Photofragmentation of C₆₀ in the extreme ultraviolet: statistical analysis on the appearance energies of C_60−2n^z+ (n ≥ 1, z = 1–3)

Abstract

The ion yield curves for C_60−2n^z+ (n = 1–5, z = 1–3) produced by photoionization of C₆₀ are measured in the photon energy (hν) range of 25–150 eV. The appearance hν values are higher by 30–33 eV than the thermochemical thresholds for dissociative ionization of C₆₀ leading to C_60−2n^z+. Evaluation is made on the upper limits of the internal energies of the primary C₆₀^z+ above which C_60−2n+2^z+ fragments (n ≥ 1) cannot escape from further dissociating into C_60−2n^z+ + C₂. These upper limits agree well with the theoretical internal energies of C₆₀^z+ corresponding to the threshold for the formation of C_60−2n^z+. The photofragmentation of C₆₀^z+ is considered to be governed by the mechanism of internal conversion of the electronically excited states of C₆₀^z+, statistical redistribution of the excess energy among a number of vibrational modes, and sequential ejection of the C₂ units.

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Introduction

The C₆₀ molecule with a compact structure of a truncated icosahedron exhibits an exceptionally high stability. However, mass spectrometric studies of C₆₀ have revealed that appreciable fragmentation occurs when the system gains energy in excitation and ionization processes. Fragmentation mechanisms have been studied by laser multiphoton ionization,^1–3 heavy-ion excitation,^4,5 or electron impact ionization.^6–8 Decomposition of C₆₀^z+ (z ≥ 1) primarily formed is known to lead to fragment ions with even numbered carbon atoms (C_60−2n^z+, n = 1, 2,…) via sequential loss of C₂ units from C₆₀^z+ ions in high-vibrational states. In contrast, experimental studies of single photon excitation are very limited.^9–13 Recent results on the relative cross section of the fullerene fragments from C₆₀ in the region of valence electron excitation show that the appearance photon energies of C_60−2n⁺ and C_60−2n²⁺ are higher by 30–40 eV than the thermochemical thresholds for dissociative photoionization of C₆₀.¹² In a limited case of C₆₀ + hν → C₅₈⁺ + C₂ + e⁻ Yoo et al.⁹ have discussed this large kinetic shift in terms of unimolecular decay modelled by quasiequilibrium theory. However, they could not determine the theoretical appearance energy with a good accuracy, since a reliable value for the binding energy of C₆₀⁺ was not available at that time. Until then there has been no effort to apply quasiequilibrium theory to dissociative photoionization of C₆₀ and to clarify the fragmentation mechanism of the fullerene ions in which large excess energy is initially deposited.¹⁴ In this paper we perform systematic measurements of the yield curves of the fragment ions, C_60−2n⁺, C_60−2n²⁺ and C_60−2n³⁺, in a wide photon energy range of hν = 25–150 eV. Tunable synchrotron radiation that we have utilized was found to be very powerful for determining the appearance energies of respective fragment ions and the critical internal energies of C₆₀^z+ required for the formation of C_60−2n^z+. These critical internal energies are then compared with the appearance internal energies of C_60−2n^z+ predicted by theoretical calculations based on the RRKM theory. This allows us to discuss the detailed mechanisms of unimolecular reactions induced by equilibration of the excess energy among enormous density of states of the fullerene system.

Experimental

All the measurements have been carried out at the bending magnet beamline BL2B equipped with an 18 m spherical grating monochromator of Dragon type constructed in the UVSOR synchrotron radiation facility in Okazaki.^15,16 The Experimental set-up for photoionization mass spectrometry of C₆₀ has been described in details elsewhere.^17–19 Briefly a molecular beam of C₆₀ was produced by heating the sample powder to approximately 680 K. Monochromatized synchrotron radiation was focused onto the C₆₀ beam. The produced photoions were extracted by a pulsed electric field, mass-separated by a time-of-flight (TOF) mass spectrometer, and detected with a microchannel plate electron multiplier. In order to normalize the ion counts the fluxes of the molecular and light beams were monitored throughout the measurement by a silicon photodiode and a crystal-oscillator surface thickness monitor, respectively.

