Jet-cooled laser-induced fluorescence spectroscopy of methylcyclohexoxy radicals

Abstract

Cyclohexoxy and its methyl substituted variants play an important role in atmospheric chemistry. Direct spectral observation of these radicals can provide information about their structures and serve as convenient diagnostics for their monitoring. In this work, we report the first time observation of the LIF spectra of 2-, 3-, and 4-methylcyclohexoxy radicals in supersonic jet-cooled conditions. All spectra are consistent with a single conformer, and thermodynamic analysis of the conformers suggests that the conformer has the diequatorial (e, e) chair structure. Vibrational frequency analysis was performed using CASSCF/6-31+G(d) method on the B̃ state of radicals and the vibronic bands were assigned. The origin band of the methyl substituted cyclohexoxy shifted to red with the decrease of the separation distance between the methyl group and the oxygen atom on the ring. Different spectral character of 2-methylcyclohexoxy radical suggested that the neighboring methyl group affected the behavior of the radical on the B̃ excited state.

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Introduction

Cyclic-alkoxy radicals, the oxidation intermediates of cycloaliphatic hydrocarbons which form a major fraction in modern fuels, play an important role in atmospheric chemistry.^1–3 In cyclic-alkoxy radicals, the cyclohexoxy radical and its substituted variants are of special interest due to the particular stability of the six-membered ring.^4,5 Several techniques including Fourier transform infrared spectroscopy,⁶ air-sampling atmospheric pressure ionization tandem mass spectrometry,² and UV absorption spectroscopy¹ were used to detect the precursors or products in the atmospheric reaction of cyclohexoxy for monitoring the changes in cyclohexoxy concentration indirectly.

Direct spectral observation of cyclohexoxy and its substituted variants would provide information about their structures and serve as convenient diagnostics for their monitoring. Zhang et al. demonstrated these advantages by observing the laser-induced fluorescence (LIF) excitation spectrum of cyclohexoxy,⁷trans-4-methylcyclohexoxy, and d11-cyclohexoxy radicals⁸ in near ambient temperature conditions and used the LIF intensity as a probe in the kinetic study of the radicals' reaction with O₂. However, little is known about the changes in spectroscopy and chemistry of the cyclohexoxy derivatives induced by the substitution on the six-membered ring. High resolution spectra under jet-cooled conditions hold the potential for a better understanding of these matters.⁹ The conformational and spectroscopic studies of substituted cyclohexoxy will help understand the dependence of the energetics and reactivity of cyclic-alkoxy species on the substitution location of the ring. It will also contribute to the fundamental chemical and structure investigation of ring compounds.

In this work, we obtained the LIF spectra of 2-, 3-, and 4-methylcyclohexoxy radicals for the first time in supersonic jet-cooled conditions. Vibrationally resolved spectroscopic bands were assigned in assistance with quantum chemical calculations using B3LYP/6-31+G(d) and CASSCF/6-31+G(d) methods. Different spectral characters of 2-, 3-, and 4-methylcyclohexoxy radicals were observed and the spectra were assigned to specific conformers. The effect of substitution of a methyl group on different locations of the cyclohexoxy ring to the spectral property of the radicals was discussed.

Experimental

The experimental setup was described previously in ref. 10. Briefly, it consists of a dye laser (Narrowscan, Radiant Dyes) pumped by the second harmonic (532 nm) of a Nd:YAG laser (Surelite III, Continuum). The laser output was frequency-doubled to generate the UV radiation required to probe the X̃ − B̃ transition of substituted cyclohexoxy radicals. Photolysis of the precursor molecules was achieved using the third harmonic (355 nm) of another Nd:YAG laser (Surelite II, Continuum), with power of typically 30 mJ per pulse. The methylcyclohexanyl nitrite precursors were synthesized by dropwise addition of sulfuric acid to a mixture of an appropriate methylcyclohexanol and sodium nitrite.¹¹ Single isomer samples cis-3-methylcyclohexanol (95%), trans-4-methylcyclohexanol (98%), and cis-4-methylcyclohexanol (98%) were purchased from Alfa Aesar (UK). The cis-trans mixtures of 2-methylcyclohexanol (97%), 3-methylcyclohexanol (99%), and 4-methylcyclohexanol (99%) came from Alfa Aesar (UK) and Aladdin Company (China). A backing pressure of ∼0.1 atm argon passed over the nitrite sample and expanded into a vacuum chamber using a standard pulse valve (General Valve) with a 0.5 mm orifice. The photolysis beam was focused just above the throat of the nozzle, and the radicals produced were excited about 10 mm downstream by the counter-propagating probe beam. The total fluorescence was collected perpendicular with an f = 80 mm lens and imaged onto a photomultiplier tube (Hamamasu, CR110). The valve was operated in a continuous mode. The chamber vacuum was maintained using a molecular pump (600 L s⁻¹) backed with a mechanical pump (8 L s⁻¹). The initial vacuum was ∼3 × 10⁻³ Pa and increased to ∼7 Pa when injecting the sample.

