A laser spectroscopic study of the X2IIg, A2IIu, and B2∑u + states of BS2: Renner-Teller, spin-orbit, and K -resonance effects

Article abstract of DOI:10.1063/1.1898221

The lowest-lying vibronic levels of the X, A, and B states of B S2 have been investigated at high resolution using a combination of room-temperature absorption and supersonic jet data. In both cases, the B S2 radical was prepared in an electric discharge using a precursor gas mixture of B Cl3, C S2, and either helium or argon. Extensive absorption spectra were obtained for the 000 and 211 bands of the A Πu2 - X Πg2 electronic transition in the visible. The A - X 211 and B Σu+2 - X Πg2 211 bands of jet-cooled B S2 were also studied with laser-induced fluorescence techniques. By fitting the 000 bands of both electronic transitions simultaneously, we were able to precisely determine the spin-orbit splittings in both the A and X states. Similarly, the 211 bands were fitted in a merged analysis in order to determine the relative separations of the vibronic components of the ground and first excited state bending levels as accurately as possible. Due to a large spin-orbit splitting and small Renner-Teller interaction, the A state bending level shows small but definite K -resonance effects, which were fitted using a full matrix for the four components of v2′ =1. The resulting parameters were used along with previously published data to refine the Renner-Teller analyses in both the A Πu2 and X Πg2 electronic states. Where possible, the fitted constants and observed boron isotope splittings have been shown to be in accord with theoretical estimates of their sign and magnitude.

Full text of DOI:10.1063/1.1898221

A laser spectroscopic study of the X ̃ Π g 2 , A ̃ Π u 2 , and B ̃ Σ u + 2 states of B S 2 :
Renner–Teller, spin-orbit, and K -resonance effects
Sheng-Gui He, Dennis J. Clouthier, Allan G. Adam, and Dennis W. Tokaryk
Citation: The Journal of Chemical Physics 122, 194314 (2005); doi: 10.1063/1.1898221
View online: http://dx.doi.org/10.1063/1.1898221
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THE JOURNAL OF CHEMICAL PHYSICS 122, 194314 ͑2005͒
2
2
2
+
˜
˜
˜
A laser spectroscopic study of the X ⌸g, A ⌸ , and B ⌺u states of BS2:
Renner–Teller, spin-orbit, and K-resonance effeucts
Sheng-Gui He and Dennis J. Clouthiera͒
Department of Chemistry, University of Kentucky, Lexington, Kentucky 40506-0055
Allan G. Adam
Department of Chemistry and Centre for Laser, Atomic, and Molecular Sciences, University of New
Brunswick, Fredericton, New Brunswick, Canada E3B 6E2
Dennis W. Tokaryk
Department of Physics and Centre for Laser, Atomic, and Molecular Sciences, University of New
Brunswick, Fredericton, New Brunswick, Canada E3B 5A3
͑Received 28 February 2005; accepted 7 March 2005; published online 18 May 2005͒
˜ ˜
˜
The lowest-lying vibronic levels of the X, A, and B states of BS2 have been investigated at high
resolution using a combination of room-temperature absorption and supersonic jet data. In both
cases, the BS2 radical was prepared in an electric discharge using a precursor gas mixture of
BCl3,CS2, and either helium or argon. Extensive absorption spectra were obtained for the 000 and 211
2
2
1
2
+
2
1
˜
˜
˜ ˜
˜
˜
bands of the A ⌸u-X ⌸g electronic transition in the visible. The A-X 21 and B ⌺u-X ⌸g 21 bands
of jet-cooled BS2 were also studied with laser-induced fluorescence techniques. By fitting the 000
bands of both electronic transitions simultaneously, we were able to precisely determine the
1
˜
˜
spin-orbit splittings in both the A and X states. Similarly, the 21 bands were fitted in a merged
analysis in order to determine the relative separations of the vibronic components of the ground and
first excited state bending levels as accurately as possible. Due to a large spin-orbit splitting and
˜
small Renner–Teller interaction, the A state bending level shows small but definite K-resonance
effects, which were fitted using a full matrix for the four components of Ј=1. The resulting
v2
parameters were used along with previously published data to refine the Renner–Teller analyses in
2
2
˜
˜
both the A ⌸u and X ⌸g electronic states. Where possible, the fitted constants and observed boron
isotope splittings have been shown to be in accord with theoretical estimates of their sign and
magnitude. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.1898221͔
I. INTRODUCTION
fluorescence ͑LIF͒ detection. In agreement with an earlier
matrix isolation study by Brom, Jr. and Weltner, Jr.,5 we
found that angular momentum coupling is almost negligible
The electronic spectrum of boron dioxide BO2 has been
thoroughly studied with both classical1 and laser-based2
spectroscopic techniques. Recently, we published the first de-
tailed gas phase investigations3,4 of the spectrum of boron
disulfide BS2. The ground-state electron configuration of lin-
ear BS2 is
2
˜
in the A ⌸u excited state but that the ground state exhibits a
substantial Renner–Teller effect ͓⑀=−0.2098͑17͔͒. Rota-
0
˜ ˜ ˜ ˜
tional analysis of the A-X and B-X 00 bands proved that the
radical is linear with the boron disulfide ͑SBS͒ structure and
˜
˜
bond lengths of r0͑X͒=1.6649͑2͒ Å,r0͑A͒=1.7129͑1͒ Å,
2
2
2
4
3
˜
…͑␴ ͒ ͑␴ ͒ ͑␲ ͒ ͑␲ ͒ X ⌸ ,
g
u
u
g
g
˜
and r0͑B͒=1.6812͑1͒ Å. The spin-orbit coupling constants
were determined to be −405.163͑4͒ cm−1 for the ground state
with
and
˜
and −259.148͑12͒ for the A state. The vibrational frequencies
were determined in all three states, except for the B state ␻3,
2
2
2
3
4
˜
…͑␴ ͒ ͑␴ ͒ ͑␲ ͒ ͑␲ ͒ A ⌸
g
u
u
g
u
˜
˜
as the antisymmetric stretching mode is not active in the B-
˜
X spectrum.
