J. Phys. Chem. 1996, 100, 19783-19788
19783
Vibronic Couplings in the C 1s f nsσg Rydberg Excited States of CO2 Jun-ichi Adachi and Nobuhiro Kosugi* Institute for Molecular Science, Myodaiji, Okazaki 444, Japan
Eiji Shigemasa and Akira Yagishita Photon Factory, National Laboratory for High Energy Physics, Tsukuba 305, Japan ReceiVed: July 8, 1996; In Final Form: October 8, 1996X
Fragment ion yields in the C 1s f Rydberg excitation region of CO2 were measured in the 90° and 0° directions relative to the electric vector of the linearly polarized light. The C 1s f ns (n ) 3, 4), npπ and npσ (n ) 3-7), and nd (n ) 3, 4) Rydberg transitions are clearly observed and show some vibrational structures. The dipole-forbidden C 1s(σg) f 3sσg Rydberg transition is the strongest of all the Rydberg transitions, and the ion yield in the 90° direction is dominant. This indicates that the bending vibration is predominantly coupled with the 3sσg Rydberg state and the intensity-lending dipole-allowed state is a very strong π* resonance, only 2 eV lower than the 3sσg state. On the other hand, in the 4sσg Rydberg state the vibronic coupling through the antisymmetric stretching mode is strongly observed in the 0° direction. This is probably because the 4sσg state approaches another intensity-lending state with Σu+ symmetry and goes away from the π* resonance. The angle-resolved ion-yield technique is very powerful for elucidating the vibronic coupling mechanism.
I. Introduction Electronic structures of the inner-shell excited states of several diatomic molecules are investigated by measuring the angular dependence of the fragment ions using linearly polarized soft X-rays.1-14 These newly developed spectroscopic techniques are related to the axial recoil mechanism15 applied to the innershell decay process. The ionic fragmentation following the Auger decay takes place in a much shorter time than the period of the molecular rotation; therefore, the fragment ion has a memory of the molecular orientation and symmetry upon the photoabsorption process. The fragment ions are detected in the parallel direction (0°) to the electric vector of the incident light for the parallel transition (∆Λ ) 0) and are detected in the perpendicular direction (90°) for the perpendicular transition (∆Λ ) (1). The present authors have developed angle-resolved ion-yield spectroscopy for the diatomic molecule and called it “symmetry-resolved” spectroscopy;9,10 for example, for the molecules with Σ symmetry in the ground states, the spectra of the inner-shell excited states with Σ and Π symmetries can be obtained by measuring the ion yields in the 0° and 90° directions, respectively. The next concern is whether the symmetry-resolved spectroscopy is valid or not for polyatomic molecules.16 Some groups have discussed the validity and limitation of the axial recoil mechanism for H2O,17 N2O,16,18,19 and CO2.20 It is a very important finding that for the linear molecule N2O the fragment ions following the core-to-π* excitations partly lose the memory of the molecular orientation and symmetry upon photoabsorption.16 This phenomenon is rationalized by the Renner-Teller effect, where the 2-fold degeneracy of the π* excited state in the linear polyatomic molecule is removed through coupling with the bending vibration and the molecule is most stabilized at a bent geometry. On the other hand, the symmetry resolution for the core-to-Rydberg and core-to-σ* excitations is complete * To whom correspondence should be addressed. FAX: +81-564-542254. E-mail:
[email protected] X Abstract published in AdVance ACS Abstracts, December 1, 1996.
