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CH4+: a fluxional ion?
Journal of Electron Spectroscopy and Related Phenomena 108 (2000) 169–176 www.elsevier.nl / locate / elspec
CH 1 4 : a fluxional ion? R. Signorell*, M. Sommavilla Laboratorium fur Physikalische Chemie, ETH Zurich, CH-8092 Zurich, Switzerland Received 13 September 1999
Abstract High resolution pulsed-field-ionization (PFI) zero-kinetic-energy (ZEKE) photoelectron spectra of CH 4 and its isotopomers have been recorded for the first time. These spectra show extensive progressions of rotationally resolved transitions. The vibrational structure of the Jahn–Teller distorted ions at low excitation energies have been analysed in terms of a one-dimensional model for the pseudorotational motion of the ions. The analysis of the rotational structure confirms a 1 fluxional behavior for CH 1 2000 Elsevier 4 , whereas CD 2 H 2 in its vibronic ground state can be treated as a rigid rotor. Science B.V. All rights reserved. Keywords: Methane radical cation; Isotopomers of the methane cation; Jahn–Teller distortion; PFI–ZEKE photoelectron spectroscopy
1. Introduction As the most simple organic cation and one of the simplest systems subject to a Jahn–Teller distortion in the electronic ground state the methane radical cation is of fundamental interest. This has led to many experimental [1–15] as well as theoretical [16–27] investigations on CH 1 4 and its isotopomers. The early ab initio study of Meyer [18] first established a large Jahn–Teller distortion from the tetrahedral geometry of the triply degenerate electronic ground state ( 2 F2 ) to a set of twelve equivalent C2v -symmetrical equilibrium structures. Large amplitude tunneling motions in the ionic ground state have been found in subsequent calculations using various levels of ab initio theory [19–24]. The most detailed experimental information about the vibronic ground state of the methane cation has *Corresponding author. E-mail address: [email protected] (R. Signorell)
been obtained through Coulomb explosion experiments [11–15] and electron spin resonance (ESR) studies [9,10]. Some uncertainty remains in the interpretation of the Coulomb explosion measurements [15], so that the minimum structure of CH 1 4 could not be unambiguously determined. In their ESR investigations, Knight et al. [9,10] provided experimental evidence for a C2v -symmetrical minimum structure for the CD 2 H 21 cation but found that the ESR spectrum of CH 41 is an approximately isotropic quintet. Until recently no rotationally resolved spectra of CH 1 4 and its isotopomers were available. Therefore, the ionization potential could not be determined accurately (see references in Ref. [4]) let alone the Jahn–Teller distortion. With the first rotationally resolved PFI–ZEKE photoelectron spectra of CH 1 and CD 2 H 21 published recently 4 [28,29] the situation has completely changed. In this paper we report the analysis of the rovibrational structure of these spectra in terms of a onedimensional model for the pseudorotation. We ex-
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ploit the symmetry breaking through isotopic substitution in CD 2 H 21 to obtain the first rotational analysis of the methane cation.
2. Experimental The photoelectron / photoion spectrometer and the extreme ultraviolet (XUV) light source used in the present experiments have been described in previous publications [30,31]. For the present study, the XUV light was generated by resonance-enhanced sumfrequency mixing in a xenon gas beam using the two-photon resonance (5p)6 1 S0 →(5p)5 6p[1 / 2] (J5 0) at a wavenumber of 80 118.974 cm 21 . The laser system was operated at a resolution of 0.2 cm 21 . Molecules were excited with a single photon to long-lived high (n . 300) Rydberg states located below successive ionization thresholds. The pulsedfield-ionization (PFI) zero-kinetic-energy (ZEKE) photoelectron spectra were recorded by monitoring electrons produced by field ionization as a function of the laser wavenumber. The electric field pulses were applied | 13 ms after photoexcitation to avoid undesired signals from background water [32]. The ZEKE photoelectron spectra were recorded with electric field pulse sequences of (35 / 2123 mV/ cm) and (35 / 2160 mV/ cm) in the case of CH 4 and CD 2 H 2 , respectively (see Section 3). Under these conditions the resulting resolution in the photoelectron spectra (FWHM) is better than 0.7 cm 21 . The photoionization spectrum of CH 4 shown in Section 3 was measured by recording the ion yield as a function of the laser wavenumber. A pulsed electric field of 88 V/ cm was applied to extract the ions.
3. Results and discussion
3.1. Adiabatic ionization potential of CH4 Previous experimental values for the first adiabatic ionization potential of CH 4 lie in a wide range between 100 900 and 103 078 cm 21 (see references in Ref. [4]). Fig. 1 shows the high resolution PFI– ZEKE photoelectron spectrum of CH 4 in the region between 100 800 and 102 600 cm 21 . In our previous work [28] the first adiabatic ionization potential was
Fig. 1. Section of the rotationally resolved PFI–ZEKE photoelectron spectrum of CH 4 . The spectrum was obtained with a sequence of pulsed electric fields of 35 and 2123 mV/ cm.
located in the center of the first observed vibrational band in the PFI–ZEKE photoelectron spectrum at a value of: IP5101 773635 cm 21 . The uncertainty of 635 cm 21 represents the half width at half maximum of the rotational contour of this vibrational band. Compared with previous results this constitutes an improvement by more than a factor of two. Because of the Jahn–Teller distortion in CH 1 4 it was supposed that the Franck–Condon factors for the transitions from the neutral ground state to the ionic ground state would be too small to be observed. Based on this assumption, Rabalais et al. [7] extrapolated an adiabatic ionization potential of about 100 900 cm 21 from their partially resolved photoelectron spectrum. Given the rotational resolution of our ZEKE spectrum and the high sensitivity, the absence of signal below |101 773 cm 21 in Fig. 1 would require an abrupt change in the Franck– Condon factors. Such a behavior is very implausible. Fig. 2a represents the PFI–ZEKE photoelectron spectrum of CH 4 in the region of the lowest observed band. The CH 1 4 ion signal is depicted in Fig. 2b as a function of the ionization wavenumber. The occurrence of the CH 41 ion threshold near the lowest observed band in the ZEKE photoelectron spectrum gives additional evidence for the value of the adiabatic ionization potential to be around 101 773 cm 21 . The ion signal essentially follows the integrated ZEKE electron signal drawn in Fig. 2a.