2
+
u
2
1
4
4
˜
…͑␴ ͒ ͑␴ ͒ ͑␲ ͒ ͑␲ ͒ B ⌺
g
u
u
g
Despite our previous efforts, two aspects of the spectros-
copy of BS2 remained incomplete. The first concerns the
relative separations of the bending levels in the ground and
first excited states. The A˜-˜X transition is parallel polarized,
so that transitions between levels of the same K value are
observed, but the relative energies of the various K levels
within a given vibrational state remain unknown. In previous
work,4 some progress was made in this regard by identifica-
excited states. Using the pulsed electric discharge jet tech-
nique with a precursor mixture of BCl3 and CS2 in argon, we
˜ ˜
were able to study the A-X ͑760–530 nm͒ and B˜-X˜ ͑420–390
nm͒ band systems of jet-cooled BS2 using laser-induced
a͒
Author to whom correspondence should be addressed. Electronic mail:
dclaser@uky.edu
0021-9606/2005/122͑19͒/194314/9/$22.50
122, 194314-1
© 2005 American Institute of Physics
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194314-2
S.-G. He et al.
J. Chem. Phys. 122, 194314 ͑2005͒
1
˜ ˜
tion of the four components of the B-X 21 hot band, which
cies, its concentration in the cell modulated with the dis-
charge current, and hence so did the laser beam intensity
when tuned to a transition of BS2. The laser wave meter was
calibrated at the start of each day against 5–6 lines of atomic
uranium or argon detected optogalvanically in a U/Ar hol-
low cathode lamp. Agreement with the atomic lines was typi-
cally within 0.001 cm−1, and we estimate the measurement
accuracy for strong, unblended lines of BS2 to be about
0.003 cm−1.
gave the relative separations of the ground state ␯Љ levels to
2
an accuracy of about 0.5 cm−1. These have been refined in
1
˜ ˜
the present work by recording the B-X 21 band at high reso-
lution, whose rotational analysis accurately defines the rela-
tive separations of the ground-state bending levels.
The second missing piece of information concerns
2
˜
K-resonance effects. In the A ⌸u state, the spin-orbit cou-
pling is large and the Renner–Teller effect is very small, so
that the ␬ 2⌺g− and 2⌬3/2 components of the first bending level
B. LIF spectroscopy of jet-cooled BS2
͑␯Ј=1͒ are nearly degenerate, as are ␮ 2⌺g+ and 2⌬5/2. As first
2
2
2
2
+
2
1
described for NCO ͑Ref. 6͒ and more fully explored for the
boron dioxide,2 calcium hydroxide7,8 and strontium
hydroxide9 radicals, these near coincidences lead to a K-type
resonance interaction between the rotational levels of the ⌺
and ⌬ components, so that the four components of the 211
bands cannot be satisfactorily fitted independently. This as-
˜
˜
˜
˜
˜
˜
High-resolution A ⌸u-X ⌸g and B ⌺u-X ⌸g 21 band
11
2
2
0
LIF spectra of jet-cooled BS2 and the A ⌸u-X ⌸g 00 band
of 10BS2 were obtained as previously described3,4 using
pulsed discharge jet techniques. A precursor mixture of 3%
BCl3 in argon was passed at a pressure of 40 psi over the
surface of a room-temperature sample of liquid carbon disul-
fide before expansion through a molecular-beam valve ͑Gen-
eral Valve, Series 9͒ into the vacuum chamber. A pulsed elec-
trical discharge apparatus, consisting of a black Delrin flow
channel equipped with a pair of stainless steel ring elec-
trodes, was mounted at the exit of the pulsed valve and was
used to fragment the precursor mixture, producing BS2
which expanded and cooled downstream. A small reheat tube
attached to the end of the discharge apparatus enhanced the
yield of BS2 and suppressed the background glow of excited
state argon atoms.
2
2
0
1
˜
˜
pect was explored by recording the A ⌸u-X ⌸g 00 and 21
bands in absorption at room temperature and analyzing the
rotational structure in these spectra, along with new LIF data
obtained from jet-cooled BS2. Small but significant
K-resonance effects were found in the levels of e parity of
the ⌬3/2 and ␬ 2⌺g− components of the first bending level of
2
the first excited electronic state.
II. EXPERIMENT
A. Absorption spectroscopy
High-resolution ͑0.035 cm−1͒ LIF spectra were obtained
by interrogating the expansion 1.5-cm downstream of the
reheat tube with the beam of a 308-nm pumped Lambda-
Physik ScanMate2E dye laser equipped with an intracavity
étalon. The A˜-˜X bands were pumped directly with the dye
In experiments conducted at the University of New
Brunswick, BS2 was created in a room-temperature ac dis-
charge through a flowing mixture of 1–2 Torr of helium, to
which trace amounts ͑a few tens of milliTorr͒ of boron
trichloride and carbon disulphide were added. The exact
pressure of each gas was optimized at the beginning of each
experiment. The discharge voltage wave form was a half-
rectified sinusoid at a frequency of 2900 Hz. At its peak, the
current through the gas mixture was 700 mA.
The discharge cell was a Pyrex tube 80 mm in diameter
and 106 cm long. Two water-cooled electrodes were placed
70 cm apart, centered along the length of the tube. Helium
gas was admitted through the stems of the electrodes, while
the mixture of helium, BCl3, and CS2 entered through
1/4-in. diameter ports a few centimeters closer to the ends of
the cell. A set of White cell mirrors with a 1-m radius of
curvature was mounted into the endcaps of the Pyrex tube to
permit laser light to pass up to 16 times through the dis-
charge products.
