A study of the molecular structure and Renner-Teller effect in the A2Πu-X2Πg electronic spectrum of jet-cooled boron disulfide, BS2

Article abstract of DOI:10.1063/1.1582849

The A²Π_u-X²Π_g band system of gas phase BS₂ was re-examined using the techniques of supersonic expansion cooling with laser-induced fluorescence (LIF) detection. Rotational analysis of high-resolution spectra of both spin-orbit components of the O₀⁰ band confirmed that the electronic transition is between a pair of inverted ∏ states, and effective ground and excited state structures were obtained for the first time. A combination of LIF and dispersed fluorescence data was used to obtain a rather complete Renner-Teller analysis of the ground state manifold of vibrational levels.

Full text of DOI:10.1063/1.1582849

A study of the molecular structure and Renner–Teller effect in the à 2 Π u –X̃ 2 Π g
electronic spectrum of jet-cooled boron disulfide, BS 2
Sheng-Gui He, Corey J. Evans, and Dennis J. Clouthier
Citation: The Journal of Chemical Physics 119, 2047 (2003); doi: 10.1063/1.1582849
View online: http://dx.doi.org/10.1063/1.1582849
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 119, NUMBER 4
22 JULY 2003
A study of the molecular structure and Renner–Teller effect in the
2
2
˜
˜
A ⌸u –X ⌸g electronic spectrum of jet-cooled boron disulfide, BS2
Sheng-Gui He, Corey J. Evans, and Dennis J. Clouthiera)
Department of Chemistry, University of Kentucky, Lexington, Kentucky 40506-0055
͑Received 12 February 2003; accepted 25 April 2003͒
2
2
˜
˜
The A ⌸u –X ⌸g electronic band system of jet-cooled boron disulfide (BS2) has been recorded in
the 760–530 nm region by laser-induced fluorescence ͑LIF͒ and wavelength resolved emission
techniques. The free radical was produced in a pulsed electric discharge jet using a precursor
mixture of BCl3 and CS2 in argon. The LIF spectrum consists of a long progression of strong bands
involving the ␯Ј ͑B–S stretching͒ mode and combinations involving 2␯Ј and 2␯Ј3 , as well as many
1
2
hot bands built on the 211 band. Detailed analysis of the spectrum shows that the ground state
exhibits a substantial Renner–Teller effect with ⑀ϭϪ0.2012 and a spin–orbit coupling constant of
AϭϪ413.80 cmϪ1. Angular momentum coupling is negligible in the excited state, which has a
much smaller spin–orbit coupling constant of AϭϪ259.15 cmϪ1. The vibrational frequencies of
11BS2 are ␻Љ1ϭ542.8, ␻2Љϭ285.0, ␻3Љϭ1010.5, ␻Јϭ514.1, ␻Јϭ309.7, and ␻Јϭ1543.6 cmϪ1
.
1
2
3
Rotational analysis of the 000 band allowed a determination of the effective molecular structures as
r0Љ(BS)ϭ1.6648(4) Å and rЈ0(BS)ϭ1.7127(5) Å. Ab initio methods have been used to predict the
BS2 spectroscopic parameters and good agreement with experiment was found. Our present
understanding of the LIF spectrum is in accord with the pioneering analysis of the absorption
spectrum of matrix isolated BS2 published by Brom and Weltner ͓J. Mol. Spectrosc. 45, 82 ͑1973͔͒
three decades ago. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1582849͔
I. INTRODUCTION
the products in neon matrices at 4 K. In their analysis, they
identified the same three bands near 410 nm as found in
earlier gas phase work and concurred with the previous as-
Relatively little is known about the electronic spectra of
polyatomic transient boron-containing molecules. Most of
the available information comes from matrix infrared
studies1 or low-resolution photoelectron observations2 on
neutrals and their ions. A recent search of the NIST database3
for boron-containing species yielded 198 entries, of which
only BO2 and BH2 have been studied in the gas phase with
resolution sufficient to resolve the vibrational and rotational
structure. Although the triatomic species of the types
X–BvO and X–BvS (XϭH,D,F,Cl,Br) have been rather
extensively studied by microwave and infrared spectroscopy,
their electronic spectra remain unknown.
There is one other boron-containing species, boron disul-
fide (BS2), whose electronic spectrum has been thoroughly
surveyed. In early gas phase work, Koryazhkin and
Mal’tsev4 identified two band systems, a group of three
bands at ϳ410 nm and a much more extensive system ex-
tending from 550 to 825 nm. Both systems showed clear
rotational structure, although bands between 550–650 nm
appeared diffuse, which was ascribed to a predissociation
process in the excited state. Their fragmentary analysis of the
complex spectra obtained at high temperatures suggested that
BS2 is bent in at least one of the electronic states.
ϩ
2
2
˜
˜
signment of the system as B ⌺u –X ⌸g . The band system
origin was given as 24 072 cmϪ1 with an upper state B–S
symmetric stretching frequency of ␯Ј1ϭ516 cmϪ1. They re-
2
ϩ
0
˜
assigned
˜
a
band at 417.1 nm as B ⌺ (0,0 ,0)
–A ⌸1/2(0,00,0) which gave the ground state spin–orbit
splitting as Ϫ440 cmϪ1. A very thorough study of the exten-
sive band system in the 720–500 nm region showed that this
2
2
2
Ϫ1
˜
˜
was the A ⌸u –X ⌸g transition with T0ϭ13 766 cm and
negligible angular momentum coupling ͑Renner–Teller ef-
fect͒ or Fermi resonance effects in the excited state. The
upper state spin–orbit interval was found to be Ϫ263 cmϪ1
with vibrational frequencies of ␯Јϭ506 cmϪ1
,
␯Ј
1
2
ϭ311 cmϪ1, and ␯Јϭ1535 cmϪ1. A combination of matrix
3
infrared absorption, visible emission, and isotope data gave
ground state vibrational frequencies of ␯Љϭ510 cmϪ1, ␯Љ
1
2
ϳ120 cmϪ1, and ␯Љϭ1015 cmϪ1. All of the evidence sug-
3
gested that the radical is linear with the SBS molecular struc-
ture in all three electronic states. The bands observed in the
gas phase in the 720–820 nm region4 were suggested to be
due to species other than BS2 .
Little further experimental or theoretical work has been
done on BS2 . In 1986, Briggs and Simmons6 attributed 2
sets of absorption bands near 412 and 625 nm produced in
the gas phase flash photolysis of BCl3 in the presence of CS2
or OCS to the ‘‘previously unreported BS2 radical.’’ Hassan-
zadeh and Andrews7 reported detection of the antisymmetric
stretching vibration, ␯3ϭ1015.7 cmϪ1, in argon matrix in-
The most definitive work comes from a single matrix
infrared and optical study by Brom and Weltner5 published
in 1973. The authors produced BS2 by vaporizing zinc sul-
fide and boron mixtures at high temperatures and trapping
a͒
Author to whom correspondence should be addressed.
