# Ring-Opening Competes with Peroxidation in Fenchone Low-Temperature Autoignition

Dario Vassetti, Giorgia Cenedese, Jonathan Honorien, Zeynep Serinyel, Philippe Dagaut, Lydia Boualem, Bruno Moreau, Sandro Gail, Fabrice Foucher, Guillaume Dayma, et al.

► To cite this version:

Dario Vassetti, Giorgia Cenedese, Jonathan Honorien, Zeynep Serinyel, Philippe Dagaut, et al. "Ring-Opening Competes with Peroxidation in Fenchone Low-Temperature Autoignition." Journal of Physical Chemistry A, 2025, 129 (13), pp.3113-3131. 10.1021/acs.jpca.4c08396. hal-05002381

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Ring-opening competes with peroxidation in
Fenchone low-temperature autoignition

Dario Vassetti<sup>1,2</sup>, Giorgia Cenedese<sup>3,4</sup>, Jonathan Honorien<sup>1,2</sup>, Zeynep Serinyel<sup>3,4</sup>, Philippe

Dagaut<sup>3</sup>, Lydia Boualem<sup>3</sup>, Bruno Moreau<sup>5</sup>, Sandro Gail<sup>1</sup>, Fabrice Foucher<sup>4,5</sup>, Guillaume

Dayma<sup>3,4</sup>, Andre Nicolle<sup>1,*</sup>

1-Aramco Fuel Research Center, Rueil-Malmaison, 92852, France

2-EMITECH - EMC France, 4 Allée de la Rhubarbe, 78260 Achères, France

3- CNRS-INSIS, ICARE, 1C avenue de la Recherche Scientifique, 45071 Orléans cedex 2,
France

4- Université d'Orléans, rue de Chartres, 45100 Orléans, France

5- PRISME, Université d'Orléans, rue de Chartres, 45100 Orléans, France

ABSTRACT

We report an atypical competition of fenchyl radical β-scission with peroxidation at low-
temperature and unravel the impacts of strain energy and ring substituent location on their
respective contributions. Our RRKM modeling reveals that radicals positioned on secondary
carbons are the fastest-scission ones, exhibiting maximum local ring relief. Dimethyl substituents
contribute to increased local strain compared to norbornane, hindering bridge scission and leading
to cyclopentene and isoprene products. The dimethyl corset generates extra torsional strain during
HO₂ elimination from QOOH, while ether formation is favored by electron donation from the
carbonyl group. The fall-off extent is also affected by steric hindrance insofar as it increases bridge
stiffness, leading to a lower vibrational partition function and low-pressure rate constant. Further,
methyl-induced restrictions on reactant reorganization are found to modulate an enthalpy-entropy
compensation in Korcek reaction of fenchyl hydroperoxide. Unlike in our previous stirred reactor
experiments, the impact of fenchyl peroxidation on reactivity is notable under our new rapid
compression machine (RCM) experiments. The present model predicts contrasted fenchyl
selectivities with radical position, β-scission and peroxidation prevailing respectively for
F₁/F₂/F₃/F₄ and F₅/F₆ radicals. The kinetic mechanism accurately predicts the experimental IDT
but indicates a slight first-stage pressure inflection point at the lower experimental temperature,
which could not be confirmed experimentally. This new insight into fenchone ring-opening and
closing mechanisms under high pressure oxidation can be useful for other polycyclic ketones.
## 1. BACKGROUND

The oxidation of fenchone, a high-energy density (>35 MJ/kg) and high-octane-number (>90)¹ potential fuel blendstock component²,³, a volatile intermediate involved in forest fires⁴, a precursor of organic aerosols⁵ and flame-synthesized nanomaterials⁶,⁷, is of particular environmental significance but insufficiently investigated. Understanding its oxidation kinetics not only benefits fenchone as a fuel but also biofuels combustion involving fenchone as an intermediate⁸,⁹,¹⁰.

We recently unveiled its thermal oxidation kinetics in a jet stirred reactor¹ operating at 10 atm. Our previous kinetic model incorporated H-abstraction and fenchyl radicals β-scission and isomerization, capturing major measured intermediates such as methane, ethylene and formaldehyde. Fenchone primary decomposition was found to involve mostly radicals F₃, F₄ (ring radicals, as depicted on Figure 1) and F₆ (radical on gem-dimethyl group), leading to methyl cyclopentenyl radicals and isoprene. However, due to the high octane number of fenchone, the oxidation extent at low-temperature (< 800 K) was modest under these conditions. These results called for dedicated experiments and modeling at higher pressures, which is deemed appropriate to enhance cycloalkane low-temperature reactivity¹¹.

<figure><img src="image_2.png" /></figure>

The Negative Temperature Coefficient (NTC) behavior in the low-temperature oxidation of hydrocarbons is characterized by a decrease of overall reactivity as temperature rises. This results notably from the decreased selectivity of the branching peroxidation of alkyl radicals R+O₂→RO₂ with respect to the pseudo-terminating step R+O₂→alkene+HO₂ (followed by 2HO₂→H₂O₂+O₂), slowing down chain branching with increasing temperature¹². This regime may result in a two-stage ignition controlled successively by RO₂ and HO₂ reactions¹³. While the first-stage ignition of n-alkanes has been shown to be influenced by the competition between alkyl peroxidation and their β-scission¹⁴, the impact of this competition on cycloalkanes has not been charted extensively beyond cyclohexane¹⁵.

Cycloalkanes exhibit distinct NTC behaviors compared to n-alkanes due to conformational constrains arising from ring strain¹⁶,¹⁷, increasing energy barriers¹⁸ and, overall, providing less favorable H-shift sites¹⁹ for the alkylperoxy radicals (RO₂) isomerization to alkyl hydroperoxides
67 (QOOH). With respect to n-alkanes, strained cycloalkanes tend to favor ring-opening reactions
68 due to lower bond energies but hinder H-shift²⁰, affecting their reactivity. The competition between
69 ring-opening and peroxidation is temperature-dependent. At lower temperatures, peroxidation
70 mechanisms are more prominent, while β-scission and dehydrogenation²¹ tend to dominate at
71 higher temperatures, leading respectively to aliphatic or cyclic alkenes²²,²³, with differing effects
72 on aromatics formation²⁴. Tert-butyl-cyclohexanone peroxidation at ambient temperature was
73 found to generate alkoxy radicals which undergo β-scission to form cyclohexandione and
74 pivalaldehyde²⁵.

75 The presence of alkyl substituents, such as in dimethylcyclohexane, affects these ring-opening
76 reactions by making some bonds more prone to scission. Monomethyl substituents in cycloalkanes
77 were found to favor ring-opening reactions over peroxidation²⁶, while gem-dimethyl substitution
78 can lead to a Thorpe-Ingold angular compression²⁷, affecting both energetic and entropic barriers
79 for scission²⁸. The substituents not only impact ignition behavior²⁹ but also soot formation
80 pathways³⁰,³¹.

81 Studies of strained rings opening largely focused on biradicals formation under pyrolytic
82 conditions³²,³³,³⁴, while the fate of monoradicals formed by H-abstraction on bicycloalkanes is of
83 major importance under practical conditions³⁵,³⁶. Unlike some other cyclic ketones³⁷, no
84 resonance-stabilized α-fenchyl radicals may be formed by H-abstraction on fenchone. Also, unlike
85 in the case of cyclopentanone³⁸, Cα-ether formation is hindered by the crowded neighbourhood of
86 ketone function, therefore a back-to-back comparison with cyclopentanone is inadequate.
87 However, due to the lack of availability of thermal oxidation studies for dimethyl-
88 cyclopentanone³⁹, cyclopentanone may serve as a starting point to frame expectations about how
89 fenchone may behave differently. The barriers of oxocyclopentanyl radicals scission lie below and
90 above⁴⁰ the cyclopentyl radical value of 33 kcal/mol⁴¹, suggesting that the carbonyl effect on ring-
91 opening kinetics is radical-dependent. Fenchyl ring openings, which were identified in our
92 previous sensitivity analyses as key reactions¹ in Fenchone oxidation, along with QOOH
93 decomposition⁴², may be expected to be strongly pressure-dependent⁴³.

