17 August 2001
Chemical Physics Letters 344 (2001) 75±84
www.elsevier.com/locate/cplett
Transition metal sul®de studies: the pure rotational
spectrum of the CuS radical …X2Pi †
J.M. Thompsen, L.M. Ziurys *
Department of Chemistry, Department of Astronomy, Steward Observatory, The University of Arizona,
933 North Cherry Avenue, Tucson, AZ 85721, USA
Received 27 March 2001; in ®nal form 31 May 2001
Abstract
The pure rotational spectrum of CuS in its X2 Pi ground state has been recorded using direct absorption techniques
in the range 140±540 GHz. This radical was produced by the reaction of copper vapour with CS2 . Both the v ˆ 0 and
v ˆ 1 states of 63 CuS were observed, as well as the 65 CuS …v ˆ 0† isotopomer. 25, 13, and 8 rotational transitions were
recorded for these three species, respectively. Both the X ˆ 1=2 and X ˆ 3=2 spin±orbit ladders were observed. Accurate
rotational, spin±orbit, and lambda-doubling constants were subsequently determined for these molecules. These data
suggest that 3d-sul®des have subtle bonding di€erences relative to the corresponding 3d-oxides. Ó 2001 Elsevier
Science B.V. All rights reserved.
1. Introduction
It has been long established that transition
metals play an important role in many ®elds, including catalysis, organic synthesis, stellar atmospheres, and cosmochemistry. Of particular
interest are the 3d-row of transition metals, which
have relatively large natural abundances because
of their production in non-explosive nucleosynthesis [1]. Also, the 3d-orbitals of these metals
have energies comparable to the 2p orbitals of
oxygen, nitrogen, and carbon. Therefore quite
interesting simple compounds of these elements
form that possess a mixture of ionic and covalent
bondings [2,3]. These molecules are useful for examining bonding schemes in simple metal systems,
*
Corresponding author. Fax: +1-520-621-1532.
E-mail address: [email protected] (L.M. Ziurys).
which then can be generalised to bulk properties
[4].
High-resolution spectroscopy is an avenue by
which 3d transition-metal compounds can be investigated. One class of such molecules that has
been studied extensively in the past 15±20 years by
various spectroscopic techniques is the transitionmetal oxides [2]. Spectra of the series of 3d-oxides
from ScO to CuO have been recorded involving
both ground and excited electronic states using
optical, infrared, and millimeter techniques [5±9].
Such investigations have clearly demonstrated that
these oxides contain single, double, and triple
bonds with a mixture of ionic and covalent components [3,4]. Moreover, the bonding type changes
across the periodic table as the energy of the 3dorbitals decreases relative to the oxygen 2p orbital.
Transition metal sul®des are another class of
interesting 3d molecules. Unlike the oxides, these
species are not well studied experimentally,
0009-2614/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 0 0 9 - 2 6 1 4 ( 0 1 ) 0 0 6 9 3 - 5
76
J.M. Thompsen, L.M. Ziurys / Chemical Physics Letters 344 (2001) 75±84
although other metal-containing sul®de systems
have been investigated such as AlS, CaS, MgS,
NaS, and KS [10±13]. Theoretical calculations
predict that the isovalent 3d metal sul®des have
similar properties to the 3d-oxides, except with
longer and weaker bonds [3,4]. To date, however,
high-resolution spectroscopic investigations of
these compounds have been limited such that
trends across the periodic table cannot yet be fully
evaluated. To our knowledge, high-resolution
spectra exist only for a few of these molecules,
such as ScS [14] and TiS [15].
In an e€ort to provide complementary data on
these metal sul®des, we have begun to record the
pure-rotational spectra of such compounds in the
millimeter/sub-millimeter region. One particular
molecule of interest is CuS. Investigations of
copper monosul®de have had a somewhat long
history when compared with other 3d metal sul®des, and thus CuS is a natural starting point for
our investigations. Initial studies of this molecule
were carried out by Biron in the 1970s [16,17] who
examined the A ! X system and suggested it arose from a 2 R ! 2 P transition. In 1985, David
et al. [18] obtained laser excitation spectra of the
A2 R X2 Pi system for both 63 CuS and 65 CuS.