S0022-3654(96)02025-4 CCC: $12.00
in the linear polyatomic molecule as well as in the diatomic molecule. The core-to-Rydberg and core-to-σ* excited states of the liner molecule have linear stable geometries, where the Renner-Teller effect in the degenerate state is negligibly weak in the π-type Rydberg state; therefore, the anisotropy in the fragmentation is directly related to the molecular orientation and symmetry upon photoabsorption.16,21 Another recent progress in inner-shell spectroscopy is the development of high-resolution soft X-ray monochromators.22-25 This enables us to study molecular vibrational spectroscopy even in the inner-shell region.26,27 Recent work14,16,21,28-32 has revealed clear evidence of vibronic coupling and Rydbergvalence mixing in some inner-shell excited states. Combination with the angle-resolved ion-yield measurement is very important to reveal several new features in the inner-shell vibrational spectra. For example, the electronic structure of the inner-shell excited states of the linear triatomic molecule CO2 is widely investigated with electron energy loss spectroscopy (EELS)33,34 and photoabsorption spectroscopy using synchrotron radiation;20,35-37 nevertheless, there are still some unsettled interpretations. What is the origin of the 292.7 eV peak? The peak is assigned to the C 1s f 3s Rydberg excitation but it is dipoleforbidden. Wight and Brion33 suggested that the dipoleforbidden transition is easily observed in the EELS measurement. Sivkov et al.35 pointed out that the 3s Rydberg orbital is similar to the valence type and the vibronic interaction causes the removal of the dipole-forbidden character. Schwarz and Buenker38 showed theoretically that the term value for the 3s Rydberg state is relatively large due to the mixing with the valence σg* orbital in the linear geometry. Tronc et al.34 and Ma et al.37 assigned the 292.7 eV peak to the 3s Rydberg state on the basis of the large term value calculated by Schwarz and Buenker. However, some important questions remain to be answered: what vibrational state is coupled with the C 1s f 3s Rydberg state and what electronic state (intensity-lending state) is mixed with the C 1s f 3s Rydberg state through the vibronic coupling?39 © 1996 American Chemical Society
19784 J. Phys. Chem., Vol. 100, No. 51, 1996
Adachi et al.
The dipole-forbidden state with a symmetric geometry can be dipole-allowed in some asymmetric geometries through coupling with asymmetric molecular vibrations. Therefore, the anisotropy of fragmentation on the photoabsorption of linearly polarized light is related to the vibrational mode coupled in the vibronically allowed state, in other words, to the symmetry of the intensity-lending dipole-allowed state.21 In the present work, high-resolution angle-resolved ion-yield spectra are investigated in the C 1s f Rydberg excitation region of CO2. The vibrational modes coupled with the dipoleforbidden C 1s f 3s and 4s Rydberg excited states are clearly elucidated by means of the angle-resolved ion-yield measurement. In addition, the Rydberg-valence mixing is discussed for some C 1s f Rydberg excited states from the viewpoint of potential energies along specific vibrational coordinates. II. Methods Experiments were carried out using a 10 m grazing-incidence monochromator installed at the soft X-ray undulator beamline BL-2B of the Photon Factory storage ring.25 Fragment photoions emitted from the interaction region of monochromatic light and sample gas were detected simultaneously using two channeltrons. The channeltrons were set on a plane perpendicular to the incident light and in the 0° (parallel) and 90° (perpendicular) directions relative to the electric vector of the linearly polarized light. The acceptance angle of the fragment ions in the detectors was limited to about (10° with the apertures of retardation electrodes, to which +3 V was applied; no thermal ion can reach the detector with the retardation fields. Since the angular distribution of the fragment ion in CH4 is isotropic above the C 1s ionization threshold, the C 1s spectra of CH4 were measured to calibrate the detection efficiencies of the two channeltrons.4 Furthermore, to correct imperfect linear polarization, which is caused by a tilted polarization plane, nonlinear polarization components, acceptance angle of the detectors, detection efficiencies, and other factors, the angleresolved ion yield spectra of CO were measured at the C 1s f π* excitation, because the ions should be observed only in the 90° direction.7,9,16 It was estimated that the spectrum observed in the 0° direction involved about 20% of the spectrum observed in the 90° direction (vice versa). The photon-energy scale was calibrated using the 3s Rydberg peak (292.74 eV, A1 in Figure 2) on the basis of the C 1s EELS spectrum of CO2 reported by Tronc et al.34 III. Results and Discussion Figure 1 shows the angle-resolved ion-yield spectra for the C 1s core region of CO2, in which the imperfect linear polarization was removed. The lowest energy peak observed at 290.77 eV is assigned to the C 1s(σg) f πu* bound state resonance. As discussed in the previous work,16 the ion yields at the π* peak are observed in the 0° direction as well as in the 90° direction. The fragment ions observed in the 0° direction arise mainly from the bending motion in the in-plane π* state stabilized by the Renner-Teller effect.16 The ion yield observed in the 0° direction is dependent on the strength of the RennerTeller effect, as discussed for the C 1s f π* excited state in CO2, OCS, and CS2.40 The ground state of NO2 is the core-equivalent species for both the C 1s f π* excited state of CO2 and the Nt (terminal N) 1s f π* excited state of N2O. This means that the potential energy surfaces for these π* states are almost the same, but does not mean that the C 1s f π* and Nt 1s f π* transitions show similar spectral features. The Nt 1s f π* peak width of N2O (0.74 eV)16 is larger than the C 1s f π* one of CO2 (0.63
Figure 1. C K-edge ion-yield spectra of CO2 measured with moderate energy resolution. The solid line is the ion yield observed in the 90° direction and the dotted line in the 0° direction.