94 Amaiz et al.⁴⁴ found a decarbonylation barrier for norbornenone around 30 kcal/mol, while
95 Ghildina et al.⁴⁵ obtained 80 kcal/mol for cyclopentadienone, highlighting the impact of ring strain
96 and resonance stabilization. Despite some previous evidence of strain promoting effect on
97 reactivity⁴⁶,⁴⁷,⁴⁸,⁴⁹, it is not clear how fenchone ring strain may influence the respective importances
98 of R / QOOH radicals β-scission, ether formation and Korcek reaction⁵⁰ at low-temperatures.

99 The present study aims to extend the previous fenchone oxidation mechanism¹ to analyze new
100 high-pressure rapid compression machine (RCM) ignition experiments thanks to first-principle-
101 based pressure-dependent phenomenological kinetic modeling.

102

103

104 2. METHODS

105 2.1 Experimental set up
Experimental ignition delay time (IDT) measurements were conducted at the single-piston rapid compression machine (RCM) facility of the University of Orleans. The RCM contains a creviced piston pneumatically driven and braked close to the top dead center by a hydraulic technique. The total duration of compression is about 27 ms. Further details of the RCM can be accessed elsewhere⁵¹, only a brief description of this machine is presented here.

The errors of measurement of in-cylinder pressure, intake pressure, intake temperatures, and mass flow rate are ± 1%, ± 1 mbar, ± 2 K and ± 1%, respectively. In order to obtain the targeted stoichiometric fuel/oxygen ratio, the gaseous fuel was premixed with synthetic air from Air Liquide. Before the preparation of mixtures, the reservoir was cleaned by flux of air and then pumped out to reach vacuum condition (< 1 mbar). The weight of the liquid fuel introduced into the reservoir was determined as the difference in the weight of the syringe before and after the introduction. The temperature of the reservoir was maintained at 353 K to ensure the total vaporization of the liquid fuels. A mechanic agitation was conducted to ensure the mixture homogeneity.

For each measurement, the pressure at the top dead center ($p_c$) and the temperatures at top dead center ($T_c$) were obtained by regulating the intake pressure and the piston initial temperature. $T_c$ is calculated thanks to the isentropic relation involving the ratio $\gamma$ of specific heats:

$$ \int_{T_0}^{T_c} \frac{\gamma}{\gamma-1} \frac{dT}{T} = \ln\left(\frac{p_c}{p_0}\right) $$

Levo-fenchone/O₂/N₂/Ar mixtures were considered at two equivalence ratios ($\Phi$=0.5 and 1, corresponding to the fraction of fenchone/O₂ ratio to its stoichiometric value) and $p_c$ = 40 atm. The heat loss during a RCM experiment was taken into account by deriving an “effective volume” profile based on a non-reactive experiment where oxygen was removed from mixture under the same initial conditions as those of the targeted reactive experiments (Figure 2).

Table S₄ provides operating conditions for each diluent composition (mole ratio (N₂+Ar)/O₂ = 3.761) conferring a bespoke $\gamma$ ratio. The main IDT (standard deviation ±5%) is defined as the duration between the end of compression and the maximum dp/dt value (Figure 2).
<figure><img src="image_3.png" /><figcaption>Figure 2 – Example of pressure histories for a stoichiometric mixture (diluent 20% Ar/80% N₂, pc = 40 bar, Tc = 810 K). The non-reactive experiment was used to determine an “effective volume” profile for modeling. The “model” profile refers to simulation result with the present kinetic model using the prescribed homogeneous reactor volume.</figcaption></figure>

## 2.2 Kinetic modeling

The modeling approach follows closely our previous study⁵². The stationary points of the lowest-energy conformers potential energy surface (PES) were optimized at the M06-2X/def2-DZVP level of theory with Orca⁵³, which has been shown to predict geometries and frequencies of organic species accurately⁵⁴,⁵⁵, i.e within 0.01 Å and 50 cm⁻¹. Intrinsic Reaction Coordinate (IRC) analyses confirmed the connection of transition state (TS) with reactant wells. 1D Hindered rotor scans were performed at the M06-2X level for PES wells and TS for low frequency modes (< 400 cm⁻¹). Post Hartree-Fock energy calculations were performed at the DLPNO-CCSD(T)-F12/def2-DZVP-F12 level of theory for each structure along the reaction coordinate, which is sufficiently close to the basis set limit to obtain accurate relative electronic energies (i.e within 2 kcal/mol) for the present system. Based on the zero-point-energy-corrected PES obtained, the MESS code⁵⁶ was used to solve the energy-resolved Master equation within the chemically significant eigenvalue approach. The MESS inputs as well as T₁ diagnostics (Table S3) for the structures modeled are provided in Supporting Information. Tunneling corrections were estimated at the CTST level using the asymmetric Eckart model. All reactions exhibiting low barriers (< 10 kcal) with respect to either reactant or product were treated using VTST. The reaction symmetry factors, including rotational and optical symmetry were determined using corresponding xTB subroutine⁵⁷. The standard exponential model was used for the collisional energy transfer kernel $\langle \Delta E_d \rangle = 200 \left( \frac{T}{300} \right)^{0.75} \text{ cm}^{-1}$, the Lennard-Jones parameters being $\epsilon / k_B = 68$ K and 572 K, $\sigma = 3.61$ Å and 7.99 Å for N₂ and fenchyl radicals, respectively, based on RMG group additivity estimates⁵⁸.
159 Natural Bond Orbital (NBO) analyses of stationary points were done with the Gaussian 16
160 software<sup>59</sup> at the M06-2X level.

161 The first-principle-based phenomenological kinetic rate constants obtained in the present work
162 were fitted in PLOG format and used to enhance a previously published fenchone oxidation
163 mechanism¹. Levo-fenchyl radicals (Figure 1) were specifically considered for low-temperature
164 alkylperoxy steps as the presence of diastereoisomers was found to influence slightly rate
165 constants⁶⁰. Additional consumption reactions of β-scission products and corresponding
166 thermochemical data were generated using RMG software. The barriers for dihydroperoxide
167 U(OOH)₂ decomposition to hydroperoxy ethers, initially estimated by RMG, were raised by 4
168 kcal/mol to improve the agreement with measured autoignition delays, while staying within the
169 ranges reported for cyclopentyl dihydroperoxides⁶¹. The final mechanism is provided in Chemkin
170 format as a Supporting Information. Both equatorial and axial F₆ radicals β-scissions were
171 accounted for by Chemkin duplicate reaction formalism, which sums corresponding rate constants.
172 The RCM and jet stirred reactor modeling was performed using respectively a bespoke variable-
173 volume Ideal Gas Reactor model implemented with Cantera toolkit⁶² and the Aurora library of
174 Chemkin-Pro software⁶³.