0021-9606/2003/119(4)/2047/10/$20.00
2047
© 2003 American Institute of Physics
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2048
J. Chem. Phys., Vol. 119, No. 4, 22 July 2003
He, Evans, and Clouthier
frared studies of the reactions of laser ablated boron atoms
with carbon disulfide. Ortiz8 used electron propagator theory
to obtain theoretical predictions of the structures (Dϱh sym-
metry for all states͒, vibrational frequencies, and adiabatic
excitation energies of BS2 in various electronic states. Most
recently, Orlova and Goddard9 reported density functional
calculations on small radicals containing boron and alumi-
num, concentrating on species for which unrestricted
Hartree–Fock methods showed spatial symmetry breaking.
For BO2 and BS2 , all selected exchange-correlation func-
tionals produced symmetry adapted solutions and structures
and vibrational frequencies in good agreement with experi-
ment.
galvanic lines from neon- and argon-filled hollow cathode
lamps. High-resolution ͑0.04 cmϪ1͒ spectra of the 000 band of
BS2 were obtained in the same jet apparatus using a 308 nm
pumped Lambda-Physik ScanMate2E dye laser equipped
´
with an intracavity etalon, and calibrated to an estimated
accuracy of Ϯ0.003 cmϪ1 using I2 LIF spectra.13,14 The LIF
and calibration spectra were recorded simultaneously with a
digital data acquisition system of our design.15
Emission spectra were obtained using a similar discharge
jet apparatus. Tunable dye laser radiation crossed the super-
sonic expansion 1.5 cm downstream of the discharge and the
resulting fluorescence was focused with an f/1.5 lens system
onto the entrance slit of a 0.55 m scanning monochromator
͑Jobin Yvon-Spex Triax Series 550͒. The emission spectra
were recorded by fixing the excitation laser on the strongest
feature ͑the maximum of the R branch͒ of a band in the LIF
spectrum and scanning the monochromator. The pulsed fluo-
rescence signals were detected with a cooled, red-sensitive
photomultiplier ͑RCAC31034A͒ amplified 800 times, pro-
cessed using a gated integrator and recorded digitally. Emis-
sion from argon and neon pulsed discharge lamps was col-
lected approximately 100 ␮s after the BS2 emission and used
In the present work, we have re-examined the
2
2
˜
˜
A ⌸u –X ⌸g band system of gas phase BS2 using the tech-
niques of supersonic expansion cooling with laser-induced
fluorescence ͑LIF͒ detection. Rotational analysis of high-
resolution spectra of both spin–orbit components of the 000
band confirms that the electronic transition is between a pair
of inverted ⌸ states, and effective ground and excited state
structures have been obtained for the first time. A combina-
tion of LIF and dispersed fluorescence data has been used to
obtain a rather complete Renner–Teller analysis of the
ground state manifold of vibrational levels.
to calibrate the spectra to an estimated accuracy of Ϯ3 cmϪ1
.
A 1200 line/mm grating blazed at 750 nm was employed in
this work, with a bandpass of 0.3–0.5 nm, depending on the
strength of the signal.
II. EXPERIMENT
III. RESULTS AND ANALYSIS
The LIF spectrum of jet-cooled boron disulfide was first
observed in our laboratory by the technique of laser ablation.
The 1064 nm beam of a Nd:YAG laser was focused onto the
surface of a boron nitride rod and the ablation products were
entrained in a gas pulse of 5%–10% H2S in 60 psi of argon.
After supersonic expansion cooling, the products were inter-
rogated with a tunable dye laser and the subsequent fluores-
cence detected through an appropriate cutoff filter with a
A. Vibronic analysis and the Renner–Teller effect
1. LIF spectra
As will be subsequently shown, BS2 is a linear molecule
with the structure SBS. Boron has two isotopes 11B(80.1%)
and 10B(19.9%) so both the 11BS2 and 10BS2 isotopomers
are expected to be present in the spectra. The vibrational
˜ ˜
frequencies are labeled using the Herzberg conventions as ␯
photomultiplier. In this fashion, the A–X bands of BS2 in the
1
(␴g , symmetric BS stretch͒, ␯ (␲g,u , bend͒, and ␯ (␴u ,
antisymmetric BS stretch͒. The ground state electron con-
720–550 nm region were readily observed, although the
spectra suffered from low signal to noise ratio and large shot-
to-shot instabilities.
2
3
2
2
4
3
2
˜
3
figuration is ...(␴g) (␴u) (␲u) (␲g) X ⌸g ͑inverted͒,
2
2
4
2
It was subsequently discovered that much better spectra
could be obtained using the pulsed discharge jet
technique.10,11 A gas mixture of 3% BCl3 and 1% CS2 in
argon, contained in a stainless steel cylinder equipped with a
regulator, was injected at a pressure of 40 psi with a pulsed
molecular beam valve ͑General Valve, series 9͒ into a flow
channel prior to supersonic expansion into a vacuum cham-
ber. In the flow channel, an electric discharge between two
stainless steel ring electrodes fragmented the precursor mol-
ecules and formed BS2 by subsequent chemical reactions. It
was found that the strongest LIF signals were obtained with-
out a reheat tube12 on the end of the discharge apparatus.
In the LIF experiments, the supersonic expansion of the
discharge products was intercepted 1.5 cm downstream of
the discharge by the beam of a tunable dye laser ͑Lumonics
HD-500͒. The resulting fluorescence was imaged by a 5 cm
focal length lens through an appropriate cutoff filter onto
the photocathode of a high-gain photomultiplier tube
͑EMI9816QB͒. Low-resolution ͑0.1 cmϪ1͒ LIF spectra were
excited in the 760–530 nm range and calibrated using opto-
˜
with excited states ...(␴g) (␴u) (␲u) (␲g) A ⌸u ͑in-
ϩ
u
2
1
4
4
2
˜
verted͒, and ...(␴g) (␴u) (␲u) (␲g) B ⌺ . The ␲ orbit-
u
als are bonding and the ␲ orbitals are essentially pure 3p␲
g
nonbonding orbitals on the sulfur atoms. Assuming Dϱh
symmetry in all the combining states, the vibronic selection
rules are ⌬ ϭ0,Ϯ1,Ϯ2,... and ⌬ or ⌬ 3ϭ0,Ϯ2,... with
v1
v2
v
2
2
˜
˜
A ⌸u,1/2 –X ⌸g,3/2 , etc. transitions forbidden by the ⌬⌺
ϭ0 selection rule in case a coupling. In the case of signifi-
cant angular momentum coupling ͑Renner–Teller effect͒ in
one or both combining states, the equivalent vibronic selec-
tion rule is ⌬Pϭ0, where Pϭ͉⌳ϩlϩ⌺͉ϭ͉Kϩ⌺͉.
˜ ˜
Several attempts to excite emission from the B–X band
system at 415 nm were unsuccessful, indicating that the
ϩ
2
˜
B ⌺u state does not have an appreciable quantum yield of
˜ ˜
fluorescence. The LIF spectrum of the A–X band system of
jet-cooled BS2 was found to extend from 13 200 cmϪ1 ͑760
nm͒ to 18 850 cmϪ1 ͑530 nm͒. At first glance, the spectrum
appears quite complicated, as shown in Fig. 1, with a series
of strong bands separated by intervals of ϳ505 cmϪ1 inter-
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2
2
˜ ˜
2049
J. Chem. Phys., Vol. 119, No. 4, 22 July 2003
The A ⌸u–X ⌸g spectrum of BS2
˜ ˜
FIG. 1. A low-resolution LIF spectrum of the central portion of the A–X
band system of jet-cooled BS2 . The 1n0 and 10n202 cold bands are identified
with the 2⌸3/2–2⌸3/2 component at higher energy and the 2⌸1/2–2⌸1/2 com-
ponent at lower energy. Two weaker hot bands of the type 1n0211 are identi-
fied at the bottom of the figure, each with four components in order of
FIG. 2. A low-resolution LIF spectrum of the low wave number region of
˜ ˜
the A–X band system of jet-cooled BS2 . The spin–orbit and Renner–Teller
components and isotope effects are identified for the various bands.
