THE JOURNAL OF CHEMICAL PHYSICS 123, 164312 共2005兲
High-resolution spectroscopy of CoS „X 4⌬i…: Examining 3d transition-metal
sulfide bonds
M. A. Flory, S. K. McLamarrah, and L. M. Ziurysa兲
Department of Chemistry, Department of Astronomy, and Steward Observatory, University of Arizona,
Tucson, Arizona 85721
共Received 18 July 2005; accepted 31 August 2005; published online 26 October 2005兲
The pure rotational spectrum of CoS, the cobalt sulfide radical, has been measured using direct
absorption techniques in the frequency range of 180– 540 GHz. This study is the first spectroscopic
investigation of any kind of this molecule. CoS was created by reacting cobalt vapor with H2S. Four
spin components were identified in the spectra of this species, one of which exhibited lambda
doubling, identifying the ground state as 4⌬i. Transitions arising from the lowest spin component of
the less abundant Co 34S isotopomer have also been detected, as well as from v = 1 and v = 2 of the
main species. The spectra were readily identified because each spin component exhibited an octet
pattern arising from the 59Co spin of I = 7 / 2. The data were fit using Hund’s case 共a兲 Hamiltonian,
and rotational, fine-structure, hyperfine, and lambda-doubling constants were determined. The
hyperfine parameters support a ␦3␲2 electron configuration and are consistent with some orbital
overlap between the metal and sulfur atoms. From the rotational constant, the bond length of CoS
was calculated to be r0 = 1.977 985 06共10兲 Å. This bond length is significantly shorter than that of
MnS or FeS, in contrast to the bond distances found in the oxide analogs which are all similar in
value. These results indicate that the 3d metal sulfides differ somewhat from their oxide
counterparts, probably due to the availability of sulfur p orbitals for bonding. © 2005 American
Institute of Physics. 关DOI: 10.1063/1.2083507兴
I. INTRODUCTION
Transition-metal sulfides have a wide array of applications. These compounds, for example, are used as solid lubricants, in particular zinc and molybdenum sulfides.1 They
are also relevant to materials science, as sulfur is known to
migrate to the interior of a metal, altering its structure and
mechanical properties.2 Transition-metal sulfides have been
proposed as catalysts that could have promoted metabolism
in the early development of life on Earth,3 and, in solid-state
form, are thought to compose certain types of interstellar
dust grains.4
Because of their interesting chemical properties, diatomic 3d sulfides provide an arena for theoretical studies.
These compounds often have many unpaired electrons that
are subject to correlation and relativistic effects.5 The presence of d electrons also increases the complexity of orbital
interactions. While theorists have devoted considerable attention to their oxide counterparts,6 the sulfides have not
been as widely studied.2,6,7 It is therefore uncertain whether
they behave similarly to the oxides, which, for example, become more covalent across the periodic table.6
Most 3d transition-metal oxides have been characterized
by high-resolution spectroscopic methods;8 the availability
of experimental data probably explains in part the theoretical
interest. In contrast, the number of extensive spectroscopic
studies on the sulfide analogs has been fairly limited. For
example, the B 2⌺+-X 2⌺+ electronic transition of ScS and
a兲
Electronic mail: [email protected]
0021-9606/2005/123共16兲/164312/9/$22.50
the b 1⌸-X 3⌬, B 3⌸-X 3⌬, and C 3⌬-X 3⌬ transitions of TiS
have been recorded with rotational resolution by Fenot et al.9
and Cheung et al.,10 respectively. In contrast, only the
C 4⌺−-X 4⌺− transition of VS,11 the B 5⌸−1-X 5⌸−1 transition
of CrS,12 and the 关17.4兴 3⌺−0 -X 3⌺−0 transition of NiS 共Ref.
13兲 have been investigated. Submillimeter-wave, pure rotational studies have also been conducted for only MnS, FeS,
and CuS.14–16 Clearly, additional investigations of sulfide
species need to be carried out, in particular those for which
the electronic ground state is uncertain.6,7
In this paper, we present the first laboratory study of CoS
using any spectroscopic method. Twenty-two rotational transitions of this radical in the frequency range of
180– 540 GHz were measured. The electronic ground state
has been identified as 4⌬i due to the presence of four finestructure components of decreasing intensity, the weakest of
which undergoes lambda doubling. In addition, the hyperfine
splittings due to the 59Co spin of I = 7 / 2 were observed. In
this paper, these experimental results and their analysis are
presented. An interpretation of the spectroscopic parameters
and their implications for bonding in CoS are also given.