Two dyes, Styryl8 and Pyridine2 (Exciton, USA), were used to provide the tunable excitation laser source for the methylcyclohexoxy LIF spectra. Lasers were operated at 10 Hz rate and sequentially controlled by a Digital Pulse Generator (DG535, SRS). The output of the photomultiplier was digitized on an oscilloscope (Tektronics, TBS3032B) and the gated signal was integrated by a LabView program. LIF spectra were obtained by recording the integrated fluorescence signal intensity while continuously scanning the excitation laser wavelength. While measuring the spectra, the dye laser wavelength was scanned at 0.01 nm per step and all the spectral intensities were corrected by subtracting the background obtained with the photolysis laser off.

Computational

The conformational analysis of cyclohexane and cyclohexoxy was well addressed in the literature.^9,12,13 It is known that there are two types of conformer for cyclohexoxy, chair form and twisted-boat form. The twisted-boat conformers are ∼6 kcal mol⁻¹ higher in energy than chair conformers.⁹ Hence, only chair conformers are likely present under our experimental conditions.^7–10 Therefore, we will concentrate our studies on the chair conformers. For methylcyclohexoxy radicals, oxygen and methyl group can be treated as the two substitute groups of the cyclohexane chair. In this view, there are two isomers (cis and trans) in each methylcyclohexoxy radical. For every isomer, two different conformers can exist according to the axial or equatorial position that the oxygen and the methyl group take (Table 1). The geometry optimization of all chair conformers of methylcyclohexoxy radicals was performed using B3LYP/6-31+G(d) and CASSCF/6-31+G(d) for ground state and excited state, respectively. Vibrational frequency analysis was conducted for the ground and excited states to assist the assignment of experimental spectra. The adiabatic excitation energy between the X̃ and B̃ states was obtained by the CASSCF/6-31+G(d) method with a scaled factor of 0.89. All calculations were performed using Gaussian 03 program.¹⁴

Table 1 Ground state energies of methylcyclohexoxy radicals calculated by the B3LYP/6-31+G(d) method

Substitutes	Isomer	Chair conformer^a	E(rel)+ ΔZPE ^b/kcal mol^−1
a The notation of substitution position is in the order of (oxygen, methyl group). b The energies are relative energy to the (e, e) conformer of each methylcyclohexoxy radical.
2-Methylcyclohexoxy	cis	(e, a)	2.29
		(a, e)	0.83
	trans	(e, e)	0
		(a, a)	2.68
3-Methylcyclohexoxy	cis	(e, e)	0
		(a, a)	2.61
	trans	(e, a)	2.44
		(a, e)	0.58
4-Methylcyclohexoxy	cis	(e, a)	2.32
		(a, e)	0.66
	trans	(e, e)	0
		(a, a)	2.98

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Results and discussion

The LIF spectra of 2-, 3-, and 4-methylcyclohexoxy taken in supersonic jet conditions are shown in Fig. 1. Like cyclohexoxy,⁹ the spectra of 3- and 4-methylcyclohexoxy have rich spectral content with great complexity. For 2-methylcyclohexoxy, the spectrum appears considerably simplified with no significant bands observed at ∼1000 cm⁻¹ above the origin band although its origin band has comparable intensity as the origin bands of the other two methylcyclohexoxy radicals.

Fig. 1 Laser-induced fluorescence spectra of methylcyclohexoxy radicals in supersonic jet conditions: (a) 4-methylcyclohexoxy, (b) 3-methylcyclohexoxy, (c) 2-methylcyclohexoxy.

