THE JOURNAL OF CHEMICAL PHYSICS 122, 144309 共2005兲
Complete valence double photoionization of SF6
R. Feifela兲 and J. H. D. Eland
Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QZ,
United Kingdom
L. Storchi and F. Tarantelli
Dipartimento di Chimica, Università di Perugia, and CNR I.S.T.M, Via Elce di Sotto 8,
06123 Perugia, Italy
共Received 14 December 2004; accepted 25 January 2005; published online 11 April 2005兲
Single photon double ionization of SF6 has been investigated at the photon energies 38.71, 40.814,
and 48.372 eV by using a recently developed time-of-flight photoelectron–photoelectron
coincidence spectroscopy technique which gives complete two-dimensional e− – e− spectra. The first
complete single photon double ionization electron spectrum of SF6 up to a binding energy of
⬃48 eV is presented and accurately interpreted with the aid of Green’s function ADC共2兲
calculations. Spectra which reflect either mainly direct or mainly indirect 共via interatomic coulombic
decay of F 2s holes兲 double ionization of SF6 are extracted from the coincidence map and discussed.
A previous, very low value for the onset of double ionization of SF6 is found to energetically
coincide with a peak structure related to secondary inelastic scattering events. © 2005 American
Institute of Physics. 关DOI: 10.1063/1.1872837兴
I. INTRODUCTION
Sulphur hexafluoride 共SF6兲 is important for its high dielectric strength in high voltage applications 共see Ref. 1, and
references therein兲 and is widely used in plasma etching processes 共see Ref. 2, and references therein兲. To understand its
physical and chemical behavior in various circumstances
properly, knowledge of its electronic structure is essential.
The electronic configuration of SF6 in its neutral ground state
can be denoted as
共core兲22关共4a1g兲2共3t1u兲6共2eg兲4兴
⫻共5a1g兲2共4t1u兲6共1t2g兲6共3eg兲4共1t2u兲6共5t1u兲6共1t1g兲6 ,
where the square brackets denote the inner-valence orbitals
with ionization potentials in the range of outer-valence
double ionization. Several investigations have been carried
out accordingly, in particular using conventional photoelectron spectroscopy in both the valence and core regions, and
have created much information concerning the cationic states
共see Refs. 3–7, and references therein兲.
Various types of coincidence experiments have been performed in order to investigate the complex fragmentation
behavior of SF6. Hitchcock et al. conducted electron impact
excited electron-ion coincidence studies both in the S 2p ionization region 共160– 230 eV兲8 and in the valence shell ionization region 共15– 63 eV兲9 in order to determine photoabsorption and photofragmentation cross sections for SF6. They
also studied dissocative and nondissociative double ionization and found that dissociative double ionization is an appreciable fraction of all double ionization events even close
to the double ionization threshold. Furthermore, they “visually estimated” from the onsets of their oscillator strength
a兲
Electronic mail: [email protected]
0021-9606/2005/122共14兲/144309/9/$22.50
curves, threshold potentials for ions produced in photofragmentation of SF6, in particular for SF2+
4 共33± 2 eV兲 and for
共40±
1
eV兲
which
were
found
to
be about 6 eV lower
SF2+
2
than the pioneering values of Dibeler and Mohler.10 Masuoka
and Samson11 reported partial cross sections for the singly
+
charged fragments 关SFm
共m = 0 – 5兲 + F+兴 and doubly charged
2+
fragments 关SFn 共n = 0 – 4兲兴 created upon single photon
double ionization in the 75– 125 eV region using a technique
related to that of Refs. 8 and 9. Frasinski et al.12 determined
threshold values for formation of fragment ion pairs by making use of a photoion–photoion coincidence setup, and found
the lowest threshold value of 41.1 eV for the formation of
both SF+5 + F+ and SF+3 + F+; moreover, the fragment ion pair
SF+3 + F+2 seems to occur at the same threshold value according to their investigations. About the same time, Joachims et
al.13 measured appearance energies for formation of dications with a photoionization mass spectrometer and reported
2+
2+
in Ref. 13 SF2+
4 to occur at 38.5 eV, SF3 at 42.6 eV, SF2 at
2+
43.8 eV, and SF at 54.7 eV. Eland and Treeves-Brown14
performed photoelectron–photoion–photoion coincidence experiments in order to investigate doubly charged ion dissociation patterns of SF6 in greater detail and derived kinetic
energy release distributions. This work was later on elaborated by Hsieh and Eland15 applying a position sensitive detector which allowed them to measure the momentum vector
of two coincident fragment ions and hence allowed to determine charge separation mechanisms, most clearly for
SF+3 – F+ formation. Creasy and co-workers16 applied a
threshold photoelectron–photoion coincidence technique to
study “state-selectively” the fragmentation channels and
branching ratios for the valence states in the binding energy
range 15– 28 eV. Recently, Peterka et al.17 applied an ion
122, 144309-1
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144309-2
J. Chem. Phys. 122, 144309 共2005兲
Feifel et al.
imaging technique in the same energy region and characterized the angular and translational energy distributions of the
product ions.
