Angle-resolved photoion spectroscopy of NO2 and SO2

Angle-resolved photoion spectroscopy of NO2 and SO2

T. Gejoa,*, Y. Takatab,1, T. Hatsuib, M. Nagasonob, H. Ojib,N. Kosugia,b, E. Shigemasaa

a UVSOR Facility, Institute for Molecular Science, Okazaki 444-8585, Japanb Department of VUV Photoscience, Institute for Molecular Science, Okazaki 444-8585, Japan

Received 12 June 2002

Abstract

Based on recent conceptual and technological improvements for soft X-ray monochromators, a varied-line-spacing

plane grating monochromator of the Hetrrick type is installed on the bending-magnet beamline BL4B in the UVSOR

facility with a second generation VUV ring of the beam energy of 0.75 GeV. The BL4B has enabled us to realize various

spectroscopic investigations under high resolution conditions in the energy range of 90–800 eV. High-resolution angle-

resolved photoion-yield spectra (ARPIS) of NO2 and SO2 have been measured in the N and O K-shell excitation re-

gions. The fragment-ion yield spectra measured at 0� and 90� relative to the electric vector of the light reveal excitation

symmetries of complicated electronic states. The spectral features are interpreted in comparison with other transition

systems, and quantum chemical calculations show strong or weak Rydberg-valence mixing depending on the excitation

site in the molecule.

� 2002 Elsevier Science B.V. All rights reserved.

1. Introduction

Inner-shell photoabsorption spectroscopy is

one of the fundamental probes of molecular elec-

tronic and geometric structures [1]. Polarized

photoabsorption spectroscopy is the most power-ful tool to reveal their symmetries. The K-shell

excited state of free molecules is sometimes inves-

tigated by measuring the angular distribution of

fragment ions emitted with respect to the linear

polarization of synchrotron radiation [2–18]. In

this kind of spectroscopic techniques, the angular

distribution is related to the molecular orientation

upon the photoabsorption, because the lifetime of

the molecular K-shell excited state (s � 10�14 s) is

dominated by the Auger decay to dissociative

states with repulsive force like the Coulomb ex-plosion and is much shorter than the molecular

rotational period (s � 10�10 s). We have developed

a symmetry-resolved spectroscopy by measuring

angle-resolved spectra of the fragment-ion yield,

which achieves complete symmetry resolution be-

tween the DK ¼ 0 (parallel) and DK ¼ �1 (per-

pendicular) transitions in diatomic molecules

[6–11]. Furthermore, we have extended the angle-resolved photoion-yield spectroscopy (ARPIS) to

linear triatomic molecules [12–15] and linear

Chemical Physics 289 (2003) 15–29

www.elsevier.com/locate/chemphys

*Corresponding author. Fax: +81-564-55-7400.

E-mail address: [email protected] (T. Gejo).1 Present address: RIKEN, Spring-8, Sayo-gun, Hyogo 679-

5148, Japan.

0301-0104/03/$ - see front matter � 2002 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0301-0104(02)00724-3

mail to: [email protected]

acetylene [17]. It is found that the symmetry res-

olution is almost complete for dipole-allowed

transitions such as 1s–r� and 1s–Rydberg excited

states in the diatomic molecules. However, the

symmetry resolution is incomplete in Renner–

Teller split 1s–p� transitions [12–14], vibronicallyinduced 1s–Rydberg transitions [13,15], and other

vibronic couplings [17,18], where the excited states

are strongly coupled with bending vibrations.

Therefore, it is concluded that the deexcitation to

dissociative states takes place during low-energy

vibrations involving the bending motion but at

neither equilibrium geometries in the ground nor

excited states [12–18], where it should be noticedthat the anisotropic fragmentation is observable

even in symmetrical molecules such as CH4

through Jahn–Teller couplings with bending vi-

brations [15]. Moreover, in the case of linear tri-

atomic molecules, the ARPIS data for the total

fragment ions are not directly related to the sym-

metry of the excited state due to the three-body

fragmentation in addition to the bending vibra-tion. The central atom following the three-body

fragmentation is emitted much slower than the

terminal atoms, and, as a result, the ARPIS with a

high retarding potential can reduce a contribution

from the central atom [16].

The previous ARPIS measurements have been

achieved with undulator-radiation sources, which

have the great advantages on the degree of linearpolarization and on the intensity under high reso-

lution condition, and now widely provide tunable,

intense, and highly polarized soft X-rays through-

out the K-shell ionization range in molecules con-

taining first-row and second-row elements. On the

other hand, soft X-ray monochromators for the

bending-magnet (BM) synchrotron radiation have

been used to perform various studies on molecularvibrational spectroscopy at the K-shell threshold of

chemically important elements like C, N, and O;

however, the photon flux is limited to less than 108

photons/s under high resolution conditions [19,20]

and is not sufficient for ARPIS, photoelectron

spectroscopy, and fluorescence spectroscopy ap-

plied to molecular science. At the UVSOR facility

in the Institute for Molecular Science (IMS), onlyone soft X-ray monochromator [21] for high reso-

lution spectroscopy was being used. Although the

maximum resolving power of �4000 at 400 eV is

achievable, it is impossible to maintain such high

resolution in the entire photon energy range due to

the complex scanning mechanism [21].

Recently, we have constructed a new BM based

monochromator at BL4B in the UVSOR facilitywith a second-generation storage ring. A varied-

line-spacing plane grating monochromator (VLS-

PGM) based on the Hetrrick-type design [22] has

been chosen to achieve high energy resolution in

the soft X-ray range [23–28]. In this paper it is

shown that the BM based monochromator can

provide reasonable photon flux with high resolu-

tion in the soft X-ray range, which allows us torealize the ARPIS measurements under high res-

olution conditions. We have investigated the N 1s

and O 1s excited states of bent triatomic molecules

SO2 and NO2 based on the ARPIS measurements

and ab initio SCF-CI (self-consistent field and

configuration interaction) calculations.

