JOURNAL OF CHEMICAL PHYSICS
VOLUME 116, NUMBER 23
15 JUNE 2002
Molecules in high spin states: The millimeter and submillimeter spectrum
of the MnS radical „ X 6 ⌺ ¿ …
J. M. Thompsen, M. A. Brewster, and L. M. Ziurys
Department of Chemistry, Department of Astronomy, and Steward Observatory, University of Arizona,
Tucson, Arizona 85721
共Received 25 June 2001; accepted 19 March 2002兲
The pure rotational spectrum of MnS ( v ⫽0) in its X 6 ⌺ ⫹ ground state has been recorded using
millimeter and submillimeter direct absorption techniques in the range 160–502 GHz. MnS was
synthesized in the gas phase by the reaction of manganese vapor and CS2 in a high-temperature
Broida-type oven. Fourteen rotational transitions for this radical were measured, each consisting of
six fine-structure components. In the lower rotational lines, hyperfine structure, arising from the
55
Mn nuclear spin of 5/2, was also resolved in each spin component. These data were analyzed using
a case 共b兲 Hamiltonian, and rotational, fine structure, and hyperfine parameters determined for MnS.
In the analysis, the third-order correction to the spin-rotation interaction, ␥ S , and the fourth-order
spin–spin coupling term, ␪, were found necessary for an acceptable fit. The hyperfine constants
determined suggest that MnS is more covalent than MnO, but more ionic than MnH. There
additionally appears to be considerable sd ␴ hybridization in molecular orbital formation for this
molecule. Bond lengths of the 3d transition-metal sulfides were compared as well, and those of
MnS, CuS, and TiS do not follow the trend of their oxide analogs. This result indicates that there are
significant bonding differences between transition-metal sulfides and transition-metal oxides.
© 2002 American Institute of Physics. 关DOI: 10.1063/1.1476931兴
I. INTRODUCTION
Of all the 3d transition-metal elements, manganese is
one of the most interesting from various chemical aspects.
First of all, its valence electron configuration is 4s 2 3d 5 ;
hence, it has five unpaired d-electrons that can participate in
bonding. Consequently, manganese forms compounds with a
variety of geometries and coordination numbers, including
pentagonal bipyramidal and dodecahedral structures.1,2 There
is also an extensive chemistry concerning Mn–C bonds, often with alkyl groups or cyclopentadienyl complexes.3,4
Some of the interesting properties of this element arise from
the fact that it has virtually no electron affinity, unlike the
other first-row transition metals.
Obtaining a better understanding of the bonding in manganese compounds is therefore of general practical use. One
avenue by which such information can be readily obtained,
especially at a fundamental level, is by recording highresolution gas-phase spectra of manganese-containing molecules. Such data can not only yield bond lengths and structures, but also electron configurations, electron distributions,
and orbital types for a given species. Such information is
particularly valuable in evaluating the high spin states exhibited by manganese compounds. Surprisingly, only a few
manganese-containing species have been studied via highresolution spectroscopy. Electronic transitions have been recorded and analyzed only for MnF,5,6 MnCl,7 MnH,8
MnO,9,10 and MnS,11,12 for example. These studies have
shown that the electronic spectra of manganese compounds
are very complicated with many low-lying excited states and
hence numerous perturbations.10,12 These works also identified the electronic ground states of these molecules. The
0021-9606/2002/116(23)/10212/9/$19.00
manganese halides and MnH have 7 ⌺ ⫹ ground states originating from 9 ␴ 1 1 ␦ 2 4 ␲ 2 10␴ 1 or 11␴ 1 1 ␦ 2 5 ␲ 2 12␴ 1 electron
configurations.5,6 The manganese oxide and sulfide species
have one less electron, and consequently 6 ⌺ ⫹ ground
states.10,12 These high spin-states are interesting quantum
mechanical systems.
Up to the present, only one manganese-bearing molecule
has been examined via its pure-rotational spectrum: MnO.13
This study was quite fruitful in that the hyperfine structure of
the 55Mn nucleus (I⫽5/2) was resolved, resulting in the determination of the manganese hf constants. Measurement of
these parameters enabled the character of the valence molecular orbitals to be evaluated, which could directly be compared with theoretical predictions.14,15 For example, the 9␴
nonbonding orbital of MnO was found to have approximately an equal contribution of the 4s and 3d ␴ atomic orbitals of the manganese atom.13
In an effort to further the understanding of bonding in
manganese-bearing molecules, and the nature of transition
metal compounds in general, we have recorded the purerotational spectrum of MnS in its X 6 ⌺ ⫹ ground electronic
state. This study greatly improves upon the previous optical
investigations by Douay et al., who recorded the A 6 ⌺ ⫹
→X 6 ⌺ ⫹ electronic transition.11,12 On the order of 400 separate spectral features were measured for MnS in the frequency range of 163–502 GHz, including lines from each
fine-structure level and their individual hyperfine components. These data have been analyzed and fine-structure and
hyperfine parameters established for the first time. This work
on MnS, to our knowledge, is the fourth study of a 6 ⌺
ground electronic state with high rotational resolution, and
10212
© 2002 American Institute of Physics
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J. Chem. Phys., Vol. 116, No. 23, 15 June 2002
hence additionally provides a good test of spectroscopic
theory for high spin states. In this paper we present our results and interpret them in the context of bonding in
transition-metal sulfides and oxides, and predict additional
properties of manganese sulfide.
II. EXPERIMENT
The spectra of MnS were recorded via direct absorption
techniques utilizing one of the spectrometers in the Ziurys
group. Details of the specific spectrometer arrangement can
be found elsewhere.16 Briefly, the apparatus consists of a
tunable millimeter/submillimeter wave radiation source, a reaction cell, a metal vapor source, and an InSb hot bolometer
detector cooled to 4 K. The radiation source consists of a
Gunn oscillator coupled to a Schottky diode multiplier. The
operational range of this source spans 65–540 GHz, depending on the specific Gunn/multiplier combination. The reaction cell is a free-space chamber 共0.7 m in length兲 employing
a double-wall design such that the chamber walls are cooled.