The electronic states of the dications have been the subject of several previous works. Griffiths and Harris18 determined, by double charge transfer spectroscopy, the lowest
double ionization threshold to be at 38.9± 0.5 eV; their data
suggest that at least two more electronically excited states of
exist between 38.9 and 44 eV. Bancroft and
SF2+
6
co-workers19 performed a comparative study of normal and
resonant Auger electron spectra for excitations both around
the S 2p and the F 1s edges. They found that the normal
Auger spectra are essentially grouped into two parts, one of
which consists of transitions whose final states have two
holes in the outer valence orbitals and a second which comprises transitions whose final states have one hole in an outer
valence orbital and one in an inner-valence orbital. However,
no further assignments were made for the observed double
hole states in the normal Auger spectra. Sato et al.,20 building on the results of Ref. 19, performed Auger electron–
photoion and photoion–photoion coincidence experiments
and found that the dications having two holes in the outer
valence orbitals dissociate into various fragments, while
those having one hole in the outer valence and one hole in
the inner valence orbitals mostly dissociate into atomic ionic
fragments F+ and S+. Lange et al.21 recently presented an
extensive study on the fragmentation of SFn+
6 共n 艌 2兲 produced by impact of 2 MeV He2+ ions, which was accompanied by quantum chemical ab initio calculations of the vertical double ionization potentials in the valence region; they
calculated the lowest vertical double ionisation potential of
SF6 to be 39.0 eV. Furthermore, they calculated appearance
energies for various fragmentation channels of doubly ionized SF6 at 0 K including zero-point vibration energy at the
so-called “MP2/TZVPP” level and received similar values
2+
for the formation of SF2+
4 and SF2 as reported before by
Ref. 9, and they predicted the lowest fragmentation channel,
SF+5 + F+, to occur as low as 31.33 eV. More recently, Yencha
and co-workers22 recorded the first threshold photoelectron–
photoelectron coincidence 共TPEsCO兲 spectrum of SF6 and
suggested that inner valence SF+6 states play a major role in
the formation of the SF2+
6 ion states; interestingly, the onset
of double ionization was found in their work to occur at
31.98± 0.02 eV.
In the recently developed time-of-flight photoelectron–
photoelectron coincidence spectroscopy technique 共TOFPEPECO兲 applied here,23 the energies of all the electrons
ejected in pairs at each chosen photon energy are measured.
Complete maps of intensity as a function of the two energies
give both the dication spectrum and details of the photoionization process itself. We present in this work the first complete single photon double ionization electron spectrum of
SF6 up to a binding energy of ⬃48 eV. Our interpretation is
based on information obtainable from the coincidence map
itself and on a new ab initio theoretical simulation of the
spectrum performed by the Green’s function ADC共2兲
method.24
II. EXPERIMENT AND DATA ANALYSIS PROCEDURES
Electron–electron coincidence data of SF6 were recorded
by means of a recently developed time-of-flight electron–
electron coincidence 共TOF-PEPECO兲 technique23,25,26 at the
selected photon energies 38.71, 40.814, and 48.372 eV. This
technique is based on a magnetic bottle type spectrometer as
described in detail by Ref. 27. Briefly, wavelength selected
light from a pulsed low-pressure discharge helium lamp ionizes an effusive jet of the target gas in a crossed beam configuration. Electrons from ionization are directed by the inhomogeneous magnetic field of a conically shaped
permanent magnet to follow nominally on-axis the field lines
inside a long solenoid to the 5.5 m distant multichannel plate
detector. The helium lamp works at a typical repetition rate
of 8 kHz and emits light pulses which are about 10 ns long.
The timing of electron signals is referenced either to an electrical pulse generated when the lamp “fires” or to the simultaneous visible light pulse detected by a photomultiplier.
Pairs of electrons arriving within 20 ␮s of each other are
recognized as true coincidences. The times of flight can be
fitted with good precision to the simple form
t=
D
− t0 ,
共E + E0兲1/2
共1兲
with just two fitting parameter t0 and E0. The flight length D
is fixed to 9265 ns 共eV兲−1/2. Energy calibration of the spectra
is done by recording the well-known single electron spectrum of molecular oxygen before and after each run. In order
to check for secondary collisions of electrons with the target
gas, the pressure was varied from 6.5⫻ 10−6 to 3.3
⫻ 10−5 mbar in the interaction region. Commercially available SF6 gas with a stated purity of ⬎99% was used for the
experiments. The purity of the gas has been checked carefully by recording the single electron valence band spectrum
before and after each coincidence run.
