Chemical
Physics
ELSEVIER
Chemical Physics 192 (1995) 333-353
An experimental and theoretical study of the valence shell
photoelectron spectrum of sulphur hexafluoride
D.M.P. Holland a, M.A. MacDonald a, P. Baltzer b, L. Karlsson b, M. Lundqvist b,
B. Wannberg b, W. von Niessen c
a SERC Daresbury Laboratory, Daresbury, Warrington, Cheshire, WA4 4AD, UK
b Uppsala University, Department of Physics, Box 530, S-751 21 Uppsala, Sweden
c Institutfiir Physikalische und Theoretische Chemie der Technischen Universiti~t, D-38106, Braunschweig, Germany
Received 25 July 1994
Abstract
The complete valence shell photoelectron spectrum of sulphur hexafluoride has been studied using Hell and synchrotron
radiation. The high resolution HelI excited spectrum has allowed a detailed analysis to be made of the vibrational structure
exhibited in the photoelectron bands associated with ionisation from the outer valence orbitals. New vibrational structure has
been observed in the C 2E8 and the F 2A~ photoelectron bands. The spectra recorded with synchrotron radiation demonstrate
that shape resonance phenomena affect the photoionisation dynamics, and clear evidence is provided for both the t2g and the eg
shape resonances. However, the results show that photoelectrons associated with gerade symmetry orbitals also exhibit resonant
behaviour, and this is discussed in terms of interchannel coupling and the possibility that the t~u shape resonance might occur
above threshold for valence shell ionisation. An essentially structureless photoelectron intensity distribution is observed throughout the entire region for binding energies greater than 25 eV, and this suggests a strong coupling to continuum states. A
perturbative Green's function method has been employed to evaluate the ionisation energies and pole strengths associated with
the six outermost molecular orbitals, and the results show an improved agreement with the experimental values.
1. Introduction
Sulphur hexafluoride provides perhaps the clearest
example of shape resonance phenomena affecting the
photoabsorption spectra of inner valence and core level
molecular orbitals. Many investigations have been performed to measure the absorption spectra in the energy
regions encompassing the S Is, S 2s and 2p, and the
F ls thresholds, and these studies have shown that the
spectra are dominated by a few intense and broad features, occurring both above and below the ionisation
threshold. This is accompanied by a drastic reduction
in intensity for structure associated with Rydberg transitions. Originally, Nefedov [1] and Dehmer [2] dis0301-0104/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved
S S D I 0 3 0 1 - 0 1 0 4 ( 9 4 ) 0 0 3 8 1-5
cussed this anomalous intensity distribution for
cage-like molecules in which a central atom is surrounded by a shell of electronegative atoms. A barrier,
formed in the effective molecular potential near the
electronegative ligands, partitions the states into either
inner-well or outer-well states, localised in different
regions of space. The virtual valence orbitals, located
within the inner well, have a strong overlap with the
initial state and this results in enhanced intervalence
spectral features. In contrast, the overlap between the
initial state and a Rydberg orbital is poor because Rydberg orbitals are located in the outer well. Hence, low
spectral intensities are associated with Rydberg transitions. In addition, the potential barrier can support
334
D.M.P. Holland et al. / Chemical Physics 192 (1995) 333-353
inner-well, valence states which lie above the ionisation
threshold and an electron excited into one of these
quasi-stationary states will be temporarily trapped by
the barrier before escaping into the continuum. More
recently, shape resonance phenomena have been
observed in many molecules not containing a cage of
electronegative ligands. Consequently, Dill and Dehmer [3] have presented a more general theoretical
approach in which the excited electron is temporarily
trapped by the anisotropic molecular field. In certain
well-defined energy ranges, resonant scattering of the
excited electron leads to an enhancement in specific
outgoing partial wave channels.
The potential barrier concept has proved extremely
successful in interpreting the major spectral features
observed in the vicinity of the K and L edges of SF 6
[4-17]. The assignment of these features, based upon
evidence from X-ray emission experiments [ 9,18,19 ]
and theoretical predictions of the ground state molecular orbital configuration [20-27], has been discussed
by Dehmer [ 2 ]. Four shape resonances have been identified, with the alg and the hu resonances occurring
below the ionisation threshold, and the t2g and the eg
resonances lying in the continuum. The major features
have been interpreted within the independent electron
approximation by applying dipole selection rules to
identify which molecular orbitals may couple to specific shape resonantly enhanced channels. However,
even for the K and L shell absorption spectra, some
weak structure was observed which could not be interpreted within this model. Dehmer [2] suggested that
these dipole forbidden features might be due to vibronically induced transitions, and more recently Ferrett et
al. [28] have suggested that two of the weak peaks
lying above the sulphur I s threshold are associated with
multielectron transitions. Nevertheless, although some
small uncertainties still need to be resolved, the description of the core shell absorption spectra in terms of a
potential barrier model is generally successful.
The interpretation of the absorption spectrum corresponding to excitation from the outer valence molecular orbitals is not so well established [8,15,29-35].
As with the core level absorption spectrum, all the
prominent structure observed in the outer valence
region may be attributed to intervalence transitions.
The two most recent interpretations have been carried
out by Sze and Brion [ 15] and by Mitsuke et al. [34]
using a term value analysis. In both cases it was
assumed that the 6alg and the 6hu states lay below the
ionisation threshold, and the 2t2g and the 4eg states
occurred in the continuum. For the most part the assignments of the two analyses are in good accord. In the
ion-pair formation work of Mitsuke et al. it was
observed that the strongest peaks in the F - efficiency
curve coincided with transitions into Rydberg states.
Thus, their spectra facilitated the identification of structure associated with Rydberg transitions. Mitsuke et al.
give term values varying between 3.8 and 4.4 eV for
transitions from the valence orbitals into the 6tlu state,
with the corresponding values from Sze and Brion varying between 3.5 and 4.4 eV.
Three previous gas phase [36-38] and one condensed phase [ 39 ] photoelectron spectroscopy studies
have been performed using synchrotron radiation to
measure the partial cross sections [ 36-39] and photoelectron angular distributions [37] for the outer
valence orbitals. Although some of the results can be
explained by applying a one-electron, shape resonance
model, several well-documented difficulties remain.
Little evidence has been found of the resonance predicted to occur in the eg channel. In contrast, the t2g
resonance appears to influence both dipole allowed and
dipole forbidden channels. These anomalies have been
discussed in terms of continuum-continuum coupling
by Dehmer et al. [ 37 ], whilst Addison-Jones et al. [ 38 ]
have suggested that the resonance in the hu channel
might be shifted above the ionisation threshold for transitions involving the outer valence orbitals.
Dehmer et al. have emphasised that interpreting the
shape resonance effects in valence shell spectra
depends upon establishing the ground state molecular
orbital configuration. This issue has attracted considerable attention in the past because photoelectron spectra [36-38,40--44] have revealed six peaks with
binding energies less than 30 eV, whereas ionisation
from seven molecular orbitals should be possible in this
energy range. Thus, one of the peaks must contain
contributions from two valence levels. This assignment
problem has been discussed in considerable detail [ 2124,36-38,40--44], and in the present work the molecular orbital sequence suggested by Dehmer et al. [37]
has been adopted. Thus, in octahedral symmetry, Oh,
the ground state configuration for the valence levels
may be written as
D.M.P. Holland et al. /Chemical Physics 192 (1995) 333-353
(4a~g) (3t6u) (2e 4) (5a~Zg)(4t6u) (lt6g) 4
6
(3eg)
( lt2u,
5t6u) (lt6g)
lAlg,
with the four lowest lying virtual valence orbitals being
(6alg) (6hu) (2t2g) (4%).