Figure 2. Angle-resolved ion-yield spectra in the C 1s f Rydberg region of CO2 measured with high-energy resolution (∆E ≈ 70 meV). The solid line is the ion yield observed in the 90° direction and the dotted line in the 0° direction.
eV). This is probably because N2O has an asymmetric geometry and the Nt 1s f π* excitation involves more vibronic levels with the antisymmetric stretching (ν3) mode. On the other hand, the relative intensity of the ion yield in the 0° direction for the C 1s f π* excited state of CO2 is larger than for the Nt 1s f π* excited state of N2O.16 The branching ratio of the C+ ion emitted from the C 1s f π* excited state of CO2 is 27%, as reported by Hitchcock et al.,41 and the branching ratio of the Nc+ ion from the Nt 1s f π* excited state of N2O is estimated to be at most 8% by using the photoelectron-photoionphotoion coincidence results of LeBrun et al.18 This indicates that the three-body fragmentation following the C 1s f π* excitation in CO2 more easily occurs than following the Nt 1s f π* in N2O. When the three-body fragmentation occurs at a bent geometry, the central atom (C+ for CO2 and Nc+ for N2O) is ejected parallel to the direction of the transition dipole moment; that is, the central atom is mainly observed in the 0° direction. Thus, the greater intensity of the ion yield in the 0° direction can be related to the larger branching ratio of the threebody fragmentation. Figure 2 shows the high-resolution angle-resolved ion-yield spectra for the C 1s f Rydberg region of CO2. The Rydberg peaks observed are assigned to C 1s f ns (n ) 3, 4), np (n ) 3-7), and nd (n ) 3, 4) Rydberg excitations, as shown in Table 1. The following discussion is focused on these Rydberg states.
C 1s f nsσg Rydberg Excited States of CO2
J. Phys. Chem., Vol. 100, No. 51, 1996 19785
TABLE 1: Assignments of the Rydberg States with Vibrational Structures in the C 1s Absorption Spectrum of CO2 Shown in Figures 1 and 2: Transition Energies Eexcit (eV, Uncertainties of (0.05 eV), Term Values TV (eV), Effective Principal Quantum Numbers n*; The Ionization Potential, IP, Is 297.70 eV, Estimated by Extrapolating the npπ Rydberg Series assignments no.
Eexcit
TV
(n*)
A1 A2 A3 A4 A5 A6 B1 B2 B3 B1′ B2′ B3′ C1 C1′ D E1 E2 E1′ E2′ F G1 G2 H I
292.74 292.85 292.98 293.10 293.21 293.40 294.96 295.13 295.29 294.95 295.14 295.34 295.62 295.70 296.20 296.39 296.55 296.39 296.58 296.82 296.92 297.10 297.18 297.34
4.96 4.85 4.72 4.60 4.49 4.30 2.74 2.57 2.41 2.75 2.56 2.36 2.08 2.00 1.50 1.31 1.15 1.31 1.12 0.88 0.78 0.60 0.52 0.36
(1.66)
(2.23) (2.22) (2.56) (3.01) (3.22) (3.22) (3.93) (4.18) (5.11) (6.15)
this worka
Ma et al.37
3sσg (0 1 0) (1 1 0) (2 1 0) (0 1 2) (1 1 2)
3s
3pπu (0 0 0) (1 0 0) (2 0 0) 3pσu (0 0 0) (1 0 0) (2 0 0) 4sσg (0 1 0) (0 0 1) 3d 4pπu (0 0 0) (1 0 0) 4pσu (0 0 0) (1 0 0) 4d 5pσu,πu (0 0 0) (1 0 0) 6pπu 7pπu
3p
v (ν1) v (ν1) v (ν3)
v (ν1) v
3d 4s 4p v (ν1)
5p 6p
a
The ni in (n1, n2, n3) means the vibrational quantum number of the νi mode, and the ν1, ν2, and ν3 modes correspond to the symmetric stretching, bending, and antisymmetric stretching modes, respectively.