III. THEORETICAL METHODS
The calculations of the double ionization spectrum of
SF6 reported in this paper were carried out using the secondorder Green’s function algebraic diagrammatic construction
method.24 This is a powerful direct approach for the theoretical study of ionization processes, leading to a sparse symmetric eigenvalue problem in the space of the ionic configurations, represented in the basis of the Hartree–Fock orbitals
of the neutral system. The eigenvalues of the system are the
ionization energies, while the eigenvectors are related to the
spectroscopic amplitudes. For double ionization, the ADC共2兲
configuration space comprises all the two-hole 共2h兲 configurations 共the main space兲 and their three-hole-one-particle
single excitations 共3h1p兲. The matrix elements in the main
space are of second order in the electron repulsion and of
first order in the remaining space. Therefore, the ADC eigensolutions provide results which are accurate beyond second
order with respect to the naked 2h configurations, and beyond first order for the satellite excitations. This is essentially equivalent to ionized state energies obtained by configuration interaction including also the vast space of 4h2p
configurations. The ADC共2兲 method is implemented in a di-
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144309-3
Valence photoionization of SF6
FIG. 1. Double ionization electron spectra of SF6 recorded at the photon
energies 38.71, 40.814, and 48.372 eV. In all three spectra, the signal rises
strongly around 37.5 eV binding energy.
rect integral-driven algorithm28 coupled to a block-Lanczos
iterative diagonaliser29 which provides fast convergence onto
the spectral envelope of the main space eigenvector projection, even when individual eigenvectors are not fully
converged.30
The Hartree–Fock preliminary calculations have been
performed on SF6 at the experimental geometry 共r
= 1.564 Å兲31 with the GAMESS-UK program32 using a contracted Gaussian double zeta33 plus polarization34 basis set.
The computed double ionization spectrum is fully converged
up to 60 eV binding energy.
IV. EXPERIMENTAL RESULTS
In Fig. 1 we present double ionization electron spectra of
SF6 obtained from the full coincidence data sets which were
recorded at the photon energies 38.71, 40.814, and
48.372 eV. In all three spectra, the signal rises strongly at
⬃37.5± 0.1 eV binding energy, and the observed features remain essentially the same 共as far as they can be investigated兲
for all chosen photon energies as guided by the dashed lines.
Below 37.5 eV binding energy an extended tail is visible in
all the spectra with an onset at around 25 eV; it arises from
false coincidence events, and its relative height depends on
instrumental conditions.
In order to account for possible pressure-dependent
spectral features we recorded the double ionization electron
spectrum of SF6 for different gas pressures in the interaction
region. In Fig. 2 we show the 48.372 eV spectrum recorded
at pressures p = 6.5⫻ 10−6 mbar 共lower panel兲 and p = 3.3
⫻ 10−5 mbar 共higher panel兲, respectively. The broad background below 37.5 eV binding energy increases in intensity
at the higher pressure, but in addition we observe four peaks
in the high pressure spectrum starting at a binding energy of
31.33 eV 共peak value兲, separated by ⬃1.2 eV each. This energy spacing is similar to that of the first four outermost
single electron valence bands of SF6 as reported by Ref. 5;
hence the pressure-dependent peaks arise from secondary
collision of primary electrons with the target gas leading to
single ionization of a second neutral SF6 molecule. The po-
J. Chem. Phys. 122, 144309 共2005兲
FIG. 2. Double ionization electron spectra of SF6 measured for different gas
pressures in the interaction region. The arrow indicates the extraordinarily
low value reported by Yencha et al. 共Ref. 22兲 for the onset of double ionization of SF6.
sition of the first pressure-induced peak 共⬃31.5 eV兲 closely
matches twice the vertical ionization energy for the lowest
state of SF+6 . Such inelastic scattering features, already
known from conventional photoelectron spectroscopy 共see,
e.g., Ref. 35兲, can be seen in TOF-PEPECO spectra of all
molecules at sufficiently high pressure.36 We note that the
valley between the first and the second peak located at
31.98± 0.02 eV 共marked by the arrow in Fig. 2兲 corresponds
exactly to the value for the onset of double ionization of SF6
reported by Yencha et al.,22 which suggests that this extraordinarily low value may have a similar origin.