II. EXPERIMENT
The rotational spectrum of CoS was recorded using the
high-temperature, millimeter/submillimeter direct absorption
system of Ziurys et al. The details of this instrument are
described elsewhere.17 Briefly, millimeter-wave radiation
originating at a Gunn oscillator/Schottky diode multiplier
source is passed through a polarizing grid and a series of
mirrors into a reaction chamber. This chamber is a double-
123, 164312-1
© 2005 American Institute of Physics
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164312-2
Flory, McLamarrah, and Ziurys
pass system with a 45° rooftop reflector at the far end. The
radiation passes back through the cell and optics before being reflected by the polarizing grid into a He-cooled InSb
detector. The frequency source is modulated at a rate of
25 kHz, and signals are recorded at 2f using a lock-in amplifier.
The CoS radical was produced by reacting cobalt vapor
with pure H2S. A metal vapor was obtained by melting chips
of cobalt 共Aldrich 99.5%兲 in a Broida-type oven through
resistive heating. Because of cobalt’s high melting point
共⬃1495 ° C兲, the crucible was wrapped in zirconia insulation. Hydrogen sulfide was added over the top of the crucible; between 15 and 20 mTorr of H2S resulted in the best
signal. As a chemical test, CS2 was also used as a precursor
and the same spectra were obtained. Use of a dc discharge
was not found necessary. Also, no carrier gas was used, as it
did not increase the signal-to-noise ratio. The reaction mixture exhibited no obvious fluorescence, consistent with other
cobalt studies conducted in this laboratory. Both Co 32S and
Co 34S were observed in the natural abundance of sulfur
共 32S : 34S = 22.5: 1兲.
Because no previous spectroscopic studies of this molecule had been conducted, an extensive initial search was
required. A key factor in locating lines was the hyperfine
octet pattern generated by the cobalt nuclear spin of I = 7 / 2.
However, this pattern collapsed at higher frequencies in certain fine-structure components 共⍀ = 3 / 2 and 1 / 2兲, which initially was misleading. Searching at lower frequencies revealed hyperfine octets for all four spin components.
Revisiting the higher-frequency region, transitions were observed at the predicted values based on the low-frequency
data. These octets were either partially or completely collapsed.
Transition frequencies were measured by averaging an
even number of scans, taken in both increasing and decreasing frequencies. These scans were 5 MHz in coverage, and
two to four were necessary to obtain an adequate signal-tonoise ratio. Center frequencies were determined by fitting the
observed lines to Gaussian profiles. The instrumental accuracy is approximately ±50 kHz. Typical linewidths were
0.6– 1.5 MHz over the range of 180– 539 GHz.
III. RESULTS
After scanning ⬃40 GHz in frequency continuously
over the range of 460– 500 GHz, it was possible to establish
harmonic relationships among observed lines; further transitions could then be accurately predicted. An illustration of
the established spectral pattern is given in Fig. 1. Here the
J = 36.5→ 37.5 transition of CoS near 465 GHz is displayed,
showing approximate relative intensities. 共The hyperfine
splitting is too small to be visible on this scale.兲 As the figure
demonstrates, the fine-structure components have a fairly
regular progression, indicative of case 共a兲 coupling, and only
the ⍀ = 1 / 2 component is split by lambda doubling. The J
= 37.5→ 38.5 transition for Co 34S is also visible, as are
some of the transitions arising from the v = 1 and v = 2 excited states. These additional features helped to confirm the
4
⌬i pattern.
J. Chem. Phys. 123, 164312 共2005兲
FIG. 1. A stick diagram illustrating the typical rotational pattern in CoS,
which confirms the ground-state assignment as 4⌬i. Here the J = 37.5
← 36.5 rotational transition of Co 32S, observed in the range of
459– 468 GHz 共black lines兲 is shown, as well as the J = 37.5← 36.5 rotational transition arising within excited vibrational states 共dashed lines兲 and
one line originating from the J = 38.5← 37.5 transition of Co 34S 共gray
scale兲. Each line actually represents a hyperfine octet, but this detail is not
given. A quartet spin-orbit pattern is evident in these data and follows a case
共a兲 coupling scheme. Lambda doubling is observed in the weakest spin
component; in this case ⍀ = 1 / 2.
Sample transition frequencies recorded for CoS in its
ground vibrational state are presented in Table I. The complete list of recorded frequencies is available electronically in
EPAPS.18 A total of 22 rotational transitions were measured,
spanning the frequency range of 180– 540 GHz. For many of
these transitions, all four fine-structure components 共⍀
= 7 / 2 , 5 / 2 , 3 / 2 , 1 / 2兲 were recorded, and ⌳ doubling was observed in the ⍀ = 1 / 2 ladder. Each of the spin components is
further split into an octet by the 59Co nuclear spin, as mentioned, such that a total of 40 hyperfine lines were observed
per rotational transition, as shown in Table I. However, it
was not always possible to observe all hyperfine lines within
a given octet. For example, the octets in the ⍀ = 5 / 2 and ⍀
= 3 / 2 components begin to collapse at J = 38.5→ 39.5
共⬃490.8 GHz兲 and at J = 30.5→ 31.5 共⬃392.2 GHz兲, respectively. The ⍀ = 1 / 2 hyperfine structure starts blending together at J = 20.5→ 21.5 共⬃268 GHz兲, and by J = 35.5
→ 36.5 共⬃455– 456 GHz兲, only a single feature remains. A
secure assignment of the ⍀ = 1 / 2 component therefore required measurements at lower J than did that of the other
components. The frequencies of some hyperfine transitions
could not be recorded because of contamination by interloping features; these lines are included in the data sets but were
not used in the fit and therefore do not have accompanying
residuals. In all, 453 lines were recorded and fitted for the
v = 0 ground state of the main CoS isotopomer.
