Core excitation in O3 localized to one of two symmetry-equivalent chemical bonds: Molecular alignment through vibronic coupling

Article abstract of DOI:10.1063/1.1881192

Core excitation from terminal oxygen OT in O3 is shown to be an excitation from a localized core orbital to a localized valence orbital. The valence orbital is localized to one of the two equivalent chemical bonds. We experimentally demonstrate this with the Auger-Doppler effect which is observable when O3 is core excited to the highly dissociative OT 1 s-1 7 a11 state. Auger electrons emitted from the atomic oxygen fragment carry information about the molecular orientation relative to the electromagnetic-field vector at the moment of excitation. The data together with analytical functions for the electron-peak profiles give clear evidence that the preferred molecular orientation for excitation only depends on the orientation of one bond, not on the total molecular orientation. The localization of the valence orbital " 7 a1 " is caused by mixing of the valence orbital " 5 b2 " through vibronic coupling of antisymmetric stretching mode with b2 symmetry. To the best of our knowledge, it is the first discussion of the localization of a core excitation of O3. This result explains the success of the widely used assumption of localized core excitation in adsorbates and large molecules.

Full text of DOI:10.1063/1.1881192

Core excitation in O 3 localized to one of two symmetry-equivalent chemical bonds:
Molecular alignment through vibronic coupling
K. Wiesner, A. Naves de Brito, S. L. Sorensen, N. Kosugi, and O. Björneholm
Citation: The Journal of Chemical Physics 122, 154303 (2005); doi: 10.1063/1.1881192
View online: http://dx.doi.org/10.1063/1.1881192
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THE JOURNAL OF CHEMICAL PHYSICS 122, 154303 ͑2005͒
Core excitation in O3 localized to one of two symmetry-equivalent chemical
bonds: Molecular alignment through vibronic coupling
K. Wiesnera͒
Department of Physics, Uppsala University, P.O. Box 530, 751 21 Uppsala, Sweden
A. Naves de Britob͒
Laboratório Nacional de Luz Síncrotron, P.O. Box 6192 CEP: 3084-971 Campinas, San Paulo, Brazil
S. L. Sorensen
Department of Synchrotron Radiation Research, Institute of Physics, University of Lund,
P.O. Box 118, 221 00 Lund, Sweden
N. Kosugi
Ultraviolet Synchrotron Orbital Radiation (UVSOR), Institute for Molecular Science, Myodaiji,
Okazaki 444-8585, Japan
O. Björneholm
Department of Physics, Uppsala University, P.O. Box 530, 751 21 Uppsala, Sweden
͑Received 21 June 2004; accepted 4 February 2005; published online 15 April 2005͒
Core excitation from terminal oxygen OT in O3 is shown to be an excitation from a localized core
orbital to a localized valence orbital. The valence orbital is localized to one of the two equivalent
chemical bonds. We experimentally demonstrate this with the Auger–Doppler effect which is
observable when O3 is core excited to the highly dissociative OT1s−17a11 state. Auger electrons
emitted from the atomic oxygen fragment carry information about the molecular orientation relative
to the electromagnetic-field vector at the moment of excitation. The data together with analytical
functions for the electron-peak profiles give clear evidence that the preferred molecular orientation
for excitation only depends on the orientation of one bond, not on the total molecular orientation.
The localization of the valence orbital “7a1” is caused by mixing of the valence orbital “5b2”
through vibronic coupling of antisymmetric stretching mode with b2 symmetry. To the best of our
knowledge, it is the first discussion of the localization of a core excitation of O3. This result explains
the success of the widely used assumption of localized core excitation in adsorbates and large
molecules. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.1881192͔
I. INTRODUCTION
Core-excited O3 has been studied both with ion and elec-
tron spectroscopies.1–5 The core-excited state OT1s−17a1 has
1
been shown to be ultrafast dissociating.4 Ultrafast dissociat-
ing molecules dissociate on the same time scale as the elec-
tronic Auger decay, which is in the femtosecond range. We
take advantage of this characteristic to obtain information
about the preferred molecular orientation relative to the elec-
tric light vector ͑e-vector͒ during core excitation. The reso-
nant Auger electron ͑RAE͒ signal from the O3 molecules that
dissociate before they undergo RAE decay ͑Ϸ10%͒ is an
atomic oxygen RAE signal. The atomic Auger electrons ob-
tain additional momentum from the emitting fragment as a
consequence of the preceding dissociation. This additional
momentum is detected as a shift in energy in the RAE spec-
trum and can be used to determine the dissociation direction
of the fragment. Since we study a two-body dissociation this
direction gives full information about the molecular orienta-
tion before dissociation. The molecular orientation before
dissociation is to a very good approximation identical to the
orientation during excitation since rotation is two orders of
magnitude slower than the Auger decay. Hence, the RAE
spectrum from the fragment contains information about the
molecular orientation at the time of excitation.