Results

Fig. 1 shows TOF mass spectra of the parent C₆₀^z+ and fragment C_60−2n^z+ (n ≥ 1, z = 1–3) ions produced from C₆₀. Taking mass spectra with scanning the monochromator we could measure the yield curves for C_60−2n^z+ as a function of hν. Figs. 2 and 3 illustrates the curves for C_60−2n²⁺ with n = 1–5 and C_60−2n³⁺ with n = 1 and 2, respectively. The results of C_60−2n³⁺ can be reported for the first time. To our knowledge the curves of C_60−2n^z+ (z = 1 and 2) above 100 eV have not been published. The yield curves for C_60−2n^z+ are considered to provide fractional abundances of C_60−2n^z+ within ∼25 μs after ionization, at least around the onset region for each ion. With decreasing the size of 60–2n the appearance photon energies AE(n,z) for a given z shift to higher hν positions and the curves rise more gently towards a peak. After reaching the peak all the curves decline steadily. Table 1 summarizes AE(n,z) for C_60−2n^z+ with n = 1–5 and z = 1–3. We determined AE(n,z) by reading the photon energy at which the ion yield reaches 5% of the peak height after subtracting an appropriate background. Values of AE(n,z) are found to be higher by 30–33 eV than the thermochemical thresholds^6,8 for dissociative photoionization of C₆₀ leading to C_60−2n^z+. Reinköster et al. have found similar large kinetic shifts¹² but their appearance hν positions for z = 1 and 2 are higher by 2–8 eV than those in Table 1, probably due to their insufficient statistics. Contrarily, the appearance energies measured in electron impact ionization⁷ show good agreement with our values.

Fig. 1 Time-of-flight mass spectra of the parent and fragment ions produced by photoionization of C₆₀ at four different photon energies.

Fig. 2 Ion yield curves of C_60−2n²⁺ ions (n = 1–5) obtained from time-of-flight mass spectra.

Fig. 3 Ion yield curves of C_60−2n³⁺ ions (n = 1 and 2) obtained from time-of-flight mass spectra.

Table 1 Appearance photon energies AE(n,z) for the formation of the C_60−2n^z+ ions from C₆₀. All energies are in eV

n	C60−2n^z+	z = 1	z = 2	z = 3
a C60−2n^z+ fragment ions are not detectable.
1	C58^z+	44 ± 1	55 ± 1	73 ± 1
2	C56^z+	49 ± 1	60 ± 1	82 ± 1
3	C54^z+	56 ± 1	66 ± 1	—^a
4	C52^z+	—^a	74 ± 1	—^a
5	C50^z+	—^a	80 ± 1	—^a

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When C₆₀ is photoionized at hν = AE(n,z), we are able to write the maximum internal energy E_max(n,z) initially transmitted to C₆₀^z+ as

E_max(n,z) = AE(n,z) + E_v – IP(z) (1)

by assuming the kinetic energy of the emitted photoelectron to be zero. Here, E_v denotes the vibrational energy of C₆₀ at the sample temperature of 680 K, and IP(z) is the ionization potential of C₆₀ for the formation of C₆₀^z+ (see Fig. 4). In this study, E_v = 3.3 eV is assumed and IP(z) taken from the literature^7,20,21 are 7.6, 19.0 and 35.6 eV for z = 1, 2 and 3, respectively. We have evaluated E_max(n,z) from eqn. (1) using E_v and IP(z) and listed the resultant values in Table 2 for C_60−2n^z+ with n = 1–5 and z = 1–3. It is expected that E_max(n,z) is nearly equal to the upper limit of the internal energies of the primary C₆₀^z+ above which C_60−2n+2^z+ fragments cannot escape from further dissociating into C_60−2n^z+ + C₂. Table 2 reveals two trends in the dependences of E_max(n,z) on n and z of the fragments. First, the difference E_max(n + 1,z) − E_max(n,z) depends weakly on n, varying from 5 to 9 eV. This may reflect a weak n-dependence^6,8 of the binding energies for the unimolecular reaction

C_60−2n+2^z+ (n ≥ 1) → C_60−2n^z+ + C₂ (2)

Second, E_max(n,z) for a given n is almost unchanged irrespective of z. This remarkable finding, together with the prominent kinetic shifts, implies that internal conversion of the electronically excited states of C₆₀^z+ results in redistribution of the excess energy among the vibrational degrees of freedom followed by successive ejection of the C₂ units, as illustrated schematically in Fig. 4.

Fig. 4 Scheme of the energetics of the C₂ loss in dissociative photoionization of C₆₀. The photofragmentation of C₆₀^z+ is considered to be governed by the mechanism of internal conversion of the electronically excited states of C₆₀^z+, statistical redistribution of the excess energy among a number of vibrational modes, and successive ejection of the C₂ units.

