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Orbital theory for diastereoselectivity in electrophilic addition
Tetrahedron Letters 57 (2016) 2029–2033
Contents lists available at ScienceDirect
Tetrahedron Letters journal homepage: www.elsevier.com/locate/tetlet
Orbital theory for diastereoselectivity in electrophilic addition Yuji Naruse ⇑, Yousuke Hasegawa, Kurumi Ikemoto Department of Chemistry and Biomolecular Science, Gifu University, Yanagido, Gifu 501-1193 Japan
a r t i c l e
i n f o
Article history: Received 16 February 2016 Revised 21 March 2016 Accepted 24 March 2016 Available online 30 March 2016 Keywords: Electrophilic addition Diastereoselectivity Orbital phase theory Cyclic orbital interaction Bond model analysis
a b s t r a c t Electrophilic attack to a double bond is often observed anti to the most electron-donating r-bond at the a-position (hereafter, we refer to this as the extended anomeric effect). This preference is believed to result from the antiperiplanar effect between the bond that is formed between the double bond and the electrophilic reagent, and the donating vicinal r-bond which is located on the substituent at the a-position. From an orbital viewpoint, however, it is still unclear why the approach of the electrophile anti to the substituent results in stabilization or why the frontier molecular orbital (FMO) deforms, expanding toward the reagent with this antiperiplanar interaction. We demonstrate here that cyclic orbital interaction including geminal bond participation plays an important role in the diastereoselectivity in electrophilic addition. We examined our idea using the electrophilic addition of chlorine to 3-substituted propenes as a model reaction. Our bond model approach should contribute to a better understanding of orbital mixing in FMO. Ó 2016 Elsevier Ltd. All rights reserved.
The stereoelectronic effect, which affects the selectivity and reactivity of organic reactions, has been investigated for a long time.1–3 With regard to diastereoselectivity in electrophilic addition,4,5 the extended anomeric effect, which here refers to a preference for the electron-donating vicinal r-bond rC-D anti to the electrophile approach (Fig. 1a), is often considered.1–3 The anomeric effect was originally recognized as a preference for a CAO bond at the axial position in the anomeric position, i.e., a CAO bond located vicinal to the oxygen in saccharides (Fig. 1b).6 This preference is based on the antiperiplanar interaction between the lone pair on the oxygen and the r⁄ orbital of the CAO bond. A similar electron flow is expected in the extended anomeric effect. Electron delocalization to the electrophile is supported by the donating rC-D bond at the vicinal position, which is anti to the electrophile approach. This mechanism depends on vicinal interaction, which originates from the antiperiplanar effect from the r bond of the substituent D at the a-position. To explain this diastereoselectivity, the electrophile-p-complex has previously been proposed to be stabilized with the vicinal donating r-bond at the anti position (Fig. 2).3,4 In this proposal, stabilization between rC-D and LUMO, which consists of pC@C and the vacant orbital on the electrophile, should be essential for the diastereoselectivity. No destabilization should be expected from the interaction between LUMO and r⁄C-A orbitals, since they are vacant orbitals. However, LUMO should mainly be a combination of p⁄C@C and the vacant orbital on the electrophile. Moreover, the electrophile should make a bond with the carbon at the terminal ⇑ Corresponding author. http://dx.doi.org/10.1016/j.tetlet.2016.03.077 0040-4039/Ó 2016 Elsevier Ltd. All rights reserved.
CH2 due to the Markovnikov rule, so that interaction between pC@C and the vacant orbital on the electrophile should be considered at the terminal carbon. For the FMO theory, the electrophile, an acceptor, attacks in a direction so as to maintain the largest overlap with the HOMO as a result of the interaction between pC@C and rC-D (Fig. 3). There are no explanations for why the HOMO shows larger expansion anti to the r electron-donating substituent D with interaction between pC@C and rC-D, or why the chlorinep-complex is stabilized with the vicinal donating r-bond at the anti position. Thus, the theory still requires some empirical rule based on experimental results. If this rule could be consistent with theoretical chemistry, especially from the perspective of bond interaction, it would be a powerful tool for both experimenters and theoreticians for the rational design of new functional molecules and reactions with high efficiency and selectivity. Here we show that cyclic orbital interaction including geminal bond participation7 is important for determining the p-facial selectivity of the double bond in the extended anomeric effect. First, we considered the orbital phase among the bonds.8 Both the p and r orbitals in the C@C double bond are orthogonal and cannot interact with each other. However, they should be combined in-phase toward the electrophile as a result of the extended anomeric effect, since the p and r orbitals of the C@C double bond are donors and the vacant orbital of the electrophile /⁄E—such as the r⁄ orbital in halogen molecule X2—is an acceptor. For cyclic orbital interaction to provide stabilization, the orbital phase requirements must be satisfied: (i) donating orbitals are out-of-phase; (ii) the donating and accepting orbitals are in-phase; and (iii) accepting orbitals are in-phase.8
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E
O
E
E
O D (a)
D
(b)
D
D
Figure 1. Vicinal bond interactions: the extended anomeric effect (a) and the (original) anomeric effect (b).