A successful model of molecular valence electronic
structure is the formation of delocalized molecular valence
orbitals out of localized atomic valence orbitals. Core-to-
valence excitation in small molecules is therefore treated as a
delocalized process. On the other hand core-valence interac-
tion in large molecules is often assumed to be limited to the
site of the core-excited atom. This is the case even for mol-
ecules with several symmetry-equivalent atoms, thus allow-
ing for a symmetry break. When is it reasonable to treat a
core-valence excitation as localized? We present O3, which
despite being a small molecule, exhibits core excitation lo-
calized to one of the two symmetry-equivalent bonds OC-OT
͑OC and OT are the center and terminal atoms͒. We attribute
this effect to a vibronic coupling between two core-excited
states involving the valence orbitals 7a1 and 5b2. This causes
an energetically favorable symmetry lowering and allows for
the localization.
a͒
Present address: Center for Computational Science and Engineering, Uni-
versity of California, Davis, CA 95616.
Electronic mail: karoline@cse.ucdavis.edu
b͒
On leave from Institute of Physics, University of Brasilia, Brazil.
0021-9606/2005/122͑15͒/154303/5/$22.50
122, 154303-1
© 2005 American Institute of Physics
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154303-2
Wiesner et al.
J. Chem. Phys. 122, 154303 ͑2005͒
In this paper we present calculations of the molecular
orientation during core excitation and find that one chemical
bond is preferably parallel to the electric-field vector. This
represents a symmetry break which we explain with the well-
known concept of vibronic coupling.
II. EXPERIMENT
The experimental data shown in Fig. 3 were published in
Ref. 4. The core-excited state investigated was the
OT1s−17a11 at 535.85-eV excitation energy. In literature this
core resonance is often designated as “␴*” resonance. The
experiments were performed at the undulator beam line I411
͑Ref. 6͒ at the MAX II storage ring of the Swedish National
Synchrotron Laboratory in Lund, Sweden. The RAE spectra
were measured with a photon energy resolution of 120 meV
and an electron spectrometer resolution of 140͑10͒ meV. The
ozone sample was generated in a commercial ozone genera-
tor ͑Ozone Technology, Sweden͒ by discharging oxygen ͑O2͒
of industrial quality in an electric field. The O2/O3 mixture
was then distilled to a purity of Ϸ99%. For further experi-
mental details, see the original paper.4
FIG. 1. Definition of the angles ␪ and ␣.
sition. In the present experiment we are sensitive only to
electrons from ultrafast dissociated molecules. The time
scale of autoionization for those electrons is a few femtosec-
onds, which is about two orders of magnitude faster than
molecular rotation. Thus measurement of ␤ provides infor-
mation about the symmetry of the transition.
In order to obtain a theoretical electron profile for a two-
body dissociation following a transition with a certain ␤ pa-
rameter, we need to integrate the angular distribution over all
angles, since we describe a sample of randomly oriented
molecules. The extra fragment momentum from dissociation
is transferred to the electron. The measurement determines
the projection cos ␪ of the momentum along the detection
axis. With the e-vector and the detection axis aligned, the
integral over an infinitesimal interval ␦␪ becomes
III. FUNCTIONS FOR ELECTRON-PEAK PROFILES
The O3 molecule belongs to the symmetry group C2␯
with four irreducible representations for electronic orbitals:
a1, a2, b1, and b2. To be consistent with the nomenclature in
the original experimental paper we define the molecule lying
in the yz plane. The OT1s atomic core orbitals combine ger-
ade to form the molecular orbital ͑MO͒ 2a1 and ungerade to
form 1b2. The transition to the unoccupied 7a1 MO is dipole
allowed from both the 2a1 and the 1b2 core MOs. Thus, the
transition to the OT1s−17a11 core-excited state is actually two
transitions from the two nearly degenerate OT core MOs. The
symmetry of the transition is A1 and B2, respectively. In the
following it is assumed and likely to be correct that the tran-
sition probability for the two is the same.