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Fig. 2. (a) PFI–ZEKE photoelectron spectrum in the region of the lowest observed band (experimental conditions as in Fig. 1). The integrated ZEKE electron signal is represented by the dashed line. (b) Photoionization spectrum of CD 2 H 1 2 (ion signal) in the same region as the spectrum in (a). The pulsed electric extraction field amounted to 88 V/ cm.
3.2. Vibrational structure In Fig. 1 one recognizes an isolated band around 101 773 cm 21 corresponding to the transition to the vibrational ground state of CH 41 . However, at higher excitation energies no simple vibrational band structure can be distinguished. This complex vibrational structure can be understood on the basis of ab initio calculations [20,22] which predict low potential barriers between six of the 12 equivalent C2v symmetrical minima. The interconversion between these minima occurs through pseudorotations connecting subsets of three equivalent minima. As a first step in the interpretation of the experimental spectrum we neglect interferences between the four different pseudorotations. A simple one-dimensional
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model results which is formulated in terms of the Fukui reaction path determined by Frey and Davidson [22]. The remaining 3N 2 7 degrees of freedom are included through appropriate zero-point energy corrections. More details, including the explicit ¨ solution of the rovibrational Schrodinger equation, are described in Refs. [28,32]. The resulting ab initio prediction for the vibrational structure of CH 1 is indicated as a stick 4 spectrum in Fig. 3b. The three-fold symmetry results in A and E tunneling levels. For the vibrational ground state the (A, E)-splitting amounts to 3.6 cm 21 , whereas the next vibrational level is already split by 44.8 cm 21 . This split level lies close to the top of the one-dimensional potential barrier and is thus very sensitive to its height. Compared with the measured spectrum, the prediction overestimates the distance between the first two vibrational bands. To obtain a better agreement, we have adjusted the ab initio potential barrier height of 634.4 cm 21 by linear stretching of the potential to fit the measured gap [28]. An adjusted barrier height of 500 cm 21 yielded the vibrational stick spectrum in Fig. 3c. The tunneling splitting of the ground and the first excited vibrational band are increased to 5.8 and 60.9 cm 21 , respectively. Because of the zero-point energy effects and the higher masses of the deuterium atoms, the tunneling 1 splitting in CD 1 4 is reduced compared with CH 4 . The ab initio model predicts (A, E)-splittings of 0.2 and 4.3 cm 21 for the ground and the first excited vibrational state, respectively. The small splitting of the first excited vibrational level is caused by the large distance of this level from the top of the potential barrier. As expected from this prediction, the PFI–ZEKE photoelectron spectrum of CD 1 4 really consists of two isolated bands corresponding to the lowest and the first excited vibrational band. The measured and ab initio calculated gap between these two bands are in good agreement for this isotopomer. Incomplete deuteration of CH 41 partially removes the degeneracy of electronically equivalent structures and thus suppresses the pseudorotational tunneling process. For CDH 1 and CD 2 H 21 the three-fold 3 symmetry of the pseudorotational motion is broken and a dense vibrational structure is expected. We have again compared the measured gap between the
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Fig. 3. (a) PFI–ZEKE photoelectron spectrum of CH 4 between 101 600 and 102 300 cm 21 . (b) Ab initio prediction of the vibrational transitions obtained from a one-dimensional model for the pseudorotation with a barrier height of V5634.4 cm 21 . The calculated spectrum is drawn as a stick spectrum without intensity simulation. (c) Simulated vibrational bands obtained with the adjusted barrier height of V5500 cm 21 .
first two bands with the ab initio prediction. The experimental gaps in the partially deuterated iso1 topomers are much smaller than in CH 1 4 or CD 4 , in good accordance with the calculations. In particular, our pseudorotational model predicts the vibrational ground state of CD 2 H 21 to be an isolated vibrational state of A9-symmetry, separated from all higher vibrational states by at least 112 cm 21 . The corresponding ground state wave function is localized near the energetically lowest minimum. This property distinguishes CD 2 H 21 from the other investigated isotopomers, and indicates that CD 2 H 21 is likely to have a simple rotational structure. More details concerning the different isotopomers of the methane cation will be reported in a future publication [32].
3.3. Rotational structure As pointed out in the previous subsection, ab initio calculations predict the CD 2 H 21 ground state to be separated and localized. In a next step we have thus calculated its rovibrational structure within our onedimensional pseudorotational model by diagonalizing the rovibrational problem in the product basis of the
vibrational eigenfunctions and the symmetric rigid rotor functions. The results predict CD 2 H 21 to behave like an effective rigid rotor in its vibrational ground 1 1 state. The rotational constants (A 1 0 , B 0 , C 0 ) of the rigid rotor correspond to that of the C2v -symmetrical minimum structure with short C–D-bonds (see Fig. 3 in Ref. [29]). To compare this theoretical prediction with the high resolution PFI–ZEKE photoelectron spectrum shown in the upper trace of Fig. 4, we have calculated the rotational structure of the vibrationless CD 2 H 2 X˜ 1 A 1 → CD 2 H 21 X˜ 2 B2 transition. Experimental and predicted spectra agreed surprisingly well, which enabled the assignment of the rotational structure observed experimentally. On the basis of this assignment we have performed a non-linear least 1 squares fit of the ionic rotational constants A 1 0 , B0 1 1 and C 0 and the band centre n 00 . The measured and calculated line positions are given in Ref. [29]. During the refinement the rotational constants of neutral CD 2 H 2 were held fixed at the values A 0 5 4.302777763.8 ? 10 26 cm 21 , B0 5 3.505883863.5 ? 10 26 cm 21 and C0 5 3.050059963.7 ? 10 26 cm 21 (see Ref. [33]). Table 1 lists the fitted band centre, the adiabatic ionization potential and the refined
R. Signorell, M. Sommavilla / Journal of Electron Spectroscopy and Related Phenomena 108 (2000) 169 – 176 Table 1 Spectroscopic constants of CD 2 H 1 2 , the experimental values are determined from a least squares fit of all assigned transitions in the pulsed-field-ionization zero-kinetic-energy photoelectron spectrum of the vibrationless CD 2 H 2 X˜ 1 A 1 → CD 2 H 21 X˜ 2 B2 photoelectronic transition Constant a
n˜ 00 IP b a,c A1 0 1d Ae B 01 a,c d B1 e a,c C1 0 1d Ce
Value / cm 21 101 851.0960.10 101 852.361.4 4.366760.029 4.467 3.833860.036 3.942 2.463560.029 2.460
a Uncertainty represents three standard deviations (see Ref. [29]). b The uncertainty stems from the accuracy of the calibration of both lasers, the accuracy of the field correction and the statistical error of the fit. c Experimental value for the rotational constant. d Ab initio value from UMP2 / cc-pVQZ calculations.