Cyclic orbital interactions are initially considered for interactions among three bodies. For interactions among more than three bodies, they are still applicable if (i) the cyclic orbital interaction is monocyclic, i.e., the bonds interact with adjacent bonds but not with those in a remote position; and (ii) the cyclic orbital interaction must be divided into only two parts, the donor and acceptor parts, and not into four, six, or so on.9 The donor part consists of the donating orbitals only, such as lone pair(s) n, p and r orbitals. The acceptor part is solely a combination of vacant orbitals, such as p⁄ and r⁄ orbitals. With these additional requirements, the cyclic orbital interaction satisfies the requirements for producing stabilization. Now let us suppose cyclic orbital interaction including geminal bond participation. The vicinal rC-D/vic and geminal rCAC/gem orbitals should be out-of-phase, since they are donors.10,11 The geminal rCAC/gem and rC@C orbitals should also be out-of-phase, since they are also donors. The energy gap between r and r⁄ orbitals is rather large, so that we can consider there to be little interaction between them. In addition, little interaction is expected between the rCAC/gem and pC@C orbitals, since the rCAC/gem bond is initially on the nodal plane of the C@C bond, and interaction between the vicinal rC-D/vic and rC@C orbitals located in a rather remote position should be considerably small. Furthermore, the rCAC/gem and rC-D/vic orbitals, which overlap at the back lobe, are combined out-of-phase with the vacant orbital on the electrophile /⁄E. Although they are donor–acceptor interactions, delocalization from these orbitals to the electrophile /⁄E is suppressed since they cannot interact without destabilization. The phase of geminal bond interaction has been studied previously (Fig. 4).11 Based on these considerations, the phase condition between /⁄E–pC@C–rC-D/vic–rCAC/gem–rC@C– is phase-continuous, as shown in Figure 5. The phase-continuous cyclic orbital interaction should stabilize the TS, which should accelerate the reaction. To examine our idea, we performed calculations for a model reaction, i.e., the electrophilic addition of chlorine to propene (substituent D = H).12,13 We located the p-complex (DE = 1.9 kcal/mol) and two TS’s (DHà = 22.3 kcal/mol and
destabilization El
El
A stabilization
outside
inside
LUMO anti
D Figure 2. Proposed orbital interaction in diastereoselective electrophilic addition.3 Note that the direction of the arrow is corrected to show the electron flow.
Figure 3.
donor - donor
donor - acceptor
acceptor - acceptor in phase
out of phase
Figure 4. Phase relationship in geminal delocalization.10,11
FMO interaction in-phase
φ* E E πC=C
donor
σC=C σC-C/gem
D
σC-D/vic
out-of-phase πC=C
φ*E acceptor
in-phase
σC-D/vic
out-of-phase σC-C/gem
σ C=C
out-of-phase
Figure 5. Cyclic orbital interaction /⁄E–pC@C–rC-D/vic–rCAC/gem–rC@C-.
26.2 kcal/mol, respectively; BMK/6-311+G(d)//B3LYP/6-31G(d),14,15 Fig. 6). Interestingly, the syn-TS leads to the syn addition of chloride, while anti addition is more common in electrophilic addition. Based on careful inspection with IRC calculations, it seems to avoid the large charge separation in the chloride attack to the anti face of the three-membered ring that includes chlorine cation ion. A preference for anti addition in electrophilic addition seems to occur in polar solvents, where the solvent acts as a nucleophile, or with the participation of multiple molecules. The electronic structure of the TS was subjected to the bond model analysis (BMA).16,17 We used the bond model shown in Figure 7. The overlaps Sij and the elements of the density matrix Pij are shown in Table 1. The phase should be evaluated when Sij >0. For the bond interactions rCAH/vic–rCAC/gem and rCAC/gem–rC@C, the overlaps Sij are negative. The sign of Pij should be reversed and the phase condition of the BMA output is also reversed with a change in the sign of one of the two orbitals. Finally, the combination of two orbitals is in-phase when Pij >0, and out-of-phase when Pij <0. Overall, the net phase condition is not in agreement with our prediction (Table 1). However, in TS, the pC@C orbital strongly interacts with Cl+ ion, and chlorine is more electronegative than carbon. Thus, the occupied pC@C orbital should be considerably electron-deficient. The interaction between the occupied orbitals of pC@C and rCAH/vic should no longer be repulsive. This is confirmed by a low value (0.8086) of the orthogonal element of the density matrix Pii of pC@C, and the bonding nature of bond interaction between pC@C and rCAH/vic, evaluated with the interbond energy IBE (IBEij = 0.0184 a.u.).18
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Table 1 Overlaps Sij and elements of the density matrix Pij (HF/6-31G(d)//B3LYP/6-31G(d)) in syn-TS (B3LYP/6-31G(d))
Cl
Cl
pC@C-u⁄+Cl pC@C-rCAH/vic rCAH/vic-rCAC/gem rCAC/gem-rC@C rC@C-u⁄+Cl
2.777 Å
2.899 Å 76.3°
81.4°
Overlap Sij
Elements of the density matrix Pij
Phase condition
0.2613 0.1157 0.1105 0.1051 0.2479
0.7250 0.0104 0.2049 0.1173 0.0418
In-phase In-phase Out-of-phase Out-of-phase In-phase
Table 2 Phase relationship in the propene part in syn-TS (RHF/6-31G(d)//B3LYP/6-31G(d))
π-complex( ΔE = -1.9) Cl
3.159 Å Cl 1.939 Å 66.1°
1.899 Å 68.9°
Cl 2.020 Å 66.0°
syn-TS(ΔH = 22.3)
3.338 Å 1.950 Å 71.1°
Cl
pC@C-rCAH/vic rCAH/vic-rCAC/gem rCAC/gem-rC@C
Overlap Sij
Elements of the density matrix Pij
Phase condition
0.1436 0.1049 0.1093
0.3014 0.1181 0.1344
Out-of-phase Out-of-phase Out-of-phase
anti-TS(ΔH = 26.2)
BMK/6-311+G(d)//B3LYP/6-31G(d) Figure 6. Optimized structures and relative energies (in kcal/mol, ZPE corr.) from propene and Cl2.
