a CS(S = 0) AF-S(MS = 0,dxz) F-T(S = 1,dz2) AF-T(MS = 1) (S)-1-H, Conformer b CS(S = 0) AF-S(MS = 0,dxz) F-T(S = 1,dz2) AF-T(MS = 1) (S)-2-CMe,f CS(S = 0) AF-S(MS = 0,dxz) F-T(S = 1,dz2) (S)-2-H, Conformer ae,f CS(S = 0)g AF-S(MS = 0,dxz) F-T(S = 1,dz2) (S)-2-H, Conformer b CS(S = 0) AF-S(MS = 0,dxz) F-T(S = 1,dz2) AF-T(MS = 1)

a

(a) Synthetic precursor (S)-1-Cl, precatalyst (S)-1-Me, cyclometalated (S)-1-CM formed over time, and proposed active species (S)-1-H; (b) conformers of (S)-1-Me observed in the X-ray crystal structure (R = Me, Cl, H, BIP drawn simplified, L = 2,6diisopropylaryl, all data adapted from ref 11).

antiferromagnetic singlet (AF-S), ferromagnetic triplet (F-T), and AF triplet (AF-T, Figure 2). For AF-S and F-T, the singleelectron excitation from Co to BIP can occur from a dz2 or a dxz orbital.6 Both possibilities were evaluated, with the lower solution reported here. The X-ray crystal structure of (S)-1-Me shows two conformers (here referred to as a and b, Scheme 1b),11 which can interconvert through rotation around the N− C* bond (Figure 1). Both forms were evaluated here. Calculations were performed with B3LYP, as also applied in other studies on similar complexes.6,22 Dispersion corrections17 were included here, which appear important for relative spinstate energies (vide inf ra).23 Computed energies are given in Table 2 and optimized geometries in Figure 3 and Figure S1− S8, Supporting Information (SI). NMR results for 1-Cl and 1-Me were interpreted as showing an overall diamagnetic state with a thermally accessible triplet.11 For (S)-1-Cl, the computed ΔG values indicate that the AF-T state is 2.4 kcal/mol lower than the AF-S state (Table 2). If an approximate energy correction obtained through spin projection (eqs 1−3) is included, the AF-S state is preferred by 1 kcal/mol, in line with experimental results. The small singlet− triplet gap indicates a significant thermal triplet population and suggests that (S)-1-Cl might be a spin crossover complex, like the symmetric N-alkyl CoBIP-Cl complexes.22 (S)-1-Me (conformer a, Figure 3) shows a preferred AF-S ground state, around 2 kcal/mol below the triplet states F-T and AF-T (5 kcal/mol after spin projection). For conformer b, all energies are ∼1−3 kcal/mol higher than for a (Table 2). Selected geometrical parameters for (S)-1-Me are compared to the X-ray structure11 in Table S1 (SI). The AF-S geometry has somewhat overestimated bond lengths, which is a consequence of spin contamination. The AF-T geometry shows elongated N−Co bonds and significant displacement of Co out of the BIP plane. The cyclometalated complex (S)-1-CM shows a preferred AF-S ground state, with the lowest lying triplet being F-T. The AF-T state lies more than 11 kcal/mol above AF-S, possibly because an out-of-plane displacement of the S = 3/2 Co center

⟨S2⟩

ΔH

ΔG

ΔGprod

0.809 2.030 2.668

7.9 0.0 3.5 −0.2

8.1 0.0 2.4 −2.4

13.2 0.0 7.6 1.0

0.868 2.021 2.724

9.9 0.0 2.5 4.9

9.6 0.0 1.9 2.4

14.2 0.0 6.5 5.5

0.877 2.019 2.704

11.1 0.8 3.3 8.2

10.5 1.5 3.3 5.4

15.0 1.5 7.8 8.5

0.894 2.022 2.596

10.6 0.0 1.7 10.2

11.3 0.0 2.6 12.6

13.3 0.0 4.5 11.4

0.876 2.019 2.542

10.5 0.0 1.3 6.6

11.0 0.0 0.9 5.3

15.6 0.0 5.5 8.0

0.888 2.018 2.556

15.3 4.4 5.6 11.0

16.9 5.3 5.5 11.2

21.5 5.5 10.1 13.9

0.883 2.020

9.9 0.0 2.9

11.3 0.0 2.5

14.3 0.0 5.5

0.896 2.019

6.0 0.0 0.7

6.8 0.0 0.8

7.9 0.0 1.9

0.888 2.018 2.620

14.2 3.6 4.6 9.2

15.4 4.9 5.0 8.2

16.5 4.6 6.2 7.5

a

Relative to AF-S (a) of a given complex. bFor a and b see Scheme 1b. For spin states see Figure 2. dSpin-projected energy (eq 1−3). eAF-T not stable. fCalculations performed on (R)-enantiomer, but energies identical to (S). gForms agostic interaction between tBu and Co. c

is difficult to achieve for the cyclometalated complex. To our knowledge, this is the first study of the electronic structure of a cyclometalated Co-BIP complex. For the presumed active catalyst species, (S)-1-H, AF-S is the ground state, with F-T being the lowest lying triplet (Table 2). The b conformer is around 5 kcal/mol above a on all spin surfaces, making it unlikely that b is catalytically relevant. The (S)-2-CM catalyst behaves differently than (S)-1-CM. In the presence of H2 alone, (S)-2-CM does not appear to form the monohydride (S)-2-H. However, addition of SubI results in C