rotational constants. The adiabatic ionization potential of CD 2 H 2 is determined from the band centre 21 n1 00 by taking into account a correction of 1.2 cm
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for the influence of the electric field ionization sequence. In addition to the experimentally determined rotational constants, theoretical equilibrium 1 1 values for these constants (A 1 e , B e and C e ) are indicated in Table 1. They correspond to UMP2 / ccpVQZ values calculated using Gaussian 94 software [34]. The pure ab initio rotational constants agree with all experimental constants up to the expected effect of vibrational averaging. The lower trace in Fig. 4 represents a simulation of the spectrum obtained with the ionic spectroscopic constants derived in the least squares fit. The spectrum consists of five rotational branches which correspond to changes in the total angular momentum quantum number (neglecting electron spin) of DN 5 N 1 2 N 5 0,61,62. N 1 and N stand for the total angular momentum quantum number neglecting electron spin of CD 2 H 21 and CD 2 H 2 , respectively. Intensities were simulated by assuming a Boltzmann distribution of the neutral ground state rotational levels at 7 K and taking into account the space degeneracy and the spin statistical factors. Possible differences in the electronic transition moments are included in a simple way by weighting the different rotational
˜ 2 Fig. 4. Rotationally resolved PFI–ZEKE photoelectron spectrum of the vibrationless CD 2 H 2 X˜ 1 A 1 → CD 2 H 1 2 X B 2 transition (upper trace). The spectrum was obtained with a sequence of pulsed electric fields of 35 and 2160 mV/ cm. The simulated ZEKE spectrum (see text) is shown in the lower trace. The spectrum has Gaussian line shapes of 0.7 cm 21 FWHM.
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branches with factors CDN (C0 5 1, C1 5 C21 5 0.75, C2 5 C22 5 0.5). The analysis of the measured spectrum in terms of parity selection rules clearly elucidates another intensity effect in the spectrum. All transitions accompanied by the emission of a photoelectron of even parity are stronger in intensity than transitions emitting an odd parity photoelectron. To take into account this observation, the intensities of the former are weighted by a factor of four relative to the latter in the simulated spectrum. We have proposed two possible explanations for this behavior in Ref. [29]. The parity-dependent intensity could either be understood by the partial wave expansion of the f2 molecular orbital of ground state CD 2 H 2 ((1a 1 )2 ,(2a 1 )2 ,(1f2 )6 ) or by mixing of high Rydberg electron orbital angular momentum states with other photoionization channels. The agreement between experimental and theoretical rotational constants shown in Table 1 clearly supports a C2v -symmetrical equilibrium structure for the methane cation. The same symmetry for the equilibrium structure was also found to be consistent with the experimental results of the matrix ESR measurements of CD 2 H 1 of Knight et al. [9]. 2 Assuming a C2v -symmetrical equilibrium structure we further determined an experimental r 0 structure for CD 2 H 1 2 from the data in Table 1 (see Ref. [29]). Because only three structural parameters can be determined from the rotational constants one coordinate was held fixed at the UMP2 / cc-pVQZ equilibrium value. The most realistic experimental geometry was obtained fixing the DCD angle. Table 2 contains the resulting experimental structure. The main difference between the fitted and the ab initio
structure (also listed in Table 2) is the increase of the H–H distance. It must be noted at this point that the ab initio calculation gives an equilibrium structure whereas vibrational effects also contribute to the approximate experimental structure. The rotationally resolved PFI–ZEKE photoelectron spectrum of CH 4 in the region of the adiabatic ionization potential is depicted in Fig. 5a. The resolution in the spectrum (FWHM) is |0.6 cm 21 . In contrast to the situation in CD 2 H 21 , this spectrum cannot be simulated with a rigid C2v -symmetrical rotor. This finding is consistent with the ab initio prediction for the vibrational ground state level of CH 1 mentioned in the previous subsection. The 4
Table 2 Ab initio r e structures and experimental r 0 structures for the C2v -symmetrical ground state of CD 2 H 1 2
UMP2 / cc-pVQZ Experiment b a
a
˚ C–H / A
˚ C–D/ A
/HCH / 8
/DCD/ 8
1.1770
1.0755
55.2009
125.3380
1.194(6)
1.077(6)
59.5(17)
125.3380 c
r e structure. Experimental r 0 structure. Uncertainties represents the maximum deviation that results from changing the experimental rotational constants within their uncertainties (see Table 1). c This coordinate is held fixed at the UMP2 / cc-pVQZ value. b
Fig. 5. (a) Rotationally resolved PFI–ZEKE photoelectron spectrum of the vibrationless CH 4 X˜ 1 A 1 → CH 41 X˜ 2 A 1 transition. The spectrum was obtained with a sequence of pulsed electric fields of 35 and 2123 mV/ cm. (b) Ab initio prediction of the ZEKE spectrum calculated with the ab initio barrier of V5634.4 cm 21 . The spectrum has Gaussian line shapes of 0.6 cm 21 FWHM. (c) Calculated ZEKE spectrum obtained with the adjusted barrier height of V5500 cm 21 . The spectrum has Gaussian line shapes of 0.6 cm 21 FWHM.
