## Forscchung

G) Computational Chemistry

G) Computational Chemistry

**Keywords**: Addition; Alkoxyl radical; O-Alkyl isourea; Bromocyclization; Bromohydrin ether; Fragmentation; Homolytic substitution; Radical clock; Stereoselective synthesis; Thiazolethione; Thiohydroxamic acid.

**Summary**: The *p*-chlorocumyloxyl radical adds *exo*-specifically to bicyclo[2.2.1]heptene with a rate constant of *k* = 1 × 10^{7} M^{–1} s^{–1} at room temperature. Trapping of the 2-*exo*-(*p*-cumyloxy)-norborn-3-yl occurs preferentially from the *endo*-face to furnish 2,3-trans-configured bromohydrinethers major products. The propensity of alkoxyl radicals to add *exo*-specifically to norbornene arises from strain associated with the *endo*-addition, as derived from a Marcus-analysis of density functional-calculated reaction energies and barriers.

Introduction and outline:

**Scheme 1**. Elementary reactions for determining the rate constant *k*^{AR} for cumyloxyl radical addition to norbornene via the *p*-chlorocumyloxyl-“radical clock”-technique (Ar = *p*ClC_{6}H_{4}).

For investigating the origin of the *exo*-specificity in intermolecular alkoxyl radical addition we modelled barriers for the *exo*- and the *endo*-addition of the *tert*-butoxyl radical (**Ia**) and the methoxyl radical (**Ib**) to norbornene, using electronic structure methods.

**Results**: Based on method assessment for reproducing relative energies of radicals and transition structures from our own studies, and from work of other groups, we chose Becke’s 3 parameter hybrid functional (B3LYP) and Becke’s half and half functional (BHandHLYP) in combination with the 6-31+G** basis set for conducting the computational analysis. The selected basis set includes diffuse *and* polarization functions, needed for reproducing experimental selectivity in radical additions. For exploring basis set dependence, the results were supplemented by BHandHLYP/6311G**-calculations.

Equilibrium structures of readicals **Ia/b** and norbornenee, transition structures *exo*/*endo*-**IIa**/**b**, and conformationally flexible products **IIIa**/**b** were located on respective potential energy surfaces using an established procedure. Calculation of second derivatives (Hessian matrix) that lacked in negative eigenvalues or imaginary frequency by diagonalization, characterized computed structures of alkoxyl radicals **Ia**/**b**, norbornene, and bicyclic carbon radicals *exo*/*endo*-**IIIa/b** as minima. Exactly one imaginary frequency *i* associated with an O,C2- stretching vibration characterizes computed intermediates *exo*-**IIa/b **and *endo*-**IIa**/**b** as transition structures with respect to C,O-bond formation (Table 1).

**Scheme 2**. Structure formulae and indexing of reactands for modeling alkoxyl radical addition to norbornene [R = C(CH_{3})_{3} for **Ia**, **IIa**, and **IIIa**; R = CH_{3} for **Ib**, **IIb**, and **IIIb**; see also Table 1].

**Table 1**. Selected geometrical parameters of transition structures *exo*/*endo*-**IIa**/**b**^{a}

* ^{a}* Figures B3LYP/6-31+G** structures, numbers in parentheses to BHandHLYP/6-31+G** structures, and values in brackets to BHandHLYP/6-311G** structures (○ and ● symbolize key H-atoms relevant for explaining stereoselectivity).

Computed zero-point vibrational energy-corrected electronic barriers (D*E*^{‡}) were split into an intrinsic term (D*E*^{‡}* _{i}* ) and a thermodynamic component (D

**Figure 1**. Potential energy curves *E*(*x*) for reaction associated with an energy change *D*_{ R}*E* across a barrier *DE*^{‡}, having an intrinsic barrier *DE*^{‡}* _{i}*, according to Marcus-theory, and harmonic potentials of identical curvature for initial (

Calculated atomic distances, angles and energy differences change gradually but not fundamentally, as the applied theoretical methods were varied. Theory predicts strongly exothermic reactions and thus a high barrier of the reverse reaction, which correlates experimentally with kinetic reaction control for the addition. Reaction energies for *exo*- and *endo*-additions of the individual radicals are similar. When compared to methoxyl radical addition, the *tert*-butoxyl radical additions, however, are less exothermic. Calculated O...C2-distances of 2.0–2.2 Å and values for the *x*^{‡} parameter between 0 and 0.3 correlate with early transition structures on the reaction coordinates. Modelled transition structure *exo*-**IIb** at *x*^{‡} = –0.8 from B3LYP-calculation in this sense poses an exception requiring to use BHandHLYP-computed values for discussing this reaction. Computed Gibbs free energies at 298.15 K favor transition structures *exo*-**IIa**/**b **by 15–18 kJ over structures *endo*-**IIa**/**b**, which corresponds to theoretical exo/endo-ratios of >99:1. These numbers correlate with the experimental findings.

The origin of the exo-selectivity in alkoxyl radical additions to norbornene in this model arises from subtle geometrical changes occurring in an early phase of the reaction. As the radical approaches the p-bond, the hydrogen at the attacked olefinic carbon moves backward. The vicinal olefinic hydrogen, on the other hand, shifts toward the incoming radical (cf. angles H1–C1–C2–H1 and H3–C3–C4–H4 in Table 4). In transition structures *endo*-**IIa**/**b** these changes lead to an eclipsing of hydrogens at the attacked carbon and the proximal bridgehead position. In the approach from the opposite side, that is via intermediate *exo*-**VIIa**/**b**, the same hydrogens show synclinal orientation leading to less torsional strain (Table 4). These strain effects arising are evident from lower intrinsic barriers D*E*^{‡}* _{i}* for exo-additions, while thermodynamic contribution D

In terms of steric effects, it becomes apparent from the computed numbers that *tert*-butoxyl radical additions are throughout the study associated with higher intrinsic and lower thermodynamic barriers than methoxyl radical additions. These trends are attributed to a small but systematic size effects on alkoxyl radical reactivity

**Concluding remarks**: Geometrical changes occuring at alkene carbons in an transition structure as an oxygen radical approaches an alkene in an addition give rise to torsional strain, effectively controlling facial selectivity in oxygen radical addition to carbon-carbon double bonds.

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**Cooperation**:

Prof. Dr. Hartmut Fuess, TU Darmstadt.

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**Leading References**:

Tertiary Alkoxyl Radicals from 3-Alkoxythiazole-2(3*H*)-thiones. C. Schur, N. Becker, U. Bergsträßer, T. Gottwald, J. Hartung, *Tetrahedron***2011**, *67*, 2338–2347; DOI:10.1016/j.tet2010.12.071.

Preparation and Structural Characterization of the Isomuscarines. I. Kempter, B. Frensch, T. Kopf, R. Kluge, R. Csuk, I. Svoboda, H. Fuess, J. Hartung, *Tetrahedron*, **2014***70*, 1918–1927, DOI: 10.1016/j.tet.2013.12.085.

**Funding**:

Deutsche Forschungsgemeinschaft. Land Rheinland-Pfalz.