The jet-cooled LIF spectra of cis-4-methylcyclohexoxy and trans-4-methylcyclohexoxy were also obtained separately. The trans isomer yielded a spectrum (Fig. 2a) which basically resembled the spectrum of the cis-trans mixture (Fig. 1a), while some very weak signals were not accountable in the mixture spectrum. The LIF spectrum obtained from the cis-4-methylcyclohexoxy (Fig. 2b) proved that the weak features were from the cis isomer. Similar isomer behavior of 4-methylcyclohexoxy in the near-ambient-temperature cell was reported by Zhang, et al.⁸ However, our high resolution spectrum taken under low-temperature supersonic jet conditions revealed that hot bands and low resolution complicated the assignment of the LIF spectrum in near ambient temperature conditions. It is necessary to reassign the LIF spectrum with high resolution. Considering of the spectral significance, we will focus our analysis on the spectrum of trans-4-methylcyclohexoxy.

Fig. 2 The LIF spectra of individual isomers of 4-methylcyclohexoxy: (a) trans-4-methylcyclohexoxy, (b) cis-4-methylcyclohexoxy.

For the trans-4-methylcyclohexoxy isomer, there are two possible chair conformers, diequatorial (e, e) and diaxial (a, a). Theoretical calculation predicted that the (e, e) conformer was 2.98 kcal mol⁻¹ lower in energy than the (a, a) conformer (Table 1). This is consistent with the stability studies of cyclohexane and its substitutes in the literature.^12,13 On the other hand, analysis of the rotationally resolved LIF spectra of chain alkoxy radicals revealed that the conformer which was calculated to be lowest in energy had always been observed although multiple conformers could co-exist in supersonic jet non-equilibrium conditions.^15–18 As for the cyclohexoxy radical, the lowest energy conformer (chair-equatorial) was identified as the spectral carrier in the jet-cooled LIF experiment.⁹ Hence, we will analyze the spectrum of the trans-4-methylcyclohexoxy radical using the calculated parameters of the diequatorial (e, e) conformer.

The lowest three electronic states X̃, Ã , and B̃ of alkoxy radicals were well defined in the literature.^19–22 The observed LIF spectra were the transition between the B̃ and X̃ states, which corresponds to the promotion of one electron from the σ orbital of the C–O bond (HOMO-2) to the half-filled non-bonding orbital (HOMO) that mainly localized on O atom. In the CASSCF/6-31+G(d) calculation, we chose an active space of 9 electrons distributed in 7 orbitals, involving the non-bonding orbitals of the O atom and the σ orbital of the C–O bond. The other active orbitals and electrons were chosen by the program automatically. The experimental band origin of trans-4-methylcyclohexoxy radical was at 26 906 cm⁻¹. The calculated adiabatic excitation energy between the X̃ and B̃ states of the chair (e, e) conformer was 26 610 cm⁻¹. Six vibrational progressions were observed in the LIF spectrum of trans-4-methylcyclohexoxy (Fig. 2a). The intervals of the six progressions are all ∼690 cm⁻¹. The origin bands of progressions B, C, D, E, F are shifted to 268 cm⁻¹, 358 cm⁻¹, 437 cm⁻¹, 538 cm⁻¹, 626 cm⁻¹ higher frequency with respect to the origin in progression A. The chair (e, e) conformer of trans-4-methylcyclohexoxy has a C_s symmetry and the calculated lowest 20 harmonic vibrational frequencies (in Mulliken notation²³) are given in Table 2. The same number (0.95) is used to scale the CASSCF(9,7)/6-31+G(d) harmonic frequencies in the B̃ state and ground state, while the scale factor of 0.98 is used for B3LYP/6-31+G(d) calculated ground state frequencies. The assignments of the vibronic bands in the low frequency region of the experimental spectrum and bands in progressions are summarized in Table 3. Band A^*, which is at 694 cm⁻¹ above the origin band (band A), has typical C–O stretch motion in the calculation. Therefore, progression A (band A, A^*, A^**) can be assigned as C–O stretch progression. Band B, which is 268 cm⁻¹ higher in frequency with respect to band A, is the swing motion (ν₅₅) of the C–CH₃ and C–O bonds. But progression B possesses a same interval like progression A, which is the frequency of C–O stretch. Hence, progression B is a combination progression of ν₅₅+ν_CO. Band C, D, E are ring-stretch (ν₃₀), ring-scissors (ν₂₈), and ring-breathing (ν₂₇) modes respectively. Band F is the combination band of ν₅₅+ν₃₀. Correspondingly, progression C, D, E, and F are the combination progressions of ν₃₀+ν_CO, ν₂₈+ν_CO, ν₂₇+ν_CO, and ν₅₅+ν₃₀+ν_CO. The domination of the progressions in C–O stretch is not surprising as a large change in C–O bond length (, , CASSCF(9,7)/6-31+G(d)) was seen in the calculation of the B̃ − X̃ excitation of methylcyclohexoxy. The intensity distribution in the progressions was mainly determined by Franck–Condon principle. However, quantitative results cannot be drawn from the band intensities as the fluctuation of laser power at different laser frequencies was not normalized although efforts were taken to stabilize the laser energy at a certain value (typically 3 mJ).