2
2
increasing energy as
␮
␬
2⌺–␬ 2⌺,
⌬
3/2–2⌬3/2
,
⌬
5/2–2⌬5/2
,
and
2⌺–␮ 2⌺.
significant Renner–Teller interaction. The lower and upper
levels with the same symmetry and P quantum number are
distinguished by the ␮ and ␬ labels, respectively. This pat-
tern is repeated with the addition of further levels for the
higher bending states.
spersed with a very large number of weaker features. The
505 cmϪ1 interval is readily assigned as the upper state sym-
metric 11B–S stretching frequency and the 10n (2⌸3/2–2⌸3/2
)
With these considerations in mind, we turn our attention
to the LIF bands that involve the bending levels. The
progression extends to eight members, indicating a substan-
tial change in bond length on electronic excitation. Each in-
pair of bending transitions 220 (␮ 2⌸3/2–2⌸3/2
)
and
tense band in the 1n0 progression is accompanied by a weaker
202 (␬ 2⌸3/2–2⌸3/2) were assigned to medium intensity
bands at 14 542.48 cmϪ1 and 14 790.01 cmϪ1, respectively,
giving an upper state splitting of 247.53 cmϪ1. The weaker
220 (␮ 2⌸1/2–2⌸1/2) and 202 (␬ 2⌸1/2–2⌸1/2) bands were
found at 14 127.42 and 14 395.14 cmϪ1, with an interval of
267.72 cmϪ1. The spin–orbit splitting in the 220 band is
14 542.48–14 395.14ϭ147.34 cmϪ1, almost identical to the
145.6 cmϪ1 splitting of the 000 band, implying little or no
upper state Renner–Teller effect, as concluded in the matrix
2
⌸
1/2–2⌸1/2 spin–orbit component 146 cmϪ1 to lower en-
ergy, due to incomplete cooling of the spin–orbit levels in
the expansion, and a 10BS2 isotopomer band to higher en-
ergy. At the short wavelength end of the spectrum the
1n0320 (nϭ0–4) series of bands appears, assigned based on
the large isotope effect and vibrational interval, starting with
the intense 320 band at 16 998.33 cmϪ1. These assignments of
progressions involving the stretching fundamentals are in
agreement with the analysis of the absorption spectrum5 at 4
K, with a matrix shift of 60–70 cmϪ1 to lower wave num-
bers.
Figure 2 shows that even at the long wavelength end of
the spectrum there are many more bands than expected for
purely cold band absorption, suggesting a significant popu-
lation of higher vibrational and spin–orbit components in the
supersonic expansion. The 11BS2 000(2⌸3/2–2⌸3/2) band was
readily assigned as the strongest feature at 13 913.76 cmϪ1
,
with a weaker spin–orbit component at 13 768.16 cmϪ1, and
10BS2 –11BS2 isotope shift of 11.84 cmϪ1
In order to make further progress, we must consider the
a
.
bending modes and the Renner–Teller effect. A schematic
diagram of the first few bending levels in the ground or ex-
cited state manifolds is given in Fig. 3 for the two cases of a
substantial Renner–Teller interaction, as is found in the
ground state, and negligible Renner–Teller effect, as is found
in the excited state. The 0 1 0 (
,
, 3) levels have four
v1 v2 v
FIG. 3. Schematic diagram of the bending levels of BS2 for ⑀ϭ0 ͑left͒ and
⑀Ͻ0 ͑right͒. The energy levels on the left were calculated using the upper
components, the inner ⌬5/2 and ⌬3/2 levels which are sepa-
rated by approximately the spin–orbit coupling constant, A,
and the outer ␮ 2⌺ and ␬ 2⌺ components, which are sepa-
rated by more than the spin–orbit splitting in the case of a
state (A 2⌸u) constants given in Table II, with the Fermi resonance param-
˜
eter W1 set equal to 0.0. The energy levels on the right were calculated with
the same set of parameters with the addition of ⑀ϭϪ0.2.
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2050
J. Chem. Phys., Vol. 119, No. 4, 22 July 2003
He, Evans, and Clouthier
2
TABLE I. Cold bands in the A ⌸i –X 2⌸i LIF spectrum of jet-cooled BS2 . In each case the vibronic symmetry (2Sϩ1⌸P) given is the same for the upper
˜
˜
and lower states.
Band maximum ͑cmϪ1
͒
Band maximum ͑cmϪ1
͒
11BS2
Assignment
10BS2
Assignment
11BS2
10BS2
105
140220
105
⌸
1/2
2
000
000
⌸
2
13 768.16
13 913.76
14 127.42
14 273.32
14 395.14
14 418.88
14 542.48
14 619.39
14 770.84
14 776.78
14 790.01
14 888.45
14 922.33
15 035.78
15 109.72
15 184.80
15 254.37
15 278.20
15 282.15
15 380.52
15 423.76
15 527.87
15 598.41
15 668.87
15 736.66
15 772.51
15 777.27
15 871.18
15 922.94
16 018.49
16 084.90
16 152.32
16 260.74
13 780.00
13 926.20
16 274.07
16 360.88
16 419.90
16 507.73
16 634.71
16 747.46
16 768.22
16 857.83
16 914.38
16 996.43
16 998.33
17 116.04
17 182.39
17 259.40
17 352.80
17 405.80
17 457.82
17 493.21
17 599.34
17 662.07
17 845.10
17 894.31
17 940.31
17 985.47
18 081.39
18 139.46
18 215.30
18 334.75
18 421.26
18 474.73
18 561.88
18 687.79
18 821.61
16 292.03
1/2
3/2
2
2
⌸
␬
2
⌸
1/2
202
␮
2
⌸
⌸
2
16 438.18
16 548.62
1/2
3/2
101
⌸
1/2
140220
130240
140220
106
␮
␮
␬
2
⌸
⌸
⌸
2
2
2
14 285.60
3/2
3/2
3/2
202
101
␬
2
⌸
1/2
2
14 431.82
14 579.91
⌸
3/2
202
␮
␮
␮
2
⌸
2
⌸
2
16 789.10
16 944.83
16 935.48
3/2
1/2
1/2
3/2
110220
204
⌸
302
⌸
⌸
2
2
1/2
2
⌸
1/2
106
102
⌸
150220
302
␮
2
⌸
2
1/2
3/2
202
␬
␬
2
⌸
2
⌸
3/2
2
17 135.44
3/2
110220
102
⌸
1/2
140240
220320
107
␮
␮
2
⌸
⌸
2
3/2
1/2
2
14 935.56
15 071.99
⌸
2
3/2
110220
110220
␮
␮
␮
␮
2
⌸
⌸
⌸
⌸
3/2
1/2
1/2
110320
2
2
1/2
204
⌸
2
107
220320
110320
⌸
3/2
2
2
3/2
110240
103
⌸
␬
⌸
2
1/2
1/2
2
15 292.25
17 630.48
17 758.39
⌸
2
⌸
3/2
1/2
110220
120220
103
␬
␬
2
⌸
⌸
220320
