JOURNAL OF CHEMICAL PHYSICS
VOLUME 115, NUMBER 24
22 DECEMBER 2001
The pure rotational spectra of SrSH „ X̃ 2 A ⬘ … and SrS „ X 1 ⌺ ¿ …:
Further studies in alkaline-earth bonding
D. T. Halfen, A. J. Apponi, J. M. Thompsen, and L. M. Ziurys
Department of Astronomy, Department of Chemistry, and Steward Observatory, University of Arizona,
Tucson, Arizona 85721
共Received 15 August 2001; accepted 28 September 2001兲
The pure rotational spectrum of the SrSH radical in its ground electronic (X̃ 2 A ⬘ ) and vibrational
states has been measured using millimeter/submillimeter-wave direct absorption techniques. This
work is the first observation of SrSH with rotational resolution. The spectrum of its deuterium
isotopomer SrSD and SrS (X 1 ⌺ ⫹ ) has been recorded as well. These species were created by the
reaction of strontium vapor and H2S, in the presence of a dc discharge. SrS was also made with CS2.
For SrSH and SrSD, eight rotational transitions were recorded, respectively, for which asymmetry
components up to K a ⫽8 were measured; fine structure was also resolved in each component.
Thirteen transitions of SrS in each of its v ⫽0, 1, and 2 states have additionally been observed.
These data have been analyzed and spectroscopic parameters determined for all three species,
including spin-rotation terms for the strontium hydrosulfides. From an r 0 structure calculation, the
bond angle in SrSH was determined to be 91.48共3兲°, very close to that of H2S and CaSH. This
geometry indicates that SrSH is a covalently bonded molecule, as opposed to linear 共and ionic兲
SrOH. The Sr–S bond length in SrSH was also found to be greater than that of SrS 共r Sr—S
⫽2.705 Å versus 2.441 Å兲, indicating a change in bond order. In addition, the spin-rotation
interaction in SrSH and SrSD includes a small contribution from the off-diagonal term, (␧ ab
⫹␧ ba )/2, resulting from the crossing of energy levels with ⌬J⫽0, ⌬K a ⫽⫾1. Second-order
spin-orbit coupling appears to make a significant contribution to the spin-rotation splitting, as well,
which must arise from mixing of the à 2 A ⬘ and B̃ 2 A ⬙ excited states. © 2001 American Institute
of Physics. 关DOI: 10.1063/1.1419060兴
I. INTRODUCTION
Metal–oxygen and metal–sulfur bonds are important in
many areas of chemistry. For example, proteins often involve
coordinates of metals with oxygen and sulfur-donating
ligands.1 Metal oxide and sulfide compounds also play a role
in high temperature chemistry, corrosion processes, and even
chemical vapor deposition.2 Furthermore, simple molecules
of this type are often present in stellar atmospheres, such as
TiO, and are actually used to classify types of stars.3 Naturally, it is of interest to examine the properties of metal oxide
and metal sulfide species, and, in fact, many theoretical studies already exist which investigate this topic.4 –7 Such calculations suggest that, although the sulfide analogs of metal–
oxygen molecules are isovalent, there are subtle bonding
differences between these two classes of compounds which
result in structural variations. A striking example of such
differences is the alkaline-earth monohydroxide species versus their sulfur equivalents, the hydrosulfides.
Many spectroscopic studies of alkaline-earth metal hydroxides 共M–OH, M⫽Mg, Ca, Sr, Ba兲 have already been
conducted, including measurements of various electronic
transitions.8 –11 Millimeter-wave spectra of these molecules
have been carried out as well.12–16 These works have shown
that CaOH, SrOH, and BaOH are rigidly linear in their
X 2 ⌺ ⫹ electronic states, and are ionically bound. MgOH, on
the other hand, has been found to be quasilinear,17 that is, it
0021-9606/2001/115(24)/11131/8/$18.00
has a linear structure on average, but with large amplitude
bending motions. In this species there is therefore a lower
energy barrier to a bent structure, the expected geometry for
a covalently bound molecule like H2O. Consequently,
MgOH has less ionic character than the other hydroxides.
Interestingly, the F excited electronic state of CaOH also has
a bent geometry.8
A somewhat different trend is seen in the alkaline-earth
hydrosulfides, molecules with the general formula M–SH.