The present experimental and theoretical study of
the complete valence shell photoelectron spectrum of
sulphur hexafluoride has been undertaken to examine
several key issues. Firstly, synchrotron radiation has
been used to measure photoelectron spectra of the entire
valence region to obtain branching ratios and angular
distributions up to a photon energy of 120 eV. These
spectra enable shape resonance phenomena affecting
the outer valence orbitals to be examined. Furthermore,
inner valence transitions due to ionisation from the 4al g,
3t~u and 2% orbitals have been studied. Secondly, high
resolution HeII excited photoelectron spectra have
been recorded so that a full analysis of the vibrational
structure associated with ionisation from the outer
valence orbitals may be performed. This is important
because it provides detailed information regarding the
potential surfaces of the electronic states. Such knowledge is useful both in the assignment of the spectrum
and to draw conclusions about dissociation mechanisms and pathways. Previous experimental studies
have indicated that two of the photoelectron bands may
be affected by Jabn-Teller distortion. Indeed, some of
the early confusion concerning the ground state molecular orbital sequence was caused by one ofo the peaks
appearing as a doublet when excited at 584 A. Thirdly,
ionisation energies and pole strengths for the six outermost molecular orbitals have been calculated by
applying a perturbative Green's function approach.
2. Experimental procedure
2.1. Synchrotron radiation studies
The photoelectron spectra were recorded using a
hemispherical electron energy analyser and synchrotron radiation emitted by the Daresbury Laboratory
storage ring. Detailed descriptions of the design and
performance of the monochromator [45,46 ], the electron spectrometer [47], and the experimental procedure [48] have been reported previously, so only a
brief account will be given.
335
A toroidal grating monochromator was used to produce
monochromatic radiation in the 17-120 eV photon
energy range with a bandwidth which was varied from
about 50 meV at 17 eV to 150 meV at 120 eV. The
hemispherical electron energy analyser could be
rotated about an axis which coincided with the photon
beam, thus enabling photoelectron angular distributions to be measured. As the radiation from the monochromator was elliptically polarised, the differential
cross section in the dipole approximation, assuming
randomly oriented target molecules and electron analysis in a plane perpendicular to the photon propagation
direction, can be expressed in the form [49]
d°"
°'t°~( 1+ /3
)
d--~ = 4rr
~(3Pcos20+l)
,
where/3 is the photoelectron asymmetry parameter, 0
is the photoelectron ejection angle relative to the major
polarisation axis, and P is the polarisation of the incident radiation. At each photon energy, photoelectron
spectra were recorded at 0 = 0 ° and 0=90 °, thus
allowing the angular distribution parameter to be determined once the polarisation had been deduced. The
transmission efficiency of the analyser was determined
by monitoring the total electron count as a function of
photon energy, and hence photoelectron energy, for an
inert gas. Argon photoelectron spectra were recorded
for electron energies varying from approximately
threshold to 130 eV. By combining these results with
the total absorption cross section, and taking into
account the contributions from higher order radiation
[ 46], the transmission efficiency of the analyser could
be evaluated. Fig. 1 shows a spectrum recorded at
0= 0 ° with a photon energy of 110 eV. The spectra
were analysed by dividing the binding energy range
into the regions specified in Table 1. The error bars
shown in Figs. 2 and 4 arise from a combination of the
statistical error, and a possible systematic error due to
uncertainties in the analyser transmission efficiency
and the polarisation of the incident radiation.
2.2. Hell excited spectra
The Hell excited photoelectron spectra were
recorded in Uppsala on a high resolution spectrometer
that has been described recently [50]. It incorporates
a hemispherical electrostatic energy analyser with a
mean radius of 144 mm. Ionisation of the sample takes
336
D.M.P. Holland et al. / Chemical Physics 192 (1995) 333-353
X 2Tlg
A,B 2Tlu, 2T2u
SF6+
hv = 110 eV
E 2Tlu
D z'l'2g
C 2Eg
o
13.
F 2Alg
15
210
215
30
35
410
45
50
51fi 610
iS
Bindingenergy(eV)
Fig. I. A photoelectronspectrum of SF~ recorded at a photon energy of 110 eV.
place in a gas cell and the photoelectrons enter into the
analyser via a slit system and an electron lens. The
electrons are detected by a microchannel plate system
incorporating a phosphor screen to transform the electron pulses to light pulses that are read by a CCD camera. The signals are read and stored by a personal
computer connected on-line.
Resonance radiation from a discharge in helium is
used for the photoionisation. The radiation is generated
by a microwave powered ECR source [51], which
gives a very high intensity both of HeI and HelI radiation and a narrow linewidth ( < 1 meV).
The sample gas was commercially obtained with a
purity of better than 99%, and a pressure of a few mTorr
Table 1
Energy regions used in the analysis of the photoelectron spectra
recorded with synchrotron radiation
Region
Energy range (eV)
Encompassed states
1
2
3
4
5
6
7
8
9
!0
14.90-16.35
16.35-17.90
17.90-19.10
19.10-20.90
21.90-23.50
26.20-27.60
27.60-35.90
35.90-42.80
42.80~6.00
46.00-49.00
X
A,B
C
D
E
F
was used during recording of the spectra. A small
amount of krypton was mixed with the sample gas for
the purpose of energy calibration of the spectra. The
energies used for the Kr 4PI/2,3/2lines were 14.6657
eV and 13.9998 eV, respectively.By this means, an
accuracy of better than I m e V is obtained for welldefined linesin the spectrum.
3. Computational methods and technical details
The calculations on SF6 were performed using an S F distance of 2.9484 a.u. and the SCF calculation was
carried out with the program system MOLCAS [52].
Three basis sets were employed in the present work, all
of which derive from the atomic natural orbital (ANO)
basis set of Widmark et al. For the F atom it is
[14s9p5d3f] [53] and for the S atom it is
[ 17s12p5d4f] [54]. Different contractions were chosen for different purposes. The smallest contracted
basis set, denoted basis A, was (4s2p 1d) on the F atoms
and (6s4pld) on the S atom. The next contraction,
basis B, was (5s3pld) on the F atoms and (7s5p2d)
on the S atom, and finally, basis C, was for a contraction
of (6s4p2dlf) on the F atoms and (7s5p2dlf) on the
S atom. The total SCF energy obtained during basis C
was - 994.373606 au.
337
D.M.P. Holland et al. / Chemical Physics 192 (1995) 333-353
The ionisation energies and their pole strengths,
which are a measure of the relative intensities, were
calculated with many-body Green's function methods
which include the effects of electron correlation. For
all the valence levels, including the satellite lines, the
ADC (3) approach (third order algebraic diagrammatic
construction) was employed [55]. It has been shown
that the ionic main states are treated accurately to third
order in the electron-electron interaction in this
method, whereas states dominated by two-hole-oneparticle excited configurations (satellite lines) are
treated accurately only to first order in the interaction.
Empirically it has been found that the first few satellite
states are reasonably well described by the ADC(3)
method, but that the descriptions of the higher states
are only semi-quantitative. This is especially the case
when the density of satellite lines is very high. Another
deficiency is associated with the choice of basis set.
