- Email: [email protected]
Rydberg and valence states in the C 1s photoabsorption and resonance Auger spectra of CH3F
1 December1995
CHEMICAL PHYSICS LETTERS
ELSEVIER
Chemical PhysicsLetters 246 (1995) 475-480
Rydberg and valence states in the C Is photoabsorption and resonance Auger spectra of CH 3F N. Kosugi a, K. Ueda b, y. Shimizu b, H. Chiba h, M. Okunishi b, K. Ohmori b, Y. Sato h, E. Shigemasa c a Institute for Molecular Science, Myodaiji, Okazaki 444, Japan b Research Institute for Scientific Measurements, Tohoku University, Sendai 980-77, Japan c Photon Factory, National Laboratory for High Energy Physics, Tsukuba 305, Japan
Received 21 August1995;in final form 15 September 1995
Abstract
Comparison of the high-resolution C ls electron-yield spectrum of CH3F with that of CH 4 reveals that the trc_ F state manifests in a broad and strong feature below the 3s Rydberg band and all the other features are nearly the same as in CH 4. This is supported by improved virtual orbital calculations using the relaxed core-hole potential and avoiding spurious mixing between Rydberg and valence states. In the resonance Auger electron spectra the participant Auger decay rate following the cry_r excitation, -- 15%, is much larger than that of the Rydberg excitations, 1-5%.
1. Introduction
Recent progress in high-resolution inner-shell spectroscopy enables us to study molecular vibrational spectroscopy even in the inner-shell energy region [1,2]. Recent work [3-9] has opened up clear evidence of vibronic coupling and Rydberg-valence mixing in inner-sheU spectroscopy as well as in valence-shell spectroscopy. For example, high-resolution C ls excitation spectra of CH 4 show the C ls ~ 3pt 2 Rydberg transition [10-12] with complicated features on the higher energy side and weak features on the lower energy side. Those features were discussed by relating to vibronic coupling, Jahn-Teller splitting, and Rydberg-valence mixing; however, those were not consistently interpreted until recently. The present authors have successfully assigned those structures based on the resonance Auger electron spectra [13] and ab initio improved
virtual orbital (IVO) calculations [14] using the relaxed Hartree-Fock potential for the ionized state; furthermore, they have shown that the participant and spectator Auger decays following the C 1s excitations are correlated with the character of excited states: valence or Rydberg, because the participant decay rate becomes smaller as the orbital occupied by an excited electron becomes more delocalized [9]. It is expected that comparison of the C ls spectra of CH3F with those of CH 4 brings us a definite and consistent interpretation of complicated features observed for the two molecules; the similarity arises from the CH 3 component and the difference arises from the C - F bond. In CH3F it is important to resolve a conflict between the experimental and theoretical interpretations on the locations of the 3s Rydberg state and the valence state of the C - F antibonding (try_ F) character [15,16]. The purpose of the present work is to characterize the C ls excited
0009-2614/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0009-2614(95)01 121-8
476
N. Kosugi et al. / Chemical Physics Letters 246 (1995) 475-480
states in the photoabsorption spectrum of CH3F and to investigate the Rydberg and valence states based on the same approaches as in the previous work on the C I s photoabsorption spectrum of CH 4 [9].
0.01141, 0.00589, and 0.00334, ~'p = 0.0440, 0.01970, 0.01013, 0.00573, and 0.00349, ~'d = 0.02820, 0.01447, 0.00817, and 0.00496. The calculations were performed by using the originally developed code GSCF3 [18,22] on a MIPS RS3330 workstation.
2. Methods The experiments were carried out on a 10 m grazing incidence monochromator [17] in the undulator beamline BL-2B at the Photon Factory (KEK-PF). Monochromatized photons were focused onto an effusive beam of the CH3F gas. For the total electronyield measurement the photon band pass was = 60 meV and the electrons emitted were collected by a channeltron. The photon energy scale was calibrated against some absorption lines of CH 4 and CF4 [10]. For the electron energy analysis the photon band pass was = 0.6 eV and a 10 cm hemispherical electron spectrometer mounted at the magic angle against the direction of polarization of the incident light and was operated in the constant pass-energy mode of 30 eV; the electron energy resolution was = 0.7 eV. The intensity of the electron energy spectra was normalized for the incident photon intensity and the sample gas pressure. The lowest C ls excited state was obtained directly by an ab initio SCF calculation with explicit consideration of the core hole. The lowest SCF solution corresponded to the C ls ~ trc" F al valence excited state. To avoid spurious mixing between valence and Rydberg orbitals, the relaxed HartreeFock potential for the C ls ionized state was obtained by a partial SCF calculation [18] within the orbital manifold orthogonalized with the crc*_F SCF orbital, and subsequently the C ls--* Rydberg excited states were obtained with the IVO method [14] using the relaxed but orthogonalized potential [19]. Primitive basis functions were taken from (73/7) and (6) contracted Gaussian-type functions of Huzinaga et al. [20]. They were augmented with d-type polarization functions for C: ~a = 1.335 and 0.288. The contraction schemes were (4111111/31111/ l* 1") for C, (721/511) for F, and (411) for H. The innermost 2s exponent for C was changed to 1.04773 from 5.15800. The basis set proposed by Kaufmann et al. [21] was used to describe 3s-4s, 3p-4p, and 3d-4d Rydberg orbitals: ~'s = 0.075, 0.02530,
3. Results and discussion
3.1. Photoabsorption spectrum Fig. 1 shows the high-resolution electron-yield spectrum in the C ls threshold region of CH3F. Table 1 shows the energies of peaks observed in comparison with the calculated ones. No correspondence to feature 1 shown in Fig. 1 can be seen in the spectrum of C H 4 [9-12], but all the other features are nearly the same as in the C 1s Rydberg spectrum of CH4; in other words, the effect of the C - F bond manifests mainly in feature 1. It is most probable to assign feature 1 to the C ls excitation to the C - F antibonding (Crc_F) orbital [15,16]. As previously discussed [9], the C - H antibonding (cr~_ H) states in CH 4 are located above the ionization threshold and are smeared out in the continuum. It is reasonable that the cry_ F state is located below the ionization threshold because the electron affinity level of F is rather low (3.399 eV for F, 1.263 eV for C, 0.754 eV for H) and the N - F bond between F and the coreequivalent atom is much weaker than the N - H bond. Hitchcock and Brion [15,16] showed that the C ls excitations to the cry_ x orbitals are clearly observed below the Rydberg band in CH3CI, CH3Br and CH3I and claimed that the the C ls excitation to the try_ F orbital should be observed as the lowest absorption band by extrapolating linear correlations [23] in the methyl halides between the C ls ionization potentials and respective transition energies. The CH3F molecule belongs to the C3v symmetry. The t2-symmetry orbitals in the Ta symmetry are split into the an-symmetry and e-symmetry orbitals in the C3v symmetry. When the C - F bond is set on the z axis, the trc*_F orbital has the a t symmetry along the z axis and the trc'_ H orbital with the e symmetry is on the xy plane. This means that contributions from the C - F bond are dominant in the a 1 manifold. Feature 1 corresponds to the try_ r a n state.