The most heavily studied member of this family has been
CaSH. It was first investigated by Fernando et al. 共1991兲,
who observed the à 2 A ⬘ -X̃ 2 A ⬘ , B̃ 2 A ⬙ -X̃ 2 A ⬘ , and
C̃ 2 A ⬘ -X̃ 2 A ⬘ transitions of this molecule, as well as those of
SrSH, at low 共1 cm⫺1兲 resolution, determining approximate
term energies and vibrational frequencies.18 Further studies
of the à 2 A ⬘ -X̃ 2 A ⬘ transition of CaSH were conducted by
Jarman and Bernath,19 who obtained rotational constants for
both states. In addition Scurlock et al.20 recorded the
B̃ 2 A ⬙ -X̃ 2 A ⬘ system of this molecule at rotational resolution. These studies demonstrated that, in contrast to the linear
hydroxides, CaSH and SrSH have bent structures. More recently, millimeter-wave studies of MgSH, CaSH, and CaSD
have been conducted by Taleb-Bendiab and co-workers;21,22
these authors found MgSH to be bent as well. Thus, the
geometry of these species indicates a far greater degree of
covalent bonding than the linear hydroxides.
11131
© 2001 American Institute of Physics
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11132
Halfen et al.
J. Chem. Phys., Vol. 115, No. 24, 22 December 2001
In order to extend these past experiments, we have measured the pure rotational spectra of SrSH and SrSD in their
2
A ⬘ ground states at millimeter/submillimeter wavelengths.
This work is the first laboratory observation of SrSD. Rotational and spin-rotation parameters have been accurately determined for both SrSH and SrSD, which enabled an r 0
structure to be calculated. The pure rotational spectrum of
SrS in its 1 ⌺ ⫹ ground state and its v ⫽0, 1, and 2 vibrational
states has also been measured for comparison. Here we
present these data and examine their implications for bonding in the alkaline-earth hydrosulfides.
II. EXPERIMENT
The rotational spectra of the SrSH and SrSD radicals
were recorded using one of the millimeter-wave spectrometers of the Ziurys group, which is described in detail
elsewhere.23 Briefly, the instrument consists of a Gunn
oscillator/Schottky diode multiplier source operating in the
range 65–550 GHz, a gas cell incorporating a Broida-type
oven, and an InSb detector.
The SrSH radical was produced in a low-pressure dc
discharge through a flowing mixture of strontium vapor,
H2S, and argon. The metal vapor was generated using a
Broida-type oven. The strongest signals were observed by
reacting strontium vapor with about 1 mTorr of H2S, added
over the top of the oven, while flowing 20 mTorr of Ar
carrier gas from beneath the heated metal. A discharge current of 350 mA was typically used. Bright blue-colored
plasma was always observed when the radical was produced,
arising presumably from atomic emission of strontium. Facile production of the SrSD radical was achieved by replacing
H2S in the above mixture with D2S 共99% enrichment, Cambridge Isotope Laboratories兲.
Although strong lines of SrS were also observed under
the same reaction conditions as SrSH, CS2 was used as a
precursor for these measurements. The SrS molecule was
produced in a dc discharge of strontium vapor, 10 mTorr of
CS2, and 10 mTorr of argon with a discharge current of 300
mA. Like SrSH, optimal signals were obtained when the CS2
was added over the top of the oven while the argon was
flowed from underneath the heating element. Evidence of
SrS in the production of SrSH showed that the chemical
mixture was sufficiently reactive to remove both hydrogen
atoms from H2S.
To identify the spectrum of SrSH, a fairly wide search
was initially conducted in the frequency range 350–370
GHz, approximately six times the effective rotational constant calculated ab initio by Chan and Hamilton.24 In the
course of this search, numerous doublets split by about 57
MHz were observed, which were then identified as a pattern
of a-type transitions for a near prolate asymmetric rotor with
a single unpaired electron. 共The a-dipole moment in SrSH
should be larger than the b-dipole by about a factor of 25, in
analogy to CaSH.22兲 The rotational constants estimated from
these data indicated that the lines originated from SrSH. Additional transitions of this molecule were then identified by
continuously scanning over the region 373–394 GHz. Thereafter, more selective searches could be conducted to identify
further spectral features, as the pattern had clearly been es-
tablished. The final assignments were based on the harmonic
relationships among individual K a components, and using
the approximate expression for a near prolate top:25
␯ J⫺1→1 ⫽ 关 B⫹C⫾ 21 共 B⫺C 兲 ␦ K a ,1⫺D NK K 2a 兴 J
冋
⫺ 4D J ⫹
册
共 B⫺C 兲 2
J 3.