2. Experimental

2.1. Beamline description

A schematic layout of the optical elements of

the present VLS-PGM is shown in Fig. 1. In front

of all optical elements, there is an aperture, located

1.9 m from the source position. The usual settingof this aperture is 3:8 mm ðVÞ � 14:3 mm (H),

which limits the half acceptance angle to

1 mrad ðVÞ � 3:75 mrad (H). The radiation is de-

flected horizontally by a cylindrical mirror M0.

This also serves as a vertical focusing mirror which

focuses the radiation onto an entrance slit S1 with

1:1 magnification. This magnification realizes a

line image with almost no aberration at the en-trance slit S1. It should be noted that we have in-

stalled the cylindrical mirror M0 vertically (sagittal

focusing) in order to realize this high horizontal

acceptance angle and 1:1 magnification. This is an

unusual configuration: normal Kark–Patlik con-

figuration uses two longitudinal cylindrical mirrors

[21,24]. However, the application of this configu-

ration to our beamline needs much smaller mag-nification, which results in the poor image at the

entrance slit. Therefore, it is crucial to install a

16 T. Gejo et al. / Chemical Physics 289 (2003) 15–29

sagittal mirror as M0, because this makes the dis-

tance from the source point as short as possible. A

cylindrical mirror M1 is located 1.1 m behind M0,

and focuses the radiation horizontally. M0 and M1

(Si substrates) are cooled from both sides by wa-

ter-cooled copper blocks coated with Ni.

The spherical mirror M2 is one of the most

important optical elements to achieve high reso-

lution, which focuses the radiation through the

entrance slit S1 onto an exit slit S2. The slits can be

set to opening widths ranging from 0 to 1000 lm.Two holographically ruled laminar profile planegratings with varied-line-spacings are designed to

cover the energy range from 90 to 800 eV. The

gratings with the groove densities of 267 and 800

lines/mm at the central positions cover the spectral

ranges of 90–270 and 270–800 eV, respectively,

and are interchangeable without breaking the

vacuum condition. A constant deviation angle of

the gratings is 174� and the fixed entrance and exitslit arm lengths are 4.0 and 4.006 m. The refo-

cusing mirror M3 has a toroidal shape, which fo-

cuses the monochromatized radiation on the

sample. The incidence angle of M3 is 87.5�, in or-

der to make the exit beam horizontal. All the op-

tical elements are coated with Au. TOYAMA

manufactured the beamline components and also

performed the initial installation and alignment of

the beamline. M0; M1 and M3 were made by Ca-

non, and M2 and gratings were produced by Carl

Zeiss. A monochromator-control/data acquisition

program has been written in Labview (NationalInstruments). A differential pumping section is

installed in between the M3 refocusing mirror

chamber and the focusing position, in order to

avoid rapid contamination of the optical elements,

since this beamline has been constructed for the

study of not only solid state but also gaseous

samples. This considerably isolates the refocusing

mirror from the experimental station. It has beenconfirmed that the pressure increase of the exper-

imental chamber was attenuated by a factor of

about 105 in the refocusing mirror chamber. A

mesh coated with Au is installed in the differential

pumping section, to monitor the photon intensity

I0 for normalization.

2.2. Photoabsorption and angle-resolved photoion-

yield experiments

A conventional gas cell system with leak tight

thin windows and a silicon photodiode (model

AXUV-100) supplied by International Radiation

Detectors were used to measure photoabsorption

spectra. A 1500 �AA aluminum window from Luxel

was installed at the upperstream of the gas cell.

Fig. 1. Schematic layout of the VLS-PGM beamline BL4B at UVSOR.

T. Gejo et al. / Chemical Physics 289 (2003) 15–29 17

The silicon photodiode was set at the downstream

of the gas cell, and was utilized to measure the

photon intensity after photoabsorption by sample

gases in the cell. A typical gas pressure in the cell

was about 100 mTorr, which was measured by a

baratron from MKS. The experimental setup forangle-resolved photoion spectroscopy is shown

schematically in Fig. 2. Two identical ion detectors

(channeltrons) with retarding grids were posi-

tioned to detect the photoions emitted at 0� and90� with respect to the electric vector of the inci-

dent light, respectively. The ARPIS spectrum at 0�(I0) was obtained by counting the signals for the

energetic fragment ions (>2 eV), detected by the at0� positioned detector, as a function of the photonenergy. The I90 spectrum was obtained by the same

procedure using the at 90� positioned detector.

These two spectra were measured simultaneously

by a single scan of the monochromator. The dif-

ferent detection efficiencies of the two analyzers

have been corrected using the same coefficient as

determined in the calibration measurements forN2, because the experimental arrangement has

been unchanged during the course of the mea-

surements. The valence contributions are consid-

ered as being constant in the K-shell excitation

regions. The typical background pressure in the

experimental chamber during the course of the

ARPIS measurements was about 5� 10�5 Torr.

The gas samples were all commercially available

and used without further purification except for

NO2. Since it was found that the commercially

available NO2 gas contains a considerable amount

of NO molecules as an impurity, NO2 gas was

purified by cooling and pumping the cylinder priorto use. No dimers are expected to be present at the

low pressure employed in the present experiments

[29].

2.3. Evaluation of the beamline

2.3.1. Photon flux

The silicon photodiode is used to measure theabsolute photon fluxes for two gratings. With the

entrance and exit slit openings set at 25 and 10 lm,corresponding to the theoretical resolving power

of 10 000 at 400 eV with the 800 lines/mm grating,

the photocurrent from the photodiode was mea-

sured behind the sample position. The photocur-

rent was converted into the absolute photon flux,

taking account of the quantum efficiency of thephotodiode. The data obtained are normalized to

a stored electron ring current of 100 mA. Fig. 3

Fig. 2. The experimental setup for angle-resolved photoion

spectroscopy.