N. Kosugi et al. / Chemical Physics Letters 246 (1995) 475-480 ,,,,i,,
,,i,
,,,i,,,,i,
,,,i
,,,,i,,,,,
,,,,
i,,,,i,,,,i,,,,i,,,
n=3 II I
,i,,,,
4 I
5 I
I
Vl'3V2
[~l~J
3
n=3
.
II
4 5 I
I
v~.~ v z •-
c.¢"
288
289
:
290
I
I npal, nde
I
~borg
4
13sa' :'/
287
I ....
I
6I 91 I 291
292
l 293
294
PHOTON ENERGY (eV)
Fig. 1. High-resolution electron-yield spectrum of CH3F in the C ls threshold region measured at the photon energy resolution of -- 60 meV. The C ls ~ npe and npa I + nde Rydberg series are clearly identified as well as C l s ~ t r ~ _ F a I. The vibrational excitations are also identified, where J'L3 denotes the C - F stretching vibration (u I) and symmetrical CH 3 bending vibration (1)3), and v 2 is the C - H stretching vibration.
On the other hand, the cry_a e state is located above the threshold, though some parts of them are probably mixed with the Rydberg states similarly to the case of c a 4 [9]. Feature 1 shows a broad absorption band, indicating that the N - F bond is weak but is still repulsive.
477
As shown in Table 1, the term value (T) of feature 2 is nearly the same as that of the lowest peak observed in CH 4, where the latter peak is assigned to the dipole-forbidden C ls a I ~ 3 s a 1 Rydberg transition in the Td symmetry but has its intensity through vibronic couplings [24-26], in other words, through geometry distortions allowing the mixture of dipole-allowed valence states. In CH3F with the C3v symmetry, the C ls ai ~ 3sa~ excitation is dipole-allowed by itself, but its intensity should arise from dipole-allowed p components hybridized with the 3s orbital. Hitchcock and Brion [15] noticed that feature 2 is stronger than the 3s a l Rydberg peak in C H 4 and explained this by the lower symmetry in CH3F. In other words, valence contribution is larger in the 3s a~ orbital in CH3F. It is reasonable that the valence mixing in the 3s a] orbital arises from the trc*_F a~ orbital related to feature 1. The npe (Px, P y ) a n d nde (dxy, dx2_y2) Rydberg series on the xy plane of CH3F are related to the npt 2 and ndt 2 Rydberg series in C H 4. Above the 3s Rydberg band, peaks 3, 9 and 11 are assigned to the 3pe, 4pe and 5pe Rydberg states with quantum defects ( 8 ) of 0.79-0.85, corresponding to the C ls ~ 3pt 2, 4pt 2 and 5pt 2 Rydberg states of CH 4 with 8 = 0.74-0.76 [9]. On the other hand, peaks 6,
Table 1 Assignments of the excited states in the C ls absorption spectrum shown in Fig. 1. Transition energies Eexcit (eV, uncertainties of 4-0.05 eV), term values Texpt and Tcalc (eV), effective principal quantum numbers n*, and oscillator strengths fcatc No.
ECx¢it
T~,q,, a ( n * )
Tcalc ( n ' )
f¢.1¢
Assignment b
1 2 3 4 5 6
289.08 289.57 290.46 290.58 290.87 291.44
4.32 (1.77) 3.83 (1.88) 2.94 (2.15) 2.82 (2.19) 2.53 (2.32) 1.96 (2.63)
4.06 (1.83) 3.76 (1.91) 2.72 (2.24)
0.05206 0.00067 0.00454
o'~_ F a] 3s a, 3pc
7 8 9 10
291.56 291.86 292.08 292.36
1.84 (2.72) 1.54 (2.97) 1.32 (3.21) 1.04 (3.62)
11 12
292.62 292.77
0.78 (4.18) 0.63 (4.65)
+ v~(v3) + 1)2 1.72 (2.81) 1.69 (2.83)
0.00243 0.00172
3de ~pa I + ul(v 3) + v2
1.28 0.96 0.93 0.72
(3.27) (3.77) (3.82) (4.36)
0.00172 0.00126 0.00086 0.00082
4pe 4de 4pa, 5pe 5de, 5pa,
a The ionization potential is 293.40 eV, estimated by extrapolating the npe Rydberg series. b In the C ls spectrum of CH 4, the term values (eV) and effective quantum numbers (in parentheses) are 3.66 (1.93), 2.72 (2.24), and 2.04 (2.58) for 3sa] + vib., 3pt 2, and 3dt 2, respectively [9]. The orbital symmetries in CH3F are as follows: npa I along the z axis ( C - F bond), npe along the x or y axis, nde on the xy plane (CH3). Peak 8 might have additional contributions from 3da I (z2), 3de (xz, yz) and 4s a I.
478
N. Kosugi et al. / Chemical Physics Letters 246 (1995) 475-480
10 and 12 are assigned to the 3de, 4de and 5de Rydberg states with 8 = 0.35-0.38, corresponding to the C ls ~ 3dt 2, 4dt 2 and 5dt 2 Rydberg states of C H 4 with 8 = 0.42-0.45 [9]. In the previous assignments of the methyl halides [15,16] the C ls ~ ndt 2 Rydberg series was completely missing, considering that usually 8 - - 0 . 0 for nd Rydberg series; instead Hitchcock and Brion [15,16] assigned peak 6 to the 3pa~ Rydberg state. Robin [27] firstly pointed out that the C ! s ~ 3d Rydberg excited state is observable with a large term value (i.e. small effective principal quantum number n* or large 8) in CH 4. Koch and Peyerimhoff [28] predicted theoretically that the 3dt 2 Rydberg state with 8 --~0.4 (n* = 2.6) has a transition probability comparable to the 3pt 2 Rydberg state in CH 4. Very recently the present authors have shown experimentally and theoretically that the C ls ---, ndt 2 Rydberg series is observed for not only 3dt 2 but also 4dt 2 and 5dt 2 in C H 4 [9]. The similarity in the spectral feature between CH 4 and CH3F confirms the present assignment of the npe and nde Rydberg series in CH3F. Peaks 4, 5, 7 and 8 are not yet assigned. But these are easily assigned to the vibrational structures accompanying the two strong Rydberg transitions, 3p (peak 3) and 3d (peak 6), by comparing with the C H 4 spectrum [9]. The vibrational spacings observed are as follows: AE3. 4 = 0.12, AE6. 7 = 0.12, AE3, 5 = 0.41, and AE6. 8 = 0.42 eV. In the ground state of CH3F, the vibrational spacings for ~q(C-F stretching mode), v2(C-H stretching mode), and t, 3 (symmetrical CH 3 bending mode) are 130, 363, and 182 meV, respectively. Therefore, peak 4 and peak 7 are assigned to the z,1 (or)'3) vibrational excitation, and peak 5 and peak 8 are assigned to the 1'2 vibrational excitation. Considering that the spacing of the C - H stretching vibration is increased by 11% in the C 1s excited state of CH 4 [9], it is reasonable that the spacing for the ~'2 mode is increased by 13% in CH3F.