175

176 **3. RESULTS AND DISCUSSION**

177 **3.1 Fenchyl ring opening: Potential Energy Surfaces**

178 **3.1.1 Bridge (F₁), Bridgehead (F₂) and Ring (F₄) radicals**

179 For easy reference, the Simplified Molecular Input Line Entry System (SMILES) is provided for
180 each intermediate in the present mechanism (Supporting Information). All channels except those
181 leading to some anti-Bredt products (GD(4), ZS(19)) exhibit tight saddlepoints (Figure 3 and S1).
182 6-membered alkene GD(4) is consistently⁶⁴ less strained than 5-membered bridge alkene GD(1).
183 As in the case of other cyclic ketones⁶⁵, the lowest barrier is obtained for C-C scissions in α-
184 position of the carbonyl group (resp. 6.8, 11.0 and 15.2 kcal/mol for F₄, F₁ and F₂). Notably, the
185 15.2 kcal/mol barrier for S(224) formation from F₂ (reaction R1)

<figure><img src="image_4.png" /></figure>

186

187 is markedly lower than the value of 23 kcal/mol reported by Sirjean et al.⁶⁶ for 1-methyl-3-
188 methylidene-cyclopentane radical formation from norbornyl radical (reaction R2)

<figure><img src="image_5.png" /></figure>

189

190 Weakly bound acyl radicals, such as S(224), S(279) or GD(6) (Figure 3) may experience prompt
191 decomposition, as the dissociation of their rovibrationally excited population may occur prior to
192 their collisional relaxation to Boltzmann distribution<sup>67</sup>, bypassing thermalization and leading
193 directly to lighter products. Döntgen et al.<sup>68</sup> investigated the impact of non-Boltzmann radical
194

distributions on β-scission kinetics for hundreds of radicals. They found that ester radicals are conducive to prompt decomposition at low-temperature (<800 K), while aldehydic and cycloalkylic radicals are hardly affected below 1200 K. Although ethers ketoalkoxy (OQO) radicals resulting from ketohydroperoxides (OQOOH) decomposition can be affected by prompt decomposition at low temperature⁶⁹, the quantification of these effects is outside of the present study which focuses on R / OQOOH conversion for a cyclic ketone.

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200

The computed energetic barrier for CH₂-CH₂ scission in fenchyl ring F₂→ZS(16) of 21.5 kcal/mol is markedly lower than previous values of 33 kcal/mol for cyclopentyl radicals⁷⁰ but close to 21.1 kcal/mol obtained for ethylnorbornyl⁷¹. Further, the 22.5 kcal/mol barrier for F₄ bridgehead bond breaking to GD(5) (reaction R3)

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203

<figure><img src="image_6.png" /></figure>

204

205

is in excellent agreement with the barrier of 23.2 kcal/mol obtained by Morozov et al.⁷² for JP10 monoradical bridgehead scission. This suggests that the detrimental impact of polarization of carbonyl put forward for cyclopentanone³⁸ with respect to cyclopentane may not affect strongly the present barriers for C-C scissions occuring in β, γ or δ positions of carbonyl.

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207

208

209

<figure><img src="image_7.png" /></figure>

210

211

Figure 3 – Relative ZPE-corrected electronic energies of key stationary points (represented with Avogadro⁷³ and Openbabel⁷⁴ for the β-scission of (a) F₂ and (b) F₄ fenchyl radicals at the DLPNO-CCSD(T) level. Dotted lines represent reaction coordinate. The name of products in the present kinetic mechanism are indicated for reference.

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215
<figure><img src="image_8.png" /><figcaption>Figure 4 – Evolution of fenchyl radical geometry along the β-scission IRC for F<sub>2</sub>→ZS(19) and F<sub>4</sub>→GD(6). The respective SOMO obtained in the NBO calculations are represented at the 0K saddlepoint. C<sup>q</sup>, C<sup>O</sup> and C<sup>e</sup> denote respectively quaternary, carbonylic and eliminated carbons from F<sub>x</sub> radicals.</figcaption></figure>

Figure 4 compares geometries along the IRC for one Anti-Bredt product formation F<sub>2</sub>→ZS(19) versus low-barrier C-C<sup>O</sup> β-scission F<sub>4</sub>→GD(6), the prevailing path for F<sub>4</sub> scission, corresponding to the maximum local ring strain relief (as shown in next section). While the C<sup>O</sup>-O bond length of F<sub>4</sub> shrinks early with respect to C-C distance of breaking bond (X-axis) in the case of GD(6), the C<sup>rad</sup>-C<sup>α</sup> length of F<sub>2</sub> transits to double bond only after methyl relaxation through OC<sup>O</sup>CC<sup>6</sup> dihedral rotation compatible with sp<sup>2</sup> hybridization. In both cases, singly occupied orbital (SOMO) is significantly delocalized (Figure 4), favoring electron donation with other orbitals. The present NBO analyses indicate that the oxygen lone pair n<sub>O</sub> interacts with the breaking bond orbital σ<sup>*</sup><sub>CC</sub>, stabilizing the corresponding transition states<sup>75</sup> by around 10 kcal/mol. This stabilization does not lower the saddlepoint sufficiently to produce ZS(19) significantly (i.e., at least ppb level), unless specific trapping agents<sup>76</sup> are employed. In the case of F<sub>4</sub>→GD(6), an additional donation n<sub>O</sub>→π<sup>*</sup><sub>C=O</sub> further dramatically stabilizes the transition state by around 110 kcal/mol, in line with previous reports on similar systems<sup>77</sup>. This may explain a markedly lower barrier than previous ones reported for analogous methylcyclopentane<sup>78</sup>, JP-10<sup>79</sup>, cyclohexanone<sup>80</sup> and cyclopentanone<sup>65</sup> ring openings, indicating that the trade-off between ring frustration and radical delocalization effects<sup>81</sup> may herein lead to a lower reaction barrier. As a consequence, the F<sub>4</sub> branching ratio to GD(6) remains higher than 0.95 over the 500-1300 K range.

### 3.1.2 Gem-dimethyl (F<sub>6</sub>) and methyl (F<sub>5</sub>) radicals

The systematically higher scission barriers for F<sub>6</sub> axial with respect to F<sub>6</sub> equatorial (Figure 5) are due to a more intense steric hindrance (i.e Pauli repulsion<sup>82</sup> for C<sup>6</sup>-H...H-C<sup>3</sup>) in the equatorial
243

reactant well, which vanishes in the transition state. However, in the case of F₂, axial methyl departure is disfavored energetically with respect to equatorial one, leading to ZS(19), as a result of stronger stabilization of methyl by carbonyl in the equatorial plane. Comparing methyl scission products ZS(10) (exo methyl scission) with ZS(19) (endo methyl scission), we confirm the generality of Sirjean's rule⁴¹ that reaction barriers increase as the C=C bond is being formed within the cycloalkylic ring instead of on the side chain.

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249

<figure><img src="image_9.png" /></figure>

250

251

<caption>Figure 5 – Relative ZPE-corrected electronic energies of key stationary points for the β-scission of axial and equatorial F₆ fenchyl radicals at the DLPNO-CCSD(T) level. Dotted lines represent reaction coordinate. The name of products in the present kinetic mechanism are indicated for reference.</caption>

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262

F₅ β-scission barriers (Figure S₃) are similar to axial F₆ ones, albeit less contrasted. However, F₅ can also undergo a single-step⁸³,⁸⁴ Dowd-Beckwidth ring expansion (Figure S₇) with a barrier of 21.7 kcal/mol, comparable to F₅ scission barriers. The C⁵CO angle of 112° in that 6-trigonal-endo Baldwin cyclization⁸⁵ TS deviates slightly from the ideal Bürgi-Dunitz angle of 109° due to ring strain, electrostatic and Pauli interactions⁸⁶, as shown by the interaction indicator (IRI, Figure S₇), C₅...Co motion being channeled across most attractive (<0.2) and least repulsive (>0.2) interaction zones.