Fig. 3. Output photon flux for a ring beam current of 100 mA.

The data were measured with vertical widths of 25 and 10 lmfor the entrance and exit slits, respectively. A black dot shows

the theoretical photon flux at 550 eV.


shows the normalized photon intensity curves for

two gratings at the present VLS-PGM beamline.

The photon flux for the 267 lines/mm grating is

more than 1� 109 photons/s in the photon energy

range of 90–270 eV, while that for the 800 lines/

mm grating ranges from 108 to 109 photons/s inthe photon energy region from 300 to 1000 eV,

which is a little smaller than our estimation

ð7� 108 photons/s/100 mA at 550 eV). This dis-

crepancy is probably attributable to an error in the

focal length of the first mirror M0, an overly op-

timistic estimation of the grating efficiencies in the

calculations, and carbon and oxygen contamina-

tion of the optical elements.

2.3.2. Resolution

Resolution is an important index for the per-

formance of monochromators. However, the ex-

perimental determination of the resolving power is

strongly dependent on the natural line widths as-

sumed in the deconvolution procedure. In the

following line shape analyses, the values of theGaussian broadening, which was assumed to re-

flect the instrumental resolution, are determined

by using Voigt functions, and the Lorentzian

natural linewidths were fixed to the smallest values

found in the literature [28,30]. Note that there are

some uncertainties in this estimation of the re-

solving power owing to the error in the fitting

routine and underestimation of the Lorentziannatural linewidth [28,30]. As examples, the inner-

shell photoabsorption spectra of N2 and O2 were

measured with the grating of 800 lines/mm and

that of Ar was also measured with the 267 lines/

mm grating. The resolving power dependences of

the K-shell photoabsorption spectra of N2 at the N

1s! p� resonance are presented in Fig. 4. The

combinations of the entrance and exit slit openingsutilized were 50–20, 25–10, and 12.5–5 lm, re-spectively. It is difficult to determine the trans-

mission function of the monochromator with the

N 1s! p� excitation of N2, because the natural

linewidths of this state are not well-established.

Temporarily, the natural line width having Lo-

rentzian shape is assumed to be Cnat ¼ 109 meV

[28]. The best-fits by the least-squares method re-sult in the Gaussian widths of 140, 91 and less than

40 meV, corresponding to the resolving power of

2860, 4400, and more than 10 000, respectively. At

the slit openings of 12.5–5 lm, each line shape ofthe vibrational structures in the measured spec-

trum resembles the Lorentzian profile and thus it

becomes impossible to be expressed by the Voigt

profile any more. Fig. 5 shows the high resolution

photoabsorption spectrum of N2 in the K-edge

Fig. 4. Absorption spectra of N2 at the N 1s! p� resonance.

Fig. 5. Absorption spectrum of N2 in the K-edge region.


region, except for the p� resonance. The asym-

metric slit widths of 25–10 lm was used. A small

structure attributed to 7pp Rydberg states can be

resolved. Vibrational side bands are clearly ob-

served in the lowest Rydberg series, and small fine

structures around 415 eV which arise from thedouble excitations are also obviously detected. The

achieved resolving power for this measurement

exceeds 5000 and is comparable with the highest

resolving power reported from undulator-based

SGM beamlines [25].

Fig. 6 indicates the K-shell photoabsorption

spectrum of O2. The entrance and exit slit open-

ings were set at 15 and 7.5 lm, which correspondto the theoretical resolving power of 10 000 at the

oxygen K-edge region. Many fine structures due to

the Rydberg excitations and their vibrational side

bands are detected on the broad enhancements

owing to the r� resonances. Due to these compli-

cated absorption features, the estimation of the

monochromator resolution from the measured

spectrum is difficult in the case of O2. From thecomparison with all available spectra of the Ryd-

berg resonances around 530 eV, the resolving

power obtained here is more than 5000. Fig. 7

shows the photoabsorption spectrum in the vicin-

ity of the 2p ionization thresholds of Ar measured

with the use of the 267 lines/mm grating. ThisFig. 6. Absorption spectrum of O2 in the K-edge region.

Fig. 7. (a) Absorption spectrum of Ar in the 2p excitation re-

gion. Ar 2p3=2 ! nd Rydberg series up to n ¼ 7 are clearly seen.

(b) Blowup of the 2p3=2 ! 4s peak. The peak was fitted with a

Voigt function whose Lorentzian width was Cnat ¼ 111 meV,

which provides an experimental broadening of 64.0 meV.


spectrum was recorded with the entrance and exit

slit openings of 15 and 7.5 lm, respectively. TheAr 2p3=2 ! nd Rydberg series up to n ¼ 7 are

clearly seen in Fig. 7. The fitting procedure with a

Voigt function, whose Lorentzian width was fixed

at Cnat ¼ 111 meV [31], provides an experimentalbroadening of 64.0 meV. This value corresponds

to a resolving power of about 4000.

Our experimental setup for the ARPIS mea-

surements requires the photon intensity to be more

than 108 photons/s, in order to obtain spectra with

reliable signal-to-noise ratios. It is found that the

performance of our monochromator is high en-

ough to realize high resolution ARPIS measure-ments in the entire photon region of interest.