In comparing the double ionization electron spectrum
recorded at 48.372 eV photon energy with the TPEsCO results of Yencha et al.,22 both similarities and dissimilarities
can be encountered. In both cases strong broad structures are
observed with an onset around 37.5 eV. However, whereas
the TPEsCO spectrum shows essentially a single broad spectral feature centered about 40.44 eV binding energy and
which falls off substantially around 43 eV, the complete
electron–electron spectrum shown in Figs. 1 and 2 consists
of two broad parts with a distinct minimum around 39.66 eV
and which falls off less rapidly toward higher binding energies.
In order to give an interpretation of their TPEsCO spectrum, Yencha et al.22 compared it with the corresponding
inner valence part of both the ordinary and the threshold
photoelectron spectrum. They found in particular that the
centroid of the TPEsCO spectrum at 40.44 eV is very close
to the centroid of the partially unresolved structures between
⬃37 and ⬃45 eV binding energy in the conventional photoelectron spectrum which may, in a simplified picture, be associated with the formation of the 共2eg兲−1 共36– 40.5 eV region兲, the 共3t1u兲−1 共40.5– 43 eV region兲 and the 共4a1g兲−1
共43– 45.5 eV region兲 inner valence states of SF+6 共cf. Ref. 5兲;
already from the early calculations reported by Siegbahn et
al.3 it is known that those orbitals are predominantly of F 2s
character. On this basis, Yencha et al.22 suggested that double
ionization in SF6 may proceed predominantly through the
inner-valence ionic states followed by autoionization with
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144309-4
Feifel et al.
J. Chem. Phys. 122, 144309 共2005兲
FIG. 3. Comparison of the single electron spectrum and the double ionization electron spectrum of SF6 measured simultaneously at the photon energy
48.372 eV.
formation of the two lowest states of SF2+
6 . A similar comparison is made in Fig. 3, where we display the single electron spectrum 共upper panel兲 recorded simultaneously in our
experiment with the double ionization electron spectrum
共lower panel兲 of SF6 at 48.372 eV photon energy. The wellknown outer valence F 2A1g state of SF+6 at the binding energy of 26.82± 0.02 eV 共cf. Ref. 5兲 is included for reference
purposes. As can be seen, the spectral regions between ⬃37
and ⬃45 eV appear to be fairly similar as they consist in
both cases of broad, overlapping features; in particular the
main features of the double ionization electron spectrum occur at somewhat lower binding energies compared to the
features in the single electron spectrum as indicated by the
dashed lines, which makes the interpretation of Yencha et
al.22 interesting for further investigations.
In order to get a deeper insight into single photon double
ionization of SF6, it is helpful to study the coincidence map
itself. In Fig. 4 we display, in isometric perspective, the complete coincidence map of SF6 recorded at 48.372 eV photon
energy, where the intensity is shown as a function of the sum
of the two electron energies E1 + E2 on both the kinetic and
ionization energy scales 共into the page兲, and the kinetic energy of one of the electrons E1 共across the page兲. As we can
see, the intensity varies quite strongly in the low kinetic energy region of E1, but it is fairly uniform in the region close
FIG. 4. Complete coincidence map of SF6 recorded at 48.372 eV photon
energy in isometric perspective, where the intensity is shown as a function
of the sum of the two electron energies E1 + E2 relative to the photon energy
共into the page兲 and the kinetic energy of one of the electrons E1 共across the
page兲.
FIG. 5. Comparison of differently obtained double ionization electron spectra. 共a兲 The spectrum where all electrons were taken 共cf. Figs. 1–3兲; 共b兲 the
spectrum obtained by choosing a slice of coincidence events from the low
kinetic energy region of Fig. 4 共E1 from 0 to 1 eV kinetic energy at 38 eV
binding energy and from proportionally narrower ranges at lower electron
pair energies兲; 共c兲 a similarly created spectrum, where a much narrower E1
range of 0 – 0.1 eV kinetic energy at 38 eV binding energy was chosen; 共d兲
the spectrum created by selecting a slice of coincidence events from the
fairly uniform area close to the main diagonal of Fig. 4, where the width of
the slice was chosen to vary from 2 eV at 38 eV binding energy to proportionally narrower values at lower electron pair energies.
to the main diagonal of this plot. Double ionization spectra
of SF6 can be projected from the coincidence map in various
different ways by taking either all electrons or only certain
selections of them. In Fig. 5 we show a comparison of different double ionization electron spectra. Panel 共a兲 presents
the spectrum where all electrons were taken 共cf. Figs. 1–3兲;
panel 共b兲 shows the spectrum obtained by choosing a slice of
coincidence events from the low kinetic energy region of
Fig. 4 共E1 from 0 to 1 eV kinetic energy at 38 eV binding
energy and from proportionally narrower ranges at lower
electron pair energies兲; panel 共c兲 shows a similarly created
spectrum, where a much narrower E1 range of 0 – 0.1 eV
kinetic energy at 38 eV binding energy was chosen; panel 共d兲
shows the spectrum created by selecting a slice of coincidence events from the fairly uniform area close to the main
diagonal of Fig. 4, where the width of the slice was chosen to
vary from 2 eV at 38 eV binding energy to proportionally
narrower values at lower electron pair energies. Clearly, the
spectra are rather different; in particular, spectrum 共b兲 and 共c兲
show, in comparison to spectrum 共d兲, drastic changes in relative intensity of certain features as marked by the arrows and
the dashed lines, and appear generally to be less structured.
