Core excitations of naphthalene: vibrational structure versus chemical shifts.

Abstract

High-resolution x-ray photoelectron emission (XPS) and near-edge x-ray absorption fine structure (NEXAFS) spectra of naphthalene are analyzed in terms of the initial state chemical shifts and the vibrational fine structure of the excitations. Carbon atoms located at peripheral sites experience only a small chemical shift and exhibit rather similar charge-vibrational coupling, while the atoms in the bridging positions differ substantially. In the XPS spectra, C-H stretching modes provide important contributions to the overall shape of the spectrum. In contrast, the NEXAFS spectrum contains only vibrational progressions from particular C-C stretching modes. The accuracy of ab initio calculations of absolute electronic transition energies is discussed in the context of minute chemical shifts, the vibrational fine structure, and the state multiplicity.

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J apan Advanced Institute of Science and TechnologyJ apan Advanced Institute of Science and Technology
J AIST RepositoryJ AIST Repository
https://dspace.jaist.ac.jp/
Title
Core exci tati ons of naphthal ene: Vi brati onal
structure versus chem i cal shi fts
Author(s)
M i nkov, I. ; Gel ' m ukhanov, F. ; Fri edl ei n, R. ;
O si kow i cz, W . ; Suess, C. ; O hrw al l , G. ; Sorensen,
S. L. ; Braun, S. ; M urdey, R. ; Sal aneck, W . R. and
Agren, H .
CitationJ ournal of Chem i cal Physi cs, 121(12): 5733-5739
Issue Date2004-09-22
TypeJ ournal Arti cl e
Text versionpubl i sher
URLhttp: //hdl . handl e. net/10119/4518
Rights
Copyri ght 2004 Am eri can Insti tute of Physi cs.
Thi s arti cl e m ay be dow nl oaded for personal use
onl y. Any other use requi res pri or perm i ssi on of
the author and the Am eri can Insti tute of Physi cs.
The fol l ow i ng arti cl e appeared i n I. M i nkov, F.
Gel ' m ukhanov, R. Fri edl ei n, W . O si kow i cz, C.
Suess, G. O hrw al l , S. L. Sorensen, S. Braun, R.
M urdey, W . R. Sal aneck, H . Agren, J ournal of
Chem i cal Physi cs, 121(12), 5733-5739 (2004) and
m ay be found at
http: //l i nk. ai p. org/l i nk/?J CPSA6/121/5733/1
Description

Page 2

Core excitations of naphthalene:
Vibrational structure versus chemical shifts
I. Minkov and F. Gel’mukhanova)
Theoretical Chemistry, Roslagstullsbacken 15, Royal Institute of Technology, S-106 91 Stockholm, Sweden
R. Friedlein, W. Osikowicz, and C. Suess
Department of Physics, Linko ¨ping University, IFM S-581 83 Linko ¨ping, Sweden
G. O¨hrwall
Department of Physics, Uppsala University, P.O. Box 530, S-751 21 Uppsala, Sweden
S. L. Sorensen
Department of Synchrotron Radiation Research, Institut of Physics, Lund University, P.O. Box 118,
S-221 00 Lund, Sweden
S. Braun,b)R. Murdey, and W. R. Salaneck
Department of Physics, Linko ¨ping University, IFM S-581 83 Linko ¨ping, Sweden
H. A˚gren
Theoretical Chemistry, Roslagstullsbacken 15, Royal Institute of Technology, S-106 91 Stockholm, Sweden
?Received 4 May 2004; accepted 28 June 2004?
High-resolution x-ray photoelectron emission ?XPS? and near-edge x-ray absorption fine structure
?NEXAFS? spectra of naphthalene are analyzed in terms of the initial state chemical shifts and the
vibrational fine structure of the excitations. Carbon atoms located at peripheral sites experience only
a small chemical shift and exhibit rather similar charge-vibrational coupling, while the atoms in the
bridging positions differ substantially. In the XPS spectra, C-H stretching modes provide important
contributions to the overall shape of the spectrum. In contrast, the NEXAFS spectrum contains only
vibrational progressions from particular C-C stretching modes. The accuracy of ab initio
calculations of absolute electronic transition energies is discussed in the context of minute chemical
shifts, the vibrational fine structure, and the state multiplicity.