Table II lists a sample of transition frequencies recorded
for the excited vibrational states of the main isotopomer and
for Co 34S. Again, the complete list of frequencies is available electronically in EPAPS.18 Only the lower spin components were observed for these species, as shown in the table.
A total of five transitions were recorded for the v = 1 state for
the ⍀ = 7 / 2 and 5 / 2 ladders, respectively, while only four
were measured in the v = 2 level 共⍀ = 7 / 2 only兲—a total of
Downloaded 11 Dec 2005 to 150.135.114.19. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
164312-3
J. Chem. Phys. 123, 164312 共2005兲
Spectroscopy of CoS
TABLE I. Selected rotational transition frequencies for Co 32S共X 4⌬i:v = 0兲 共in MHz兲.
J+1
16.5
18.5
30.5
←
←
←
←
J
15.5
17.5
29.5
F+1
13
14
15
16
17
18
19
20
13
14
15
16
17
18
19
20
13
14
15
16
17
18
19
20
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
F
12
13
14
15
16
17
18
19
12
13
14
15
16
17
18
19
12
13
14
15
16
17
18
19
⍀
3.5
15
16
17
18
19
20
21
22
15
16
17
18
19
20
21
22
15
16
17
18
19
20
21
22
27
28
29
30
31
32
33
34
27
28
29
30
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
14
15
16
17
18
19
20
21
14
15
16
17
18
19
20
21
14
15
16
17
18
19
20
21
26
27
28
29
30
31
32
33
26
27
28
29
3.5
1.5
1.5
3.5
1.5
␯obs
204 969.021
204 960.462
204 950.360
204 938.732
204 925.619
204 910.948
204 894.785
204 877.104
205 668.196
205 663.082
205 657.062
205 650.227
205 642.505
205 633.957
205 624.574
205 614.408
␯o−c
0.110
0.071
0.027
−0.010
−0.007
−0.042
−0.056
−0.082
−0.002
−0.022
−0.053
−0.020
−0.017
−0.003
−0.010
−0.011
⍀
2.5
Parity
0.5
e
e
e
e
e
e
e
e
f
f
f
f
f
f
f
f
229 776.741
229 769.529
229 761.248
229 751.903
229 741.483
229 729.969
229 717.400
229 703.742
230 566.702
230 562.486
230 557.626
230 552.174
230 546.121
230 539.448a
230 532.236
230 524.412
0.070
0.029
0.003
−0.005
−0.010
−0.032
−0.035
−0.055
−0.019
−0.017
−0.033
−0.025
−0.012
2.5
0.002
−0.013
378 484.164
378 481.084
378 477.729
378 474.162
378 470.373
378 466.321
378 462.030
378 457.511
379 801.902
379 800.027
379 798.236
379 796.366
−0.035
−0.008
−0.021
−0.010
0.018
0.023
0.030
0.053
0.216
−0.027
−0.054
−0.028
0.5
2.5
e
e
e
e
e
e
e
e
f
f
f
f
f
f
f
f
␯obs
205 416.733
205 409.460
205 400.834
205 390.912
205 379.705
205 367.187
205 353.440
205 338.394
205 878.248
205 876.414
205 874.452
205 872.156
205 869.746
205 867.148
205 864.407
205 861.555
205 996.515
205 994.763
205 992.766
205 990.508
205 988.103
205 985.520
205 982.794
205 979.932
␯o−c
−0.131
−0.094
−0.084
−0.057
−0.012
0.011
0.082
0.116
0.115
0.043
0.091
0.024
0.029
−0.004
−0.067
−0.170
0.103
0.072
0.047
−0.011
−0.016
−0.029
−0.045
−0.091
230 280.719
230 274.594
230 267.572
230 259.629
230 250.773
230 240.985
230 230.298
230 218.704
230 815.658
230 814.231
230 812.631
230 810.965
230 809.172
230 807.244
230 805.203
230 803.053
230 934.006
230 932.571
230 931.077
230 929.398
230 927.530
230 925.542
230 923.524
230 921.459
379 318.447
379 315.950
379 313.232
379 310.293
379 307.189
379 303.858
379 300.325
379 296.592
−0.068
−0.080
−0.056
−0.027
0.009
0.027
0.054
0.075
0.091
0.038
−0.024
−0.005
0.015
0.006
−0.030
−0.114
0.112
0.015
0.029
0.013
−0.053
−0.116
−0.103
−0.049
−0.033
−0.002
0.008
−0.001
0.027
0.033
0.042
0.058
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164312-4
J. Chem. Phys. 123, 164312 共2005兲
Flory, McLamarrah, and Ziurys
TABLE I. 共Continued.兲
J+1
←
J
F+1
31
32
33
34
←
←
←
←
←
F
30
31
32
33
⍀
␯obs
379 794.321
379 792.209
379 789.932
379 787.497
␯o−c
−0.044
0.005
0.023
0.018
⍀
␯obs
␯o−c
36.5
←