A Coherent 699-29 dye laser operated with Pyridine 2
provided tunable laser radiation with a bandwidth of about 1
MHz. Typically, a 200-mW beam entered the cell, and after
8–16 passes through the discharge the laser light was de-
tected with a reverse-biased silicon photodiode. Neutral den-
sity and bandwidth limiting optical filters placed between the
cell and detector kept the photodiode from saturating, and
reduced the detection of stray discharge fluorescence. The
electrical signal from the photodiode was processed with a
two-channel lock-in amplifier ͑SRS 830͒ referenced to the
discharge modulation frequency. Since BS2 is a reactive spe-
˜ ˜
laser beam, whereas pumping and calibration of the B-X
bands in the 420–408-nm region were accomplished by
Raman-shifting the laser output as described in detail
elsewhere.4 The spectra were calibrated to an estimated ac-
curacy of ±0.003 cm−1 using I2 LIF spectra.10,11 The LIF and
calibration spectra were recorded simultaneously with a digi-
tal data acquisition system of our design.12
III. RESULTS AND ANALYSIS
Boron disulfide ͑SBS͒ is a linear molecule whose vibra-
tional frequencies are labeled using the Herzberg conven-
tions as ␯ ͑␴g, symmetric BS stretch͒, ␯ ͑␲u, bend͒, and ␯
1
2
3
͑␴u, antisymmetric BS stretch͒. In electronic spectra, even
quantum number changes ͑⌬v=0, ±2,…͒ are expected for
␯ and ␯3, with no restrictions on ⌬v1. In the case of signifi-
2
cant angular momentum coupling ͑Renner–Teller effect͒ in
one or both combining states, the equivalent vibronic selec-
tion rule is ⌬P=0 where P=͉⌳+l+⌺͉=͉K+⌺͉. Boron has
two isotopes, 11B ͑80.1%͒ and 10B ͑19.9%͒, so transitions of
both the 11BS2 and 10BS2 isotopomers are expected to be
present in the spectra. Since B32S2 has two equivalent sulfur
nuclei with zero nuclear spin, half of the rotational levels are
missing such that only even or odd values of N exist for ⌺
vibronic levels and alternate ⌳-doubling components are ab-
sent for the ⌸ and ⌬ levels.
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194314-3
Spectroscopy of BS2
J. Chem. Phys. 122, 194314 ͑2005͒
FIG. 1. High-resolution absorption spectra of the
2
2
0
2
A ⌸u −X ⌸g 00 ͑ ⌸3/2 −2⌸3/2͒ band of BS2. The top
panel shows the rotational structure and assignments for
the R1 and P1 branches at high J and the bottom panel
˜
˜
shows the band head at 13913.795 cm−1
.
␬ 2⌺−-␬ 2⌺− components of jet-cooled 11BS2. These bands
exhibited weak to moderately strong Q branches which were
used to confirm the rotational numbering prior to fitting each
component independently to obtain sets of preliminary rota-
tional constants. These constants were used along with those
from our previous analysis of the ␮ 2⌺+-␮ 2⌺+ component3
to predict the rotational lines in the room-temperature ab-
sorption spectra, which established the rotational numbering
and allowed assignments to be made up to N=94 for the ⌺
bands and J=95.5 for the ⌬ bands. It was found that the
rotational line frequencies of the absorption and LIF data,
although calibrated using very different methods, agreed
very well in the regions of overlap and could be simulta-
neously least-squares fitted without detectable wave-number
offsets, attesting to the quality of the measurements.
A. Observed spectra
2
2
˜
˜
The boron disulfide A ⌸u-X ⌸g absorption spectrum
was scanned in a series of contiguous segments from
13700–13965 cm−1, encompassing both spin-orbit compo-
nents of the 000 band and all four components of the 211 hot
band, which are clearly shown in our previously published
LIF spectrum3 of jet-cooled BS2. As shown in Fig. 1, the
11BS2 000 absorption band was quite intense and largely free
of overlap, so that the rotational branches were readily iden-
tified up to a maximum of J =118.5 and easily assigned with
Ј
the aid of our previous rotational constants obtained from jet
spectra. We were also able to assign a series of weaker lines
in the same region to the two components of the 000 band of
10BS with J values up to 84.5. The 21 band rotational lines
Ј
2
1
were weaker and often overlapped to some extent, but were
still readily apparent as illustrated by the spectrum in Fig. 2,
which shows the low-N rotational lines of the weakest
͑␬ 2⌺−g-␬ 2⌺−u͒ component.
Figure 3 shows the vibronic levels in the B˜, A˜, and X˜
states and the corresponding transitions studied by absorp-
tion and LIF jet spectroscopy in this work. Although the
1
In order to assign and fit the 211 band, we first recorded
A-X 21 band rotational analyses gave the absolute separa-
˜ ˜
high-resolution spectra of the ⌬5/2-2⌬5/2, 2⌬3/2−2⌬3/2, and
tions of the combining levels in the two electronic states,
2
˜ ˜
FIG. 2. A portion of the high-resolution A-X absorption
spectrum of the ␬ 2⌺g− −␬ 2⌺u− component of the 211 band
of BS2 showing the rotational structure and
assignments.
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194314-4
S.-G. He et al.
J. Chem. Phys. 122, 194314 ͑2005͒
boron isotope effect which was not apparent in our previous
study.4 Figure 4 shows a small segment of the 2⌺u+-2⌸1/2
component in which the intense 11BS2 R22 branch is identi-
fied, along with a series of weaker rotational lines to the red
which we assign to the 10BS2 isotopomer.