Physics. ?DOI: 10.1063/1.1784450?
© 2004 American Institute of
I. INTRODUCTION
In recent years, significant technological advances allow
the production of highly monochromatic, polarized x-ray
synchrotron radiation with a spectral resolving power of the
order of 104. High experimental resolution is the key to ob-
serve vibrational fine structure and minute initial state
chemical shifts in free molecules1–4and possibly even in
adsorbates.5,6The high resolution may even reveal ‘‘hidden’’
processes, in particular, the nuclear dynamics connected with
ionization processes,7–10electronic excitations,11–13or possi-
bly even effects associated with charge transport at
interfaces6,14and in solids12,13,15,16might be studied. The en-
ergy separation between core-electronic states on different
sites,17,18and the existence of selection rules for transitions
to unoccupied valence orbitals,19,20make core excitations
particularly useful for the study of partial or local charge and
vibrational density distributions in small and medium-size
molecules,18and of the geometrical relaxation associated
with the presence of charges.21Different valence electron
densities at the various atomic sites give rise to differences in
the total energies of excitations, usually called ‘‘initial state
chemical shifts’’of core levels.22Shifts of a fraction of an eV
are sufficient to produce distinguishable lines in the spectra.
The dynamics of nuclear relaxation processes can in
some cases be resolved thanks to the high-energy resolution.
Recent advances in experimental techniques call for a better
understanding of the underlying physical processes by simu-
lations of x-ray spectra with refined theoretical models. The
study of processes in medium-size molecules like naphtha-
lene ?Fig. 1? might provide an understanding of even more
complex systems, larger molecules, and even solids.
In a system with two or more equivalent atoms, photo-
ionization or core excitation gives rise to several almost de-
generate electronic transitions. It is well known23that such
quasidegenerate excited states interact with each other via
nontotally symmetric vibrational modes. This results in the
localization of core holes. In the case of nonequivalent atoms
of the same chemical element, on the other hand, the
quasidegeneracy of the core-excited states is lifted. An accu-
rate calculation of electronic and vibrational energies is
therefore crucial to reveal the nature of interactions between
a charge or an excitation and the coupled nuclear-electronic
system of the molecule.
In the present paper we report high-resolution C(1s)
photoionionization and x-ray absorption spectra of the free
naphthalene molecule followed by their interpretation in
a?Permanent address: Institute of Automation and Electrometry, 630090 No-
vosibirsk, Russia.
b?Formerly S. Marciniak.
JOURNAL OF CHEMICAL PHYSICSVOLUME 121, NUMBER 1222 SEPTEMBER 2004
57330021-9606/2004/121(12)/5733/7/$22.00© 2004 American Institute of Physics
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Page 3

terms of electronic and vibronic relaxation mechanisms. In
particular, the relation between excitations at chemically
shifted atomic sites and their coupling to molecular vibra-
tions is discussed.
II. EXPERIMENT
The gas-phase spectra were obtained at beamline I411 at
MAX-Lab in Lund, Sweden.24A gas cell with an external
feed was used allowing high local gas densities ?local pres-
sure ?1?10?5mbar) and moderate temperatures of 40
?20°C in the target zone.
The Scienta SES-200 photoelectron spectrometer was
turned to the ‘‘magic angle’’ ?54.7°? between the electric
field vector of the light and the direction of the electron
emission. The near-edge x-ray absorption fine structure
?NEXAFS? spectrum was recorded in 5 meV photon energy
steps with the Auger yield technique. The C KLL Auger
electrons were collected with a kinetic-energy window be-
tween 240 and 274 eV. The intensity was normalized by the
incoming photon flux as measured using the current from a
gold grid. For energies at the C(1s) absorption edge, a pho-
ton energy resolution of 50–60 meV was employed. For the
x-ray photoelectron spectroscopy ?XPS? measurements, the
spectral width of the incident radiation was matched with the
energy resolution of the analyzer. The total energy resolution
for the C(1s) XPS line measured with 350 eV photons is
estimated to be about 75 meV.