Table 2 Calculated lowest 20 vibrational frequencies (cm⁻¹) of the diequatorial chair conformer of trans-4-methylcyclohexoxy radical in its ground state and B̃ excited state^a

Assignment	Symmetry	CASSCF(9,7)^bB̃	CASSCF(9,7)^bX̃	B3LYP^cX̃
a All calculations employed the 6-31+G(d) basis set. b A uniform scale factor of 0.95 was used. c The calculated B3LYP frequencies are scaled by 0.98.
ν 32	a′	108	109	106
ν 57	a′′	214	219	211
ν 56	a′′	240	241	228
ν 31	a′	245	250	244
ν 55	a′′	267	256	252
ν 54	a′′	331	336	328
ν 30	a′	355	377	364
ν 29	a′	426	426	411
ν 28	a′	456	455	431
ν 53	a′′	463	465	450
ν 27	a′	536	596	579
ν 26	a′	694	781	749
ν 25	a′	797	814	769
ν 52	a′′	817	851	795
ν 24	a′	884	914	808
ν 51	a′′	908	951	882
ν 50	a′′	975	960	933
ν 23	a′	989	991	948
ν 22	a′	999	1024	951
ν 21	a′	1009	1032	1001

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Table 3 Assignment of the bands observed in vibrational progressions and in the low-energy region of the LIF spectrum of trans-4-methylcyclohexoxy radical. Bands are named as in Fig. 2

trans-4-Methylcyclohexoxy chair (e, e) conformer
Band	Experimental^a	Predicted^b	Assignment
a Observed band maxima (cm^−1) relative to at 26 906.3 cm^−1. b Scaled CASSCF(9, 7)/6-31+G(d) frequencies (scale factor 0.95) for the fundamentals, and sum of the fundamental frequencies (cm^−1) for combination and overtone bands.
A	0
B	268	267	ν 55
C	358	355	ν 30
D	437	456	ν 28
E	538	536	ν 27
F	626	622	ν 55+ν30
A^*	694	694	ν 26 (νCO)
	717	723	ν 55+ν28
	795	797	ν 25
	805	811	ν 30+ν28
	860
	895	884	ν 24
B^*	960	961	ν 55+νCO
	974	975	ν 50
	984	999	ν 22
C^*	1049	1049	ν 30+νCO
D^*	1128	1150	ν 28+νCO
E^*	1230	1230	ν 27+νCO
F^*	1315	1316	ν 55+ν30+νCO
A^**	1385	1388	2νCO
B^**	1649	1655	ν 55+2νCO
C^**	1736	1743	ν 30+2νCO
D^**	1816	1844	ν 28+2νCO
E^**	1914	1924	ν 27+2νCO