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Figure 3. Geometry-optimized spin states for (S)-1-Me (a conformer) with selected spin populations (>0.08, italic): (a) AF-S(MS = 0,dxz), (b) FT(S = 1,dz2), (c) AF-T(MS =1) (spin densities given with contour value 0.015, major in red, minor in blue).

successful hydrogenation (Scheme 2).11 This implies that (S)2-H might be formed only in the presence of substrate (vide

CM shows one isomer, but in solution, two isomers are detected (with a ratio of ∼1:2 to ∼1:4).11 The identity of the minor isomer is unclear. Here it is proposed that the two isomers of (S)-1-CM have the methine hydrogen of the cyclohexyl group pointing either in the same direction as C*− H or opposite to it (Figure 4). The two forms are for simplicity referred to as syn and anti. The X-ray structure of (S)-1-CM shows the syn-form11 (which is lower than anti by 1.9 kcal/ mol), whereas the X-ray structures of the noncyclometalated species ((S)-1-Cl, (S)-1-Me) show the anti-form,11 which is preferred once the CM bond is broken (syn-(S)-1-Me is 4.0 kcal/mol higher in energy). Cyclometalation of (S)-1-Me could occur in several steps: rotation around C*−CCy to convert anti(S)-1-Me to syn-(S)-1-Me (with an estimated barrier of ∼10 kcal/mol based on linear-transit calculations) and subsequent formation of the CM bond, with a barrier of 26.7 kcal/mol (TSMetoCM, Table 3, entry II). The reaction energy is −11.6 kcal/mol, making formation of (S)-1-CM very favorable. (S)-1-CM can react with H2 to give (S)-1-H (Scheme 1), which has a reaction energy of 0.0 kcal/mol (Table 3, entry III). The transition state (TS) for cleavage of syn-(S)-1-CM to syn(S)-1-H (TS1CMtoH) involves dissociation of the CCy−Co bond and abstraction of a proton from H2, with a barrier of 21.7 kcal/ mol. The formed syn-(S)-1-H can then rotate around C*−CCy (with a barrier of 4.2 kcal/mol relative to syn-(S)-1-H) to give anti-(S)-1-H, which is 2.1 kcal/mol lower in energy. Overall, the computed results for catalyst 1 are in good agreement with experiment (Scheme 1),11 reproducing the observed formation of (S)-1-H from (S)-1-Me and (S)-1-CM and showing that conversion of the methyl species to the CM complex has a higher barrier than (S)-1-H formation, providing a rationalization for the slow cyclometalation. The computations also rationalize the reported solid-state structures,11 with a preferred syn-conformation for (S)-1-CM versus a preferred anticonformation for noncyclometalated species. The presence of syn- and anti-forms (Figure 4) could explain why two isomers of (S)-1-CM have been observed in solution. The (S)-2-CM complex does not react with H2 to give (S)-2H (Scheme 2). The computed energies show that this reaction is unfavorable (Table 3, entry IV), with a reaction energy of 4.4 kcal/mol for formation of (S)-2-H (conformer a, 9.2 kcal/mol for conformer b). The computed barrier is 25.1 kcal/mol (Table 3, entry IV), which is somewhat higher than for (S)-1CM. In experiments,11 (S)-2-CM hydrogenates SubI, but not SubA (Table 1, Scheme 2). The calculations show that coordination of SubI to (S)-2-H stabilizes the monohydride species and reduces the overall reaction energy to +0.3 kcal/ mol (Table 3, entry VI), whereas SubA does not have this effect (reaction energy +4.6 kcal/mol, Table 3, entry V). These results elegantly explain the reactivity pattern of (S)-2-CM

Scheme 2. Variants of Complex 2a

a Synthetic precursor (S)-2-Cl, precatalyst (S)-2-CM, and putative active species (S)-2-H (BIP drawn simplified, L = 2,6-diisopropylaryl, all data adapted from ref 11).

inf ra). The electronic structures of (S)-2-CM and (S)-2-H are evaluated here. The lowest lying state for (S)-2-CM is AF-S, with F-T a few kcal/mol higher (Table 2). For the putative catalytic species (S)-2-H, the ground state is also AF-S. The gap from AF-S to F-T is small (Table 2), whereas the AF-T state is not stable. The b conformer of (S)-2-H is ∼5 kcal/mol above a on all spin surfaces, indicating that a is predominantly present in solution. Catalyst Activation. The complexes (S)-1-Me, (S)-1-CM, and (S)-2-CM are precatalysts, with the active species assumed to be the corresponding monohydrides ((S)-1-H and (S)-2-H, Schemes 1 and 2). The activation and cyclometalation processes are studied here in order to shed light on the activity of these complexes (Table 3; for optimized transition-state geometries, see Figure S9, SI). For (S)-1-Me, the activation process involves a σ-bond metathesis reaction between H2 and BIPCo-CH3, resulting in CH4 release and formation of (S)-1-H, with a barrier of 23.0 kcal/mol (TSMetoH, Table 3, entry I). The formation of (S)-1-H is highly favorable, with a reaction energy of −11.6 kcal/mol (note that spin projection of the energies was not possible24). (S)-1-Me is converted into (S)-1-CM over time or if the mixture is heated (Scheme 1).11 The X-ray structure of (S)-1D