The differences in spectral appearance can be rationalized as
follows; spectrum 共b兲 and 共c兲 are strongly dominated by coincidence events related to low kinetic energy electrons
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144309-5
Valence photoionization of SF6
J. Chem. Phys. 122, 144309 共2005兲
V. THEORETICAL ANALYSIS OF THE SPECTRUM
AND DISCUSSION
FIG. 6. Electron distributions related to two different parts of the dicationic
spectrum as marked by the dashed lines.
whose distribution is seen to be structured 共cf. Fig. 4兲 and
which probably originate from molecular autoionization involving the inner valence electronic states of SF+6 as proposed by Yencha et al.22 It is noteworthy that spectrum 共c兲 is
indeed very reminiscent to the TPEsCO spectrum reported in
Ref. 22. In contrast, spectrum 共d兲, where electrons with
nearly equal energies are taken from a region which shows
no structure in the coincidence map, is probably representing
a direct SF2+
6 spectrum.
By returning our attention to the double ionization spectrum where all electrons were taken into account 共cf. Figs.
1–3兲, and focusing on the gross features below and above the
spectral minimum at 39.66 eV binding energy, the question
arises if different double ionization mechanisms are operating in these two parts. In particular, one could think of one
region reflecting primarily direct and the other one indirect,
dissociative double ionization routes as observed before for
other systems 共see Refs. 36–41, and references therein兲. The
threshold values for formation of fragment ion pairs and the
nonexistence of stable SF2+
6 ions demonstrate that all double
ionization in SF6 is dissociative. If separate double ionization
mechanisms were operating, one could expect to see a difference in the electron distributions related to the formation
of the relevant parts of the dication spectrum. In Fig. 6 we
show the electron distributions related to two different parts
of the dicationic spectrum as marked by the dashed lines, one
below the minimum at 39.66 eV and another one above. As
we can see, the electron distributions are very much the same
in the two cases. Furthermore, the complete electron–
electron coincidence map 共cf. Fig. 4兲 does not contain any
features at constant kinetic energy E1 which could be related
to autoionization in fragment fluorine atoms, in contrast to
other molecules such as oxygen where indirect atomic autoionization is found to be dominant.39–41 Thus there is no
direct evidence for involvement of dissociative indirect
double ionization in SF6, but the observations cannot entirely
exclude it.
In order to analyze the double ionization spectrum in
greater depth and provide a more theoretically profound interpretation, we have carried out a detailed ab initio simulation using the Green’s function ADC共2兲 method,24 of postHartree–Fock second-order accuracy. Such calculations have
been successfully used in the past to study the double ionization of many molecular systems 共for a recent example see
Ref. 42兲. Key features of the method are that it is efficient
enough to permit the accurate calculation of the whole manifold of double ionization transitions and that, using a population analysis of the double ionization eigenvectors,43 we
can obtain a neat and useful picture of the two-hole density
distribution in the final states in terms of localized atomic
components.
The computed double ionization spectrum of SF6 comprises nearly 29 000 electronic states up to a binding energy
of 110 eV, a number of states which attests to the complexity
of such spectra and calculations. The density of states increases dramatically with the ionization energy, but it is high
even at low energy: over 100 dicationic states are computed
to lie in the lowest 10 eV of the spectrum. The population
analysis of the eigenvectors yields a decomposition of the 2h
projection 共i.e., the part expressible as ejection of two electrons from the Hartree–Fock occupied orbitals, with no further excitations; this part—as long as ground state electron
correlation may be treated as a perturbation—is experimentally the most relevant part兲 in four localized components,
which, using a well-established notation,43 we shall denote as
F−1F⬘−1, S−1F−1, F−2, and S−2. The first component, F−1F⬘−1,
measures the fraction of two-hole charge where the two
holes are localized each on a different fluorine atom. On
simple electron and atom counting arguments, this component may be expected to be dominant. S−1F−1 gives the twohole component with one vacancy on sulfur and one on a
fluorine atom, while S−2 and F−2 express the portion of twohole density where both holes are localized on sulfur and on
a single fluorine, respectively. In octahedral SF6, the pairs of
fluorine atoms are not all equivalent. Consequently, the
F−1F⬘−1 component may be further subdivided in two terms,
one measuring the charge involving pairs of vicinal fluorine
atoms and the second expressing the localization of the holes
on pairs of equatorially opposed 共distal兲 fluorines.