πC=C
σC-H/vic
σC-C/gem
σC=C
Figure 8. BMA outputs of the orbital phase of the propene part in syn-TS.
Cl Cl
H
σC-C/gem σC-H/vic Figure 9. Contour plot of HOMO of propene in TS.
Figure 7. Bond model of syn-TS for BMA.
In fact, BMA with the removal of chlorine (i.e., propene part only) showed that the phase relationship is consistent with our prediction (Table 2, Fig. 8). Apparently, the HOMO of propene in TS extends anti to the vicinal rCAH bond (Fig. 9). The amount of delocalization is evaluated by considering the ratio of the coefficient of the electron-transferred configuration to that of the ground configuration, |CT/CG|.16 Interestingly, delocalization from rCAH/vic and rCAC/gem to u⁄+Cl gives values (|CT/CG|) of 0.1193 and 0.0502, respectively (Fig. 10), while they cannot delocalize directly to u⁄+Cl since direct delocalization should be suppressed with out-of-phase combination of the orbitals. Furthermore, to test the effectiveness of electron delocalization, we calculated the conformational dependence of the |CT/CG| value around the CAC bond at the geminal position. The dihedral angle a is determined as shown in Figure 11, and the results with constrained conformations are shown in Figure 12 (a Table is shown in the Supplementary content). Naturally, delocalization from the C@C double bond, which is determined by evaluating the sum of the |CT/CG| values from pC@C and rC@C orbitals, is maximized at the optimized TS. Note that the maximal value for |CT/CG| from rCAC/gem to u⁄+Cl is at a dihedral angle of 105°, while delocalization
Cl σC-H/vic
|CT/CG|= 0.1193 H
+ Cl
Cl ϕ*
σC-C/gem |CT/CG|= 0.0502
Figure 10. Electron delocalization |CT/CG| in propene–Cl2 syn-TS (HF/6-31G(d)// B3LYP/6-31G(d)).
from rCAH/vic to u⁄+Cl is at 90°, where pC@C and rCAH/vic are almost parallel. However, the TS is not located at these points. Both delocalizations should be effective in the TS. Houk previously pointed out that the most electron-withdrawing r-bond prefers to occupy the position eclipsed to the C@C double bond.4 The orbital energy of rC@C is lower than that of rCAHA/gem. This is supported by the values of the diagonal elements of the Fock matrix in the bond orbital basis Fii (1.0903 a.u. for rC@C and 0.8241 a.u. for rCAHA/gem). Thus, rCAHA/gem is more electron-donating, which results in greater stabilization by the
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C2
Hin C3 C1
0.95
α
D
Figure 11. Dihedral angle a, D-C3–C2–C1.
0.9 4.0
2.0 0.0 -120.0 -110.0 -100.0 -90.0
0.12 4.0 0.11 2.0 0.0 -120.0 -110.0 -100.0 -90.0
0.05 -70.0
-80.0
α/deg
|CT/CG|
ΔE /kcal/mol
1.97
Table 3 Phase relationship in the 1-butene part in 1-butene–Cl2 syn-TS (RHF/6-31G(d)// B3LYP/6-31G(d)) Overlap Sij
Elements of the density matrix Pij
Phase condition
0.1228 0.1128 0.1056
0.2921 0.1295 0.1327
Out-of-phase Out-of-phase Out-of-phase
Cl
Cl ϕ*
Cl
σC-C/vic
0.05 -80.0
-70.0
Figure 14. Conformational dependence of the difference in energy from the optimized syn-TS (D = CH3) structure DE ( in red, B3LYP/6-31G(d), ZPE corr.) and | CT/CG| values of rCAC/gem to u⁄+Cl (N in black) and rCAH/vic to u⁄+Cl ( in blue) (HF/631G(d)//B3LYP/6-31G(d)).
In fact, HOMO of propene in TS in a bond orbital basis LCBO-MO (HOMO) is expressed as:
propene in propene—Cl2 TS :
WHOMO ¼ 1:0102upC@C 0:2806urCAH=vic þ 0:0654urCAC=gem
Figure 12. Conformational dependence of the difference in energy from the optimized syn-TS (D = H) structure DE ( in red, B3LYP/6-31G(d), ZPE corr.), |CT/CG| values of rCAC/gem to u⁄+Cl (N in black) and rCAH/vic to u⁄+Cl ( in blue), and sum of |CT/ CG| values of pC@C to u⁄+Cl and rC@C to u⁄+Cl ( in green) (HF/6-31G(d)//B3LYP/6-31G (d)).
pC@C-rC-D/vic rC-D/vic-rCAC/gem rCAC/gem-rC@C
0.85
|CT/CG|
ΔE /kcal/mol
HA
+
σC-C/gem
|CT/CG|= 0.0955 CH |CT/CG|= 0.0506 3 Figure 13. Electron delocalization |CT/CG| in 1-butene–Cl2 syn-TS (HF/6-31G(d)// B3LYP/6-31G(d)).
antiperiplanar effect. However, this antiperiplanar delocalization is P not at a maximum for the TS structure ( IBEr-r⁄ = 0.1335 a.u.), which is located at angle a = 110°, where the dihedral angle is ca. P 180° between the rC2-HA and rC3-Hin bonds ( IBEr-r⁄ = 0.1340 a.u.). Other donating substituents, such as a methyl group, should show the same phase relationship. We performed calculations for 1-butene (D = CH3) to confirm our idea. The BMA analysis for their syn-TSs showed the same phase relationships, exactly as expected (Table 3).