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264

### 3.1.3 Structure-property relation for β-scission

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271

In order to get a compact representation of the PES obtained, a 61 ring-opening reaction database (Table S₁ in Supporting information including both Fₓ and QₓOOH β-scissions) was curated from the present computed barriers at 0K as well as those from Ghent group on JP10 alkylic ring opening⁷⁹. Based on quantum (CM5 Hirshfeld charges computed at the M062X/cc-pVDZ level of theory) and Mordred (1-3D) descriptors⁸⁷ generated from optimized cartesian coordinates of the reactant wells, we obtained a list of candidate descriptors by cophenetic clustering using py-QSAR software⁸⁸, identifying potential overfitting (high R² and low Q²) beyond 5 descriptors. We
272 discarded the descriptors with lower interpretability such as Burden matrix eigenvalues and
273 performed multi-linear regressions with increasing numbers of descriptor, starting with ΔrH0K.
274 Adding an electron delocalization parameter (2-Noccupancy) suggested by Sterling et al.⁸⁹ for strained
275 ring opening did not improve the fit accuracy in the present case. The 3-descriptor structure-
276 property relation providing the best expressivity/generalizability trade-off for k-fold cross-
277 validation (R² = 0.83, Q² = 0.78, RMSE = 4.3 kcal/mol, Parity plot in Figure S6) writes:

$$278 \qquad E_{\text{barrier}} (\text{kcal/mol}) = 0.671 \Delta_{\text{rH0K}} + 51.96 q_{\text{radical}} - 0.916 \text{ATSC2s} + 21.96$$

279 The slope of ΔrH0K (accounting for strain energy contribution) is in line with previously proposed
280 Evans-Polanyi relations for similar ring openings⁴¹, while the positive slope for CM5 atomic
281 charge of radical site (qradical) aligns with an inhibiting effect of radical site electrophilicity (i.e less
282 negative carbon charge) on β-scission, stimulating present research on nucleophile-driven strain
283 release⁹⁰. The ATSC2s descriptor (centered Moreau-Broto autocorrelation of lag 2 weighted by
284 intrinsic state) was already featured in other radical reactions⁹¹. It herein accounts for electron-
285 donating (nucleophilic) methyl or attracting (electrophilic) methylhydroperoxy substituents
286 respectively lowering and raising β-scission barriers⁹².

287
288 **3.2. Fenchyl ring opening: Rate constants**

289 **3.2.1 Impact of strain energies on reactivity**
290
291 Figure 6(a) provides the total ring-opening rate constants for each fenchyl radical. F₁ and F₄ β-
292 scissions are the fastest ones, exhibiting lower energetic barriers than other scissions. A
293 comparison with norbornyl systems suggests that bridgehead scission is less affected by additional
294 methyl substituents than bridge scission. According to our calculations, variational TST effects on
295 rate constants remain moderate for the present β-scissions. In the case of the anti-Bredt channel
296 leading to ZS(19) (Figures 3-4), the C...CH₃ breaking bond distance at the dynamical bottleneck
297 decreases from 2.87 Å to 2.73 Å for temperatures transiting from 300 K to 500 K. This distance is
298 much higher than the saddlepoint for methylcyclohexyl scission to methyl radical⁹³ (dC-CH₃,TS =
299 2.27 Å). Arrhenius plots for the remaining fenchyl β-scissions are provided in Supporting
300 Information (Figures S₄ and S₅). Figures 6b and 6c show a good agreement with similar rate
301 constants previously computed³⁵,⁶⁶, although bridge opening rate (Figure 6b) seems slightly more
302 affected by additional substituents than ring opening rate (Figure 6c).

302
<figure><img src="image_10.png" /><figcaption>Figure 6 – Rate constants of ring beta scission channels for fenchyl radicals. (a) relates to the total rate constants of fenchyl Fₓ radicals scission (and their norbornyl/JP10 analogs in dotted lines) at infinite pressure. The rate constants of Gao et al.³⁵ and Sirjean et al.⁶⁶ for similar scissions (leading respectively to 2-cyclopentyl-cyclopentenyl and 4-methyl-cyclohexenyl radicals) were added as dotted lines for comparison with F₃ scission channels. Dashed and continuous lines (b) correspond respectively to CTST and VTST rate constants.</figcaption></figure>

Overall reactivity can be correlated to the strain energies of Fenchyl radicals. According to Figure 7, F₂ and F₄ involve the highest ring strain energies, while F₁ and F₄ exhibit the highest total strains (bond, angular and dihedral) among fenchyl radicals. F₄ features a spread of strain around the ring, while F₂ strain is more localized. For both radicals, C²-C⁹ bond exhibits a significantly longer length (1.57 Å) than the standard one (1.54 Å), still far from the diamantane dimer value (1.70 Å)⁹⁴. Di-methyl substituents contribute to increase local strain with respect to norbornane, consistently with prior results on substituted strained rings⁹⁵. The (additional) olefinic strain (OS) energy of the 3,4-alkene (fenchenone) of Figure 7 is around 17 kcal/mol, ranking it as ‘Schleyer-observable’⁹⁶, while ZS(19) OS energy lies around 27 kcal/mol, i.e at the lower boundary of instability range, in line with previous reports⁶⁴.
<figure><img src="image_11.png" /><figcaption>Figure 7 – Strain energies (kcal/mol) computed by Strainviz software⁹⁷ at the M06-2X level of theory. Structures are split into H-capped fragments which are optimized and internal coordinates (bond length, angle, torsional angle) are relaxed to their lowest energy configuration. The change in energy for each coordinate provides the corresponding strain energy. Ring strain denotes overall dihedral strain of bicyclic ring. Total strain sums bond, angular and dihedral contributions of all atoms.</figcaption></figure>

The evolution of the Interaction Region Indicator (i.e., the gradient of electron density divided by density, Figure 8) during the course of the bridge scission reveals that a sharp H...H Pauli repulsion of C² (bridge) hydrogens with C⁶ (methyl) and C⁴ (methylene) hydrogens constrain strongly the transition state C³C⁴CC¹ dihedral angle, the C¹H₂ group being channeled by two arrow-shape repulsive interaction zones. This entropic effect may explain the change in Arrhenius plot intercept (Figure 6b) with respect to the norbornane case. The hinderance of bridge scission by methyl substituents has mechanistic consequences.
<figure><img src="image_12.png" /></figure>

Figure 8 – Interaction Region Indicator⁹⁸ in the C¹H¹C¹H⁶ plane for the transition state from fenchyl F₃ radical to trimethyl-methylene-cyclohexenone radical ZS(1), using Multiwn software⁹⁹. Dashed black line represent the breaking bond. Other depicted atoms correspond to the projection of their position on the C¹H¹C¹H⁶ plane. Values higher than 0.2 denote zones of notable repulsion, while dark blue denotes notable attraction (covalent or H bonding)

### 3.2.2 Branching ratios

The products formed align with previous decomposition studies of bornylic compounds¹⁰⁰,¹⁰¹. Present scission branching ratios indicate that the five-membered rings formation systematically prevails over the whole pressure and temperature range studied, while the six-membered ring products (from bridge scission) were previously found to dominate at lower temperatures in the case of JP10 decomposition⁷², i.e. in absence of methyl substituents. Similar to β-scissions, ring expansions are affected by steric effects of methyl substituents¹⁰². Yet, the Dowd-Beckwidth ring expansion of F₅ radical (reaction R4)

<figure><img src="image_13.png" /></figure>

herein contributes up to 50% to its unimolecular consumption (Figure 9), competing effectively with ring β-scission.
<figure><img src="image_14.png" /><figcaption>Figure 9 – Branching ratios of F₁, F₂, F₅ and F₆ fenchyl radicals unimolecular conversion as a function of temperature and pressure. Skeletal formulas represent respective channel products.</figcaption></figure>

Despite the stabilizing hyperconjugation $nO→σ^*_{Cq-C5}$ and retrodonation $σ_{Cq-C5}→π^*CO$ in the transition state (cf. Figure S7 in Supporting Information), the energetic barrier (21 kcal/mol) for ring expansion is markedly higher than that obtained for aliphatics such as tert-butyl ketones¹⁰³ (around 10 kcal/mol), in line with recent findings on methylcyclopentanone³⁹.