To investigate how localized and delocalized descrip-
tions of core excitation in O3 lead to experimentally observ-
able differences, we derived analytical functions for peak
profiles of electron spectra for different transition symme-
tries. The premises for the two different models, the localized
and the delocalized, are summarized in Fig. 2.
We will start with the derivation for the case of a di-
atomic molecule which is the simplest case and the result
will be of use later. We simplify the derivation by aligning
the detection axis and the e-vector ͑for the angle definitions,
see Fig. 1͒. The angular distribution for photoexcitation,
f͑␪͒, about the polarization of the exciting radiation
͑e-vector͒ ͑for a one-photon excitation in the dipole approxi-
mation͒ is given by7
␪
2␲
1
I͑cos ␪͒ =
f͑␪ ͒d␪ d␸,
͑2͒
Ј
Ј
͵ ͵
␦
␪+␦
0
␦ → 0
͑3͒
͑4͒
1
␤
3
4
=
1 −
+
␤ cos2 ␪.
ͩ ͪ
2
2
The kinetic energy released in the dissociation will
broaden the profile. When scaling the profile to electron ki-
netic energy, the maximum width of the profile is
m
⌬͑cos ␪͒max = 2 f Ef
͑5͒
me
with the kinetic energy of the fragment Ef, the electronic
mass me, and the fragment mass mf.
We write out the explicit form of the function for a ⌺
transition ͑␤=2͒,
3
I͑cos ␪͒⌺ = cos2 ␪.
͑6͒
2
This is different from the electron-peak profiles derived in
Ref. 8, since this reference uses an invalid geometric factor.
The electron profile for the ⌺ transition is shown in Fig. 2 on
the left.
For the details of the derivation of the electron-peak pro-
files for bent molecules of C2␯ symmetry we refer to Appen-
dix A. Here we only give the final result for the sum of the
two transitions A1 and B2 relevant to our experiment,
1
f͑␪͒ =
͓1 + ␤P2͑cos ␪͔͒,
͑1͒
4␲
where ␪ is the angle between the molecular symmetry axis
and the e-vector, ␤ is the anisotropy parameter, and
P2͑cos ␪͒= 1 ͑3 cos2 ␪−1͒ is the Legendre polynomial of order 2.
2
The spatial anisotropy parameter ␤ can range from ϩ2 for a
pure parallel transition to Ϫ1 for a pure perpendicular tran-
3
8
IA +B = ͑1 + cos2 ␪͒.
͑7͒
1
2
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154303-3
Core excitation in O3
J. Chem. Phys. 122, 154303 ͑2005͒
FIG. 2. The excitation and dissociation processes according to the model for localized ͑left͒ and delocalized excitations ͑right͒, respectively. The core-excited
atoms ͑ء͒ are gray shaded. The profiles at the bottom are added to the measured spectrum in Fig. 3.
The profile is shown in Fig. 2 on the right. Equation ͑6͒
for a profile of a diatomic molecule can be used for describ-
ing excitation localized to one bond in a polyatomic mol-
ecule. Equation ͑7͒ represents excitation delocalized over all
bonds.
limited experimental resolution. The Lorentzian function
with a FWHM of 149 meV accounts for the lifetime broad-
ening, where we assumed the same core hole lifetime as that
of O2.9 The convoluted profile is shown as a dashed line in
Figs. 2 ͑right͒ and 3. The solid line in Fig. 3 is the likewise
convoluted profile for ⌺ transition, also shown in Fig. 2
͑left͒. We assume an angle of 20° between fragmentation and
symmetry axis. This angle accounts for momentum conser-
vation. In addition an angle of 7° between the orbital and the
bond is taken into account, as calculated by Oji et al.10 The
only free parameter in both functions is ⌬͑cos ␪͒max, which
depends on the kinetic energy released by dissociation, see
Eq. ͑5͒.