3.2. Theoretical predictions In the previous section the features observed for CH3F are assigned to the C ls ~ trc_ F a 1 (z), 3s a 1, npe (Px, Py) and nde (dxy , dx2_yz) transitions and their vibrational levels, where the z axis is set along the C - F bond. As shown in Table 1, the present
theoretical calculations confirm these assignments which are based on the comparison with the spectra of CH 4. However, the npa) (Pz) and nda 1 (dz2) transitions are not yet assigned. The npa I (Pz) and nda 1 (dz2) orbitals can be related to the dipoleallowed npt 2 and ndt 2 Rydberg orbitals in C H 4 but are greatly modified by the C - F bond in CH3F. The trc_ F a 1 (z) excited state takes part in precursors for the npa I (Pz) Rydberg series, and the npa 1 (pz) Rydberg states are orthogonalized to the try_ F al state. Therefore, it is expected that npa I (Pz) Rydberg states have smaller term values than the npe (Px, Py) Rydberg states. The calculations predict that the npa 1 (Pz) Rydberg states have nearly the same term values ( A E = 0.03 eV) as the nde (dxr, dx2_y2) Rydberg states, but these two Rydberg series are not mixed with each other due to different symmetries. It might be an evidence of 3pa~ and 3de Rydberg states that peak 6 has a shoulder in the lower energy side. The assignments by Hitchcock and Brion [15,16] and by Robin [27] were correct regarding the position of the 3pal Rydberg state, though Hitchcock and Brion missed the nd Rydberg series and Robin assigned the 3d Rydberg state to the higher energy. On the other hand, the calculations predict that the term value (T) = 1.389 eV (n* = 3.13) and the oscillator strength ( f ) = 0.0003 for the 3da I (dz2) Rydberg state, indicating that the 3da~ Rydberg orbital is hybridized with neither 3pa~ Rydberg nor trc_ H a~. It should be noted that the trc_ H t 2 orbital of CH 4 is d-type rather than p-type in C H 4 and nd Rydberg orbitals are hybridized with the trc*_H orbital as well as np Rydberg orbitals [9]. In addition to the nde (dxy, dx2_r2) Rydberg series observed strongly, there is another nde Rydberg series on the xz and yz plane (dxz, dyz) of CH3F. Since this corresponds to the dipole-forbidden nde Rydberg series in CH 4, it is expected that the nde (dxz, dy z) Rydberg series is very weak in CH3F. The calculations predict that T = 1.434 eV ( n * = 3.08) and f = 0.0004 for the 3de (dxz, dr z) Rydberg state. These nd Rydberg transitions are weak and the results are not shown in Table 1. But it might be possible that the 3da~ (dz~)+ 3de (dxz, dy z) Rydberg transitions contribute to peak 8. Hitchcock and Brion [16] cited the unpublished work by Schwarz and Meinhart and showed that their single particle calculations, which were based
N. Kosugi et al. / Chemical Physics Letters 246 (1995) 475-480
on the equivalent ionic core virtual orbital model, predicted the existence of only one orbital of mixed Rydberg-valence character but their preliminary multiconfigurational calculations predicted the existence of two closely spaced electronic transitions in the lower energy region (features 1 and 2 as shown in Fig. 1). The present calculations are also based on the single particle approximation, but have predicted the existence of two closely spaced electronic transitions: (r~_ F a~ and 3sa~. In the present calculations the Rydberg manifold is orthogonalized with the ~C-F al SCF orbital. This procedure is essential to avoid spurious mixing between Rydberg and valence orbitals and to ensure the orthogonalization between the core-to-valence and core-to-Rydberg states as demonstrated in the O 1s excited states of 02 [7,19]. In the single particle calculations by Schwarz and Meinhart (see Ref. [16]) spurious mixing between Rydberg and valence orbitals caused wrong assignments to the 3p and 3d Rydberg states as well as the 3s Rydberg state.
3.3. Resonance Auger spectra Fig. 2 shows the on-resonance electron spectra following the C ls --* (r~_ F a~ (peak 1), 3pe (peak 3), and 3pa I + 3de (peak 6) excitations and the off-resonance photoelectron spectrum (bottom). The normal Auger spectrum excited by photons at energy of 294 eV is also given for comparison (top). The on-resonance spectra in Fig. 2 are shown in the form of difference spectra in which the off-resonance reference spectrum was subtracted from the raw onresonance spectra. The resonance enhancement of the photoelectron bands following participant Auger decays is observed in addition to the satellite bands following spectator Auger decays, whose overall profile is similar to the normal Auger band. The participant-to-total Auger decay ratios IpA are obtained as = 1 5 % for C l s ~ G r c _ F a 1, = 5 % for C ls ~ 3pe, and = 1% for C ls ~ 3pa I + 3de. The participant Auger decay occurs as a result of the interaction involving an excited electron and valence electrons, whereas the spectator Auger decay occurs as a result of the interaction involving two valence electrons. The smaller IpA values for C ls ~ 3pe and C l s ~ 3 p a l + 3 d e than for C l s - ) c r ~ _ F a 1 indicate that the interaction between the Rydberg and
479
DIP = I (C K) - KE (eV) 40 60 80
20
100
120
hv=294eV 4
-,.'~;; ~ ) •
2
a b o v e I (C K) •
normal Auger
° 0
I
~
¢
"~ 0 >I-
.,~a¢;
5
1
I hv=291.5eV
3pa. 3de
~.'~:~. "~,.~1,..~..~L_
- .