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The cis isomer of 3-methylcyclohexoxy radical yielded the same spectrum (Fig. 3) as that obtained from the cis-trans 3-methylcyclohexoxy mixture (Fig. 1b). Comparing the two chair conformers of cis-3-methylcyclohexoxy, the (e, e) conformer is 2.61 kcal mol⁻¹ lower in energy than the (a, a) conformer. Therefore, the diequatorial conformer is assigned as the spectrum carrier. For cis-3-methylcyclohexoxy, three vibrational progressions stand out in the LIF spectrum. The intervals of the three progressions are all ∼680 cm⁻¹. Progression A consists of four peaks (bands A, A^*, A^** and A^***). The bands of other progressions are displaced to higher frequency with respect to each peak in progression A: ∼246 cm⁻¹ higher for progression B, 379 cm⁻¹ higher for progression C. The chair (e, e) conformer of cis-3-methylcyclohexoxy has a C₁ symmetry and the assignments of the vibronic bands are listed in Table 4. Band A is at 26 677 cm⁻¹, which is consistent with the calculated adiabatic excitation energy (26 664 cm⁻¹) of the chair (e, e) conformer of cis-3-methylcyclohexoxy. The band (band A^*) at 683 cm⁻¹ above the origin band has typical C–O stretch motion. The vibronic bands at 1363 cm⁻¹ (band A^**) and 2039 cm⁻¹ (band A^***) above are assigned as the first and second overtones of the C–O stretch mode. Therefore, progression A can be assigned as C–O stretch progression. Band B, which is 246 cm⁻¹ higher in frequency with respect to band A, is the swing motion (ν₅₄) of the C–O and C–CH₃ bonds. Progression B possesses a same interval like progression A, which is the frequency of C–O stretch. Hence, progression B is a combination progression of ν₅₄+ν_CO. Band C is the ring-stretch mode (ν₅₁), indicating that progression C is a combination progression of ν₅₁+ν_CO.

Fig. 3 Vibrational progressions in the LIF spectrum of cis-3-methylcyclohexoxy.

Table 4 Assignment of the bands observed in vibrational progressions and in the low-energy region of the LIF spectrum of cis-3-methylcyclohexoxy radical. Bands are named as in Fig. 3

cis-3-Methylcyclohexoxy chair (e, e) conformer
Band	Experimental^a	Predicted^b	Assignment
a Observed band maxima (cm^−1) relative to at 26 677.4 cm^−1. b Scaled CASSCF(9, 7)/6-31+G(d) frequencies (scale factor 0.95) for the fundamentals, and sum of the fundamental frequencies (cm^−1) for combination and overtone bands.
A	0
B	246	244	ν 54
	276	278	ν 53
	348	349	ν 52
C	379	380	ν 51
	450	454	ν 49
	466	463	ν 48
	522	525	ν 47
	624	624	ν 54+ν51
A^*	683	680	ν 46 (νCO)
B^*	928	924	ν 54+νCO
C^*	1061	1060	ν 51+νCO
A^**	1363	1360	2νCO
B^**	1606	1604	ν 54+2νCO
C^**	1738	1740	ν 51+2νCO
A^***	2039	2040	3νCO

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As for 2-methylcyclohexoxy, no vibrational progression was observed. The assignment of 2-methylcyclohexoxy LIF spectrum was based on the calculation results of the chair (e, e) conformer of trans-2-methylcyclohexoxy radical (Table 5). The chair (e, e) conformer of the trans-2-methylcyclohexoxy also has a C₁ symmetry. The origin band is at 26 275 cm⁻¹ compared to the calculated adiabatic excitation energy 26 198 cm⁻¹. Band B, which is 332 cm⁻¹ above the origin band has the ring-twist motion. The adjacent band C and band D, which are 400 cm⁻¹ and 410 cm⁻¹ higher in frequency with respect to band A, are assigned as the C–CH₃ swing mode and ring-stretch mode, respectively. Band E and F are ring-breathing mode and ring-scissors mode. The calculated strongest vibration motion, C–O stretch (676 cm⁻¹ in frequency) was not observed in the spectrum. The strong intensity of the origin band in the LIF spectrum of 2-methylcyclohexoxy indicates that the amount of the radicals generated in the jet was comparable with other substituted methylcyclohexoxy radicals. The fact that no C–O stretch vibrational band was observed from 2-methylcyclohexoxy radical, and the silence of its LIF spectrum 1000 cm⁻¹ beyond the origin band, suggest that nonradiative relaxation channels might set in at low excitation energies above the vibrationless level of the B̃ state.