35.5
33
34
35
36
37
38
39
40
←
←
←
←
←
←
←
←
32
33
34
35
36
37
38
39
3.5
452 698.225
452 695.953
452 693.626
452 691.105
452 688.470
452 685.659
452 682.769
452 679.720
−0.072
−0.090
−0.027
−0.021
0.009
0.004
0.061
0.103
2.5
453 694.903
453 693.015
453 691.198
453 689.072
453 686.940
453 684.714
453 682.360
453 679.924
0.087
−0.024
0.052
−0.065
−0.070
−0.049
−0.036
0.017
39.5
←
38.5
36
37
38
39
40
41
42
43
36
37
38
39
40
41
42
43
36
37
38
39
40
41
42
43
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
←
35
36
37
38
39
40
41
42
35
36
37
38
39
40
41
42
35
36
37
38
39
40
41
42
3.5
489 760.063
489 757.963
489 755.918
489 753.910a
489 751.690a
489 749.224a
489 746.748
489 744.173
0.050
−0.096
−0.081
2.5
490 837.304
490 836.190a
490 833.865
490 832.122
490 830.341
490 828.464
490 826.497
490 824.375
492 088.154
492 088.154
492 088.154
492 088.154
492 088.154
492 088.154
492 088.154
492 088.154
492 207.399
492 207.399
492 207.399
492 207.399
492 207.399
492 207.399
492 207.399
492 207.399
0.299
Parity
0.081
0.119
0.5
e
e
e
e
e
e
e
e
f
f
f
f
f
f
f
f
−0.024
−0.072
−0.066
−0.061
−0.051
−0.099
−0.189
−0.157
−0.114
−0.063
⬍0.001
0.073
0.157
0.254
−0.153
−0.131
−0.097
−0.050
0.011
0.087
0.178
0.287
a
Unresolved lines, not included in least-squares fit.
96 lines. Four transitions of Co 34S 共v = 0兲 were also studied
in the ⍀ = 7 / 2 ladder. No excited vibrational data were recorded for this isotopomer.
Representative spectra of CoS are presented in Figs. 2
and 3. Figure 2 is a composite of the first three fine-structure
components 共⍀ = 7 / 2, 5 / 2, and 3 / 2兲 of the J = 18.5→ 19.5
rotational transition. All three spin components are shown on
the same intensity scale, and their intensity steadily decreases from ⍀ = 7 / 2 to 5 / 2 to 3 / 2. The octet pattern arising
from the cobalt nuclear spin is also clearly visible. It can be
seen that the hyperfine splitting is largest in the ⍀ = 7 / 2 ladder and becomes progressively smaller as ⍀ decreases in
value. Figure 3 shows the ⍀ = 1 / 2 component of the J
= 18.5→ 19.5 transition. This figure is a composite of two
scans, and the ⌳ doublets are indicated by e and f. The two
sets of hyperfine octets for this spin component, marked by
lines underneath the spectra, have less overall splitting than
do the other ⍀ components. The relative intensity ratio of all
four spin components is 10:4:1.7:0.7, considering the com-
bined intensity of the ⍀ = 1 / 2 lambda doublets. These data
suggest a rotational temperature of Trot ⬇ 520 K based on an
overall spin-orbit splitting of 兩6A兩 ⬃ 1380 K.
IV. ANALYSIS
The data for Co 32S were analyzed using an effective
case 共a␤兲 Hamiltonian of the form
Heff = Hrot + Hss + HSO + Hmhf + HeqQ + Hld ,
共1兲
where the terms account for molecular frame rotation 共Hrot兲,
electron spin-electron spin interaction 共Hss兲, spin-orbit coupling 共HSO兲, magnetic hyperfine interactions 共Hmhf兲, electric
quadrupole effects 共HeqQ兲, and ⌳ doubling 共Hld兲. Initially, it
was necessary to constrain the spin-orbit parameter A, the
spin-spin parameter ␭, and the higher-order spin-spin parameter ␩ to establish a preliminary fit. They were temporarily
fixed to the values derived for CoO 共Ref. 19兲 until other
constants could be established. They were all allowed to vary
in the final fit. Because of the wide range of J values re-
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164312-5
J. Chem. Phys. 123, 164312 共2005兲
Spectroscopy of CoS
TABLE II. Selected rotational transition frequencies for Co 32S 共X 4⌬i , v = 1 , 2兲 and Co 34S 共v = 0兲 共in MHz兲.