c 关 A⫺ 共 B⫹C 兲 /2兴
共1兲
Upon the correct assignment of one of the K a ⬎0 ladders, the
remaining K a structure could be determined without further
difficulty. A similar method was used to identify the rotational spectrum of SrSD in a continuous survey over the
range 330 to 357 GHz.
The frequency measurements were typically made from
scans 5 MHz wide, obtained by averaging an equal number
of those increasing and decreasing in frequency. Each line
profile was fit to an appropriate Gaussian function to determine the line center. Linewidths ranged from 970 to 1300
kHz for unblended features and as high as 2000 kHz for
blended K a components. Experimental accuracy is estimated
to be ⫾70 kHz.
III. RESULTS
Because SrSH is a near-prolate asymmetric rotor with a
X̃ A ⬘ electronic ground state, it is best modeled using a
Hund’s case 共b兲 basis. As a result, each energy level is labeled by N K a , K c , where N is the rotational quantum number.
The quantum number J indicates the fine structure, where J
⫽N⫹S.
To summarize, a total of eight separate rotational transitions were measured for SrSH and SrSD. These data sets are
available electronically.26 Transition frequencies were measured for 146 lines of SrSH and 185 lines for SrSD in the
frequency range 330–370 GHz. 共In certain instances, some
components were obscured by SrS or other unknown features.兲 Generally, asymmetry components with K a ⫽0
through 6 were measured for SrSH, and with K a ⫽0 through
8 for the SrSD transitions. In every K a component, the spinrotation doublets were resolved with splittings of ⬃57.5
MHz and ⬃56 MHz for the main and deuterated isotopomers, respectively. Hyperfine splitting, arising from the
proton in SrSH and the deuteron in SrSD, on the other hand,
was not observed. Also, no b-type transitions were recorded.
The observed spectral pattern and relative intensities of
each K a asymmetry doublet are illustrated in Fig. 1, which
shows a stick figure of the N⫽61→62 transition of SrSH
around 353 GHz, and the N⫽60→61 transition of SrSD
around 338 GHz, neglecting spin-rotation interactions. The
asymmetry doublets are readily resolved in both molecules
for K a ⫽1 and 2, as the figure illustrates. The K a ⫽3 lines, on
the other hand, are partially blended for SrSH but not for
SrSD. Higher asymmetry doublets (K a ⭓4) are collapsed for
both molecules. The observed relative intensities of the K a
components are consistent with a Boltzman distribution with
a rotational temperature of T rot⭐350 K. This relatively low
rotational temperature is observed even though the metal vapor was created at a much higher temperature in the Broida
oven 共⬃950 K兲. Apparently, by cooling the walls of the cell
2
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J. Chem. Phys., Vol. 115, No. 24, 22 December 2001
Rotational spectra of SrSH and SrS
11133
FIG. 2. Representative spectrum of SrSH (X̃ 2 A ⬘ ) showing a section of the
N⫽61→62 rotational transition. Each K a component is split into doublets
by fine structure interactions, as indicated by ⬃(␧ bb ⫹␧ cc )/2. The K a ⫽0
lines can be seen in the spectrum, as well as the lower frequency K a ⫽2
asymmetry doublet. The K a ⫽3 asymmetry components are effectively collapsed, as are the K a ⫽4 doublets. This figure is a composite of four 110
MHz scans, each about 2 min in duration.
FIG. 1. Stick diagram of the N⫽61→62 rotational transition of SrSH
(X̃ 2 A ⬘ ) near 353 GHz, and the N⫽60→61 rotational transition of SrSD
(X̃ 2 A ⬘ ) near 338 GHz, showing the positions and approximate relative
intensities of the K a asymmetry components. The spin-rotation splittings are
neglected for simplicity. The K a ⫽1 components are the most widely split,
while the K a ⫽3 components are virtually collapsed in SrSH, but are nicely
resolved doublets in SrSD. The higher K a doublets have completely collapsed and their intensities are thus increased. The intensities follow a Boltzmann distribution with T rot⭐350 K for both SrSH and SrSD.
conditions under which these reactive free radicals are generated.