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pseudorotational model yields a (A, E)-tunneling splitting which has the same magnitude as a rotational quantum. Therefore, a complex rovibrational structure is expected. The ab initio prediction for the rotational structure of the vibrationless ˜ 2 A photoelectronic transiCH 4 X˜ 1 A 1 → CH 1 4 X 1 tion is shown in Fig. 5c. Note that the ionic state is classified in the molecular symmetry group C3v in accordance with the three-fold symmetry of the pseudorotation. Fig. 5b displays the calculated spectrum assuming a barrier height of 500 cm 21 instead of the ab initio barrier (634.4 cm 21 ). Within the scope of the one-dimensional model, these simulations include exact rovibrational energies for the ionic states. For both spectra only changes in the total angular momentum (neglecting electron spin) of DN 5 N 1 2 N 5 0,61 have been included. The neutral CH 4 was treated as a rigid tetrahedral rotor (B55.241 cm 21 , see Ref. [35]). The intensities in the calculated spectra were obtained by assuming that only the lowest rotational state of each nuclear permutation symmetry is significantly populated in the supersonic gas expansion. Besides the spin statistical factors, the space degeneracy is also included. Moreover, transitions accompanied by the emission of a photoelectron of even or odd parity are weighted by the same weight in the simulation. A comparison of the measured spectrum in Fig. 5a with the simulated spectra in Fig. 5b and c does not show a line by line agreement. A possible explanation for this observation is a deficiency in the calculated path. However, even if the calculated path is largely correct the coupling between the three degenerate minima could still produce a complicated rotational structure that is very sensitive to fine details of the path. Given the high degeneracy of CH 1 4 , a model of the rotational structure may also have to include couplings not considered in the one-dimensional model. For instance, we have tried to estimate the coupling between minima belonging to different equivalent pseudorotations. The resulting value of 3.9 cm 21 is comparable to the pseudorotational tunneling splitting of 3.6 cm 21 (see previous subsection). A detailed model of the observed rotational structure therefore has to take into account the tunneling between all six equivalent minima. This might be achieved by an effective Hamiltonian approach coupling six identical asymmetric rotors.
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4. Conclusions In the present study we have reported the first rotationally resolved PFI–ZEKE photoelectron spectra of CH 4 and its isotopomers. The rotational resolution and the high sensitivity of our apparatus enabled the determination of the first adiabatic ionization potentials with unprecedented accuracy. The measurements of several isotopomers have been used to elucidate the Jahn–Teller distortion in the methane cation. The fact that CD 2 H 21 was found to behave like an effective rigid rotor in its vibronic ground state allowed a direct investigation of the static Jahn–Teller distortion. The results of the analysis of the rotationally resolved ZEKE spectrum of CD 2 H 1 in terms of a rigid rotor model are 2 consistent with the C2v -symmetrical minimum structure predicted by the ab initio calculations. This finding is in agreement with previous matrix ESR measurements of CD 2 H 21 by Knight et al. [9]. From our experimental results we have been able to derive an approximate experimental equilibrium structure for the methane cation. The dynamical aspects of the Jahn–Teller effect are described by a simple onedimensional model for the pseudorotation in CH 1 4 and its isotopomers. The predictions of this model agree well with the vibrational structures in the isotopomeric spectra near the adiabatic ionization potentials. This reveals the pseudorotation as the major contribution to the dynamic Jahn–Teller distortion at low excitation energies. In the case of CH 1 4 , low barriers between equivalent minima and the high degeneracy convey the picture of a fluxional ion, for which the concept of a static molecular structure is meaningless.
Acknowledgements We thank Prof. F. Merkt for his constant support and stimulating discussions. This work is supported financially by the Robert Gnehm Stiftung and the ¨ ETH Zurich.
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[2] A.J.C. Nicholson, J. Chem. Phys. 43 (1965) 1171. [3] W.A. Chupka, J. Berkowitz, J. Chem. Phys. 54 (1971) 4256. [4] J. Berkowitz, J.P. Greene, H. Cho, J. Chem. Phys. 86 (1987) 674. [5] B.P. Pullen, T.A. Carlson, W.E. Moddeman, G.K. Schweitzer, W.E. Bull, F.A. Grimm, J. Chem. Phys. 53 (1970) 768. [6] C.R. Brundle, M.B. Robin, H. Basch, J. Chem. Phys. 53 (1970) 2196. [7] J.W. Rabalais, T. Bergmark, L.O. Werme, L. Karlsson, K. Siegbahn, Physica Scripta 3 (1971) 13. [8] A.W. Potts, W.C. Price, Proc. R. Soc. London A 326 (1972) 165. [9] L.B. Knight Jr., J. Steadman, D. Feller, E.R. Davidson, J. Am. Chem. Soc. 106 (1984) 3700. [10] L.B. Knight Jr., G.M. King, J.T. Petty, M. Matsushita, T. Momose, T. Shida, J. Chem. Phys. 103 (1995) 3377. [11] D.S. Gemmell, E.P. Kanter, W.J. Pietsch, J. Chem. Phys. 72 (1980) 1402. [12] Z. Vager, E.P. Kanter, G. Both, P.J. Cooney, A. Faibis, W. Koenig, B.J. Zabransky, D. Zajfman, Phys. Rev. Lett. 57 (1986) 2793. [13] Z. Vager, in: R. Naaman, Z. Vager (Eds.), The Structure of Small Molecules and Ions, Plenum, New York, 1988, p. 105. [14] Z. Vager, T. Graber, E.P. Kanter, D. Zajfman, Phys. Rev. Lett. 70 (1993) 3549. [15] D. Kella, Z. Vager, J. Chem. Phys. 102 (1995) 8424. [16] J. Arents, L.C. Allen, J. Chem. Phys. 53 (1970) 73. [17] R.N. Dixon, Mol. Phys. 20 (1971) 113. [18] W. Meyer, J. Chem. Phys. 58 (1973) 1017. ´ de la Vega, A. Segovia, J. Fernandez ´ [19] J.M. Garcıa Rico, J.I. ´ Fernandez Alonso, J. Mol. Struc. 123 (1985) 203. [20] M.N. Paddon-Row, D.J. Fox, J.A. Pople, K.N. Houk, D.W. Pratt, J. Am. Chem. Soc. 107 (1985) 7696.