Although the ANO basis set is quite an extended one,
it lacks Rydberg type functions to describe the Rydberg
series converging onto the double ionisation threshold.
For these specific reasons, but also quite generally for
large molecules such as SF6, quantitative results cannot
be expected in the inner valence region. The ADC(3)
approach employs a multiroot Davidson diagonalisation method [56] and about 200 solutions were
extracted for each symmetry from matrices of dimension up to 16000. However, this approach breaks down
at higher energies where a very large number of states
was found having zero pole strength. This occurred far
below the threshold for F 2s ionisation. A pole search
diagonalisation approach [57], which makes use of
extensive configuration selection, and which is therefore less reliable, was employed to obtain the higher
energy states. These results are taken from a previous
calculation [58].
For the ADC(3) calculations basis A was used,
because, if the larger basis set had been employed, we
would have been unable to extract a sufficient number
of satellite lines. However, this basis set is inadequate
for giving quantitative results for the outer valence ionisation energies. Electron correlation effects are
extremely strong in SF6 as can be seen from the shifts
in ionisation energies obtained using the Koopmans'
approximation compared to the values obtained from
the Green's function technique. Furthermore, the large
number of electrons to be correlated on the F atoms
requires a large basis set. For these reasons, in the
Table2
The resultsfromthe OVGFcalculation
Orbital
lonisationenergy(eV)
Pole strength
ltlg
5t~u
lt2u
3eg
lt2g
4tlu
16.02
17.26
17.34
18.40
20.14
22.85
0.91
0.92
0.91
0.92
0.91
0.91
calculation of the outer valence ionisation energies
another, perturbative Green's function method was
employed, the so-called outer valence Green's function
(OVGF) method [59,60]. In these calculations, all
diagrams are taken into account which appear up to the
third order in the electron-electron interaction, together
with normalisation terms which take into account
higher order corrections in an approximate manner. For
the OVGF calculations described by Weigold et al.
[58] bases B and C were employed. However, an additional calculation has now been performed using a
larger basis set of (7s5p2dlf) on the F atoms and
(6s4p2dlf) on the S atom. The new results are presented in Table 2.
4. Results and discussion
4.1. Synchrotron radiation studies
4.1.1. The overall spectrum
Photoelectron spectra were recorded using synchrotron radiation for excitation energies between 17 and
120 eV, and Fig. 1 shows a spectrum measured at 110
eV which encompasses the 14.5 to 67 eV binding
energy region. At low binding energies six photoelectron bands are clearly discernible and are associated
with ionisation from the seven outermost molecular
orbitals. The bands correspond well with the configuration (5a2g) (4t6,) (lt6g) (3eg4) (lt6u,5t6u) (lt6g),
where a combination of the lt2u and the 5tlu orbitals is
assumed to be responsible for the second photoelectron
band. These bands have been recorded at high resolution using HelI excitation, and a detailed analysis of
the vibrational structure is presented in Section 4.2.
The ionisation energies and pole strengths associated
with the six outermost valence orbitals, reported in
338
D.M.P. Holland et al. /Chemical Physics 192 (1995)333-353
Table 2, are in better accord with the experimental
values than were the previous results [58]. Thus, in
the outer valence region the interpretation of the photoelectron spectrum is relatively straight forward and
good agreement is achieved between experiment and
theory. At higher binding energies a complex band
structure is observed in the 38-46 eV range which may
be associated with ionisation from the (4a2g) (3t6~)
(2e~) molecular orbitals which are mainly formed
from the F 2s atomic orbitals.
In addition to the features discussed above, a more
or less continuous underlying intensity is apparent,
extending from about 25 eV to the high energy limit of
the spectrum. This intensity is present in all spectra and
can be seen clearly even in the range of the band at 26.8
eV recorded with HeII radiation (see Section 4.2).
Thus, this is not a background caused by the spectrometers, but a true intensity related to photoelectron transitions in S F 6. Weak features associated with
many-electron states are often observed in inner
valence photoelectron spectra at binding energies
above approximately 20 eV, and the intensity discernible in the present spectra below the threshold for the
Auger process is most likely of similar origin. However, the observation of a continuous intensity distribution is unusual and suggests that, in this case, the
many-electron states form an essentially continuous
repulsive potential surface in the Franck-Condon
region. This surface could be formed, in part, through
strong vibronic interactions mixing together the electronic states. Above the Auger threshold, shake-off
processes may also lead to a continuous intensity distribution.
4.1.2. Outer valence orbitals
The results are presented in the form of photoelectron
intensity branching ratios and angular distributions.
The branching ratio is defined as the intensity in a
particular region divided by the sum of intensities in
all the energetically accessible regions. For photon
energies less than 60 eV, photoelectron spectra were
recorded for binding energies between 14.5 and 29 eV,
a range which encompasses the strong peaks corresponding to ionisation from the X-F electronic states,
but not the weak structure associated with the inner
valence orbitals. Trial spectra showed that the intensities of the inner valence features were very small for
photon energies less than 60 eV. For photon energies
greater than 60 eV the highest photoelectron binding
energy was increased to 49 eV. As a consequence, the
branching ratios presented in Fig. 2 show a step at a
photon energy of 60 eV. Furthermore, as the intensity
associated with the inner valence structure increased
very slowly with excitation energy, any uncertainty in
the background subtraction resulted in a considerable
change in the branching ratios for regions 7-10. Thus
some caution should be exercised in assessing the
results for these regions for photon energies close to 60
eV.
Branching ratios have been measured previously by
Gustafsson [36] for photon energies up to 54 eV, by
Dehmer et al. [37] up to 30 eV, and by Addison-Jones
et al. [38] up to 100 eV. The present results display
the same general characteristics as observed in previous
studies, although some small quantitative discrepancies
are apparent. However, as the discussion and interpretation of the data are primarily dependent upon the
overall trends, small differences are of less concern. In
order to obtain the absolute photoionisation partial
cross sections for regions 1-6, the branching ratios for
these regions have been combined with the absolute
total photoionisation cross section measured by Holland et al. [35] for photon energies up to 26 eV. The
absolute photoabsorption cross sections recorded by
Lee et al. [31] and by Vinogradov and Zimkina [7]
have been used at higher energies. The resulting absolute partial cross sections are presented in Fig. 3, to
facilitate comparison with previous experimental and
theoretical results. Analysis of the absorption spectra
due to excitation from the K and L shells reveals that,
of the four features attributed to shape resonances,
those corresponding with the atg and the t~u resonances
are located approximately 8 and 4.5 eV below threshold, respectively, and those associated with the t2g and
the eg resonances occur approximately 3 and 15 eV
above threshold, respectively. The term values quoted
are approximate averages of the values given by Sze
and Brion [ 15]. An interpretation of the valence shell
photoionisation dynamics within a model combining
dipole selection rules with the independent electron
approximation would allow only orbitals of ungerade
symmetry to access the t2g and the eg shape resonances.
However, as previous investigators have noted [ 3639], the t2g shape resonance appears to influence not
only the lt2u, 5t~ and the 4t~u dipole allowed orbitals,
but also the 1t2g and the 3eg orbitals where it is dipole
339
D.M.P. Holland et al. / Chemical Physics 192 (1995) 333-353
O.OE
10
SF6* X 2Tlg
~I~
Region 1
0.6
02
2Alg
F
0.03
i~ }ttttttttlt}
0.00
t2g eg
t2,~ eg
Region 6
it
~ttt{ttttt
!