þ 0:0195urCAC þ . . . where a plus sign denotes in-phase combination, while a minus sign indicates out-of-phase combination. This is not consistent with our expectation due to the poor donating character of a CAH bond. However, a better r-donating substituent of a methyl group led to good agreement with our prediction.
1-butene in 1-butene—Cl2 TS : WHOMO ¼ 0:9908upC@C 0:3031urCAH=vic 0:0471urCAC=gem 0:2609urCAC þ . . . The change in delocalization from rCAC/gem to u⁄+Cl is small for the model reaction of propene–Cl2. Substitution with a methyl group enhances the donating character of rC-D/vic. Thus, a large change in delocalization should be expected. We examined the conformational dependence for the model reaction of 1-butene– Cl2. |CT/CG| from rCAC/gem has its maximal values at TS (Figs. 13 and 14, a Table is shown in the Supplementary content), and becomes larger than that in propene in propene–Cl2 TS. In conclusion, cyclic orbital interaction including geminal delocalization, /⁄E–pC@C–rC-D/vic–rCAC/gem–rC@C–, is phase-continuous to stabilize the TS, which is important in diastereoselectivity for electrophile approach anti to the electron-donating r-bond (the extended anomeric effect). The deformation of HOMO of substituted propene mainly results from the orbital mixing of pC@C, rC-D/vic, rCAC/gem and rC@C. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.tetlet.2016.03. 077. References and notes 1. (a) Pine, S. H. In Organic Chemistry, 5th ed.; McGraw-Hill: New York, 1987. Chapter 7; (b) Morrison, R. T.; Boyd, R. N. In Organic Chemistry, 6th ed.; Prentice Hall International: London, 1992. Chapter 11. 2. Kirby, A. J. In Stereoelectronic Effect; Oxford University Press: Oxford, U.K, 1996. Chapter 6. 3. Houk, K. N.; Paddon-Row, M. N.; Rondan, N. G.; Wu, Y.-D.; Brown, F. K.; Spellmeyer, D. C.; Metz, J. T.; Li, Y.; Loncharich, J. Science 1986, 231, 1108.
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Y. Naruse et al. / Tetrahedron Letters 57 (2016) 2029–2033 4. Haller, J.; Strassner, T.; Houk, K. N. J. Am. Chem. Soc. 1997, 119, 8031. 5. Early experimental results: (a) Stork, G.; Kahn, M. Tetrahedron Lett. 1983, 24, 3951; (b) Cha, J. K.; Christ, W. J.; Kishi, Y. Tetrahedron 1984, 40, 2247. 6. Delongchamps, P. In Stereoelectronic Effects in Organic Chemistry; Pergamon Press: Oxford, U.K, 1983. 7. Review Naruse, Y.; Inagaki, S. Chem. Lett. 2007, 36, 820. 8. (a) Inagaki, S. In Orbitals in Chemistry; Springer: Berlin-Heidelberg, 2009; (b) Inagaki, S. Top. Curr. Chem. 2009, 289, 83. 9. Inagaki, S.; Hirabayashi, Y. Inorg. Chem. 1982, 21, 1798. 10. The orbital phase in antiperiplanar interaction was previously reported. Inagaki, S.; Mori, Y.; Goto, N. Bull. Chem. Soc. Jpn. 1990, 63, 1098. 11. Inagaki, S.; Goto, N.; Yoshikawa, K. J. Am. Chem. Soc. 1991, 113, 7144. 12. Yamabe, S.; Minami, T.; Inagaki, S. J. Chem. Soc. Chem. Commun. 1988, 532. 13. Gaussian09 rev. B.01; Gaussian: Wallingford, CT, 2010. 14. B3LYP functional in DFT calculations: Becke, A. D. J. Chem. Phys. 1993, 98, 5648. 15. BMK method in DFT calculations: Boese, A. D.; Martin, J. M. L. J. Chem. Phys. 2004, 121, 3405. 16. The electronic structure W is expanded into the electron configuration U in the bond orbital basis.
+ 1
2
3
1
2
3
Φ T(2-1)
Ψ
Φ G Ground
Configuration
+
+ 1
2
+
3
Φ T(3-2)
Φ T Electron-Transferred Configuration
W ¼ CG UG þ RCT UT þ . . . The ratio of the coefficient of the electron-transferred configuration CT to that of the ground configuration CG, |CT/CG| is a good index for delocalization. 17. Bond Model Analysis 1.1, Inagaki, S.; Ikeda, H.; Ohwada, T.; Takahama, T. 1996– 2013.; See: Inagaki, S.; Ikeda, H. J. Org. Chem. 1998, 63, 7820; Iwase, K.; Inagaki, S. Bull. Chem. Soc. Jpn. 1996, 69, 2781; Inagaki, S.; Ohashi, S.; Yamamoto, T. Chem. Lett. 1997, 26, 977; Ikeda, H.; Inagaki, S. J. Chem. Phys. A 2001, 47, 10711. 18. Interbond energy IBE is derived from the following equation:
IBEij ¼ Pij ðHij þ Fij Þ where Hij and Fij are elements of the core Hamiltonian and Fock matrices in the bond orbital basis, respectively.