J+1
←
J
F+1
←
F
v
⍀
␯obs
␯o−c
⍀
␯obs
␯o−c
␯
⍀
␯obs
␯o−c
36.5
34
35
36
37
38
39
40
41
←
←
←
←
←
←
←
←
33
34
35
36
37
38
39
40
1
3.5
462 653.078
462 650.911
462 648.574
462 646.157
462 643.627
462 641.154
462 638.450
462 635.465
0.058
0.006
−0.086
−0.129
−0.155
0.004
0.060
−0.038
2.5
463 667.620
463 665.686
463 663.896
463 661.938
463 659.955
463 657.936
463 655.535
463 653.457
0.160
−0.068
−0.048
−0.094
−0.063
0.033
−0.153
0.083
2
3.5
460 243.719a
460 241.545
460 239.280
460 236.911
460 234.527
460 231.840
460 229.151
460 226.168
0.040
0.002
−0.012
0.088
0.012
0.061
−0.058
35
36
37
38
39
40
41
42
←
←
←
←
←
←
←
←
34
35
36
37
38
39
40
41
1
474 942.808
474 940.686
474 938.540
474 936.299
474 933.925
474 931.450
474 928.865
474 926.197
0.073
−0.033
−0.043
−0.029
−0.028
−0.009
0.018
0.080
2.5
475 983.910
475 982.074
475 980.360
475 978.582
475 976.679
475 974.713
475 972.590
475 970.412
0.153
−0.057
−0.049
−0.010
−0.003
0.035
0.008
0.018
2
472 467.943a
472 466.864
472 464.738
472 462.517
472 460.153
472 457.648
472 455.058
472 452.381
−0.017
−0.025
−0.008
−0.016
−0.047
−0.046
−0.015
32
Co S
37.5
←
38.5
←
37.5
3.5
Co 34S
37.5
←
36.5
34
35
36
37
38
39
40
41
←
←
←
←
←
←
←
←
33
34
35
36
37
38
39
40
0
3.5
447 449.585
447 447.358
447 445.228
447 442.808
447 440.300
447 437.575
447 434.830
447 432.039
0.008
−0.090
0.039
0.008
0.019
−0.058
−0.026
0.088
←
37.5
35
36
37
38
39
40
41
42
←
←
←
←
←
←
←
←
34
35
36
37
38
39
40
41
0
3.5
459 337.494
459 335.332
459 333.268
459 330.961
459 328.684
459 326.100
459 323.545
459 320.944
−0.003
−0.136
−0.051
−0.088
0.025
−0.050
0.022
0.168
38.5
3.5
a
Unresolved lines not included in least-squares fit.
corded 共13.5–42.5兲, it was necessary to include several centrifugal distortion terms. The parameters D, AD, ␭D, ␭H, and
␩D were needed to accurately fit the data.
To fit the ⌳ doublets in the ⍀ = 1 / 2 component, the
terms ñ⌬, õ⌬, and p̃⌬ were used, as described by Brown et
al.20 The ñ⌬ parameter appears as a diagonal term for ⍀
= 1 / 2 in the ⌳-doubling matrix. The two other terms are
off-diagonal for ⍀ = 1 / 2. Although well defined as fitting parameters, õ⌬ and p̃⌬ therefore may not represent true orbital
angular momentum effects and may not be reliable. An observation of ⌳ doubling in the other spin components would
be needed to establish them as such. The parity assignment
of the ⌳ doublets was arbitrary.
The hyperfine structure was analyzed using the parameters a, b, 共b + c兲 and eqQ. A centrifugal distortion term 共b
+ c兲D was also needed. According to Cheung and Merer,21
any molecule with a spin multiplicity of quarter or higher
requires an additional hyperfine term, bs. The use of this
constant, however, did not improve the fit, and the term itself
in this case was not statistically determined. A similar situa-
FIG. 2. Representative spectrum of the J = 19.5← 18.5 rotational transition
of Co 32S 共X 4⌬i兲, showing the first three spin-orbit components of this molecule 共⍀ = 7 / 2 , 5 / 2 , 3 / 2兲. This spectrum is a composite of data obtained at
three separate frequencies plotted on the same intensity scale 共see Fig. 1兲.
There are therefore two discontinuities in the x axis. The octet hyperfine
pattern arising from the cobalt nuclear spin of I = 7 / 2 is clearly resolved in
each sublevel, which show regularly decreasing intensities characteristic of
a degenerate state. These three data sets are 90 MHz wide each and were
acquired in a single 60 s scan.