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Table 3. Relative Reaction Energies and Barriers (kcal/mol) for Activation and Cyclometalation of (S)-1-Me, (S)-1-CM, and (S)-2-CMa

a

All calculations performed on the a conformer of a given species (Scheme 1b). See Figure 4 for definition of syn and anti.

Alkene Hydrogenation Mechanism. DFT studies on a highly truncated model of a symmetric CoBIP complex with ethylene as substrate indicated a stepwise hydrogenation mechanism, involving hydride transfer to the coordinated alkene, followed by H2 coordination to Co and rate-limiting proton transfer to yield the alkane product.5 Closed-shell electronic states were obtained for most species; only two geometries along the reaction path were reported to give an AF-S state: the monohydride complex (prior to substrate coordination) and the alkyl intermediate formed upon hydride transfer.5 The barrier for H2 coordination was not computed explicitly, although it could be rate-limiting. Here the full hydrogenation mechanisms of catalysts 1 and 2 (Figure 1) have been computed with a realistic substrate, evaluation of different spin states (Figure 2), and analysis of the enantioselectivity. In particular, an alternative hydrogenation and isomerization pathway is proposed, which has consequences for the yield and the stereochemical outcome of the reaction. The reaction pathway for (S)-1-Me-mediated hydrogenation is here presented with SubI, which is the only substrate that can be hydrogenated by both CoBIP catalysts (Table 1). SubI can coordinate to the active species (S)-1-H in different binding

Figure 4. (a) Proposed syn- and anti-forms of (S)-1-CM (with syn observed in the X-ray structure11) and (b) syn- and anti-forms of nonCM complexes (with anti observed in X-ray structures,11 R = Cl, Me, or H; L = 2,6-diisopropylaryl).

(Scheme 2): Significant formation of the active species (S)-2-H is feasible only in the presence of SubI. In the presence of H2 alone or H2 and SubA, the catalyst remains in the energetically preferred cyclometalated state, which is inactive. E

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Or3 and Or4, probably due to dispersion interactions between substrate and BIP. The preference for Or1 over Or2 is due to less steric interactions with the 2,6-diisopropylaryl group. The detailed mechanism computed for (S)-1-Me-catalyzed hydrogenation of SubI is given in Scheme 3. The relative Gibbs free energies in Or1 are presented in Table 4 (for optimized geometries see Figures S11−S13, SI; for full hydrogenation mechanism in Or2, see Table S2 and Figure S14−S17, SI). Energy corrections due to spin projection are not included, because reliable computation of the HS−BS gap was not possible.24 Following formation of the alkene-coordinated species (species II, Scheme 3), the first reaction step in Or1 involves hydride transfer from Co to the terminal alkene carbon (TSH‑_transfer, III, Co−H− = 1.52 Å, H···CSubI = 1.54 Å, imaginary frequency = 719.5i cm−1), with ΔG⧧ = −0.9 kcal/ mol relative to (S)-1-H and free SubI (3.1 kcal/mol relative to II, Table 4). This corresponds to a 2,1-insertion of the substrate into the Co−H bond. Both reactant (II) and TSH‑_transfer (III) prefer an AF-S electronic state. The intermediate formed (Alkyl_Interagostic, IVag) has a relative energy of −3.7 kcal/mol (Table 4) and has closed-shell character (in calculations without dispersion, an AF-S state is obtained). The optimized geometry shows an agostic interaction between the transferred hydrogen and Co (Co···HSubI = 1.71 Å, H−CSubI = 1.18 Å, Figure 6). This interaction has to be broken in order to allow the complex to bind an incoming H2 molecule. The intermediate without agostic interaction, Alkyl_Inter%agostic (IV, Figure 6), breaks symmetry to give an AF-S or AF-T electronic state (Figure 2). The AF-T state is highly preferred (Table 4), which is partly due to displacement of the high-spin cobalt out of the BIP plane, resulting in less steric interactions between the substrate and the N-aryl and N-alkyl substituents. The results indicate that a low-spin (SCo = 0 or 1/2) → highspin (SCo = 3/2) spin crossover can occur for alkyl intermediate IV (Figure 6).

modes (Figure 5, for optimized geometries see Figure S10, SI). The substrate prefers to coordinate such that steric interactions

Figure 5. Binding modes of SubI to (S)-1-H (R = Cy) and (S)-2-H (R = tBu). Energies (kcal/mol) relative to free SubI + (S)-1-H/(S)-2-H, in parentheses relative to (S)-1-CM/(S)-2-CM. Or1/Or2 result in 2,1insertion and Or3/Or4 in 1,2-insertion of SubI into the Co−H bond (numbers mark atom to which initial H− transfer occurs).

