Journal of Molecular Spectroscopy 257 (2009) 213–216
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Journal of Molecular Spectroscopy
journal homepage: www.elsevier.com/locate/jms
The pure rotational spectrum of ZnS (X1R+)
L.N. Zack, L.M. Ziurys *
Department of Chemistry, Department of Astronomy, Steward Observatory, University of Arizona, 933 N. Cherry Ave., Tucson, AZ 85721, USA
a r t i c l e
i n f o
Article history:
Received 14 June 2009
In revised form 14 August 2009
Available online 21 August 2009
Keywords:
Zinc sulfide (ZnS)
Rotational spectroscopy
Equilibrium parameters
a b s t r a c t
The pure rotational spectrum of ZnS (X1R+) has been measured using direct-absorption millimeter/submillimeter techniques in the frequency range 372–471 GHz. This study is the first spectroscopic investigation of this molecule. Spectra originating in four zinc isotopologues (64ZnS, 66ZnS, 68ZnS, and 67ZnS)
were recorded in natural abundance in the ground vibrational state, and data from the v = 1 state were
also measured for the two most abundant zinc species. Spectroscopic constants have been subsequently
determined, and equilibrium parameters have been estimated. The equilibrium bond length was calculated to be re 2.0464 Å, which agrees well with theoretical predictions. In contrast, the dissociation
energy of DE 3.12 eV calculated for ZnS, assuming a Morse potential, was significantly higher than past
experimental and theoretical estimates, suggesting diabatic interaction with other potentials that lower
the effective dissociation energy. Although ZnS is isovalent with ZnO, there appear to be subtle differences in bonding between the two species, as suggested by their respective force constants and bond
length trends in the 3d series.
Ó 2009 Elsevier Inc. All rights reserved.
1. Introduction
Interest in transition-metal containing compounds is
widespread, encompassing numerous fields and a variety of applications [e.g. 1–4]. Therefore, it is crucial that bonding characteristics in these types of molecules are well-understood, especially on
the most basic (i.e. diatomic) level. If periodic trends in bond
lengths, dipole moments, and dissociation energies, for example,
are understood for diatomic species, that information can be applied to larger molecules or bulk structures.
To date, several classes of 3d diatomic compounds have been
studied extensively from both theoretical and experimental (gasphase and solid-state) perspectives. For example, the oxide and
fluoride series have been well characterized [5–24]. In general,
however, zinc-bearing species have been neglected in such investigations, which tend to focus exclusively on scandium through copper. The omission of zinc is puzzling, because a complete picture of
3d bonding cannot be formed without it. Recent spectroscopic
studies have sought to correct this deficiency with measurements
of high-resolution spectra of ZnF [15], ZnCl [25], and ZnO [5].
Experimental work concerning ZnS has been very limited. In
1933, Sen-Gupta measured crude absorption spectra of ZnS in
the k 7000–1900 region and estimated the heat of dissociation of
this molecule [26]. Mass spectrometry has also been employed
for dissociation energy measurements [27,28]. More recently, Xray emission spectroscopy of ZnS crystals [29] and luminescence
* Corresponding author. Fax: +1 520 621 5554.
E-mail addresses: [email protected] (L.N. Zack), [email protected]
(L.M. Ziurys).
0022-2852/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved.
doi:10.1016/j.jms.2009.08.009
spectroscopy of colloidal ZnS nanoparticles at ultraviolet, visible,
and infrared wavelengths [3] have been used to probe the band
structure of this compound. However, those studies only provided
data relevant to the bulk properties and crystal structures, so questions regarding basic bonding characteristics at a molecular level
for zinc sulfide have remained unanswered.
Zinc sulfide has been included in a number of ab initio studies
that examine bonding of the 3d (Sc–Zn) or group 12 (Zn, Cd, and
Hg) metals with chalcogens. Early calculations using ASED-MO
theory determined a Zn–S bond length, re = 2.12 Å [30], and this
investigation also noted similarities in periodic trends between
bulk and diatomic 3d sulfides; the correlation between single molecule and bulk properties was also recognized in later works conducted at higher levels of theory [31,32]. DFT, MRCI, and CCSD
calculations concerning ZnS have been more recently performed,
but vary in their usage of relativistic corrections, including spin–
orbit interactions, interference correlation effects, and small-core
pseudopotentials [31–39]. In general, however, these studies predict a relatively narrow range of re 2.04–2.12 Å for the Zn–S bond
lengths. Predictions of the vibrational frequency, xe, for this molecule also fall into a limited span, 412–478 cm1, while there is less
agreement regarding its dissociation energy (De 1.06–2.63 eV).