A. Origin of the Intensity of 3sσg Rydberg. In Figure 2, the lowest energy peak A observed at 292.74 eV is assigned to the C 1s(σg) f 3sσg Rydberg state by several groups.20,33-38 Since the σg f σg transition is dipole-forbidden, the 3sσg Rydberg state should borrow its intensity from dipole-allowed states through coupling with the molecular vibrations: antisymmetric stretching and bending. The 3sσg Rydberg state is mixed with a dipole-allowed intensity-lending state with Σu+ symmetry through coupling with the antisymmetric stretching vibration, e.g. (0 0 1), and mixed with a dipole-allowed state with the Πu symmetry through coupling with the bending vibration, e.g. (0 1 0), where (n1 n2 n3) means the vibrational quantum numbers ni of the νi modes and the ν1, ν2, and ν3 modes correspond to the symmeric stretching, bending, and antisymmetric stretching vibrations, respectively. In general, the electronic state with Σu+ symmetry is mixed through coupling with the (k 2l 2m+1) vibrational mode and that with the Πu symmetry is mixed through coupling with the (k 2l+1 2m) one, where k, l, m ) 0, 1, 2, ‚‚‚. Since the C 1s f 3sσg Rydberg transition is dipole-forbidden within the symmetric geometry, the angular distribution of the fragment ions should be related to the symmetry of the dipoleallowed intensity-lending states mixed with the 3sσg state. In the present spectra shown in Figure 2, the fragment ions following the 3sσg Rydberg excitation are mainly observed in the 90° direction relative to the electric vector of the linearly polarized light. This indicates straightforwardly that the dipoleallowed state mixed with the 3sσg Rydberg state has Πu symmetry; in other words, the 3sσg state is strongly coupled with the bending mode. The dipole-allowed intensity-lending state with the Πu symmetry is undoubtedly the π* resonance state, which is located at 290.77 eV and is only 2 eV lower than the 3sσg state, as shown in Figure 1.
Very recently Bozek et al.20 have determined the anisotropy parameters β of the fragment ions following the C 1s excitation by means of the photoelectron-photoion coincidence (PEPICO) and photoion-photoion coincidence (PIPICO) techniques. They reported that the β values for the 3sσg Rydberg excitation are negative (-0.5 for O+ yield and -0.4 for CO+ yield and -0.3 for O+-CO+ coincidence signals with PIPICO) except the positive value for C+ (β ) +0.1). The negative β value indicates that the angular distribution of fragment ions is attributed to the sin2 θ distribution and that the fragment ions are predominantly emitted in the 90° direction. Since the present measurement is based on the “partial” ion yields (“partial” means the yield only for highly kinetic energies >3 eV), the results by Bozek et al. cannot be directly compared with the present results without information of the branching ratios and kinetic energies. Hitchcock et al.41 determined the branching ratios of the fragment ions CO+, O+, and C+ following the C 1s f π* excitation as 21%, 41%, and 27% in the TOF mass spectra, respectively. Assuming that the branching ratios following the 3sσg Rydberg excitation are nearly equal to those following the π* excitation, the present result (“partial” ion yields dominant in the 90° direction) is consistent with the result by Bozek et al. (β < 0 for the “total” ion yields). The feature at 292.7 eV is observed also in the 0° direction. The progression observed in the 90° direction starts from the (0 1 0) level; on the other hand, if there is large contribution from the coupling with the antisymmetric stretching mode, the progression observed in the 0° direction would start from the (0 0 1) level and the peak shape and energy of the 3sσg Rydberg state observed in the 0° direction would be different from those in the 90° direction. The peak shape and energy in the 0° direction, however, is very similar to those in the 90° direction; therefore, the coupling with the antisymmetric stretching mode is not dominant in the 3sσg Rydberg state. The fragment ions ejected without keeping the molecular orientation and symmetry upon