A Broida-type oven is incorporated into the chamber for
metal vapor production. The reaction chamber uses a quasioptical, double-pass focusing scheme with a foam-backed
Mylar window at one end of the cell, and a rooftop reflector
at the other. Radiation is propagated to the cell by two offset,
ellipsoidal mirrors. It is then focused to a waist at the rooftop
reflector, which subsequently rotates the radiation by 90° and
reflects the beam back through the cell. After the second pass
through the mirrors, the beam is then reflected by a wire grid
through a final lens, and into the detector. FM modulation of
the radiation source at 25 kHz is employed to achieve phasesensitive detection.
MnS was synthesized by reacting manganese vapor with
carbon disulfide in the presence of a dc discharge. As quite
elevated temperatures were necessary to vaporize manganese
共⬃1300 °C兲, the Broida oven was heavily lined with zirconia
insulation. Manganese chips 共Aldrich 99%兲 were used as the
metal vapor source. As the chips were rather large in size,
they were first crushed and then packed into an alumina crucible. The crucible was then resistively heated. Approximately 15–20 mTorr of argon was flowed into the chamber
underneath the crucible to entrain the metal vapor. The carbon disulfide 共⬃10 mTorr兲 was then added over the top of
the alumina crucible. A dc discharge was applied to the reactants to form the sulfide. Discharge conditions were typically a current of 600 mA at 40–50 V. A pale green color was
noticed upon discharge of the reactants.
Initial measurements were carried out by scanning regions of frequency space based on the rotational constants
provided by the optical studies.11,12 Once spectral features of
the molecule were identified, transition frequencies were
measured by averaging an even number of scans in increasing and decreasing frequency. Typically, scans 5 MHz in
frequency width were used, averaging four such scans. To
determine center frequencies, the lines were fit with Gaussian profiles. Individually resolved hyperfine lines had linewidths ranging from 500 to 900 kHz. The experimental accuracy is estimated to be ⫾100 kHz.
The spectrum of the MnS radical
10213
III. RESULTS
Transition frequencies recorded for MnS are presented in
Table I. As is apparent in the table, 14 rotational transitions
of this radical were measured, indicated by quantum number
N. However, because the electronic ground state of MnS is
6 ⫹
⌺ , each rotational transition is split into six spin components (S⫽5/2), corresponding to ⌺⫽5/2, 3/2, 1/2, ⫺1/2,
⫺3/2, and ⫺5/2. This splitting is primarily due to spin–spin
(Ŝ•Ŝ) and spin–rotation (N̂•Ŝ) interactions, and the spin
components are labeled by quantum number J, as indicated
in Table I. 共Quantum number J signifies the total angular
momentum of the system, neglecting nuclear spin.兲 In addition, 55Mn has a nuclear spin of I⫽5/2. This spin couples
with the total angular momentum, J, to produce hyperfine
splittings, labeled by the quantum number F, where F̂⫽Î
⫹Ĵ. The hf quantum number of the lower level, F ⬙ , is
shown across the top header in Table I as a function of J ⬙ . In
principle, there are six individual hyperfine components per
spin level, or 36 total hf lines per rotational transition. As
Table I illustrates, the majority of the individual hf components were measured for each rotational transition. However,
as N increases in value, the hyperfine splitting begins to collapse in the large 兩⌺兩 spin states such that by the N⫽42
→43 transition, only the ⌺⫽⫾1/2 spin levels have resolvable hf components. These hf lines, in fact, are also partially
collapsed such that only two to three features are observed as
opposed to the expected six. 共The collapsed hf lines were not
included in the final data fit, as indicated by the absence of
residuals in Table I.兲
The evolution of the hyperfine interaction is shown in
Figs. 1, 2, and 3. Figure 1 presents the N⫽14→15 transition
near 175 GHz. The six individual spin components are
clearly present in this spectrum, and are labeled by the ⌺
quantum number. Each spin state is subsequently split into
six hyperfine components, which are all resolved for the ⌺
⫽1/2, ⫺1/2, ⫺3/2, and ⫺5/2 levels and are visible in the
data. For the other spin states, the hyperfine splitting is still
partially collapsed.
Figure 2 shows an expanded version of the hyperfine
splittings of the ⌺⫽⫺1/2 (J⫽13.5→14.5) spin level. Here
the six hyperfine lines, indicated by quantum number F, are
clearly resolved.
Figure 3 displays the behavior of the angular momentum
coupling at high N-values. In this figure, a spectrum of the
N⫽42→43 transition near 501 GHz is displayed. Here the
hf components of the ⌺⫽⫾3/2 and ⫾5/2 levels are totally
collapsed into single lines, making the sextet spin pattern
highly obvious. In the ⌺⫽⫾1/2 ladders, the hyperfine splitting is still visible, but is only partially resolved. The majority of transitions at these higher frequencies show a similar
pattern, although they are not included in the data set of
Table I.
IV. ANALYSIS
The data were analyzed using an effective 6 ⌺ Hamiltonian of the following form:
Heff⫽Hrot⫹Hsr ⫹Hss ⫹Hhf .
