Supporting Information. Substitutent Rate Effects

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1 Supporting Information Gosteli Claisen Rearrangement: DFT Study of Substitutent Rate Effects Julia Rehbein* and Martin Hiersemann* Fakultät Chemie, Technische Universität Dortmund, Dortmund, Germany SI- Figure SI-1 free energy profile for (E,E)-1a SI-4 Figure SI-2 free energy profile for (E,Z)-1b SI-5 Figure SI- free energy profile for (Z,E)-1c SI-6 Figure SI-4 free energy profile for (Z,Z)-1a SI-7 Table SI-1 geometric data for (E,E)-1a SI-8 Table SI-2 geometric data for (E,Z)-1b SI-9 Table SI- geometric data for (Z,E)-1c SI-10 Table SI-4 geometric data for (Z,Z)-1d SI-11 SI-12 Table SI-5 Table SI-6 BLYP/6-1G*+PCM(solvent = 1,2- dichloroethane) free energies of 1a-d BLYP/6-1G*+PCM(solvent = 1,2- dichloroethane) free energies of [1a-d] SI-1 Table SI-7 geometric data for 2a,b

2 SI-14 SI-15 SI-16 SI-17 SI-18 SI-19 SI-20 SI-21 SI-22 Table SI-8 Table SI-9 Figure SI-5 Figure SI-6 Figure SI-7 Figure SI-8 Figure SI-9 Figure SI-10 Figure SI-11 BLYP/6-1G*+PCM(solvent = 1,2- dichloroethane) energies and geometric data for [st-1a-d] BLYP/6-1G*+PCM(solvent = 1,2- dichloroethane) energies and geometric data for st-1a-d at K BLYP/6-1G*+PCM(solvent = 1,2- dichloroethane)-relative free energies G rel for st- 1a-d and [st-1a-d] Newman projection of [st-1a-d], k rel,exp, G ts rel and ΔG rel BLYP/6-1G*+PCM(solvent = 1,2- dichloroethane)-mulliken atomic charges BLYP/6-1G*+PCM(solvent = 1,2- dichloroethane)-structures for (E,E)-1a BLYP/6-1G*+PCM(solvent = 1,2- dichloroethane)-structures for (E,Z)-1b BLYP/6-1G*+PCM(solvent = 1,2- dichloroethane)-structures for (Z,E)-1c BLYP/6-1G*+PCM(solvent = 1,2- dichloroethane)-structures for (Z,Z)-1d SI-2

3 [st-(e,e)-1a] BLYP/6-1G* i-pr [sc-(e,e)-1a] i-pr BLYP/6-1G* S R sc-syn-2a i-pr sc-2a* could not be located on PES st-(e,e)-1a* st-(e,e)-1a i-pr sc-(e,e)-1a i-pr sc-(e,e)-1a* 1. G rel [kcal/mol] BLYP/6-1G* 2. G [Hartree] BLYP/6-1G*. G rel [kcal/mol] BLYP/6-1G*+PCM(1,2-dichloroethane) 4. G [Hartree] BLYP/6-1G*+PCM (1,2-dichloroethane) i-pr st-2a* S R st-syn-2a i-pr s-trans pathway s-cis pathway FIGURE SI-1. Calculated free energy profile for the Gosteli Claisen rearrangement of (E,E)-1a. SI-

4 [st-(e,z)-1b] BLYP/6-1G* i-pr [sc-(e,z)-1b] i-pr BLYP/6-1G* i-pr 4R R sc-anti-2b sc-2b* could not be located on PES converged to s-trans s-trans pathway st-(e,z)-1b* st-(e,z)-1b i-pr sc-(e,z)-1b i-pr sc-(e,z)-1b* G rel [kcal/mol] BLYP/6-1G* 2. G [Hartree] BLYP/6-1G*. G rel [kcal/mol] BLYP/6-1G*+PCM(1,2-dichloroethane) 4. G [Hartree] BLYP/6-1G*+PCM (1,2-dichloroethane) i-pr st-2b* s-cis pathway R R st-anti-2b i-pr FIGURE SI-2. Calculated free energy profile for the Gosteli Claisen rearrangement of (E,Z)-1b. SI-4