'
I
I hv=290.5eV
/~.
z~ lo
0
,
J
5 e-
',
3pe
~
i
i
,
i
,,.
hv=289.1 eV
~'i
* Ge_~l)
) PlUmp 3 P4 .._,; :1 r ~ . ~ . ~ , . , . . . . 20 40
, 60
--- I hv=287eV 9ff resollance 80 100 120
IP = hv - KE (eV) Fig. 2. E l e c t r o n s p e c t r a o f C H 3 F e x c i t e d b y p h o t o n s t u n e d to o f f - r e s o n a n c e (hv = 2 8 7 eV), C Is ~ (r~_ F a I (hv = 289.1 eV), C l s ~ 3pe(hv = 2 9 0 . 5 eV), C l s ~ 3 p a I + 3 d e ( h v = 2 9 1 . 5 eV), a n d a b o v e - t h r e s h o l d (hv = 2 9 4 eV), m e a s u r e d at the p h o t o n e n e r g y r e s o l u t i o n o f = 0.6 eV. T h e o f f - r e s o n a n c e a n d r e s o n a n c e A u g e r s p e c t r a are p l o t t e d a g a i n s t the i o n i z a t i o n p o t e n t i a l IP = hv - K E a n d the n o r m a l A u g e r s p e c t r u m is p l o t t e d a g a i n s t the d o u b l e i o n i z a t i o n potential D I P = I(CK)- KE, w h e r e l(CK)= 293.40 eV.
valence electrons is less contributive than the interaction between the (r~_ F and valence electrons. The present observation for the 3p and 3d Rydberg states is consistent with the previous observation for CH 4, where the IpA values for the 3s, 3p, and 3d Rydberg states are less than 5.5% [9]. It should be noted also in Fig. 2 that the different photoelectron bands are enhanced by the different excitations; that is, P2 and P3 are enhanced the by C ls ~ (rC*_F al excitation while P1 and P2 are enhanced by the C ls --* 3pe excitation. The electron configuration of the ground state of CH3F is (lal) 2(2al)2(3al)2(4al)2(le)4(5al)2(2e) 4. P1 is the 2e -I photoelectron band, P2 corresponds to both the 5a[ i and le-1 bands, and P3 is the 4a[ 1 band [29]. The 2e and 4a I orbitals are of -rr (pseudo) and trc_ H bonding characters, the 5a I orbital is of trc_ F bond-
480
N. Kosugi et al. / Chemical Physics Letters 246 (1995) 475-480
ing character, and the le orbital is of w-type nonbonding F character. The observed selectivity of the participant decay channels indicates that the electron excited in the a I (e) orbital interacts with the valence electrons of the same symmetry, a I (e), more effectively than with the valence electrons of the different symmetry, e (a~). By using this characteristic it might be possible to separate the 5a~-1 and le -1 bands overlapped in the same energy region in higher resolution Auger electron spectra.
Acknowledgement The present authors are grateful to Professor A. Yagishita and Professor Y. Azuma of KEK-PF for their help during the experiment. This experiment was carded out with the approval of the Photon Factory Program Advisory Committee (Proposal No. 94-168).
References [1] C.T. Chen, Y. Ma, and F. Sette, Phys. Rev. A 40 (1989) 6737. [2] M. Domke, C. Xue, A. Puschmann, T. Mandel, E. Hudson, D.A. Shirley and G. Kaindl, Chem. Phys. Letters 173 (1990) 122; 174 (1990) 668(E). [3] G. Remmers, M. Domke, A. Puschmann, T. Mandel, C. Xue, G. Kaindl, E. Hudson and D.A. Shirley, Phys. Rev. A 46 (1992) 3935. [4] E. Hudson, D.A. Shirley, M. Domke, G. Remmers, A. Puschmann, T. Mandel, C. Xue and G. Kaindl, Phys. Rev. A 47 (1993) 361. [5] G. Returners, M. Domke and G. Kaindl, Phys. Rev. A 47 (1993) 3085. [6] J. Schirmer, A.B. Trofimov, K.J. Randall, J. Feldhaus, A.M. Bradshaw, Y. Ma, C.T. Chen and F. Sette, Phys. Rev. A 47 (1993) 1136. [7] A. Yagishita, E. Shigemasa and N. Kosugi, Phys. Rev. Letters 72 (1994) 3961.
[8] J. Adachi, N. Kosugi, E. Shigemasa and A. Yagishita, J. Chem. Phys. 102 (1995) 7369. [9] K. Ueda, M. Okunishi, H. Chiba, Y. Shimizu, K. Ohmori, Y. Sato, E. Shigemasa and N. Kosugi, Chem. Phys. Letters 236 (1995) 311. [10] M. Tronc, G.C. King, R.C. Bradford and F.H. Read, J. Phys. B 9 (1976) L555; M. Tronc, G.C. King and F.H. Read, J. Phys. B 12 (1979) 137. [11] J. Schirmer, A.B. Trofimov, K.J. Randall, J. Feldhaus, A.M. Bradshaw, Y. Ma, C.T. Chen and F. Sette, Phys. Rev. A 47 (1993) 1136. [12] G. Remmers, M. Domke and G. Kaindl, Phys. Rev. A 47 (1993) 3085. [13] L. Ungier and T.D. Thomas, J. Chem. Phys. 82 (1985) 3146. [14] W.J. Hunt and W.A. Goddard III, Chem. Phys. Letters 3 (1969) 414. [15] A.P. Hitchcock and C.E. Brion, J. Electron. Spectry. 13 (1978) 193. [16] A.P. Hitchcock and C.E. Brion, J. Electron. Spectry. 17 (1979) 139. [17] A. Yagishita, S. Masui, T. Toyoshima, H. Maezawa and E. Shigemasa, Rev. Sci. Instrum. 63 (1992) 1351. [18] N. Kosugi and H. Kuroda, Chem. Phys. Letters 74 (1980) 490. [19] N. Kosugi, E. Shigemasa and A. Yagishita, Chem. Phys. Letters 190 (1992) 481. [20] S. Huzinaga, J. Andzelm, M. Klobukowski, E. RadzioAndzelm, Y. Sasaki and H. Tatewaki, Gaussian basis sets for molecular calculations (Elsevier, Amsterdam, 1984). [21] K. Kaufmann, Ch. Nager and M. Jungen, Chem. Phys. 95 (1985) 385. [22] N. Kosugi, Theoret. Chim. Acta 72 (1987) 149. [23] P. Hochmann, P.H. Templet, H.-t. Wang and S.P. McGlynn, J. Chem. Phys. 62 (1975) 2588. [24] G.R. Wight and C.E. Brion, J. Electron. Spectry. 4 (1974) 25. [25] P.S. Bagus, M. Krauss and R.E. LaVilla, Chem. Phys. Letters 23 (1973) 13. [26] A.P. Hitchcock, M. Pocock and C.E. Brion, Chem. Phys. Letters 49 (1977) 125. [27] M.B. Robin, Higher excited states of polyatomic molecules, Vol. III (Academic Press, New York, 1985) p. 88, p. 124. [28] A. Koch and S.D. Peyerimhoff, Chem. Phys. Letters 195 (1992) 104. [29] A.W. Ports, H.J. Lempka, D.G. Streets and W.C. Price, Phil. Trans. Roy. Soc. London A 268 (1970) 59.