As shown on Figures S4 and S5 (in Supporting Information), the extent of fall-off (pressure dependence of rate constant) is highly contrasted among the fenchyl radicals. As shown on figure 7, the bridgehead and bridge strains increase for F₁ radical with respect to F₃, F₁ exhibiting a higher overall strain than F₃ (64.5 and 60.8 kcal/mol respectively). This angular strain adds up to steric hindrance to increase bridge stiffness¹⁰⁴. The frequencies of the hindered stretching and bending modes increase as the square root of bond stiffness, resulting in a lower vibrational partition function $Q_{vib}$ than the off-bridge F₃ radical. The inverse Laplace transform of $Q_{vib}$, the vibrational density of states N(E), increases as well¹⁰⁵. The low-pressure rate constant k₀ is in turn proportional to the Boltzmann average of N(E+E₀), E₀ denoting scission threshold energy. Figure 10 illustrates that, for similar bridgehead scissions, the three-orders-of-magnitude difference of N(E+E₀) between F₁ and F₃ translates directly into similar k₀/k∞ ratios. The pronounced fall-off for F₁ scission results in a contrasted evolution of branching ratios as a function of temperature.
<figure><img src="image_15.png" /><figcaption>Figure 10 – Comparison of the trans-ro-vibrational densities of states of F₁ (orange) and F₃ (blue) radical according to RRKM theory (extracted with Kisthelp software¹⁰⁶ and their impact on the falloff extent at 900 K denoted by dotted vertical black lines for F₁→GD(3) and F₃→S(660).</figcaption></figure>

### 3.3. Fenchyl peroxy radicals ($F_xO_2$) evolution

#### 3.3.1 $F_xO_2$ isomerization to $Q_xOOH$

Alkylperoxy radicals kinetics has been studied only partially for norbornane¹⁰⁷, JP-10¹⁰⁸,¹⁰⁹ and pinene¹¹⁰ liquid-phase oxidation. For structural reasons, $Q_\alpha OOH$ and hence enol-peroxy radicals cannot be formed³⁷,³⁸. The present *ab initio* study focused on gas-phase $F_1O_2$, $F_4O_2$, $F_5O_2$ and $F_6O_2$ radicals conversion (Figure 11, Tables S₂-S₃ and RRKM input in Supporting Information) due to the contribution of these radicals to fenchone conversion fluxes, as shown in the phenomenological kinetics section below. Due to the modest share of peroxidation in $F_3$ consumption (<5%), $R_3O_2$ isomerization rate was estimated from previous cyclopentane kinetics¹¹¹, its products being merged with $Q_4OOH$ (Figure S₁₈). $F_2O_2$ isomerization to QOOH was estimated from RMG rate rules.

With respect to cycloalkanes, the existence of tricyclic transition states to fenchyl hydroperoxy ($Q_xOOH$) radicals introduces additional strain, which may lead to higher barriers¹¹². Figure 11 compares the present isomerization rate constants with literature. In the case of $Q_6OOH$-5 6-membered TS featuring a H-transfer from a neighbouring primary carbon, the steric hindrance is minimal, while the stabilizing delocalization $\pi_{CO}\rightarrow\sigma^{*}_{Cq-C6}$ contributes to lower TS energy (by 4 kcal/mol), leading to a lower barrier with respect to Villano et al.¹¹³ and Yang et al.¹¹⁴ cyclic TS. Conversely, H-transfer from tertiary $C^5$ in $Q_1OOH$ 5-membered TS does involve significant steric hindrance but does not benefit from any stabilizing electron delocalization from keto group. Logically, the 6-membered TS leading to $Q_5OOH$-3 (Figure S₁₅) which exhibits neither similar delocalization nor steric hindrance, has a rate constant at 900 K of $10^{5.3}$ s⁻¹, i.e. close to Villano's
value for primary radicals. It is important to keep in mind that Villano (and present) study rely on Pitzer-Gwinn independent rotors approximation, which may lead to slightly overestimated rate constants¹¹⁵. The reasons for the higher extent of fall-off with respect to that obtained by Yang et al.¹¹⁴ on methylcyclohexane may be similar to above ones, i.e steric hindrance arising from extra bridge and impacting QOOH frequencies, hence a lower $k_0 / k_\infty$ ratio. Further, the lower activation energy than that of JP-10 hydroperoxy formation (21.7 vs 24.7 kcal/mol) can be attributed to additional TS stabilization of 1.5 kcal/mol by $\sigma_{C_0-Cq} \rightarrow \sigma^{*}_{C_3-O}$ electron donation to the 6-membered $C^9C^3OOHC^1$ ring (Figure 11).

<figure><img src="image_16.png" /><figcaption>Figure 11 – (a) Comparison of present isomerization rate constants (continuous lines) with existing rate rules for aliphatics¹¹³ (dotted) and methyl cyclohexane¹¹⁴ (dashed). LUMO+1 orbitals are represented for $Q_6OOH$ (primary) and $Q_1OOH$ (tertiary) transition states (TS). (b) Comparison of pressure-dependency $F_6OO$ isomerization with methylcyclohexyl peroxy radicals H-shift¹¹⁴, both occurring through similar 7-membered TS (blue and red lines for 1 and 10 atm). Black curves : comparison of high pressure rate constants of similar isomerizations for $F_4OO$ and JP-10 peroxy¹⁰⁸. Displayed structures denote respective transition states.</figcaption></figure>

### 3.3.1 QOOH / FOOH decomposition

In our ab initio study, we focus on $Q_4OOH$ and $Q_6OOH$ decomposition as archetypal ring- and methyl-hydroperoxy radicals (Figure 12). Other $Q_xOOH$ radical decomposition kinetics is estimated from RMG rate rules. Water elimination from QOOH to form a dione is not herein studied due to its high barrier (> 40 kcal/mol) and its previous report for $Q_\alpha OOH$ only³⁸. Similar to $F_2$ (Figure 9), $Q_6OOH$-2 radical β-scission has a high branching ratio (0.40-0.95) to a 5-membered product ($S1-Q_6OOH_2$), although the 6-membered product ($S4-Q_6OOH_2$) becomes dominant above 1000 K (Figure S17). A comparison of respective rate constants suggests that the
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additional -OOH substituent (with respect to F₂) does not alter the activation entropy for S4-Q₆OOH₂ formation, since Q₆OOH-2 bridge scission is similarly hindered rotationally as in F₂ case. Conversely, CqCo β-scission suffers from extra OOH steric hinderance to C³C²CqC⁶ dihedral rotation, impairing its activation entropy.

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<figure><img src="image_17.png" /></figure>

434

<figure><img src="image_18.png" /></figure>

435

<caption>Figure 12 – (a) Relative DLPNO-CCSD(T) ZPE-corrected electronic energies (kcal/mol) of key stationary points for the equatorial (a) and axial (b) Q₄OOH conversion. (c) Korcek pathway for (closed-shell) fenchyl hydroperoxide (F₄OOH).</caption>

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According to Figure 12b, Q₄OOH-3 shows a slightly lower barrier to oxirane formation (7 kcal/mol) than similar hydroperoxy radicals from cyclopentane¹¹¹ and cyclopentanone³⁸ (9 and 11 kcal/mol respectively). This indicates that bond and angular strains may have promoting impacts for this reaction, while the ketone function hardly affects the barrier to ether. Figure 7 shows that the corresponding dihedral strain (about the C³-C⁴ bond) is indeed higher for fenchyl hydroperoxy (2.4 kcal/mol) than for cyclopentanone ring (1.3 kcal/mol).