5 i-pr 4R S sc-anti-2b [st-(z,e)-1c] sc-2b* BLYP/6-1G* st-(z,e)-1c* st-(z,e)-1c i-pr sc-(z,e)-1c i-pr [sc-(z,e)-1c] i-pr sc-(z,e)-1c* G rel [kcal/mol] BLYP/6-1G* 2. G [Hartree] BLYP/6-1G*. G rel [kcal/mol] BLYP/6-1G*+PCM(1,2-dichloroethane) 4. G [Hartree] BLYP/6-1G*+PCM (1,2-dichloroethane) i-pr st-2b* i-pr BLYP/6-1G* R S i-pr st-anti-2b s-trans pathway s-cis pathway FIGURE SI-. Calculated free energy profile for the Gosteli Claisen rearrangement of (Z,E)-1c. SI-5

6 i-pr i-pr [st-(z,z)-1d] BLYP/6-1G* [sc-(z,z)-1d] BLYP/6-1G* R S sc-syn-2a i-pr sc-2a* st-(z,z)-1d* st-(z,z)-1d i-pr sc-(z,z)-1d G rel [kcal/mol] BLYP/6-1G* 2. G [Hartree] BLYP/6-1G*. G rel [kcal/mol] BLYP/6-1G*+PCM(1,2-dichloroethane) 4. G [Hartree] BLYP/6-1G*+PCM(1,2-dichloroethane) i-pr sc-(z,z)-1d* i-pr st-2a* R S i-pr st-syn-2a s-trans pathway s-cis pathway FIGURE SI-4. Calculated free energy profile for the Gosteli Claisen rearrangement of (Z,Z)-1d. SI-6

7 TABLE SI-1. Gosteli Claisen rearrangement of the (E,E)-configured allyl vinyl ether 1a. BLYP/6-1G*+PCM(solvent = 1,2- dichloroethane) bond order of the breaking (d 1 C1 ) and the forming bond (d C C ), dihedral angles ω, charge separation δ between the allylic and oxallylic segment and dipole moments μ for the allyl vinyl ethers and transition states. BLYP/6-1G*-values in parenthesis. d 1 C1 d C C ω c δ d μ e entry cmpd [Å] n a [Å] n b [ ] [AU] [D] 1 sc-1a (1.428) (5.256) (+1) (0.5) (2.) [sc-1a] (2.021) (0.7) (2.27) (0.28) ( 8) (0.4) (2.6) st-2a 4 st-1a (5.409) (1.556) ( 156) (1.7) (1.427) (5.258) ( 154) (0.45) (2.1) [st-1a] (2.027) (0.7) (2.57) (0.28) (+124) (0.45) (.2) 6 sc-2a (5.1) (1.55) (+4) (4.) a Bond order n in % calculated according to Pauling: n = exp[(d ave d ts ) / 0.6]. b Bond order n in % calculated according to Pauling: n = exp[(d α- ke d ts ) / 0.6]. c as defined in Table SI-5. d Mulliken charge separation between the allylic and oxallylic segment of the allyl vinyl ether as defined in Figure SI-7. e Dipole moments calculated by Mulliken Population Analysis (MPA) 1 or Natural Population Analysis (NPA) 2, were identical. SI-7

8 TABLE SI-2. Gosteli Claisen rearrangement of the (E,Z)-configured allyl vinyl ether 1b. BLYP/6-1G*+PCM(solvent = 1,2- dichloroethane) bond lengths of the breaking (d 1 C1 ) and the forming bond (d C C ), dihedral angles ω, charge separation δ between the allylic and oxallylic segment and dipole moments μ for the allyl vinyl ethers and transition states. BLYP/6-1G*-values in parenthesis. d 1 C1 d C C ω c δ d μ e entry cmpd [Å] n a [Å] n b [ ] [AU] [D] 1 sc-1b (1.427) (5.18) +11 (0.5) (2.2) ( 1) [sc-1b] (1.986) (0.9) (2.2) (0.27) ( 7) (0.44) (2.5) st-2b 4 st-1b (5.154) (1.551) ( 174) (1.5) (1.427) (5.22) (+155) (0.54) (2.4) [st-1b] (1.99) (0.9) (2.47) (0.28) (+11) (0.46) (.1) 6 sc-2b (5.1) (1.55) (+4) (4.) a Bond order n in % calculated according to Pauling: n = exp[(d ave d ts ) / 0.6]. b Bond order n in % calculated according to Pauling: n = exp[(d α- ke d ts ) / 0.6]. c as defined in Table SI-5. d Mulliken charge separation between the allylic and oxallylic segment of the allyl vinyl ether as defined in Figure SI-7. e Dipole moments calculated by Mulliken Population Analysis (MPA) 1 or Natural Population Analysis (NPA) 2, were identical. SI-8