!
I
t
!
l
08-
I
i
I
0.06
A,B 2T1u,2T2u
~
04-
Region 2
#I~ llllil{lll
0.03,
{
1
~
t2ff eg
00-
I
I
I
!
I
0.00,
0.2'
t
0.1.
016~ l
I
t
I
tttttttttt t
Region 3
t2g eg
Ii
I
l
I
l
'
~
0.08,
I
'
tttttt t
0.1
I
3.04 •
Region 9
Region 4
t2g eg
I
0.2
I
O.00
!
t
I
I
40
3.02 -
Region 5
Region 10
t2g eg
20
tit t
I
3.04 •
~ttt~ttt{ t
I
-
I
E 2Tlu
0.1
0.0
Region 8
tttttttttttt
D 2T2g
lllll
0.0
tttttt
0.0,
I
0.2
I
ttt tt
rn
i
Region 7
C 2Eg
Z 0.08-
0.00
llllllllill
i
~0
dO
I;o
i~o
3.00 -
2'0
4%
60
80
160
1~0
Photon energy (eV)
Fig. 2. Photoelectron intensity branching ratios of SF 6 associated with the various energy regions specified in Table 1. The branching ratio is
defined as the intensity in a particular region divided by the sum of intensities in all the energetically accessible regions.
340
D.M.P. Holland et al. I Chemical Physics 192 (1995) 333-353
60
!0.
SF6+ X 2Tlg
D 2T2g
30
I0-
IIllIl~o~
O
'8
} ttI'F
0
70
I
It
I
o F i ~l
u
o~,
!
I
0 •
15"
!
I
t
!
!
I
O
A,B 2Tlu, 2T2u
E 2Tlu
10"
35
5"
t
O
"5
"5
o
0
0I
I
20
<
I
I
I
it '
C 2Eg
I
I
10
!
I
F 2Alg
I
2'0
4'0
do
120
2'O
8'0
120
Photon energy (eV)
Fig. 3. Absolute photoionisation partial cross sections for energy regions 1-6 of the photoelectron spectrum of SF6.
forbidden within the independent electron approximation. Furthermore, the valence shell branching ratios
reported by Gustafsson [ 36] provided little evidence
for the eg shape resonance. However, in the more recent
study performed by Addison-Jones et al. [ 38 ], features
appeared in the valence shell branching ratios which
were attributed to the eg shape resonance.
Against this background, the present electronic state
branching ratios and photoelectron angular distributions shown in Figs. 2 and 4 provide firm evidence for
both the t2g and the eg shape resonances affecting the
valence shell.photoionisation dynamics. Nevertheless,
the interpretation of the results is not without difficulty.
For regions 1-6, the positions of the t~gand the eg shape
resonances are marked on the figures, irrespective of
whether transitions into these channels are dipole
allowed or forbidden. The positions have been esti-
mated by using reasonable averages of the valence shell
term values given by Sze and Brion [ 15] and by Mitsuke et al. [34]. The values used were 5.2 and 15.5 eV
for the t28 and the eg channels, respectively, and for
convenience the results are summarised in Table 3.
Fig. 4 shows that the asymmetry parameters for the
X, (A, B), C and D states all pass through a very
distinct minimum around h v = 22-23 eV. A somewhat
similar behaviour was observed by Dehmer et al. [ 37 ].
Although their measurements were restricted to photon
energies less than 30 eV, in the region of overlap the
agreement between the two sets of data is very good.
However, the present results illustrate that the asymmetry parameters for the C and the D states exhibit
further structure at higher photon energies which
appears to correlate with the location of the eg shape
resonance. The asymmetry parameter for the C state
D.M.P. Holland et al. / Chemical Physics 192 (1995) 333-353
1.8.
1.2
1.8,
t2g eg
t2g
tto0tttt
1.2-
tttt
0.8
SF6+ X 2Tlg
Region1
N
i
1.2
i
I
Region6
101.2- ,
I
i
i
!
3.8-
A,B 2Tlu,2T2u
Region2
i
iiiiiiii I tt
li~l
~/~
0.0
1.2-
F 2Alg
).4-
i Crtttt~tt{~
0.4
E
I
t2g eg
0.8
•
~tttttttt t~ttt
).8-
0.4 ~|/
0.0
eg
341
3.4.
t
{I~1~}
Region7
0.0 ..1
I
I
!
t2g eg
!
,
tt{ttt ttt
e~
o..
~, 0.8EE
>, 0.4
i
1.2 -t
i
0.8-~
C 2Eg
i
!
t
0.4.,
Region8
Region3
0.0
o
0.0-
o
,
#_
I
,
0.8
1.2-
'
0.8-
0.4
~I{~}~}
j''
0.0
1.2
0.8
0.4-
I
I
I
1.2- '
I, ~'~tttttttt tt
0.8-
I~~R{}I~
0.4-
0.0.
4'o
~'o
8'o
100
i
tttttttttttt
Region5
t
2'o
i
E 2Tlu
i
Region9
I
'
J
0.4-
D 2T2g Region4
0.0l
IIIIIIIIIIIEI
!
I I I i I } I ~' { I I i
t2g eg ~
1.2
i
iiiiiiiii
'
0.0.
120
2'0 4'o
Photonenergy(eV)
!
!
Region10
6'o
do 1~o 12o
Fig. 4. Photoelectron angular distributions of SF o associated with the various energy regions specified in Table 1.
D.M.P. Holland et al. /Chemical Physics 192 (1995) 333-353
le 3
mated positions of the t2g and the eg shape resonances, irrespecof whether transitions into particular channels are dipole allowed
3rbidden
Electronic state
x 2Tig
A/B 2Tl~,2T2u
C 2Eg
D 2T2g
E 2Th,
F 2Alg
Energy location of
resonance (eV)
t2~
eg
20.7
21.9
23.2
24.5
27.9
32.0
30.9
32.1
33.4
34.7
38.1
42.2
plays two very distinct minima, at approximately 23
I 40 eV, and a local maximum around 30 eV. The
mmetry parameter for the D state shows a local
limum around 35 eV. Thus, the present results dem;trate that the influence of the eg shape resonance on
ence shell photoionisation is more clearly discerned
he photoelectron asymmetry parameters than in the
nching ratios.
Fhe interpretation of the resonant behaviour
;erved in the photoelectron angular distributions and
:tronic branching ratios in terms of shape resonances
~ends upon the energy location of the 6hu state. Most
vious interpretations have assumed that the tlu shape
onance occurs below threshold for valence shell ion:ion based upon evidence from core and inner shell
orption spectra and valence shell calculations
1,37 ]. It was first suggested by Fock and Koch [ 39 ]
t the tl~ shape resonance might be situated above
~shold for valence shell excitation. They noted that
energy locations of the shape resonances in carbon
xide showed a steady progression towards higher
etic energy in going from inner shell absorption, via
gas-phase and solid-phase valence shell absorption
I photoemission, to electron scattering on the neutral
lecule. Indeed, for electron scattering from sulphur
:afluoride, all four shape resonances have been
;erved by Kennerly et al. [ 61 ] in agreement with the
culated cross sections of Dehmer et al. [ 62 ]. Owing
differences in screening between core and valence
dl vacancies, the location of shape resonances for
ence shell excitation may shift a few eV towards
:her kinetic energy compared to core excitation locaas. For electron scattering, shifts towards higher
kinetic energy are caused by stronger coulombic repulsion. By analogy with carbon dioxide, Fock and Koch
suggested that the maximum observed close to threshold in the partial cross sections associated with gerade
orbitals, might be due to excitation into the 6hu state.