Here we report the first spectroscopic study of ZnS in the gasphase. High-resolution rotational spectra of this species in its
X1R+ ground electronic state were obtained using millimeter/
sub-millimeter direct-absorption methods. Four zinc isotopologues
were observed in the v = 0, and in certain cases, v = 1 states. Here
these measurements are presented, along with a spectral analysis.
The results are also compared with data recently acquired for the
oxide analog, ZnO.
214
L.N. Zack, L.M. Ziurys / Journal of Molecular Spectroscopy 257 (2009) 213–216
2. Experimental
The spectrum of ZnS was measured using one of the Ziurys’
group spectrometers described in detail elsewhere [40]. To summarize, the spectrometer is a double-pass, direct-absorption system. Phase-locked Gunn oscillators and Schottky diode
multipliers are used as the radiation source over a frequency range
of approximately 65–850 GHz. The radiation is propagated quasioptically through a water-cooled steel cell using a series of lenses,
a polarizing grid, and a rooftop reflector before being directed into
a helium-cooled InSb hot-electron bolometer detector.
To produce ZnS, zinc vapor was reacted with H2S gas in the
presence of a DC discharge operated at approximately 250 mA at
200 V. A Broida-type oven was used to melt zinc pieces (99.9%
Aldrich) in an alumina crucible. Approximately 2 mTorr of H2S
was added over the top of the oven, while roughly 20 mTorr of
argon carrier gas was added through the oven bottom. Argon gas
was also flowed over the lenses at each end of the cell to prevent
zinc from coating the optics, a common problem with this metal.
No previous gas-phase spectroscopic studies of ZnS have been
published; therefore, continuous scanning over the frequency
range 375–418 GHz (approximately 8B) was initially conducted
in order to locate and assign transitions. Harmonic patterns for
four zinc isotopologues (64ZnS, 66ZnS, 67ZnS, and 68ZnS) in the
ground vibrational state were identified first, based on their relative intensities and frequency spacings. The remaining lines were
summarily assigned as v = 1 satellite lines for the two most abundant isotopologues. Hyperfine structure arising from the 67Zn nucleus (I = 5/2) was not observed, typical for a closed-shell species.
To determine precise transition frequencies, Gaussian curves
were fit to lines obtained by averaging equal numbers of scans in
increasing and decreasing frequency over a 5 MHz scan width. In
general, one to three scan averages were necessary to achieve a
sufficient signal-to-noise ratio. Typical line widths were 1.2–
1.6 MHz over the frequency range 372–471 GHz. Instrumental
accuracy is estimated to be ±50 kHz.
3. Results and analysis
Four isotopologues of ZnS were identified in natural abundance
(64Zn: 66Zn: 67Zn: 68Zn = 48.6: 27.9: 4.1: 18.8%). Eight rotational
transitions were measured for each isotopologue in the ground
vibrational state, as well as for 64ZnS in its v = 1 state; seven tran-
sitions were measured for the v = 1 state of 66ZnS. In total, 47 lines
were recorded and are listed in Table 1.
Representative spectra of the main isotopologue, 64ZnS (X1R+),
are shown in Fig. 1. Here, lines originating in the v = 0 and v = 1
vibrational levels are displayed. There is a frequency break in the
data in order to show both features.