110220320
120320
␮
⌸
3/2
2
2
3/2
1/2
2
␮ ⌸
2
1/2
1/2
15 438.63
15 566.69
⌸
⌸
1/2
3/2
120220
130220
110240
120240
120220
104
␮
␮
␮
␮
⌸
⌸
⌸
⌸
⌸
108
110220320
120320
⌸
2
2
2
2
2
2
3/2
1/2
3/2
1/2
3/2
3/2
2
␬
⌸
2
18 123.49
18 240.59
⌸
3/2
110220320
110220320
␮
␮
⌸
⌸
2
3/2
1/2
2
␬
2
2
⌸
2
240320
␮
⌸
1/2
3/2
130220
104
␬
2
⌸
130320
⌸
1/2
2
1/2
120220320
130320
␬
⌸
2
15 939.27
16 057.98
⌸
3/2
1/2
130220
140220
120240
130220
␮
␮
␮
␬
⌸
⌸
⌸
⌸
⌸
2
2
2
2
2
18 614.40
18 721.38
3/2
1/2
3/2
3/2
3/2
120220320
110240320
140320
␮
⌸
⌸
2
3/2
3/2
2
␮
2
⌸
1/2
work. If we assume that the upper state spin–orbit constant is
the average of the 22 level splittings or ϳ258 cmϪ1, then the
ground state value is ϳ404 cmϪ1. Using the 202 ␬ 2⌸3/2–000
viously from the components of the 220 band, further
strengthening the conclusion that the Renner–Teller effect is
negligible in the upper state. The hot band pattern of four
main components is repeated extensively throughout the
spectrum in 1n0211 and 10n211320 progressions, as illustrated in
Fig. 1. The 231 and 251 bands were also identified, along with
progressions involving ␯Ј and 2␯Ј . A few hot bands involv-
and 220 ␮ 2⌸3/2–000
⌸
intervals of ϳ876 cmϪ1
2
2
⌸
3/2
3/2
and ϳ629 cmϪ1, most of the remaining cold bands in the
spectrum were assigned as various combinations of the
three vibrations. The weak 240 (␮ 2⌸3/2–2⌸3/2
)
and
1
3
240 (␮ 2⌸1/2–2⌸1/2) bands were assigned along with combi-
ing ␯Љ , such as the 101202 band shown in Fig. 2, were also
1
nation bands involving ␯Ј and 2␯Ј3 , but the corresponding
1
assigned.
transitions to the ␬ 2⌸3/2 and ␬ 2⌸1/2 levels were not found.
The cold band assignments, isotope shifts, and spin–orbit
components are summarized in Table I.
We have used the Renner–Teller model described in our
previous work16 on the ⌸i ground state of SiCH to fit the
2
˜
vibronic levels of the A state of BS2 . Although the initial
The very large number of weaker transitions that could
not be assigned as cold bands were found to be hot bands
originating primarily from the various components of the 21
vibrational state, positively identified with the aid of the
emission spectra ͑vide infra͒. As shown in Fig. 2, the four
main components of the 211 band were observed, as well as
the two weaker ␬ 2⌺Ϫ –␮ 2⌺ϩ and ␮ 2⌺ϩ –␬ 2⌺Ϫ transi-
indications were that the Renner–Teller effect was negli-
gible, we wanted an unbiased fitting method that would re-
veal any small angular momentum coupling effects without
a priori assumptions. Since the transitions do not give the
upper state energy level splittings directly, due to the restric-
tive ⌬Pϭ0 selection rule, we elected to fit combination dif-
ferences rather than transitions. This approach has the advan-
tage of being able to extract the spin–orbit and Renner–
Teller parameters indirectly, through their variation with the
energy level splittings as a function of the vibrational quan-
tions ͑not shown in Fig. 2͒ at 14 205.79 and 13 530.40 cmϪ1
.
These transitions allow an independent calculation of the up-
per state 21 level spin–orbit splitting, yielding a value of
258.0 cmϪ1, in good agreement with the value deduced pre-
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2
2
˜ ˜
2051
J. Chem. Phys., Vol. 119, No. 4, 22 July 2003
The A ⌸u–X ⌸g spectrum of BS2
TABLE II. Vibrational parameters ͑in cmϪ1͒ for the ground and electronic
tum numbers. By extending the matrix given in Ref. 16, we
included all three vibrations, as well as spin–orbit coupling,
Renner–Teller effects, anharmonicity, and possible Fermi
resonances between 2␯Ј and ␯Ј and higher combinations.
The vibrational energy levels on the diagonal of the matrix
were written as
excited states of 11BS2 .
2
2
˜
X
˜
A
⌸
⌸
u
g
2
1
Parameter
Experiment
Ab initiob
Experiment
Ab initiob
542.767(61)a
284.962(46)
1010.510(11)
550.4
282.7
944.1
Ϫ428
¯
514.129(12)
309.686͑98͒
1543.634͑70͒
Ϫ259.148(12)
Ϫ0.515͑59͒
2.844͑72͒
0.0
1.4359͑96͒
0.0
15.1080(65)
0.0
Ϫ0.548͑17͒
1.124͑99͒
Ϫ4.461͑39͒
Ϫ7.154͑32͒
¯
514.4
316.8
1569.7
Ϫ257
¯
␻
␻
␻
A
␣
␣
⑀
g4
gK
W1
W2
x11
x12
x13
x23
x33
1
2
G
͒ϭ␻
͒ϩ␻ 2ϩ1͒ϩ␻
͑v ͑v3
3
͒ϩx11 ͒
͑v21
͑v
͑v1
1
2
3
Ϫ413.802(74)
¯
ϩx12
͑v1 ͑v
͒
2ϩ1͒ϩx13
͑v1v3
͒
͑v2
͒ϩx23 ϩ1͒
͑v3
A
2
A
¯
¯
¯
͑v23
ϩx33 ͒.
3
͑1͒
Ϫ0.2012͑34͒
2.7854(54)
¯
Ϫ0.224
¯
0.008
¯
Note that we have explicitly subtracted off the zero-point
¯
¯
contribution of ␻ and ␻3 . The diagonal spin–orbit interac-
1
19.0202(88)
1.031(11)
¯
¯
¯
tion as a function of vibrational level was written as
0.0
¯
¯
¯
3
A
i
¯
¯
¯
A ϭAϪ
␣
͒,
͑2͒
͑vi
͚
v
Ϫ7.829(89)
Ϫ1.853(51)
6.244(34)
¯
¯
iϭ1
¯
¯
where the ␣Ai terms account for the variation of the spin–
orbit coupling parameter with vibrational energy. The
Renner–Teller Hamiltonian contributes off-diagonal ele-
¯
¯
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.
ments with ⌬Kϭ0, ⌬⌳ϭϮ2, and ⌬ 2ϭ0, Ϯ2 that depend
v
bCCSD͑T͒/aug-cc-pVTZ calculations.
on the Renner–Teller parameter ⑀ and ␻2 , which is the ‘‘av-
erage’’ of the harmonic bending frequencies of the two po-
tentials. The anharmonicity of the bending levels depends on
the anharmonic force constants g4 and gˆ 4 and the parameter
gK which accounts for the K dependence of the mixing of the
vibrational levels of the ⌸ state with other ⌺ and ⌬ states.