B. 000 band rotational analyses
˜
In order to determine the vibronic splittings of the X and
˜
A state =0 levels as precisely as possible, we elected to fit
v
0
the A-X and B-X 00 bands of 11BS2 simultaneously. The
Hamiltonian matrix for the ground and first excited state case
͑a͒ 2⌸ levels was that given, for example, in Ref. 13 and
˜ ˜
˜ ˜
both spin-orbit components ͑2⌸3/2 and ⌸1/2͒ were included
2
˜
in the least-squares analysis. For the B state, the energy lev-
3
els were fitted to the usual ⌺+ expressions. A total of 378
2
˜ ˜
A-X rotational lines from jet and absorption data and 87
˜ ˜
B-X lines from jet data were fitted with equal weights to an
overall standard deviation of 0.0029 cm−1, comparable to the
measurement uncertainty in both types of experiment. The
resulting constants are given in Table I. We also fitted a total
FIG. 3. Schematic diagram of the vibronic levels and transitions of 11BS2
studied in this work. The energy levels on the left are from the 000 bands and
the energies for the rotationless levels are given relative to the energy of the
˜
of 208 A-X rotational transitions of 10BS2, including both
X
=0, 2⌸ level. Similarly, the energy levels on the right are from the
v
˜ ˜
3/2
observed 211 bands and are given relative to the X 2 =1,␮ 2⌺+ level. The
˜
v
u
spin-orbit components. In this case, we fixed B ,A , and AЈ
Ј
Ј
d
approximate separations of the =0 and 2 =1 levels in each state have been
v
v
at the values previously determined for 11BS2 and varied all
of the lower-state constants and the remaining upper state
parameters with the results reported in Table I.
˜
calculated from data obtained in the A state Renner–Teller analyses and are
given in the center of the diagram.
they did not shed any light on the spacings between the
components in a given electronic state. For this purpose, we
recorded new high-resolution spectra of all four components
C. K-resonance interactions in the 211 bands
1
˜ ˜
Our preliminary analysis of the A-X 21 band as a set of
four noninteracting components showed that some of the up-
per state levels did not fit very well, particularly at high
2
+
2
1
of the B ⌺u-X ⌸g 21 band of jet-cooled 11BS2. These are
identified in our previously published low-resolution
spectrum4 in the 23750-25000-cm−1 region. Since all four
transitions terminate on a single 2⌸ vibronic level in the
upper state, as shown in Fig. 3, they can be used to establish
the relative energies of the four components of the ground
˜
˜
values of J . This is a result of a K-resonance interaction
Ј
between the various vibronic components of the 2=1 level
of the excited state. Such a situation arises when the spin-
v
orbit coupling is much larger than the Renner–Teller ͑elec-
state 2=1 level, which subsequently give the relative ener-
v
trostatic͒ splitting, so that the 2=1 levels coalesce into two
v
˜
sets of nearly degenerate levels ͑in this case ␮ 2⌺g+;2⌬5/2 and
␬ 2⌺−g ;2⌬3/2͒. These levels can then interact through vibra-
gies of the bending components in the A state. We have also
˜ ˜
rerecorded the B-X 00 bands in order to try to determine the
0
0
2
+
2
˜ ˜
FIG. 4. A small portion of the B-X 00 ͑ ⌺u − ⌸1/2
͒
band laser-induced fluorescence spectrum of jet-cooled
BS2. The R22͑J ͒ branch of 11BS2 is identified by the
Љ
vertical leaders and the corresponding transitions of the
10BS2 species are labeled by the dashed lines. Transi-
tions with an asterisk are LIF signals due to an un-
known impurity that has a fluorescence lifetime much
shorter than that of BS2.
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194314-5
Spectroscopy of BS2
J. Chem. Phys. 122, 194314 ͑2005͒
TABLE I. Molecular constants ͑in cm−1͒ for the X,A, and B =0 levels of BS .
˜ ˜
˜
v
2
2
2
2
+
0
0
˜
˜
˜
X ⌸g 00
A ⌸u 0
B ⌺u 0
Parameter
11BS2
10BS2
11BS2
10BS2
Parameter
11BS2
a
B
108D
A
0.09512663͑81͒
1.1361͑52͒
−405.16273͑29͒
−0.8738͑62͒
0.2519͑16͒
0.09512091͑9͒
1.1978͑89͒
−405.84441͑17͒
−0.8082͑6͒
0.3285͑86͒
0.0
0.08988179͑81͒
1.0626͑52͒
−259.6240͑3͒
−0.1766͑61͒
0.4636͑16͒
13839.38921͑8͒
378
0.08988179b
1.1079͑97͒
−259.624b
−0.1766b
B
0.09329379͑98͒
0.875͑27͒
108D
102␥
0.74004͑98͒
104Ad
102͑p+2q͒
T0
0.5284͑86͒
13851.57308͑10͒
208
0.0
T0
24189.53503͑18͒
c
c
#
#
87
d
d
␴͑cm−1
͒
0.0027
0.0026
␴͑cm−1
͒
0.0037
aThe numbers in parentheses are 3␴ error limits and are right justified to the last digit on the line; sufficient additional digits are quoted to reproduce the
original data to full accuracy.
bParameter fixed at the 11BS2 value.
cNumber of transitions fitted.
dOverall standard deviation of fit.