3. Theoretical

The O 1s and N 1s core-to-valence excited states

of SO2 and NO2 were calculated by multi-reference

configuration interaction including single anddouble excitations (MR-SDCI) [32]. The molecu-

lar geometries for the calculations were taken from

those for the ground states. The CI calculations

were carried out using SCF (self-consistent field)

orbitals for the doublet or triplet 1s ionized states,

which were obtained from the use of the GSCF3

code [33,34]. Symmetry-adapted molecular orbi-

tals were used even for the O 1s excited states witha localized character, which can be taken into ac-

count through MR-SDCI. A well-balanced de-

scription of both the ground state and the core

hole states was considered, where the orbital de-

pendence can be mostly removed by a reasonable-

scale CI expansion [32]. The contraction scheme

for basis functions of N and O was (4111111/3112)

for core-excited atoms and (721/52) for others,taken from the contracted Gaussian-type func-

tions (73/7), as proposed by Huzinaga et al. [35].

The sulfur basis function (5321/521) was taken

from the contracted functions (533/53) [35]. They

were augmented with d-type polarization func-

tions ðad ¼ 0:421 for S, ad ¼ 1:154 for O, and

ad ¼ 0:864 for N) [35]. The core-to-Rydberg ex-

cited states were calculated with the static ex-change calculations using the SCF orbitals for the

core ionized states as previously calculated [7,8].

Basis functions for s-, p-, and d-type Rydberg

states were expanded as follows: as ¼ 0:075, 0.027,0.0064, 0.0022, 0.0012; ap ¼ 0:048, 0.020, 0.0058,0.0020, 0.0011; ad ¼ 0:035, 0.012, 0.0034, 0.0015.

4. Results and discussion

4.1. O K-edge of SO2

The SO2 molecule has three unoccupied valence

orbitals, 3b�1; 9a�1 and 6b

�2, which can be associated

with the three S 3p orbitals, where SO2 has an

electronic structure of S4þ½ð3sÞ2ð3pÞ0� ðO2Þ2 in thelimit of an ionic bonding picture and the 3b1; 9a1and 6b2 orbitals correspond to out-of-plane S3p

p ðpout), in-plane S3p p ðpinÞ and in-plane S3p r,respectively [16]. All the S1s (1a1) excitations to the

3b�1, 9a�1 and 6b

�2 orbitals are dipole-allowed and are

found to be lying below the S1s! Rydberg exci-

tations with the term values of 10.4, 5.7, and 4.8 eV,

respectively [16]. In SO2, the chemical bond betweenS and O is not so strong, and even the excitation to

the most antibonding r� ð6b2) orbital is located

below the ionization threshold. The single excita-

tions to all the unoccupied valence orbitals are ob-

served below the ionization threshold even in the

case of the O1s absorption spectra assigned previ-

ously [36,37], though there are twoO1s orbitals, 1b2and 2a1. The 1b2–2a1 splitting caused by the inter-action between the two O 1s orbitals is expected to

be negligible and does not change the situation.

Fig. 8(a) shows the O K-edge photoabsorption

spectrum of SO2. The entrance and exit slit open-

ings were set at 20 and 10 lm, respectively, to get aresolving power of �5000. The photon energy

scale was calibrated on the basis of the absorption

spectra of O2 [7,11]. The lowest photoabsorptionfeature A observed at 530.56 eV is well separated

from the higher features. The feature A is attrib-

uted to the O 1srð2a1Þ ! p�ð3b1) transition, con-sidering its term value of 9.27 eV. It should be

noted that the B1 state is dipole-allowed out-of-

molecular plane (p�Þ transition from the A1

ground state, the A1 and B2 states are dipole-

allowed in-plane transitions, and the A2 state isdipole-forbidden; the p�ð3b1) orbital is not acces-sible with the O 1srð1b2) electron. Between the


lowest 1s! p� excitation at 530.56 eV and the O

K-shell ionization threshold at 539.83 eV, the

spectral feature is dominated by some broad bands

labeled as B, C, and D at �535 eV (term values of�5 eV) arising from the 1s! in-plane excitations,

which consist of the O 1s! 9a�1 (dipole-allowed B2

from 1b2 and A1 from 2a1) and O 1s! 6b�2 (di-

pole-allowed A1 from 1b2 and B2 from 2a1) tran-

sitions. The structures E, F, and G are

comparatively weak and have term values of 2.24,

1.63, and 0.75 eV, respectively; therefore, they are

possibly assigned to the lowest s-type (4s or 5s)and p-type (4p or 5p) Rydberg transitions. In the

continuum, two broad bands are observed around

540.80 and 542.69 eV, which are attributable to

double excitations or S 3d-type shape resonances,

because there are no other singly excited valence

states than the 1s! 3b�1; 9a�1 and 6b�2 transitions.

Fig. 8(b) indicates the present O K-edge ARPIS

spectra of SO2, where the dots and the solid line

represent I90 and I0, respectively. The peak A is

definitely assigned to the O 1s(2a1Þ ! pð3b1Þ exci-tation. However, the features of B–D in Fig. 8 are

difficult to assign even with the help of the ARPIS

spectra. To reveal more details of the features B–D

assigned to the 1b2=2a1ðO1sÞ ! 9a�1=6b�2 excita-

tions, we have measured retarding potential de-

pendence of the anisotropy parameterb as in the

previous work on the S 1s excitation [16]. The

higher retarding potential can reduce contributionsto the b-value from the three-body fragmentation,

especially, central ions with different anisotropic

fragmentation [16], and then we have only to focus

on the relative angle of the transition dipole di-

rection and the broken O–SO bond. The b-value isobtained from the measured quantities I0 and I90 byuse of the following definition:

b ¼ 2ðI0 � I90ÞI0 þ 2I90

:

As long as the two-body dissociation takes place

between the O and SO fragments, the anisotropyparameter can be used as the asymmetric parameter

b ¼ 3 cos2 h� 1, where h is the angle between the

broken bond and the transition dipole direction. If

the ground state C2v geometry with the equilibrium

bond angle he ¼ 119:33� is kept during the frag-

mentation, the two-body fragmentation results in

b ¼ 1:23 ðh ¼ 30:3�Þ for the B2 A1 (1b2 ! 9a1and 2a1 ! 6b2) transitions and b ¼ �0:23 ðh ¼59:7�) for A1 A1ð2a1 ! 9a1 and 1b2 ! 6b2), and

b ¼ �1 ðh ¼ 90�Þ for B1 A1 ð2a1 ! 3b1) as

previously discussed [16]. If the C2v geometry is

lowered due to the core hole localization on one

oxygen atom, it is no meaning to distinguish 2a1and 1b2, resulting in b � þ2 and )1, consideringthe orbital character of 9a1 and 3b1 [16].