CHEMICAL PHYSICS LETTERS
ELSEVIER
Chemical PhysicsLetters 246 (1995) 475-480
Rydberg and valence states in the C Is photoabsorption and resonance Auger spectra of CH 3F N. Kosugi a, K. Ueda b, y. Shimizu b, H. Chiba h, M. Okunishi b, K. Ohmori b, Y. Sato h, E. Shigemasa c a Institute for Molecular Science, Myodaiji, Okazaki 444, Japan b Research Institute for Scientific Measurements, Tohoku University, Sendai 980-77, Japan c Photon Factory, National Laboratory for High Energy Physics, Tsukuba 305, Japan
Received 21 August1995;in final form 15 September 1995
Abstract
Comparison of the high-resolution C ls electron-yield spectrum of CH3F with that of CH 4 reveals that the trc_ F state manifests in a broad and strong feature below the 3s Rydberg band and all the other features are nearly the same as in CH 4. This is supported by improved virtual orbital calculations using the relaxed core-hole potential and avoiding spurious mixing between Rydberg and valence states. In the resonance Auger electron spectra the participant Auger decay rate following the cry_r excitation, -- 15%, is much larger than that of the Rydberg excitations, 1-5%.
1. Introduction
Recent progress in high-resolution inner-shell spectroscopy enables us to study molecular vibrational spectroscopy even in the inner-shell energy region [1,2]. Recent work [3-9] has opened up clear evidence of vibronic coupling and Rydberg-valence mixing in inner-sheU spectroscopy as well as in valence-shell spectroscopy. For example, high-resolution C ls excitation spectra of CH 4 show the C ls ~ 3pt 2 Rydberg transition [10-12] with complicated features on the higher energy side and weak features on the lower energy side. Those features were discussed by relating to vibronic coupling, Jahn-Teller splitting, and Rydberg-valence mixing; however, those were not consistently interpreted until recently. The present authors have successfully assigned those structures based on the resonance Auger electron spectra [13] and ab initio improved
virtual orbital (IVO) calculations [14] using the relaxed Hartree-Fock potential for the ionized state; furthermore, they have shown that the participant and spectator Auger decays following the C 1s excitations are correlated with the character of excited states: valence or Rydberg, because the participant decay rate becomes smaller as the orbital occupied by an excited electron becomes more delocalized [9]. It is expected that comparison of the C ls spectra of CH3F with those of CH 4 brings us a definite and consistent interpretation of complicated features observed for the two molecules; the similarity arises from the CH 3 component and the difference arises from the C - F bond. In CH3F it is important to resolve a conflict between the experimental and theoretical interpretations on the locations of the 3s Rydberg state and the valence state of the C - F antibonding (try_ F) character [15,16]. The purpose of the present work is to characterize the C ls excited
0009-2614/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0009-2614(95)01 121-8
476
N. Kosugi et al. / Chemical Physics Letters 246 (1995) 475-480
states in the photoabsorption spectrum of CH3F and to investigate the Rydberg and valence states based on the same approaches as in the previous work on the C I s photoabsorption spectrum of CH 4 [9].
0.01141, 0.00589, and 0.00334, ~'p = 0.0440, 0.01970, 0.01013, 0.00573, and 0.00349, ~'d = 0.02820, 0.01447, 0.00817, and 0.00496. The calculations were performed by using the originally developed code GSCF3 [18,22] on a MIPS RS3330 workstation.
2. Methods The experiments were carried out on a 10 m grazing incidence monochromator [17] in the undulator beamline BL-2B at the Photon Factory (KEK-PF). Monochromatized photons were focused onto an effusive beam of the CH3F gas. For the total electronyield measurement the photon band pass was = 60 meV and the electrons emitted were collected by a channeltron. The photon energy scale was calibrated against some absorption lines of CH 4 and CF4 [10]. For the electron energy analysis the photon band pass was = 0.6 eV and a 10 cm hemispherical electron spectrometer mounted at the magic angle against the direction of polarization of the incident light and was operated in the constant pass-energy mode of 30 eV; the electron energy resolution was = 0.7 eV. The intensity of the electron energy spectra was normalized for the incident photon intensity and the sample gas pressure. The lowest C ls excited state was obtained directly by an ab initio SCF calculation with explicit consideration of the core hole. The lowest SCF solution corresponded to the C ls ~ trc" F al valence excited state. To avoid spurious mixing between valence and Rydberg orbitals, the relaxed HartreeFock potential for the C ls ionized state was obtained by a partial SCF calculation [18] within the orbital manifold orthogonalized with the crc*_F SCF orbital, and subsequently the C ls--* Rydberg excited states were obtained with the IVO method [14] using the relaxed but orthogonalized potential [19]. Primitive basis functions were taken from (73/7) and (6) contracted Gaussian-type functions of Huzinaga et al. [20]. They were augmented with d-type polarization functions for C: ~a = 1.335 and 0.288. The contraction schemes were (4111111/31111/ l* 1") for C, (721/511) for F, and (411) for H. The innermost 2s exponent for C was changed to 1.04773 from 5.15800. The basis set proposed by Kaufmann et al. [21] was used to describe 3s-4s, 3p-4p, and 3d-4d Rydberg orbitals: ~'s = 0.075, 0.02530,
3. Results and discussion
3.1. Photoabsorption spectrum Fig. 1 shows the high-resolution electron-yield spectrum in the C ls threshold region of CH3F. Table 1 shows the energies of peaks observed in comparison with the calculated ones. No correspondence to feature 1 shown in Fig. 1 can be seen in the spectrum of C H 4 [9-12], but all the other features are nearly the same as in the C 1s Rydberg spectrum of CH4; in other words, the effect of the C - F bond manifests mainly in feature 1. It is most probable to assign feature 1 to the C ls excitation to the C - F antibonding (Crc_F) orbital [15,16]. As previously discussed [9], the C - H antibonding (cr~_ H) states in CH 4 are located above the ionization threshold and are smeared out in the continuum. It is reasonable that the cry_ F state is located below the ionization threshold because the electron affinity level of F is rather low (3.399 eV for F, 1.263 eV for C, 0.754 eV for H) and the N - F bond between F and the coreequivalent atom is much weaker than the N - H bond. Hitchcock and Brion [15,16] showed that the C ls excitations to the cry_ x orbitals are clearly observed below the Rydberg band in CH3CI, CH3Br and CH3I and claimed that the the C ls excitation to the try_ F orbital should be observed as the lowest absorption band by extrapolating linear correlations [23] in the methyl halides between the C ls ionization potentials and respective transition energies. The CH3F molecule belongs to the C3v symmetry. The t2-symmetry orbitals in the Ta symmetry are split into the an-symmetry and e-symmetry orbitals in the C3v symmetry. When the C - F bond is set on the z axis, the trc*_F orbital has the a t symmetry along the z axis and the trc'_ H orbital with the e symmetry is on the xy plane. This means that contributions from the C - F bond are dominant in the a 1 manifold. Feature 1 corresponds to the try_ r a n state.