Thirteen rotational transitions were observed for SrS
(X 1 ⌺ ⫹ ) for each of its v ⫽0, 1, and 2 vibrational states in
the range from 450 to 540 GHz, a total of 39 lines. This data
set is also available electronically.26
IV. ANALYSIS
The data for SrSH and SrSD were analyzed with a modified S-reduced Hamiltonian of Watson27 in the I r basis. The
with chilled water, enough collisions occurred to substantially reduce the temperature of the reaction mixture. In doing so, the intensity of the spectral lines of SrSH reach a
maximum near 350 GHz, as opposed to higher frequencies,
enhancing the peak absorption coefficient by about a factor
of two in the regions scanned.
In Fig. 2, a representative spectrum of a section of the
N⫽61→62 rotational transition of SrSH is presented. Visible in these data are the 共collapsed兲 K a ⫽3 and 4 asymmetry
components, the K a ⫽0 lines, and the lower frequency component of the K a ⫽2 doublets. The pattern is somewhat complicated because each K a component is additionally split into
spin-rotation doublets by the amount (␧ bb ⫹␧ cc )/2
⬇57.5 MHz. The other K a ⫽2 asymmetry component occurs
at a higher frequency than shown in the figure.
Figure 3 displays a segment of the spectrum of the N
⫽60→61 rotational transition of SrSD. In contrast to SrSH,
the asymmetry doublets for K a ⫽3 are clearly split apart in
this spectrum. The K a ⫽4 doublets, however, are collapsed,
and the lower frequency K a ⫽2 asymmetry doublet is visible
in this spectrum, as well. Again, every K a component is further split into fine structure doublets, as indicated in the figure. The SrSD signals also appear stronger than those of
SrSH 共cf. Fig. 2兲. This effect is due to the varying chemical
FIG. 3. Representative spectrum displaying part of the N⫽60→61 rotational transition of SrSD (X̃ 2 A ⬘ ). Both asymmetry doublets corresponding
to K a ⫽3 can be seen in the figure, separated by about 20 MHz, each which
is again split because of fine structure interactions. The spin-rotation splitting is indicated on the spectrum by ⬃(␧ bb ⫹␧ cc )/2. The K a ⫽4 doublets are
completely collapsed, and the lower frequency K a ⫽2 asymmetry doublet is
also present. This spectrum is a composite of three 110 MHz scans, each
about 1 min in duration.
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11134
Halfen et al.
J. Chem. Phys., Vol. 115, No. 24, 22 December 2001
TABLE I. Spectroscopic constants for SrSH (X̃ 2 A ⬘ ), SrSD (X̃ 2 A ⬘ ), and SrS (X 1 ⌺ ⫹ ). a
A
B
C
D N /D 0
D NK
d1
d2
H0
H NK
H KN
h3
L NK
L KKN
P KN
␧ aa
␧ bb
␧ cc
(␧ ab ⫹␧ ba )/2
D Ns
⌬ 0 共amuÅ2兲
Be
De
␣e
rms of fit
SrSH
SrSD
291 070共89兲
2877.4075共26兲
2845.5456共25兲
0.001 381 75共12兲
0.194 96共17兲
⫺1.637(15)⫻10⫺5
⫺2.117(20)⫻10⫺6
149 691.0共69兲
2812.3329共23兲
2755.7352共21兲
0.001 352 323共96兲
0.173 432共71兲
⫺3.037(13)⫻10⫺5
⫺6.017(13)⫻10⫺6
6.15(18)⫻10⫺7
1.67(13)⫻10⫺4
⫺3.86(20)⫻10⫺11
⫺1.32(49)⫻10⫺9
⫺1.84(53)⫻10⫺6
1.26(70)⫻10⫺8
52.6共2.6兲
56.187共76兲
58.716共73兲
⫺4.03共41兲
⫺3.33(81)⫻10⫺9
0.2303共6兲
5.537(87)⫻10⫺7
3.32(12)⫻10⫺5
5.7(17)⫻10⫺12
⫺2.0(14)⫻10⫺10
⫺1.241(54)⫻10⫺7
SrS
SrSb
3614.2266共29兲
3614.45共26兲
0.001 405 85共29兲
0.001 467共58兲
1.72(30)⫻10⫺12
37.1共1.5兲
54.909共63兲
57.101共63兲
⫺5.68共54兲
⫺2.80(64)⫻10⫺9
0.3146共3兲
0.111
0.058
3621.43共11兲
0.001 402 38共83兲
⫺14.391共64兲
0.060
3621.59共30兲
0.001 460共57兲
⫺14.229共63兲
In MHz, for v ⫽0; errors quoted are 3␴ in the last quoted digit.