Later experimental and theoretical work by AddisonJones et al. [38] also indicated that the tlu resonance
lay in the continuum. Addison-Jones et al. calculated
the partial cross sections for the valence orbitals using
the Multiple Scattering Xc~ method with 20% overlapping spheres. They claim that molecular cross sections
calculated using this degree of overlap generally provide a better agreement with experimental data than
those employing touching spheres. However, they
emphasise that the resonance positions and cross sections are dependent on a somewhat arbitrary choice of
input parameters. Their calculations predicted that the
t2g and the eg resonances occur 8.18 and 20.42 eV,
respectively, above threshold, which is about 3 eV
higher than reported in previous theoretical work
[ 24,37 ]. Furthermore, their work indicated that the tlu
resonance occurs 2.05 eV above threshold, in contrast
to previous calculations which predicted that this resonance lay below threshold. Table 4 summarises the
predictions of the various calculations.
The positions of the resonant features in Figs. 2 and
4 coincide reasonably well with the marked locations
of the t2g and the eg shape resonances using the term
values of 5.2 and 15.5 eV, respectively. These experimentally derived values compare reasonably well with
the theoretical predictions of Levinson et al. [ 24 ], and
Dehmer et al. [ 37 ]. Incorporating the values calculated
by Addison-Jones et al. does not appear to improve the
agreement between experiment and theory. However,
the early calculations [24,37] predicted that the only
shape resonances occurring in the continuum were the
t2g and the eg, to which orbitals of gerade symmetry
Table 4
Predicted locations of shape resonancesin the photoionisationof SF6
Investigators
Levinson et al. [241
Dehmer et al. [37]
Addison-Jones et al. [ 38 ]
Resonance symmetry and
energy location
above threshold (eV)
tlu
t2g
eg
15.6
2.05
5.1
5.7
8.18
20.42
D.M.P. Holland et al. / Chemical Physics 192 (1995) 333-353
should be unable to couple within the single-electron
model. Thus the observed resonant behaviour for the
ltlg, 3% and lt2g orbitals close to threshold is difficult
to interpret. This difficulty may be overcome, if, as
proposed by Addison-Jones et al., the tlu shape resonance lies in the continuum.
An alternative interpretation, involving interchannel
coupling (either discrete-continuum or continuumcontinuum), has been suggested by Dehmer et al. [ 37]
for the observed resonant behaviour in the partial cross
sections and photoelectron angular distributions.
Examples of continuum-continuum coupling affecting
the predicted occurrences of shape resonance phenomena based upon the independent electron model, have
been reported for the (2tru) -1B 2~u+ channel in nitrogen [ 63-65 ] and the (3(r~) - 1B 2~u+ channel in carbon
dioxide [66,67]. Although the coupling between
molecular photoelectrons and residual electrons is usually weak, because continuum electrons are so diffuse
as to have negligible amplitude in the molecular interior, shape resonances provide a mechanism for trapping the electron, and thereby enhancing interchannel
coupling [63]. Consequently, resonant features may
appear in normally nonresonant channels due to shape
resonantly enhanced continuum-continuum coupling.
It is conceivable that continuum-continuum coupling provides the mechanism for transferring the shape
resonant behaviour predicted for the lt2u , 5tlu and 4tlu
orbitals into the gerade symmetry orbitals. In this manner, the minima observed in the/3 parameters for the
X, (A, B), C and D valence states in the vicinity of
22-23 eV may all be associated with the tEg shape
resonance. The influence of the higher energy, eg, shape
resonance is observed very clearly in the asymmetry
parameters for the C, D and E states. The distinct local
minima around 35 and 42 eV displayed in the/3 values
for the D and E states are probably the clearest experimental evidence of the eg shape resonance. Again, this
interpretation of the high energy features relies heavily
on the assumption of strong continuum-continuum
coupling, because neither the 3eg nor the lt2g orbital
would be able to access the eg shape resonance within
the single-electron model. Thus, in summary, it appears
that continuum-continuum coupling involving the
shape resonantly enhanced 5t~ -~ 2t2g transition might
be responsible for the minima observed in the asymmetry parameters for the X 2Tlg, the C 2Eg and the
D 2TEg states around 22-23 eV. At higher energies a
343
similar coupling mechanism, but involving a transition
from the 4tlu orbital into the eg shape resonance, might
account for the observed resonant behaviour.
The interpretation of the C state behaviour presents
additional difficulties because the asymmetry parameter for this orbital exhibits pronounced structure
throughout the energy range from threshold to approximately 50 eV. The photoelectron band associated with
ionisation from the 3eg orbital has been studied previously [36--44] and has been the subject of some controversy. At some excitation energies the band exhibits
a very distinct doublet structure, and this has variously
been interpreted as indicating that the band encompassed more than one molecular orbital, that autoionisation effects were important at certain energies, or that
the doublet resulted from Jahn-Teller distortion.
Baltzer et al. [ 68 ] have recently reinvestigated the photoelectron band corresponding to ionisation from the
3% orbital in the photon energy range between 20.0
and 22.0 eV, and strong resonant behaviour was
observed.
The general trends observed in the branching ratios
for energy regions 1-5 are in good agreement with
previous investigations [ 36-39]. However, as with the
asymmetry parameters, the interpretation is complicated by the evidence that resonance features are
observed strongly in channels predicted to be nonresonant within a single-electron model. Although it
might be possible to interpret the structure occurring a
few eV above threshold as being due to transitions into
the 6tlu state lying in the continuum, as has been suggested by Addison-Jones et al. [38], this interpretation
is more difficult to apply to the C state branching ratio
which passes through a deep minimum around 30 eV.
Another mechanism that deserves consideration is
the possibility that discrete--continuum channel coupling (autoionisation) affects the valence shell photoelectron dynamics. In the energy range of interest,
Codling [29] observed a Rydberg series attributed to
(5alg) -lnptlu. However, the series is very weak and
unlikely to exert a major influence. A strong broad peak
has been observed in the photoabsorption spectrum
around 23.4 eV [35], and has been assigned to either,
or both, of the shape resonantly enhanced intervalence
transitions 5alg --* 6tlu, and 5tlu ~ 2t2g [ 15,34]. A further prominent feature occurs at 28.2 eV [ 35 ] and has
been attributed to the shape resonantly enhanced transition 4tlu--~2tEg [15,34]. At higher energies, two
344
D.M.P. Holland et al. / Chemical Physics 192 (1995) 333-353
much weaker features have been observed at 35.8 and
45.6 eV [ 15]. Clearly, the major peak at 23.4 eV coincides almost exactly with the position of the minima
observed in the asymmetry parameters of regions 1-5.
Furthermore, some of the/3 parameters exhibit structure in the vicinity of the peak at 28.2 eV. Thus autoionisation from shape resonantly enhanced transitions
might contribute to the observed resonant behaviour.