[21] K. Takeshita, J. Chem. Phys. 86 (1987) 329. [22] R.F. Frey, E.R. Davidson, J. Chem. Phys. 88 (1988) 1775. [23] M.S. Reeves, E.R. Davidson, J. Chem. Phys. 95 (1991) 6551. [24] R.J. Boyd, K.V. Darvesh, P.D. Fricker, J. Chem. Phys. 94 (1991) 8083. [25] R.F. Frey, E.R. Davidson, in: R. Naaman, Z. Vager (Eds.), The Structure of Small Molecules and Ions, Plenum, New York, 1988, p. 209. [26] M. Matsushita, T. Momose, T. Shida, L.B. Knight Jr., J. Chem. Phys. 103 (1995) 3367. [27] F. Marinelli, M. Roche, Chem. Phys. 146 (1990) 219. [28] R. Signorell, F. Merkt, J. Chem. Phys. 110 (1999) 2309. [29] R. Signorell, M. Sommavilla, F. Merkt, Chem. Phys. Lett. 312 (1999) 139. [30] R. Signorell, H. Palm, F. Merkt, J. Chem. Phys. 106 (1997) 6523. [31] F. Merkt, A. Osterwalder, R. Seiler, R. Signorell, H. Palm, H. Schmutz, R. Gunzinger, J. Phys. B: At. Mol. Opt. Phys. 31 (1998) 1705. [32] R. Signorell, F. Merkt, unpublished results, a full report of our photoelectron spectroscopic measurements on CH 4 , CDH 3 , CD 2 H 2 and CD 4 and their analysis with the onedimensional pseudorotation model is in preparation. [33] J.C. Deroche, G. Guelachvili, J. Mol. Spectrosc. 56 (1975) 76. [34] M.J. Frisch, Æ. Frisch, J.B. Foresman, Gaussian 94 User’s Reference, Gaussian Inc., Pittsburgh, 1994. [35] J.P. Champion, J.C. Hilico, L.R. Brown, J. Mol. Spectrosc. 133 (1989) 244.
CH 1 4 : a fluxional ion? R. Signorell*, M. Sommavilla Laboratorium fur Physikalische Chemie, ETH Zurich, CH-8092 Zurich, Switzerland Received 13 September 1999
Abstract High resolution pulsed-field-ionization (PFI) zero-kinetic-energy (ZEKE) photoelectron spectra of CH 4 and its isotopomers have been recorded for the first time. These spectra show extensive progressions of rotationally resolved transitions. The vibrational structure of the Jahn–Teller distorted ions at low excitation energies have been analysed in terms of a one-dimensional model for the pseudorotational motion of the ions. The analysis of the rotational structure confirms a 1 fluxional behavior for CH 1 2000 Elsevier 4 , whereas CD 2 H 2 in its vibronic ground state can be treated as a rigid rotor. Science B.V. All rights reserved. Keywords: Methane radical cation; Isotopomers of the methane cation; Jahn–Teller distortion; PFI–ZEKE photoelectron spectroscopy
1. Introduction As the most simple organic cation and one of the simplest systems subject to a Jahn–Teller distortion in the electronic ground state the methane radical cation is of fundamental interest. This has led to many experimental [1–15] as well as theoretical [16–27] investigations on CH 1 4 and its isotopomers. The early ab initio study of Meyer [18] first established a large Jahn–Teller distortion from the tetrahedral geometry of the triply degenerate electronic ground state ( 2 F2 ) to a set of twelve equivalent C2v -symmetrical equilibrium structures. Large amplitude tunneling motions in the ionic ground state have been found in subsequent calculations using various levels of ab initio theory [19–24]. The most detailed experimental information about the vibronic ground state of the methane cation has *Corresponding author. E-mail address: [email protected] (R. Signorell)
been obtained through Coulomb explosion experiments [11–15] and electron spin resonance (ESR) studies [9,10]. Some uncertainty remains in the interpretation of the Coulomb explosion measurements [15], so that the minimum structure of CH 1 4 could not be unambiguously determined. In their ESR investigations, Knight et al. [9,10] provided experimental evidence for a C2v -symmetrical minimum structure for the CD 2 H 21 cation but found that the ESR spectrum of CH 41 is an approximately isotropic quintet. Until recently no rotationally resolved spectra of CH 1 4 and its isotopomers were available. Therefore, the ionization potential could not be determined accurately (see references in Ref. [4]) let alone the Jahn–Teller distortion. With the first rotationally resolved PFI–ZEKE photoelectron spectra of CH 1 and CD 2 H 21 published recently 4 [28,29] the situation has completely changed. In this paper we report the analysis of the rovibrational structure of these spectra in terms of a onedimensional model for the pseudorotation. We ex-
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ploit the symmetry breaking through isotopic substitution in CD 2 H 21 to obtain the first rotational analysis of the methane cation.
2. Experimental The photoelectron / photoion spectrometer and the extreme ultraviolet (XUV) light source used in the present experiments have been described in previous publications [30,31]. For the present study, the XUV light was generated by resonance-enhanced sumfrequency mixing in a xenon gas beam using the two-photon resonance (5p)6 1 S0 →(5p)5 6p[1 / 2] (J5 0) at a wavenumber of 80 118.974 cm 21 . The laser system was operated at a resolution of 0.2 cm 21 . Molecules were excited with a single photon to long-lived high (n . 300) Rydberg states located below successive ionization thresholds. The pulsedfield-ionization (PFI) zero-kinetic-energy (ZEKE) photoelectron spectra were recorded by monitoring electrons produced by field ionization as a function of the laser wavenumber. The electric field pulses were applied | 13 ms after photoexcitation to avoid undesired signals from background water [32]. The ZEKE photoelectron spectra were recorded with electric field pulse sequences of (35 / 2123 mV/ cm) and (35 / 2160 mV/ cm) in the case of CH 4 and CD 2 H 2 , respectively (see Section 3). Under these conditions the resulting resolution in the photoelectron spectra (FWHM) is better than 0.7 cm 21 . The photoionization spectrum of CH 4 shown in Section 3 was measured by recording the ion yield as a function of the laser wavenumber. A pulsed electric field of 88 V/ cm was applied to extract the ions.