The rotational constants, B0 and D0, of zinc sulfide were determined by fitting the data with the program SPFIT [41]. The results
are listed in Table 2. Higher order centrifugal distortion constants
were not needed in order to successfully fit the data of this diatomic species (rms of fits: 10–16 kHz). Because vibrationally excited states were observed for 64ZnS and 66ZnS, a least-squares
analysis could be used to establish equilibrium parameters (Be,
De, ae, and be) according to the expressions [42]:
1
2
1
Dv ¼ De þ be v þ
2
Bv ¼ Be ae
vþ
ð1Þ
ð2Þ
From these parameters the harmonic vibrational frequency, xe,
anharmonic correction, xexe, and dissociation energy, DE, were
estimated according to the following relationships [42]:
xe 4B3e
De
!12
xe xe Be
DE ð3Þ
ae xe
6B2e
!2
þ1
ð4Þ
x2e
4xe xe
ð5Þ
The values for these parameters, along with the equilibrium
bond length, re, are listed in Table 2.
4. Discussion
The pure rotational spectra of ZnS have been measured. These
spectra display a characteristic zinc isotope pattern and are consistent with a molecule having a X1R+ ground state, as predicted by
theory [30–39]. These data are the first high-resolution spectroscopic measurements of this molecule.
The equilibrium bond distance of ZnS was determined to be
re 2.0464 Å, based on two vibrational states. This value is in
excellent agreement with theoretical predictions, which range
Table 1
Transition frequencies for ZnS (X1R+)a.
J0
J00
v
64
m
33
34
35
36
37
38
40
41
42
34
35
36
37
38
40
41
42
a
32
33
34
35
36
37
39
40
41
33
34
35
36
37
39
40
41
In MHz.
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
66
ZnS
mobscalc
372
383
394
405
417
428
450
461
072.494
312.402
549.133
782.628
012.800
239.552
682.455
898.392
0.028
0.010
0.011
0.008
0.006
<0.000
0.005
0.130
381
392
403
414
425
448
459
470
096.161
267.552
435.640
600.387
761.723
073.724
224.195
370.846
0.015
0.022
0.005
0.013
0.007
0.007
0.007
0.008
67
ZnS
m
68
ZnS
mobscalc
m
377
388
399
410
421
443
455
466
379
390
401
412
423
446
457
468
377
388
453.171
577.179
698.004
815.526
929.716
147.698
251.325
351.209
270.558
330.111
0.032
0.007
0.029
0.006
0.001
0.008
0.008
0.009
0.016
0.020
410
421
443
454
465
439.672
489.437
578.528
617.644
653.042
0.001
0.002
0.011
0.002
0.003
605.094
675.054
741.917
805.501
865.783
976.060
025.849
071.949
ZnS
mobscalc
m
0.013
0.016
0.021
0.005
0.002
0.016
0.005
0.020
375
386
397
408
419
441
452
463
mobscalc
817.323
835.077
849.714
861.131
869.277
875.363
873.127
867.240
0.020
0.003
0.016
0.003
0.002
0.002
0.003
0.009
215
L.N. Zack, L.M. Ziurys / Journal of Molecular Spectroscopy 257 (2009) 213–216
64
1 +
ZnS (X Σ ): J = 37
2.2
36
Sulfides
v=0
2.1
2 +
Σ
3
Δ
r (A)
2.0
v=1
4 -
5
Σ
Π
6 -
Σ
5
2
Δ
4
Δ
Oxides
3 -
Σ
2
1.7
2 +
Σ
3
1.6
Δ
4 -
Ti
V
Σ
5
Π
6 -
Σ
5
Δ
4
1 +
Π Σ
Δ
3 -
Co
Ni
Π
1 +
Σ
Σ
1.5
Sc
414581
414606
417000
Frequency (MHz)
Fig. 1. Spectrum of the J = 37
36 transition of 64ZnS (X1R+) in the v = 0 and v = 1
states near 416 GHz. There is a frequency break in the figure to show both lines. The
spectrum is a composite of two 110 MHz wide scans, each of which was collected in
60 s and cropped to 40 MHz.