IV. RESULTS
We now compare the experimental data with the analyti-
cally derived profiles for localized and delocalized excita-
tions, Eqs. ͑6͒ and ͑7͒. A fragment Auger electron peak fol-
lowing OT1s−17a1 excitation4 is shown in Fig. 3. The
1
analysis of the other fragment peaks in Ref. 4 is analogous
and leads to the same conclusions. The electron signal is
double peaked due to the Doppler effect described in Ref. 4.
The profile that should apply if a delocalized description of
this transition was valid is the A1+B2 profile, Fig. 2 ͑right͒
and Eq. ͑7͒. We convoluted the profile with a Gaussian and a
Lorentzian function. The Gaussian function with a full width
at half maximum ͑FWHM͒ of 140 meV accounts for the
V. DISCUSSION
It is clear from Fig. 3 that the sum of electron-peak
profiles for A1 and B2 transitions ͑dashed line͒ does not re-
produce the experiment. The profile for a ⌺ transition ͑solid
line͒, on the other hand, agrees very well with the experi-
ment. The two profiles represent two different models for
excitation, see Sec. III and Fig. 2. The A1+B2 profile repre-
sents a transition delocalized over the molecule, while the ⌺
profile represents a transition localized to one bond. It is
obviously the latter case we observe here, a transition local-
ized to one bond. The excitation probability for each bond is
given as a probability, determined by its orientation relative
to the light vector and is independent on the orientation of
the other bond. In other words, the molecular symmetry is
broken. This result is schematically summarized in Fig. 4. A
discussion of the localization follows in the next paragraph.
An explanation for the observed localization can be
found in the mechanism of vibronic coupling.11,12 Whenever
two states of the same total symmetry ͑electronic
+vibronic͒ are close in energy, they can couple to each other.
Thus states of different electronic symmetry can couple via
suitable vibrational modes. If they couple via an asymmetric
mode of b2 symmetry the molecular symmetry is lowered.
This is what happens in the given core excitation in O3. The
FIG. 3. RAE spectrum of O3 ͑circles͒ excited to OT1s−17a11. The solid and
dotted lines are the profiles from Fig. 2 for ⌺ transition and A1 +B2 transi-
tion, respectively.
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154303-4
Wiesner et al.
J. Chem. Phys. 122, 154303 ͑2005͒
ACKNOWLEDGMENTS
K. J. Børve, A. Lindgren, and J. Åberg are gratefully
acknowledged for helpful discussions. This work was sup-
ported by the Foundation for Strategic Research ͑SSF͒, the
Swedish Research Council ͑VR͒, the Göran Gustavsson
Foundation as well as by the Swedish Foundation for Inter-
national Cooperation in Research and Higher Education
͑STINT͒. One of the authors ͑A.N.B.͒ would like to thank
CNPq-Brazil and FAPESP-Brazil for financial support.
APPENDIX: DERIVATION OF ELECTRON-PEAK
PROFILES
We derive the explicit electron-peak profiles for A1 and
B2 transitions of bent molecules of C2␯ symmetry. The main
difference compared to the diatomic-molecule case is that the
axis of fragmentation and the symmetry axis are not aligned.
In other words, the angular distribution for photoexcitation
depends on the angle between the e-vector and the symmetry
axis, whereas the measured coordinate depends on the angle
between the e-vector ͑which is equal to the detection axis͒
and the fragmentation axis ͑see Fig. 1͒. We therefore need to
take into account the angle ␣ between symmetry axis and
axis of fragmentation. The way this is done is by rotating the
reference frame of the transition dipole into the reference
frame of the axis of fragmentation.