共1兲
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F ⬙ ⫽J ⬙ ⫹5/2b
F ⬙ ⫽J ⬙ ⫹3/2b
F ⬙ ⫽J ⬙ ⫹1/2b
F ⬙ ⫽J ⬙ ⫺1/2b
F ⬙ ⫽J ⬙ ⫺3/2b
10214
TABLE I. Observed rotational transition frequencies of MnS (X 6 ⌺ ⫹ ). a
F ⬙ ⫽J ⬙ ⫺5/2b
J ⬙ →J ⬘
␯ obs
␯ o-c
␯ obs
␯ o-c
␯ obs
␯ o-c
␯ obs
␯ o-c
␯ obs
␯ o-c
␯ obs
␯ o-c
13→14
10.5→11.5
11.5→12.5
12.5→13.5
13.5→14.5
14.5→15.5
15.5→16.5
163 864.709
163 803.479
163 624.389
163 566.692
163 489.583
163 447.329
⫺0.074
⫺0.026
⫺0.270
⫺0.257
0.180
0.099
163 860.282
163 806.076
163 638.445
163 626.717
163 494.758
163 452.049
⫺0.017
⫺0.011
0.293
0.270
0.197
0.067
163 859.238
163 809.950
163 650.496
163 622.354
163 498.301c
163 454.739c
⫺0.094
0.001
⫺0.398
⫺0.097
163 861.925
163 815.315
163 663.790
163 618.004
163 499.930c
163 455.160c
0.040
0.077
⫺0.153
⫺0.134
163 868.269
163 822.090
163 678.530
163 612.328
163 499.930c
163 453.701
⫺0.153
0.076
0.059
⫺0.207
163 878.435
163 830.498
163 703.400
163 603.821
163 498.301c
163 450.263
⫺0.044
0.129
0.068
⫺0.026
14→15
11.5→12.5
12.5→13.5
13.5→14.5
14.5→15.5
15.5→16.5
16.5→17.5
175 540.008
175 477.490
175 312.228
175 253.534
175 176.611
175 131.418
0.006
0.002
⫺0.079
⫺0.198
0.143
0.057
175 536.070
175 479.481
175 324.160
175 306.998
175 181.218
175 135.653
0.025
0.010
0.131
⫺0.041
0.167
0.056
175 535.003
175 482.649
175 336.016
175 303.238
175 184.329c
175 138.280c
⫺0.100
0.036
0.674
⫺0.111
175 537.230
175 487.048
175 347.049
175 299.247
175 185.865c
175 138.280c
0.046
0.010
⫺0.127
⫺0.089
175 542.515
175 492.841
175 360.552
175 293.995
175 185.890c
175 137.136
⫺0.140
0.038
0.060
⫺0.017
175 551.151
175 500.064
175 382.064
175 285.827
175 184.724c
175 134.114
⫺0.181
0.075
0.110
⫺0.059
15→16
12.5→13.5
13.5→14.5
14.5→15.5
15.5→16.5
16.5→17.5
17.5→18.5
187 215.501
187 151.788
186 997.962
186 938.108
186 861.479
186 813.847
⫺0.051
⫺0.003
⫺0.057
⫺0.180
0.072
⫺0.056
187 212.040
187 153.360
187 008.055
186 985.821
186 865.661
186 817.729
⫺0.002
0.026
0.090
⫺0.068
0.153
⫺0.024
187 211.125
187 155.945
187 017.839
186 982.857
186 868.387c
186 820.154c
⫺0.022
0.007
⫺0.204
⫺0.049
187 213.019
187 159.735
187 028.695
186 979.159
186 869.881c
186 820.154c
0.146
0.042
⫺0.107
⫺0.055
187 217.483
187 164.697
187 041.067
186 974.169
186 869.881c
186 819.119
⫺0.035
0.040
0.053
⫺0.025
187 224.778
187 170.968
187 059.895
186 966.580
186 868.819c
186 816.416
⫺0.037
0.065
0.097
⫺0.045
16→17
13.5→14.5
14.5→15.5
15.5→16.5
16.5→17.5
17.5→18.5
18.5→19.5
198 890.846
198 825.920
198 681.557
198 620.586
198 544.408
198 494.849
⫺0.011
0.019
⫺0.033
⫺0.152
0.118
0.034
198 887.970c
198 827.142
198 690.013
198 663.326
198 548.106
198 498.283
0.015
⫺0.012
⫺0.039
0.125
0.038
198 886.812
198 829.346
198 698.949
198 661.041
198 550.581
198 500.329c
⫺0.074
0.040
⫺0.055
⫺0.023
0.147
198 887.970c
198 832.580
198 708.731
198 657.677
198 551.998c
198 500.329c
198 892.346
198 836.891
198 720.089
198 652.989
198 551.998c
198 499.543
0.015
0.042
0.060
⫺0.001
198 898.669
198 842.373
198 736.740
198 645.921
198 551.998c
198 497.051
0.016
0.045
0.095
⫺0.026
210 565.512
210 499.429
210 363.059
210 301.109
210 225.265
210 174.062
0.004
⫺0.001
⫺0.011
⫺0.034
0.115
0.021
c
210 562.019
210 500.476
210 370.122
210 339.378
210 228.590
210 177.176
0.064
⫺0.018
⫺0.040
0.100
0.022
210 561.622
210 502.272
210 378.163
210 337.740
210 230.875
210 178.892c
⫺0.052
0.009
⫺0.040
⫺0.013
0.148
210 563.101
210 505.098
210 387.088
210 334.666
210 232.083c
210 178.892c
210 566.691
210 508.886
210 397.526
210 330.279
210 232.083c
210 178.892c
0.071
0.034
0.032
⫺0.020
210 572.197
210 513.731
210 412.394
210 323.673
210 232.083c
210 176.044
0.005
0.034
0.064
⫺0.076
15.5→16.5
16.5→17.5
17.5→18.5
18.5→19.5
19.5→20.5
20.5→21.5
222 239.176
222 171.996
222 042.443
221 979.432
221 904.063
221 851.526
⫺0.017
⫺0.082
⫺0.014
⫺0.091
0.073
0.004
c
222 235.899
222 174.476
222 055.537
222 012.863
221 909.124c
221 855.867c
⫺0.033
0.017
⫺0.062
⫺0.031
c
222 240.095
222 180.253
222 073.422
222 006.008
221 910.329c
221 855.867c
0.062
⫺0.011
0.079
⫺0.025
222 244.928
222 184.664
222 086.812
221 999.886
221 910.329c
221 853.334
0.021
0.085
0.115
⫺0.052
16.5→17.5
17.5→18.5
18.5→19.5
19.5→20.5
20.5→21.5
21.5→22.5
c
233 911.941
233 843.605c
233 719.710
233 655.773
233 580.840
233 527.194