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164312-6
J. Chem. Phys. 123, 164312 共2005兲
Flory, McLamarrah, and Ziurys
h = a⌳ + 共b + c兲⌺.
共2兲
The constants and overall errors for these fits can also be
found in Table III.
V. DISCUSSION
A. The ground state of CoS
FIG. 3. Spectrum of the ⍀ = 1 / 2 spin component of the rotational transition
also shown in Fig. 2 共J = 19.5← 18.5兲 showing the ⌳ doublets that comprise
this sublevel, labeled by e and f. This figure is a composite of two separate
data sets separated by a break in the frequency scale. 共The actual ⌳-doublet
separation is 120 MHz兲. Here, the Co hyperfine components are indicated
by lines underneath each octet. Each spectrum is an average of two 50 MHz
scans, each a minute in duration.
tion was found for d⌬, a term used to account for differences
in hyperfine splittings within a lambda doublet. The quadrupole coupling constant eqQ was found to improve the fit, but
in the end also had an uncertainty larger than its value. As a
consequence, in the final fit its value was fixed to −30 MHz.
Resulting spectroscopic constants for CoS can be found in
Table III. The overall rms for the final global fit was 81 kHz.
Constants from fits of the individual ⍀ ladders can be found
in EPAPS.18
For the data sets of the Co 34S isotopomer and the excited vibrational states of Co 32S, the individual ⍀ ladders
were fit separately because not all four spin components
were measured in both cases. Each ⍀ component was fit to a
rotational B, D, and hyperfine h, defined by the Frosch and
Foley parameters by the expression22
The observation of four spin components of uniformly
varying intensity, with ⌳ doubling in the weakest component, establishes the ground state of CoS as X 4⌬i. This term
is the same as that found in CoO. The presence of ⌳ doubling and the obviously nonuniform intensities of the spin
components rule out a 4⌺− ground state, which had been
proposed by Anderson et al.7 The likely electron configuration for CoS in its ground state is 关core兴4␲411␴21␦35␲2.
B. Lambda-doubling interactions
The ⌳ doubling observed in CoS is present only in the
⍀ = 1 / 2 spin component, in contrast to CoO, where it was
present in both the ⍀ = 1 / 2 and 3 / 2 ladders. The magnitude
of the splitting in the sulfide is approximately one-third
that observed for the oxide. For example, ñ⌬
= −19.676共11兲 MHz for CoS, while this parameter is
−51.103共16兲 MHz for CoO.19 Because CoS is a heavier molecule, the excited electronic states lie closer to the ground
state than CoO. As a consequence, the perturbing ⌸ and ⌺
states should have a greater effect on the ⌳-doubling splitting in CoS. However, the ñ⌬ parameter of the oxide and of
the sulfide scale roughly as the relative rotational constants,
suggesting that the ⌸ and ⌺ terms lie at similar energies in
both molecules.
An estimate of the energies of the perturbing ⌺ and ⌸
states can be made from the lambda-doubling parameters by
applying perturbation theory.20 As noted previously, how-
TABLE III. Fitted spectroscopic constants for CoS 共X 4⌬i兲 in MHz.a
B0
D
A
AD
␭
␭D
␭H
␩
␩D
ñ⌬
õ⌬
p̃⌬
a
b
b+c
共b + c兲D
eqQ
h
rms
r0
v=0
v = 1, ⍀ = 7 / 2
v = 1, ⍀ = 5 / 2
v = 2, ⍀ = 7 / 2
Co 34S, v = 0, ⍀ = 7 / 2
6 228.463 46共60兲
0.004 051 65共26兲
−4 807 000共32 000兲
−0.795共29兲
668 000共28 000兲
1.065共65兲
−0.000 001 26共18兲
−89 000共19 000兲
−0.378共73兲
−19.676共11兲
−0.055 7共39兲
−0.000 120共18兲
691.5共1.9兲
−357共13兲
−238.3共3.1兲
0.182 4共79兲
−30b
6179.878 6共39兲
0.004 014 9共13兲
6193.574 0共92兲
0.004 066 8共32兲
6147.800 0共83兲
0.004 031 2共28兲
5976.291 8共24兲
0.003 704 30共81兲
1016.2共4.8兲
0.054
1152共13兲
0.084
1008.1共6.1兲
0.043
1023.0共4.8兲
0.069
0.081
1.977 985 06共10兲 Å
共Values in parentheses are 3␴ errors to the place reported.兲
Held fixed.
a
b
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164312-7
J. Chem. Phys. 123, 164312 共2005兲
Spectroscopy of CoS
ever, õ⌬ and p̃⌬ appear only as off-diagonal terms for the
⍀ = 1 / 2 component. Hence, their values are a measure of the
deviation of the lambda-doubling splitting from being linear
in 共J + 1 / 2兲; they are also likely to be highly correlated. The
ñ⌬ constant, on the other hand, is in the diagonal matrix
element for ⍀ = 1 / 2 and therefore arises from true angular
momentum effects. Assuming that unique ⌸ and ⌺ excited
electronic states are the cause of ⌳ doubling in CoS, ñ⌬ can
be defined as20
ñ⌬ ⬵
− 24冑5a3B
,
共E⌬ − E⌸兲2共E⌬ − E⌺兲
共3兲
where B is the rotational constant and a is the spin-orbit
parameter associated with the one-electron operator 兺iail̂iŝi.