2
tional l-type doubling effects, complicated by the ⌳ doubling
present in the original components of the bending level.
slightly different B values for the ⌬,␮ 2⌺g+, and ␬ 2⌺g− com-
ponents of 2=1, Brown has recently shown15 that the addi-
v
In fitting the 2=1 data, we have again chosen to fit the
v
tion of a single extra term to the effective Hamiltonian can
be used to eliminate this discrepancy. The new term, with
parameter ⑀␻2D, is a type of centrifugal distortion correction
to the Renner–Teller coupling and removes both the vibronic
dependence of the rotational constant B and centrifugal dis-
tortion constant D for a given vibrational level and the
anomalously strong dependence of the spin-rotation param-
eter ␥ on the bending vibrational quantum number. With this
modification, the effective Hamiltonian includes a single
spin-orbit splitting constant A and a single spin-rotation pa-
rameter ␥, as well as the minor quantities ⑀2␻22/2͑2␻2−A͒
=⑀2␣ and ⑀2␻22/2͑2␻2+A͒=⑀2␤ which appear in the diago-
nal elements. We have used ⑀ as a good approximation to the
parameter ⑀corr which appears in the matrix14 as an off-
diagonal term that couples the ␮ 2⌺1/2 and ␬ 2⌺1/2 basis
functions and has a complicated dependence on ␻2 and A. As
shown in Table II and described in detail elsewhere,2,8 the
⌳-type doubling generates off-diagonal terms, with param-
1
˜ ˜
˜ ˜
A-X and B-X 21 bands simultaneously, which allowed us to
accurately determine the positions of the
components for
v2
all three states relative to the X 2=1 ␮ 2⌺+ level. We have
˜
v
u
fitted the four vibronic components of Љ=1 with separate
v2
energy-level expressions since they are well separated ͑see
Fig. 3͒ and there are no significant K-resonance effects. They
were fitted using the matrix elements and energy-level ex-
˜
pressions given in Eqs. ͑4͒–͑6͒ of Ref. 2. The B 2=1 state
v
was modeled using the Hund’s case ͑b͒ energy-level expres-
sions
2
F1͑N͒ = T0 + B͓N͑N + 1͒ − 1͔ − D͓N͑N + 1͒ − 1͔
1
2
1
2
+ ␥N ϯ qv͓N͑N + 1͔͒,
͑1͒
͑2͒
2
F2͑N͒ = T0 + B͓N͑N + 1͒ − 1͔ − D͓N͑N + 1͒ − 1͔
1
2
1
2
− ␥N ± qv͓N͑N + 1͔͒,
where the upper and lower signs refer to the e and f levels,
eters ͑p+2q͒ and q, that connect the ⌺ and ⌬ levels. The
respectively.
2
˜
⌬
level is largely unaffected by this interaction since it is
5/2
The Hamiltonian used to fit the A state 2=1 levels is
v
only coupled to the distant ␬ 2⌺g− component, whereas the
essentially that given in Ref. 14 and the effective Hamil-
tonian matrix used in the present work is given in Table II.
Although previous analyses2,7–9 have usually obtained
much closer ␬ 2⌺g− and ⌬3/2 components can interact more
2
strongly. The l-type doubling, with parameters qv and ͑pv
TABLE II. The Hamiltonian matrix for the A ⌸u 2 =1 level of BS2.a
2
˜
v
͉2⌬5/2 , ±͘
͉2⌬3/2 , ±͘
͉␮ 2⌺+g , ±͘
͉␬ 2⌺−g , ±͘
T0 + 1 A+2gk −3⑀2␣
−͑z−3͒ B− 2 ␥−2D͑z−2͒
−2 qv͓z͑z−1͔͒
±2 qv͓z͑z−3͔͒
1
1
1
1/2
1/2
1/2
͓
͔
2
+B͑z−4͒ −D͑z2 −7z+13͒
1
2
1
2
T0 − 1 A−␥+2gk −3⑀2␤
+B z−D͑z2 +z−3͒
±q͓z͑z+1͔͒
+
͑pv +2 qv͒ z1/2
ϯ21 ͑p+2q͒z1/2
−
qv͓z͑z+1͔͒
1/2
1/2
2
T0 + 1 A−⑀2␣±⑀␻
+B͑z+2͒−D͑z2 +5z+5͒
z
1/2
1/2
ϯ⑀␻2 ϯ⑀␻ ͑z+2͒−͑z+1͒
2D
2D
2
1
͓
͔
z
ϫ B− 2 ␥−2D͑z+2͒
T0 − 1 A−␥−⑀2␤±⑀␻
1/2
Symmetric
2D
2
+B͑z+2͒−D͑z2 +5z+5͒
1
2
a
The upper and lower signs correspond to the e and f parity levels, respectively, and z= J+ 2 ,␣=␻22 /2͑2␻2 −A͒, and ␤=␻22 /2͑2␻2 +A͒. The ␮ and ␬ symbols
͑
͒
2
+
2
−
refer to the
⌺
͑lower͒ and
⌺
͑upper͒ levels, respectively.
g
g
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194314-6
S.-G. He et al.
TABLE III. Molecular constants ͑in cm−1
J. Chem. Phys. 122, 194314 ͑2005͒
2 =1 levels of 11BS2.
˜
͒ for the X˜,A˜, and B
v
2
2
2
+
1
1
˜
˜
˜
Parameter
␮ 2⌺+u
X ⌸g 21
A ⌸u 2
Parameter
B ⌺u 2
a
T0
0.0
T0
B
14075.16522͑13͒
T0
B
24419.61080͑19͒
0.0935227͑12͒
0.007202͑16͒
6.228͑86͒
B
108D
␥
0.09542180͑94͒
1.3909͑92͒
0.134651͑15͒
−10.05͑72͒
0.09010929͑92͒
1.2529͑93͒
−258.55611͑34͒
4.4289͑59͒
309.488b
108D
␥
A
⑀␻
105qv
108␥d
2
2
⌬
T0
200.71723͑21͒
␻
2
u
B
108D
0.09552019͑91͒ 103⑀␻
0.1251͑53͒
0.0112b
0.0272b
2D
1.3257͑91͒
−384.93668͑30͒
−1.84579͑74͒
416.85314͑13͒
0.09553013͑96͒
1.4013͑99͒
⑀2␣
⑀2␤
gK
A
104Ad
T0
0.74000͑12͒
0.004636b
0.0b
␬ 2⌺−u
p+2q
B
108D
q
105qv
5.7157͑26͒
␥
0.154492͑14͒
−40.85͑75͒
108␥d
c
#
496
97
d
␴͑cm−1
͒
0.0029
0.0029
aThe numbers in parentheses are 3␴ error limits and are right justified to the last digit on the line; sufficient
additional digits are quoted to reproduce the original data to full accuracy.
bFixed in the least-squares analysis.
cNumber of transitions fitted.
dOverall standard deviation of fit.