233 916.696
233 854.650
233 759.645
233 674.388
233 586.543c
233 528.919
0.065
0.100
0.041
⫺0.032
17.5→18.5
18.5→19.5
245 582.968c
245 513.926c
245 587.075
245 523.605
⫺0.004
⫺0.001
17→18
18→19
20→21
222 236.899
222 172.996
222 048.342
222 014.003
221 907.105
221 854.363
0.123
⫺0.021
0.021
0.076
0.003
c
⫺0.025
⫺0.097
⫺0.004
0.004
233 909.581
233 844.081c
233 724.645
233 687.086c
233 583.667
233 529.767
245 580.455c
245 514.360c
c
0.013
0.096
⫺0.022
233 908.893
233 845.649
233 731.103
233 686.352c
233 584.524c
233 531.272c
245 580.455c
245 515.577
222 236.899
222 176.926
222 063.753
222 010.129
221 910.329c
221 855.867c
⫺0.052
0.037
⫺0.081
⫺0.040
0.017
0.065
⫺0.019
c
0.029
⫺0.038
0.060
233 909.581
233 847.787
233 738.627
233 683.915
233 586.543c
233 531.272c
245 580.455c
245 517.432
⫺0.048
⫺0.050
⫺0.059
c
0.005
⫺0.067
⫺0.022
⫺0.006
233 911.941
233 850.755
233 747.526
233 680.017
233 586.543c
233 531.272c
245 582.968c
245 520.133
⫺0.017
0.022
⫺0.080
0.013
Downloaded 30 May 2002 to 128.196.209.95. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp
0.031
⫺0.006
⫺0.024
0.111
⫺0.178
⫺0.216
⫺0.176
Thompsen, Brewster, and Ziurys
19→20
14.5→15.5
15.5→16.5
16.5→17.5
17.5→18.5
18.5→19.5
19.5→20.5
0.049
⫺0.081
⫺0.022
⫺0.009
J. Chem. Phys., Vol. 116, No. 23, 15 June 2002
N ⬙ →N ⬘
F ⬙ ⫽J ⬙ ⫹5/2b
N ⬙ →N ⬘
21→22
22→23
23→24
24→25
42→43
F ⬙ ⫽J ⬙ ⫹1/2b
F ⬙ ⫽J ⬙ ⫺1/2b
F ⬙ ⫽J ⬙ ⫺3/2b
F ⬙ ⫽J ⬙ ⫺5/2b
J ⬙ →J ⬘
␯ obs
␯ o-c
␯ obs
␯ o-c
␯ obs
␯ o-c
␯ obs
␯ o-c
␯ obs
␯ o-c
␯ obs
␯ o-c
19.5→20.5
20.5→21.5
21.5→22.5
22.5→23.5
245 394.834
245 330.089
245 255.619
245 200.977
⫺0.037
⫺0.071
0.089
0.003
245 398.884
245 358.236c
245 258.156
245 202.904c
⫺0.017
245 404.748
245 358.236c
245 259.805c
245 204.692c
⫺0.019
245 411.649
245 355.977
245 260.781c
245 204.692c
⫺0.075
0.005
245 419.929
245 352.390
245 260.781c
245 204.692c
0.038
⫺0.011
245 430.964
245 347.084
245 260.781c
245 202.904c
0.043
⫺0.018
18.5→19.5
19.5→20.5
20.5→21.5
21.5→22.5
22.5→23.5
23.5→24.5
257 252.300c
257 182.424c
257 067.789
257 002.288
256 928.203
256 872.793
⫺0.037
⫺0.063
0.049
⫺0.007
257 250.317c
257 182.820c
257 071.096
257 028.017c
256 930.571
256 874.690c
257 256.086
257 191.230
257 100.554
257 017.827
256 932.990c
256 874.241c
0.035
⫺0.022
0.028
⫺0.073
19.5→20.5
20.5→21.5
21.5→22.5
22.5→23.5
23.5→24.5
24.5→25.5
268 920.130c
268 849.291c
268 738.532
268 672.328
268 598.682
268 542.567
⫺0.018
⫺0.063
0.069
⫺0.024
268 918.208c
268 849.645c
268 741.170
268 695.951c
268 600.837
268 544.231c
268 923.410
268 857.346
268 768.340
268 686.691
268 603.071c
268 544.231c
0.035
⫺0.037
0.037
⫺0.032
20.5→21.5
21.5→22.5
22.5→23.5
23.5→24.5
24.5→25.5
25.5→26.5
280 586.045c
280 514.776c
280 406.987
280 340.195
280 266.945
280 210.229
⫺0.002
⫺0.028
0.097
⫺0.036
280 584.173c
280 514.776c
280 409.081
280 362.290c
280 268.876
280 211.862c
280 588.912
280 521.809
280 434.191
280 353.349
280 270.979c
280 211.862c
0.014
⫺0.018
0.049
0.065
21.5→22.5
22.5→23.5
23.5→24.5
24.5→25.5
25.5→26.5
26.5→27.5
292 249.957c
292 178.009c
292 073.031
292 005.755
291 932.873
291 875.705
⫺0.051
⫺0.026
0.081
⫺0.037
292 248.166c
292 178.009c
292 074.772
292 025.005c
291 934.575
291 877.195c
292 252.491
292 184.230
292 097.968
¯
291 936.662c
291 877.195c
0.008
0.059
0.034
22.5→23.5
23.5→24.5
24.5→25.5
25.5→26.5
26.5→27.5
27.5→28.5
303 911.686c
303 839.281c
303 736.682
303 668.984
303 596.467
303 538.867
⫺0.085
⫺0.010
0.090
⫺0.073
303 910.091c
303 839.281c
303 738.089
303 686.773c
303 598.117
305 540.252c
303 913.945
303 845.029
303 759.615
303 680.675
303 599.966c
305 540.252c
⫺0.056
⫺0.024
0.039
0.214
39.5→40.5
40.5→41.5
41.5→42.5
42.5→43.5
43.5→44.5
44.5→45.5
501 741.609c
501 663.051c
501 578.137c
501 507.878c
501 441.507c
501 383.075c
501 741.609c
501 663.051c
501 578.137c
501 512.914c
501 441.507c
501 383.075c
0.077
⫺0.015
0.069
⫺0.027
0.053
⫺0.012
0.015
0.046
⫺0.089
0.069
⫺0.007
257 250.317c
257 183.995
257 076.367
257 028.017c
256 932.040c
256 876.258c
268 918.208c
268 850.884
268 745.994
268 695.951c
268 602.230
268 545.824c
280 584.173c
280 515.841
280 413.460
280 362.290c
280 270.979c
280 213.890c
292 248.166c
292 178.905
292 078.724
292 026.390
291 936.662c
291 878.533c
303 910.091c
¯
303 741.968c
303 688.197
303 599.966c
303 541.600c
501 741.609c