with the Cy group are minimized. In Or1 and Or2, the substrate double bond is aligned with the Co−H bond and the substrate bulk is placed below the BIP ligand (with Cy pointing above BIP). In Or3 and Or4, the double bond is essentially pointing in opposite direction of Or1 and Or2, with the substrate bulk pointing outward. Or1 and Or2 are favored over

Scheme 3. Computed Mechanism for Alkene Hydrogenation and Isomerization with Chiral CoBIPa

a

Hydrogenation can occur through I to VII (green shading). Rotation of IV to IVi (white shading) can lead to an alternative hydrogenation pathway (Vi to VIIi, brown shading) or can result in isomerization to a different alkene (IIIi to Ii, blue shading). White shading indicates species that might undergo an AF-S →AF-T spin crossover. Asterisks indicate the chiral alkane product. F

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Table 4. Computed Energies (kcal/mol) for Hydrogenation of SubI in Or1 (pro-(S)) with (S)-1-Me (a conformer)a structure (S)-1-H + free SubI (S)-1-H-SubI (pro-Sa) TSH‑_transfer Alkyl_Interagostic Alkyl_Inter%agostic Hydrogenation without rotation TSH2_binding InterH2 TSH+_transfer (S)-1-H + free (S)-ProdI Isomerization TSrotation Alkyl_Inter%agostic_i Alkyl_Interagostic_i TSH‑_transfer_i (S)-1-H-SubI_isomer (pro-S) (S)-1-H + free SubI_isomer Hydrogenation af ter rotation TSH2_binding_i InterH2_i TSH+_transfer_i (S)-1-H + free (S)-ProdI a

speciesb

⟨S2⟩BS

spin state

I+SubI II III (IVag)c IV

AF-S AF-S AF-S CSd AF-S [AF-T]

0.876 0.477 0.112

V VI VII I+ProdI

AF-S CS AF-S AF-S

0.239

VIII IVi (IVag_i)c IIIi IIi Ii+isomer

AF-S [AF-T] AF-S [AF-T] CS AF-S AF-S AF-S

0.638 [2.553] 0.248 [2.483]

Vi VIi VIIi Ii+ProdI

AF-S CS AF-S AF-S

0.331 [2.489]

0.258 0.509 0.876

ΔG 0.0 −4.2 −0.9 −3.7 −4.7 [−13.2]

−20.7 −26.6 −17.0 −26.6

0.581 0.876

0.202 0.747 0.876

ΔH 0.0 −21.7 −18.3 −20.4 −21.1 [−27.5]

−7.8 [−16.8] −17.6 [−22.6] −12.6 −10.7 −14.7 −4.2 −15.9 −24.2 −14.2 −26.6

4.6 −1.1 8.4 −17.8 10.8 [−0.8] −0.7 [−8.0] 5.3 7.6 2.1 −4.3 9.3 1.2 11.1 −17.8

See Figure 5, all anti-geometries (Scheme 1b). bCorresponding species in Scheme 3. cIntermediate with agostic Co−H interaction, Figure 6. Breaks symmetry for dispersion-free geometry.

d

implies that at the alkyl intermediate VI the substrate rotates around the Co−CSub bond (TSrotation, VIII) to give a rotated alkyl species IVi, which undergoes hydride elimination (IIIi, Scheme 3) to form the alkene isomer. As observed for the alkyl intermediate IV (Figure 6), the TS for rotation of the alkyl (VIII) can be located on either an AF-S (ΔG⧧ = 10.8 kcal/mol) or an AF-T surface (ΔG⧧ = −0.8 kcal/mol, Table 4). The lower energy of the AF-T species is partly due to the fact that Co displacement out of the BIP plane facilitates rotation around the Co−alkyl bond. The computed energies indicate that for SubI bound in Or1, rotation of the alkyl intermediate is likely to occur only if the system can undergo a spin transition to the AF-T state (as the AF-S rotation barrier is higher than the hydrogenation barrier, 8.4 kcal/mol, VII, Table 4). The subsequent hydride elimination TS (IIIi) has a barrier of 7.6 kcal/mol, slightly lower than hydrogenation (VII, Table 4), indicating that significant amounts of SubI_isomer might be formed. Note that the isomerization mechanism as shown in Scheme 3 is possible only for binding modes allowing for 2,1insertion (Or1 or Or2, Figure 5) and not for 1,2-insertion modes (Or3 or Or4). Interestingly, it is also possible that the rotated alkyl species IVi does not proceed through hydride elimination (IIIi), but instead binds H2 and undergoes hydrogenation to yield the alkane product (steps Vi to VIIi, Scheme 3) with the same stereochemical configuration as for hydrogenation without rotation. For SubI bound in Or1, the barrier for hydrogenation after rotation is 11.1 kcal/mol (VIIi, Table 4), indicating that it is less likely to occur than hydrogenation without rotation (ΔG⧧ = 8.4 kcal/mol, VII, Table 4). The energetic results for SubI bound in Or1 are summarized in Figure 7. Note that the relative barriers of the different reaction pathways (hydrogenation with or without rotation or isomerization) are dependent on the substrate binding mode (for SubI bound in Or2, see Figure S17, SI).