Their subsequent analysis resulted in estimates of
the rotational, centrifugal distortion and lambdadoubling constants, and con®rmed that the electronic ground state was 2 Pi . In the last decade,
further optical studies of electronic transitions
have been conducted; Lefebvre et al. [19] investigated the D ! X transition, and David et al. [20]
studied the E ! X, F ! X, and G ! X systems.
The most recent work was done by O'Brien et al.
[21], who examined the Y ! X transition in the
near-infrared utilising Fourier-transform methods.
Here we report the ®rst measurement of the
pure rotational spectrum of CuS in its X2 Pi
ground electronic state in the millimeter/sub-millimeter region. Multiple transitions were recorded
for the main copper isotopomer 63 CuS in the v ˆ 0
and v ˆ 1 vibrational states and for the
65
CuS …v ˆ 0† isotopomer. Lines originating from
both the X ˆ 1=2 and the X ˆ 3=2 spin±orbit
ladders were observed for most transitions measured. These data were analysed to obtain rotational, spin±orbit, centrifugal distortion, and
lambda-doubling parameters, as well as a bond
length. The spectroscopic constants were found to
be in good agreement with past optical measurements. In addition, we discuss properties of CuS
compared with other 3d metal sul®des, and their
bonding relative to the 3d-oxides.
2. Experimental
The spectra of CuS were recorded via direct
absorption techniques utilising one of the spectrometers of the Ziurys group. Details of the experimental apparatus can be found elsewhere [22].
Brie¯y, the spectrometer consists of a tunable
millimeter/sub-millimeter-wave radiation source, a
reaction cell, and an InSb detector cooled to 4 K.
The radiation source is a phase-locked Gunn oscillator coupled with a Schottky diode multiplier,
with an operational range of 65±545 GHz. The
reaction cell is a free-space chamber (0.7 m in
length) with a double-wall design such that chilled
water can be used for cooling. A Broida-type oven
is incorporated into the chamber for metal vapour
production. The cell utilises a quasi-optical, double-pass focusing scheme with a foam-backed
Mylar window at one end of the cell and a rooftop
re¯ector at the other. Radiation is propagated to
the cell using two o€set ellipsoidal mirrors. The
incoming beam is focused to a waist at the rooftop
re¯ector, which subsequently rotates the beam
polarisation by 90° and re¯ects the beam back
through the cell. After the second pass through the
mirrors, the beam is re¯ected by a wire grid into
the detector. FM modulation of the radiation
source at 25 kHz is used for phase-sensitive detection.
CuS was synthesised by reacting copper vapour,
produced by the oven, with carbon disul®de (CS2 )
in the presence of a dc discharge. The oven was
heavily lined with zirconia insulation to achieve an
adequate temperature for vapourisation. Copper
granules (Aldrich, 99%) were used as the metal
vapour source. Argon was ¯owed into the reaction
cell from beneath the oven to an approximate
partial pressure of 20 mTorr, entraining the copper
vapour. The carbon disul®de (5±10 mTorr) was
then added over the oven containing the copper.