501 663.051c
501 578.137c
501 514.943c
501 441.507c
501 383.075c
0.039
⫺0.040
0.116
0.005
⫺0.028
0.038
0.025
⫺0.016
0.057
0.145
0.169
257 250.317c
257 185.638
257 082.791
257 026.194
256 932.990c
256 876.258c
268 918.208c
268 852.307
268 751.875
268 694.413
268 603.071c
268 545.824c
280 584.173c
280 517.219
280 418.872
280 360.990
280 270.979c
280 213.890c
292 248.166c
292 180.233
292 083.657
292 025.005c
291 936.662c
291 878.533c
303 910.091c
303 841.195
303 745.948c
303 686.773c
303 599.966c
303 541.600c
501 741.609c
501 663.051c
501 582.710c
501 514.943c
501 441.507c
501 383.075c
⫺0.036
⫺0.040
⫺0.003
⫺0.006
⫺0.057
⫺0.059
0.020
⫺0.075
0.256
0.043
⫺0.131
0.044
257 252.300c
257 188.073
257 090.438
257 022.819
256 932.990c
256 876.258c
268 920.130c
268 854.489
268 759.001
268 691.312
268 603.071c
268 545.824c
280 586.045c
280 519.186
280 425.567
280 357.726
280 270.979c
280 213.890c
292 249.957c
292 181.999
292 089.980
¯
291 936.662c
291 878.533c
303 911.686c
303 842.805
303 752.159
303 684.080
303 599.966c
303 541.600c
⫺0.020
0.018
⫺0.032
⫺0.017
0.001
⫺0.045
⫺0.009
0.023
⫺0.100
⫺0.015
0.022
⫺0.022
0.006
⫺0.212
501 741.609c
501 663.051c
501 582.710c
501 512.914c
501 441.507c
501 383.075c
501 741.609c
501 663.051c
501 585.723c
501 512.000c
501 441.507c
501 383.075c
The spectrum of the MnS radical
25→26
F ⬙ ⫽J ⬙ ⫹3/2b
J. Chem. Phys., Vol. 116, No. 23, 15 June 2002
TABLE I. 共Continued.兲
a
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10215
In MHz.
Denotes lower level quantum number, F ⬙ of the transition F ⬙ →F ⬙ ⫹1.
c
Blended or partially resolved lines; not included in final fit.
b
10216
J. Chem. Phys., Vol. 116, No. 23, 15 June 2002
Thompsen, Brewster, and Ziurys
FIG. 1. Spectrum of the N⫽14→15 rotational transition of 55MnS in its
X 6 ⌺ ⫹ state ( v ⫽0), obtained near 175 GHz. The sextet pattern, which
arises from fine structure interactions and is labeled by ⌺, is apparent in the
spectrum. Superimposed on this pattern is the hyperfine structure, which
splits each spin component into an additional six lines. MnS thus follows a
typical case 共b兲 pattern. This scan is a composite of five 100 MHz scans,
each approximately 90 s in duration.
FIG. 3. Spectrum of the N⫽42→43 transition of MnS measured near 501
GHz. While the six spin states are clearly apparent in this spectrum, the
hyperfine structure is completely collapsed in the ⌺⫽⫾5/2 and ⌺⫽⫾3/2
ladders, as expected in a case b ␤ J coupling scheme. Partial resolution of the
hyperfine lines is evident, however, in the ⌺⫽1/2 and ⌺⫽⫺1/2 ladders.
The scan is a composite of five 100 MHz scans each approximately 90 s in
duration.
This Hamiltonian is comprised of terms that model the molecular frame rotation (Hrot) including its centrifugal distortion, the spin–spin coupling (Hss ), the spin–rotation coupling (Hsr ), and the magnetic hyperfine interactions (Hhf).
The coupling scheme employed in this analysis is the Hund’s
case b␤ J basis; hence, the angular momenta follow the couplings Ĵ⫽N̂⫹Ŝ and F̂⫽Ĵ⫹Î. This scheme is entirely appropriate, given the sextet pattern readily apparent in the MnS
spectra.
The spin–spin interaction in this Hamiltonian consists of
the first-order spin–spin term, ␭, its centrifugal distortion
correction, ␭ D , and the higher-order spin–spin coupling, ␪,
written for simplicity in Hund’s case 共a兲 notation,17
2兲
Ĥss ⫽Ĥ共ss2 兲 ⫹Ĥ共sscd
⫹Ĥ共ss4 兲
⫽ 23 ␭ 共 3S Z2 ⫺S2 兲 ⫹ 32 ␭ D 关 21 共 3S Z2 ⫺S2 兲 N2
⫹ 12 N2 共 3S Z2 ⫺S2 兲兴
⫹
␪
共 35S Z2 ⫺30S2 S Z2 ⫹25S Z2 ⫺6S2 ⫹3S4 兲 .
12
共2兲
The spin–rotation term used consists of the usual ␥ N̂•Ŝ interaction, its centrifugal distortion correction, and because of
the high-spin multiplicity involved, a higher-order spin–
rotation coupling which is characterized by ␥ S . This additional term involves a third-order spin–orbit interaction and
is best expressed in spherical tensor notation,18
Ĥsr ⫽
FIG. 2. Spectrum of the ⌺⫽⫺1/2 fine structure component of the N⫽14
→15 rotational transition of MnS near 175.35 GHz. Here all six individual
hyperfine components, which arise from the nuclear spin of Mn (I⫽5/2),
are resolved; they are labeled by quantum number F. The scan is approximately 85 MHz in width and represents a single scan of approximately 90 s
in duration.