Figure 6. Alkyl intermediate IV formed following hydride transfer to SubI. Without agostic interaction, a high-spin state is preferred.

For hydrogenation to proceed, H2 has to coordinate to the complex, which is successful only on a low-spin surface. The TS for H2 coordination (TSH2_binding, V, Co···H2 = 2.50 and 2.57 Å, imag. freq. = 130.9i cm−1) has a barrier of 4.6 kcal/mol and prefers an AF-S state. The formed intermediate (InterH2, VI) has a relative energy of −1.1 kcal/mol (Table 4). The final TS (TSH+_transfer, VII, imag. freq. = 1094.1i cm−1, H···H = 1.05 Å, H···C*SubI = 1.56 Å), corresponding to a metathesis-type (stereoselective) proton transfer from Co−H2 to the formally anionic prochiral carbon of SubI, has a barrier of 8.4 kcal/mol and is thus rate-limiting. A transition state for an oxidative addition type reaction with dihydride formation prior to proton transfer was not found, in agreement with previous results.5 The formed (S)-alkane has a relative energy of −17.8 kcal/mol (Table 4). In experimental studies, the conversion of SubI with one of the CoBIP catalysts, (S)-2-CM, leads to accumulation of an undesired side product, namely, the endocyclic alkene isomer of SubI (SubI_isomer).11 On the basis of the results computed here, it is proposed that CoBIP complexes are able to catalyze a competing isomerization reaction through hydride addition/ elimination (an alternative proton abstraction/addition mechanism is ruled out, Figure S18, SI). The isomerization pathway G

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Figure 7. Computed energies (ΔG, Table 4) for (S)-1-Me-mediated hydrogenation and isomerization of SubI (Or1, pro-(S); see inset of species II; see Scheme 3 for mechanistic details).

Preferred Electronic States during Hydrogenation. The optimized geometries along the hydrogenation and isomerization pathways (Scheme 3) mostly prefer AF-S electronic states, with the intermediates Alkyl_Interagostic (IVag) and InterH2 (VI) apparently preferring a CS solution (Table 4). Note that a transition from AF-S to CS does not require a spin-flip, but only a stronger overlap of the orbitals involved in the AF coupling. If the overlap is very strong, a covalent (closed-shell) interaction occurs. This appears highly geometry-dependent (without dispersion corrections, a minimally different geometry is obtained for Interagostic, which shows an AF-S electronic state) and is probably also functional dependent.25 For the free catalyst, (S)-1-H, the ferromagnetic triplet (F-T, Figure 2) is less than 1 kcal/mol above the AF-S state (Table 2). However, the F-T state appears irrelevant during catalysis. Optimization of the structures along the hydrogenation path on the F-T or AF-T surface results in much higher energies (or unstable species leading to dissociation of ligands), with the notable exception of the alkyl intermediate IV and TSrotation VIII (Scheme 3), which might undergo an AF-S → AF-T crossover, as discussed above (Figure 6). It cannot be excluded that B3LYP erroneously favors a high-spin state for IV, as recently suggested for a related FeBIP complex (Figure S19, SI).26 For FeBIP, the AF-T state is 7.9 kcal/mol favored over AF-S (ΔE, B3LYP), although experimental evidence suggests that AF-S is the ground state at low temperatures.26 As a test case, the calculations on FeBIP have been repeated here. The previous result is reproduced if energetic corrections are omitted, but inclusion of dispersion, thermal, and solvent corrections reduce the gap between AF-S and AF-T to 1.6 kcal/ mol, with spin projection providing a lowering to 0.6 kcal/mol (Table S3, SI). Thus, the erroneous preference for the highspin state should be small with the computational protocol employed here, far smaller than the preference of IV for the AF-T state (∼9 kcal/mol, Table 4).

As an additional evaluation of the spin-state preference of IV, calculations were performed with DFT functionals with varying degree of Hartree−Fock exchange (10−50%, Table S4, SI). Although the low-spin/high-spin gaps vary greatly, all functionals tested, BHandHLYP (50%), B3LYP (20%), B3LYP* (15%), and TPSSh (10%), predict the high-spin state AF-T to be the ground state of the alkyl intermediate IV. Enantioselectivity of SubI Hydrogenation with (S)-1Me. SubI can be hydrogenated with either (S)-1-Me or (S)-2CM (Figure 1).11 With (S)-1-Me, a low ee of 39% (S) is observed, whereas with (S)-2-CM, a unprecedented ee of 96% (S) was obtained, but accompanied by accumulation of an alkene isomer in the product mixture (Table 1).11 The analysis below seeks to shed light on the differences in enantioselectivity and product compositions for SubI hydrogenation with the two CoBIP catalysts. Elucidation of the stereocontrol of chiral CoBIP requires optimization of the lowest lying rate-limiting pro-(R) and pro(S) transition states for a given substrate. This is particular challenging for (S)-1-Me due to the following aspects: (i) the active monohydride species (S)-1-H has a significant degree of conformational flexibility (with conformations studied here being a/b and syn/anti, Scheme 1b, Figure 4); (ii) hydrogenation can occur with and without rotation of the alkyl intermediate (Scheme 3); (iii) the starting alkene might isomerize (Scheme 3), and the isomer might be hydrogenated, possibly with a selectivity significantly different from that of the starting alkene. In the following, all of the above points are addressed. Initially, it is evaluated how the conformational flexibility of the catalyst affects the selectivity. The computations show that the a conformer of the active species (S)-1-H is preferred over the b conformer by >4 kcal/mol (Table 2, Scheme 1b). The ratelimiting proton transfer barrier for SubI in Or1 with the b conformer is also more than 4 kcal/mol higher than for a. Thus, H