Rovibrational results from Ref. 34.
a
b
Hamiltonian consists of terms for molecular-frame rotation
and spin-rotation interactions, including their centrifugal distortion corrections, namely,
Ĥ eff⫽Ĥ rot⫹Ĥ sr .
共2兲
The second term in Eq. 共2兲 concerns the spin-rotation
tensor.28 For a molecule with nonorthorhombic symmetry,
five elements of this 3⫻3 tensor can, in principle, be
determined.29 These include the diagonal spin-rotation terms
␧ aa , ␧ bb , and ␧ cc , and the off-diagonal elements ␧ ab and
␧ ba . However, the latter terms make indistinguishable contributions to the rotational energies, and hence, in practice,
only one constant can be determined, (␧ ab ⫹␧ ba )/2.
Spectroscopic parameters for SrSH and SrSD were actually obtained by fitting the data with the nonlinear leastsquares SPFIT code developed by H. M. Pickett.30 The resulting constants are given in Table I. Ten centrifugal distortion
constants were found necessary for SrSH and nine for SrSD.
These parameters include three sixth order terms 共H NK ,
H KN , and h 3 兲, two eighth order corrections 共L NK and L KKN 兲,
and, for SrSH, one tenth order term ( P KN ). Use of these
higher order corrections is not unexpected. Sextic parameters
were used to fit both MgSH21 and CaSH,22 where transitions
up to K a ⫽6 and K a ⫽4 were analyzed. For CaSD, the octic
term L NK was found necessary, as well,22 for measurements
with K a ⭐5. However, these data sets did not encompass as
wide a range of rotational transitions or as many K a components as those of SrSH and SrSD. Data sets of comparable
size, such as those of CaNH2 共Ref. 31兲 and SrNH2, 32 required several eighth and tenth order centrifugal distortion
constants.
The spin-rotation constants for SrSH and SrSD were all
found to be positive. In contrast, ␧ aa was found to be
negative for MgSH, CaSH, and CaSD, with decreasing
magnitude 关MgSH: ␧ aa ⫽⫺51.2(1.8) MHz; CaSH: ␧ aa
⫽⫺14.4(9.3) MHz; CaSD: ␧ aa ⫽⫺6.1(7.2) MHz兴. In fact,
within the quoted 3␴ error, ␧ aa for CaSD is effectively zero.
Hence, this trend suggests that ␧ aa for SrSH should be positive. Furthermore, in the symmetric top limit, ␧ aa enters into
the energy eigenvalues only as a K 2 term, while (␧ bb
⫹␧ cc )/2 is also dependent on a separate term in N only.
Evaluation of ␧ aa is therefore linked to the K ladder
structure.33 The data sets of SrSH and SrSD contain more
measurements of K a components than those of MgSH,
CaSH, or CaSD. Consequently, the ␧ aa parameter has been
generally better determined for the strontium molecules
关␧ aa ⫽52.6(2.6) MHz and 32.1共1.5兲, respectively兴. Also, the
J quantum number and thus the sign of the spin-rotation
parameters can be precisely assigned since an effect caused
by the (␧ ab ⫹␧ ba )/2 term has the selection rule ⌬J⫽0. This
effect is discussed later.