Finally, possible Fermi resonance effects between levels of
A few typical spectra are shown in Fig. 4. Excitation of the
2
⌸
3/2–2⌸3/2 component of the 000 band yields a very simple
spectrum with strong emission predominantly down to levels
with vibrational energies of 509 and 591 cmϪ1. The former
interval is assigned as the ground state B–S symmetric
stretching fundamental and the latter is the energy of the
the type
,
,
and ( Ϫ1), ( ϩ2),
v1 v2
were included
v3
v1 v2 v3
as a function of the parameters W1 and W2 first introduced
22 (␮ 2⌸3/2
) level above the zero-point. The rest of
by Hougen.17
the bands are constrained by the selection rules to be transi-
tions down to 2⌸3/2 levels of the ground state, but the assign-
ments are not immediately obvious. Excitation of the
110202 (␮2⌸3/2–2⌸3/2) transition gives a similar pattern, with
two levels near 590 cmϪ1 and many more transitions to
higher levels in the ground state.
In the least squares analysis, 146 upper state combina-
tion differences were fitted by varying 12 constants to give
an overall standard deviation of 0.41 cmϪ1, with residuals
(obs.Ϫcalc.) less than or equal to 1.0 cmϪ1. The Renner–
Teller parameter ⑀ was found to be negligible and was con-
strained to 0.0 cmϪ1 in the final analysis. Although the 10n
progression is very regular with only a slight anharmonicity,
it was necessary to include the Fermi resonance parameter
W1 in the fitting process to obtain a satisfactory analysis.
Careful consideration of the experimental observations
showed that the 1n22 ␬ 2⌸3/2 and 1n22 ␮ 2⌸1/2 vibrational
intervals decrease more rapidly than the corresponding
1n22 ␮ 2⌸3/2 and 1n22 ␬ 2⌸1/2⌬G values, which can only
be explained by Fermi interactions of the 1n22 levels with
the 1nϩ1 levels from below and the 1nϪ124 levels from
above. Examination of the wave functions indicated that
Fermi resonance effects are fairly minor at low quantum
numbers, but have a substantial effect for higher energy lev-
els. The resulting constants are summarized in Table II.
Excitation of the 320 band gives a very different emission
spectrum, with fluorescence predominantly down to the 32
level in the ground state, with weaker transitions to 34 and
combinations of ␯Љ or ␯Љ with these levels. These assign-
1
2
ments were confirmed by obtaining the emission spectrum of
the 10BS2 isotopomer, which shows the requisite isotope
shifts as shown in Fig. 4. Half of the 32 interval gives ␯Љ
3
ϭ1024 cmϪ1, in accord with the matrix infrared value5 of
1014.6 cmϪ1
.
In our analysis of the ground state vibrational levels, we
fitted ground state combination differences obtained from the
various emission spectra to the same Renner–Teller model as
used for the excited state. As the emission data are at least
ten times less precise than the LIF data, we were unable to
determine as many lower state constants. In the final analy-
sis, 11 parameters were used to fit 86 combination differ-
ences to an overall standard deviation of 2.36 cmϪ1 and re-
siduals less than 5.5 cmϪ1. The resulting constants are
presented in Table II. As a check on the analysis, the con-
stants in Table II, obtained by independent least squares
analyses of ground and excited state combination differ-
ences, were used to calculate the transition frequencies for
2. Emission spectra
The ground state energy levels were studied by record-
ing emission spectra obtained by excitation of the R-branch
maxima of various bands in the LIF spectrum. Emission
2
spectra were acquired by pumping fifteen ⌸3/2–2⌸3/2 and
2
⌸
1/2–2⌸1/2 cold bands and ten 2⌺–2⌺ and 2⌬–2⌬ hot
bands of 11BS2 and three ⌸3/2–2⌸3/2 cold bands of 10BS2 .
2
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2052
J. Chem. Phys., Vol. 119, No. 4, 22 July 2003
He, Evans, and Clouthier
FIG. 5. The experimentally derived and ab initio calculated manifolds of
low-lying energy levels in the ground state of 11BS2 . The ab initio results
were calculated using the constants given in Table II. The symmetries of the
ab initio levels are the same as their experimental counterparts except as
explicitly noted.
FIG. 4. Representative emission spectra of jet-cooled BS2 . The wave num-
ber scale is displacement from the laser line, giving a direct measure of the
ground state vibrational energy. In each case, the LIF transition pumped by
the laser is given in boldface at the left of the spectrum and the resonance
position in the energy hierarchy of such calculated levels, as
indicated in Fig. 4.
fluorescence signal is enhanced by scattered laser light. In spectrum A,
2
obtained by pumping the
⌸
3/2–2⌸3/2 component of the 000 band of 11BS2 ,
2
the lower state
⌸
energy levels are labeled numerically in order
3/2
B. Rotational analysis
of their calculated energies. Spectrum B was obtained by pumping the
2
2
We have recorded two bands, the 000 band ͑both spin–
␮
⌸
3/2–2⌸3/2 component of the 101220 band and the ground state
energy levels are labeled in calculated energy order. Spectrum C is that
⌸
3/2
orbit components͒ and the 211 band (␮ 2⌺gϩ –␮ 2⌺uϩ compo-
2
obtained by pumping the
⌸
3/2–2⌸3/2 component of the 302 band of 11BS2 ,
and spectrum D is that of the corresponding 10BS2 isotopomer.
nent͒ with sufficient resolution to resolve the rotational struc-
2
ture, as shown in Fig. 6. The red-degraded
⌸
3/2–2⌸3/2
component of the 000 band shown in Fig. 6 has a prominent
Q-branch, a simple P-branch, and an R-branch that forms a
head at high values of J. Due to the nuclear statistical
weights, only half of the ⌳ doubling levels are present, im-
plying that the two sulfur atoms with Iϭ0 are equivalent, so
that the molecule must have the symmetric SBS structure.
The much weaker 211 2⌺–2⌺ band shows well-resolved
spin-splittings in the P and R branches and poorly resolved
satellite branches. Only odd values of the quantum number N
are evident in the lower 2⌺ state, due to the nuclear statistical
weights, proving it to be ⌺u rather ⌺u . This transition is
the strongest of the 211 components ͑Fig. 2͒, so it must origi-
nate from the lower or ␮ 2⌺uϩ state. Since only ⌺ vibronic
levels can be assigned to one or the other of the two potential
functions generated by bending the molecule, it is clear that
the lower potential curve, with the smaller vibrational fre-
quency, is symmetric (Vϩ in Herzberg’s notation18͒ with re-
spect to reflection in the molecular plane and the upper, with
the larger vibrational frequency, is antisymmetric (VϪ).
several observed hot and cold band LIF transitions which
were found to be reliably predicted, limited primarily by the
precision of the ground state constants determined from low-
resolution emission data.