photoabsorption have been observed at the degenerate 1s f π* excited states of some linear triatomic molecules, CO2, CS2, OCS,40 and N2O.16 The 1s f π* excited states have stable bent geometries due to the Renner-Teller effect and are coupled with highly excited bending vibrations. On the other hand, since the 3sσg Rydberg state is nondegenerate and has no Renner-Teller effect, the molecule should keep the linear geometry. Therefore, it is erroneous to simply think that the fragmentation following the inner-shell excitation is related directly to the stable geometry. We have to consider that the Auger decay followed by the fragmentation occurs during the vibrational motion.16,21,40,42 Considering that the β value is +0.1 for the PEPICO signals of the C+ ions at 292.7 eV,20 it is most probable that the fragment ions observed in the 0° direction mainly come from the energetic C+ ions (>3 eV) emitted perpendicularly to the molecular axis during the bending motion around the linear stable geometry. B. Vibrational Structures in 3sσg Rydberg. The vibrational fine structures A1-A6 are observed in the 3sσg Rydberg state as shown in Figure 2. Ma et al.37 observed similar vibrational structures A1-A4 and tentatively assigned features A2 and A3 to the totally symmetric stretching mode and A4 to the antisymmetric stretching mode. To evaluate the vibrational frequencies and intensities, the curve fitting was carried out assuming six structures A1-A6. Coville and Thomas43 showed that the lifetime broadening for the C 1s hole state of CO2 is about 66 meV. In the present fitting the vibrational components are satisfactorily described by the Lorentzian functions with about 95 meV fwhm. This is consistent considering the energy
19786 J. Phys. Chem., Vol. 100, No. 51, 1996 resolution of the monochromator used in the present experiments, ∆E ≈ 70 meV. As summarized in Table 1, the fine structures A2-A5 are separated by about 110, 240, 360, and 470 meV from the first peak A1. The first peak A1 borrows undoubtedly its intensity through coupling with the lowest bending vibration, (0 1 0), as already discussed. It is also reasonable that the fine structures A2-A5 borrow their intensities from the C 1s f π* resonance state through coupling with the bending vibrations, because no strong dipole-allowed state with Σu+ symmetry is located near the 3sσg Rydberg state. The most plausible assignment is shown in Table 1; A2-A5 are assigned to the (1 1 0), (2 1 0), (0 1 2), and (1 1 2) levels, respectively. On the basis of the core equivalent model, the electronic structure of the C 1s ionized state OC*O+ (* denotes an atom with a core hole) is approximated as that of ONO+ in the ground state. Considering that the ν1 (sym str), ν2 (bend), and ν3 (antisym str) vibrational frequencies of ONO+ in the ground state are 173.2 (1397), 79.2 (639), and 292.8 meV (2362 cm-1),44 the vibrational frequencies for the OC+*O are estimated as 173.2, 83.6, and 309.2 meV, respectively, after the mass correction. The energy splitting between A1 (0 1 0) and A2 (1 1 0) is 110 meV and is much smaller than 173.2 meV. Schwarz and Buenker38 pointed out that the 3sσg Rydberg orbital is strongly mixed with the σg* orbital of antibonding character in the linear geometry.45 If there is such a Rydberg-valence mixing, the potential energy surface of the 3sσg Rydberg excited state becomes shallower than that of the C 1s ionized state. Thus, the C-O bond in the mixed state is lengthened and weakened, and the ν1 vibrational frequency is lowered. The higher progression in A4-A6 shows different intensities from the ν1 progression in A1-A3; therefore, we have to take into account the ν2 and ν3 vibrational excitations. The energy splittings between A1 and A4 and between A2 and A5 are the same, 360 meV. This splitting possibly corresponds to ∆v(ν2) ) 2 or ∆v(ν3) ) 2. Furthermore, the ratios between the intensities of the vibrational structures are given as follows:
I(A1):I(A2) ) 1:0.63 I(A4):I(A5) ) 1:0.64 I(A1):I(A4) ) 1:0.17 I(A2):I(A5) ) 1:0.17 It is clear that the relationship between A1 and A2 is the same as that between A4 and A5. This indicates that the structure A5 is due to an additional ν1 quantum to the A4 level. Thus the A4 and A5 are assigned to either (0 1 2) and (1 1 2) or (0 3 0) and (1 3 0). However, the bending vibrational spacing between (0 1 0) and (0 3 0) should be much smaller than 360 meV; therefore, the A4 and A5 are conclusively assigned to (0 1 2) and (1 1 2). Using the ν3 vibrational frequency of the core-equivalent species ONO+, the energy for the two quanta of the ν3 mode is ca. 600 meV and is too large to explain the experimental energy splittings between A1 and A4 and between A2 and A5, 360 meV. The mixing between the 3sσ Rydberg and σg* valence orbitals affects the potential energy curve along the antisymmetric stretching coordinate Q3 as well as Q1 and lowers the ν3 vibrational frequency similarly to the case of the ν1 mode. C. 3pσu and 3pπu Rydberg. Peak B observed at 294.96 eV is assigned to the dipole-allowed C 1s f 3p Rydberg excitation. Since the symmetric stretching mode is mainly excited in the Rydberg states,16 the fragment ions keep information on the molecular orientation and symmetry upon the
Adachi et al. photoabsorption process. Therefore, peak B observed in the 90° direction is definitely assigned to the 3pπu Rydberg excitation and that in the 0° direction to the 3pσu one. It is interesting that the vibrational structures of the 3pπu and 3pσu Rydberg states are different. The relative intensities between the vibrational structures in the 3pπu Rydberg state, I(B1):I(B2):I(B3), are about 1.0:0.33:0.06 with 170 meV spacing; on the other hand, those in the 3pσu one, I(B1′):I(B2′): I′(B3), are about 1.0:1.0:0.25 with 190 meV spacing. Clark and Mu¨ller46 showed that the in the C 1s photoelectron spectrum of CO2 the vibrational frequency of the symmetric stretching mode is 170 meV and the relative intensities of the vibrational structures are 1.0:0.38:0.07. Their result is in good agreement with the present result for the 3pπu Rydberg state, but is significantly different from the result for the 3pσu. On the basis of the equivalence core approximation, the C 1s f 3p Rydberg excited states of CO2 are approximated as the 6a1 f 3p Rydberg states of NO2. Tapper et al.47 reported that the vibrational frequencies for the ν1 mode are nearly the same, 174 and 171 meV in the 6a1 f 3pσu and 3pπu Rydberg excited states. This is also inconsistent with the present observation. The potential energy curve along the totally symmetric normal coordinate Q1 in the 3pσu Rydberg excited state is significantly different from the potential energy curves in the C 1s ionized state and 3pπu Rydberg excited state. Considering that the vibrational frequency in the 3pσu Rydberg state (190 meV) is relatively large, the perturbing state should be different from that in the 3sσg Rydberg state and have the Σu+ symmetry. Plausible candidates for the perturbing state are the σu* shape resonance state located at ca. 15 eV above the threshold and some doubly excited states with Σu+ symmetry located near the threshold. Wight and Brion,33 Sham et al.,34 and Schmidbauer et al.48 assigned the structures at ∼300 and ∼304 eV to doubly excited states such as C 1s σgπg f πu*σg*. At the present stage we cannot satisfactorily explain the larger vibrational spacing in the 3pσu Rydberg state. The explanation remains to be made with highly sophisticated theoretical calculations on the potential energy surface of the 3pσu Rydberg state. D. 4sσg Rydberg. Peak C observed at 295.62 eV was tentatively assigned to the 3d Rydberg state by Ma et al.37 The effective quantum number n* for this peak is 2.56. Usually the quantum defects for the nd Rydberg series are nearly zero. The n* number for the 3sσg Rydberg state (A1) is 1.66 (quantum defect δ ) 1.34), and the n* for the 3p Rydberg state (B1) is 2.23 (δ ) 0.77). Therefore, it is more reasonable that peak C is assigned to the 4sσg Rydberg excited state with δ ) 1.44, as shown by Tronc et al.34 They noticed that the 3s and 4s Rydberg excitations do not have the same quantum defects, due to the strong