Each scan was saved separately to minimize the effects
of beam instabilities during the measurements. During nor-
mal, stable operation, drifts at the MAX-II storage ring are
typically ?1 meV/min. The photon energies and the kinetic
energies of the electrons were calibrated from the position of
the Ar(2p) line excited by first and second-order light. Ab-
solute photon and electron energies have an uncertainty of
about 100 meV.
III. THEORY
Our calculations are based on the linear coupling
model—the excited state potential energy surface ?PS? Eexc
is approximated by a displaced ground state harmonic poten-
tial surface. While the minimum of the excited state PS
might be displaced from that of the ground state, a similar
curvature is assumed to be present. In spite of its simplicity,
this model is known to be of good accuracy for a number of
cases.25,26Using harmonic approximation, the Hamiltonian
has the following form ?atomic units?:
???
?Q?
Hˆ??
?2
2?1
2??
2Q?
2?,
?1?
where Q?and ??are the normal coordinates and the fre-
quencies of the vibrational mode ?. The displacement d?of
each normal mode’s excited state PS from the ground state
geometry is connected to the gradient of the PS
d??G?
??
2,
G???Eexc
?Q?
.
?2?
In order to obtain the probability for excitation from the
ground state vibrational level 0 to a vibrational level n?for a
particular mode ?, the overlap integral between the two vi-
bronicwavefunctions
?the
amplitude?23is needed,
Franck-Condon
?FC?
?0?n?????1?n?e??x/2?x?n?/2?
?n?!
.
?3?
Here x???d?
which depends on the excited state PS gradient G?.
The total overlap integral is a product of contributions of
all individual modes
2/2?G?
2/2??
3is a dimensionless parameter,
?0?n???
?
?0?n??.
?4?
It should be noted that the excited state PS gradient and
FC amplitude ?3? could differ for the ionization and the ex-
citation processes. The reason for this can be easily under-
stood in terms of the Koopmans’ theorem,
G?
ion?
?
?Q??E?1s?1??E0???
?
?Q??1s,
G?
exc?
?
?Q??E?1s→???E0???
?
?Q??????1s?,
where ?1sand ??are the orbital energies of the 1s and the
?th orbital. Comparison of these gradients shows that the
vibrational structure of NEXAFS and XPS spectra is differ-
ent because of the (???/?Q?) term. Notice that in our simu-
lations we calculated the gradients strictly, without using the
Koopmans’ approximation.
The x-ray absorption cross section was calculated in the
Born-Oppenheimer approximation
?abs?????
e,n
f0e?0?n?2
????Ee?E0????n
e??0??2??2,
?5?
where ? is the photon frequency; f0e is the oscillator
strength of the electronic transition 0→e; Ee, ?n
?0are the excited and ground state electronic and vibrational
energies, respectively; ?0?n?2is the FC factor.
The cross section of the core-ionization process reads
e, and E0,
FIG. 1. The naphthalene molecule and its chemically different atomic sites.
5734J. Chem. Phys., Vol. 121, No. 12, 22 September 2004Minkov et al.
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Page 4

?XPS?E???
N,n
DN
2?E??0?n?2
e??0??2??2.
?BE?IN???n
?6?
Here BE???E, is the energy of the photoelectron on a
binding energy scale, E the kinetic energy of the photoelec-
tron, and INthe C(1s) binding energy of the Nth carbon
atom. In the simulations the square of the transition dipole
moments of the photoionization process, DN
to be equal for all atoms. This approximation holds only for
large photoelectron energies.
Calculation of both core excitation and ionization are
performed using the independent channel approximation.27
This approximation is valid because of the large energy and
spatial separation of core orbitals of different atoms. This
approach has previously been tested and justified to be of
good accuracy.28–30
2(E), is assumed
IV. COMPUTATION
The geometry of the molecule has been optimized with
the GAUSSIAN 03 package31at the B3LYP/6-311G** level.
