Computational Study of the Cyclization of 5-Hexenyl, 3-Oxa-5-Hexenyl and 4-Oxa-5-Hexenyl Radicals

Albert R. Matlin, Matthew C. Leyden

Department of Chemistry and Biochemistry, Oberlin College, Oberlin, USA.

DOI: 10.4236/ijoc.2013.33021                

Abstract

The intramolecular cyclization of 5-hexenyl radicals continues to be an important synthetic method for the construction of five-membered rings. The synthetic utility arises from the high degree of regioselectivity to give predominantly cyclopentyl products in high yield under mild conditions. Recently we reported product cyclization studies on 4-oxa perturbed 5-hexenyl radical. In this paper, we report our results from a computational study (UB3LYP and UCCSD (T)) of the cyclization of a series of 5-hexenyl and 3-and 4-oxa-5-hexenyl radicals. Three highly conserved cyclization tran-sitions states (exo-chair, exo-boat and endo-chair) were located for 10 acyclic radicals. Activation energies were calcu-lated for the three modes of cyclization for each radical. Calculated values for the exo/endo cyclization ratios had a high level of agreement with experiment and predictions were offered for two cases that have not been experimentally tested. The increased percentage of exo-cyclization with 3-and 4-oxa substitution is the result of an increase in the energy dif-ference between the exo-and endo-chair transition states compared to the hydrocarbon systems. The decreased rate of cyclization of the 4-oxa compounds is primarily due to the stabilization of the initial acyclic radical by the vinyl ether linkage. The increase in the rate of cyclization with 3-methyl substitution is due to the increased conformational energy of the starting acyclic radical.

Keywords

Radical Cyclizations; Activation Energies; UB3LYP; UCCSD (T)

1. Introduction

Radical cyclizations continue to be extremely useful reactions for the construction of ring systems via single [1-5] and tandem cyclizations [6-9]. The utility of these reactions stems from the relatively mild reaction conditions (low to moderate temperature and neutral pH), which makes the system compatible with multiple functionalities and the predictable regioselectivity of the cyclization. The cyclization of 5-hexenyl radical based systems has been the most widely employed and studied radical ring-closure reaction. Beckwith established rules to predict the regiochemical outcome for radical cyclizations [10]. In general, these systems cyclize under kinetic control to give exo cyclopentyl products. This is in contrast to the intermolecular addition of radicals to alkenes, which in general add endo [11,12].

In the mid-1980’s, Beckwith and Schiesser [13,14] and Spellmeyer and Houk [15] presented force-field molecular mechanics based models to analyze the intramolecular cyclization of radicals. These studies were quite successful in explaining the regiochemistry of the cyclizations and, in some cases, offered explanations for relative rates of the reactions. Both of these studies concluded that these exothermic cyclizations were characterized by an early transition state and that exo versus endo selectivity could be attributed to conformational and steric factors in the transition state. More recently, several groups have successfully employed DFT and/or ab initio methods to analyze a variety of radical cyclizations [16-19]. A few years ago, we reported a kinetic and product study on the cyclization of a series of 4-oxa-5-hexenyl radicals [20]. We found that 4-oxa substitution increased the preference for exo cyclization and decreased the rate of cyclization 3.7-fold compared to the related hydrocarbon 5-hexenyl radicals. In order to better understand these effects we initiated a computational study of the 4-oxa-5-hexenyl intramolecular radical cyclizations. The study was expanded to 5-hexenyl radicals and 3-oxa-5-hexenyl radicals in order to make comparisons using the same computational models. Here we present UB3LYP and UCCSD (T) calculations on ten 5-hexenyl-based radical cyclizations (Figure 1).

2. Computational Methods

Global energy minima conformations of the acyclic 5-hexenyl radicals (1, 4, 7) and the cyclization products (2, 3, 5, 6, 8, 9) were determined using the Spartan 08 program at UHF-3-21G level of theory [21]. These geometries were further optimized using UB3LYP/6-311+ G (d,p) in the Gaussian 03 program [22]. Transition states (TS) were identified at the UB3LYP/6-31G (d) level of theory and then further optimized at UB3LYP/6-311+ G (d,p). All stationary points were analyzed by calculation of their vibrational frequencies. G˚ values were calculated at 298 K and 1 atm. All transition states had one imaginary frequency that corresponded to the reaction coordinate for cyclization. Single-point energies were determined at the UCCSD (T)/6-31G (d) level of theory using geometries from the UB3LYP/6-31G (d) calculations: (UCCSD (T)/6-31G (d)// UB3LYP/6-31G (d)). All reported UCCSD (T) total electronic energies were not corrected for zero-point energy (ZPE).