valence mixing in the 3sσg Rydberg state as predicted theoretically by Schwarz and Buenker.38 The transition to the 4sσg Rydberg state is dipole-forbidden and should borrow its intensity from dipole-allowed states through the vibronic coupling as well as the 3sσg Rydberg excitation. As shown in Figure 2 the shapes of the 4sσg Rydberg bands observed in the 0° and 90° directions are different from each other and feature C1′ in the 0° direction spreads on the higher energy side. Although the fine structures are too obscure to carry out the curve analysis, it is probable that the progression observed in the 90° direction starts from the bending vibration of the (0 1 0) level; on the other hand, the progression observed in the 0° direction starts from the antisymmetric vibration of the (0 0 1) level, which has a larger gap from the (0 0 0) level; that is, the origins of features C1 and C1′ are different, in contrast to the 3sσg Rydberg state. It is reasonable to think that feature C1′ in the 0° direction borrows its intensity from
C 1s f nsσg Rydberg Excited States of CO2
J. Phys. Chem., Vol. 100, No. 51, 1996 19787
an excited state with Σu+ symmetry through coupling with the antisymmetric stretching mode. Why is the vibronic coupling through the antisymmetric stretching mode enhanced in the 4sσg Rydberg excited state? It is probably because the 4sσg state approaches an intensity-lending state with the Σu+ symmetry and goes away from the π* resonance. Plausible candidates for the intensity-lending state are the σu* shape resonance state and some doubly excited states with Σu+ symmetry, similarly to the case of the perturbed 3pσu Rydberg state. It should be noted that in the case of the coupling with the bending mode the fragment ions are observed not only in the 90° direction but also in the 0° direction, but in the case of the coupling with the antisymmetric stretching mode the ions are observed only in the 0° direction, because the vibrationally excited molecule in the stretching mode emits fragment ions along the molecular axis while keeping the linear symmetry and orientation upon the photoabsorption process. E. Higher Rydberg. A weak feature D is observed at 296.20 eV. Ma et al.37 tentatively assigned it to the 4s Rydberg excited state. However, the effective quantum number n* for this structure is 3.01. It is more reasonable to assign it to the 3d Rydberg state considering that δ ) -0.01. The ndσg and ndπg Rydberg transitions are dipole-forbidden and should borrow their intensities from dipole-allowed states through the vibronic coupling as well as the nsσg Rydberg transition. In the higher energy region, features E-I are observed. It is expected that higher C 1s f nsσg Rydberg transitions (n > 4) can hardly contribute to the structures E-I because the 4sσg Rydberg transition (feature C) is much weaker than the 3sσg Rydberg transition (feature A). Furthermore, since the 3d Rydberg transition (feature D) is very weak, it is not so easy to observe higher C 1s f nd Rydberg transitions (n > 3). Feature F observed mainly in the 0° direction is tentatively assigned to the 4d Rydberg states considering its effective quantum number, n* ) 3.93. The other features, E, G, H, and I, arise from dipoleallowed C 1s f np Rydberg series; the npπu Rydberg series are observed up to n ) 7 (B, E, G, H, I) in the 90° direction and the npσu Rydberg series are up to n ) 5 (B, E, G) in the 0° direction. On the basis of the term values of the npπu Rydberg series the ionization threshold energy is estimated to be 297.70 eV and is in good agreement with the ionization potential determined by the X-ray photoelectron spectra, 297.71 eV.49 The shape of the vibrational fine structure of the 4pπu Rydberg state (E1 and E2) is nearly the same as that of the 3pπu state (B1 and B2), but the vibrational structure of the 4pσu Rydberg state (E1′ and E2′) is different from that of the 4pπu one, similarly to the case of the 3pσu Rydberg state (B1′ and B2′). The higher npσu Rydberg states are also perturbed by some doubly excited and shape resonance states with Σu+ symmetry.