The vibrational analysis has been done at a ?10,10?-CASSCF
level of theory, with the same 6-311G** basis set using the
DALTON program package.32All transition dipole moments
and excitation energies were calculated using a modified ver-
sion of the DEMON code33employing the ?DFT ?DFT—
density functional theory? method. Two different nonlocal
density functionals were tested: BP86 and PBE ?for both
exchange and correlation energy?. In order to account for
core-hole relaxation, we have made use of a double-basis
technique.34For all carbon atoms, except the one undergoing
core excitation, an effective core-potential basis set of good
quality was used. In order to properly describe changes in the
electronic structure of the excited atomic center, the region in
its vicinity is described by a much larger, diffuse IGLO-III
basis set. Structural relaxation could be responsible for
breaking or lowering the symmetry of the core-excited
system.1,3Therefore, no symmetry was preassumed in any
part of the core-hole calculation.
In all of the mentioned codes there is no implemented
procedure for an analytical derivation of excited state energy
gradients. Therefore, the gradients ?2? needed for obtaining
FC factors have been calculated by a numerical differentia-
tion of the excited state PS. For each mode, three points of
the PS were calculated: one at the ground state geometry and
two symmetrically displaced in positive and negative direc-
tions (Q??0, ?7.26 a.u. ?amu). The centered derivative of
these three points was taken.
The displaced geometries were generated using the fol-
lowing transformation:
Xim?X0m?Aim,?
Q?
?1822,
where Ximis the displaced Cartesian coordinate i of the atom
m ?in a.u.?, X0mis the ground state Cartesian coordinate, Q?
is the normal coordinate of the normal vibrational mode ?
?in a.u. ?amu); Aim,?is a matrix transforming the normal to
Cartesian coordinates.
Two different values for the life-time vibrational broad-
ening have been chosen to account for the different spectral
resolution achieved in the NEXAFS and XPS experiments.
The half width at half maximum is ??45 meV for the NEX-
AFS simulations, while ??70 meV for XPS. For each set of
spectra, ? is assumed to be the same for all transitions.
V. RESULTS AND DISCUSSION
A. XPS
In Fig. 2 the experimental and simulated C(1s) photo-
electron spectra are presented ?Figs. 2?a? and 2?b?, respec-
tively?. The calculated vertical binding energies of the C(1s)
electrons at the three distinguishable carbon atom sites of the
naphthalene molecule ?denoted C1, C2, and C3 in Fig. 1? are
listed in Table I. These values are about 1 eV lower than
those obtained experimentally. Such a difference is expected
in the framework of the ?DFT method.27It was also found
that the results produced by the PBE and BP86 functionals
differ insignificantly.
Clearly, the shapes of the experimental and theoretical
spectra match quite well allowing an assignment of the indi-
vidual spectral features ?Fig. 3?. The spectrum does not ex-
hibit any resolved vibrational fine structure. Nevertheless,
vibrational degrees of freedom determine the width and the
shape of the individual C1, C2, and C3 lines forming the
overall profile ?see Figs. 2?b? and 3?.
The intense peak at the low-binding-energy side arises
from a superposition of spectral weight for the C2 and C3
atomic sites. The chemical shift between these sites is quite
small,28about 25 meV. The profiles of the two contributions
are almost identical, which indicates that the photohole
couples to similar vibrational modes on both atomic sites.
The main contribution comes from coupling to C-C stretch-
FIG. 2. Experimental ?a? and calculated ?b? C (1s) photoelectron spectrum
of naphthalene.
TABLE I. Vertical C (1s) binding energies for the three symmetrically dis-
tinguishable carbon atoms in naphthalene.
C1C2 C3
IN(eV)289.303288.965 288.988
5735 J. Chem. Phys., Vol. 121, No. 12, 22 September 2004 Core excitations of napthalene
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Page 5

ing modes and only minor excitations of C-H stretching.
However, the region of the C-C stretching modes is domi-
nated by only one of them ?Fig. 3 and Tables II, III, and IV?.