Contents lists available at ScienceDirect
Tetrahedron Letters journal homepage: www.elsevier.com/locate/tetlet
Orbital theory for diastereoselectivity in electrophilic addition Yuji Naruse ⇑, Yousuke Hasegawa, Kurumi Ikemoto Department of Chemistry and Biomolecular Science, Gifu University, Yanagido, Gifu 501-1193 Japan
a r t i c l e
i n f o
Article history: Received 16 February 2016 Revised 21 March 2016 Accepted 24 March 2016 Available online 30 March 2016 Keywords: Electrophilic addition Diastereoselectivity Orbital phase theory Cyclic orbital interaction Bond model analysis
a b s t r a c t Electrophilic attack to a double bond is often observed anti to the most electron-donating r-bond at the a-position (hereafter, we refer to this as the extended anomeric effect). This preference is believed to result from the antiperiplanar effect between the bond that is formed between the double bond and the electrophilic reagent, and the donating vicinal r-bond which is located on the substituent at the a-position. From an orbital viewpoint, however, it is still unclear why the approach of the electrophile anti to the substituent results in stabilization or why the frontier molecular orbital (FMO) deforms, expanding toward the reagent with this antiperiplanar interaction. We demonstrate here that cyclic orbital interaction including geminal bond participation plays an important role in the diastereoselectivity in electrophilic addition. We examined our idea using the electrophilic addition of chlorine to 3-substituted propenes as a model reaction. Our bond model approach should contribute to a better understanding of orbital mixing in FMO. Ó 2016 Elsevier Ltd. All rights reserved.
The stereoelectronic effect, which affects the selectivity and reactivity of organic reactions, has been investigated for a long time.1–3 With regard to diastereoselectivity in electrophilic addition,4,5 the extended anomeric effect, which here refers to a preference for the electron-donating vicinal r-bond rC-D anti to the electrophile approach (Fig. 1a), is often considered.1–3 The anomeric effect was originally recognized as a preference for a CAO bond at the axial position in the anomeric position, i.e., a CAO bond located vicinal to the oxygen in saccharides (Fig. 1b).6 This preference is based on the antiperiplanar interaction between the lone pair on the oxygen and the r⁄ orbital of the CAO bond. A similar electron flow is expected in the extended anomeric effect. Electron delocalization to the electrophile is supported by the donating rC-D bond at the vicinal position, which is anti to the electrophile approach. This mechanism depends on vicinal interaction, which originates from the antiperiplanar effect from the r bond of the substituent D at the a-position. To explain this diastereoselectivity, the electrophile-p-complex has previously been proposed to be stabilized with the vicinal donating r-bond at the anti position (Fig. 2).3,4 In this proposal, stabilization between rC-D and LUMO, which consists of pC@C and the vacant orbital on the electrophile, should be essential for the diastereoselectivity. No destabilization should be expected from the interaction between LUMO and r⁄C-A orbitals, since they are vacant orbitals. However, LUMO should mainly be a combination of p⁄C@C and the vacant orbital on the electrophile. Moreover, the electrophile should make a bond with the carbon at the terminal ⇑ Corresponding author. http://dx.doi.org/10.1016/j.tetlet.2016.03.077 0040-4039/Ó 2016 Elsevier Ltd. All rights reserved.
CH2 due to the Markovnikov rule, so that interaction between pC@C and the vacant orbital on the electrophile should be considered at the terminal carbon. For the FMO theory, the electrophile, an acceptor, attacks in a direction so as to maintain the largest overlap with the HOMO as a result of the interaction between pC@C and rC-D (Fig. 3). There are no explanations for why the HOMO shows larger expansion anti to the r electron-donating substituent D with interaction between pC@C and rC-D, or why the chlorinep-complex is stabilized with the vicinal donating r-bond at the anti position. Thus, the theory still requires some empirical rule based on experimental results. If this rule could be consistent with theoretical chemistry, especially from the perspective of bond interaction, it would be a powerful tool for both experimenters and theoreticians for the rational design of new functional molecules and reactions with high efficiency and selectivity. Here we show that cyclic orbital interaction including geminal bond participation7 is important for determining the p-facial selectivity of the double bond in the extended anomeric effect. First, we considered the orbital phase among the bonds.8 Both the p and r orbitals in the C@C double bond are orthogonal and cannot interact with each other. However, they should be combined in-phase toward the electrophile as a result of the extended anomeric effect, since the p and r orbitals of the C@C double bond are donors and the vacant orbital of the electrophile /⁄E—such as the r⁄ orbital in halogen molecule X2—is an acceptor. For cyclic orbital interaction to provide stabilization, the orbital phase requirements must be satisfied: (i) donating orbitals are out-of-phase; (ii) the donating and accepting orbitals are in-phase; and (iii) accepting orbitals are in-phase.8
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E
O
E
E
O D (a)
D
(b)
D
D
Figure 1. Vicinal bond interactions: the extended anomeric effect (a) and the (original) anomeric effect (b).