9 TABLE SI-. Gosteli Claisen rearrangement of the (Z,E)-configured allyl vinyl ether 1c. BLYP/6-1G*+PCM(solvent = 1,2-dichloroethane) bond lengths of the breaking (d 1 C1 ) and the forming bond (d C C ), dihedral angles ω, charge separation δ between the allylic and oxallylic segment and dipole moments μ for the allyl vinyl ethers and transition states. BLYP/6-1G*-values in parenthesis. entry cmpd d 1 C1 d C C ω c δ d μ e [Å] n a [Å] n b [ ] [AU] [D] 1 sc-1c (1.44) (5.526) ( 7) (0.52) (2.1) [sc-1c] (2.017) (0.8) (2.64) (0.26) ( 16) (0.44) (2.2) st-2c 4 st-1c (5.154) (1.551) (+174) (1.5) (1.446) 0.6 (5.548) 0.24 (+17) (0.54) (2.0) (0.6) (0.24) [st-1c] (2.04) (2.70) (+145) (0.46) (.6) 6 sc-2c (5.1) (1.55) (+4) (4.) a calculated according to Bond order n in % calculated according to Pauling: n = exp[(d ave d ts ) / 0.6]. b Bond order n in % calculated according to Pauling: n = exp[(d α-ke d ts ) / 0.6]. c As defined in Table SI-5. d Mulliken charge separation between the allylic and oxallylic segment of the allyl vinyl ether as defined in Figure SI-7. e Dipole moments calculated by Mulliken Population Analysis (MPA) 1 or Natural Population Analysis (NPA) 2, were identical. SI-9

10 TABLE SI-4. Gosteli Claisen rearrangement of the (Z,Z)-configured allyl vinyl ether 1d. BLYP/6-1G*+PCM(solvent = 1,2-dichloroethane) bond lengths of the breaking (d 1 C1 ) and the forming bond (d C C ), dihedral angles ω, charge separation δ between the allylic and oxallylic segment and dipole moments μ for the allyl vinyl ethers and transition states. BLYP/6-1G*-values in parenthesis. entry cmpd d 1 C1 d C C ω c δ d μ e [Å] n a [Å] n b [ ] [AU] [D] 1 sc-1d (1.44) (5.585) (+7) (0.52) (2.0) [sc-1d] (2.000) (0.40) (2.82) (0.25) ( 16) (0.45) (2.2) st-2a 4 st-1d (5.409) (1.556) ( 156) (1.5) (1.446) (5.578) (+172) (0.54) (2.) [st-1d] (2.005) (0.9) (2.75) (0.25) ( 150) (0.46) (.5) 6 sc-2a (5.1) (1.55) (+4) (4.) a calculated according to Bond order n in % calculated according to Pauling: n = exp[(d ave d ts ) / 0.6]. b Bond order n in % calculated according to Pauling: n = exp[(d α-ke d ts ) / 0.6]. c as defined in Table SI-5. d Mulliken charge separation between the allylic and oxallylic segment of the allyl vinyl ether as defined in Figure SI-7. e Dipole moments calculated by Mulliken Population Analysis (MPA) 1 or Natural Population Analysis (NPA) 2, were identical. SI-10

11 TABLE SI-5. Gosteli Claisen rearrangement of 1a-d. BLYP/6-1G*+PCM(solvent = 1,2-dichloroethane) free energies of 1a-d at K. i-pr i-pr ω [deg] i-pr st-1a sc-1a st-1b sc-1b i-pr i-pr +ω [deg] st-1c sc-1c st-1d sc-1d entry configuration conformation compound G [Hartree] G relative [Hartree] G relative [kcal/mol] 1 (E,E) s-trans st-1a s-cis sc-1a (E,Z) s-trans st-1b s-cis sc-1b (Z,E) s-trans st-1c s-cis sc-1c (Z,Z) s-trans st-1d s-cis sc-1d SI-11

12 TABLE SI-6. Gosteli Claisen rearrangement of the allyl vinyl ether 1a-d. BLYP/6-1G*+PCM(solvent = 1,2-dichloroethane) free energies of the transition states [1a-d] at K. [c-st-1a] = chairlike transition state for the Gosteli Claisen rearrangement of the allyl vinyl ether 1a. b = boatlike, sc = s-cis. i-pr i-pr i-pr i-pr [st-1a] [sc-1a] [st-1b] [sc-1b] [st-1c] [sc-1c] [st-1d] [sc-1d] entry configuration conformation compound G [Hartree] G relative [Hartree] G relative [kcal/mol] 1 (E,E) s-trans [st-1a] s-cis [sc-1a] (E,Z) s-trans [st-1b] s-cis [sc-1b] (Z,E) s-trans [st-1c] s-cis [sc-1c] (Z,Z) s-trans [st-1d] s-cis [sc-1d] SI-12