Since many modes are involved, a clear vibrational splitting
cannot be observed.
C-H vibrational contributions are absent for the C1 site
which is not connected to hydrogen atoms. Since fewer
modes are involved at C1, the profile also appears slightly
more structured and does not have a pronounced tail like
those of the two other sites. The binding energy for the C1
site is about 0.3 eV higher than that of the C2 and C3 sites.
The C1 peak overlaps with the long tails of the C2 and C3
atoms leading to a plateau in the total spectrum.
It is instructive to compare the coupling between core
holes and vibrations to the charge-vibrational coupling for
valence holes in naphthalene. The ionization of the highest
occupied molecular orbital ?HOMO? exhibits a pronounced
high frequency progression of about 180 meV, which is at-
tributed to the superposition of two unresolved, totally sym-
metric C-C stretching modes of 170.4 and 196.8 meV inter-
acting nonadiabatically, and small contributions of C-H out-
of-plane bending modes of about 60 meV.10A strong
increase of the coupling to such low-frequency vibrations is
observed for ionization of valence states at higher binding
energy, e.g., of the HOMO-1 and HOMO-2.10
A strong dependence of the charge-vibrational coupling
on the orbitals involved is confirmed by the present results
for core ionization. While low-energetic C-H out-of-plane
bending modes are dominant for some valence levels, such
as for the HOMO-2, they are virtually absent in the case of
core ionization. Additionally, the dominance of a single C-C
stretching mode for the C(1s) ionization does not match the
behavior for any of the valence orbitals and might also not be
expected since the creation of a core hole breaks the high
symmetry of the molecule.1,3
B. NEXAFS
The measured C(1s) NEXAFS spectrum in the region
of the x-ray absorption threshold and in a wider photon en-
ergy range ?inset? is shown in Fig. 4. There is only a weak
resemblance to an earlier spectrum from condensed naphtha-
lene films.35The originally dominating ?* resonance has
theoretically been described28to be actually composed of
two resonances. These resonances are now clearly resolved.
The first resonance denoted ?1* occurs between ???284.7
and 285.4 eV; the second denoted ?2* between ???285.6
and 286.5 eV. Additional resonances denoted 3, 4, 5, and ?6*
with contributions from either ?* or ?* symmetry28have
their maxima at about ???287.3, 288.5, 290.2, and 293.8
eV.
In the present highly resolved spectrum, the ?1* reso-
nance exhibits even a very pronounced fine structure with
individual peaks split by about 170 meV. Such a progression
is characteristic for C-C stretching modes. For a relatively
large molecule like naphthalene, the presence of this clearly
resolved vibrational fine structure is remarkable, since it re-
quires confinement of excitations to only one atomic site, or,
in case of two or more sites that the chemical shift between
them coincides ?accidently? with the vibrational energy of
about 170 eV. Furthermore, the sharpness of the peaks ?with
a width of the order of 160 meV? points to a rather selective
FIG. 3. Spectral lines of the vibrationally resolved XPS for the three atomic
sites, without life-time broadening. Numbers indicate the particular vibra-
tional mode which is excited.
TABLE II. Franck-Condon factors for the strongest vibrational modes
C (1s) photoionization at the C1 site—XPS.
Mode
? ?eV?
Symmetry
FC factors
?0?0?2
?0?1?2
?0?2?2
11
12
23
28
30
38
39
0.210
0.205
0.151
0.129
0.125
0.099
0.082
Ag
B3u
B2u
B3u
B3u
Ag
Au
0.954
0.988
0.989
0.979
0.974
0.426
0.923
0.044
0.012
0.011
0.021
0.025
0.363
0.073
0.001
0.000
0.000
0.000
0.000
0.155
0.003
TABLE III. Franck-Condon factors for the strongest vibrational modes
C (1s) photoionization at the C2 site—XPS.
Mode
? ?eV?