The molecular spin-orbit constant A for 4⌬ states is related to
a via the relationship a = a␦ = 3A.23 Assuming E⌸ ⬇ E⌺, the
value of ñ⌬ implies that E⌸ ⬃ E⌺ ⬃ 12 400 cm−1. Hence, the
ñ⌬ parameter suggests that there are excited 4⌸ and 4⌺ states
lying about 12 400 cm−1 above the ground 4⌬ state. Calculations and measurements for CoO indicate that there are
only 4⌺± or 4⌸ states substantially higher or lower in energy
than ⬃12 000 cm−1.24 Consequently, the decrease in ⌳ doubling in CoS relative to CoO may simply arise from a multitude of low-lying excited states that cancel each other.
Assuming a␦ is approximately equal to ␨, the atomic
spin-orbit parameter, it is possible to estimate the value of A.
If ␨共Co+兲 is used, then A = 1 / 3共−536 cm−1兲 = −179 cm−1.23 A
virtually identical value is obtained if the atomic parameter
of the neutral cobalt is ultimately used. The observed A in
CoS is −160.3共1.1兲 cm−1, in reasonable agreement with these
estimates.
C. Hyperfine structure and bonding
The proposed electron configuration for CoS for its
X 4⌬i state is 关core兴11␴21␦35␲2. Consequently, only the
single ␦ electron can contribute to the nuclear spin-orbital
parameter a. 共The contribution of the two unpaired ␲ electrons cancels.兲 The hyperfine a parameter in CoS has been
established to be 691.5 MHz, quite similar to the value for
01
= 617.9 MHz.25 This result imthe atomic cobalt of a3d共Co兲
plies that the unpaired ␦ electron is in a predominantly cobaltlike orbital, as can be expected from simple molecularorbital theory. The a parameter also gives an average
electron density about the cobalt nucleus of 具1 / r3典av = 3.70
⫻ 1031 m−3. This value is approximately the same as in CoO,
where 具1 / r3典av = 3.644⫻ 1031 m−3, but is slightly higher than
CoCl 关具1 / r3典av = 2.7⫻ 1031 m−3 共Ref. 26兲兴. This trend can be
explained in terms of a balance between the ionic character
and the atomic size. The mostly ionic compound CoCl has
the large, highly electronegative chlorine atom, which draws
electron density towards it, lowering the density around cobalt. While oxygen is more electronegative than chlorine is,
the smaller atomic size, and hence shorter bond length, enables the electron density around the cobalt atom to remain
relatively high. The sulfur atom has a low electronegativity
but is larger in size, and hence a similar electron density at
the Co atom is seen in CoO.
The Fermi contact term bF is −318 MHz in CoS. This
term arises principally from unpaired electrons in ␴ orbitals
that are formed by atomic s orbitals. However, there are no
such electrons in CoS, but the negative sign of bF is indicative that this constant results from spin polarization. Fermi
contact parameters usually are small in value when s electrons are absent, but similarly large values have been observed in CoO 共Ref. 19兲 and CrH 共Refs. 27 and 28兲. The
larger than expected magnitude perhaps can be explained by
the high spin multiplicity of these molecules; there are more
unpaired electrons to polarize and contribute to bF. Also, the
nuclear magnetic moment of the cobalt nucleus is one of the
largest among the elements, enhancing this effect.
The value of the dipolar term c is 119 MHz. Both ␲ and
␦ electrons contribute to c, which has an angular dependence
of 具3 cos2 ␪i − 1 / r3i 典. If the three unpaired electrons are in
primarily nonbonding orbitals centered on cobalt, then the
atomic angular factors should provide some measure of c.