13 TABLE SI-7. Gosteli Claisen rearrangement of the allyl vinyl ether 1a-d: BLYP/6-1G*+PCM(solvent = 1,2-dichloroethane) bond length of the newly formed C/C bond (d C C ), dihedral angles ω of the dicarbonyl moiety and, dipole moments μ for the α-keto ester 2a-b. BLYP/6-1G*-values in parenthesis. ϕ [deg] i-pr ' ' i-pr i-pr ' ' i-pr i-pr (R,4S)-st-2a (R,4R)-st-2b (S,4R)-st-2a (S,4S)-st-2b +ϕ [deg] ' i-pr ' i-pr ' i-pr ' i-pr (R,4S)-sc-2a (R,4R)-sc-2b (S,4R)-sc-2a (S,4S)-sc-2b entry cmpd rel. config. d C C [Å] φ [ ] μ [D] 1 (R,4S)-st-2a (1.556) +156 (+159) 2.1 (1.7) 2 (S,4R)-st-2a syn ( ( 16) 2.1 (1.7) (R,4S)-sc-2a (1.556) 25 ( 6) 5.4 (4.1) 4 (S,4R)-sc-2a (1.556) +2 (+5) 5.4 (4.1) 5 (R,4R)-st-2b (1.551)) +171 (+174) 1.8 (1.5) 6 (S,4S)-st-2b anti (1.551) 178 (+179) 1.8 (1.5) 7 (R,4R)-sc-2b 1.55 (1.55).8 ( 4) 5.6 (4.) 8 (S,4S)-sc-2b 1.55 (1.55) 0 ( 2) 5.6 (4.) SI-1

14 TABLE SI-8. BLYP/6-1G*+PCM(solvent = 1,2-dichloroethane) relative free energy (G ts rel) at K, bond lengths and order of the breaking (d 1 C1 ) and the forming bond (d C C ), dihedral angles ω and dipole moments μ for the transition-state structures [st-1a-d]. entry cmpd double bond configuration G ts rel d 1 C1 d C C ω c μ [kcal/mol] [Å] (n) a [Å] (n) b [ ] [D] 1 [st-1a] (E,E) (0.6) 2.82 (0.25) [st-1b] (E,Z) (0.8) 2.77 (0.25) [st-1c] (Z,E) (0.6) (0.24) [st-1d] (Z,Z) (0.7) (0.24) a Bond order n in % calculated according to Pauling: n = exp[(d ave d ts ) / 0.6] b Bond order n in % calculated according to Pauling: n = exp[(d α-ke d ts ) / 0.6] SI-14

15 TABLE SI-9. BLYP/6-1G*+PCM(solvent = 1,2-dichloroethane) relative free energies (G ave rel), bond lengths of the breaking (d 1 C1 ) bond, dihedral angles ω and dipole moments μ of the allyl vinyl ethers st-1a-d at K. entry comp config G ave a rel ΔG rel d 1 C1 ω b μ [kcal/mol] [kcal/mol] [Å] [ ] [D] 1 st-1a (E,E) st-1b (E,Z) st-1c (Z,E) st-1d (Z,Z) a Loss of stability on the way to the transition-state, relative to st-1a. Calculated according to: ΔG rel = G ave rel G ts rel for st-1b,c and ΔG rel = G ave rel + G ts rel for st-1d. b as defined in Table SI-5. SI-15

16 [st-1a] ω = +17 μ = 4.8 D 0 [st-1b] [st-1d] ω = +140 ω = +158 μ = 4.6 D μ = 5.1 D [st-1c] ω = +169 μ = 5.4 D G relative [kcal/mol] of the s-trans transition states 25.6 (26.7) (27.4) 28.2 (28.2) ΔG [kcal/mol] calculated for s-trans pathway (experimental) (27.2) ω 1.29 st-1a ω = +156 μ =.1 D.0 st-1b ω = +157 μ =.2 D st-1c ω = +171 μ = 2.9 D G relative [kcal/mol] of the s-trans allyl vinyl ethers st-1d ω = +171 μ =.1 D FIGURE SI-5. Relative free energies G rel for st-1a-d, [st-1a-d] and the calculated (experimental) free energies of activation ΔG at the BLYP/6-1G*+PCM(solvent = 1,2-dichloroethane) level of theory in kcal/mol at K. Definition of the dihedral angle ω. SI-16