It is apparent that theoretical guidance is now
required to obtain a proper understanding of the valence
shell photoionisation dynamics of sulphur hexafluoride. Good general agreement has been found amongst
the four experimental studies, and the photoelectron
angular distributions and electronic state branching
ratios are reasonably well established up to an energy
of 120 eV. Theoretical studies are needed to determine
whether the tlu shape resonance occurs above or below
threshold for valence shell ionisation, and also to quantify the effects of discrete-continuum and continuumcontinuum coupling.
4.1.3. I n n e r v a l e n c e o r b i t a l s
Theoretical investigations into the photoionisation
of inner valence molecular orbitals have shown that the
process is complicated, due to the breakdown of the
molecular orbital picture [ 69,70]. Thus, ionisation of
an inner valence molecular orbital no longer results in
the observation of a single band in a photoelectron
spectrum, as is usually the case for an outer valence
orbital, but rather in a multitude of photoelectron peaks
spread over an energy range of many electron volts.
This phenomenon is caused by electron correlation
allowing single-hole configurations to interact with
two-hole-one-particle-excited configurations. As a
consequence, the intensity associated with the main
band representing ionisation from a particular inner
valence orbital is reduced and redistributed amongst
several satellite peaks. Under such circumstances it is
no longer valid to describe the photoionisation process
within a SCF model of independent electrons.
In the inner valence region of sulphur hexafluoride
the photoelectron intensity should be derived from the
(4a2g), ( 3tl6u) and (2e~) molecular orbitals. Weigold
et al. [58] have performed an electron momentum
spectroscopy study on SF6 and have deduced the atomic
character of the various molecular orbitals. Their
results indicate that the 2% orbital is non-bonding with
F 2s character, the 3tl, orbital has a strong F 2s-S 3p
bonding character, and the 4alg orbital is S 3s-F 2s
bonding with some F 2p character. SCF calculations
[58] give binding energies of 44.62, 46.23 and 50.04
eV for the 2eg, 3t1, and 4alg orbitals, respectively.
These results may be compared with the binding energies of the three peaks which dominate the present inner
valence spectrum at 39.8, 40.9 and 44.1 eV. The overall
structure observed in the inner valence region is in
general agreement with that recorded by Gelius [41 ]
using X-ray excitation.
Fig. 5 shows an expanded view of the photoelectron
spectrum recorded at a photon energy of 110 eV,
together with the results of the many-body Green's
function calculations, for binding energies greater than
28 eV. The theoretical work indicates that numerous
satellite states should occur in the inner valence region
with intensity derived from the 2eg, 3t~u and 4alg molecular orbitals. The calculated ionisation energies of the
satellite states fall into three groups, with those states
deriving their pole strength from the 2% orbital occurring around 40.5 eV. A second group, associated with
the 3t~ orbital, clusters around 42.5 eV, and the final
group of satellite states, which derives its pole strength
from the 4alg orbital, lies between 44 and 49 eV. It is
apparent that although the many-body Green's function
approach predicts the overall features observed in the
inner valence region, a detailed comparison between
the experimental results and the theoretical predictions
is not feasible. The most serious discrepancy occurs at
binding energies between the 5a~g main line at 26.8 eV
and the start of the inner valence satellite states situated
around 40 eV. In this energy range only two, very weak,
satellite states are predicted to occur, both deriving their
intensity from the 5a~g orbital. However, the experimental spectrum displays a steady increase in photoelectron intensity as the binding energy increases from
the location of the 5a~g main line peak. A similar discrepancy occurs at high binding energies, where the
highest lying satellite state predicted from the Green's
function calculations falls at 50.4 eV. However, the
experimental spectrum displays significant intensity up
to a binding energy of 67 eV, the limit of the present
investigations. By measuring the momentum distribution of the intensity occurring in the 47-62 eV range,
Weigold et al. [ 58 ] concluded that most of the satellite
states situated in this region derived their pole strength
from the 4alg orbital. This energy range falls within the
shake-off region where a substantial photoelectron
D.M.P. Holland et al. / Chemical Physics 192 (1995) 333-353
345
.::.J,
SF6+
hv = 1 1 0 eV
¢1
.=_
Y
m
.... ..,:::,:::...
r
1
r
T
1
T--
4 = 5a1g
3 = 2eg
2 =3t~u
0.3-
1 = 4a lg
0.2.
2
3
o
Q_
2
1 1
2
1
0.1
2
2
0.0
11
1
1 1
1 21
1
l"-
g~
4s
,o
so
s~
Binding energy (eV)
Fig. 5. A photoelectron spectrum of SF6 recorded at a photon energy of 110 eV, encompassing the 28 to 55 eV binding energy region, together
with the pole strengths predicted by the many-body Green's function calculations.
intensity is often observed. Features occurring below
the double ionisation limit are usually due to manyelectron states which manifest themselves in much the
same way as single hole states, that is, they tend to give
rise to band structure rather than an extremely broad
structureless distribution. However, an alternative
interpretation is that some of the intensity could be due
to Auger decay. Such processes often generate very
broad continuous intensity distributions, particularly in
the case of Coster-Kronig transitions. Yet another pos-
sibility is that the potential surface inside the FranckCondon region for Auger transitions is strongly repulsive. In conclusion, both experimental studies demonstrate that numerous, low intensity, satellite states are
distributed throughout the 25-67 eV range, and that
this effect has, so far, not been successfully modelled
in the theoretical work.
The double ionisation threshold of sulphur hexafluoride has not been well established. Of the various
doubly charged fragments observed by Hitchcock and
346
D.M.P. Holland et aL / Chemical Physics 192 (1995) 333-353
2Ok-
SF 6
PES
hv=40.8eV
X-'TI~
E 2rlu
15 kF 2Alg
He Is
D ~T2g
~
l'
A -Tlu
B 2T2u
t!
C ~Eg
A!
5k-
0
30.0
I
29.0
I
28.0
I
27.0
I
26.0
I
25.0
I
24.0
I
23.0
I
22.0
I
21.0
/
20.0
I
19.0
I
18.0
1
17
16
I
15
Binding Energy leV)
Fig. 6. The Hell excited photoelectron spectrum between 15 and 30 eV. Very sharp lines that can be seen above 27 eV belong to the Kr 4s
spectrum used for calibration purposes.
Van der Wiel [33], SF42÷ had the lowest appearance
potential of 33 eV, which means that, at least down to
this energy, Auger processes are energetically possible.
Further lowering of the dication threshold energy could
be possible due to a large geometry distortion outside
the region accessible with appearance potential spectroscopy. There is no evidence in the present photoelectron spectra of features associated with doubly
ionised states.
Figs. 2 and 4 display the photoelectron intensity
branching ratios and angular distributions corresponding to energy regions 7-10 (Table 1). The branching
ratios show that the strength of the inner valence contribution, relative to that of the outer valence peaks,
increases gradually as the photon energy increases. The
angular distributions associated with regions 7-10
show little structure and all reach a/3 value around
unity at high excitation energies. We have recently
carried out a more detailed examination of the structure
occurring in the inner valence region and have observed
variations in the relative intensities of the dominant
features. This work will be the subject of a future publication.