The values for the atomic wave functions are d␦ = −4 / 7 and
d␲ = 2 / 7.29 The angular dependence of the three electrons in
these orbitals should then sum to nearly zero, depending only
on differences in 具1 / r3i 典, which should be small. The fact that
c has a relatively large value indicates that the orbitals on
cobalt are not strictly atomic. The 5␲ orbital must take on
some degree of sulfur character. This result agrees with the
trend in bonding for oxides described by Bridgeman and
Rothery, who assign 60% metal character to the 4␲ orbital in
NiO and 40% metal in CuO.6
D. Trends in 3D transition-metal sulfides
Because all four spin components were observed solely
in the ground vibrational state, it is only possible to accurately calculate a r0 bond length for CoS. This value is calculated to be r0 = 1.977 985 06共10兲 Å. 共For the ⍀ = 7 / 2 ladder, re is 1.978 276共16兲 Å based on Be = 6227.909共99兲 MHz
and ␣e = 32.038共70兲 MHz for this spin component only.兲 The
r0 bond distance is noticeably shorter 共by 0.04 to 0.09 Å兲
than the r0 bond length for the three other transition-metal
sulfides that have been studied using millimeter/
submillimeter spectroscopy. In these experiments it was
found that r0 = 2.0170 共17兲 Å for FeS,15 r0 = 2.055 Å for
CuS,16 and r0 = 2.068 24共37兲 for MnS.14 This decrease is consistent with the theoretical predictions of Bridgeman and
Rothery,6 which show that the re bond distance in CoS is the
shortest of the four, at 1.96 Å.
The experimental bond lengths 共r0兲 for transition-metal
monosulfides and oxides8 are displayed in Fig. 4. Only one
spin component has been observed for CrS and NiS, so the
bond lengths calculated for these molecules are estimates
only. However, the graph does demonstrate that the oxides
and sulfides follow similar patterns, with the exception of the
cobalt and nickel species. The bond length in the cobalt sulfide is significantly shorter relative to that of FeS, while the
bond distances of CoO and FeO are similar. This property
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164312-8
J. Chem. Phys. 123, 164312 共2005兲
Flory, McLamarrah, and Ziurys
for the molecule. This species was found to follow a fairly
regular case 共a兲 coupling scheme. The effect of lambda doubling is found to be smaller in the cobalt sulfide relative to
the oxide, suggesting that in CoS, lower-lying excited states
are canceling this effect. On the other hand, the hyperfine
interactions in CoS are similar to CoO and are consistent
with a ␦3␲2 electron configuration. An interesting deviation
is found in the bond length of CoS, which is shorter than
expected by comparison with the metal oxides. This effect is
attributed to the orbital overlap between the cobalt 4p and
the sulfur 3p orbitals, which cannot occur with the oxygen
2p orbitals.
FIG. 4. A graph showing the trends in experimental bond lengths 共r0兲 for the
transition-metal oxides and sulfides. 共The bond distances of CrS and NiS
were estimated from one spin component and therefore are only approximations.兲 The trends for the two sets of molecules appear similar, but with the
notable exception of cobalt; for the oxide, the bond length hardly changes
relative to iron, while that of CoS decreases by 0.04 Å relative to FeS. There
is also a discrepancy between NiS and NiO; here the NiS bond length
increases substantially relative to the oxide.
cannot be explained solely by core contraction from an increased nuclear charge because the bonding in both CoO and
CoS involves adding an electron to the nonbonding 3d␴ orbital. 共The bond length in NiS is estimated from the ⍀ = 0
component only, so it is premature to draw too many conclusions.兲
The shortened Co–S bond may be rationalized by comparing transition-metal diatomics composed of second- versus third-row main-group elements. When comparing the
metal oxides/sulfides relative to the fluorides/chlorides,26
similar trends are apparent in the bond lengths, except for
cobalt. There is a significant decrease in the bond distances
of CoS and CoCl relative to those of FeS and FeCl 共⬃0.04
and 0.11 Å兲, respectively. However, there is only a small
decrease in bond length from FeF to CoF 共⬃0.046 Å兲
and a small increase in bond length from FeO to CoO
共⬃0.012 Å兲.
It is possible that the 4p orbitals of cobalt and later metals are sufficiently low in energy to participate in bonding
with third-row elements, as suggested by Anderson et al.7 In
cobalt atom, the 4p orbital lies at −3.8 eV, while the corresponding energy of the sulfur 3p orbital is −11.7 eV.30 Although this separation of 7.9 eV is large, it may be small
enough to allow some degree of interaction. In contrast, the
oxygen 2p orbital lies at −15.9 eV,30 which implies an energy difference with respect to the cobalt 4p level of
12.2 eV; this increase in the energy difference is unfavorable
to bonding between cobalt and oxygen. A mixing of the
metal 4p and 3d orbitals in CoS would lead to the stabilization of the 4␲ bonding and 11␴ nonbonding orbitals and
produce a significant decrease in the bond length. Clearly
there are subtle differences between 3d metal bonds to sulfur
relative to oxygen.
VI. CONCLUSIONS
This study identifies the ground state of the CoS radical
as X 4⌬i and provides the first set of spectroscopic constants
ACKNOWLEDGMENTS
The authors would like to thank Professor J. M. Brown
for the use of his fitting code and Professor A. J. Merer for a
useful insight into lambda doubling in ⌬ states. This work is
supported by NSF Grant No. CHE-0411551.
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Spectroscopy of CoS
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