10
冑6
␥ S T 3 共 L̂2 ,N兲 •T 3 共 S,S,S兲 .
共3兲
According to Hougen,19 S⫹1/2 spin–rotation constants are
necessary in the effective Hamiltonian for high-spin states,
not including centrifugal distortion. Because S⫽5/2 for
MnS, three spin-rotation parameters would seem necessary.
To our knowledge, however, a term higher than ␥ S has never
been used to model experimental data. In fact, in modeling
rotational data for CrH (X 6 ⌺ ⫹ ) 共Ref. 20兲 and CrCl
(X 6 ⌺ ⫹ ), 21 even the ␥ S parameter was not used, although it
was found necessary in MnO (X 6 ⌺ ⫹ ). 13
The hyperfine Hamiltonian for MnS consists of the
Fermi contact interaction, the spin dipolar coupling, and the
electric quadrupole term. Expressions for these interactions
are found in the literature.22,23 Unlike the analysis for MnO,
however, the higher-order Fermi contact parameter b S and
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J. Chem. Phys., Vol. 116, No. 23, 15 June 2002
The spectrum of the MnS radical
10217
TABLE II. Spectroscopic constants for MnS (X 6 ⌺ ⫹ ). a
Parameter
Bv
Dv
␥
␥D
␥S
␭
␭D
␪
bF
b FD
c
eQq
RMS of fit:
r 0 ⫽2.068 24(37) Å
Submillimeter
MnS
Optical
MnS
5 845.7741共41兲
0.0037136共94兲
⫺71.800共72兲
0.000159共39兲
0.0059共36兲
10 485.0共3.1兲
⫺0.02899共27兲
⫺4.8共1.1兲
206.51共79兲
⫺0.00035共14兲
⫺27.8共1.6兲
⫺14.9共9.6兲
0.068
5 844.6共4.4兲b
0.00354共54兲b
⫺90共30兲b
¯
¯
¯
¯
¯
96共6兲c
¯
⫺135共12兲
¯
In MHz for v ⫽0, errors quoted are 3␴ and apply to the last quoted decimal
place.
b
From Ref. 11.
c
From Ref. 24.
a
the nuclear spin-rotation constant, C I , did not appreciably
improve the data fit and were not used in the final analysis,
although b F D was found necessary.
The data were analyzed using the HUNDB least-squares
program developed by Brown et al.20 Modifications were
made to the code to include the fourth-order spin–spin term
and additional hyperfine interactions. An initial fit of the data
set was made by assigning the spin components on the basis
of prior optical measurements.11,12 The hf structure was collapsed and the rotational and fine structure parameters fit.
Following this initial analysis, the hyperfine structure was
then included in the fit and these constants established. Lines
blended by 1 MHz or less were not included in the fit. A total
of 298 individual spectral features were subsequently used in
the final analysis.
The resulting spectroscopic parameters are given in
Table II, along with those previously derived from the optical
studies of MnS.11,12 Also included are the values for the b F
and c hyperfine constants obtained from the ESR measurements of Baumann et al.24 As the table shows, the B 0 , D 0 ,
and ␥ constants are in excellent agreement with the optical
values, within the quoted errors. On the other hand, there is
considerable discrepancy between the gas-phase millimeter
and ESR hf values, derived from argon matrix measurements, although the signs are consistent. The b F value from
our work is about a factor of 2 larger and the c constant a
factor of 5 smaller. Baumann et al. also measured hf constants for MnO, MnF, MnCl, and MnH.24 The Fermi contact
terms for these molecules were determined to be greater than
300 MHz, while that for MnS from the matrix studies was
found to be 96 MHz. Hence, the value for MnS is anomalously low, even though the interactions arise from the same
nucleus, 55Mn. Our b F value of 206.51 MHz is more consistent with those of other manganese molecules. These differences in hf parameters for MnS may result from the effects
of the matrix shift. The overall rms of the millimeter analysis
is 68 kHz.
FIG. 4. A qualitative molecular orbital diagram illustrating the bonding in
MnS in its X 6 ⌺ ⫹ ground state. The bonding orbitals are 10␴ and 4␲ levels,
while the antibonding orbitals are 12␴ and 5␲. The 1␦ and 11␴ orbitals are
essentially nonbonding. Three orbitals are half-filled because of the extra
stabilization obtained from 3d – 3d exchange energy.
V. DISCUSSION
These measurements have confirmed that the electronic
ground state for MnS is 6 ⌺ ⫹ . Hence, this radical has five
unpaired electrons. In analogy to MnO,13 the electronic configuration is likely to be
X 6 ⌺ ⫹ : 共 core兲共 10␴ 兲 2 共 4 ␲ 兲 4 共 1 ␦ 兲 2 共 11␴ 兲 1 共 5 ␲ 兲 2 .
共4兲
14,15
As discussed in several theoretical papers,
the 4s and 3d
atomic orbitals of manganese combine with the 3p atomic
orbital on sulfur to produce the 10␴ and 4␲ bonding molecular orbitals and the 5␲ and 12␴ antibonding ones. The 1␦
must be nonbonding due to the lack of d-orbitals on the
sulfur atom. The 11␴ orbital is considered to be primarily
nonbonding as well. However, all ␴ orbitals are formed
through sd ␴ hybridization. Hence, the 11␴ nonbonding orbital contains both s and d character. A qualitative molecular
orbital diagram illustrating this bonding scheme is given in
Fig. 4. As shown in this figure, the 1␦, 11␴, and 5␲ levels lie
at different energies. They successively fill with unpaired
electrons because of the 3d – 3d exchange energy.15
The five unpaired electrons all contribute to the extensive hyperfine structure characteristic of this molecule. However, the isotropic Fermi contact term, b F , only arises from
the contribution of s-type electrons, since it is directly proportional to the electron density at the manganese nucleus.