Table 5 Assignment of the bands observed in the low-energy region of the LIF spectrum of 2-methylcyclohexoxy radical. Bands are named as in Fig. 4

trans-2-Methylcyclohexoxy chair (e, e) conformer
Band	Experimental^a	Predicted^b	Assignment
a Observed band maxima (cm^−1) relative to at 26 274.6 cm^−1. b Scaled CASSCF(9, 7)/6-31+G(d) frequencies (scale factor 0.95) for the fundamentals, and sum of the fundamental frequencies (cm^−1) for combination and overtone bands.
A	0
B	332	323	ν 53
C	400	399	ν 50
D	410	424	ν 49
E	490	481	ν 48
F	536	549	ν 47

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Fig. 4 Enlarged LIF spectrum of 2-methylcyclohexoxy.

One hypothesis used in the assignment of 2-methylcyclohexoxy has to be noted here. Because the individual isomer of cis or trans2-methylcyclohexanol was not available, we presumably assigned the spectrum to the trans-2-methylcyclohexoxy while the spectrum was obtained with the cis-trans mixture precursor generated from 2-methylcyclohexanol. However, our calculation results (Table 1) show that the diequatorial chair conformer always has the lowest energy regardless of the different substitution location of the methyl group on the cyclohexoxy ring. In addition, the isomer with the chair (e, e) conformer, which is cis isomer for 3-methylcyclohexoxy and trans isomer for 4-methylcyclohexoxy, was proven to be the LIF spectrum carrier by the experiment. Therefore, we consider the spectrum assignment as the chair (e, e) conformer of trans-2-methylcyclohexoxy is reasonable. Further confirmation might be possible if pure trans-2-methylcyclohexanol could be obtained in the future.

In comparing of the LIF spectra of the three methylcyclohexoxy radicals in the supersonic jet (Fig. 1), the origin band is red shifted from 4-methylcyclohexoxy to 3-methylcyclohexoxy, and red shifted further in 2-methylcyclohexoxy. The red shift of the origin band might be explained by the inductive effect of the methyl group as the interaction between the methyl group and the oxygen atom increased when the two groups became closer on the ring. The spectra of 3- and 4-methylcyclohexoxy have same spectral pattern, i.e. the spectra extend over 2000 cm⁻¹ above the origin and have rich content and C–O stretch dominated vibrational progressions. This rich and long expansion spectral pattern of 3- and 4-methylcyclohexoxy radicals is consistent with the LIF spectrum of cyclohexoxy itself,⁹ implying that the effect of methyl substitution on the meta- and para-position of the ring did not change the relaxation mechanism of the radical. In contrast, the excitation LIF spectrum of 2-methylcyclohexoxy is much quieter with no significant bands observed beyond 1000 cm⁻¹ of the origin band. This suggests that other relaxation paths^4,22,24 in addition to the fluorescence route might exist on the B̃ excited state of 2-methylcyclohexoxy. A strong fluorescent band with short lifetime (∼0.18 μs compared with 1.0–1.2 μs of methylcyclohexoxy bands) was observed 2510 cm⁻¹ above its origin band. It appeared after a long silence of the 2-methylcyclohexoxy LIF spectrum and no corresponding vibration motion was found in the calculation. No such bands were observed in the same region of 3- and 4-methylcyclohexoxy spectra. We suspect that it might come from a dissociation product of 2-methylcyclohexoxy induced by the increased interaction between the ortho-methyl group and the oxygen atom on the cyclohexane ring. But no unambiguous explanation can be made at this stage as we have not yet identified the carrier of this extra band. Experimental and theoretical studies are being processed to investigate the isomerization and dissociation of the 2-methylcyclohexoxy.

Conclusion

We have reported the first observation of the jet-cooled LIF excitation spectra of 2-, 3-, and 4-methylcyclohexoxy radicals. All spectra are consistent with a single conformer, and thermodynamic analysis of the conformers suggests that the conformer has the diequatorial chair structure. Vibrational frequency analysis was performed using the CASSCF/6-31+G(d) method on the B̃ state of radicals and the vibronic bands were assigned. Three vibrational progressions and six vibrational progressions were identified and assigned for 3-methylcyclohexoxy and 4-methylcyclohexoxy, respectively. The origin band of the methyl substituted cyclohexoxy shifted to red with the decrease of the separation between the methyl group and the oxygen atom on the ring. When the methyl group and the CO group are in the neighboring position, a dissociation path might coexist with the fluorescence route for the B̃ state of 2-methylcyclohexoxy. However, because of the complexity of the spectra and conformations, further experimental and theoretical studies are required to understand the relaxation mechanism on the B̃ state of methylcyclohexoxy radicals, and rotationally resolved spectra are desired to confirm the conformer identification.