4.2. Hell excited spectra
HelI excited spectra were recorded up to a binding
energy of 30 eV and Fig. 6 shows the full spectrum
over this region. It is similar to previously reported HelI
excited spectra but is much better resolved. It should
be noted that even in the outer valence region, HelI
excited spectra are often preferable to HeI excited spectra from one point of view, namely in the determination
of Franck-Condon factors. The reason for this is that
the relative variation in kinetic energy within a band,
and hence the variation in spectrometer transmission,
is much larger in the HeI case. Extensive vibrational
structure is present in the four photoelectron bands
observed above 18 eV. This will be discussed further
in the following sections where the details of the individual bands are presented.
The vibrational modes that may become strongly
excited are the totally symmetric vl(ag) and the two
Jahn-Teller active v2(eg) and vs(t2g) modes. The energies for these modes are [71 ] : Vl = 96.1 meV, v2 = 79.8
meV and v5 = 65.0 meV.
Fig. 7 shows the two outermost photoelectron bands
corresponding to ionisation from the lhg and
(5hu + lt2u) orbitals. As can be seen, these bands are
essentially structureless in agreement with previous
studies. The first band has an almost symmetric Gaussian shape which suggests that the potential surface
inside the Franck-Condon region has an essentially
constant slope. This agrees well with the state being
repulsive, as has been found by photoelectron-pho-
D.M.P. Holland et al. / Chemical Physics 192 (1995) 333-353
SF6
PES at 40.8 eV
347
X 2Tlg
20000-
15000-
B 2T2u A 2Tlu
0
10000-
5000-
I
I
I
I
17.5
17.0
16.5
16.0
I
15.5
Binding Energy (eV)
Fig. 7. A detail of the Hell excited spectrum of SF 6 showing the two outermost photoelectron bands corresponding to ionisation from the lhg
and ( lt2u + 5ttu) orbitals.
toion coincidence (PEPICO) spectroscopy using a
helium source [72] and in similar experiments [ 73,74]
using synchrotron radiation. The peak maximum is
observed at 15.67 eV, in good agreement with previous
results [42]. The second band exhibits a shoulder at
17.2 eV which is more pronounced than in earlier spectra. This difference is probably due to the improved
stability of the spectrometer used in the present investigation. Possibly, this shoulder shows the location of
one of the electronic states giving rise to this band. The
other state then clearly must correspond to the major
peak with maximum intensity at 16.95 eV. This gives
a splitting of around 0.25 eV between the two states.
Recent calculations consistently associate the lower
ionisation energy with the 5tlu orbital and the higher
with the l t2u orbital, and this ordering is confirmed in
the present OVGF calculation, with a predicted splitting of 0.08 eV between the two states.
Fig. 8 shows the third photoelectron band, which is
associated with ionisation from the 3eg orbital. This
band has earlier been considered structureless, except
for an apparent separation into two components in the
21 eV photon energy range, as discussed in Section
4.1.2. However, the present spectrum shows a complex
vibrational structure observable over the entire photoelectron band. The separation between the peaks is very
small, which is probably the reason why this structure
has escaped detection in previous studies. Table 5 summarises the energies of observed peak maxima and
shoulders. The structure is not very well resolved and
the spacing between the lines varies which indicates
that more than one vibrational mode may be excited.
In fact, since the electronic state is susceptible to JahnTeller interactions, all the three vibrational modes u~,
u2 and v5 may contribute significantly to the structure.
The observation of this vibrational structure shows that,
contrary to the X state, the potential surface of this state
is not repulsive in the Franck-Condon region.
Since the electronic state is doubly degenerate it may
be split by the Jahn-Teller interaction into two component states. As can be seen clearly, the top of the
band is flattened, and this may indicate a splitting
between the components of about 0.2 eV. This is consistent with a substantial geometrical instability and a
permanent lowering of the molecular symmetry. TPEPICO experiments [74] show that there is a difference
in the fragmentation pattern of SF6~ between the low
and high energy parts of this state. Below 18.4 eV the
348
D.M.P. Holland et al. / Chemical Physics 192 (1995) 333-353
Table 5
only ion observed is SF~-, while above this energy
SF2- is detected. This energy agrees well with the
expected appearance of the second Jahn-Teller component, which may indicate that the different fragmentation pathways are related to differences in the
electronic and geometric properties between the lower
and upper Jahn-Teller split component states.
The intensity at the beginning of the C state band is
very low and a 0-4) transition cannot be readily identified. The first structure that is clearly associated with
this band appears at 18.14 eV and we consider this
energy an upper limit for this transition. A former value
of 18.0 eV [42] corresponds to a very weak feature
that cannot definitely be associated with this state. The
feature might be attributable to a hot band.
The fourth photoelectron band is associated with
ionisation from the lt2g orbital. A vibrational progression has previously been observed in the HeI excited
spectrum [ 42 ] and in the present HeII excited spectrum
it is even better resolved (cf. Fig. 9). The vibrational
spacings at the beginning of the band are about 73 meV.
The rounded band shape suggests that the geometry
change upon ionisation is large. This change is
expected to be accompanied by a substantial lowering
of the vibrational energy. Thus, since the 1'2 mode has
an energy in the neutral ground state that is close to the
SF6
Energies and relative intensities for the peak maxima observed in the
3e~-~ photoelectron band of SF6 obtained from the Hell excited
spectrum
Line number
Relative intensity
(eV)
1
2
3
4
5
6
7
8
9
10
18.136
18.181
18.224
18.266
18.349
18.429
18.491
t8.558
18.601
18.638
33
48
70
88
100
99
86
85
81
74
energy of the present spectrum, it seems more likely
that the progression is in the v~ mode which would be
reduced by about 24% from the neutral ground state
energy.
The present spectrum confirms the energies obtained
in a previous study [42]. As many as 14 lines can be
observed although in the high energy part they are less
well resolved than near the beginning. An increase in
linewidth becomes obvious at about 19.7 eV. The
vibrational spacing is essentially constant (cf. Table 6)
C
PES at 40.8 cV
NXXl-
I I I
4000-
:-4"
• • .s""~,-"
"J
2Eg cationic state
I
t
. .
..2--../:',...:
...4., ¢.;~.-..,~ ".-
U
0
Energy
"'-
. ,;~,...
I
I
",k: -"
~.
,:,~
2. "°
.':,
.'~.
.,?.
2000-
.,-A
t,, t.
..~
I
I
I
I
I
I
I
I
I
I
19.1
19.0
18.9
18.8
18.7
18.6
18.5
18.4
18.3
18.2
I
18.1
Binding Energy (eV)
Fig. 8. A detail of the Hell excited spectrum of SF 6 showing the third photoelectron band associated with ionisation from the 3e~ orbital.
D.M.P. Holland et al. /Chemical Physics 192 (1995) 333-353
SF6
_I
PES at 40.8 eV
D
12
I
[
10
I
I
2T2g cationic state
4
8
I
349
I
I
I
I
2
I
I
0-0
I
I
4000o
2000-
I
I
I
I
I
I
20.6
20.4
20.2
20.0
19.8
19.6
Binding
Energy
I
19.4
I
19.2
19.0
(eV)
Fig. 9. A detail of the Hell excited spectrum of SF6 showing the fourth photoelectron band associated with ionisation from the 1t2g orbital.
over the band, which may indicate that the potential
curve has a very deep minimum along the q~ normal
coordinate. The adiabatic transition occurs at 19.237
eV and is represented by a peak that is somewhat broadened due to an overlap with the F (04)) line excited
with the HelI/3 component at 48.369 eV. The comTable 6
Energies and relative intensities for the peak maxima observed in the
lt~ ] photoelectron band of SF6 obtained from the Hell excited spectrum
Vibrational quantum number
( v] mode)
Energy
(eV)
Relative intensity
0
1
2
3
4
5
6
7
8
9
10
11
12
13
19.237
19.316
19.390
19.461
19.534
19.607
19.681
19.755
19.831
19.905
19.978
20.058
20.127
20.202
12
19
32
56
73
91
100
91
88
80
67
53
42
32
plexity in the spectrum at high energies may indicate
that the vibrational excitations in this region, to some
extent, involve other modes in addition to vl, and that
vibronic coupling takes place.