The geometries determined at UB3LYP/6-31G (d) and the UB3LYP/6-311+G (d,p) levels of theory were very similar and, in general, differed by no more than 0.025 A in bond lengths, 0.2˚ in bond angles and 0.6˚ in dihedral angles. We found that the energy consequences of the

Figure 1. Cyclization of 5-hexenyl radicals.

geometries determined using the 6-31G (d) basis set vs. 6-311+G (d,p) to be insignificant when evaluated at a single level of theory: e.g. energies for UCCSD (T)/ 6-31G (d)//B3LYP/6-31G (d) were within 0.15 kcal/mol of the energies calculated using UCCSD (T)/6-31 G(d) //B3LYP/6-311+G (d,p). These small differences canceled out when we determined the activation energies (E_a = E_{(acyclic radical)} − E_{(transition state)}).

3. Results and Discussion

3.1. Transition States

We located three transition states for cyclization of the 5-hexenyl radicals that were similar to the structures previously reported by Spellmeyer and Houk (UHF-MP2/ STO-3G) [15] for the parent system: exo-chair, exo-boat and endo-chair (Figure 2). In general, we found that transition state bond lengths and bond angles for a particular transition state (e.g. exo-chair) were remarkably similar across the three systems that we examined: 5-hexenyl radical 1a, 3-oxa-5-hexenyl radical 7a and 4-oxa-5-hexenyl radical 4a. With the exception of the intrinsic difference of C-O vs. C-C bond lengths, the bond with the largest variation for a particular type of transition state is the partially formed new σ-bond which varies from system to system by a maximum of ~0.1 Å. Corresponding transition state bond angles are all within 3˚ of each other. The largest variations were seen in the dihedral angles (4˚ - 11.5˚) of the three 5-hexenyl transition states (1a-TS) compared with the respective 4-oxa-5-hexenyl transition states (4a-TS). The dihedral angles for the 5-hexenyl transition states were much closer to the values found for the 3-oxa-5-hexenyl system (7a-TS) varying only 4˚ - 7˚.

The transition state geometries for each pathway (exo-chair, exo-boat and endo-chair) across the 10 radicals examined are consistent with the previously identified early nature of the transition states (Table 1). At the transition state, the forming σ-bond (C1-C5 or C1-C6) is long at 2.25 - 2.35 Å while the breaking double bond (C5-C6) is only slightly elongated at 1.36 - 1.38 Å (compared to 1.33 Å in the acyclic radicals). Even strongly polarizing the double bond by 4-oxa substitution has only a small effect on the position of the transition states for all cyclization modes. The endo transition states have shorter C5-C6 bond lengths (~1.358 Å) than the exo transition states (~1.368 Å) and the forming bond (C1-C6 endo; C1-C5 exo) is ~0.07 Å longer for endo transition states (Table 1). These results indicate that the endocyclization mode has a slightly earlier transition state than the exo mode, which is consistent with the higher exothermicity of the endo pathway. There are also small differences in the C1-C5 bond distances in the kinetically dominant exo-chair transition states: 4a (2.255 Å) < 1a

Figure 2. Transition states for the cyclization of acyclic radical 4a.

Table 1. Comparison of select transition state bond distances. (Å, UB3LYP/6-31G geometries).

(2.276 Å) < 7a (2.295 Å). These data suggest that exochair transition state for 7a is earlier than the exo-chair transition state for 1a, which in turn is earlier than the exo-chair transition state for 4a.

This trend also follows the calculated DG_rxn (UB3LYP/ 6-311+G (d,p)//UB3LYP/6-31G (d)) for the exo mode of cyclization: 4a (−8.6 kcal/mol) ≤ 1a (−8.7 kcal/mol) < 7a (−14.4 kcal/mol).