Table 2
Rotational and equilibrium constants for ZnS (1R+).a
64
ZnS
5645.8417(51)
0.0038472(18)
0.013
5662.1143(81)
ae
32.5452(71)
0.0038372(29)
De
0.0000200(25)
be
2.0464
re (Å)
xe (cm1) 459
xexe (cm1) 2.09
3.12
DE (eV)
B0
D0
rms of fit
Be
a
66
ZnS
67
ZnS
Cr M n Fe
Cu
Zn
417025
68
ZnS
5588.9106 (50) 5561.6491(50) 5535.2749(50)
0.0037701(17) 0.0037339(17) 0.0036978(17)
0.016
0.014
0.010
5604.9376(80)
32.0540(73)
0.0037606(27)
0.0000190(24)
2.0464
457
2.07
3.12
In MHz unless otherwise indicated.
from 2.04 to 2.12 Å [30–39]. Our value agrees especially well with
Peterson et al., who calculated re 2.046 Å at the MRCI+Q level and
included relativistic effects, such as spin–orbit coupling [37]. Such
effects are expected to cause a decrease in bond length [33,43];
however, Chambaud et al. also performed calculations at the
MRCI+Q level with no relativistic corrections, and arrived at a very
similar number: re 2.048 Å [32]. Work done at other levels of
theory without relativistic corrections determined re 2.06–
2.12 Å [33,36,38], while those with relativistic corrections range
from 2.04 to 2.08 Å [35,38]. Thus, it remains unclear as to how
necessary these additional factors are in establishing the Zn–S
bond distance.
Comparison of bond lengths between the diatomic 3d oxide and
sulfide series is shown in Fig. 2, with the new ZnS data. The two
series show similar trends in bond distances, both exhibiting a
‘‘double-hump” structure, which has been attributed to asymmetrical filling of the d-orbitals [31]. One feature of particular interest
is the decrease in bond length from copper to zinc observed in both
the oxide and sulfide series. From CuO to ZnO, this decrease is from
1.7295 Å to 1.7047 Å [44,5], or a change of 0.02 Å, while from CuS
to ZnS, the difference (2.050 Å vs. 2.0464 Å) is 0.004 Å [50], almost an order of magnitude lower.
This difference may be related to variations in the ionic vs. covalent character between the two zinc species. For example, it has
been suggested that the overlap of the zinc 4s and sulfur 3p orbi-
Fig. 2. A comparison of experimentally determined bond lengths (r0: TiO, VO, CrO,
MnO, FeO, CuO, ScS, VS, MnS, FeS, and CoS; re: ScO, CoO, NiO, ZnO, TiS, CrS, NiS, CuS,
and ZnS) of the diatomic 3d oxides and sulfides [5–14,44–52]. The trends are similar
in both series, but there are variations, particularly from Mn to Zn. Such differences
likely arise from the degree of overlap between the metal 4s3d and oxygen 2s2p
orbitals relative to the metal-sulfur 3s3p orbitals.
tals is greater than that between zinc (4s) and the oxygen 2p orbitals, leading to more covalent character in the ZnS species [33,37].
In fact, in ZnO, the 4p valence orbital is almost entirely on the oxygen atom with little zinc contribution [31]. Thus, in going from
copper to zinc, the additional electron merely closes the shell of
this ionic species, shortening the bond. ZnS, on the other hand, is
more covalent, and its valence 5p orbital has some true antibonding character [31]. Addition of the electron to this orbital has some
destabilizing effect on the molecule. The Zn–S bond, therefore,
does not shorten as much.
The vibrational frequency of ZnS has been predicted by theory
to be xe 412–478 cm1 [31–34,37,39]. Our value of xe 459 cm1 falls solidly in the center of this range, but is closest to
the CPF predictions of Bauschlicher and Langhoff [33] and the MRCI
predictions of Peterson et al. [37], which yielded values of 460 and
459.4 cm1, respectively. Only one work predicted an anharmonic
constant, xexe 2 cm1 [37], which is close to our estimated value
(xexe 2.09 cm1). In contrast, the vibrational frequency and
anharmonic constant of 64ZnO (X1R+) are 738 and 4.88 cm1 [5].
Although differences in the reduced masses of ZnO and ZnS contribute to the drop in vibrational frequency and anharmonicity of
ZnS relative to ZnO, these data also indicate that there is an almost
equally important contribution from the change in force constant.
This difference in force constants reflects the variation in ionic and
covalent contributions for the two molecules.