Therefore, the unpaired electrons in the 11␴ orbital are by far
the dominant contribution to b F . This orbital, as mentioned
previously, is formed from s and d-type atomic orbitals. The
amount of s character retained in the 11␴ orbital can be
evaluated by comparing b F (MnS) to the Fermi contact term
of the Mn⫹ ion.25 This comparison assumes that the 10␴
bond is strongly polarized towards the sulfur in an Mn⫹ S⫺
type structure. Using the value of this constant for Mn⫹ of
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10218
J. Chem. Phys., Vol. 116, No. 23, 15 June 2002
Thompsen, Brewster, and Ziurys
⬃698 MHz,24 the ratio of b F (MnS)/b F (Mn⫹ )⬃0.30. Thus,
70% of the s character in the unpaired electron on manganese
is lost in the formation of MnS. In comparison, about 30% of
the s-character is lost in MnO.13
The 11␴ orbital can be written as a linear combination of
the 4s and 3d ␴ atomic orbitals, assuming the Mn⫹ S⫺ structure,
兩 11␴ 典 ⫽c 1 兩 4s 共 Mn⫹ 兲 典 ⫹c 2 兩 3d ␴ 共 Mn⫹ 兲 典 .
共5兲
⫹
As discussed in Ref. 26, the ratio of b F (MnS)/b F (Mn )
⫽c 21 . Therefore, c 22 ⬵0.7, which means that the 11␴ orbital is
predominantly 3d ␴ in character by a ratio of 2:1, relative to
the 4s contribution. In MnO, in contrast, the weighting between these two atomic orbitals is roughly equal.13 The
larger contribution of the 3d ␴ orbital in MnS suggests that
there is greater electron density between the Mn and S atoms
as opposed to Mn and O. Therefore, this orbital has more
bonding character in manganese sulfide relative to manganese oxide, and consequently MnS appears to be the more
covalent species.
This property is also apparent in evaluating the dipolar
hyperfine constant, c. As discussed by Ferrante et al.,27 the c
parameter is primarily composed of contributions from the
3d unpaired electrons in the 11␴, 5␲, and 1␦ orbitals,
冋冓
c 22 3 cos2 ␪ ⫺1
3
c⫽ g 1 g S ␮ S ␮ 1
2
5
r3
⫹
冓
2 3 cos2 ␪ ⫺1
5
r3
冔
⫹
3d ␲
冓
冔
3d ␴
2 3 cos2 ␪ ⫺1
5
r3
冔 册
.
共6兲
3d ␦
The above expression applies to both MnO and MnS, and
the only term that varies between the two species is the
c 2 constant. The angular expectation values in this equation
are 具 3 cos2 ␪⫺1典⫽4/7, 2/7, and ⫺4/7 for the 3d ␴ , 3d ␲ ,
and the 3d ␦ orbitals of the manganese atom, respectively,
while the radial value is 具 1/r 3 典 ⫽4.167 a.u.⫺3 . 28 Therefore,
the third term (3d ␦ ) makes a negative contribution to
c, while the ␲ and ␴ terms are positive. For MnO,
c⫽⫺48.199(178) MHz 共Ref. 13兲 and for MnS,
c⫽⫺27.8(1.6) MHz. The more positive value of c in
the case of MnS can only arise from the fact that c 22 is greater
in MnS than MnO, making the contribution of the first positive term larger. In fact, our estimate of c 22 from the Fermi
contact term is 0.7, while that of MnO is calculated to be
⬃0.5.13 Again, this result means that there is a larger 3d ␴
contribution in MnS relative to MnO, and as a consequence,
more electron density is located between the two atoms of
the molecule. Interestingly, using our estimated value of c 22 ,
we calculate c⫽⫺27.9 MHz, remarkably close to our measured value.
Another constant useful to compare is the quadrupole
term, which arises from both p and d orbital contributions. If
the quadrupole moment giving rise to this interaction is on
the positive pole of the molecule, then a more positive value
for eQq indicates an increase in covalent character.29 The
quadrupole parameter in MnS is somewhat more positive
关⫺14.9 共9.6兲兴 than in MnO 关⫺25.65 共1.82兲兴; however, the
error on the constant for MnS is sufficiently large such that it
TABLE III. Selected hyperfine parameters of manganese diatomics.
Molecule
a
MnH
MnFb
MnClb
MnOc
MnSc
a
Ground
state
⫹
⌺
⌺⫹
7 ⫹
⌺
6 ⫹
⌺
6 ⫹
⌺
7
7
b F 共MHz兲
Reference
279共1兲
443共6兲
376共11兲
479.87共10兲
206.51共79兲
31
30
24
13
This work
Derived from LIF measurements.
Ar matrix ESR values.
Millimeter measurements.
b
c
falls within the range of the MnO value. Additional measurements are required for a more accurate comparison.
The degree of ionic versus covalent character in manganese compounds can be evaluated for several such species by
comparing their Fermi contact parameters. These values are
listed in Table III. In order to make a meaningful comparison, it must be understood that MnH, MnF, and MnCl have
7 ⫹
⌺ ground electronic states, and consequently have one
more unpaired electron than MnO or MnS. This electron
resides in the antibonding ␴ orbital, which for MnCl is the
12␴ level 共see Fig. 4兲. Hence, there is an additional electron
contributing to b F in these molecules. Despite this fact, the
trend is clear. The Fermi contact constants are clearly smaller
for MnCl relative to MnF 关376 共17兲 MHz vs 443 共6兲 MHz兴
共Refs. 24 and 30兲 and the same for MnS 关206.51 共79兲 MHz兴
vs MnO 关479.86 共10兲 MHz兴. Hence, as one descends the
periodic table, the s-character of the orbitals of the unpaired
electrons decreases, indicating a trend towards greater covalency. The b F value of MnH, on the other hand, is 279 共1兲
MHz.31 This value is larger than that of MnS. However, MnS
has a single ␴ electron, while MnH has two. Considering this
difference, MnH clearly has the smallest Fermi contact term,
which when normalized to one electron, is b F ⬃140 MHz. It
therefore has the most covalent bond.