Fig. 9 shows the results of the retarding poten-tial dependence of the anisotropy parameter b,where the retarding potential was changed from 1

to 8 V, together with the photoabsorption spec-

trum. The b-values are strongly dependent on the

retarding potential: the b-value of the lower-energyfeature B increases from 0.1 to 0.3, while the b-

Fig. 8. (a) Absorption spectrum of SO2 in the O K-edge region.

(b) Angle-resolved ion yield spectra of SO2. Dotted and solid

lines denote I90 and I0 ion yields, respectively.


value of the higher-energy feature C decreases from

0.35 to 0.1 with increasing the retarding potential.

This behavior is completely inverse of the retarding

potential dependence in the lower and higher S 1s

excited states, where the lower is assigned to the

A1 A1 transitions of 1a1 ! 9a1 and the higher to

the B2 A1 transition of 1a1 ! 6b2 [16]. Consid-

ering that the O 1s orbitals have a1 and b2 sym-

metries, the feature B might be assigned to theB2 A1 transition (1b2 ! 9a�1 and/or 2a1 ! 6b�2)

and C to the A1 A1 transitions (2a1 ! 9a�1 and/

or 1b2 ! 6b�2), where we could not discuss which is

the lower, 9a�1 or 6b�2, and what is the feature D.

In order to assign these peaks more accurately

we have performed the SCF-CI calculations. Table

1 summarizes the experimental and calculated re-

sults and the present assignments in comparisonwith other assignments [36,37]. The calculated re-

sults show that both the 1b2 ! 9a�1 ðB2Þ and

2a1 ! 9a�1 ðA1Þ transitions contribute to the fea-

ture B but 1b2 ! 9a�1 ðB2Þ is much stronger than

2a1 ! 9a�1, and that both the 1b2 ! 6b�2ðA1Þ and2a1 ! 6b�2 ðB2Þ transitions contribute to the fea-

ture C but 1b2 ! 6b�2ðA1Þ is much stronger. That

is, the 9a�1 orbital is lower in energy than the 6b�2orbital, similarly to the case of the S 1s excitation

[16]; however, the excitations from the b2-symme-

try core orbital are dominant in the case of the O

1s excitation, resulting in the inverse retarding

potential dependence for 9a�1 and 6b�2 in the S 1s

Table 1

Assignments of the O 1s absorption spectra of SO2

Label Eexpt Texpt ðn�Þ Tcalc Assignments Ref. [37] Ref. [36]

A 530.56 9.27 (1.21) 9.67 B1 ð1sa1 ! 3b1p�Þ 3b�1 9.28 (p1) 3b�1 9.58 (p1)

9a�1 5.63 (p2)

B 535.01 4.82 (1.68) 5.11(s)a B2 ð1sb2 ! 9a�1Þ 9a�1 4.79 (p2) 6b�2; 4sa1 5.19 (p3)

5.04(w)a A1 ð1sa1 ! 9a�1ÞC 535.96 3.87 (1.87) 4.09(s) A1 ð1sb2 ! 6b�2Þ 6b�2 4.03 (p3) 4pb1 4.59 (p4)

4.01(w) B2 ð1sa1 ! 6b�2ÞD 536.48 3.35 (2.02) 3.22 4sa1 ðA1;B2Þ 4sa1 3.47 (p4) 4pa1 3.94 (p5)

E 537.59 2.24 (2.46) 2.50 4pb1 ðB1Þ 4pb2 2.22 (p5) 2.94 (p6)

1.99 4pa1 ðA1;B2ÞF 538.20 1.63 (2.89) 1.65 4pb2 ðA1;B2Þ 3da1 1.64 (p6) 4pðþ3dÞb2 2.38 (p7)

1.53 3db1ðB1ÞG 539.08 0.75 (4.26) 4da1 1.08 (p7) 3db1; a1; a2 1.67 (p8)

I.P. 539.83b

H 540.80 )0.97 Double excitation shape res. or d-type shape res. )1.27 (p10)

I 542.69 )2.86

Transition energies (E, uncertainties of �0.05 eV), experimental and calculated term values ðT Þ, effective principal quantum

numbers ðn�Þ. 1sa1 and 1sb2 correspond to the O1s orbitals with the 2a1 and 1b2 symmetries.a Strong (s) and weak (w) transitions.b Taken from Ref. [42].

Fig. 9. Retarding potential dependence of the anisotropy pa-

rameter b of SO2 in the O K-edge region, together with the

absorption spectrum.


(a1) excitation. The feature D is assigned to the O

1s(1b2=2a1Þ ! 4sa1 Rydberg excitations. The cal-

culation also shows that E is assigned to the O

1s(2a1Þ ! 4pb1 and O 1s(1b2=2a1Þ ! 4pa1 Ryd-

berg excitations and F is assigned to the O

1s(1b2=2a1Þ ! 4pb2 and O 1s(2a1Þ ! 3db1 Ryd-berg excitations.

4.2. N K-edge of NO2

The NO2 molecule has a similar molecular

structure to SO2, being bent with the terminal ox-

ygen atoms and belonging to the point group C2v.