3. Results and discussion
3.1. Adiabatic ionization potential of CH4 Previous experimental values for the first adiabatic ionization potential of CH 4 lie in a wide range between 100 900 and 103 078 cm 21 (see references in Ref. [4]). Fig. 1 shows the high resolution PFI– ZEKE photoelectron spectrum of CH 4 in the region between 100 800 and 102 600 cm 21 . In our previous work [28] the first adiabatic ionization potential was
Fig. 1. Section of the rotationally resolved PFI–ZEKE photoelectron spectrum of CH 4 . The spectrum was obtained with a sequence of pulsed electric fields of 35 and 2123 mV/ cm.
located in the center of the first observed vibrational band in the PFI–ZEKE photoelectron spectrum at a value of: IP5101 773635 cm 21 . The uncertainty of 635 cm 21 represents the half width at half maximum of the rotational contour of this vibrational band. Compared with previous results this constitutes an improvement by more than a factor of two. Because of the Jahn–Teller distortion in CH 1 4 it was supposed that the Franck–Condon factors for the transitions from the neutral ground state to the ionic ground state would be too small to be observed. Based on this assumption, Rabalais et al. [7] extrapolated an adiabatic ionization potential of about 100 900 cm 21 from their partially resolved photoelectron spectrum. Given the rotational resolution of our ZEKE spectrum and the high sensitivity, the absence of signal below |101 773 cm 21 in Fig. 1 would require an abrupt change in the Franck– Condon factors. Such a behavior is very implausible. Fig. 2a represents the PFI–ZEKE photoelectron spectrum of CH 4 in the region of the lowest observed band. The CH 1 4 ion signal is depicted in Fig. 2b as a function of the ionization wavenumber. The occurrence of the CH 41 ion threshold near the lowest observed band in the ZEKE photoelectron spectrum gives additional evidence for the value of the adiabatic ionization potential to be around 101 773 cm 21 . The ion signal essentially follows the integrated ZEKE electron signal drawn in Fig. 2a.
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Fig. 2. (a) PFI–ZEKE photoelectron spectrum in the region of the lowest observed band (experimental conditions as in Fig. 1). The integrated ZEKE electron signal is represented by the dashed line. (b) Photoionization spectrum of CD 2 H 1 2 (ion signal) in the same region as the spectrum in (a). The pulsed electric extraction field amounted to 88 V/ cm.
3.2. Vibrational structure In Fig. 1 one recognizes an isolated band around 101 773 cm 21 corresponding to the transition to the vibrational ground state of CH 41 . However, at higher excitation energies no simple vibrational band structure can be distinguished. This complex vibrational structure can be understood on the basis of ab initio calculations [20,22] which predict low potential barriers between six of the 12 equivalent C2v symmetrical minima. The interconversion between these minima occurs through pseudorotations connecting subsets of three equivalent minima. As a first step in the interpretation of the experimental spectrum we neglect interferences between the four different pseudorotations. A simple one-dimensional
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model results which is formulated in terms of the Fukui reaction path determined by Frey and Davidson [22]. The remaining 3N 2 7 degrees of freedom are included through appropriate zero-point energy corrections. More details, including the explicit ¨ solution of the rovibrational Schrodinger equation, are described in Refs. [28,32]. The resulting ab initio prediction for the vibrational structure of CH 1 is indicated as a stick 4 spectrum in Fig. 3b. The three-fold symmetry results in A and E tunneling levels. For the vibrational ground state the (A, E)-splitting amounts to 3.6 cm 21 , whereas the next vibrational level is already split by 44.8 cm 21 . This split level lies close to the top of the one-dimensional potential barrier and is thus very sensitive to its height. Compared with the measured spectrum, the prediction overestimates the distance between the first two vibrational bands. To obtain a better agreement, we have adjusted the ab initio potential barrier height of 634.4 cm 21 by linear stretching of the potential to fit the measured gap [28]. An adjusted barrier height of 500 cm 21 yielded the vibrational stick spectrum in Fig. 3c. The tunneling splitting of the ground and the first excited vibrational band are increased to 5.8 and 60.9 cm 21 , respectively. Because of the zero-point energy effects and the higher masses of the deuterium atoms, the tunneling 1 splitting in CD 1 4 is reduced compared with CH 4 . The ab initio model predicts (A, E)-splittings of 0.2 and 4.3 cm 21 for the ground and the first excited vibrational state, respectively. The small splitting of the first excited vibrational level is caused by the large distance of this level from the top of the potential barrier. As expected from this prediction, the PFI–ZEKE photoelectron spectrum of CD 1 4 really consists of two isolated bands corresponding to the lowest and the first excited vibrational band. The measured and ab initio calculated gap between these two bands are in good agreement for this isotopomer. Incomplete deuteration of CH 41 partially removes the degeneracy of electronically equivalent structures and thus suppresses the pseudorotational tunneling process. For CDH 1 and CD 2 H 21 the three-fold 3 symmetry of the pseudorotational motion is broken and a dense vibrational structure is expected. We have again compared the measured gap between the
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Fig. 3. (a) PFI–ZEKE photoelectron spectrum of CH 4 between 101 600 and 102 300 cm 21 . (b) Ab initio prediction of the vibrational transitions obtained from a one-dimensional model for the pseudorotation with a barrier height of V5634.4 cm 21 . The calculated spectrum is drawn as a stick spectrum without intensity simulation. (c) Simulated vibrational bands obtained with the adjusted barrier height of V5500 cm 21 .
first two bands with the ab initio prediction. The experimental gaps in the partially deuterated iso1 topomers are much smaller than in CH 1 4 or CD 4 , in good accordance with the calculations. In particular, our pseudorotational model predicts the vibrational ground state of CD 2 H 21 to be an isolated vibrational state of A9-symmetry, separated from all higher vibrational states by at least 112 cm 21 . The corresponding ground state wave function is localized near the energetically lowest minimum. This property distinguishes CD 2 H 21 from the other investigated isotopomers, and indicates that CD 2 H 21 is likely to have a simple rotational structure. More details concerning the different isotopomers of the methane cation will be reported in a future publication [32].