The present NBO analysis indicates that the no lone pair of exo-oriented OH departing group can interact effectively with π\*C=O, while avoiding extra steric hindrance (Figure S7). Conversely, the barrier to HO₂ elimination and alkene formation from Q₄OOH-3 lies at around 23 kcal/mol, i.e. much higher than values obtained for QOOH in simpler cyclic systems (15 kcal/mol for cyclopentane and cyclopentanone). As shown on Figure S7, the trade-off between steric hindrance and dispersion¹¹⁶ from C⁶ methyl groups influences the saddlepoint geometry during HO₂ elimination. This dimethyl corset-like effect¹¹⁷ results in a C²C³C⁴H dihedral angle of 28° (vs. 18° obtained by Khanniche in the case of cyclopentanone sister reaction³⁸, corresponding to an extra torsional strain¹¹⁸. The C³-C⁴ torsional strain persists in the fenchene (3,4-alkene) well, as displayed on Figure 7. Further, the present shorter C³C⁴ distance of 1.37 Å (vs. 1.40 Å for cyclopentanone) indicates a saddlepoint closer to cycloalkene geometry than in the case of cyclopentanone. These effects tend to further favor cyclic ether with respect to alkene formation for Q₄OOH-3 (Figure 13b), which sets this hydroperoxy fenchyl apart from simpler cyclic ketone hydroperoxy radicals³⁸,³⁹. β-scission of Q₄OOH-1 competes effectively at high pressure and low temperature with oxetane formation due to the lower scission activation energy (Figure 13a). This illustrates that ring strain and substituents can lead to an opposite temperature-dependency of branching ratio with respect to cyclopentanone⁴⁰, highlighting an idiosynchratic kinetic behaviour.

<figure><img src="image_19.png" /><figcaption>Figure 13 – (a) Branching ratio of fenchyl hydroxyperoxy radical Q₄OOH-1 decomposition as a function of pressure and temperature. (b) High-pressure rate constant for fenchene-one and oxirane formation from Q₄OOH-3. Comparison to rate constants for similar sites on simpler rings. Skeletal formulas represent respective channel products.</figcaption></figure>
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As can be noticed from Figure 14a, Korcek pathway barriers (38.6 and 31.4 kcal/mol) are respectively higher and lower than those previously reported by Jalan et al.<sup>119</sup> for aliphatics (34.7 and 38.2 kcal/mol) for steps 1 and 2. However, in step 1, the activation entropy is higher for fenchone, resulting in significantly faster cyclic peroxide formation. This enthalpy-entropy compensation may be attributed to strain- and substituent-induced restrictions to reactant reorganization<sup>120</sup> - similar to reported ‘anti-Circe’ effect<sup>121</sup>, where the disordering of transition state implies a higher energetic barrier. While strain effects seem to prevail over barrier-lowering charge delocalization<sup>89</sup> for Korcek ring closure (step 1), the opposite effect may be noted for ring opening (step 2), where methyl substituents and norbornyl bridge stabilize the opening peroxy ring through multiple delocalizations <math>σ<sub>C5H</sub>→σ*<sub>CqC4</sub></math> (7.3 kcal/mol), <math>σ<sub>C5H</sub>→σ*<sub>CqCo</sub></math> (7.2 kcal/mol) and <math>σ<sub>C2H</sub>→σ*<sub>CqCo</sub></math> (5.1 kcal/mol), compensating the steric hindrance (negligible in Jalan’s system) between methyl and methylene groups within the tricyclic TS (Figure 14b).

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<figure><img src="image_20.png" /></figure>

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<caption>Figure 14 – Comparison of present Korcek paths with Jalan’s results. (a) Rate constants for step 1 (blue) and step 2 (red). (b) Geometric evolutions along the IRC. Reduced density gradient isosurfaces (RDG=0.5) are represented in blue at the respective saddlepoints.</caption>

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All the new ab initio isomerization and β-scission rate constants presented in the above section were implemented in a complex kinetic mechanism to unravel<sup>122</sup> the emerging competition between β-scission and peroxidation arising in the present Fenchone ignition experiments.

490
491 **3.4 Phenomenological kinetic modeling**

492 **3.4.1 Jet Stirred Reactor**

493 Our previous JSR experiments at 10 bar suggest little oxidative reactivity of Fenchone below 800
494 K. Given the typical 15% uncertainty on measured mole fraction (Figure 15), the modest
495 conversion extent predicted at Φ=0.5 (no low-T conversion at Φ=1, Figure S9) can still be
496 compatible with measurements. The new mechanism generates dampened oscillations of fenchone
497 mole fraction either at constant homogeneous reactor temperature of 638 K or in case of unsteady
498 temperature ramp-up (figure S12). Our kinetic analysis indicates that a degenerate chain branching
499 (R5) involving 50% extra carbon storage in hydroperoxy isopentane (with respect to its asymptotic
500 value) occurs during bifurcation¹²³. This aligns with the reported role of QOOH degenerate
501 branching in isothermal conversion oscillations¹²⁴ and abrupt ignition-extinction transition¹⁴.

<figure><img src="image_21.png" /></figure>

502
503 We herein reconstruct the whole reactive branch of the reactor Fendell S-curve¹²⁵,¹²⁶ (Figure S12)
504 by matching ascending-T and descending-T unsteady solutions of the stirred reactor mass balance
505 ODE at the bifurcation temperature. The corresponding input is provided in Supporting
506 Information.

507 Figures 15 and S9 show that the updated mechanism reproduces high-pressure jet stirred reactor
508 (JSR) Fenchone mole fraction profiles correctly, while predicting a slightly more pronounced
509 (albeit modest) reactivity over the 600-800 K range under fuel-lean conditions (Φ=0.5). Among
510 measured oxidation products, 1-methyl-1,3-cyclopentadiene (mcptds2d) derives from 4-
511 isobutenoxy-4-methyl-1-cyclopentene S(661) radical resulting from F₃ β-scission and
512 decomposing to methyl cyclopentenyl. The new kinetic model complementation with low-
513 temperature peroxidation pathways results in the slight flattening of mcptds2d peak. This seems
514 to indicate that the submechanism of substituted cycloalkanes (leading to mcptds2d) needs some
515 further refinement, in line with sparse literature except isopropylcyclohexane¹²⁷,¹²⁸. Sensitivity
516 analyses (Figure 15) reveal that F<sub>5</sub>/F<sub>6</sub> radical formation and subsequent peroxidation is strongly
517 promoting mcptds2d formation at 750 K but its importance vanishes at 800 K, indicating a shift
518 from alkylperoxy- to hydroperoxy-controlled oxidation regime. Conversely, acetone profile
519 prediction improves dramatically at all equivalence ratios (figure S9). According to the present
520 kinetic model, acetone is formed mainly through the (R6) sequence involving GD(6) as well:

<figure><img src="image_22.png" /></figure>

521
522 In line with the abovementioned slow alkene production from QOOH (Figure 13), the model
523 predicts that fenchenone is predominantly formed through the direct<sup>129</sup> F<sub>3</sub>+O<sub>2</sub> reaction,
524 corresponding to a major HO<sub>2</sub> source under fuel-lean conditions. Dedicated fenchenone
525 measurements would help refine and validate the corresponding pathways.
526

526
<figure><img src="image_23.png" /><figcaption>Figure 15 – Modeling profiles against previous JSR experiments¹ at 10 bar and Φ=0.5.</figcaption></figure>

Corresponding sensitivity coefficients (defined as logarithmic derivative of quantity considered with respect to Arrhenius pre-exponential factors) at 750 K (values/1.5) and 800 K. Mcptds2d denotes 1-methyl-1,3-cyclopentadiene depicted in blue. Continuous and dotted lines denote respectively present and previous¹ models.