Symmetry
FC factors
?0?0?2
?0?1?2
?0?2?2
17
19
23
35
38
39
0.170
0.167
0.151
0.105
0.099
0.082
Ag
B1g
B2u
B2g
Ag
Au
0.989
0.977
0.976
0.958
0.850
0.649
0.010
0.022
0.024
0.041
0.139
0.281
0.000
0.000
0.000
0.001
0.011
0.061
TABLE IV. Franck-Condon factors for the strongest vibrational modes
C (1s) photoionization at the C3 site—XPS.
Mode
? ?eV?
Symmetry
FC factors
?0?0?2
?0?1?2
?0?2?2
18
23
31
35
36
0.169
0.151
0.121
0.105
0.104
B2u
B2u
B1g
B2g
B3g
0.982
0.956
0.901
0.798
0.952
0.018
0.043
0.093
0.180
0.046
0.000
0.001
0.005
0.020
0.001
5736J. Chem. Phys., Vol. 121, No. 12, 22 September 2004 Minkov et al.
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Page 6

coupling to vibrations in the core-excited state. These experi-
mental observations represent a challenge to the present ac-
curacy of the theoretical treatment of electronic energies ?of
the order of a few 10 meV for photon energies of about 285
eV? and the vibrational coupling in core-excited states.
The first two NEXAFS resonances ?1* and ?2* contain
predominantly transitions from the 1s level to the lowest
unoccupied molecular orbital ?LUMO?.28Feature ?1* com-
prises overlapping contributions from vibrationally broad-
ened C2 and C3 excitations ?see Figs. 4 and 5?. The C2
contributions are slightly lower in energy and cover a wider
energy range than those from the C3 site. The C1 peak is
positioned at higher energy, as expected from the core-level
binding energies, and gives rise to the ?2* feature. Our cal-
culations show that core excitations into the LUMO at the
C1 site display a pronounced vibrational structure caused by
one particular mode ?Table V?. This fine structure is not vis-
ible in the experimental spectrum. Instead, the ?2* resonance
has a double structure ?Fig. 4?. One possible explanation for
this discrepancy could be the presence of additional contri-
butions from excitations into the LUMO?1. LUMO and
LUMO?1 in the core-excited naphthalene are separated by
?1 eV.28However, the transition into the LUMO?1 is cal-
culated to have very low intensity due to small overlap of the
LUMO?1 with the 1s orbital of the excited atomic site. This
in turn leads to quite small values for the oscillator strength
of the 1s→LUMO?1 transition. Therefore, the observed
profile of the ?2* peaks is most likely not influenced by ex-
citations into the LUMO?1. Another possible explanation is
that the last vibrational feature from the ?1* band overlaps
with the ?2* and produces a double structure ?Fig. 5?.
In the NEXAFS simulations we consider all vibrational
modes of the naphthalene molecule. The vibrational splitting
for the three atomic sites originates predominantly from two
or three modes ?Table V, VI, and VII?. All vibrational modes
?with one exception—mode 41, at site C2? are excited only
up to the second vibrational level. This indicates that the
potential surface of the excited state is only slightly dis-
placed from that of the ground state. This is very different
from the case of ?small? linear molecules, like ethylene,21
and might be a consequence of the rigidity of more two-
dimensionalsystems.Compared
structures,36the polaronic distortion accompanying charges
in two-dimensional systems is smaller.9,10Nevertheless, this
small displacement is sufficient to create visible vibrational
fine structure in the NEXAFS spectrum of naphthalene.
The main contribution in the vibrational structure is due
to C-C stretching modes ?Fig. 6 and Tables V, VI, VII?. Most
of the C-H modes show substantial gradients of the PS, how-
ever, their contribution to the vibrational splitting is quite
small. Two main reasons for this behavior can be pinpointed.
?i? First, the LUMO of naphthalene almost does not
contain contributions from the hydrogen 1s orbitals. This
implies small changes of the electronic potential in the vicin-
ity of the hydrogen atoms upon core-excitation at carbon
atoms and, consequently, only minor contributions from C-H
modes.