+2qv͒, couples both of the nearly degenerate pairs of levels
as well as contributing a longer range of ␮ 2⌺g+;2⌬3/2 inter-
action.
action is shown in Fig. 5, which gives the course of the
reduced term values for the four components of 2=1 in the
v
˜
A state, with and without the l-type and ⌳-doubling terms
In fitting the 211 bands, we were unable to vary all of the
2
included. It is apparent that the e parity levels of the ⌬3/2
˜
and ␬ 2⌺−g components are affected the most, with only mi-
nor shifts in the other levels. This is because the ͑p+2q͒ and
qv terms have the same sign in the ͗2⌬3/2͉H͉␬ 2⌺g−͘ matrix
element for the e levels, but opposite signs for the f levels.
A state constants given in Table II. This was because ⑀ for
the upper state is very small ͑0.0143 cm−1͒ and ␻ could not
2
be determined directly from the rotational analysis so that the
Renner–Teller corrections to the vibronic energies ͑⑀2␣ and
⑀2␤͒ were difficult to determine. We have used an iterative
procedure to evaluate them and fixed their values in the final
least-squares analysis. We first set ⑀2␣=⑀2␤=0, since ⑀ was
found to be essentially zero in our previous analysis,3 and
fitted the 21 bands, starting with a small value of ⑀␻ and
2
1
varying both A and ⑀␻2. This resulted in a nonzero value of
⑀␻2, which allowed a calculation of the value of ⑀, using ␻
2
˜
from our published Renner–Teller analysis of the A state
vibronic levels.3 These intermediate values of ⑀ and A were
used to calculate new values of ⑀2␣ and ⑀2␤ and the process
was repeated until consistent results were obtained. Subse-
quently, this value of ⑀ was fixed in a further Renner–Teller
fit of the excited state vibronic levels, ␻2 was refined, and the
process was repeated to self-consistency. Although this pro-
cedure was less satisfactory than a direct least-squares deter-
mination, it is unlikely to significantly affect the final result,
since both ⑀2␣ and ⑀2␤ are only of the order of 0.02 cm−1,
due to the small magnitude of ⑀. The ⌳-doubling parameter
͑p+2q͒ was fixed at the value obtained for the =0 level of
v
the A state of 11BS2 and q and pv were set to 0.0, as they
˜
FIG. 5. A reduced term value plot of the rotational energies of the four
2
components of the first bending level ͑ Ј=1͒ in the A ⌸ state of 11BS2.
were not determinable by least squares with the available
data.
In the final analysis, we fitted a total of 593 rovibronic
transitions with an overall standard deviation of 0.003 cm−1,
comparable to the measurement accuracy, with the param-
eters given in Table III. The effect of the K-resonance inter-
˜
v2
u
The filled circles are the energy levels in the absence of the K-resonance
interaction, obtained by setting the off-diagonal matrix elements between the
2⌬ and 2⌺ levels in Table II to zero. The open circles are the energy levels
calculated using the complete set of constants in Table III. The vertical
arrow indicates the predominant energy-level shift due to the K-resonance
interaction.
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194314-7
Spectroscopy of BS2
J. Chem. Phys. 122, 194314 ͑2005͒
TABLE IV. Vibrational parameters ͑in cm−1͒ for the ground and first elec-
other excited ⌺ electronic states17 ͑gk=0.74 cm−1͒. We have
tronic excited states of 11BS2.
˜
previously attributed the very small A state Renner–Teller
2
˜
2
2
˜
˜
effect to vibronic coupling of both components of the A ⌸u
Parameter
X ⌸g
A ⌸u
state ͑2A1 and B1 on bending͒ with the higher ⌺g− and ⌺+g
2
2
2
a
states ͑2B1 and 2A1, respectively, on bending͒ arising
␻
544.583͑50͒
284.00͑28͒
1010.742͑16͒
−414.432͑24͒
¯
512.7110͑87͒
309.4881͑84͒
1543.7307͑83͒
−259.4725͑91͒
−0.9668͑66͒
2.8774͑86͒
0.0143b
1
␻
␻
2
3
2
2
4
2
1
from the …͑␴ ͒ ͑␴ ͒ ͑␲ ͒ ͑␲ ͒ ͑␴ ͒ excited electron
g
u
u
g
g
configuration.3 However, this coupling will be K dependent,
A
˜
A
having the greatest effect for A state ⌺ vibronic levels and
␣
␣
2
A
3
¯
slightly less effect on levels of higher K, embodied in the
parameter gK which appears in the diagonal elements of the
matrix as gKK. This is readily seen numerically, by diagonal-
izing the Renner–Teller matrix used to analyze our data. Us-
ing the constants in Table IV but with ⑀=0 and gK=0, the
⑀
−0.2119͑18͒
2.9097͑41͒
1.282͑13͒
19.2130͑76͒
0.9500͑87͒
¯
g4
gK
1.42003͑96͒
0.74b
W1
W2
x11
x12
x13
x23
x33
14.1191͑25͒
¯
2=1 levels form two degenerate pairs with a separation of
v
−0.4770͑13͒
¯
258.50 cm−1. If ⑀ is then set to the fitted value of 0.0143, the
separation of the 2⌺ levels increases to 258.64 cm−1, with the
2⌬ levels between them with a separation of 258.46 cm−1.