J.M. Thompsen, L.M. Ziurys / Chemical Physics Letters 344 (2001) 75±84
77
Table 1
Observed rotational transition frequencies of CuS (X2 Pi )a
63
63
CuS …v ˆ 0†
J 00 ! J 0
X
Parity
mobs
mo
11:5 ! 12:5
3/2
e
f
141139.440b
141139.440b
0.018
)0.048
12:5 ! 13:5
3/2
e
f
152424.001b
152424.001b
0.028
)0.052
13:5 ! 14:5
3/2
e
f
163707.042b
163707.042b
0.041
)0.055
14:5 ! 15:5
3/2
e
f
174988.426b
174988.426b
0.035
)0.080
18:5 ! 19:5
1/2
e
f
e
f
219619.851
220071.981
220095.440b
220095.440b
e
f
e
f
3/2
19:5 ! 20:5
1/2
3/2
20:5 ! 21:5
1/2
3/2
21:5 ! 22:5
1/2
3/2
22:5 ! 23:5
1/2
3/2
23:5 ! 24:5
1/2
3/2
24:5 ! 25:5
1/2
3/2
25:5 ! 26:5
1/2
3/2
26:5 ! 27:5
1/2
3/2
65
CuS …v ˆ 1†
mobs
mo
)0.013
0.082
0.113
)0.103
218706.108b
218706.108b
230878.589
231330.593
231366.977b;c
231366.977b;c
)0.007
0.065
0.128
)0.098
e
f
e
f
242135.012
242586.782
242636.200b
242636.200b
e
f
e
f
CuS …v ˆ 0†
mobs
mo
)0.043
)0.073
217819.642b
217819.642b
)0.008
)0.075
229427.009
229876.128
229906.408b
229906.408b
0.017
0.112
)0.023
)0.062
228488.992
228936.471
228974.771b
228974.771b
)0.153
0.002
)0.020
)0.071
0.001
)0.050
0.163
)0.123
240612.507
241061.525
241104.390b
241104.390b
)0.021
0.068
)0.007
)0.059
239629.286
240076.482
240127.657b
240127.657b
0.044
0.028
)0.011
)0.042
253389.010
253840.683
253903.020b;c
253903.020b;c
0.015
)0.018
0.176
)0.097
251795.684
252244.454
252299.940b
252299.940b
0.046
)0.007
0.002
)0.063
250767.025
251214.066
251278.178b
251278.178b
0.068
0.012
0.005
0.001
e
f
e
f
264640.452
265091.982
0.018
)0.038
262976.220
263424.902
263492.958b
263492.958b
0.016
)0.016
0.019
)0.063
261902.269
262349.168
262426.152b
262426.152b
0.088
0.011
)0.039
)0.012
e
f
e
f
275889.221
276340.625
276428.847b;c
276428.847b;c
0.007
)0.052
0.227
)0.182
274154.159
274602.706
274683.335b
274683.335b
0.043
)0.008
0.048
)0.054
273034.866
273481.654
273571.583b
273571.583b
0.063
0.001
0.032
)0.033
e
f
e
f
287135.230
287586.589
287687.733b;c
287687.733b;c
0.007
0.031
0.302
)0.140
285329.309
285777.706
285870.944b
285870.944b
0.049
)0.029
0.074
)0.051
284164.773
284611.421
284714.284b; c
284714.284b; c
0.062
)0.009
0.059
)0.053
e
f
e
f
298378.365
298829.492
298943.644b;c
298943.644b;c
0.017
)0.056
0.285
)0.214
296501.543
296949.861
297055.687b
297055.687b
0.020
)0.007
0.111
)0.039
295291.842
295738.372
295854.184b; c
295854.184b; c
0.047
)0.008
0.107
0.058
e
f
e
f
309618.475
310069.506
310196.512b;c
310196.652b;c
0.001
)0.030
0.218
)0.203
307670.827
308118.959
308237.443b
308237.443b
0.035
)0.040
0.153
0.026
306415.980
306862.392
306991.144b; c
306991.144b; c
0.036
0.002
0.148
)0.078
c
c
c
78
J.M. Thompsen, L.M. Ziurys / Chemical Physics Letters 344 (2001) 75±84
Table 1 (Continued)
J 00 ! J 0
28:5 ! 29:5
X
1/2
3/2
29:5 ! 30:5
1/2
3/2
30:5 ! 31:5
1/2
3/2
31:5 ! 32:5
1/2
3/2
32:5 ! 33:5
1/2
3/2
33:5 ! 34:5
1/2
3/2
34:5 ! 35:5
1/2
3/2
41:5 ! 42:5
1/2
3/2
42:5 ! 43:5
1/2
3/2
43:5 ! 44:5
1/2
3/2