There is a substantial Renner–Teller effect in the ground
state of BS2 , with ⑀ϭϪ0.2012(34) cmϪ1. As the bending
frequency is much lower than the spin–orbit interval, this
has the effect of interleaving the levels, giving a complex
pattern of vibrational states, as illustrated in Fig. 5. A further
complication is the strong Fermi resonance between
2␯ (591 cmϪ1) and ␯ (509 cmϪ1) and the subsequent
ϩ
Ϫ
2
2
2
1
higher levels built on these two intervals. Due to these com-
plications, few of the vibrational states had contributions of
greater than 50% from a single basis state, so it was difficult
to assign vibrational quantum numbers to the levels. In most
cases, they were simply identified by their symmetry and P
quantum number and a sequential integer indicating their
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2
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˜ ˜
2053
J. Chem. Phys., Vol. 119, No. 4, 22 July 2003
The A ⌸u–X ⌸g spectrum of BS2
IV. AB INITIO CALCULATIONS
Now that reliable information is available on the struc-
ture, vibrational frequencies, spin–orbit coupling constants,
and Renner–Teller parameters for the ground and first ex-
cited state of BS2 , it is of interest to see how well these
quantities can be predicted by ab initio theory. We have used
the GAUSSIAN 98 programs21 to calculate the molecular prop-
erties at a variety of levels of theory with a range of standard
basis sets. We find reasonable agreement for most quantities
using density functional theory with the Becke three-
parameter hybrid density functional22 and the Lee, Yang, and
Parr correlation functional23 ͑B3LYP͒ along with Dunning’s
correlation-consistent triple-zeta basis sets augmented by dif-
fuse functions ͑aug-cc-pVTZ͒.24 The best results, which we
report in this work, were obtained using coupled cluster
theory including single and double excitations with a pertur-
bative treatment of triple excitations ͓CCSD͑T͔͒ and the aug-
cc-pVTZ basis set.
1
ϩ
g
ϩu ) ͑top͒ and
2
2
FIG. 6. High-resolution LIF spectra of the 21(␮
⌺
–␮
⌺
000(2⌸3/2–2⌸3/2) bands of jet-cooled 11BS2 showing the rotational assign-
ments.
The ground and excited state bond lengths were calcu-
lated to be 1.676 Å and 1.724 Å, in each case about 0.01 Å
more than the experimental r0 values. The correspondence of
the predicted vibrational frequencies with experiment is gen-
These considerations show that the sign ⑀ must be negative,
since ⑀ is proportional to ␯(Vϩ)–␯(VϪ) ͑vide infra͒.
The molecular constants were determined by least
squares fitting the transition frequencies and simultaneously
erally very good, with the exception of ␻Љ which is under-
3
estimated by ϳ6.5%. The theoretical T0 value is 13 982
cmϪ1, only 143 cmϪ1 higher than the experimental value
given in Table III.
2
varying the upper and lower state parameters. For the ⌸
The Renner–Teller parameters can also be easily derived
states, the Hamiltonian used was that given, for example, in
Ref. 19 and both spin–orbit components were fitted simulta-
neously. For the 2⌺ϩ vibronic states the energy level expres-
sions were
2
2
˜
˜
from the ab initio data. In both the X ⌸g and A ⌸u states,
theory predicts two distinct bending frequencies because, on
bending, the degenerate 2⌸ state splits into two nondegener-
ate states, one of which is symmetric with respect to the
F1 N͒ϭT ϩB N Nϩ1͒ϪDN2 Nϩ1͒2ϩ 1␥N,
͑3͒
͑
͑
͑
0
␯
2
2
2
˜
˜
molecular plane (X B2 or A A1) and one of which is anti-
2
2
F2 N͒ϭT ϩB N Nϩ1͒ϪDN2 Nϩ1͒2Ϫ 1␥ Nϩ1͒. ͑4͒
˜
˜
symmetric (X A2 or A B1). The Renner parameter ⑀ can be
͑
͑
͑
͑
2
0
␯
defined as25
The overall standard deviation of fit for both bands was
0.003 cmϪ1, comparable to the estimated accuracy of the
measurements. No perturbations were detected in either band
and the resulting constants are summarized in Table III.
More extensive tables of the vibrational and rotational as-
signments of the spectra and the results of the least squares
analysis have been deposited with EPAPS.20 The effective
(r0) molecular structures calculated from the rotational
constants are rЉ0 (B–S)ϭ1.6648(4) Å and r0Ј (B–S)
ϭ1.7127(5) Å.
2
␻ ͒2Ϫ ␻ ͒
͑
͑
͑
s
a
⑀ϭ
,
͑5͒
2
␻ ͒2ϩ ␻ ͒
͑
s
a
where ␻ is the harmonic bending frequency associated with
the symmetric state and ␻ with the antisymmetric state. The
sign of ⑀ then depends on whether the symmetric or antisym-
metric wave function belongs to the upper or ‘‘inner’’ steeper
potential with the larger harmonic frequency. The harmonic
s
a
TABLE III. Molecular constants ͑in cmϪ1͒ for 11BS2 .
2⌸i 00
0.0951209͑49͒
A
2⌸i 00
X 21
⌺
⌺
2
ϩ
1 2
ϩ
Parameter
˜
˜
Parameter
˜
˜
A 2
X
a
B
A
0.0898717͑53͒
Ϫ259.15b
0.0c
0.656͑53͒
13839.3920(1)
B
D
␥
0.095438͑94͒
0.0c
0.13459͑72͒
278.52d
0.090089͑90͒
0.0c
0.17406͑71͒
13945.9789(2)
Ϫ404.6834(3)
Ϫ0.80͑13͒
0.398͑51͒
0.0
104Ad
102(pϩ2q)
T0
T0
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.
bFrom the Renner–Teller analysis of excited state combination differences.
cParameter fixed in the final least squares analysis.
dFrom the Renner–Teller analysis of the ground state energy levels.
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129.120.242.61 On: Fri, 28 Nov 2014 10:00:04

2054
J. Chem. Phys., Vol. 119, No. 4, 22 July 2003
He, Evans, and Clouthier
consistent field ͑MCSCF͒ orbitals for the state of interest
with the geometry fixed at the CCSD͑T͒/aug-cc-pVTZ value
͑experimental bond lengths were used for BO2 test calcula-
tions͒, followed by a second order configuration interac-
tion ͑SOCI͒ and subsequent spin–orbit coupling calculation.
This method has been shown27–29 to give spin–orbit cou-
pling constants with typical errors of 10%–30% for a wide
range of nuclei. In the present work, the predicted ground
state spin–orbit splittings were BO2ϭϪ158 cmϪ1 and BS2
ϭϪ428 cmϪ1, with errors of only ϩ6.2% and ϩ3.4%, re-
spectively. The corresponding excited state values were
BO2ϭϪ102 cmϪ1 and BS2ϭϪ257 cmϪ1, with gratifyingly
small deviations from experiment of ϩ1.2% and Ϫ0.8%.