The fifth photoelectron band, associated with the
4t~ 1 (E 2Tlu) cationic state, is displayed in Fig. 10. It
shows a very distinct vibrational progression with a 0 1 spacing of 67 meV. The adiabatic transition is
observed at 22.258 eV and a hot band structure is seen
with intensity maxima at approximately 74 meV and
92 meV towards lower energy from the 0-0 peak. The
two hot band maxima probably correspond to an initial
excitation of a quantum of the v2(eg) and vl(al)
modes, respectively. Since the hot band is broad it
probably also contains some intensity due to the v5(t2g)
mode. The energies and intensities of the vibrational
lines are summarised in Table 7. As with the D state,
the 0-0 transition for the E state has a low intensity,
which suggests that a significant change in the molecular geometry and the vibrational energy takes place
upon ionisation. We therefore prefer an assignment in
terms of the vI mode rather than the b,2 mode which
would also be energetically possible. This agrees with
the assignment suggested by Holland et al. [35] for
similar vibrational structure observed in the first three
350
D.M.P. Holland et al. / Chemical Physics 192 (1995) 333-353
2-f
SF6
12
I
E 2Tlu cationic state
P E S at 40.8 eV
10
I
I
8
I
I
I
6
I
2
I
I
I
0-0
I
I
15000-
r - - ]q
O
10000-
5000-
0
23.2
1
I
I
I
I
I
I
I
23.1
23.0
22.9
22.8
22.7
22.6
22.5
22.4
I
22.3
I
22.2
I
22.1
Binding Energy (eV)
Fig. 10. A detail of the Hell excited spectrum of S F 6 showing the fifth photoelectron band associated with ionisation from the 4t]. orbital.
Table 7
Energies and relative intensities for the peak maxima observed in the
4t LI inner valence photoelectron band of SF6 obtained from the Hell
excited spectrum
Vibrational quantum number
( v~ mode)
Energy
(eV)
Relative intensity
1 vl~0
I v2~)
0-0
1
2
3
4
5
6
7
8
9
10
11
12
13
22.166
22.184
22.258
22.325
22.394
22.461
22.528
22.598
22.664
22.730
22.796
22.860
22.924
22.986
23.051
23.120
2
2
11
35
64
87
100
92
83
64
45
29
18
10
6
3
components of the 4tL 1 nsalg Rydberg series. The
vibrational spacings decrease successively, corresponding to an anharmonicity of the potential function
along the ql normal coordinate. The vibrational ener-
gies (in eV) can be calculated from the following second order polynomial obtained from a least squares
fitting of the data Evlb= 22.2215 + 0.0698(v + 1/2)
- 0.00028(v + 1/2) 2.
The innermost photoelectron band of the present
HeII excited spectrum corresponds to ionisation from
the 5a]g orbital. This band is comparatively narrow
which is clearly related to a low vibrational activity in
the cation. The band exhibits an intense peak with a
maximum at 26.823 eV and, in addition, two weaker
structures are observed at 0.171 and 0.260 eV towards
higher binding energies. The main peak can probably
be associated with the 0-0 transition and the weaker
features with vibrational excitations (cf. Table 8). In
Table 8
Energies and relative intensities for the peak maxima observed in the
5a~ 1 inner valence photoelectron band of SF6 obtained from the
Hell excited spectrum
Vibrational excitation
Energy
(eV)
Relative intensity
0-0
26.823
26.88
26.994
27.083
100
shoulder
26
11
1 vz
2 v~
3 vl
D.M.P. Holland et al. / Chemical Physics 192 (1995) 333-353
SF6
PES at 40.8 eV
lOOO0-
351
F 2Alg cationic state
3
2
I
I
0-0
I
V-q
8000-
@
6000-
4000-
2000-
I
I
I
I
I
I
27.4
27.2
27.0
26.8
26.6
26.4
Binding Energy (eV)
Fig. 11. A detail of the Hell excited spectrum of SF6 showing the sixth photoelectron band associated with ionisation from the 5a~s orbital.
some earlier studies the adiabatic energy of this state
has been found to be 27.0 eV [42,73,74], but the present study shows that the energy is in fact almost 0.2 eV
lower. Despite its relative simplicity, the band has a
remarkable shape as can be seen in Fig. 11. The dominating peak is very broad ( 130 meV) compared to the
spectrometer resolution and has a Lorentzian shape.
Moreover, the line has a shoulder at 26.88 eV, which
is thus shifted by 60 meV from the peak maximum.
Since the electronic state is non-degenerate, the vibrational structure should in the first approximation reflect
strong excitations of the Vl mode alone. Energetically,
60 meV is too small to correspond to a quantum of the
u~ mode. On the other hand, the weaker lines at higher
energies correspond well with the expected energies
for two and three quanta of this mode with a vibrational
energy of about 85 meV. The single excitation of this
mode should appear at 26.905 eV where no line can be
observed. However, some increase in the intensity can
be observed close to the expected position which may
suggest that the level indeed exists but is strongly
broadened.
The shoulder observed at 60 meV can be explained
by an excitation of a single quantum of the v2(eg)
mode. Since the electronic state is non-degenerate, this
excitation would not be allowed unless vibronic interaction is strong, which would require another electronic
state of eg or t2g symmetry being present. Such states
may well be formed in this region by many-electron
effects and be responsible for the more or less continuous underlying intensity, as discussed in Section 4.1.
The observed shape of the underlying intensity distribution indicates that the electronic states must be
strongly repulsive, which could explain the line broadening of the F 2A~g state in terms of a lifetime effect.
The potential energy surface of the F state may not
itself be repulsive, at least not along the ql and q2
normal coordinates since both the Vl and v2 modes seem
to be excited. However, by the interaction with the
repulsive states forming the background intensity, the
F state could become strongly predissociated. Since the
lowest vibrational states, particularly the vibrationless
state, are the ones that are most strongly broadened, the
crossings with the potential surface leading to the dissociation should occur near the energy minimum of the
F state. Assuming that the width of the 0-0 peak, 130
meV, is caused solely by a limitation in lifetime, the
uncertainty principle indicates that the lifetime of the
vibrationless state is only 4.9 × 10-J5 s. This agrees
well with a very fast dissociation of the molecule that
352
D.M.P. Holland et al. /Chemical Physics 192 (1995) 333-353
may be caused by the interaction with a strongly repulsive potential surface. As shown by TPEPICO experiments, several fragmentation pathways are possible,
indicating that the dissociative potential surface has a
complex shape.
Acknowledgement
We thank the Daresbury Laboratory machine and
engineering staff for their efficient operation of the
beamline and storage ring. We are grateful for financial
support from the Swedish Natural Science Research
Council, the Fonds der Chemischen Industrie and the
Science and Engineering Research Council.
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