Cyclic orbital interactions are initially considered for interactions among three bodies. For interactions among more than three bodies, they are still applicable if (i) the cyclic orbital interaction is monocyclic, i.e., the bonds interact with adjacent bonds but not with those in a remote position; and (ii) the cyclic orbital interaction must be divided into only two parts, the donor and acceptor parts, and not into four, six, or so on.9 The donor part consists of the donating orbitals only, such as lone pair(s) n, p and r orbitals. The acceptor part is solely a combination of vacant orbitals, such as p⁄ and r⁄ orbitals. With these additional requirements, the cyclic orbital interaction satisfies the requirements for producing stabilization. Now let us suppose cyclic orbital interaction including geminal bond participation. The vicinal rC-D/vic and geminal rCAC/gem orbitals should be out-of-phase, since they are donors.10,11 The geminal rCAC/gem and rC@C orbitals should also be out-of-phase, since they are also donors. The energy gap between r and r⁄ orbitals is rather large, so that we can consider there to be little interaction between them. In addition, little interaction is expected between the rCAC/gem and pC@C orbitals, since the rCAC/gem bond is initially on the nodal plane of the C@C bond, and interaction between the vicinal rC-D/vic and rC@C orbitals located in a rather remote position should be considerably small. Furthermore, the rCAC/gem and rC-D/vic orbitals, which overlap at the back lobe, are combined out-of-phase with the vacant orbital on the electrophile /⁄E. Although they are donor–acceptor interactions, delocalization from these orbitals to the electrophile /⁄E is suppressed since they cannot interact without destabilization. The phase of geminal bond interaction has been studied previously (Fig. 4).11 Based on these considerations, the phase condition between /⁄E–pC@C–rC-D/vic–rCAC/gem–rC@C– is phase-continuous, as shown in Figure 5. The phase-continuous cyclic orbital interaction should stabilize the TS, which should accelerate the reaction. To examine our idea, we performed calculations for a model reaction, i.e., the electrophilic addition of chlorine to propene (substituent D = H).12,13 We located the p-complex (DE = 1.9 kcal/mol) and two TS’s (DHà = 22.3 kcal/mol and
destabilization El
El
A stabilization
outside
inside
LUMO anti
D Figure 2. Proposed orbital interaction in diastereoselective electrophilic addition.3 Note that the direction of the arrow is corrected to show the electron flow.
Figure 3.
donor - donor
donor - acceptor
acceptor - acceptor in phase
out of phase
Figure 4. Phase relationship in geminal delocalization.10,11
FMO interaction in-phase
φ* E E πC=C
donor
σC=C σC-C/gem
D
σC-D/vic
out-of-phase πC=C
φ*E acceptor
in-phase
σC-D/vic
out-of-phase σC-C/gem
σ C=C
out-of-phase
Figure 5. Cyclic orbital interaction /⁄E–pC@C–rC-D/vic–rCAC/gem–rC@C-.
26.2 kcal/mol, respectively; BMK/6-311+G(d)//B3LYP/6-31G(d),14,15 Fig. 6). Interestingly, the syn-TS leads to the syn addition of chloride, while anti addition is more common in electrophilic addition. Based on careful inspection with IRC calculations, it seems to avoid the large charge separation in the chloride attack to the anti face of the three-membered ring that includes chlorine cation ion. A preference for anti addition in electrophilic addition seems to occur in polar solvents, where the solvent acts as a nucleophile, or with the participation of multiple molecules. The electronic structure of the TS was subjected to the bond model analysis (BMA).16,17 We used the bond model shown in Figure 7. The overlaps Sij and the elements of the density matrix Pij are shown in Table 1. The phase should be evaluated when Sij >0. For the bond interactions rCAH/vic–rCAC/gem and rCAC/gem–rC@C, the overlaps Sij are negative. The sign of Pij should be reversed and the phase condition of the BMA output is also reversed with a change in the sign of one of the two orbitals. Finally, the combination of two orbitals is in-phase when Pij >0, and out-of-phase when Pij <0. Overall, the net phase condition is not in agreement with our prediction (Table 1). However, in TS, the pC@C orbital strongly interacts with Cl+ ion, and chlorine is more electronegative than carbon. Thus, the occupied pC@C orbital should be considerably electron-deficient. The interaction between the occupied orbitals of pC@C and rCAH/vic should no longer be repulsive. This is confirmed by a low value (0.8086) of the orthogonal element of the density matrix Pii of pC@C, and the bonding nature of bond interaction between pC@C and rCAH/vic, evaluated with the interbond energy IBE (IBEij = 0.0184 a.u.).18
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Table 1 Overlaps Sij and elements of the density matrix Pij (HF/6-31G(d)//B3LYP/6-31G(d)) in syn-TS (B3LYP/6-31G(d))
Cl
Cl
pC@C-u⁄+Cl pC@C-rCAH/vic rCAH/vic-rCAC/gem rCAC/gem-rC@C rC@C-u⁄+Cl
2.777 Å
2.899 Å 76.3°
81.4°
Overlap Sij
Elements of the density matrix Pij
Phase condition
0.2613 0.1157 0.1105 0.1051 0.2479
0.7250 0.0104 0.2049 0.1173 0.0418
In-phase In-phase Out-of-phase Out-of-phase In-phase
Table 2 Phase relationship in the propene part in syn-TS (RHF/6-31G(d)//B3LYP/6-31G(d))
π-complex( ΔE = -1.9) Cl
3.159 Å Cl 1.939 Å 66.1°
1.899 Å 68.9°
Cl 2.020 Å 66.0°
syn-TS(ΔH = 22.3)
3.338 Å 1.950 Å 71.1°
Cl
pC@C-rCAH/vic rCAH/vic-rCAC/gem rCAC/gem-rC@C
Overlap Sij
Elements of the density matrix Pij
Phase condition
0.1436 0.1049 0.1093
0.3014 0.1181 0.1344
Out-of-phase Out-of-phase Out-of-phase
anti-TS(ΔH = 26.2)
BMK/6-311+G(d)//B3LYP/6-31G(d) Figure 6. Optimized structures and relative energies (in kcal/mol, ZPE corr.) from propene and Cl2.