NO2 has one additional electron as an unpairedelectron to the linear molecules CO2 of the Dah

symmetry with three unoccupied orbitals, 2p�u; 5r�g,

and 4r�u [13,14], and N2O of the Cav symmetry with

three unoccupied orbitals, 3p�; 8r�, and 9r� [12].The ð2p�uÞ

1and (3p�Þ1 states of CO2 and N2O are

degenerate and are stabilized in a bent geometry due

to the Renner–Teller effect [12–15], where 2p�u of

CO2 is split into in-plane p�ð6a�1) and out-of-planep�ð2b�1), where the former and the latter have bent

and linear stable geometries, respectively, and the

former is lower in excitation energy than the latter.

Thus, NO2 has one half-filled valence orbital 6a�1and three unoccupied valence orbitals, 2b�1; 7a

�1,

and 5b�2, which correspond to 3b�1; 9a�1, and 6b�2 in

SO2. NO2 has still strong covalent bonds betweenN

and O even with an electron in the antibonding 6a�1orbital, and the N and O 1s! 5b�2 excitations are

expected to be observed above the ionization

thresholds, similar to the case of the 1s! 4r�u ex-citation in CO2 and the 1s! 9r� excitation in N2O

[12]. This situation is different from the case of SO2

with weak S–O bonds as already discussed above.

Figs. 10(a) and (b) display the photoabsorption

and ARPIS spectra of NO2 in the Rydberg excita-tion regionwith a resolution of�3000. The dots andthe solid line represent I90 and I0, respectively. Theinner-shell excitation spectra with moderate energy

resolution have already been reported using elec-

tron energy loss spectroscopy (EELS) [38]. The

photon energy scale was calibrated on the basis of

this EELS spectra. Below the N K-shell ionization

thresholds, two strong peaks, A and B, are ob-served. The intensity of the higher-energy peak B at

403.26 eV is twice as strong as that of the lower peak

A at 401.03 eV. The higher peak B is easily assigned

to the N 1s 2a1 ! 2b1 p�ðB1) transition, and the

lower peak A is assigned to the N 1s2a1 ! 6a�1 ðA1),

as a result of the unpaired electron in the half-filled

6a1 valence orbital. These assignments are alsoreasonable, taking account ofweakR (in-plane) and

strongP (out-of-plane) characters of the lower- and

Fig. 10. (a) Absorption spectrum of NO2 in the N K-edge re-

gion. (b) Angle-resolved ion yield spectra of NO2. Dotted and

solid lines denote I90 and I0 ion yields, respectively, in the N K-

edge region. (c) Absorption spectrum of NO2 in the photon

energy range between 408 and 414 eV.


higher-energy peaks in the ARPIS spectra as shown

in Fig. 10(b), respectively. Above these two reso-

nances, the spectra exhibit relatively weak struc-

tures up to the thresholds, which may be

attributable to the Rydberg states and the Rydberg-

valence mixed states. The excitation to 7a�1 isexpected to be less contributive to the spectral in-

tensity, considering that 7a�1 of NO2 corresponds to

5r�g in CO2 and 8r� inN2 Owith s-type character on

the central atom and the excitation from theK-shell

to the s-type state should be weak [12,13,18]. In the

continuum, only one broad band around 416 eV is

observed and is attributed to a r� continuum shape

resonance originating from the strong r� antib-onding orbital of 5b�2 [38].

Fig. 10(c) represents the blowup of the photo-

absorption spectra of NO2 in N K-edge region

with a resolution of �5000. Table 2 is the sum-

mary of the present experimental results and

assignments based on the MR-SDCI and static

exchange calculations, whose results are not

explicitly shown. The calculations indicate that the

valence and Rydberg transitions converging to the

triplet ionization threshold are dominant, which

supports the assumption by Zhang et al. [38]. The

triplet and singlet separations are observed for the

3s Rydberg states, C and D, where the total spincoupling is doublet and the exchange effect in-

volving the Rydberg electron is estimated to be

0.18 eV at the most from the difference in their

term values. Furthermore, the calculations show

that the 7a�1 valence is completely dissolved in the

Rydberg sea [12,39] and cannot be assigned to a

specific peak. The 7a�1 valence is mainly mixed into

the s-type Rydberg, especially the 3s and 4s Ryd-berg (assigned to features C and G in Fig. 10), but

the intensity contribution is small, as expected

above. The features E/F, I/J, and M are mainly

attributed to p-type Rydberg transitions converg-

ing to the triplet ionization threshold. Moreover, it

is found from the calculations that the 1s! db1ðp)triplet channel is relatively strong among the

Table 2

Assignments of the N 1s absorption spectra of NO2

Label Energy TT ðn�Þ TS ðn�Þ Assignments Ref. [38]

A 401.03 11.57 12.27 6a�1 401.04 (p1) 6a�1(T)

B 403.26 9.34 10.04 2b�1(T) 2b�1(S) 403.28 (p2) 2b�1(T)

408 (p3) 4sa1(T)

C 408.92 3.68 (1.92) 4.38 3sa1(T) 408.92 (p4) 4pb1(T)

D 409.44 3.16 3.86 (1.88) 3sa1(S) 409.48 (p5) 4pa1(T)

E 409.97 2.63 (2.27) 3.33 3pb1(T)

F 410.06 2.54 (2.31) 3.24 3pa1;b2(T) 410.08 (p6) 4pb2(T)

410.48 (p7) 5sa1(T)

410.68 (p8) 7a�1(T)

G 410.74 1.87 (2.70) 2.57 (2.30) 4s/3da1(T) 3pb1(S) 410.84 (p9) 3db1(T)

H 411.04 1.56 (2.95) 2.26 (2.45) 3db1(T) 3pa1;b2(S) 411.04 (p10) 3da1; 5pb1(T)