Interestingly, the Korcek product peak (Figure S16) occurs at a similar temperature (617 K), consistent with a recent experimental detection of a similar product in jet-stirred pinene oxidation¹³⁰. All complementary Korcek paths should be included into the mechanism before further assessment.

### 3.4.2 RCM

While the impact of low-temperature chemistry on fenchone conversion remains modest in JSR conditions, it becomes vital in RCM conditions, as evidenced by the dramatic discrepancy between previous and present model conditions (Figure 16a). The updated mechanism predicts the experimental autoignition delays (IDT) in RCM within 20%, making it adequate to perform further kinetic quantitative analyses.

OH radical mole fraction (as a metric of ignition progress) is sensitive to a diverse set of pathways (Figure 16a), from initial H-abstractions on fenchone (consuming OH) to fenchyl radicals scission and peroxidation products (GD(16), U(OOH)₂) degenerate branching (producing OH). Previous works suggest that the respective contributions of β-scission and peroxidation to cycloalkyl radicals low-temperature conversion depend on ring strain²¹, ring hydroperoxydation level¹³¹ and equivalence ratio¹³². Overall, the sensitive reaction set largely overlaps with the one identified in JSR conditions (Figure 15). Temporal profiles of OH sensitivity coefficients (Figure 16b) allow to distinguish an initiation phase (t < 0.1% IDT) during which primary peroxidation/scission channels
are sensitive. Then comes a second (branching) phase up to t=50% IDT where U(OOH)₂ decomposition becomes increasingly influencial over OH formation. Finally, the (third) run-away phase is marked by significant secondary products contribution to OH production, notably isobutenyl+O₂→methacrolein+OH. The sensitivity of fencheneone formation follows tightly this phasing by becoming inhibitory to ignition (as a HO₂ producer) during the branching phase. The change of sign for Fenchone+OH=F₆+H₂O sensitivity coefficient arises from the competition of active F₆ peroxidation to U(OOH)₂ with the less branching F₄→GD(6)→iC₄H₇ channel following the OH-consuming Fenchone+OH=F₄+H₂O reaction.

<figure><img src="image_24.png" /><figcaption>Figure 16 – (a) Comparison of present experimental and modeled autoignition delays (IDT). Dashed lines: previous fenchone kinetic model¹. (b) Corresponding OH mole fraction sensitivity at 800 K. Error bars indicate typical uncertainty on T_c from previous work¹³³.</figcaption></figure>

According to Figure 17, element fluxes remain similar for both equivalence ratios considered in experiments. However, Fenchone/O₂ stoichiometry has a notable impact on fenchyl isomers distributions, as a result of varying contributions of Fenchone+OH/+HO₂ reactions to their formation (65%/35% for H-abstraction by OH/HO₂ for F₁/F₃/F₄, 95%/5% for F₅/F₆, and 35%/65% for F₂). In any case, we project that F₂ channel remains relatively minor in importance regardless of operating conditions.

Regarding F₃/F₄ paths, acetone flux decreases with an increase in equivalence ratio, consistent with previous JSR speciation¹. Our refined F₄ scission kinetics, compared to our previous study¹ implies a significant reduction in the formation of GD(5) (trimethyl vinyl cyclopentanonyl radical) from F₄ with respect to the low-barrier GD(6) product, consistent with the predicted PES (Figure
3). Overall, primary oxidation products formed in the branching phase involve mostly cyclopentenylic (GD(2), GD(11), S(661)) and isoprenic (GD(16), GD(19), ZS(8), C9H15(41)) patterns (Figure 17). This is quite typical of terpenes oxidation³¹,¹³⁴,¹¹⁰,¹³⁵ and suggests that beside the fulvene route previously identified¹ for benzene formation, the allene route could be also triggered by isoprenic intermediates conversion¹³⁶.

The respective extents of β-scission and peroxidation vary significantly with fenchyl radical site and equivalence ratio. At an operating temperature of 800 K, β-scission prevails over peroxidation for F₁, F₂, F₃, and F₄, whereas the opposite trend occurs for F₅ and F₆ leading to degenerate branching through U(OOH)₂. The resulting overall share of carbon flux from fenchone to fenchylperoxy radical is 30 % at 800 K.

<figure><img src="image_25.png" /></figure>

Figure 17 – Net Carbon fluxes (kmol/m³/s) in RCM experiments at P_c = 40 bar, T_c = 800 K, Φ = 0.5 (blue fonts) and Φ = 1 (red fonts) at 50% IDT. Arrows thickness follow the 500 and 50 mol/m³/s thresholds. Detailed paths are in given Supporting information (Figures S10 and S11). Green arrows denote steps studied in the present *ab initio* study. Grey zones delineate respective Fₓ subsets.

According to Figure S13, F5 and F6 exhibit peroxidation / β-scission ratios quite similar to those of cyclopropyl and cyclopentyl radicals for which the pressure-dependent cross-over temperature (for which ratio become unity) has been reported to be higher than 900 K¹⁷,¹³⁷,¹³⁸. The higher strain energy of cyclopropyl (than cyclopentyl) brings the cross over-temperature to around 900 K at 10 atm¹³⁸, although cyclopropyl β-scission remains slower than F5/F6 ones due to a higher barrier (21.3 kcal/mol) than for these fenchyl radicals. F1, F2 and F4 show much higher β-scissions rates than F5/F6 (Figure 6), competing unusually effectively with peroxidation down to 600 K (Figure S13) and shifting peroxidation to their secondary products.
Although no two-stage ignition profile could be distinguished from pressure profiles during our RCM experiments, our kinetic mechanism predicts a slight pressure inflection point at $Φ = 0.5$, $T_c=790$ K and $P_c=40$ atm. Figure 18a presents the temporal pressure and OH profiles predicted for $T_c=790$ K, corresponding to the lowest $T_c$ considered in experiments at this equivalence ratio.

<figure><img src="image_26.png" /><figcaption>Figure 18 – (a) Comparison of experimental (circles) and predicted pressure profile (black line) in RCM experiments at $P_c = 40$ bar, $T_c = 790$ K, $Φ = 0.5$. End of compression: 106 ms. Thin vertical dotted line denotes first-stage ignition (first pressure inflection point¹³⁹. (b) Net Species fluxes (mol/m³/s) of OH formation paths at times specified by corresponding colored open circles on OH profile (resp. 186, 187, 191 and 192 ms).</figcaption></figure>