45:5 ! 46:5
1/2
3/2
46:5 ! 47:5
1/2
Parity
63
63
CuS …v ˆ 0†
mobs
mo
e
f
e
f
332089.258
332540.018
332692.843
332693.352
)0.019
)0.031
0.121
)0.104
e
f
e
f
343319.718
343770.331
343936.124
343936.714
)0.009
)0.018
0.125
)0.098
c
65
CuS …v ˆ 1†
mobs
mo
341159.428
341607.323
341763.284
341763.357
)0.079
0.067
)0.074
)0.001
c
CuS …v ˆ 0†
mobs
mo
340215.673
340383.052
340383.476
)0.002
0.006
)0.030
)0.012
0.045
)0.009
0.076
c
e
f
e
f
355175.814
355176.724
)0.015
)0.003
350880.955
351326.867
351507.114
351507.758
e
f
e
f
365770.150
366220.488
366412.143
366413.095
)0.007
0.021
0.040
0.005
361988.727
362434.494
362627.800
362628.305
)0.047
0.019
0.084
)0.074
e
f
e
f
377440.056
377644.729
377645.733
)0.001
0.026
)0.052
373092.951
373538.542
373744.714
373745.452
)0.029
0.017
0.005
)0.037
e
f
e
f
388205.839
388655.934
388873.376
388874.795
)0.029
0.081
)0.141
0.092
384193.401
384638.843
)0.072
)0.018
e
f
e
f
399417.759
399867.759
400098.367
400099.900
)0.018
0.020
)0.067
0.173
395290.106
395735.311
)0.036
)0.063
e
f
e
f
477783.378
478232.017
478554.034
478556.484
0.060
0.063
)0.153
0.095
473617.473
473619.843
)0.047
0.035
483912.355
)0.096
484692.496
484695.012
0.035
0.050
517887.898
)0.065
528111.381
0.075
e
f
e
f
489743.920
489745.995c
0.078
)0.184
e
f
e
f
500928.452
500930.982
)0.126
)0.103
e
f
e
f
522460.018
522907.968
523282.918
523285.522
)0.017
)0.077
0.071
)0.153
e
f
533616.306
534064.189
)0.004
0.010
385762.284
386209.285
)0.077
)0.089
J.M. Thompsen, L.M. Ziurys / Chemical Physics Letters 344 (2001) 75±84
79
Table 1 (Continued)
J 00 ! J 0
X
Parity
63
mobs
47:5 ! 48:5
3/2
e
f
3/2
e
f
63
CuS …v ˆ 0†
mo
534452.240
534455.269
c
0.088
0.122
65
CuS …v ˆ 1†
mobs
mo
531069.515
531071.564
)0.001
0.072
542162.342
542164.432
0.017
)0.046
c
CuS …v ˆ 0†
mobs
528943.036
mo
c
0.042
a
In MHz.
Unresolved lines.
c
Not included in the least-squares ®t.
b
A dc discharge of 40±50 V at 300 mA was applied
to the reactants to form the sul®de. A green colour
was noticed upon discharge, consistent with
atomic emission of copper. The 63 and 65 isotopes
of copper were observed in their natural abundances (63 Cu:65 Cu ˆ 2.24:1).
Frequency measurements were carried out by
averaging an even number of scans of increasing
and decreasing frequency. Typically, scans 5 MHz
in frequency width were used. To determine centre
frequencies, lines were ®t with Gaussian pro®les.
Linewidths averaged from 500 to 1300 kHz over
the 140±540 GHz range. The experimental accuracy is estimated to be 100 kHz.
increasing J . There was no evidence for hyper®ne
interactions in the data, although the two main
isotopes of copper both possess a nuclear spin of
I ˆ 3=2. The lack of hyper®ne splitting is not unexpected. Hyper®ne splitting was seen only at low
J values (J 6 13:5) in the pure-rotational spectrum
of CuO [6].
Spectra illustrating these interactions are shown
in Figs. 1 and 2. Fig. 1 presents the J ˆ 25:5 !