Figure 7 displays the energy distribution of the population components over the whole double ionization spectrum,
obtained by Gaussian broadening of the discrete data, and
immediately enlightens the nature of the spectrum, placing
our experiment in context. The spectrum is, in its qualitative
features, similar to those of other fluorides29,42,44 and we
shall therefore give a summary description of it, referring the
reader to the previous studies for more details. As expected,
the F−1F⬘−1 character dominates in global terms, while, at the
opposite end, the S−2 component is everywhere too small to
be seen on the scale of the figure. The F−1F⬘−1 component
共and, consequently, the whole spectrum兲, exhibits three main
zones of high intensity: below 50 eV, between 60 and 75 eV,
and around 90 eV. As it is known that the fluorine components of the spectrum basically retain an atomic character,44
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144309-6
Feifel et al.
J. Chem. Phys. 122, 144309 共2005兲
FIG. 7. Plot of the computed 2h population components
of the double ionization spectrum of SF6, obtained by
Gaussian broadening of the discrete data 共FWHM
= 1 eV兲. Solid line: total F−1F⬘−1 component; dotted:
distal F−1F⬘−1 component; dashed: S−1F−1 component;
Gray-filled: F−2 component. The S−2 component is
omitted because is too small on the scale of the figure.
these three zones may be easily interpreted in terms of the
ionization of a pair of fluorine atoms. At low energy, we have
the states where both atoms have lost an outer-valence 2p
electron; in the intermediate region we see the dicationic
states where one atom is again deprived of a 2p electron,
while the other has lost an inner-valence 2s electron; and
finally, at high energy, both atoms have undergone innervalence ionization. The relative intensity of the three bands
may be easily related to the different number of available 2p
and 2s electrons. The three bands are furthermore roughly
equally spaced, reflecting the difference in binding energy of
a fluorine 2p and 2s electron, because the repulsion between
holes residing on distant atoms is approximately constant on
average. In a more refined view, note that the distal F−1F⬘−1
component increases at the low-energy end of each band,
exactly because its hole–hole repulsion energy is smaller
than in the adjacent-pair component, owing to the larger distance between the fluorine atoms. The distal F−1F⬘−1 component is of course much less intense than the vicinal counterpart due simply to the smaller number of such fluorine pairs
共1 in 5兲.
The F−2 density component, shown as a gray-filled curve
in Fig. 7, also displays an essentially atomic-like three-band
pattern, similar to the above. However, apart from the evident drop in intensity compared to the F−1F⬘−1 spectrum, we
should note two other characterizing differences. The first is
that the three F−2 zones are shifted by about 10 eV to higher
energy compared to the F−1F⬘−1 ones, because of the obviously larger repulsion energy of two electron holes confined
on a single atom. As a consequence, there is little overlap
between the F−1F⬘−1 and F−2 spectra, with the remarkable
result that the F−2 component, though globally much smaller,
peaks out dominantly in at least two regions of the double
ionization spectrum, just above 50 and around 80 eV. The
second difference is that the intermediate 2p−12s−1 region is
actually composed of two bands, one centered at about
72 eV and the second around 80 eV. This reflects the significant energy split between triplet and singlet states due to the
spatial compactness of the inner-valence hole. 共The 2s−2
single-site band above 100 eV, on the other hand, obviously
has no triplet component.兲
Finally, Fig. 7 emphasises that the S−1F−1 component of
the two-hole charge is everywhere very small and more uniform, so that it is never dominant. In fact, it tends to be
largest in the same energy regions where the F−1F⬘−1 component dominates the spectrum.
Having so characterized the double ionization spectrum
of SF6 with the help of the population analysis, we now see
clearly that the photon energy used in the experiment is sufficient to probe almost completely the outer-valence double
ionization region, corresponding essentially to the ionization
of two 2p electrons on different fluorine atoms. We can now
attempt to give a more detailed account of the experimental
spectrum based on our theoretical results. In order to do so
with quantitative accuracy, we would need to calculate the
energy-dependent double photoionization cross section for
the over 100 electronic states found below the photon energy,
but this is an impossible task. Resorting to a simpler, more
qualitative, approach, we may use the broadened 2h spectroscopic factors as a rough estimate of the spectral profile. The
results are shown in Fig. 8, below the experimental spectrum
of Fig. 5共d兲. The latter has been chosen for comparison since,
as previously discussed, it corresponds to an even energy
distribution between the two outgoing electrons and is thus
more likely to reflect a direct double photoionization mechanism. We shall later return to this point. The computed spectrum has been shifted up in energy by 1.8 eV in order to
obtain alignment with the experimental profile. The necessity
of such shift was expected42 and it may be explained as due
to a relatively deficient account of ground state electron correlation in our calculations. To realistically incorporate the
electron energy dependence of the double ionization cross
section, we have applied a linear filter to the theoretical intensity, ranging from 1 at the double ionization threshold to 0
at the photon energy of 48.372 eV, which corresponds to
vanishing electron kinetic energy.