N. Kosugi et al. / Chemical Physics Letters 246 (1995) 475-480 ,,,,i,,
,,i,
,,,i,,,,i,
,,,i
,,,,i,,,,,
,,,,
i,,,,i,,,,i,,,,i,,,
n=3 II I
,i,,,,
4 I
5 I
I
Vl'3V2
[~l~J
3
n=3
.
II
4 5 I
I
v~.~ v z •-
c.¢"
288
289
:
290
I
I npal, nde
I
~borg
4
13sa' :'/
287
I ....
I
6I 91 I 291
292
l 293
294
PHOTON ENERGY (eV)
Fig. 1. High-resolution electron-yield spectrum of CH3F in the C ls threshold region measured at the photon energy resolution of -- 60 meV. The C ls ~ npe and npa I + nde Rydberg series are clearly identified as well as C l s ~ t r ~ _ F a I. The vibrational excitations are also identified, where J'L3 denotes the C - F stretching vibration (u I) and symmetrical CH 3 bending vibration (1)3), and v 2 is the C - H stretching vibration.
On the other hand, the cry_a e state is located above the threshold, though some parts of them are probably mixed with the Rydberg states similarly to the case of c a 4 [9]. Feature 1 shows a broad absorption band, indicating that the N - F bond is weak but is still repulsive.
477
As shown in Table 1, the term value (T) of feature 2 is nearly the same as that of the lowest peak observed in CH 4, where the latter peak is assigned to the dipole-forbidden C ls a I ~ 3 s a 1 Rydberg transition in the Td symmetry but has its intensity through vibronic couplings [24-26], in other words, through geometry distortions allowing the mixture of dipole-allowed valence states. In CH3F with the C3v symmetry, the C ls ai ~ 3sa~ excitation is dipole-allowed by itself, but its intensity should arise from dipole-allowed p components hybridized with the 3s orbital. Hitchcock and Brion [15] noticed that feature 2 is stronger than the 3s a l Rydberg peak in C H 4 and explained this by the lower symmetry in CH3F. In other words, valence contribution is larger in the 3s a~ orbital in CH3F. It is reasonable that the valence mixing in the 3s a] orbital arises from the trc*_F a~ orbital related to feature 1. The npe (Px, P y ) a n d nde (dxy, dx2_y2) Rydberg series on the xy plane of CH3F are related to the npt 2 and ndt 2 Rydberg series in C H 4. Above the 3s Rydberg band, peaks 3, 9 and 11 are assigned to the 3pe, 4pe and 5pe Rydberg states with quantum defects ( 8 ) of 0.79-0.85, corresponding to the C ls ~ 3pt 2, 4pt 2 and 5pt 2 Rydberg states of CH 4 with 8 = 0.74-0.76 [9]. On the other hand, peaks 6,
Table 1 Assignments of the excited states in the C ls absorption spectrum shown in Fig. 1. Transition energies Eexcit (eV, uncertainties of 4-0.05 eV), term values Texpt and Tcalc (eV), effective principal quantum numbers n*, and oscillator strengths fcatc No.
ECx¢it
T~,q,, a ( n * )
Tcalc ( n ' )
f¢.1¢
Assignment b
1 2 3 4 5 6
289.08 289.57 290.46 290.58 290.87 291.44
4.32 (1.77) 3.83 (1.88) 2.94 (2.15) 2.82 (2.19) 2.53 (2.32) 1.96 (2.63)
4.06 (1.83) 3.76 (1.91) 2.72 (2.24)
0.05206 0.00067 0.00454
o'~_ F a] 3s a, 3pc
7 8 9 10
291.56 291.86 292.08 292.36
1.84 (2.72) 1.54 (2.97) 1.32 (3.21) 1.04 (3.62)
11 12
292.62 292.77
0.78 (4.18) 0.63 (4.65)
+ v~(v3) + 1)2 1.72 (2.81) 1.69 (2.83)
0.00243 0.00172
3de ~pa I + ul(v 3) + v2
1.28 0.96 0.93 0.72
(3.27) (3.77) (3.82) (4.36)
0.00172 0.00126 0.00086 0.00082
4pe 4de 4pa, 5pe 5de, 5pa,
a The ionization potential is 293.40 eV, estimated by extrapolating the npe Rydberg series. b In the C ls spectrum of CH 4, the term values (eV) and effective quantum numbers (in parentheses) are 3.66 (1.93), 2.72 (2.24), and 2.04 (2.58) for 3sa] + vib., 3pt 2, and 3dt 2, respectively [9]. The orbital symmetries in CH3F are as follows: npa I along the z axis ( C - F bond), npe along the x or y axis, nde on the xy plane (CH3). Peak 8 might have additional contributions from 3da I (z2), 3de (xz, yz) and 4s a I.
478
N. Kosugi et al. / Chemical Physics Letters 246 (1995) 475-480
10 and 12 are assigned to the 3de, 4de and 5de Rydberg states with 8 = 0.35-0.38, corresponding to the C ls ~ 3dt 2, 4dt 2 and 5dt 2 Rydberg states of C H 4 with 8 = 0.42-0.45 [9]. In the previous assignments of the methyl halides [15,16] the C ls ~ ndt 2 Rydberg series was completely missing, considering that usually 8 - - 0 . 0 for nd Rydberg series; instead Hitchcock and Brion [15,16] assigned peak 6 to the 3pa~ Rydberg state. Robin [27] firstly pointed out that the C ! s ~ 3d Rydberg excited state is observable with a large term value (i.e. small effective principal quantum number n* or large 8) in CH 4. Koch and Peyerimhoff [28] predicted theoretically that the 3dt 2 Rydberg state with 8 --~0.4 (n* = 2.6) has a transition probability comparable to the 3pt 2 Rydberg state in CH 4. Very recently the present authors have shown experimentally and theoretically that the C ls ---, ndt 2 Rydberg series is observed for not only 3dt 2 but also 4dt 2 and 5dt 2 in C H 4 [9]. The similarity in the spectral feature between CH 4 and CH3F confirms the present assignment of the npe and nde Rydberg series in CH3F. Peaks 4, 5, 7 and 8 are not yet assigned. But these are easily assigned to the vibrational structures accompanying the two strong Rydberg transitions, 3p (peak 3) and 3d (peak 6), by comparing with the C H 4 spectrum [9]. The vibrational spacings observed are as follows: AE3. 4 = 0.12, AE6. 7 = 0.12, AE3, 5 = 0.41, and AE6. 8 = 0.42 eV. In the ground state of CH3F, the vibrational spacings for ~q(C-F stretching mode), v2(C-H stretching mode), and t, 3 (symmetrical CH 3 bending mode) are 130, 363, and 182 meV, respectively. Therefore, peak 4 and peak 7 are assigned to the z,1 (or)'3) vibrational excitation, and peak 5 and peak 8 are assigned to the 1'2 vibrational excitation. Considering that the spacing of the C - H stretching vibration is increased by 11% in the C 1s excited state of CH 4 [9], it is reasonable that the spacing for the ~'2 mode is increased by 13% in CH3F.