Table 2 Upper limit E_max(n,z) of the internal energies (in eV) of the primary C₆₀^z+ ions above which C_60−2n+2^z+ fragments cannot escape from further dissociating into C_60−2n^z+ + C₂ (n ≥ 1)

			Observed,^aEmax(n,z)			Calculated,^bERRKM(n)
n	C60−2n+2^z+	C60−2n^z+	z = 1	z = 2	z = 3	TS-1^c	TS-3^d
a Obtained by using eqn. (1) from the appearance photon energies for the formation of C60−2n^z+ from C60 in Table 1. b Appearance internal energies of C60^z+ corresponding to Kn = 0.03Kn^max at 25 μs after photoionization of C60. The RRKM theory is employed to derive the rate constant for reaction (2) from which the Kn curves can be calculated. c E RRKM(n) determined from Fig. 5. A set of the binding energies for the TS-1 model was employed. d E RRKM(n) determined from Fig. 6. A set of the binding energies for the TS-3 model was employed. e C60−2n^z+ fragment ions are not detectable.
1	C60^z+	C58^z+	39.7 ± 1	39.3 ± 1	40.7 ± 1	40.1	40.9
2	C58^z+	C56^z+	44.7 ± 1	44.3 ± 1	49.7 ± 1	47.1	47.0
3	C56^z+	C54^z+	51.7 ± 1	50.3 ± 1	—^e	52.9	52.8
4	C54^z+	C52^z+	—^e	58.3 ± 1	—^e	58.9	59.1
5	C52^z+	C50^z+	—^e	64.3 ± 1	—^e	65.1	65.3

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Theoretical calculations

We employed the RRKM theory to derive the curves of fractional abundance (breakdown graphs) for C₆₀^z+ and C_60−2n^z+ ions (n = 1–5) as a function of the internal energy of the primary C₆₀^z+. The microcanonical rate constant k_n(ε) for reaction (2) of C_60−2n+2^z+ having internal excitation energy ε can be given by^6,8,9,22Here, α is the reaction path degeneracy, E₀ⁿ is the critical activation energy for reaction (2), G*(ε − E₀ⁿ) is the number of states for the transition state (activated complex), N(ε) is the density of states of C_60−2n+2^z+, and h is the Planck’s constant. For n ≥ 2 the ε value of C_60−2n+2^z+ is computed under the assumption that the energy available after dissociation of C_60−2n+4^z+ → C_60−2n+2^z+ + C₂ is statistically partitioned between C_60−2n+2^z+ and C₂. The detail of the calculation for reaction (2) is the same as those described in refs. 6, 8 and 9. We have used Haarhoff’s approximation²² to calculate G*(ε − E₀ⁿ) and N(ε), assuming vibrational frequencies of C_60−2n+2^z+ to be replaced by those of a neutral C₆₀ reported by Schettino et al.²³

The critical activation energies E₀ⁿ in eqn. (3) are taken from the binding energies of C_60−2n+2^z+ (n = 1–5) for reaction (2) proposed in the papers^6,8 dealing with electron impact ionization of C₆₀. Foltin et al.⁶ invoked the model with a relatively loose transition state whose reaction coordinate has a frequency of ca. 1500 cm⁻¹. This model was referred to in ref. 8 as TS-1. Later Laskin et al.³ and Matt et al.²⁴ have revised the binding energies of C_60−2n+2⁺ (n = 1–5) by assuming a totally loose transition state in which the C_60−2n⁺ and C₂ fragments tumble freely. This transition state, named TS-3 in ref. 8, was consistent with a large frequency factor in the Arrhenius relation which has been expected by a very large rotational partition function of C₂.²⁵ Moreover, Laskin et al.³ found that using a thermochemical cycle for n = 1 leads to a value of 10.0 eV for the binding energy of neutral C₆₀, in excellent agreement with the result²⁶ of ab initio calculations. In the present study, we adopted the two sets of the binding energies of C_60−2n+2^z+ recommended within RRKM theory, i.e. the sets for the TS-1 and TS-3 models. The binding energies of C₆₀⁺, for example, are 7.06 eV and 9.2 eV for TS-1 and TS-3, respectively.

Every time n is increased by 1 we removed the frequencies of six vibrational modes that were judged no longer remaining in C_60−2n+2^z+ of reaction (2). One of these six frequencies is the frequency of the reaction coordinate in the transition state. For TS-1 model we set this frequency to 931.1 cm⁻¹, the average value of the 174 frequencies of C₆₀⁺, whereas for TS-3 this frequency was set to 1574 cm⁻¹, the highest frequency (8H_g mode) of C₆₀⁺.²³ Another of the six frequencies belongs to the high-frequency 7H_g mode (1421 cm⁻¹), corresponding to the C₂ stretching vibration. The others of the six frequencies were associated with the four rotational modes of C₂ (including two pseudo-translational modes): 1H_g (266 cm⁻¹), 2H_g (431 cm⁻¹), 3H_g (709 cm⁻¹) and 1H_u (403 cm⁻¹) modes of C₆₀⁺ were chosen. In the transition state we assumed that these four frequencies decrease to 50 cm⁻¹ for the TS-3 model, following the description in ref. 8.