26:5 transition for 65 CuS …X2 Pi † in its v ˆ 0 state
near 295 GHz, showing both X ladders. This isotopomer is the copper isotope with the lower natural abundance. The lambda doublets of the
3. Results
Transition
frequencies
recorded
for
CuS …v ˆ 0†, 63 CuS …v ˆ 1†, and 65 CuS …v ˆ 0†
are presented in Table 1. As Table 1 illustrates,
rotational transitions were recorded in both the
X ˆ 1=2 and X ˆ 3=2 spin±orbit ladders for the
majority of transitions. In addition to the ®ne
structure, lambda-doubling was also observed in
the spectra. The doublets are labelled using `e' and
`f' parity assignments, which are based on the
optical work of David et al. [18]. It is evident from
the data that the lambda-doubling in the X ˆ 3=2
ladder is quite small in all the species studied, with
a maximum observed splitting of about 3 MHz. In
fact, only at high values of J (P 41.5) were the
lambda-doublets resolved into separate lines.
Lambda-doubling in the X ˆ 1=2 ladder, on the
other hand, is quite large, with an average splitting
of the order of 450 MHz, decreasing slightly with
63
Fig. 1. Spectra of the J ˆ 25:5 ! 26:5 rotational transition of
65
CuS …X2 Pi : v ˆ 0† measured near 295 GHz. Both spin±orbit
components are present in this scan. The transition originating
in the X ˆ 1=2 sublevel is split into two lines because of
lambda-doubling, labeled by e and f. In the X ˆ 3=2 component, on the other hand, the lambda doublets are not resolved,
as shown in the inset. This ®gure is a composite of seven, 100
MHz scans, each lasting about 90 s in duration.
80
J.M. Thompsen, L.M. Ziurys / Chemical Physics Letters 344 (2001) 75±84
This Hamiltonian is comprised of terms that
model the molecular frame rotation (Hrot ), the
spin±orbit coupling (Hso ), and the lambda-doubling interactions (HLD ), including their centrifugal distortion corrections. Speci®c forms of these
expressions can be found in [12,13]. As the data set
consisted of high J -levels, higher-order centrifugal
distortion corrections were found necessary in the
®t, including H (for rotation), as well as AD and
AH (corrections to the spin±orbit term). The
lambda-doubling Hamiltonian is that described by
Brown et al. [23]:
HLD ˆ 1=2…p ‡ 2q†…J‡ S‡ ‡ J S †
Fig. 2. Spectra of the J ˆ 46:5 ! 47:5 rotational transition of
63
CuS …X2 Pi : v ˆ 0) measured near 534 GHz. Again, both
X ˆ 1=2 and X ˆ 3=2 components are shown, but in this case,
the lambda-doubling is resolved in both sublevels. This interaction is much smaller in the X ˆ 3=2 ladder, where the splitting
is 3 MHz, as shown in the inset. An unknown line near 533.7
GHz is noted with an asterisk. This spectrum is a composite of
®ve 100 MHz scans, each of approximately 90 s in duration.
X ˆ 1=2 sublevel are split by a large amount, while
those of the X ˆ 3=2 ladder are completely collapsed. The inset shows an enlargement of the
collapsed doublets of the X ˆ 3=2 ladder, recorded
as a 10 MHz scan. It should be noted that the
intensity of the X ˆ 3=2 sublevel is signi®cantly
larger than the corresponding X ˆ 1=2 lines, as
would be expected for an inverted state.
Fig. 2 displays the J ˆ 46:5 ! 47:5 transition
of the main isotopomer, 63 CuS …X2 Pi ; v ˆ 0†,
near 534 GHz. Again, lines originating in both
spin±orbit components are present. Here, the
lambda-doublets of the X ˆ 3=2 ladder are resolved as individual lines. The inset shows the
splitting of these doublets enlarged in a 10 MHz
scan. A similar lambda-doubling pattern was
found also in the v ˆ 1 data.