Figure 8 shows that, in spite of some quantitative discrepancies in the relative spectral intensities, the computed
spectrum reproduces without ambiguity—in fact, with remarkable detail—most experimental features. It proves beyond doubt that the whole measured spectrum does indeed
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144309-7
Valence photoionization of SF6
J. Chem. Phys. 122, 144309 共2005兲
FIG. 8. Theoretical double ionization spectrum of SF6
shown below the experimental spectrum of Fig. 5共d兲.
The theoretical spectrum is obtained by Gaussian
broadening of the computed 2h components of the
states 共shown as vertical bars兲, with FWHM increasing
linearly from 0.5 eV at low energy to 1.0 eV. The computed intensity incorporates a linear fall-off factor going
from 1 at 38.0 eV to 0 at the threshold of 48.372 eV.
The dotted line shows the total 2h spectrum, the solid
line 共and the bar spectrum兲 omits the distal F−1F⬘−1
component.
explore the outer-valence direct vertical double ionization of
SF6. There are actually two theoretical profiles in the figure.
The dotted line results from the convolution of the total 2h
strength of the states, while the solid line 共and the associated
discrete bar spectrum兲 results by eliminating the distal
F−1F⬘−1 component. Although both spectra provide essentially the same qualitative description of the experiment, it is
very interesting to note that deleting the distal F−1F⬘−1 component markedly improves the theoretical profile at low energy, where the dropped component is largest. This suggests,
not implausibly, that dicationic states where the two holes are
to a larger extent localized on more distant atomic sites are
relatively more difficult to reach by direct double photoionization.
Both the experimental and theoretical spectra show a
first composite band below 40 eV, well separated from the
rest of the spectrum, in which three principal peaks can be
identified. This low-energy part of the spectrum comprises
states where exclusively the fluorine p lone-pairs are ionized
共the sulfur-containing components of the states are nearly
exactly vanishing here兲. The states appear to cluster in three
neatly separated groups of nearly degenerate levels, as is
evidenced by the bar spectrum. Note that the degree of neardegeneracy is such that, for example, for the highest energy
group, comprising four dicationic states, only one line is visible. Somewhat surprisingly, such tight clustering is the nontrivial result of two different contributing factors: the type of
fluorine pair involved 共whether vicinal or distal兲 and the relative orientation of their nonbonding 2p orbitals ionized,
which can be parallel, skewed 共i.e., at right angles and noncoplanar兲, and, in the vicinal case, orthogonal but coplanar. A
more detailed population analysis thus shows, for example,
that vicinal parallel F−1F⬘−1 pairs contribute nearly exclusively to the first and third groups, while the middle group of
states involves almost only vicinal coplanar orthogonal pairs
and distal parallel pairs. Skewed equatorially opposed pairs
contribute only to the two lower energy groups, while
skewed vicinal pairs appear in all three groups.
The first band is followed by an evident gap and then by
the intense broad feature appearing between 40 and 43 eV.
As attested by the computed bar spectrum, the number of
dicationic states reached in this ionization energy range is
very large and it is impossible to characterize them in terms
of orbital ionization, as configuration mixing dominates. The
states appear to give rise to two large bands, although the
theoretical spectrum exaggerates the double structure and the
relative intensities are also poorly reproduced. At higher energy the intensity declines rapidly, but both the experimental
and theoretical profiles evidence a broad composite structure
between 43 and 45 eV and a final band around 46 eV. Here
the calculations appear to begin to overestimate slightly the
relative energy of the states involved, which is not unexpected since, at high energy, correlation effects and the influence of higher excitations not included in our theoretical
scheme are more strongly felt.