FIG. 4. Illustration of valence orbital localization after excitation. The pre-
ferred molecular orientation is with the bond including the core-excited
atom ͑ء͒ parallel to the e-vector. The atomic 2p orbital is indicated, illus-
*
trating the localized ␴ orbital.
two core-excited states 1s−T17a11 and 1sT−15b12 are close in en-
ergy and are not experimentally resolved. Coupling between
those states opens up for an asymmetric vibrational mode
that lowers the symmetry and localizes the two valence or-
bitals to opposite bonds. In the lower symmetry they form
*
two ␴* orbitals: 7a1±5b2=␴
͑normalization factors ne-
left/right
glected͒, each localized to the respective bond. Thus, instead
of an excitation of a localized core electron to a delocalized
valence orbital we obtain an excitation to a localized valence
orbital. In other words, through vibronic coupling the four
delocalized excitations, expressed in C2␯ symmetry,
The angular distribution for photoexcitation, f͑␪͒, about
the polarization of the exciting radiation ͑e-vector͒ for an
3
excitation of A1 symmetry is given by f͑␪͒= cos2 ␪. The
transition dipole is aligned with the symmetry4␲axis of the
molecule. We need to integrate the angular distribution over
all angles, but in the frame of dissociation. Thus, we have to
adopt a new coordinate system which is rotated by the angle
␣ with respect to the old one, see Fig. 1. The new coordinate
1sT−left → 7a1 ± 1sT−right → 7a1,
͑8a͒
͑8b͒
1sT−left → 5b2 ± 1sT−right → 5b2,
are turned into two localized excitations ͑final state 1 in Fig.
4͒,13
˜
system is obtained through a Eulare rotation and f͑␪͒ reads
*
1
1sT−left → ␴
,
͑9a͒
left
˜
f͑␪͒
=
͓sin2 ␣ − ͑1 − cos2 ␣͒cos2␪͔.
͑A1͒
A
1
4␲
*
1sT−right → ␴
,
͑9b͒
right
The transition dipole of a B2 transition is perpendicular
*
right
assuming 1sT−left→␴
͑final state 2 in Fig. 4͒ and
to the symmetry axis and lies in the molecular plane. The
1sT−right→␴ is weak,2 as shown in Fig. 4.
*
left
3
angular distribution is given by f͑␪͒= 4␲ sin2 ␪ sin2 ␸. Trans-
formed into the rotated coordinate system it reads
1
=
͓cos2 ␣ − ͑1 − sin2 ␣͒cos2 ␪͔.
͑A2͒
˜
f͑␪͒
B
VI. CONCLUSION
2
4␲
Core excitation in O3 is found to be localized to one
chemical bond. Analytically derived functions for the
electron-peak profiles were used to identify the excitation
geometry of the molecule revealing the fact that the
OT1s−17a11 core-excited state is preferably created with one
O*T-OC chemical bond aligned to the e-vector ͑ء indicating
the core-excited atom͒. The model assumed to date for small
molecules, delocalizing the excitation over the two
symmetry-equivalent bonds, does not fit the data. We explain
the localization of the excitation with a symmetry breaking
of the valence orbital caused by vibronic coupling. Our result
provides an experimental verification for the widely used
assumption of core excitation localized to one of several
symmetry-equivalent bonds.
The integration is performed as in the diatomic case,
␪
2␲
1
I͑cos ␪͒ =
f͑␪ ͒d␪ d␸,
͑A3͒
Ј
Ј
͵ ͵
␦
␪+␦
0
␦ → 0,
͑A4͒
͑A5͒
3
4
3
4
I͑cos ␪͒ = ͑2 − 3 sin2 ␣͒cos2 ␪ + sin2 ␣,
A
1
3
4
3
4
I͑cos ␪͒ = ͑2 − 3 cos2 ␣͒cos2 ␪ + cos2 ␣.
͑A6͒
B
2
Since the core excitation OT1s−17a11 consists of two
overlapping transitions of symmetry A1 and B2 we need to
sum the intensity profiles. The final intensity profile becomes
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154303-5
Core excitation in O3
J. Chem. Phys. 122, 154303 ͑2005͒
3
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I͑cos ␪͒ + I͑cos ␪͒ = ͑1 + cos2 ␪͒.
͑A7͒
A
B
2
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