4. Analysis
The spectra were analysed using an e€ective 2 P
Hamiltonian of the following form:
Heff ˆ Hrot ‡ Hso ‡ HLD :
…1†
1=2q…J2‡ ‡ J2 †:
…2†
The lambda-doubling parameters are p and q, as
described by Mulliken and Christy [24]. The leastsquares routine used to ®t the data was the program SPFIT, developed by H.M. Pickett. Three
individual data sets were analysed: 63 CuS …v ˆ 0†,
63
CuS …v ˆ 1†, and 65 CuS …v ˆ 0†. For each set,
the spin±orbit constant was ®xed to the value determined by O'Brien et al. [21] of 433:1993 cm 1 .
The rotational constants B and D, spin±orbit parameter AD , and p and q lambda-doubling terms
were then used to ®t the observed lines. Higherorder centrifugal distortion parameters were subsequently added as needed to improve the overall
®t.
The ®nal results of the analyses are shown in
Table 2, which additionally lists the rms of the ®ts.
These values are 67, 47, and 50 kHz for the
63
CuS …v ˆ 0†, 63 CuS …v ˆ 1†, and 65 CuS …v ˆ 0†
isotopomers, respectively. As the table also illustrates, H and AH were only needed for the more
extensive data set, 63 CuS …v ˆ 0†, and at most
three centrifugal distortion corrections to the
lambda-doubling, pD ; qD and qH , were found
necessary. Additionally listed in Table 2 are the
spectroscopic constants for CuS as determined
from the optical study [18]. Here the Bv and Dv
parameters were taken as an average of the values
for the X ˆ 1=2 and X ˆ 3=2 ladders, since these
terms were not ®t globally in this work. The millimeter and optical values are in very good agreement, given the quoted uncertainties, with the
exception of the lambda-doubling parameter, q.
J.M. Thompsen, L.M. Ziurys / Chemical Physics Letters 344 (2001) 75±84
81
Table 2
Spectroscopic constants for CuS …X2 Pi †a
Parameter
Sub-millimeter
63
Ac
AD
AH 106
Bv
Dv
H 1010
p
pD
q
qD
qH 108
Optical
65
CuS
63
CuS
CuSb
65
CuS
…v ˆ 0†
…v ˆ 1†
…v ˆ 0†
…v ˆ 0†
…v ˆ 1†
…v ˆ 0†
)12 986 990
5.63467(75)
1.24(24)
5643.8603(18)
0.0047068(14)
)9.5(3.2)
453.34(21)
)0.000260(11)
)0.162(49)
)0.000120(28)
1.87(57)
)12 986 990
5.51406(54)
±
5608.32822(96)
0.00470655(35)
±
449.88(39)
)0.00027(17)
0.015(11)
)0.000099(42)
±
)12 986 990
5.58085(41)
±
5585.43980(99)
0.00461211(41)
±
448.26(10)
±
0.069(62)
)0.000265(38)
3.96(82)
±
±
±
5644.6(1.1)
0.00483(21)
±
452.1 (2.7)
±
)3.8(2.1)
±
±
±
±
±
5609.9(1.1)
0.00520(21)
±
448.5(2.7)
±
)3.3(2.1)
±
±
±
±
±
5586.2(1.1)
0.00474(21)
±
447.3(2.7)
±
)3.5(2.1)
±
±
0.047
0.050
RMS of ®t:
0.067
ae : 35.5321(42) MHz
Be : 5661.6263(24) MHz
re : 2.04988(32) A
a
In MHz; errors are 3r and apply to the last quoted decimal places.
From [18]; an average of X ˆ 1=2 and X ˆ 3=2 values.
c
Value ®xed to that in [21].
b
Our value is about an order of magnitude less than
the optical constant. We attribute this di€erence to
experimental resolution. It should be noted that
the derived constants reproduce the transition
frequencies to an accuracy better than 200 kHz,
except for a few blended lines not included in the
®nal ®t (see Table 1). Moreover, the majority of
the residuals are less than 100 kHz, the estimated
experimental accuracy.