Based on the results of our calculations, we may finally
briefly comment on the origin of the different spectra obtained by sampling different kinetic energy distribution regions, as shown in Fig. 5. In particular, as we discussed
earlier, when one of the two outgoing electrons has small
kinetic energy, an autoionization mechanism with secondary
electron emission may be thought to be playing a nonnegligible role in the double ionisation. As Fig. 3 and Ref. 5
show, singly ionized states of SF6 in the F 2s region lie indeed in the same binding energy region, and above, the lowest doubly ionized states. In Ref. 5, maxima in the innervalence photoelectron spectrum of SF6 were reported at 39.8,
40.9, and 44.1 eV and these figures are all well above the
double ionization threshold. This is quite remarkable, for the
possibility of decay of valence singly ionized states, even
inner-valence ones, by secondary electron emission is uncommon in small molecules: due to the repulsion energy
between two electron vacancies confined in a small region of
space, doubly ionized states lie normally well above the
whole 共valence兲 single ionisation spectrum. SF6 thus represents an interesting case because, as we have seen, the possibility of localization of the two holes on relatively distant
fluorine atoms lowers the repulsion energy enough to place a
large number of the outer-valence dicationic states below the
single inner-valence-hole levels. As to the expected rate for
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144309-8
J. Chem. Phys. 122, 144309 共2005兲
Feifel et al.
FIG. 9. Plot of the S−1F−1 component of the dicationic
states computed below 45.5 eV, shown below the experimental profile of Fig. 5共c兲, and obtained by Gaussian broadening 共FWHM= 1 eV兲 of the discrete data
shown as vertical bars. A fall-off filter like the one of
Fig. 8 is incorporated between 38 and 45.5 eV. Triplet
states have been reduced in intensity by 2 / 3 to simulate
a decay process.
such decay process, we recall that, in more extended chemical systems, inner-valence decay accompanied by the creation of a secondary electron vacancy in regions even very
distant from the primary hole is well known as the so-called
interatomic Coulombic decay 共ICD兲. It has been theoretically
predicted and shown to be a very efficient process,45 before
being experimentally observed.46–48 Moreover, it has been
recently shown to play an important role in the Xe 4d ionization of xenon fluorides49 and has also been observed in
2s-ionized van der Waals dimers of neon.47 On these
grounds, double ionization of SF6 by ICD may undoubtedly
be the prevailing mechanism at low enough kinetic energies
of the first electron.
Going from a direct double photoionization mechanism
to a decay one would of course change, possibly very significantly, in general, the spectral profile, even if the same
manifold of final states is reached. As previously mentioned,
the varying profiles of Fig. 5 support the hypothesis of a
change of mechanism. Our present calculations, where transition rates and line broadenings are only qualitatively estimated, do not allow us to discriminate conclusively between
the two mechanisms, and the issue is especially complicated
by the fact that more than one decaying state is involved. We
note however that the decrease in the relative intensity of the
lowest energy band in Figs. 5共b兲 and 5共c兲 suggests, reasonably, a relatively smaller rate of decay from the innervalence, more bonding, states to dicationic states where the
two vacancies are on widely separated nonbonding orbitals.
More specifically, the role of the S−1F−1 character of the
states may be enhanced in a F 2s hole decay, as has been
found for the Xe 4d decay in xenon fluorides.49 Also the
high-energy half of the spectrum appears to drop quite
sharply in relative intensity, especially in Fig. 5共c兲, probably
because of its proximity to the decay threshold. There are in
general further differences to be taken into account between
a decay mechanism and direct photoionization. One concerns
the different activity of final singlet and triplet spin states.
Another, very important one, concerns the effect of nuclear
dynamics, which is profoundly different in decay processes
from that involved in sudden direct transitions.50 This is
known to affect in very significant ways not only line broadenings, but also the effective energy positions of the spectral
bands.51 As an illustration of some of these suggestions, Fig.
9, shows a plot of the S−1F−1 population component up to
45.5 eV in comparison to the experimental spectrum of Fig.
5共c兲.
VI. SUMMARY
Single photon double ionization of SF6 has been investigated by using a recently developed time-of-flight
photoelectron–photoelectron coincidence spectroscopy technique. The first complete single photon double ionization
electron spectrum of SF6 up to a binding energy of ⬃48 eV
was presented, and spectra which reflect either mainly direct
or mainly indirect double ionization of SF6 were extracted
from the coincidence map. The theoretical Green’s function
calculations performed here have enabled us to give a complete and satisfactorily accurate description of the measured
double ionization spectrum. The charge density analysis of
the dication states has permitted a full characterization of the
spectral features and given a useful context for discussing the
indirect mechanism for producing outer valence dicationic
states via decay of inner-valence F 2s holes. It is shown that
such mechanism is in fact an intramolecular interatomic
Coulombic decay and should therefore be very efficient.
ACKNOWLEDGMENTS
Professor N. Kosugi is acknowledged for valuable discussions on the subject. R.F. would like to thank the Swedish
Research Council 共VR兲 and the Swedish Foundation for International Cooperation in Research and Higher Education
共STINT兲 for financial support of his stay at Oxford University. L.S. and F.T. thank the italian M.I.U.R. and C.N.R. for
financial support.
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