3.3. Rotational structure As pointed out in the previous subsection, ab initio calculations predict the CD 2 H 21 ground state to be separated and localized. In a next step we have thus calculated its rovibrational structure within our onedimensional pseudorotational model by diagonalizing the rovibrational problem in the product basis of the
vibrational eigenfunctions and the symmetric rigid rotor functions. The results predict CD 2 H 21 to behave like an effective rigid rotor in its vibrational ground 1 1 state. The rotational constants (A 1 0 , B 0 , C 0 ) of the rigid rotor correspond to that of the C2v -symmetrical minimum structure with short C–D-bonds (see Fig. 3 in Ref. [29]). To compare this theoretical prediction with the high resolution PFI–ZEKE photoelectron spectrum shown in the upper trace of Fig. 4, we have calculated the rotational structure of the vibrationless CD 2 H 2 X˜ 1 A 1 → CD 2 H 21 X˜ 2 B2 transition. Experimental and predicted spectra agreed surprisingly well, which enabled the assignment of the rotational structure observed experimentally. On the basis of this assignment we have performed a non-linear least 1 squares fit of the ionic rotational constants A 1 0 , B0 1 1 and C 0 and the band centre n 00 . The measured and calculated line positions are given in Ref. [29]. During the refinement the rotational constants of neutral CD 2 H 2 were held fixed at the values A 0 5 4.302777763.8 ? 10 26 cm 21 , B0 5 3.505883863.5 ? 10 26 cm 21 and C0 5 3.050059963.7 ? 10 26 cm 21 (see Ref. [33]). Table 1 lists the fitted band centre, the adiabatic ionization potential and the refined
R. Signorell, M. Sommavilla / Journal of Electron Spectroscopy and Related Phenomena 108 (2000) 169 – 176 Table 1 Spectroscopic constants of CD 2 H 1 2 , the experimental values are determined from a least squares fit of all assigned transitions in the pulsed-field-ionization zero-kinetic-energy photoelectron spectrum of the vibrationless CD 2 H 2 X˜ 1 A 1 → CD 2 H 21 X˜ 2 B2 photoelectronic transition Constant a
n˜ 00 IP b a,c A1 0 1d Ae B 01 a,c d B1 e a,c C1 0 1d Ce
Value / cm 21 101 851.0960.10 101 852.361.4 4.366760.029 4.467 3.833860.036 3.942 2.463560.029 2.460
a Uncertainty represents three standard deviations (see Ref. [29]). b The uncertainty stems from the accuracy of the calibration of both lasers, the accuracy of the field correction and the statistical error of the fit. c Experimental value for the rotational constant. d Ab initio value from UMP2 / cc-pVQZ calculations.
rotational constants. The adiabatic ionization potential of CD 2 H 2 is determined from the band centre 21 n1 00 by taking into account a correction of 1.2 cm
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for the influence of the electric field ionization sequence. In addition to the experimentally determined rotational constants, theoretical equilibrium 1 1 values for these constants (A 1 e , B e and C e ) are indicated in Table 1. They correspond to UMP2 / ccpVQZ values calculated using Gaussian 94 software [34]. The pure ab initio rotational constants agree with all experimental constants up to the expected effect of vibrational averaging. The lower trace in Fig. 4 represents a simulation of the spectrum obtained with the ionic spectroscopic constants derived in the least squares fit. The spectrum consists of five rotational branches which correspond to changes in the total angular momentum quantum number (neglecting electron spin) of DN 5 N 1 2 N 5 0,61,62. N 1 and N stand for the total angular momentum quantum number neglecting electron spin of CD 2 H 21 and CD 2 H 2 , respectively. Intensities were simulated by assuming a Boltzmann distribution of the neutral ground state rotational levels at 7 K and taking into account the space degeneracy and the spin statistical factors. Possible differences in the electronic transition moments are included in a simple way by weighting the different rotational
˜ 2 Fig. 4. Rotationally resolved PFI–ZEKE photoelectron spectrum of the vibrationless CD 2 H 2 X˜ 1 A 1 → CD 2 H 1 2 X B 2 transition (upper trace). The spectrum was obtained with a sequence of pulsed electric fields of 35 and 2160 mV/ cm. The simulated ZEKE spectrum (see text) is shown in the lower trace. The spectrum has Gaussian line shapes of 0.7 cm 21 FWHM.