17 ' ' ' ' [st-1a] [st-1b] [st-1c] [st-1d] H H H H H H ' H H H H ' H ' H H H ' H H k rel, exp = 8.6 G ts rel = 0 ΔG rel = FIGURE SI-6. Newman projection of [st-1a-d], experimentally determined relative rate constant (k rel,exp ), calculated relative free energies (G ts rel, kcal/mol) and ΔG rel as a measure for the strain energy caused by axial methyl groups. SI-17

18 δ oxallylic = 0.28 δ allylic = sc-1a [sc-1a] 0.2 δ oxallylic = 0.26 δ allylic = δ oxallylic = 0.29 δ allylic = st-1a [st-1a] 0.0 δ oxallylic = 0.26 δ allylic = δoxallylic = 0.29 δ allylic = sc-1b [sc-1b] 0. δ oxallylic = 0.25 δ allylic = δ oxallylic = δ allylic = st-1b [st-1b] δ oxallylic = 0.27 δ allylic = δ oxallylic = 0.29 δ allylic = sc-1c [sc-1c] δ oxallylic = δ allylic = δ oxallylic = 0.29 δ allylic = st-1b [st-1b] δ oxallylic = δ allylic = δ oxallylic = 0.28 δ allylic = δ 0.61 oxallylic = δ oxallylic = δ allylic = δ allylic = sc-1d [sc-1d] st-1d [st-1d] δ oxallylic = δ allylic = FIGURE SI-7. BLYP/6-1G*+PCM(solvent = 1,2-dichloroethane)-Mulliken charges; charges on hydrogen atoms have been summed into charges of heavy atoms. SI-18

19 (E,E)-sc-1a (E,E)-sc-1a* (Si,4Si)-[sc-1a] (R,4S)-st-2a* (R,4S)-st-2a could not be located on PES (E,E)-st-1a (E,E)-st-1a* (Si,4Si)-[st-1a] (R,4S)-sc-2a* (R,4S)-sc-2a FIGURE SI-8. BLYP/6-1G*+PCM(solvent = 1,2-dichloroethane)-stationary points for the Gosteli Claisen rearrangement of 1a SI-19

20 (E,Z)-sc-1b (E,Z)-sc-1b* (Si,4Re)-[sc-1b] (R,4R)-st-2b* (R,4R)-st-2b could not be located on PES (E,Z)-st-1b (E,Z)-st-1b* (Si,4Re)-[st-1b] (R,4R)-sc-2b* (R,4R)-sc-2b FIGURE SI-9. BLYP/6-1G*+PCM(solvent = 1,2-dichloroethane)-stationary points for the Gosteli Claisen rearrangement of 1b SI-20

21 (Z,E)-sc-1c (Z,E)-sc-1c* (Re,4Si)-[sc-1c] (S,4S)-st-2b* (S,4S)-st-2b (Z,E)-st-1c (Z,E)-st-1c* (Re,4Si)-[st-1c] (S,4S)-sc-2b* (S,4S)-sc-2b FIGURE SI-10. BLYP/6-1G*+PCM(solvent = 1,2-dichloroethane)-stationary points for the Gosteli Claisen rearrangement of 1c SI-21

22 (Z,Z)-sc-1d (Z,Z)-sc-1d* (Re,4Re)-[sc-1d] (S,4R)-st-2a* (S,4R)-st-2a (Z,Z)-st-1d (Z,Z)-st-1d* (Re,4Re)-[st-1d] (S,4R)-sc-2a* (S,4R)-sc-2a FIGURE SI-11. BLYP/6-1G*+PCM(solvent = 1,2-dichloroethane)-stationary points for the Gosteli Claisen rearrangement of 1d SI-22

23 1 Mulliken, R.S: J. Chem. Phys. 1956, 2, Reed, E. A.; Weinstock, R. B.; Weinhold, F. J. Chem. Phys. 1988, 8, (a) Wiberg, K. B.; Rablem, P. R.; J. Comput. Chem. 199, 14, (b) McAllister, M. A.; Tidwell, T. T. J. rg. Chem. 1994, 59, SI-2