Acknowledgements

The authors are pleased to acknowledge the financial support of this research by National Natural Science Foundation of China (Grant No. 20673013) and support from Beijing Municipal Commission of Education. We also acknowledge the grant from the Major State Basic Research Development Program (Grant No. 2007CB815206).

References

1. J. Platz, J. Sehested and O. J. Nielsen, J. Phys. Chem. A, 1999, 103, 2688–2695.
2. S. M. Aschmann, A. A. Chew, J. Arey and R. Atkinson, J. Phys. Chem. A, 1997, 101, 8042–8048.
3. O. Welz, F. Striebel and M. Olzmann, Phys. Chem. Chem. Phys., 2008, 10, 320–329.
4. L. S. Alconcel and R. E. Continetti, Chem. Phys. Lett., 2002, 366, 642–649.
5. S. Wilsey, P. Dowd and K. N. Houk, J. Org. Chem., 1999, 64, 8801–8811.
6. J. J. Orlando, L. T. Iraci and G. S. Tyndall, J. Phys. Chem. A, 2000, 104, 5072–5079.
7. L. Zhang, K. A. Kitney, M. A. Ferenac, W. Deng and T. S. Dibble, J. Phys. Chem. A, 2004, 108, 447–454.
8. L. Zhang, K. M. Callahan, D. Derbyshire and T. S. Dibble, J. Phys. Chem. A, 2005, 109, 9232–9240.
9. L. Zu, J. Liu, G. Tarczay, P. Dupré and T. A. Miller, J. Chem. Phys., 2004, 120, 10579–10593.
10. J. Lin, L. Zu and W. Fang, J. Phys. Chem. A, 2011, 115, 274–279.
11. A. H. Blatt, Organic Syntheses, Wiley Press, New York, 1966, pp. 108–109.
12. E. L. Eliel, S. H. Wilen and L. N. Mander, Stereochemistry of Organic Compounds, Wiley Press, New York, 1997.
13. D. Nasipuri, Stereochemistry in Organic Compounds, Principles and Applications, New Age International (P) Ltd. Press, New Delhi, 1994.
14. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D.Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez and J. A. Pople, Gaussian 03, Revision D.02, Gaussian, Inc., Wallingford, CT, 2004.
15. S. Gopalakrishnan, C. C. Carter, L. Zu, V. Stakhursky, G. Tarczay and T. A. Miller, J. Chem. Phys., 2003, 118, 4954–4969.
16. S. Gopalakrishnan, L. Zu and T. A. Miller, J. Phys. Chem. A, 2003, 107, 5189–5201.
17. G. Tarczay, S. Gopalakrishnan and T. A. Miller, J. Mol. Spectrosc., 2003, 220, 276–290.
18. T. A. Miller, Mol. Phys., 2006, 104, 2581–2593.
19. D. L. Osborn, D. J. Leahy and D. M. Neumark, J. Phys. Chem. A, 1997, 101, 6583–6592.
20. S. C. Foster, P. Misra, T. Y. D. Lin, C. P. Damo, C. C. Carter and T. A. Miller, J. Phys. Chem., 1988, 92, 5914–5921.
21. C. C. Carter, S. Gopalakrishnan, J. R. Atwell and T. A. Miller, J. Phys. Chem. A, 2001, 105, 2925–2928.
22. L. Lin, L. Zu, W. Fang, J. Yu and R. Liu, Chin. J. Chem., 2007, 25, 1467–1473.
23. R. S. Mulliken, J. Chem. Phys., 1955, 23, 1997–2011.
24. S. Gopalakrishnan, L. Zu and T. A. Miller, Chem. Phys. Lett., 2003, 380, 749–757.

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Footnote

† Electronic supplementary information (ESI) available: Calculated vibrational frequencies of the diequatorial chair conformers of 2-, 3-, and 4-methylcyclohexoxy radicals in its ground state and B̃ excited state are provided. See DOI: 10.1039/c1ra00216c

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