Also included in Table 2 are calculated values
of Be and ae derived from the 63 CuS constants. An
equilibrium bond length has additionally been
determined.
To a ®rst approximation, it is thought that the
3d transition-metal sul®des resemble the isovalent
oxides [3,4]. Therefore, the electron con®guration
for CuS should be analogous to CuO. For copper
monoxide, three di€erent electron con®gurations
are presumed to contribute to the ground 2 P state
[6]. The ionic con®guration is thought to be the
primary contributor …Cu‡ O †, with two other
covalent con®gurations playing a signi®cant additional role. By inference, the con®gurations that
describe the bonding in CuS are:
Cu‡ …3d10 †S …3p5 †
! 10r2 1d4 4p4 11r2 5p3 …X2 Pi †
10
5. Discussion
Measurement of the pure rotational spectrum
of CuS has con®rmed that the electronic ground
state of this molecule is 2 Pi . It has re®ned the
spectroscopic parameters for this free radical as
well, including lambda-doubling constants, and
the bond length. Such information is useful in interpreting the bonding in the 3d transition-metal
sul®de series.
1
…I†
4
Cu…3d 4s †S…3p †
! 10r2 1d4 4p4 11r2 5p3 …X2 Pi †
9
1
1
…II†
4
Cu…3d 4s 4p †S…3p †
! 10r1 1d4 4p4 11r2 5p3 12r1 …X2 Pi †:
…III†
The ®rst con®guration results from the ionic interaction of the closed shell Cu‡ …3d10 †S0 level with
the S …3p5 † 2 P levels. The 1d, 4p, and 10r orbitals
are primarily copper in character (3d Cu‡ ionic
orbitals), while the 5p and 11r levels have their
82
J.M. Thompsen, L.M. Ziurys / Chemical Physics Letters 344 (2001) 75±84
major contribution from the 3p S orbitals. The
second con®guration results from covalent bonding. Here, the bonding orbitals are formed from
linear combinations of the 3p atomic orbitals on
sulfur and the 3d and 4s atomic orbitals of copper,
resulting in the 11r and 4p bonding molecular
orbitals. Additionally, the 5p and 12r antibonding
molecular orbitals are created. The ®nal con®guration involves an electron being promoted from
the 3d to the 4p orbital. Also contributing to covalent bonding, this scheme occurs because of the
extra stabilisation gained by sulfur p-backbonding
into the empty 4p orbitals of copper. The overall
bonding scheme is illustrated in the molecular orbital diagram shown in Fig. 3.
Experimental evidence for the contribution of
the covalent con®guration could come from studies of magnetic hyper®ne interactions. Unfortunately, hyper®ne splittings have yet to be observed
in the ground state of CuS. However, the spin±
orbit constant o€ers some proof for covalency.
The important spin±orbit constants to examine are
Fig. 3. A qualitative molecular orbital diagram illustrating the
bonding in CuS in its X2 Pi ground state. The bonding orbitals
are 11r and 4p, and the antibonding ones are 12r and 5p.
those for the neutrals and the ions. If the only
con®guration present were the ionic Cu‡ S , then
the spin±orbit parameter should re¯ect primarily
that of S …p5 † which is f ˆ 326 cm 1 [25]. Instead,
the value is approximately 433 cm 1 . This constant is too large to be accounted for by only a free
electron on S , taking into account the sign change
for a p3 con®guration, and therefore must contain
some other contributions. The atomic spin±orbit
parameters for S, S‡ , Cu, and Cu‡ are 382, 483,
818 and 824 cm 1 , respectively. The larger spin±
orbit constant for CuS thus likely re¯ects contributions from neutral sulfur, neutral copper, and
Cu‡ .
Another point of comparison between the oxides and the sul®des is bond length. As described
in [2±4], the bond length of CuO increases signi®cantly relative to the other 3d-oxides. In fact, for
Another oxide
CuO, the r0 bond length is 1.729 A.
with an unusually long bond distance relative to its
[2].