A comparison of the experimentally determined ground
state vibrational energy levels and those predicted from the
ab initio vibrational frequencies, Renner–Teller parameter, ⑀,
and spin–orbit coupling constant is given in Fig. 5. The
agreement is clearly very good, illustrating once again that
ab initio theory has great potential for helping to understand
complex Renner–Teller problems. One consequence of the
large spin–orbit splitting and much smaller bending fre-
quency in the ground state of BS2 is a reordering of some of
the energy levels of the 020 vibrational state. The usual situ-
ation is shown in Fig. 3, where the excited state 020 levels
FIG. 7. The effect of bending on the electronic states of BS2 . The two
lowest curves show the calculated total energies at the B3LYP/aug-cc-pVTZ
level of theory for the ...(a2)1 (b2)2 (2A2) and ...(a2)2 (b2)1 (2B2) ground
state electron configurations at various bond angles with the bond length
fixed at its equilibrium value. The middle two overlapping curves are similar
2
are far removed from the 000 levels and the ⌽ ‘‘unique
levels’’ occur between the ␮ 2⌸ and ␬ 2⌸ levels. In the
ground state ͑Fig. 5͒, the 020 ␮⌸1/2 level is fairly close to
the 000 ␬⌸1/2 level and they interact quite strongly through
2
˜
ab initio A
⌸
excited state 2A1 and 2B1 bending potentials. The relative
u
the ⌬ 2ϭϮ2 terms in the Renner–Teller Hamiltonian,
v
splittings of the ab initio potentials within each state are to scale although
the separations of the electronic states are not. The three highest potentials
are purely schematic representations of the bent molecule states derived
pushing the 020 ␮ 2⌸1/2 above the 2⌽7/2 level, as is shown in
the ab initio prediction on the right-hand side of Fig. 5. The
2
and ␮ 2⌸3/2 levels are unaffected as there are no
ϩ
u
2
from the ...(␴g)2 (␴u)1 (␲u)4 (␲g)4 (B
⌺
)
and ...(␴g)2 (␴u)2
˜
⌽
7/2
(␲u)4(␲g)2 (␴g)1 (2⌺gϪ and
⌺
ϩg ) electron configurations. The vertical ar-
2
nearby levels of the same symmetry and P coupled to them.
2
The ⌽5/2 , ␬ 2⌸3/2 , and ␬ 2⌸1/2 levels retain the expected
rows indicate vibronic coupling between the connected states.
order because they are all affected by coupling with the cor-
responding ␮ levels of 040. In reality, the situation is even
more complex, due to Fermi resonance effects, as illustrated
on the left-hand side of Fig. 5. The 020 ␮ 2⌸3/2 level is
displaced upwards due to the Fermi interaction with
1002⌸3/2 ͑the level mixing is so strong here that assigning
the vibrational quantum numbers is quite arbitrary͒, scram-
bling the vibrational states even further.
frequency of the zero-order bending potential, ␻2 , is ob-
tained from the ab initio bending frequencies as25
1
2
2
ͱ
␻2ϭ
␻ ͒2ϩ ␻ ͒
.
͑6͒
͓͑
͑
͔
s
a
The relative order of the two ground state potentials was
2
2
determined by calculating the energies of the B2 and A2
states at various bond angles, with the bond length fixed at
2
the optimized value. As shown in Fig. 7, the A2 potential is
V. DISCUSSION
2
above the B2 potential, so ␻aϾ␻ and therefore ⑀ is nega-
s
tive, as is found experimentally. In the excited state we find
that the two potential curves are very close together with
2A1Ͼ2B1 so that ⑀ is small and positive. Theoretical values
In this work we have established the molecular structure
of BS2 for the first time, with a ground state bond length of
1.6648͑4͒ Å which increases by almost 0.05 Å to 1.7127͑5͒Å
in the excited state. The ground state bond length is ϳ0.05 Å
longer than that of boron monosulfide ͑BS͒ (reϭ1.6092 Å)
͑Ref. 30͒ and more than 0.1 Å greater than the 1.555 Å bond
length of CS2 . The elongation of the bond on electronic
excitation mirrors that found in BO2 ͑1.265 Å–1.302 Å͒
͑Ref. 31͒ and is as expected for a transition which promotes
of ⑀ and ␻ were calculated from Eqs. ͑5͒ and ͑6͒ and show
2
excellent agreement with experiment, as summarized in
Table II. Of particular interest is the prediction that the ex-
cited state Renner–Teller parameter, derived from vibrational
frequencies of 315.5 and 318.0 cmϪ1, is 0.008 cmϪ1, in ac-
cord with our analysis of the LIF spectrum which shows that
⑀ is too small to be determined.
an electron from the bonding ␲ orbitals to the nonbonding
u
The other quantity of interest is the spin–orbit coupling
constant, A, which we have calculated using the full Breit–
Pauli Hamiltonian as implemented in the GAMESS program.26
This involved optimizing the multiconfiguration self-
␲ orbitals.
g
Although most of our analysis has concentrated on the
more abundant 11BS2 species, the boron isotope effects in the
LIF and emission spectra confirm many of the assignments.
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2
2
˜ ˜
2055
J. Chem. Phys., Vol. 119, No. 4, 22 July 2003
The A ⌸u–X ⌸g spectrum of BS2
Using the upper and lower state vibrational frequencies
given in Table II and the Teller–Redlich product rule32 ex-
pressions, which predict
Merer for this explanation͒. The Renner–Teller effect is a
manifestation of vibronic interactions in orbitally degenerate
electronic states. The Hamiltonian for the interaction can be
simplified by considering the first two terms of a multipole
expansion,41
2mS
1ϩ
␻
␻
10BS2͒
11BS2͒
␻
␻
10BS2͒
m 10
͑
B͒
͑
͑
͑
͑
2
2
3
3
ͱ
H ϭj ␳ cos͑␯Ϫ␹͒ϩj ␳2 cos 2͑␯Ϫ␹͒ϩ¯ ,
͑8͒
ϭ
ϭ
ϭ1.041 58
11
Ј
1
2
BS2͒
2mS
1ϩ
m 11
͑
B͒
where ␳ is the angle through which the molecule has bent
and ␯ and ␹ are the electronic and nuclear bending coordi-
nates. The first or dipolar term vibronically couples elec-
tronic states of the linear molecule that differ by ⌬⌳ϭϮ1,
while the second or quadrupolar term couples the two com-
ponents of a ⌸ state with the selection rule ⌬⌳ϭϮ2. Both
effects contribute to the splitting of the bending levels within
the electronic ⌸ state and are described by the single Renner
parameter ⑀. The three state model of Gauyacq and Jungen,42
in which the problem is simplified by considering only the
two components of the ⌸ state and a single vibronically
coupled ⌺ state, allows one to assess the relative effects of
the two terms in Eq. ͑8͒ and it is generally found that the
dipolar or vibronic coupling term predominates.43–45 Unfor-
tunately, we cannot apply the three state model directly to
BS2 , as we were unable to determine the ground state value
of gK since the absolute positions of the unique levels rela-
tive to the other bending levels are not available from the
experimental data.
͑7͒
and no boron isotope effect for ␯1 , we calculate the 000 band
isotope effect (10B–11B) in the harmonic approximation to
be ϩ12.11 cmϪ1, in excellent agreement with the ϩ11.84
cmϪ1 value observed experimentally. Similarly, the experi-
mental ratios of the 2␯Љ3 , 4␯Љ , and 2␯Ј intervals for the two
3
3
isotopomers are 1.041, 1.041, and 1.044, in good agreement
with theory.