I 411.32 1.28 (3.26) 1.98 (2.62) 4pb1(T) 4s/3da1(S) 411.28 (p11) 5pa1(T)

J 411.40 1.20 (3.37) 1.90 (2.78) 4pa1;b2(T) 4s/3da1(S) 411.52 (p12) 4db1; 6pb1(T)

K 411.57 1.03 (3.63) 1.73 (2.80) 5s/4da1(T)

L 411.71 0.89 (3.91) 1.59 (2.93) 4db1(T) 411.76 (p13) 6pa1; 4da1; 5db1(T)

M 411.89 0.71 (4.38) 1.41 (3.11) 5p(T) 411.96 (p14) 5da1; 7pb1; 7pa1(T)

5da1; 6da1; 7da1(T)

N 411.99 0.61 (4.72) 1.31 (3.22) 6s/5da1(T) 4pb1(S)

O 412.11 0.49 (5.27) 1.19 (3.38) 6p(T) 4pa1;b2(S)

P 412.22 0.38 (5.98) 1.08 (3.55) 5db1(T) 5s/4da1(S)

Q 412.47 0.13 0.83 (4.05) 4db1(S)

I.P.a 412.6 413.3

Q 416.43 5b�2-shape res 416.16 (p16) 5b�2

Transition energies in eV, term values ðT Þ for triplet and singlet ionization thresholds, TT and TS (uncertainties of �0.05 eV), andeffective principal quantum numbers n�.

a Taken from Ref. [43].


1s! d-type transitions and the features H, L and

P have the same type of contributions.

4.3. O K-edge of NO2

Fig. 11(a) shows the photoabsorption spectrumof NO2 in the O K-edge region with an energy

resolution of �5000. Fig. 11(b) demonstrates theARPIS spectra with a resolution of �3000. Thedots and the solid line denote I90 and I0, respec-tively. The photon energy scale was also calibrated

on the basis of the EELS spectra of NO2 [38]. The

splitting caused by the interaction between two O

1s orbitals (1b2 and 1a1) is expected to be negligi-ble as already discussed for SO2. The lowest two

features A and B are the same as in the N 1s ex-

citation spectra shown in Fig. 10, and are simply

assigned to the O 1s1a1=1b2 ! 6a�1 ðA1;B2) and O

1s 1a1 ! 2b�1 ðB1) transitions, respectively, where

the O 1s 1b2 ! 2b�1 ðA2) transition is dipole-for-

bidden. In NO2, the O 1s 1a1 transition is also

contributive, in contrast to the O 1s 1b2 transitionin SO2. On the other hand, the other part is not

well resolved in Fig. 11. Fig. 11(a) shows rather

strong features in the Rydberg excitation region,

and a comparatively strong and broad enhance-

ment above the ionization thresholds. The latter is

assigned to the O1s! 5b�2 shape resonance, simi-

lar to the case of the N 1s excitation, though

J€uurgensen and Cavell [36] assigned the shape res-onance to the a1 symmetry.

Table 3 recapitulates the experimental and cal-

culated results and assignments, in comparison

with the other assignments [36,38]. The excited

states converging to the triplet ionized state are

lower in energy than the states converging to the

singlet, in disagreement with one of the previous

work [36], but in good agreement with the other[38]. Similar to the case of the N 1s excitation, the

calculations manifest that the 7a�1 valence is com-

pletely dissolved in the Rydberg sea [12,39] and

cannot be assigned to a specific peak. The 7a�1valence is mainly mixed into the s-type Rydberg,

especially the 4s and 5s Rydberg (assigned to the

features D and E in Fig. 11). In contrast to the

central N 1s excitation, the terminal O 1s to 7a�1excitation is strongly contributive to the spectral

intensity, as discussed in the O 1s and terminal N

1s excitations of CO2 and N2 O [12,13,18].

4.4. Comparison with other triatomic molecules

Table 4 compares the present results for the

core-to-valance excited state and Rydberg-valencemixed state in SO2 and NO2 with the previous

results [12,13,16,18,40] for SO2 (S 1s) and CO2;N2

O and O3. N2 O and CO2 are isoelectronic and

have one degenerate p� orbital and two r� orbitals.The lower r� orbital (CO 5r�g and N2 O 8r�) has scharacter at the central atom and p character at

the terminal atoms with a strong antibonding

combination, indicating s-type or gerade-typecharacter on the whole. The higher r� orbital (CO4r�u and N2 O 9r�) has p character at all the atoms

Fig. 11. (a) Absorption spectrum of NO2 in O K-edge region.

(b) Angle-resolved ion yield spectra of NO2 in the O K-edge

region. Dotted and solid lines denote I90 and I0 ion yields, re-

spectively.


with a strongest antibonding combination, indi-

cating p-type or ungerade-type character on the

whole. The excitation to the higher r� orbital isobserved as a shape resonance. On the other hand,NO2 and O3 have additional electron(s) in the p�

orbital and have bent structure due to the Renner–

Teller effect. The p� orbital is split into a1 and b1orbitals, where a1 is half-occupied in NO2 and is

fully occupied in O3 and SO2. The chemical bonds

are weakened and stretched, more in O3 than in

NO2. Thus, the excitation to the higher r� orbital(NO2 /O3 5b

�2) is observed as a shape resonance in

NO2 but as a bound state in O3. The valence state

of SO2 is isoelectronic with that of O3, but the

unoccupied orbitals have mainly sulfur 3p com-

ponents and the chemical bond is much weaker

than O3. This is consistent with the observationthat the bound-state excitation to the highest r�

orbital (O3 5b�2, SO2 6b�2) is not identified in O3,

probably due to strong mixing with some p-type

Rydberg states, but is clearly observed below the

Rydberg manifold in SO2.