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branches with factors CDN (C0 5 1, C1 5 C21 5 0.75, C2 5 C22 5 0.5). The analysis of the measured spectrum in terms of parity selection rules clearly elucidates another intensity effect in the spectrum. All transitions accompanied by the emission of a photoelectron of even parity are stronger in intensity than transitions emitting an odd parity photoelectron. To take into account this observation, the intensities of the former are weighted by a factor of four relative to the latter in the simulated spectrum. We have proposed two possible explanations for this behavior in Ref. [29]. The parity-dependent intensity could either be understood by the partial wave expansion of the f2 molecular orbital of ground state CD 2 H 2 ((1a 1 )2 ,(2a 1 )2 ,(1f2 )6 ) or by mixing of high Rydberg electron orbital angular momentum states with other photoionization channels. The agreement between experimental and theoretical rotational constants shown in Table 1 clearly supports a C2v -symmetrical equilibrium structure for the methane cation. The same symmetry for the equilibrium structure was also found to be consistent with the experimental results of the matrix ESR measurements of CD 2 H 1 of Knight et al. [9]. 2 Assuming a C2v -symmetrical equilibrium structure we further determined an experimental r 0 structure for CD 2 H 1 2 from the data in Table 1 (see Ref. [29]). Because only three structural parameters can be determined from the rotational constants one coordinate was held fixed at the UMP2 / cc-pVQZ equilibrium value. The most realistic experimental geometry was obtained fixing the DCD angle. Table 2 contains the resulting experimental structure. The main difference between the fitted and the ab initio
structure (also listed in Table 2) is the increase of the H–H distance. It must be noted at this point that the ab initio calculation gives an equilibrium structure whereas vibrational effects also contribute to the approximate experimental structure. The rotationally resolved PFI–ZEKE photoelectron spectrum of CH 4 in the region of the adiabatic ionization potential is depicted in Fig. 5a. The resolution in the spectrum (FWHM) is |0.6 cm 21 . In contrast to the situation in CD 2 H 21 , this spectrum cannot be simulated with a rigid C2v -symmetrical rotor. This finding is consistent with the ab initio prediction for the vibrational ground state level of CH 1 mentioned in the previous subsection. The 4
Table 2 Ab initio r e structures and experimental r 0 structures for the C2v -symmetrical ground state of CD 2 H 1 2
UMP2 / cc-pVQZ Experiment b a
a
˚ C–H / A
˚ C–D/ A
/HCH / 8
/DCD/ 8
1.1770
1.0755
55.2009
125.3380
1.194(6)
1.077(6)
59.5(17)
125.3380 c
r e structure. Experimental r 0 structure. Uncertainties represents the maximum deviation that results from changing the experimental rotational constants within their uncertainties (see Table 1). c This coordinate is held fixed at the UMP2 / cc-pVQZ value. b
Fig. 5. (a) Rotationally resolved PFI–ZEKE photoelectron spectrum of the vibrationless CH 4 X˜ 1 A 1 → CH 41 X˜ 2 A 1 transition. The spectrum was obtained with a sequence of pulsed electric fields of 35 and 2123 mV/ cm. (b) Ab initio prediction of the ZEKE spectrum calculated with the ab initio barrier of V5634.4 cm 21 . The spectrum has Gaussian line shapes of 0.6 cm 21 FWHM. (c) Calculated ZEKE spectrum obtained with the adjusted barrier height of V5500 cm 21 . The spectrum has Gaussian line shapes of 0.6 cm 21 FWHM.
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pseudorotational model yields a (A, E)-tunneling splitting which has the same magnitude as a rotational quantum. Therefore, a complex rovibrational structure is expected. The ab initio prediction for the rotational structure of the vibrationless ˜ 2 A photoelectronic transiCH 4 X˜ 1 A 1 → CH 1 4 X 1 tion is shown in Fig. 5c. Note that the ionic state is classified in the molecular symmetry group C3v in accordance with the three-fold symmetry of the pseudorotation. Fig. 5b displays the calculated spectrum assuming a barrier height of 500 cm 21 instead of the ab initio barrier (634.4 cm 21 ). Within the scope of the one-dimensional model, these simulations include exact rovibrational energies for the ionic states. For both spectra only changes in the total angular momentum (neglecting electron spin) of DN 5 N 1 2 N 5 0,61 have been included. The neutral CH 4 was treated as a rigid tetrahedral rotor (B55.241 cm 21 , see Ref. [35]). The intensities in the calculated spectra were obtained by assuming that only the lowest rotational state of each nuclear permutation symmetry is significantly populated in the supersonic gas expansion. Besides the spin statistical factors, the space degeneracy is also included. Moreover, transitions accompanied by the emission of a photoelectron of even or odd parity are weighted by the same weight in the simulation. A comparison of the measured spectrum in Fig. 5a with the simulated spectra in Fig. 5b and c does not show a line by line agreement. A possible explanation for this observation is a deficiency in the calculated path. However, even if the calculated path is largely correct the coupling between the three degenerate minima could still produce a complicated rotational structure that is very sensitive to fine details of the path. Given the high degeneracy of CH 1 4 , a model of the rotational structure may also have to include couplings not considered in the one-dimensional model. For instance, we have tried to estimate the coupling between minima belonging to different equivalent pseudorotations. The resulting value of 3.9 cm 21 is comparable to the pseudorotational tunneling splitting of 3.6 cm 21 (see previous subsection). A detailed model of the observed rotational structure therefore has to take into account the tunneling between all six equivalent minima. This might be achieved by an effective Hamiltonian approach coupling six identical asymmetric rotors.
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4. Conclusions In the present study we have reported the first rotationally resolved PFI–ZEKE photoelectron spectra of CH 4 and its isotopomers. The rotational resolution and the high sensitivity of our apparatus enabled the determination of the first adiabatic ionization potentials with unprecedented accuracy. The measurements of several isotopomers have been used to elucidate the Jahn–Teller distortion in the methane cation. The fact that CD 2 H 21 was found to behave like an effective rigid rotor in its vibronic ground state allowed a direct investigation of the static Jahn–Teller distortion. The results of the analysis of the rotationally resolved ZEKE spectrum of CD 2 H 1 in terms of a rigid rotor model are 2 consistent with the C2v -symmetrical minimum structure predicted by the ab initio calculations. This finding is in agreement with previous matrix ESR measurements of CD 2 H 21 by Knight et al. [9]. From our experimental results we have been able to derive an approximate experimental equilibrium structure for the methane cation. The dynamical aspects of the Jahn–Teller effect are described by a simple onedimensional model for the pseudorotation in CH 1 4 and its isotopomers. The predictions of this model agree well with the vibrational structures in the isotopomeric spectra near the adiabatic ionization potentials. This reveals the pseudorotation as the major contribution to the dynamic Jahn–Teller distortion at low excitation energies. In the case of CH 1 4 , low barriers between equivalent minima and the high degeneracy convey the picture of a fluxional ion, for which the concept of a static molecular structure is meaningless.
Acknowledgements We thank Prof. F. Merkt for his constant support and stimulating discussions. This work is supported financially by the Robert Gnehm Stiftung and the ¨ ETH Zurich.
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