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conformer b of the catalyst should not be relevant for the stereochemical outcome of SubI hydrogenation. For free (S)-1-H, the anti-form is preferred over the syn-form by 2.1 kcal/mol (Figure 4). The SubI-coordinated species (Or1, II) shows a similar energy difference between syn and anti of 2.5 kcal/mol. However, for the proton transfer transition state in Or1 (VII), the syn-form is 0.9 kcal/mol below the antiform. Conversion of anti to syn for the SubI-coordinated alkyl intermediate (IV) has a barrier of 5.6 kcal/mol relative to the anti-form (1.4 kcal/mol relative to free (S)-1-H). The results imply that rapid interconversion of syn and anti can occur and that both forms need be taken into account for evaluating the stereoselectivity. The hydrogenation of SubI was evaluated in the different binding modes Or1 to Or4 (Figure 5), with both syn- and anticonformations (with the discussion below concentrating on the anti-forms). Hydrogenation of SubI in Or1 is favored without rotation of the alkyl intermediate (VII vs VIIi, Table 4), with a rate-limiting barrier of 8.4 kcal/mol. However, if rotation can occur on an AF-T surface (implying a very low barrier for rotation of −0.8 kcal/mol), the overall barrier for isomerization becomes similar to hydrogenation (7.6 kcal/mol, IIIi, Table 4). Or1 could thus lead to formation of both SubI_isomer and (S)Prod. For SubI bound in Or2, hydrogenation after rotation is preferred (VII vs VIIi, Table S2, SI), with a rate-limiting barrier of 8.3 kcal/mol. However, the barrier for alkene isomerization is somewhat lower (5.7 kcal/mol, III, Table S2, SI). Or2 should thus primarily lead to formation of SubI_isomer and some (R)Prod. The binding modes Or3 and Or4 of SubI are respectively 11.3 and 6.3 kcal/mol above Or1 (Figure 5), but might nonetheless be catalytically relevant. However, the hydride transfer TS (III) in Or3 and Or4 has barriers of respectively 20.2 and 9.7 kcal/mol, which is larger than the overall hydrogenation barriers in Or1 and Or2 (vide supra). Or3 and Or4 are thus not considered relevant for the stereochemical outcome of SubI hydrogenation. The final product enantioselectivity should depend on if the formed trisubstituted SubI_isomer can be hydrogenated by (S)1-Me. Coordination of SubI_isomer to (S)-1-H can occur in binding modes Or1 to Or3 (Or4 leads to substrate dissociation), with relative energies 6.3, 1.3, and 2.0 kcal/mol, respectively (Figure 8, for optimized geometries see Figure S20, SI). The preference for Or3 over Or1 is due to less steric interactions with the 2,6-diisopropylaryl group and favorable dispersion interactions with C*-Me of the catalyst. The low binding energies in Or2 and Or3 suggest that (S)-1-H is able to hydrogenate SubI_isomer. Binding of SubI_isomer in Or2 (Figure 8) leads to the same complex that is formed when SubI in Or2 is converted into isomer (IIi, Table 4, Scheme 3). Thus, the lowest lying pro-(R) binding modes of SubI and SubI_isomer exist on the same reaction pathway, and the proton transfer TSs are the same, with the lowest TS exhibiting a barrier of 8.3 kcal/mol (VIIi, Table S2, SI). An identical situation is seen for Or1 of SubI_isomer, which is on the same pathway as Or1 of SubI, with the lowest TS having a barrier of 8.4 kcal/mol (VII, Table 4). For Or3 of SubI_isomer, initial hydride transfer occurs to the prochiral carbon, and the alkyl intermediate formed is not on the same reaction path as SubI. Upon coordination of H2, the alkyl intermediate spontaneously rotates around the CSubI−

Figure 8. Binding modes of SubI_isomer to (S)-1-H (R = Cy) and (S)-2-H (R = tBu). Energies in kcal/mol (relative to free substrate and (S)-1-H/(S)-2-H, in parentheses relative to (S)-1-CM/(S)-2-CM). Numbers mark the atom to which initial hydride transfer occurs (with the internal double bond labeled 2 and 3).