shows the same vibrational structure as in the 90° direction. Therefore, the bending vibration is predominantly coupled with the 3sσg Rydberg state and the intensity-lending dipole-allowed state is a very strong π* resonance state, only 2 eV lower than the 3sσg state, as shown in Figure 1. On the other hand, in the C 1sσg f 4sσg Rydberg transition (peak C), the ion yields in the 90° and 0° directions are comparable and show different fine structures. This indicates that the ion yield in the 0° direction is related to the dipole-allowed state with Σu+ symmetry and the antisymmetric stretching vibration is also coupled with the 4sσg Rydberg state. Why is the vibronic coupling through the antisymmetric stretching mode enhanced in the 4sσg Rydberg excited state? It is probably because the 4sσg state approaches an intensity-lending state with Σu+ symmetry and goes away from the π* resonance mixed through coupling with the bending vibration. The ionic fragmentation following the Auger decay takes place in a much shorter time than the period of the molecular rotation. In the linear triatomic molecules the axial recoil mechanism is valid for the core-to-Rydberg and core-to-σ* excitations, but the fragment ions following the core-to-π* excitations partly lose the memory of the molecular orientation and symmetry upon photoabsorption.16,40 This is because the 2-fold degeneracy in the π* excited state of the linear molecule is removed due to the Renner-Teller effect and the excited state has a bent stable geometry. On the other hand, since the nondegenerate C 1s(σg) f 3sσg Rydberg state of CO2 has no Renner-Teller effect, it keeps the linear geometry. Therefore, the anisotropy of the ionic fragmentation following the innershell excitation should be related to the molecular Vibration but not to the stable geometry.21 It is most probable that the Auger decay followed by the fragmentation occurs during the molecular vibration.16,21,40,42 In other words, in the inner-shell excitation of polyatomic molecules the axial recoil mechanism fails when the bending Vibration is highly excited by the Renner-Teller or Jahn-Teller effect and vibronic coupling, but is valid when only the stretching (symmetric, antisymmetric) vibration is excited. Furthermore, of the higher Rydberg members the npπu Rydberg series are observed for n ) 3-7 (B, E, G, H, I) in the 90° direction and the npσu Rydberg series are observed for n ) 3-5 (B′, E′, G) in the 0° direction. The 3d and 4d Rydberg states (D and F) are also found. The vibrational structures of the 3pσu and 4pσu Rydberg states observed in the 0° direction are different from the vibrational structures of the 3pπu and 4pπu Rydberg state observed in the 90° direction and of the C 1s ionized state.46 The npσu Rydberg states have significantly different potential energy curves along the totally symmetric normal coordinate through the mixing with some doubly excited states with Σu+ symmetry and/or the σu* shape resonance.
IV. Summary
Acknowledgment. The present authors are grateful to the staff of the Photon Factory for the stable operation of the storage ring and to Professor Hideto Kanamori, Tokyo Institute of Technology, for useful comments on the assignment of the vibronic coupling. The present work has been performed under approval of the Photon Factory Committee (Proposal No. 92G142).
The high-resolution angle-resolved ion-yield spectra were measured in the C 1s f Rydberg excitation region of CO2. The C 1s(σg) f 3sσg Rydberg transition (peak A) is dipole-forbidden but is the strongest of all the Rydberg transitions observed, as shown in Figures 1 and 2. In general, the nsσg state can borrow its intensity from dipole-allowed states through coupling with molecular vibrations: antisymmetric stretching and bending modes. The nsσg Rydberg state is mixed with dipole-allowed intensity-lending states with Σu+ and Πu symmetries through coupling with the antisymmetric stretching and bending vibrations, respectively. In the 3sσg Rydberg peak the ion yield in the 90° direction, which is related to the dipole-allowed state with Πu symmetry, is dominant and the yield in the 0° direction
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