Data from mass spectrometric measurements set upper limits
of D0 2.1 eV based on the reaction: ZnS ! Zn þ 12 S2 [27,28], while
Sen-Gupta’s extrapolation from the absorption spectra produced a
value of 1.34 eV [26]. Theoretical values encompass the range
DE 1.06–2.63 eV [30,31,33–35,37,39], with one of the lowest values from calculations by Wu et al., who corrected for zero-point
vibrational energies [39]. (Note that, for simplicity, D0 and DE are
used interchangeably here, as the zero-point energy correction
should not considerably alter the values.) The dissociation energy
calculated in this study (DE 3.12 eV, assuming a Morse potential)
is higher than all previous works, both theoretical and experimental. This disagreement might be an indication that ZnS is more stable than previously thought, or that the assumption of a Morse
potential is too simplistic. Because the dissociation energy is based
on only a few low-lying levels, however, it may not be an accurate
representation of the behavior of the potential curve as a whole.
This is especially true when there are several other nearby
potentials. In that case, the potential energy curve of interest
216
L.N. Zack, L.M. Ziurys / Journal of Molecular Spectroscopy 257 (2009) 213–216
may interact diabatically with the other curves and bend to avoid
curve crossings. This situation could lead to an overestimation of
the dissociation energy in the single potential Morse approximation. Further theoretical studies of ZnS may be required.
5. Conclusions
[19]
[20]
[21]
[22]
[23]
[24]
[25]
High-resolution rotational spectroscopy has been used to measure the spectrum of ZnS. The X1R+ ground state has been confirmed, and spectroscopic constants and equilibrium parameters
have been established. These values are in good agreement with
theoretical predictions, with the exception of the dissociation energy. Additional studies of ZnS are needed to further constrain
the physical properties of this molecule.
Acknowledgment
This work was supported by NSF Grant CHE-07-18699.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
G.D. Cody, Annu. Rev. Earth Planet. Sci. 32 (2004) 569–599.
S. Hony, J. Bouwman, L.P. Keller, L.B.F.M. Waters, A&A 393 (2002) L103–L106.
D. Denzler, M. Olschewski, K. Sattler, J. Appl. Phys. 84 (1998) 2841–2845.
X. Liu, J. Cui, L. Zhang, W. Yu, F. Gu, Y. Qian, Mater. Lett. 60 (2006) 2465–2469.
L.N. Zack, R.L. Pulliam, L.M. Ziurys, J. Mol. Spectrosc. 256 (2009) 186–191.
W.J. Childs, T.C. Steimle, J. Chem. Phys. 88 (1988) 6168–6174.
K. Namiki, S. Saito, J.S. Robinson, T. Steimle, J. Mol. Spectrosc. 191 (1998) 176–
182.
M.A. Flory, L.M. Ziurys, J. Mol. Spectrosc. 247 (2008) 76–84.
P.M. Sheridan, M.A. Brewster, L.M. Ziurys, Astrophys. J. 576 (2002) 1108–1114.
K. Namiki, S. Saito, J. Chem. Phys. 107 (1997) 8848–8853.
M.D. Allen, L.M. Ziurys, J.M. Brown, Chem. Phys. Lett. 257 (1996) 130–136.
S.K. McLamarrah, P.M. Sheridan, L.M. Ziurys, Chem. Phys. Lett. 414 (2005) 301–
306.
V.I. Srdanov, D.O. Harris, J. Chem. Phys. 89 (1988) 2748–2753.
T. Steimle, K. Namiki, S. Saito, J. Chem. Phys. 107 (1997) 6109–6113.
M.A. Flory, S.K. McLamarrah, L.M. Ziurys, J. Chem. Phys. 125 (2006) 19304.
M.A. Lebeaultdorget, C. Effantin, A. Bernard, J. Dincan, J. Chevaleyre, E.A.
Shenyavskaya, J. Mol. Spectrosc. 163 (1994) 276–283.
R.S. Ram, P.F. Bernath, J. Mol. Spectrosc. 231 (2005) 165–170.
R.S. Ram, P.F. Bernath, S.P. Davis, J. Chem. Phys. 116 (2002) 7035–7039.
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]
[45]
[46]
[47]
[48]
[49]
[50]
[51]
[52]
O. Launila, J. Mol. Spectrosc. 169 (1995) 373–395.
P.M. Sheridan, L.M. Ziurys, Chem. Phys. Lett. 380 (2003) 632–646.