πC=C
σC-H/vic
σC-C/gem
σC=C
Figure 8. BMA outputs of the orbital phase of the propene part in syn-TS.
Cl Cl
H
σC-C/gem σC-H/vic Figure 9. Contour plot of HOMO of propene in TS.
Figure 7. Bond model of syn-TS for BMA.
In fact, BMA with the removal of chlorine (i.e., propene part only) showed that the phase relationship is consistent with our prediction (Table 2, Fig. 8). Apparently, the HOMO of propene in TS extends anti to the vicinal rCAH bond (Fig. 9). The amount of delocalization is evaluated by considering the ratio of the coefficient of the electron-transferred configuration to that of the ground configuration, |CT/CG|.16 Interestingly, delocalization from rCAH/vic and rCAC/gem to u⁄+Cl gives values (|CT/CG|) of 0.1193 and 0.0502, respectively (Fig. 10), while they cannot delocalize directly to u⁄+Cl since direct delocalization should be suppressed with out-of-phase combination of the orbitals. Furthermore, to test the effectiveness of electron delocalization, we calculated the conformational dependence of the |CT/CG| value around the CAC bond at the geminal position. The dihedral angle a is determined as shown in Figure 11, and the results with constrained conformations are shown in Figure 12 (a Table is shown in the Supplementary content). Naturally, delocalization from the C@C double bond, which is determined by evaluating the sum of the |CT/CG| values from pC@C and rC@C orbitals, is maximized at the optimized TS. Note that the maximal value for |CT/CG| from rCAC/gem to u⁄+Cl is at a dihedral angle of 105°, while delocalization
Cl σC-H/vic
|CT/CG|= 0.1193 H
+ Cl
Cl ϕ*
σC-C/gem |CT/CG|= 0.0502
Figure 10. Electron delocalization |CT/CG| in propene–Cl2 syn-TS (HF/6-31G(d)// B3LYP/6-31G(d)).
from rCAH/vic to u⁄+Cl is at 90°, where pC@C and rCAH/vic are almost parallel. However, the TS is not located at these points. Both delocalizations should be effective in the TS. Houk previously pointed out that the most electron-withdrawing r-bond prefers to occupy the position eclipsed to the C@C double bond.4 The orbital energy of rC@C is lower than that of rCAHA/gem. This is supported by the values of the diagonal elements of the Fock matrix in the bond orbital basis Fii (1.0903 a.u. for rC@C and 0.8241 a.u. for rCAHA/gem). Thus, rCAHA/gem is more electron-donating, which results in greater stabilization by the
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C2
Hin C3 C1
0.95
α
D
Figure 11. Dihedral angle a, D-C3–C2–C1.
0.9 4.0
2.0 0.0 -120.0 -110.0 -100.0 -90.0
0.12 4.0 0.11 2.0 0.0 -120.0 -110.0 -100.0 -90.0
0.05 -70.0
-80.0
α/deg
|CT/CG|
ΔE /kcal/mol
1.97
Table 3 Phase relationship in the 1-butene part in 1-butene–Cl2 syn-TS (RHF/6-31G(d)// B3LYP/6-31G(d)) Overlap Sij
Elements of the density matrix Pij
Phase condition
0.1228 0.1128 0.1056
0.2921 0.1295 0.1327
Out-of-phase Out-of-phase Out-of-phase
Cl
Cl ϕ*
Cl
σC-C/vic
0.05 -80.0
-70.0
Figure 14. Conformational dependence of the difference in energy from the optimized syn-TS (D = CH3) structure DE ( in red, B3LYP/6-31G(d), ZPE corr.) and | CT/CG| values of rCAC/gem to u⁄+Cl (N in black) and rCAH/vic to u⁄+Cl ( in blue) (HF/631G(d)//B3LYP/6-31G(d)).
In fact, HOMO of propene in TS in a bond orbital basis LCBO-MO (HOMO) is expressed as:
propene in propene—Cl2 TS :
WHOMO ¼ 1:0102upC@C 0:2806urCAH=vic þ 0:0654urCAC=gem
Figure 12. Conformational dependence of the difference in energy from the optimized syn-TS (D = H) structure DE ( in red, B3LYP/6-31G(d), ZPE corr.), |CT/CG| values of rCAC/gem to u⁄+Cl (N in black) and rCAH/vic to u⁄+Cl ( in blue), and sum of |CT/ CG| values of pC@C to u⁄+Cl and rC@C to u⁄+Cl ( in green) (HF/6-31G(d)//B3LYP/6-31G (d)).
pC@C-rC-D/vic rC-D/vic-rCAC/gem rCAC/gem-rC@C
0.85
|CT/CG|
ΔE /kcal/mol
HA
+
σC-C/gem
|CT/CG|= 0.0955 CH |CT/CG|= 0.0506 3 Figure 13. Electron delocalization |CT/CG| in 1-butene–Cl2 syn-TS (HF/6-31G(d)// B3LYP/6-31G(d)).
antiperiplanar effect. However, this antiperiplanar delocalization is P not at a maximum for the TS structure ( IBEr-r⁄ = 0.1335 a.u.), which is located at angle a = 110°, where the dihedral angle is ca. P 180° between the rC2-HA and rC3-Hin bonds ( IBEr-r⁄ = 0.1340 a.u.). Other donating substituents, such as a methyl group, should show the same phase relationship. We performed calculations for 1-butene (D = CH3) to confirm our idea. The BMA analysis for their syn-TSs showed the same phase relationships, exactly as expected (Table 3).