The addition of gK=0.74 cm−1 does not affect the separation
¯
−8.064͑122͒
−1.899͑70͒
6.211͑45͒
89
−4.6940͑40͒
−7.1863͑38͒
¯
2
c
#
150
of either set of levels, but shifts the ⌬ levels up by 2gK so
d
that the ⌬3/2 appears above the ␬ 2⌺g− level, as is observed
2
␴ ͑cm−1
͒
2.15
0.49
aThe numbers in parentheses are 1␴ error limits and are right justified to the
last digit on the line; sufficient additional digits are quoted to reproduce the
original data to full accuracy.
experimentally.
Although the K-resonance effects are observed in the
˜
2=1 level of the A state, there are no avoided crossings
v
b
˜
Taken from the rotational analysis of the A state v2 =1 level.
evident in our data. As a result of the large A value and gK
=0.74 cm−1, the ⌬ levels are Ϸ1.5 cm−1 above the ⌺ levels at
low J. As is evident in Fig. 5, levels of the same e/ f parity
approach each other quite slowly, so that any avoided cross-
ing must occur at high J. Using the parameters in Table III,
we calculate that such crossings would occur at J=174.5͑e͒
cNumber of combination differences fitted.
dOverall standard deviation of fit.
D. Renner–Teller analyses
The analyses of the 211 bands provided very precise con-
and 201.5͑f͒ for the ⌺−g /2⌬3/2 and ⌺g+/2⌬5/2 pairs of levels,
respectively, well beyond the range of the present data.
The parameters obtained in the K-resonance analysis of
˜
2
2
˜
˜
stants for the X and A state 2=1 levels, as well as improved
v
values for the =0 spin-orbit splittings in both states. We
v
used these constants to calculate the vibronic or “rotation-
less” energies of each of the levels, as shown in Fig. 3, and
these were used as input, along with previous single vibronic
level emission data, to improve the Renner–Teller analyses
of both states. The details of the Renner–Teller matrix ap-
proach are given in previous work.3,16 In the ground state,
the parameters changed little from previous values, although
gK increased from a value of 0.83 to 1.28 cm−1. In the ex-
cited state, the parameters are also consistent with previous
the 2=1 level of the A state seem quite reasonable. A single
v
B value fits a wide range of data and the ⑀␻2D parameter is of
the order of 4 MHz, very similar to the values found for
other molecules with ⌸ electronic states. In Fig. 3, we
15
2
˜
have used the A state 21−00 splitting calculated from the
Renner–Teller analysis along with the relative energies of the
various levels obtained by rotational analysis to obtain the
˜
˜
=1− 2=0 energy differences in the X and B states. The
v2
v
results, although the rotational analysis allowed ⑀␻ and gK
2
values of 275.88 cm−1 and 303.31 agree well with the X state
˜
to be determined for the first time. The results are presented
in Table IV.
=1͑␮ 2⌺͒− =0͑2⌸ ͒ interval of 275.88 cm−1 calculated
v2
v
3/2
˜
from the Renner–Teller analysis and the B state value of ␯Ј
2
=302.9 cm−1 calculated as half the 2␯2=605.8 cm−1 interval
IV. DISCUSSION
18
observed in the B˜-˜X spectrum. Using the Nielsen formula
In this work we have obtained a very detailed under-
standing of the lowest bending levels of the ground and first
excited states of BS2. Although the energy-level structure in
the ground state is entirely normal, the alert reader may have
˜
2
2
2
2B2
␨ ␻
2k
q =
␯
1 + 4
͑3͒
͚
ͫ
ͬ
␻2 − ␻
2
2
␻
2
k=1,3
k
noticed an anomaly in the 2=1 levels of the A state—the
v
⌬
level is above the ␬ 2⌺g− level, as shown in Figs. 3 and
2
3/2
2
5. The usual situation is that the “unique” levels ⌬5/2 and
we calculate q =6.12ϫ10−5 cm−1, in good agreement with
⌬
lie between the outermost ␮ 2⌺g+ and ␬ 2⌺g− levels,
2
␯
3/2
the experimental value of 5.72ϫ10−5 cm−1. If we assume
but BS2 is unusual with large spin-orbit coupling ͑A
˜
Ϸ−259 cm−1͒,
a
very small Renner–Teller effect ͑⑀
that the ⌳-doubling in the A state is primarily a result of an
˜
=0.0143͒ and a significant value of the parameter that de-
interaction with the B state, then the pure precession approxi-
scribes the K dependence of the coupling of the 2⌸ state with
mation indicates that19
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194314-8
S.-G. He et al.
J. Chem. Phys. 122, 194314 ͑2005͒
˜
2ABl͑l + 1͒
E⌸ − E⌺
The boron isotope effect in the B state was a little more
p⌸ = ␥⌺ =
.
͑4͒
difficult to determine. In previous work, we were unable to
detect any rotational lines ascribable to the 10BS2 isotopomer
The experimental numbers are p⌸=0.0046 cm−1 and ␥⌺
in the strong ⌺-2⌸3/2 component of the B-X 00 band and
2
0
˜ ˜
=0.0072 cm−1 for the 2=1 levels, with similar values for
v
assumed that the rotational lines of the two isotopomers were
the zero-point levels, which compare favorably with p⌸
accidentally coincident.4 Unfortunately, ␯ is unknown for
=0.009 cm−1 calculated from Eq. ͑4͒.
3
the excited state, but a calculation of the isotope effect using
the unscaled/scaled ͑0.95͒ ab initio frequencies4 of
1052/999 cm−1 gives isotope effects of 1.2/0.16 cm−1. As
shown in Fig. 4, the 2⌺-2⌸1/2 component of the 000 band
exhibits a few lines that can be assigned to the 10BS2 species.