M.D. Allen, L.M. Ziurys, J. Chem. Phys. 106 (1997) 3494–3503.
R.S. Ram, P.F. Bernath, S.P. Davis, J. Mol. Spectrosc. 173 (1995) 158–176.
M. Benomier, A. van Groenendael, B. Pinchemel, T. Hirao, P.F. Bernath, J. Mol.
Spectrosc. 233 (2005) 244–255.
F. Ahmed, R.F. Barrow, A.H. Chojnicki, C. Durfour, J. Schamps, J. Phys. B. At. Mol.
Phys. 15 (1982) 3801–3818.
E.D. Tenenbaum, M.A. Flory, R.L. Pulliam, L.M. Ziurys, J. Mol. Spectrosc. 244
(2007) 153–159.
P.K. Sen-Gupta, Proc. R. Soc. Lond. Ser. A 143 (1934) 438–454.
J.R. Marquart, J. Berkowitz, J. Chem. Phys. 39 (1963) 283–285.
G. de Maria, P. Goldfinger, L. Malaspina, V. Piacente, Trans. Faraday Soc. 61
(1965) 2146–2152.
R. Laihia, J.A. Leiro, K. Kokko, K. Mansikka, J. Phys. Condens. Matter. 8 (1996)
6791–6801.
A.B. Anderson, S.Y. Hong, J.L. Smialek, J. Phys. Chem. 91 (1987) 4250–4254.
A. Bridgeman, J. Rothery, J. Chem. Soc. Dalton Trans. 00 (2000) 211–
218.
G. Chambaud, M. Guitou, S. Hayashi, Chem. Phys. 352 (2008) 147–156.
C.W. Bauschlicher, S.R. Langhoff, Chem. Phys. Lett. 126 (1986) 163–168.
A.I. Boldyrev, J. Simons, Mol. Phys. 92 (1997) 365–379.
P. Deglmann, R. Ahlrichs, K. Tsereteli, J. Chem. Phys. 116 (2002) 1585–
1597.
K.P. Jensen, B.O. Roos, U. Ryde, J. Chem. Phys. 126 (2007) 014103.
K.A. Peterson, B.C. Shepler, J.M. Singleton, Mol. Phys. 105 (2007) 1139–
1155.
S.G. Raptis, M.G. Papadopoulos, A.J. Sadlej, J. Chem. Phys. 111 (1999) 7904–
7915.
Z.J. Wu, M.Y. Wang, Z.M. Su, J. Comp. Chem. 28 (2006) 703–714.
L.M. Ziurys, W.L. Barclay Jr., M.A. Anderson, D.A. Fletcher, Rev. Sci. Instrum. 65
(1994) 1517–1522.
H.M. Pickett, J. Mol. Spectrosc. 148 (1991) 371–377.
W. Gordy, R.L. Cook, Microwave Molecular Spectra, Wiley, New York, 1984.
P. Pyykkö, Chem. Rev. 88 (1988) 563–594.
T.C. Steimle, A.J. Marr, D.M. Goodridge, J. Chem. Phys. 107 (1997) 10406–
10414.
Q. Ran, W.S. Tam, A.S.-C. Cheung, A.J. Merer, J. Mol. Spectrosc. 220 (2003) 87–
106.
J.M. Thompsen, M.A. Brewster, L.M. Ziurys, J. Chem. Phys. 116 (2002) 10212–
10220.
S. Takano, S. Yamamoto, S. Saito, J. Mol. Spectrosc. 224 (2004) 137–144.
M.A. Flory, S.K. McLamarrah, L.M. Ziurys, J. Chem. Phys. 123 (2005) 164312.
T. Yamamoto, M. Tanimoto, T. Okabayashi, Phys. Chem. Chem. Phys. 9 (2007)
3744–3748.
J.M. Thompsen, L.M. Ziurys, Chem. Phys. Lett. 344 (2001) 75–84.
R.L. Pulliam, A.J. Higgins, L.M. Ziurys, in preparation.
R.L. Pulliam, L.M. Ziurys, in preparation.