Discussion

Figs. 5 and 6 show the fractional abundance K_n for C_60−2n^z+ ions (n = 1–5) as a function of the internal energy of the primary C₆₀^z+ at 25 μs after photoionization of C₆₀. Here, the TS-1 and TS-3 models are employed in Figs. 5 and 6, respectively. Every curve reaches a peak of K_n = K_n^max at 7–10 eV above its onset. We defined the appearance internal energy E_RRKM(n) for the formation of C_60−2n^z+ as the internal energy of C₆₀^z+ corresponding to K_n = 0.03K_n^max. The values of E_RRKM(n) determined from Figs. 5 and 6 are listed in the seventh and eighth columns of Table 2. For the formation of C₅₈^z+, C₅₆^z+ and C₅₄^z+E_RRKM(n) from Fig. 6 are 40.9, 47.0, and 52.8 eV, respectively, in excellent agreement with the observed maximum internal energies E_max(1,z), E_max(2,z) and E_max(3,z), respectively. These results are the manifestation of the validity of the present statistical treatment: large amounts of the internal energy of C₆₀^z+ is equilibrated among the vibrational degrees of freedom, and subsequent photofragmentation proceeds through reaction (2) via a transition state with the activation energy of E₀ⁿ.

Fig. 5 Fractional abundance curves of C₆₀^z+ and C_60−2n^z+ ions (n = 1–5) at 25 μs after photoionization of C₆₀ obtained by using the RRKM theory to calculate the rate constant for reaction (2). TS-1 model (ref. 8) is adopted for the transition state, but the frequency of the reaction coordinate is modified to 931.1 cm⁻¹.

Fig. 6 Fractional abundance curves of C₆₀^z+ and C_60−2n^z+ ions (n = 1–5) at 25 μs after photoionization of C₆₀ obtained by using the RRKM theory to calculate the rate constant for reaction (2). TS-3 model (ref. 8) is adopted for the transition state.

The fractional abundance in Fig. 5 or 6 allows us to simulate the yield curve for C_60−2n^z+ (n ≥ 1) as a function of hν, if the partial photoionization cross section σ(hν,E) at hν for the initial formation of C₆₀^z+ with the internal energy E is known. The ion yield Y_n,z(hν) for the C_60−2n^z+ fragment can be expressed as

For photon energies close to the threshold for fragmentation into C_60−2n^z+ + nC₂ the partial cross section σ(hν,E) is assumed to be independent of hν, because K_n(E) takes nonzero values only in a narrow E range above the threshold for fragmentation (see Figs. 5 and 6). As a consequence, the derivative of Y_n,z(hν) with respect to hν may satisfy the relationwhere E′ = hν + E_v − IP(z). The dependence of σ(E′) on the internal energy is much weaker than that of K_n(E′). It is then likely from eqn. (5) that the derivative of the ion yield curve for C_60−2n^z+ (n ≥ 1) is proportional to the K_n curve of C_60−2n^z+ shifted by IP(z) − E_v. Fig. 7 shows the curves of the derivative of Y_n,2(hν) which are calculated by using the yield curves of Fig. 2 at photon energies close to the threshold for fragmentation. The peak positions of the derivative curves for n = 1–4 appear to be in fair agreement with those of the fractional abundance curves in Figs. 5 and 6.

Fig. 7 Derivative of the ion yield curves of C_60−2n²⁺ ions (n = 1–5) with respect to hν. The observed curves in Fig. 2 are used and the energy scale of the abscissa is shifted by IP(2) − E_v = 15.7 eV.

The ion yield of the parent C₆₀^z+ can be represented by the same expression as eqn. (4) by using the fractional abundance of C₆₀^z+ in Figs. 5 or 6. This fractional abundance is found to be more than 97% below E ∼ 40 eV, so that the C₆₀^z+ yield is strongly affected by the partial cross section σ(hν,E) in a wide range of from E = 0 to ∼40 eV. Therefore, the C₆₀^z+ yield becomes markedly higher than the yields of C_60−2n^z+ (n ≥ 1). This statement is confirmed by the observed TOF spectra in Fig. 1. It is also worth noting that eqn. (5) is no longer valid for the parent ion owing to a strong dependence of σ(hν,E) on hν.

Acknowledgements

We are greatful to Mr Haruyama for sample preparation and purification. This work has been supported by a Grant-in-Aid for Scientific Research (Grant No. 14340188) from the Ministry of Education, Science, Sports and Culture, Japan, and by a grant for scientific research from Research Foundation for Opto-Science and Technology.

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