Co bond, and the resulting proton transfer TS has a barrier of 9.0 kcal/mol (VII, Table S5, SI). To evaluate the final stereochemical outcome of (S)-1-Memediated conversion of SubI, hydrogenation of both SubI and SubI_isomer needs to be taken into account. It is assumed that the differences in coordination cost are not relevant, but that the selectivity solely is governed by the barrier heights (Curtin−Hammett principle). As outlined (vide supra), the relevant TSs have barriers of 8.4 kcal/mol (Or1, pro-(S), VII, Table 4), 8.3 kcal/mol (Or2, pro-(R), VIIi, Table S2, SI), and 9.0 kcal/mol (Or3, pro-(S), Table S5, SI, all anti-geometries). The corresponding barriers in syn-conformation are respectively 7.5, 9.2, and 9.8 kcal/mol. The resulting ee (on the basis of all syn- and anti-TSs) is 60% (S). If IEFPCM is included in the optimizations, the relative barrier changes are small (0.1 to 0.2 kcal/mol), with a resulting ee of 53% (S). The results are in good agreement with the low experimental ee of 39% (S)11 (note that the relationship between barrier and ee is exponential27). Scheme 4 summarizes the overall results for (S)-1-Me-catalyzed hydrogenation of SubI. Enantioselectivity of SubI Hydrogenation with (S)-2CM. The experimental enantioselectivity of (S)-2-CM-mediated hydrogenation of SubI is 96% (S), which is significantly higher than for (S)-1-Me (39% (S), Table 1).11 However, SubI hydrogenation with (S)-2-CM is accompanied by accumulation of SubI_isomer in the product mixture, which is not observed with (S)-1-Me.11 The above analysis predicts that for (S)-2-CM the proposed active species (S)-2-H is stabilized in the presence of SubI (Table 3, entry VI). This is the case only when SubI is bound in Or1 (Figure 5). The second lowest binding orientation (Or2) does not stabilize (S)-2-H much, with a binding energy of 3.9 kcal/mol relative to free (S)-2-CM (Figure 5). Binding modes Or3 and Or4 are respectively 9.7 and 6.2 kcal/mol relative to free (S)-2-CM. Conversion to (S)-2-H should thus primarily be driven by formation of Or1. Only the a conformer of (S)-2-H is expected to be catalytically relevant, as the b conformer is 4.9 I

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isomerization barrier is slightly lower than hydrogenation (6.2 kcal/mol, IIIi, Table S6, SI). Or1 would thus lead to (S)-ProdI and SubI_isomer. For SubI bound to (S)-2-H in Or2 (Figure 5), hydrogenation preferably occurs after rotation (ΔG⧧ = 6.2 kcal/mol, VIIi), but the overall isomerization barrier is very low (2.6 kcal/mol, III, Table S7, SI), indicating that essentially all SubI should be converted to isomer. This is not supported by experiments, which reported 56% isomer in the product mixture.11 There are various scenarios that can explain this finding: (i) the barrier for isomerization is underestimated, (ii) some of the formed isomer is hydrogenated, (iii) Or2 is not active, because (S)-2-H is not stabilized relative to (S)-2-CM. These points are evaluated below. The excess amount of isomer predicted by calculations could be due to the fact that the barrier for isomerization relative to hydrogenation is underestimated, because the computed energies could not be corrected through spin projection.24 Due to the different nature of the rate-limiting TSs for respectively isomerization (III/IIIi) and hydrogenation (VII/ VIIi, Scheme 3), these might be affected differently by spin projection. It is also important to note that in experiment there is a vast excess of H2, which might be a driving force toward hydrogenation rather than isomerization, despite the lower computed barrier for isomerization. The calculations thus cannot predict how much isomer is formed in experiment, but they clearly indicate significant formation of SubI_isomer. A crucial point is whether SubI_isomer can be hydrogenated by (S)-2-CM. Coordination of SubI_isomer to (S)-2-H costs 6.5 kcal/mol relative to free (S)-2-CM (Or1, Figure 8). This implies that SubI_isomer does not stabilize the active catalyst form (S)-2-H, which in the presence of SubI_isomer rather would be in the inactive (S)-2-CM state. It is therefore predicted here that in the presence of SubI_isomer alone, (S)2-CM is not activated and isomer hydrogenation does not occur. However, as long as the reaction mixture also contains SubI, which can stabilize (S)-2-H formation, some of the isomer might be hydrogenated, which could occur through the same four TSs as SubI (Or1 and Or2, VII and VIIi, ΔG⧧ = 6.2 to 8.6 kcal/mol, Tables S6 and S7, SI) or through Or3 (Figure

Scheme 4. Summary of Results for (S)-1-Me-Catalyzed Hydrogenation of SubIa

a

SubI can be hydrogenated directly (preferred in Or1) or after rotation (preferred in Or2), or isomerize instead. The isomer is hydrogenated through the same pathways as SubI (Or1 and Or2) or through a different binding mode (Or3).