3d neighbours is MnO, where r0 ˆ 1:648 A
This trend for the 3d transition-metal oxides is
shown in Fig. 4, where the experimental values for
bond distances are plotted, creating a `doublehumped' structure [3]. A similar trend is predicted
by ab initio calculations and is graphed in Fig. 4 as
well. It is thought that the unusual increase in
bond distance for CuO partly results from the
decrease in energy of the 3d orbitals of copper
Fig. 4. Experimental and theoretical r0 -values for the transition
metal 3d-oxides and 3d-sul®des, comparing relative trends of
these compounds. Theory predicts the sul®des to mimic the
oxides, but experimental data indicate subtle di€erences.
J.M. Thompsen, L.M. Ziurys / Chemical Physics Letters 344 (2001) 75±84
relative to the other 3d metals, and in comparison
to the 2p oxygen orbital. The 3d electrons eventually `drop out' of the bonding picture. The
closed shell con®guration (3d10 ) of copper also
contributes to this e€ect [2±4].
As shown in Fig. 4, an identical pattern is
theoretically calculated to exist for the 3d-sul®des.
Recent experimental high-resolution data for
these species, however, given in Table 3, indicate
that this behaviour is not as pronounced as in the
oxides. Table 3 presents metal sul®de bond lengths
for the fourth-row elements, including the 3d
transition-metals. The data show a gradual
[13]) to
decrease in bond length from KS (2.817 A
ScS (2.139 A [14]), and then to CuS, where
The bond distance for
the r0 -value is 2.055 A.
copper sul®de therefore never exceeds that of the
other sul®de compounds. In fact, it is smaller than
that of MnS, which has recently been measured in
[26]. These experithis laboratory to be 2.068 A
mental values are also plotted in Fig. 4, for
comparison. The `double-humped' structure seen
in the 3d-oxides is not yet apparent in the sul®de
counterparts.
It should be noted that in a very recent theoretical paper on the 3d-sul®des and oxides,
Bridgeman and Rothery [3] calculated an re bond
In comlength for CuS. The value is re ˆ 2:07 A.
parison, our experimental re bond length is 2.0499
This value is shorter than the predicted theoA.
retical value.
It appears that even with an incomplete data
set, there are subtle bonding di€erences between
the 3d metal sul®des relative to the oxides. Some
variation is expected, as the electronegativity of
sulfur is less than that of oxygen. Therefore, there
will be more tendency in the sul®des to share
electrons via covalent bonds [3]. Moreover, the 3p
Table 3
Bond lengths for diatomic metal sul®des
Molecule
Ground state
r0 (A)
Reference
KS
CaS
ScS
TiS
MnS
CuS
2
2.817
2.320
2.139
2.082
2.068
2.055
[13]
[11]
[14]
[15]
[26]
This work
Pi
R‡
2 ‡
R
3
D
6 ‡
R
2
Pi
1
83
level of sulfur is about 4 eV higher in energy than
the 2p orbital of oxygen [27]. Thus, there may be
better energy overlap between the 3p orbitals of
sulfur and the 4s orbital of copper. Consequently,
the covalent electron con®guration already mentioned may be playing a more important role in the
bonding in CuS as compared to CuO.
6. Conclusions
The pure rotational spectrum of a 3d transitionmetal sul®de has been measured for the ®rst time:
CuS …X2 Pi †. The analysis has resulted in re®nement of the rotational, spin±orbit, and lambdadoubling constants for this molecule. The bonding
in CuS must contain some covalent character, as
suggested by the spin±orbit constant, and therefore has similar properties to CuO. On the other
hand, the bond length in copper monosul®de does
not increase relative to the other known 3d transition-metal sul®des, in particular MnS. In this
sense, CuS di€ers from CuO and sul®de behaviour
appears to vary from that of the 3d-oxides. Differences in electronegativity and p-orbital energies
of sulfur relative to oxygen cause such changes.
High-resolution data for other 3d metal sul®des
are certainly needed to further examine these
trends.
Acknowledgements
This research is supported by NSF Grant CHE98-17707.
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