3.2. Theoretical predictions In the previous section the features observed for CH3F are assigned to the C ls ~ trc_ F a 1 (z), 3s a 1, npe (Px, Py) and nde (dxy , dx2_yz) transitions and their vibrational levels, where the z axis is set along the C - F bond. As shown in Table 1, the present
theoretical calculations confirm these assignments which are based on the comparison with the spectra of CH 4. However, the npa) (Pz) and nda 1 (dz2) transitions are not yet assigned. The npa I (Pz) and nda 1 (dz2) orbitals can be related to the dipoleallowed npt 2 and ndt 2 Rydberg orbitals in C H 4 but are greatly modified by the C - F bond in CH3F. The trc_ F a 1 (z) excited state takes part in precursors for the npa I (Pz) Rydberg series, and the npa 1 (pz) Rydberg states are orthogonalized to the try_ F al state. Therefore, it is expected that npa I (Pz) Rydberg states have smaller term values than the npe (Px, Py) Rydberg states. The calculations predict that the npa 1 (Pz) Rydberg states have nearly the same term values ( A E = 0.03 eV) as the nde (dxr, dx2_y2) Rydberg states, but these two Rydberg series are not mixed with each other due to different symmetries. It might be an evidence of 3pa~ and 3de Rydberg states that peak 6 has a shoulder in the lower energy side. The assignments by Hitchcock and Brion [15,16] and by Robin [27] were correct regarding the position of the 3pal Rydberg state, though Hitchcock and Brion missed the nd Rydberg series and Robin assigned the 3d Rydberg state to the higher energy. On the other hand, the calculations predict that the term value (T) = 1.389 eV (n* = 3.13) and the oscillator strength ( f ) = 0.0003 for the 3da I (dz2) Rydberg state, indicating that the 3da~ Rydberg orbital is hybridized with neither 3pa~ Rydberg nor trc_ H a~. It should be noted that the trc_ H t 2 orbital of CH 4 is d-type rather than p-type in C H 4 and nd Rydberg orbitals are hybridized with the trc*_H orbital as well as np Rydberg orbitals [9]. In addition to the nde (dxy, dx2_r2) Rydberg series observed strongly, there is another nde Rydberg series on the xz and yz plane (dxz, dyz) of CH3F. Since this corresponds to the dipole-forbidden nde Rydberg series in CH 4, it is expected that the nde (dxz, dy z) Rydberg series is very weak in CH3F. The calculations predict that T = 1.434 eV ( n * = 3.08) and f = 0.0004 for the 3de (dxz, dr z) Rydberg state. These nd Rydberg transitions are weak and the results are not shown in Table 1. But it might be possible that the 3da~ (dz~)+ 3de (dxz, dy z) Rydberg transitions contribute to peak 8. Hitchcock and Brion [16] cited the unpublished work by Schwarz and Meinhart and showed that their single particle calculations, which were based
N. Kosugi et al. / Chemical Physics Letters 246 (1995) 475-480
on the equivalent ionic core virtual orbital model, predicted the existence of only one orbital of mixed Rydberg-valence character but their preliminary multiconfigurational calculations predicted the existence of two closely spaced electronic transitions in the lower energy region (features 1 and 2 as shown in Fig. 1). The present calculations are also based on the single particle approximation, but have predicted the existence of two closely spaced electronic transitions: (r~_ F a~ and 3sa~. In the present calculations the Rydberg manifold is orthogonalized with the ~C-F al SCF orbital. This procedure is essential to avoid spurious mixing between Rydberg and valence orbitals and to ensure the orthogonalization between the core-to-valence and core-to-Rydberg states as demonstrated in the O 1s excited states of 02 [7,19]. In the single particle calculations by Schwarz and Meinhart (see Ref. [16]) spurious mixing between Rydberg and valence orbitals caused wrong assignments to the 3p and 3d Rydberg states as well as the 3s Rydberg state.
3.3. Resonance Auger spectra Fig. 2 shows the on-resonance electron spectra following the C ls --* (r~_ F a~ (peak 1), 3pe (peak 3), and 3pa I + 3de (peak 6) excitations and the off-resonance photoelectron spectrum (bottom). The normal Auger spectrum excited by photons at energy of 294 eV is also given for comparison (top). The on-resonance spectra in Fig. 2 are shown in the form of difference spectra in which the off-resonance reference spectrum was subtracted from the raw onresonance spectra. The resonance enhancement of the photoelectron bands following participant Auger decays is observed in addition to the satellite bands following spectator Auger decays, whose overall profile is similar to the normal Auger band. The participant-to-total Auger decay ratios IpA are obtained as = 1 5 % for C l s ~ G r c _ F a 1, = 5 % for C ls ~ 3pe, and = 1% for C ls ~ 3pa I + 3de. The participant Auger decay occurs as a result of the interaction involving an excited electron and valence electrons, whereas the spectator Auger decay occurs as a result of the interaction involving two valence electrons. The smaller IpA values for C ls ~ 3pe and C l s ~ 3 p a l + 3 d e than for C l s - ) c r ~ _ F a 1 indicate that the interaction between the Rydberg and
479
DIP = I (C K) - KE (eV) 40 60 80
20
100
120
hv=294eV 4
-,.'~;; ~ ) •
2
a b o v e I (C K) •
normal Auger
° 0
I
~
¢
"~ 0 >I-
.,~a¢;
5
1
I hv=291.5eV
3pa. 3de
~.'~:~. "~,.~1,..~..~L_
- .