Outside of the hf parameters, the spin constants determined in this work can reveal some additional properties of
MnS. It is generally the case that second-order spin–orbit
interactions dominate the spin–spin term, ␭.32 The selection
rules for spin–orbit interactions in a 6 ⌺ ⫹ state are ⌬S⫽0,
⫾1 and ⫹ ↔ ⫺. Therefore, a main perturber to the 6 ⌺ ⫹
ground state in MnS is likely to be a 4 ⌺ ⫺ excited state.
Consequently, the spin–orbit contribution to ␭ in the ground
state is32
1 兩 具 4 ⌺ ⫺ 兩 ĤSO兩 X 6 ⌺ ⫹ 典 兩 2
␭ ⬇
.
8 ⌬E 共 4 ⌺ ⫺ ⫺X 6 ⌺ ⫹ 兲
SO
共7兲
If one assumes that the spin–orbit interaction between these
two states is directly proportional to the spin–orbit constant
of manganese ( ␨ ⬃325 cm⫺1 ), 32 then this expression simplifies to
␭ SO⬇
␨ 共 Mn兲 2
1
.
8 ⌬E 共 4 ⌺ ⫺ ⫺ 6 ⌺ ⫹ 兲
共8兲
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J. Chem. Phys., Vol. 116, No. 23, 15 June 2002
The spectrum of the MnS radical
If it is the case that ␭⬃␭ SO for MnS, then there is an excited
4 ⫺
⌺ state approximately 38 000 cm⫺1 higher in energy than
the ground state. To date, there is no observation of such a
state.
Is it valid to assume that ␭⬃␭ SO? A test of this approximation can be made by calculating the value of ␪ under
similar assumptions and then comparing it to the observed
value. As noted in Corkery et al.,20 ␪ can be estimated from
the expression,
兩␪兩⬃
␨ 共 Mn兲 4
.
⌬E 共 ⌺ ⫺ ⫺ 6 ⌺ ⫹ 兲 3
4
共9兲
Using ⌬E⬃38 000 cm⫺1 , 兩␪兩 is found to be ⬃6 MHz, very
close to the experimental value of ␪ ⫽⫺4.8(1.1) MHz.
The r 0 bond length determined from this study is 2.0682
Å. This value is in reasonable agreement with theory. For
example, Bauschlicher and Maitre predict r e ⫽2.11 Å, 14
while Bridgeman and Rothery calculate r 0 ⫽2.04 Å. 15 On
the other hand, the MnS bond distance is slightly longer than
that of CuS, which is r 0 ⫽2.055 Å, 33 and slightly shorter
than TiS (r 0 ⫽2.082 Å). 34 This behavior does not follow the
trends exhibited by the 3d-oxides. As described by Merer35
and supported by theoretical calculations,14,15 the 3d-oxides
exhibit three peaks in bond length at ScO, MnO, and CuO.
In fact, the CuO bond distance is the largest of the group
at r 0 ⫽1.729 Å. This ‘‘double-humped’’ trend for the
transition-metal oxides has been discussed by Bridgeman
and Rothery.15 The increase in bond distance in MnO and
CuO is thought to result from increased occupation of the
antibonding 4␲ orbital.
This trend in bond lengths is not nearly as apparent in
the 3d-sulfides, if it is present at all. The MnS bond length is
in fact longer than that of CuS, although the copper compound has an additional electron in the antibonding 5␲ orbital. Titanium sulfide has no ␲-antibonding electrons; yet,
its bond length is longer than that of MnS. In contrast, in the
metal-oxide species, the TiO bond length is r 0 ⫽1.623 Å,
significantly smaller than that of ScO 共1.668 Å兲, MnO 共1.648
Å兲, and CuO 共1.729 Å兲.35 These differences indicate that the
bonding properties of the 3d-metal sulfides differ from those
of their oxide counterparts. This variation must arise from
the fact that the 3p orbitals of sulfur are closer in energy to
the 3d and 4s orbitals of the transition metals than the requisite 2p orbitals of oxygen. The 3p orbitals are also more
diffuse in spatial distribution than those of the 2p levels.
Certainly additional transition metal sulfide species need to
be investigated experimentally at high spectral resolution
共i.e., NiS, CoS, FeS, etc.兲 before the properties of 3d
transition-metal sulfides can be quantitatively evaluated relative to their oxide counterparts.
VI. CONCLUSIONS
Measurement of the pure-rotational spectrum of MnS in
its X 6 ⌺ ⫹ ground state has provided additional tests of molecular theory and has provided new data concerning the nature of 3d-sulfide species. MnS is one of the few molecules
that has been studied at high resolution in a high spin state
( 6 ⌺ ⫹ ). As is apparent from its spectrum, the radical closely
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follows a Hund’s case 共b兲 coupling scheme. Both the fourthorder spin–spin interaction and the third-order spin–orbit
correction to the spin–rotation coupling were found necessary to analyze the data set, which included 14 transitions
and 298 spectral lines. This molecule and MnO are the only
6 ⫹
⌺ species where such higher-order interactions were
found necessary for a viable analysis; they also have the
largest data sets available. The hyperfine constants determined for MnS indicate that this molecule is more covalent
than its oxide and halide analogs, and that the hybridized
sd ␴ orbital may have significant bonding character. However, this species is not more covalent than MnH. The bond
length determined for MnS is remarkably longer than that of
CuS, suggesting a trend opposite to that evident in the
3d-oxides where CuO has the greatest bond distance. There
are obviously subtle bonding differences between the sulfides and the oxides. Further spectroscopic investigation of
the 3d-block transition-metal sulfides would be enlightening.
Finally it should be noted that flow reactor, Broida-type oven
production of transition-metal species is feasible.
ACKNOWLEDGMENTS
The authors would like to thank J. M. Brown for use of
his HUNDB program code. This research was supported by
NSF Grant No. CHE-98-17707.
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