kcal/mol higher in energy (Table 2), and also the rate-limiting proton transfer transition states of the b form are around 4 kcal/mol above the a form. Once (S)-2-H is formed, the system appears to behave similar to (S)-1-H, with slight differences in the relative energies. The two 1,2-insertion modes Or3 and Or4 of SubI (Figure 5) show barriers for the first hydride transfer step (III) of respectively 15.5 and 10.1 kcal/mol (relative to (S)-2-H and free substrate), which is higher than the overall hydrogenation barriers for the 2,1-insertion modes Or1 and Or2 (vide inf ra). Or3 and Or4 are therefore not considered relevant for the stereochemical outcome. For Or1 of SubI (Figure 5), hydrogenation preferably occurs without rotation (ΔG⧧ = 7.1 vs 8.2 kcal/mol, VII vs VIIi, Table S6, SI). Rotation of the alkyl intermediate IV is expected to take place only if an AF-S → AF-T spin crossover can occur (as the rotation barrier otherwise is too high), and if it does, the

Scheme 5. Summary of Computed Results for (S)-2-CM-Catalyzed Hydrogenation of SubIa

a

The active (S)-2-H species is stabilized by SubI bound in Or1, leading to (S)-ProdI and SubI_isomer. SubI_isomer does not stabilize (S)-2-H and is not hydrogenated. (S)-2-H is expected to continuously convert to the more stable (S)-2-CM form, either during hydrogenation (through proton transfer from tBu to SubI, dashed line) or following hydrogenation (through loss of H2). J

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8, ΔG⧧ = 6.9 kcal/mol). This would result in a small excess of (R)-Prod and is not supported by experiment (ee 96% (S)11). These results indicate that SubI_isomer is not hydrogenated by (S)-2-CM to any significant amount. The combined results indicate that the most likely scenario appears to be that essentially only the SubI binding mode, which can stabilize the monohydride species relative to the (S)2-CM form, i.e., Or1 (Figure 5), is active, leading to formation of (S)-ProdI and SubI_isomer. As discussed above, it is not possible to estimate the amount of isomer relative to alkane product, but the computed barriers for hydrogenation (ΔG⧧ = 7.1 kcal/mol, VII) and isomerization (ΔG⧧ = 6.2 kcal/mol, IIIi, Table S6, SI) in Or1 are in reasonable agreement with the experimental results of 44% alkane and 56% isomer.11 The isomer accumulates and is not hydrogenated, because binding of SubI_isomer does not stabilize (S)-2-H, which rather converts back to the more stable but inactive (S)-2-CM form. Conversion of (S)-2-H to (S)-2-CM can occur through loss of H2 (Table 3, entry IV, ΔG⧧ = 20.7 kcal/mol relative to (S)-2H), or it can occur as part of the SubI hydrogenation cycle. After formation of the alkyl intermediate IV, instead of binding H2, the tBu group can transfer a proton to the substrate with simultaneous formation of the CM bond, leading to both ProdI and (S)-2-CM (Figure S21, SI). The relevant TS in Or1 has a barrier of 18.2 kcal/mol (14.4 kcal/mol in Or2). Scheme 5 summarizes the results obtained for SubI hydrogenation with (S)-2-CM.

abstraction/addition was found unfeasible. The results further show that essentially all species on the hydrogenation and isomerization pathways prefer a low-spin AF-S electronic state, with the exception of the alkyl intermediate (and the transition state for rotation thereof), which prefers a high-spin AF-T state. This indicates that a spin crossover might occur during the reaction. The differences in experimentally observed enantioselectivities of (S)-1-Me- and (S)-2-CM-catalyzed hydrogenation of SubI could be rationalized on the basis of the computed results. For (S)-1-Me, the calculations predict that the catalyst forms significant amounts of alkene isomer, but both SubI and SubI_isomer are hydrogenated with low selectivity, in agreement with the low ee obtained in experiments.11 With (S)-2CM, SubI hydrogenation should mainly occur through the binding mode stabilizing the active monohydride species, resulting in a high enantioselectivity for the product, but also substantial formation of isomer. The isomer does not stabilize the active catalyst form, explaining the experimentally observed accumulation of isomer.11 If the reaction conditions could be modified such that SubI_isomer is hydrogenated by (S)-2-CM, e.g., by increasing the H2 pressure, as has been suggested,11 this should result in a loss of the enantioselectivity.

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ASSOCIATED CONTENT

S Supporting Information *

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Additional results for FeBIP and for CoBIP-mediated hydrogenation, as referred to in the text. This material is available free of charge via the Internet at http://pubs.acs.org.

CONCLUSIONS We have presented a comprehensive quantum mechanical study of two recently reported chiral CoBIP catalysts (Figure 1, Table 1).11 Rational improvement of these is dependent on a detailed knowledge of their properties, activation pathways, and asymmetric hydrogenation mechanisms. The presented results show that the precatalysts ((S)-1-Me, (S)-1-CM, (S)-2-CM) and the active catalysts ((S)-1-H, (S)-2-H) prefer an antiferromagnetic singlet electronic state (AF-S, Figure 2), which can be described as low-spin (SCo = 1/2) Co(II) AFcoupled to anionic radical (SBIP = 1/2) BIP. For the monohydride complexes, the BS energy gap between AF-S and the ferromagnetic triplet (F-T) is small (