'
I
I hv=290.5eV
/~.
z~ lo
0
,
J
5 e-
',
3pe
~
i
i
,
i
,,.
hv=289.1 eV
~'i
* Ge_~l)
) PlUmp 3 P4 .._,; :1 r ~ . ~ . ~ , . , . . . . 20 40
, 60
--- I hv=287eV 9ff resollance 80 100 120
IP = hv - KE (eV) Fig. 2. E l e c t r o n s p e c t r a o f C H 3 F e x c i t e d b y p h o t o n s t u n e d to o f f - r e s o n a n c e (hv = 2 8 7 eV), C Is ~ (r~_ F a I (hv = 289.1 eV), C l s ~ 3pe(hv = 2 9 0 . 5 eV), C l s ~ 3 p a I + 3 d e ( h v = 2 9 1 . 5 eV), a n d a b o v e - t h r e s h o l d (hv = 2 9 4 eV), m e a s u r e d at the p h o t o n e n e r g y r e s o l u t i o n o f = 0.6 eV. T h e o f f - r e s o n a n c e a n d r e s o n a n c e A u g e r s p e c t r a are p l o t t e d a g a i n s t the i o n i z a t i o n p o t e n t i a l IP = hv - K E a n d the n o r m a l A u g e r s p e c t r u m is p l o t t e d a g a i n s t the d o u b l e i o n i z a t i o n potential D I P = I(CK)- KE, w h e r e l(CK)= 293.40 eV.
valence electrons is less contributive than the interaction between the (r~_ F and valence electrons. The present observation for the 3p and 3d Rydberg states is consistent with the previous observation for CH 4, where the IpA values for the 3s, 3p, and 3d Rydberg states are less than 5.5% [9]. It should be noted also in Fig. 2 that the different photoelectron bands are enhanced by the different excitations; that is, P2 and P3 are enhanced the by C ls ~ (rC*_F al excitation while P1 and P2 are enhanced by the C ls --* 3pe excitation. The electron configuration of the ground state of CH3F is (lal) 2(2al)2(3al)2(4al)2(le)4(5al)2(2e) 4. P1 is the 2e -I photoelectron band, P2 corresponds to both the 5a[ i and le-1 bands, and P3 is the 4a[ 1 band [29]. The 2e and 4a I orbitals are of -rr (pseudo) and trc_ H bonding characters, the 5a I orbital is of trc_ F bond-
480
N. Kosugi et al. / Chemical Physics Letters 246 (1995) 475-480
ing character, and the le orbital is of w-type nonbonding F character. The observed selectivity of the participant decay channels indicates that the electron excited in the a I (e) orbital interacts with the valence electrons of the same symmetry, a I (e), more effectively than with the valence electrons of the different symmetry, e (a~). By using this characteristic it might be possible to separate the 5a~-1 and le -1 bands overlapped in the same energy region in higher resolution Auger electron spectra.
Acknowledgement The present authors are grateful to Professor A. Yagishita and Professor Y. Azuma of KEK-PF for their help during the experiment. This experiment was carded out with the approval of the Photon Factory Program Advisory Committee (Proposal No. 94-168).
References [1] C.T. Chen, Y. Ma, and F. Sette, Phys. Rev. A 40 (1989) 6737. [2] M. Domke, C. Xue, A. Puschmann, T. Mandel, E. Hudson, D.A. Shirley and G. Kaindl, Chem. Phys. Letters 173 (1990) 122; 174 (1990) 668(E). [3] G. Remmers, M. Domke, A. Puschmann, T. Mandel, C. Xue, G. Kaindl, E. Hudson and D.A. Shirley, Phys. Rev. A 46 (1992) 3935. [4] E. Hudson, D.A. Shirley, M. Domke, G. Remmers, A. Puschmann, T. Mandel, C. Xue and G. Kaindl, Phys. Rev. A 47 (1993) 361. [5] G. Returners, M. Domke and G. Kaindl, Phys. Rev. A 47 (1993) 3085. [6] J. Schirmer, A.B. Trofimov, K.J. Randall, J. Feldhaus, A.M. Bradshaw, Y. Ma, C.T. Chen and F. Sette, Phys. Rev. A 47 (1993) 1136. [7] A. Yagishita, E. Shigemasa and N. Kosugi, Phys. Rev. Letters 72 (1994) 3961.
[8] J. Adachi, N. Kosugi, E. Shigemasa and A. Yagishita, J. Chem. Phys. 102 (1995) 7369. [9] K. Ueda, M. Okunishi, H. Chiba, Y. Shimizu, K. Ohmori, Y. Sato, E. Shigemasa and N. Kosugi, Chem. Phys. Letters 236 (1995) 311. [10] M. Tronc, G.C. King, R.C. Bradford and F.H. Read, J. Phys. B 9 (1976) L555; M. Tronc, G.C. King and F.H. Read, J. Phys. B 12 (1979) 137. [11] J. Schirmer, A.B. Trofimov, K.J. Randall, J. Feldhaus, A.M. Bradshaw, Y. Ma, C.T. Chen and F. Sette, Phys. Rev. A 47 (1993) 1136. [12] G. Remmers, M. Domke and G. Kaindl, Phys. Rev. A 47 (1993) 3085. [13] L. Ungier and T.D. Thomas, J. Chem. Phys. 82 (1985) 3146. [14] W.J. Hunt and W.A. Goddard III, Chem. Phys. Letters 3 (1969) 414. [15] A.P. Hitchcock and C.E. Brion, J. Electron. Spectry. 13 (1978) 193. [16] A.P. Hitchcock and C.E. Brion, J. Electron. Spectry. 17 (1979) 139. [17] A. Yagishita, S. Masui, T. Toyoshima, H. Maezawa and E. Shigemasa, Rev. Sci. Instrum. 63 (1992) 1351. [18] N. Kosugi and H. Kuroda, Chem. Phys. Letters 74 (1980) 490. [19] N. Kosugi, E. Shigemasa and A. Yagishita, Chem. Phys. Letters 190 (1992) 481. [20] S. Huzinaga, J. Andzelm, M. Klobukowski, E. RadzioAndzelm, Y. Sasaki and H. Tatewaki, Gaussian basis sets for molecular calculations (Elsevier, Amsterdam, 1984). [21] K. Kaufmann, Ch. Nager and M. Jungen, Chem. Phys. 95 (1985) 385. [22] N. Kosugi, Theoret. Chim. Acta 72 (1987) 149. [23] P. Hochmann, P.H. Templet, H.-t. Wang and S.P. McGlynn, J. Chem. Phys. 62 (1975) 2588. [24] G.R. Wight and C.E. Brion, J. Electron. Spectry. 4 (1974) 25. [25] P.S. Bagus, M. Krauss and R.E. LaVilla, Chem. Phys. Letters 23 (1973) 13. [26] A.P. Hitchcock, M. Pocock and C.E. Brion, Chem. Phys. Letters 49 (1977) 125. [27] M.B. Robin, Higher excited states of polyatomic molecules, Vol. III (Academic Press, New York, 1985) p. 88, p. 124. [28] A. Koch and S.D. Peyerimhoff, Chem. Phys. Letters 195 (1992) 104. [29] A.W. Ports, H.J. Lempka, D.G. Streets and W.C. Price, Phil. Trans. Roy. Soc. London A 268 (1970) 59.