The spectroscopic parameters of BS2 are similar to those
of CSϩ2 ,32–34 analogous to the resemblance of the molecular
constants of BO2 and COϩ2 recognized by Johns in his analy-
sis of the ‘‘boric acid fluctuation bands.’’ 31 For CS2ϩ ,A0Љ
ϭϪ440.4 cmϪ1, whereas for BS2 , A0ЉϭϪ413.8 cmϪ1 as is
3
g
expected for a ␲ configuration where the unpaired electron
is in an orbital which is of predominantly sulfur 3p␲ char-
acter. Both spin–orbit coupling constants are only slightly
higher than the 382.4 cmϪ1 ground state spin–orbit coupling
constant of the sulfur atom.35 The ground and excited state
stretching frequencies of CSϩ2 (␯1Љϭ617 cmϪ1
,
␯Љ
Despite the absence of data that would allow a quantita-
tive treatment, we can rationalize the observed Renner–
Teller effects based on the symmetries of the electronic states
of BS2 and the resulting vibronic coupling. As shown in Fig.
7, bending the BS2 molecule from linearity gives five states
with the irreducible representations B2 , A2 , B1 , A1 , and
3
ϭ1188 cmϪ1, ␯Ј1ϭ550 cmϪ1, and ␯Јϭ1644 cmϪ1) are
3
slightly larger than those of 11BS2 ͑Table II͒, in concert with
the bond lengths which are slightly shorter for CSϩ2 rЉ
͓
0
ϭ1.5542(4) Å and rЈ0ϭ1.615 Å].
The antisymmetric stretching frequencies of BS2 and the
related BO2 , COϩ2 , and CS2ϩ molecules are anomalous, with
␻Љ much closer to ␻Љ than expected. A simple valence force
2
2
˜
˜
B2 , derived from the linear molecule X ⌸g , A ⌸u , and
˜
ϩ
2
B ⌺u electronic states. Vibronic coupling between the
3
1
field predicts36 ␻Љ/␻Љ ratios of 1.9 (CO2ϩ)–2.6 (BS2),
2
2
ϩ
2B2 component of the ground state and the B2 (B ⌺u )
excited state accounts for the sign and magnitude of the
Renner–Teller effect in the ground state. The
...(␴g)2 (␴u)2 (␲u)4(␲g)2 (␴g)1 excited electronic con-
˜
3
1
whereas the experimental values range from 1.1 (COϩ2 )
Ϫ1.9 (BS2). The ␯Љ modes of both BS2 and BO2 also ex-
3
hibit a large ‘‘negative’’ anharmonicity ͑a positive x33 anhar-
monicity constant͒, indicative of a broad anharmonic stretch-
Ϫ
Ϫ
ϩ
figuration yields ⌺g , 2⌬g , 2⌺g , and ⌺g excited states.
On bending, the latter two states, which are expected to be
similar in energy, transform as B1 and A1 . Vibronic coupling
4
2
ing potential. In contrast, for example, CS2 has ␻3Љ/␻Љ
1
ϭ2.3 (calc.ϭ2.5) and x33ϭϪ6.57 cmϪ1
.
37 The opposite ef-
˜
fect is observed in the A excited states of BO2 and BS2 , with
˜
with these states affects the two components of the A state
␻Ј/␻1Јϭ2.4 and 3.0, respectively. Kawaguchi et al.38 have
3
almost equally, accounting for the absence of a significant
2
modeled this behavior in BO2 as due to vibronic coupling
Renner–Teller effect in the ⌸u excited state.
The matrix results of Brom and Weltner5 are in very
good agreement with the present analysis. The gas phase
excited state vibrational frequencies, ground and excited
state spin–orbit coupling constants, cold band assignments,
˜
˜
between the A and X states through the ␯ vibration, which
3
distorts the ground state antisymmetric stretching potential
and lowers the ␯Љ frequency while simultaneously raising the
3
excited state frequency. This model has been questioned,
since ab initio studies39 have shown that the frequency and
anharmonicity can be accurately reproduced within the adia-
batic approximation. However, Johnson and Rostas40 argue
that there is no fundamental difference between the two ap-
proaches. Regardless of the semantic arguments, the phe-
nomenon clearly persists in BS2 and is likely due to vibronic
˜ ˜
and A–X system origins are all very similar if one allows for
small matrix shifts. Both analyses lead to the conclusion that
the Renner–Teller effect is negligible in the upper state. The
authors assigned a weak but persistent emission feature at
749.3 nm observed while recording the matrix absorption
spectrum as the 101 band. The corresponding gas phase emis-
sion spectrum ͓Fig. 4͑A͔͒ is dominated by two strong bands
at 745.9 and 750.4 nm, assigned as 101 and 220, respectively.
Despite the general accord of the matrix and gas phase
analyses, there are a few minor differences. The lack of ir-
˜
coupling with the A state.
˜
˜
The Renner–Teller effects in the X and A states can be
best understood by consideration of vibronic coupling with
higher electronic states ͑we are indebted to Dr. Anthony
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2056
J. Chem. Phys., Vol. 119, No. 4, 22 July 2003
He, Evans, and Clouthier
regularities in the matrix spectra suggested that Fermi reso-
18 G. Herzberg, Molecular Spectra and Molecular Structure III. Electronic
Spectra and Electronic Structure of Polyatomic Molecules ͑Van Nostrand,
New York, 1966͒, p. 28.
2
˜
nance effects in the A ⌸u state are quite small, whereas
fitting the gas phase data necessitates a substantial Fermi
resonance parameter, although most of the progressions are
still quite regular. Perhaps most interesting is the matrix as-
19 T. C. Smith, H. Li, D. J. Clouthier, C. T. Kingston, and A. J. Merer, J.
Chem. Phys. 112, 3662 ͑2000͒.
20 See EPAPS Document No. E-JCPSA6-119-004328 for tables of the
ground and excited state combination differences, residuals, and predomi-
nant basis states for the ground and excited state vibrational analyses.
These tables also include the rotational assignments for the two vibronic
bands that were recorded at high resolution. A direct link to this document
may be found in the online article’s HTML reference section. The docu-
ment may also be reached via the EPAPS homepage ͑http://www.aip.org/
pubservs/epaps.html͒ or from ftp.aip.org in the directory /epaps/. See the
EPAPS homepage for more information.
signment of two bands in the spectra of both 11BS2 and 10BS2
2
as
⌸
1/2Ϫ2⌸3/2 (⌬PϭϪ1) transitions, made weakly al-
lowed by the large value of the spin–orbit coupling constant
in one of the states, which must approximate case c coupling.
We have searched out LIF spectra for these transitions but
can find no trace of them, suggesting that the breakdown of
the usual selection rule is due to the influence of the matrix.
21 M. J. Frisch, G. W. Trucks, H. B. Schlegel et al., GAUSSIAN 98, Revision
A.11, Gaussian, Inc., Pittsburgh, PA, 1998.
22 A. D. Becke, J. Chem. Phys. 98, 5648 ͑1993͒.
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This work is dedicated to Dr. William Weltner, Jr. on the
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Renner–Teller effect. This research was supported by the
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