The obtained first-stage pressure and temperature rise of 5 bar and 80 K, consistently with reported first-stage ignition for methyl cyclopentane¹⁴⁰. However, this first-stage pressure inflection point could not be distinguished experimentally (Figure 18a and Supporting Material), suggesting that the present mechanism may slightly overpredict $HO_2$ production under such conditions. Fenchenone+$HO_2$ direct formation from $F_3+O_2$ contributes to 11% of $HO_2$ formation. Although the present rate constant aligns with previously investigated cyclopentyl+O₂→cyclopentene+$HO_2$ formally direct channel¹¹, it would be useful to investigate it for Fenchyl radicals. Further, the conversion of hydroperoxy cyclic ethers¹⁴¹ formed from $U(OOH)_2$ decomposition contributes up to 4% to $HO_2$ production, calling for theoretical rate estimation beyond aliphatic oxiranes¹⁴². Complementary RCM experiments at low temperature may also be useful to address this spot qualitative discrepancy. As a more pronounced first-stage exothermicity (typically >100 K) was noticed at lower temperature (Figure S14) and since Fenchone may exist in fuel blends involving n-alkanes³, it seems worth examining how peroxidation / β-scission competition may interact under these conditions.
As pressure reaches its inflection point, OH goes through a local minimum, corresponding to a sharp rise of CH₂O+OH→HCO+H₂O (2 to 18% of OH consumption) followed by the previously identified¹⁴³ step HCO+O₂→CO+HO₂. HO₂ self-recombines in turn to H₂O₂+O₂ (46% of HO₂ consumption at inflection point) but is also partially consumed by GD(19) to generate methacrolein+methylbutenyl+OH (Figure 18b) and by H-abstraction on Fenchone (evolving from 9 to 23% of Fenchone consumption). The main OH production paths are respectively U(OOH)₂ and H₂O₂ decomposition, consistent with prior evidence for alkanes¹². Their respective shares in OH production evolve from 73/0% to 23/30% as the inflection point is reached. While the main U(OOH)₂ sources (Q₅OOH and Q₆OOH) do not dry up, β-scission share in F₅/F₆ consumption increases from 10 to 30% as temperature varies from 794 K to 869 K (green to red circle on Figure 18a), consistently with higher scission barriers than peroxidation.

Our model indicates that peroxidation of F₅/F₆ prevails up to 900 K (Figure S13) and resulting Q₅OOH and Q₆OOH have scission barriers higher than 15 kcal/mol, favoring a second O₂ addition yielding the lumped peroxo-hydroperoxy radical O₂QOOH. Only Q₄OOH decomposition to epoxy fenchone has a low barrier but F₄ scission prevails over peroxidation at 800 K (Figure S13). F₄ β-scission products further contribute to 3% of OH production through their peroxidation.

## 4. CONCLUSIONS

This study extends the previously established fenchone oxidation mechanism¹ to account for new high-pressure rapid compression machine (RCM) ignition experiments using first-principle-based, pressure-dependent kinetic modeling. The investigation of fenchyl ring opening through alkyl and hydroperoxyalkyl radical β-scission reveals that the reaction barriers are sensitive to strain energy, radical site, and ring substituent location, which impact the interplay between hyperconjugation, dispersion, and Pauli repulsion. This impacts the relative contributions of β-scission and peroxidation to fenchyl radical conversion.

F₁ and F₄ fenchyl radicals were found to be the fastest-scission ones, exhibiting maximum local ring relief. We find that dimethyl substituents contribute to increased local strain compared to norbornane, consistent with prior results on substituted strained rings. The hindrance of bridge scission by methyl substituents disfavors six-membered ring products, which is consistent with products measured in stirred reactor showing cyclopentene and isoprene patterns. The high barriers to anti-Bredt product are herein slightly lowered by hyperconjugation.

The rate constants for Q₄OOH and Q₆OOH are compared to literature values for cycloalkanes. The tricyclic transition states for RO₂ isomerization lead to higher barriers due additional strain. For Q₄OOH, a dimethyl "corset" effect generates extra torsional strain during HO₂ elimination, while ether formation is favored by electron donation from the carbonyl group. Similar methyl-induced restrictions on reactant reorganization bring out an enthalpy-entropy compensation in Korcek reaction as well. The fall-off extent can vary according to steric hindrance increasing bridge stiffness, leading to a lower vibrational partition function hence low-pressure rate constant. The impact of carbon class on RO₂ isomerization rate constant should be further studied as it appears to follow a different trend than that Villano's rules¹¹³ on aliphatics.
Unlike in our previous JSR experiments, the impact of fenchyl peroxidation on branching is pronounced under RCM conditions, contributing to 30% of fenchyl consumption at 800 K and t=50% IDT, according to our model. While low-temperature β-scission prevails for F₁/F₃/F₄ radicals, peroxidation is favored for F₅/F₆ due to their higher β-scission barriers, highlighting contrasted fenchyl selectivities with radical position. Similarly, high Q₅OOH β-scission barriers (>15 kcal/mol) favor O₂ addition. Although OH production is affected primarily by fenchyl radicals consumption paths during the branching phase, the onset of secondary products oxidation puts this competition in second place during the run-away phase of ignition experiments. The present kinetic mechanism accurately predicts the experimental IDT but also an experimentally unconfirmed two-stage ignition, indicating a transition from RO₂ to HO₂ reaction regime.

Overall, this study provides new insights into fenchone ring-opening and closing mechanisms under high-pressure oxidation which could be useful for other polycyclic ketones. Future research should characterize more extensively poly-hydroperoxides evolution in strained rings and link local strain to reactivity over a broader range of reactions¹⁴⁴. Further experiments are needed at lower temperatures (< 700 K) to fully confirm / infirm the occurrence of two-stage Fenchone ignition and constrain corresponding kinetics accordingly.

## ASSOCIATED CONTENT

The following Supporting Information is available free of charge: Additional experimental and computational details. RRKM input. Fenchone Kinetic Mechanism in Chemkin Format. Experimental pressure profile.

## AUTHORS INFORMATION

### Corresponding author

André Nicolle – Aramco Fuel Research Center, Rueil-Malmaison, 92852, France, email: andre.nicolle@aramcoverseas.com

### Authors

Dario Vassetti, Jonathan Honorien and Sandro Gail – Aramco Fuel Research Center, Rueil-Malmaison, 92852, France

Dario Vassetti and Jonathan Honorien – EMITECH - EMC France, 4 Allée de la Rhubarbe, 78260 Achères, France

Giorgia Cenedese, Zeynep Serinyel, Lydia Boualem, Philippe Dagaut and Guillaume Dayma – CNRS-INSIS, ICARE, 1C avenue de la Recherche Scientifique, 45071 Orléans cedex 2, France
704 Giorgia Cenedese, Zeynep Serinyel, Fabrice Foucher and Guillaume Dayma – Université d'Orléans, rue de Chartres, 45100 Orléans, France

706 Fabrice Foucher and Bruno Moreau – PRISME, Université d'Orléans, rue de Chartres, 45100 Orléans, France

708
709 AUTHORS CONTRIBUTIONS

710 DV: Data Curation, Formal Analysis & Methodology, Resources & Investigation, Software,
711 Validation, Writing - review & editing. GC: Data Curation, Resources & Investigation. JH: Data

712 Curation, Formal Analysis & Methodology, Resources & Investigation, Software, Validation,
713 Writing - review & editing. ZS: Conceptualization, Data Curation, Formal Analysis &

714 Methodology, Resources & Investigation, Supervision, Validation, Writing - review & editing.
715 PD: Resources & Investigation, Writing - review & editing. LB: Data Curation, Resources &

716 Investigation. BM: Resources & Investigation. SG: Resources & Investigation, Writing - review
717 & editing, Funding Acquisition & Project Administration. FF: Resources & Investigation,

718 Supervision, Validation. GD: Conceptualization, Data Curation, Formal Analysis & Methodology,
719 Resources & Investigation, Supervision, Writing - review & editing, Funding Acquisition &

720 Project Administration. AN: Conceptualization, Data Curation, Formal Analysis & Methodology,
721 Resources & Investigation, Software, Supervision, Validation, Writing - original draft, Writing -

722 review & editing, Funding Acquisition & Project Administration.
723

724 ACKNOWLEDGMENTS

725 The authors acknowledge funding from Aramco Europe and from the CAPRYSSES project (ANR-11-LABX-006-01) funded by the PIA (Programme d'Investissement d'Avenir). The reviewers are acknowledged for their helpful suggestions.

728
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