The excitation to the lower r� orbitals CO2 5r�gand N2O 8r� are expected to have a term value of

�2 eV, indicating that the r� state may be mixedwith some Rydberg states. The orbital has s or

Table 3

Assignments of the O 1s absorption spectra of NO2

Label Energy TT ðn�Þ TS ðn�Þ Assignments Ref. [36] Ref. [38]

A 530.32 10.98 11.65 6a�1 530.15 (p1) 6a�1 530.32 (p1) 6a�1(T)

B 532.36 8.94 2b�1(T) 531.99 (p2) 2b�1(S)

9.61 2b�1(S) 532.55 (p3) 2b�1(T) 532.36 (p2) 2b�1(T)

C 537.79 3.51 (1.97) 4.18 (1.80) 3s a1 (T) 537.18 (p4) 7a�1(S) 537.76 (p4) 4pb1 (T)

538.20 (p5) 4pa1 (T)

538.74 (p4) 7a�1(T) 538.82 (p6) 4pb2 (T)

5b�2(S),3pb1 (S) 539.18 (p7) 5sa1 (T)

D 539.47 1.83 (2.73) 2.50 (2.33) 7a�1=4sa1 (T) 539.82 (p6) 3pa1 (S) 5b�2(T) 539.6 (p8) 7a�1,3d,5p(T)

E 540.60 0.70 (4.41) 7a�1=5sa1 (T) 540.68 (p7) 3pb2 (S) 3pb1 (T) 540.52 (p9) 4d,6p(T)

1.37 (3.15) 7a�1=4sa1(S)

I.P.a 541.30 541.97

F 546.94 )5.64 )4.97 5b�2-shape res 545.68 (p9) a1-shape res. 547.18 (p10) 5b�2-shape res

Transition energies, term values (T, uncertainties of �0.05 eV), effective principal quantum numbers ðn�Þ. 1sa1 and 1sb2 correspondto the O1s orbitals with the 2a1 and 1b2 symmetries.

a Taken from Ref. [43].

Table 4

Summary of the core-to-valence excitations in SO2 and NO2 in comparison with CO2, N2O, and O3

Molecules Lowest p� Middle r� Highest r�

CO2, Refs. [13,18] 2p�u (�6 eV) degeneracy

removed by the Renner–Teller

effect; forbidden from O 1s ru

5r�g (�2 eV) mixed with s-type

Rydberg allowed from O 1s ru

forbidden from C and O 1s rg

4r�u ()13–17 eV) strong shaperesonance from both C and O

1s rg; forbidden from O 1s ru

N2O, Refs. [12,18] 3p� (�7 eV) degeneracy

removed by the Renner–Teller

effect

8s� (�2 eV?) mixed with s-type

Rydberg strong from terminals

(Nt and O)

9s� ()10–15 eV) strong shaperesonance from both N and O

1s weak from Nc 1s

NO2, present 6a�1 (11–12 eV) half-filled,

in-plane p�7a�1 (�2 eV?) mixed with s-type

Rydberg strong from O 1s

5b�2 ()5–6 eV) strong shape

resonance from both N and O 1s

2b�1 (9–10 eV) out-of-plane p�;forbidden from O 1s b2

weak from N 1s

O3, Ref. [40,41] 2b�1 (11–12 eV) out-of-plane p�;forbidden from terminal O 1s b2

7a�1 (4–5 eV) below the

Rydberg region

5b�2 (�2 eV?) mixed with

p-type Rydberg

SO2, present, Ref. [16] 3b�1 (�10 eV) out-of-plane p�

forbidden from O 1s b2

9a�1 (5–6 eV) below the

Rydberg region

6b�2 (4–5 eV) below the

Rydberg region

Term values (eV) in parentheses. Negative term values mean continuum states.


gerade character on the whole and can be mixed

with s-type Rydberg states. Even if so, it is difficult

to identify the Rydberg-valence mixing from the C

1s in CO2 and the central N 1s in N2 O, because

the excitations to the s/gerade orbitals are strictly

and almost forbidden from the C 1srg and thecentral N 1s, respectively. On the other hand, the

lower r� orbitals have p character at the terminal

atoms, and some excitations from the O 1s and

terminal N 1s would be enhanced due to the r�

contribution. The experiments [12,13,18] have

shown that the 3s and 4s Rydberg transitions are

enhanced but the valence states are not identified.

This means that the valence state is dissolved in thes-type Rydberg manifold due to strong mixing.

The excitation to the 7a1 orbital in NO2 has similar

s/gerade character and a similar term value to CO

5r�g and N2 O 8r�. Therefore, we have identifiedRydberg-valence mixings in the terminal O 1s ex-

citation. In O3, the excitation to the lower r� or-bital is observed below the Rydberg region due to

weak antibonding character. The lower r� states inSO2 is also observed below the Rydberg region.

5. Summary

We have constructed a new BM based beamline

BL4B at UVSOR to gain high resolution over a

wide photon energy range as well as reasonablyhigh photon fluxes. This has enabled us to carry

out the high-resolution ARPIS measurements. The

high-resolution N 1s and O 1s photoabsorption

spectra and ARPIS of NO2 and SO2 are investi-

gated in combination with the MR-SDCI and

static exchange calculations. The present work

successfully summarizes identification of p� and r�

valence states and valence-mixed Rydberg states,depending on the molecules and the excited inner-

shells (center or terminal) of the linear and bent

triatomic systems, CO2; N2O, NO2; O3 and SO2.

Acknowledgements

The authors are grateful to the staff of UVSOR,especially, Mr. E. Nakamura and Mr. N. Kondo

for their technical assistance. The present work

was partly supported by a Grant-in-Aid for

Scientific Research (B) from the Japan Society for

the Promotion of Science.

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Documents

Angle-resolved photoion spectroscopy of NO2 and SO2