The 3-methyl substituted systems give rise to a doubling of possible transition states as the methyl group can reside in either a pseudo-equatorial or pseudo-axial position. The transition states with the 3-methyl group in the pseudo-equatorial position were found to be lower in energy than the corresponding axial isomers.

3.2. Activation Energies and Exo/Endo Product Ratios

Table 2 lists the computed activation energies (E_a) calculated as the difference in the energy of the acyclic alkenyl radical in its lowest energy conformation and the energy of the specific transition state. While the trends for the DG^‡ data derived from the DFT calculations mirrored the E_a’s derived from the UCCSD (T) calculations, we found that the UCCSD (T) values more closely reproduced the experimental data for the endo/exo ratios of the cyclizations (vide infra). With this in mind, most of the discussion below will focus on the UCCSD (T) total electronic energies.

In general, we found that the exo-chair TS had the lowest E_a for a given cyclization with the notable exception of the 5-methyl substituted hydrocarbon radicals 1b and 1d where the endo-chair was the lowest energy pathway. In all cases 5-methyl substitution increased the E_a for the exo-chair TS’s (1.2 - 2.9 kcal/mol) and exo-boat TS’s (0.9 - 2.6 kcal/mol) while having a smaller effect on the endo-chair TS’s (± 0.5 kcal/mol). The increase in E_a’s of the exo-chair TS’s are due (in part) to unfavorable 1,3-diaxial interactions with the pseudoaxial methyl group and axial ring hydrogens at C1 and C3 (for 1b and 4b). The 5-methyl endo-TS’s have the pseudo axial methyl group slightly canted away from the forming cyclohexyl ring. This increases the distance of the 1,3-diaxial interactions leading to smaller changes in the endo chair E_a’s with 5-methyl substitution. Interestingly the difference in E_a for the exo-chair and endo-chair in the hydrocarbons 1a (1.9 kcal/mol) and 1c (2.2 kcal/mol) is significantly smaller than the values for 3-oxa and 4-oxa compounds 4a (5.0 kcal/mol), 4c (5.3 kcal/mol) and 7a (4.0 kcal/mol). In the hydrocarbon radicals, the increase in the energy of the exo-chair E_a pathway with 5-methyl substitution is enough to raise the exo pathway above the endo pathway. In contrast 5- methyl substitution raises the E_a of the exo-chair pathway to a greater extent in the 3- and 4-oxa compounds than in the hydrocarbon radicals, but this increase is not enough to overcome the large initial energy difference favoring the exo-cyclization pathway for 3- and 4-oxa radicals. The result is that all 3- and 4-oxa radicals are predicted to cyclize to give almost exclusively exo products (cyclopentanes), while 5-methyl substituted hexenyl radicals 1b, and 1d should cyclize to give endo (cyclohexane) dominated product mixtures. Previously Houk’s force-field based calculations led him to explain the preference for exo closure for the 5-methyl-3-oxa radical 7b on

Table 2. Calculated activation energies (kcal/mol): E_a = E_{(acyclic radical)} − E_{(transition state)}.

a. The first value is with the 3-methyl in the pseudo-equatorial position and the second value is with the 3-methyl in the pseudo-axial position.

decreased steric interactions for the exo-boat transition state with oxa versus methylene substitution at the 3-position. In contrast to our results, Houk found the exo-boat was the lowest energy transition state for both 7a and 7b.

Table 3 shows our calculated exo/endo product ratios (based on the relative E_a values) and compares these results with the available experimental data. While both the UB3LYP/6-311+G (d,p) and the UCCSD (T)/6-31G (d) calculations give excellent agreement with the experimental data, the UCCSD (T) calculations appear superior. Our calculations show that all 3-oxa and 4-oxa radicals should cyclize to give ≥95% exo products. The ratio for radical 4b stands out as the only entry that does not agree with the experimental data. In this case our calculations predict ~95% exo product and the reported value was 62%. Given the excellent agreement in the seven other cases for which we have both calculated and experimental endo/exo data suggests that there may be an error in the experimental determined value for 4b. In addition, we predict that the experimentally unobserved radical 1d will cyclize to produce an almost equal mixture of endo and exo products whereas the 4-oxa radical 4d should

Conflicts of Interest

The authors declare no conflicts of interest.

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