?ii? The FC amplitude ?given in Eq. ?3?? is strongly de-
pendent on the vibrational frequency ?Eq. ?2??, and hence,
to one-dimensional
FIG. 4. Experimental NEXAFS spectrum of naphthalene in a wider and
narrower ?inset? energy range. Individual resonances are marked as ?1* ,
?2* , 3, 4, 5, and ?6* .
FIG. 5. Calculated NEXAFS spectrum of naphthalene and the contributions
from the three chemically different atomic sites.
TABLE V. Franck-Condon factors for the strongest vibrational modes in the
core excitation at the C1 site—NEXAFS.
Mode
? ?eV?
Symmetry
FC factors
?0?0?2
?0?1?2
?0?2?2
10
11
19
35
38
0.214
0.210
0.167
0.105
0.099
B2u
Ag
B1g
B2g
Ag
0.984
0.888
0.964
0.817
0.879
0.016
0.105
0.035
0.165
0.113
0.000
0.006
0.001
0.017
0.007
5737J. Chem. Phys., Vol. 121, No. 12, 22 September 2004Core excitations of napthalene
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Page 7

higher frequency causes the FC factors to increase and
quenches the vibrational fine structure. As the C-H stretching
modes have usually higher vibrational frequencies than the
C-C modes, the effect of high gradients is diminished.
As mentioned above, feature ?1* contains overlapping
contributions from C2 and C3 excitations. In this case, the
observation of a clearly resolved vibrational splitting in the
?1* feature can only be explained if the chemical shift be-
tween these two sites matches the vibrational energy of about
170 eV. In the simulations, a chemical shift of about 200
meV is obtained, leading to a different profile in the onset
region of the ?1* resonance, and even displaying two vibra-
tional peaks. A better agreement with the experiment is
achieved when the C2 peak is artificially moved towards the
C3 peak by about 100 meV ?Fig. 7?.
All aforementioned calculations have been performed at
the ?DFT level using the DEMON code. Within this method,
an open-shell system is treated by an unrestricted formalism.
In the current implementation, an unrestricted calculation
produces a spin-contaminated state, that is, a state with small
contributions from triplet states. This introduces an error on
the level of the exchange integral between the 1s and the
electron excited into the LUMO, which could be responsible
for the discrepancy between theory and experiment. The ex-
change integral ?1s,LUMO?LUMO,1s? is estimated to be
about 0.2 eV.
In order to avoid spin-contamination, the correct singlet
state needs to be constructed. For that purpose, we tested two
different methods for computating core-hole excitation ener-
gies. These methods include the restricted open-shell
Hartree-Fock ?ROHF? technique in the program package
DALTON32and the generalized valence bond method ?GVB?
in GAMESS-US.37
As expected, ROHF performs poorly. Although it pro-
vides values close to the correct excitation energies for the
C2 and C3 sites, the calculation seems to be inaccurate be-
cause the core orbitals are described as delocalized states. It
is known21that a localized description of the core hole is
needed to account for important relaxation effects. For the
second method, using the GAMESS-US package, a Boys local-
ization procedure and a GVB calculation were employed.
The energy difference between C2 and C3 is again about 200
meV ?Table VIII?, similar to the ?DFT calculation. Con-
structing the correct spin state does not improve the chemical
shift between the C2 and C3 sites in the NEXAFS spectrum.
With a total margin of error of 100–200 meV, the
present accuracy of ab initio methods used for the calcula-
tion of relative electronic transition energies from core levels
is too coarse to reproduce these small effects.
FIG. 6. Spectral lines of the NEXAFS for the three atomic sites, without
life-time broadening. ?a? Denotes three overlapping peaks—?0→1? transi-
tion for modes 18, 19, and a double ?0→1? excitation of modes 38 and 41.
?b? Denotes a double ?0→1? excitation of modes 18 and 41.
FIG. 7. Calculated NEXAFS spectrum of naphathalene and the contribu-
tions from the three chemically different atomic sites, with the absorption
energy for the C3 site being artificially lowered by 0.1 eV.
TABLE VI. Franck-Condon factors for the strongest vibrational modes in
the core excitation at the C2 site—NEXAFS.
Mode
? ?eV?