þ 0:0195urCAC þ . . . where a plus sign denotes in-phase combination, while a minus sign indicates out-of-phase combination. This is not consistent with our expectation due to the poor donating character of a CAH bond. However, a better r-donating substituent of a methyl group led to good agreement with our prediction.
1-butene in 1-butene—Cl2 TS : WHOMO ¼ 0:9908upC@C 0:3031urCAH=vic 0:0471urCAC=gem 0:2609urCAC þ . . . The change in delocalization from rCAC/gem to u⁄+Cl is small for the model reaction of propene–Cl2. Substitution with a methyl group enhances the donating character of rC-D/vic. Thus, a large change in delocalization should be expected. We examined the conformational dependence for the model reaction of 1-butene– Cl2. |CT/CG| from rCAC/gem has its maximal values at TS (Figs. 13 and 14, a Table is shown in the Supplementary content), and becomes larger than that in propene in propene–Cl2 TS. In conclusion, cyclic orbital interaction including geminal delocalization, /⁄E–pC@C–rC-D/vic–rCAC/gem–rC@C–, is phase-continuous to stabilize the TS, which is important in diastereoselectivity for electrophile approach anti to the electron-donating r-bond (the extended anomeric effect). The deformation of HOMO of substituted propene mainly results from the orbital mixing of pC@C, rC-D/vic, rCAC/gem and rC@C. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.tetlet.2016.03. 077. References and notes 1. (a) Pine, S. H. In Organic Chemistry, 5th ed.; McGraw-Hill: New York, 1987. Chapter 7; (b) Morrison, R. T.; Boyd, R. N. In Organic Chemistry, 6th ed.; Prentice Hall International: London, 1992. Chapter 11. 2. Kirby, A. J. In Stereoelectronic Effect; Oxford University Press: Oxford, U.K, 1996. Chapter 6. 3. Houk, K. N.; Paddon-Row, M. N.; Rondan, N. G.; Wu, Y.-D.; Brown, F. K.; Spellmeyer, D. C.; Metz, J. T.; Li, Y.; Loncharich, J. Science 1986, 231, 1108.
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Y. Naruse et al. / Tetrahedron Letters 57 (2016) 2029–2033 4. Haller, J.; Strassner, T.; Houk, K. N. J. Am. Chem. Soc. 1997, 119, 8031. 5. Early experimental results: (a) Stork, G.; Kahn, M. Tetrahedron Lett. 1983, 24, 3951; (b) Cha, J. K.; Christ, W. J.; Kishi, Y. Tetrahedron 1984, 40, 2247. 6. Delongchamps, P. In Stereoelectronic Effects in Organic Chemistry; Pergamon Press: Oxford, U.K, 1983. 7. Review Naruse, Y.; Inagaki, S. Chem. Lett. 2007, 36, 820. 8. (a) Inagaki, S. In Orbitals in Chemistry; Springer: Berlin-Heidelberg, 2009; (b) Inagaki, S. Top. Curr. Chem. 2009, 289, 83. 9. Inagaki, S.; Hirabayashi, Y. Inorg. Chem. 1982, 21, 1798. 10. The orbital phase in antiperiplanar interaction was previously reported. Inagaki, S.; Mori, Y.; Goto, N. Bull. Chem. Soc. Jpn. 1990, 63, 1098. 11. Inagaki, S.; Goto, N.; Yoshikawa, K. J. Am. Chem. Soc. 1991, 113, 7144. 12. Yamabe, S.; Minami, T.; Inagaki, S. J. Chem. Soc. Chem. Commun. 1988, 532. 13. Gaussian09 rev. B.01; Gaussian: Wallingford, CT, 2010. 14. B3LYP functional in DFT calculations: Becke, A. D. J. Chem. Phys. 1993, 98, 5648. 15. BMK method in DFT calculations: Boese, A. D.; Martin, J. M. L. J. Chem. Phys. 2004, 121, 3405. 16. The electronic structure W is expanded into the electron configuration U in the bond orbital basis.
+ 1
2
3
1
2
3
Φ T(2-1)
Ψ
Φ G Ground
Configuration
+
+ 1
2
+
3
Φ T(3-2)
Φ T Electron-Transferred Configuration
W ¼ CG UG þ RCT UT þ . . . The ratio of the coefficient of the electron-transferred configuration CT to that of the ground configuration CG, |CT/CG| is a good index for delocalization. 17. Bond Model Analysis 1.1, Inagaki, S.; Ikeda, H.; Ohwada, T.; Takahama, T. 1996– 2013.; See: Inagaki, S.; Ikeda, H. J. Org. Chem. 1998, 63, 7820; Iwase, K.; Inagaki, S. Bull. Chem. Soc. Jpn. 1996, 69, 2781; Inagaki, S.; Ohashi, S.; Yamamoto, T. Chem. Lett. 1997, 26, 977; Ikeda, H.; Inagaki, S. J. Chem. Phys. A 2001, 47, 10711. 18. Interbond energy IBE is derived from the following equation:
IBEij ¼ Pij ðHij þ Fij Þ where Hij and Fij are elements of the core Hamiltonian and Fock matrices in the bond orbital basis, respectively.