These weaker lines were found to occur an average of
0.7774±0.0027 cm−1 to the red of the strong R ͑J ͒ ͑J
The value of the spin-orbit coupling constant ͓A
=−258.5561͑34͒ cm−1͔ obtained from the rotational analysis
is slightly smaller than the value of −259.472͑91͒ cm−1 ob-
tained in the Renner–Teller fit, due to the bending quantum
number dependence of the spin-orbit coupling constant A
that was included in the latter analysis. That this effect is not
just an artifact of the multiparameter fitting process is evi-
Љ
Љ
22
=7.5, 9.5, 11.5, 13.5, and 15.5͒ transitions. We theorized that
dent from the measured spin-orbit splittings in
v2
if the vibrational isotope effect was 0.0 cm−1, as it appears to
=0 ͑259.624 cm−1͒ and 2=1 ͑2⌬3/2−2⌬5/2=258.718 cm−1͒
v
2
be in the
⌸
component, then perhaps the isotope-
˜
3/2
of the A state. In standard Renner–Teller theory the effective
spin-orbit splitting for the unique levels is given to fourth
order by
dependent spin-orbit splitting in the ground state =0 level
v
would cause the −0.7774 cm−1 10BS2 isotope effect. Al-
though our rotational analysis ͑Table I͒ gives a difference in
the spin-orbit splittings of −0.682 cm−1, this value is biased
by the assumption of identical spin-orbit splittings for both
1
Aeff = A 1 − ⑀2K͑K + 1͒ .
͑5͒
͓
͔
8
The observed 0.91-cm−1 difference in Aeff cannot be ac-
counted for using Eq. ͑5͒ with ⑀=0.0143, necessitating a
further dependence of the effective spin-orbit coupling con-
stant on the bending level. Brown14 has formulated this de-
pendence as
˜
isotopomers in the A state. To obtain an unbiased estimate,
we used the parameters in Table IV, modified as necessary
by the isotope relations, to calculate the spin-orbit splittings
for BS2 ͑404.266 cm−1͒ and BS2 ͑405.043 cm−1͒, which
then predicts the B-X 00 ͑ ⌺- ⌸1/2͒ rotational transitions to
occur 0.777 cm−1 below those of the 11BS2 species. Although
the agreement between experiment and Renner–Teller theory
is fortuitously good, the sign and magnitude of the calculated
isotope shift provides strong evidence that our assignment is
correct.
11
10
0
2
2
˜ ˜
1
8
Aeff = A + ⌬A͑␯ + 1͒ 1 − ⑀2K͑K + 1͒
͑6͒
͓
͔
2
and in the case of BS2 ⑀ is so small that the term in brackets
is reliably approximated as 1. In our Renner–Teller vibronic
analysis of the ground-state levels we included a term A
−␣A͑ ͒ on the diagonal, analogous to Eq. ͑6͒, and deter-
v2
2
mined ␣A2 =−0.967 cm−1=−⌬A. It has been shown that
gK
− ␻
2
Ϸ
͑7͒
⌬A
A
ACKNOWLEDGMENTS
and our results ͑Table IV͒ yield a value of 0.77 for the left-
hand side of Eq. ͑7͒ and 1.19 for the right-hand side, which
is reasonable agreement given the approximations involved.
Two of the authors ͑A.G.A. and D.W.T.͒ thank the Uni-
versity of New Brunswick and the Natural Sciences and En-
gineering Research Council of Canada for financial support.
The work at the University of Kentucky was supported by
the National Science Foundation.
Finally, the boron isotope effects in the spectra of BS2
0
deserve some comment. The A-X 00 band of 10BS2 was ana-
˜ ˜
lyzed assuming that the excited state spin-orbit coupling con-
stant is the same as that of 11BS2. The resulting difference in
the band origins ͑10BS2−11BS2; see Table I͒ is 12.184 cm−1,
in reasonable agreement with the calculated value of
11.61 cm−1, obtained using the harmonic approximation and
the Teller–Redlich product rule expression20
1J. W. C. Johns, Can. J. Phys. 39, 1738 ͑1961͒.
2A. G. Adam, A. J. Merer, and D. M. Steunenberg, J. Chem. Phys. 92,
2848 ͑1990͒ and references therein.
3S.-G. He, C. J. Evans, and D. J. Clouthier, J. Chem. Phys. 119, 2047
͑2003͒.
4S.-G. He and D. J. Clouthier, J. Chem. Phys. 120, 4258 ͑2004͒.
5J. M. Brom, Jr. and W. Weltner, Jr., J. Mol. Spectrosc. 45, 82 ͑1973͒.
6P. S. H. Bolman, J. M. Brown, A. Carrington, I. Kopp, and D. A. Ramsay,
Proc. R. Soc. London, Ser. A 343, 17 ͑1975͒.
␻ ͑10BS ͒ ␻ ͑10BS ͒
2
3
2
2
=
␻ ͑11BS ͒ ␻ ͑11BS ͒
2
3
2
2
7J. A. Coxon, M. Li, and P. I. Presunka, J. Mol. Spectrosc. 164, 118 ͑1994͒.
8M. Li and J. A. Coxon, J. Chem. Phys. 102, 2663 ͑1995͒.
9P. I. Presunka and J. A. Coxon, J. Chem. Phys. 101, 201 ͑1994͒.
10S. Gerstenkorn and P. Luc, Atlas du Spectre D’Absorption de la Molecule
d’Iode ͑Editions du CNRS, Paris, 1978͒.
2mS
m͑10B͒
2mS
m͑11B͒
1 +
=
= 1.04158.
͑8͒
ͱ
1 +
11S. Gerstenkorn and P. Luc, Rev. Phys. Appl. 14, 791 ͑1979͒.
12R. H. Judge and D. J. Clouthier ͑unpublished͒.
13T. C. Smith, H. Li, D. J. Clouthier, C. T. Kingston, and A. J. Merer, J.
Chem. Phys. 112, 3662 ͑2000͒.
The substantial isotope effect is primarily a result of the
533 cm−1 increase in ␻ on electronic excitation.
3
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194314-9
Spectroscopy of BS2
J. Chem. Phys. 122, 194314 ͑2005͒
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