Symmetry
FC factors
?0?0?2
?0?1?2
?0?2?2
11
12
18
19
30
38
41
0.210
0.205
0.169
0.167
0.125
0.099
0.068
Ag
B3u
B2u
B1g
B3u
Ag
B1u
0.924
0.943
0.975
0.856
0.940
0.794
0.460
0.073
0.055
0.024
0.133
0.058
0.183
0.357
0.003
0.002
0.000
0.010
0.002
0.021
0.138
TABLE VII. Franck-Condon factors for the strongest vibrational modes in
the core excitation at the C3 site—NEXAFS.
Mode
? ?eV?
Symmetry
FC factors
?0?0?2
?0?1?2
?0?2?2
90.220
0.214
0.210
0.169
0.167
0.121
0.105
B1g
B2u
Ag
B2u
B1g
B1g
B2g
0.837
0.966
0.987
0.983
0.900
0.924
0.872
0.149
0.033
0.013
0.017
0.095
0.073
0.119
0.013
0.001
0.000
0.000
0.005
0.003
0.008
10
11
18
19
31
35
5738J. Chem. Phys., Vol. 121, No. 12, 22 September 2004Minkov et al.
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Page 8

VI. CONCLUSIONS
The fine structure of C(1s) photoionized and core-
excited states at the three chemically different carbon atomic
sites of the free naphthalene molecule has been experimen-
tally resolved and theoretically analyzed. Although the high
experimental resolution still represents a challenge to the cal-
culation of absolute electronic transition energies from core
levels, the spectral profile is well reproduced allowing an
asignment of individual features in the fine structure of the
spectra.
Compared to linear systems, the rigidity of the two-
dimensional lattice of the naphthalene molecule is respon-
sible for only a rather small geometrical relaxation in the
neutral core-excited or ionic final states, as manifested in the
small displacement of the potential surfaces, the vibrational
broadening of the photoelectron emission lines, and x-ray
absorption resonances.
The vibrational fine structure is dominated by particular
C-C stretching modes, and in the case of XPS of the C2 and
C3 sites also by high-energy C-H stretching modes. The sup-
pression of certain modes is found to be, to a great extent,
caused by the increase of the FC factors due to the high
frequencies of these modes. Since features arising from C-H
stretching modes are virtually absent in the naphthalene va-
lence spectrum, a strong dependence of the charge-
vibrational coupling on the electronic density distribution in
the individual orbitals is observed.
When it is possible to separate chemical shifts and vi-
brational excitations in such medium-size molecules, larger
and more complex systems can and will be addressed in the
near future with the same level of accuracy. Importantly, the
improved knowledge of electronic and vibronic relaxation
phenomena in molecules will provide an understanding of
optical and transport phenomena in molecular materials.
ACKNOWLEDGMENTS
The authors thank M. Tchaplyguine ?Uppsala University,
Sweden? for technical assistance, L. Saethre ?University of
Bergen, Norway?, and V. Coropceanu ?Georgia Institute of
Technology, Atlanta, USA? for fruitful discussions. The work
is performed in a collaboration within the Center for Ad-
vanced Molecular Materials ?CAMM?, funded by the Swed-
ish Science Foundation ?SSF? and additionally supported by
the Swedish Research Council ?VR? under Contract Nos.
12252003 and 12252020. In addition, research in Linko ¨ping
is supported by a Research Training Network ?LAMINATE,
Project No. 00135? and the EU-Growth project MAC-MES
?Project No. GRD-2000-30242?.
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TABLE VIII. Excitation energies ?in eV? and oscillator strengths (f?DFT) of
the three distinguishable carbon atoms in naphthalene using ROHF in DAL-
TON, GVB in GAMESS-US, and ?DFT in DEMON.
C1C2 C3
?ROHF
?GVB
??DFT
f?DFT
291.079
286.986
284.397
0.0162
296.653
285.955
283.583
0.0270
296.693
286.141
283.814
0.0252
1s→LUMO
5739J. Chem. Phys., Vol. 121, No. 12, 22 September 2004 Core excitations of napthalene
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