The frequencies for SrS (X 1 ⌺ ⫹ ) were fit with a simple
rotational Hamiltonian for each vibrational state. Rotational
constants for the v ⫽0, 1, and 2 states and equilibrium rotational constants were calculated. Ro-vibrational data has
been measured for SrS by Pianalto et al. who also established rotational parameters for this molecule, as shown in
Table I.34
For all three molecules analyzed in this paper, the spectroscopic constants are well determined. They reproduce the
observed transition frequencies to residuals of 40 kHz
共SrSH兲, 30 kHz 共SrSD兲, and 50 kHz 共SrS兲, not including
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J. Chem. Phys., Vol. 115, No. 24, 22 December 2001
Rotational spectra of SrSH and SrS
TABLE II. R 0 structures for alkaline-earth metal sulfides and hydrosulfides.
a
r M–S 共Å兲
r S–H 共Å兲
␪ M–S–H 共deg.兲
Ref.
MgSH
CaSH
SrSH
2.316共15兲
2.564共6兲
2.705共3兲
1.339a
1.357共51兲
1.336共4兲
87共20兲
91.0共5.4兲
91.48共3兲
21
22
This work
MgS
CaS
SrS
BaS
2.145
2.319
2.441共4兲
2.563
37
37
This work
38
Held fixed to the ab initio value.
blended K a components. It should be noted that the K a ⫽3
asymmetry doublets of SrSH and the K a ⫽4 lines of SrSD
were unusually broad and not totally collapsed; nevertheless,
they had to be measured as single frequencies. Consequently,
they introduced systematic errors to the fit, and unusually
large residuals 共see Table I: EPAPS兲.26 However, even including these data, the rms of the fits for SrSH and SrSD
were 111 kHz and 58 kHz, respectively. If these features are
excluded from the analysis, the rms of each fit improves by a
factor of 2.
V. DISCUSSION
Using the rotational constants for both isotopomers, an
r 0 structure has been calculated for SrSH using a nonlinear
least-squares fit to the principle moments of inertia. The resulting structure is presented in Table II, along with those of
MgSH and CaSH. Unfortunately, the spectrum of MgSD has
not been measured. Consequently, the S–H bond length in
the MgSH structure was fixed to that predicted by ab initio
calculations. The r 0 structure for CaSH, on the other hand,
was calculated from the rotational constants of the main and
deuterium isotopomers, and can be directly compared to that
of SrSH.
As shown in Table II, there are some trends that are
apparent in the hydrosulfides. First, the metal–sulfur bond
length increases with the size of the metal atom, as might be
expected, from 2.316 Å for MgSH to 2.705 Å for SrSH.
Second, the sulfur–hydrogen bond does not change appreciably between CaSH and SrSH, with an approximate value of
1.34 Å, very close to the equilibrium value for H2S of r e
⫽1.3356 Å. 35 Another important feature is that, within the
errors, the M–S–H bond angle is approximately the same for
all three molecules 共⬃90°兲, although there might be a slight
trend for the angle to increase as the alkaline-earth series is
descended. This bond angle is very close to that present in
H2S 共92.1°兲,35 which indicates that the alkaline-earth hydrosulfides are predominantly covalently bonded, in contrast to
their oxygen analogs. However, the suggestion of a slight
increase in angle from MgSH to SrSH may signal a small
increase in ionicity as the structure approaches linearity. If
this trend is real, then the bond angle in BaSH should be
⬃93°. Curiously, the bond angle in NaSH is ␪ ⫽92(1)°, exactly in the range of the alkaline-earth species.36
For comparison purposes, an r 0 bond length was also
calculated for SrS from the rotational constants measured in
this work. This value is listed in Table II, along with other
11135
alkaline-earth monosulfide bond distances.37,38 Another interesting property can be seen from these data, namely, that the
metal–sulfur bond length increases from the alkaline-earth
sulfides to the hydrosulfides. For example, the Sr–S bond
length in SrS is 2.441共4兲 Å, while in SrSH it is 2.705共3兲 Å. A
similar effect is found for the magnesium and calcium counterparts. This lengthening suggests a change in bond order. In
the hydrosulfides, there is a single bond between the metal
and the sulfur atom, in analogy to H2S; in the MS compounds, there may be double bond character. Also, lack of
observable hyperfine splitting in the spectra of all three hydrosulfide compounds studied suggests that the unpaired
electron resides primarily on the metal atom. 共The main isotopes of Mg, Ca and Sr do not have a nuclear spin, while
hydrogen has I⫽1/2.兲 The presence of the electron on the
metal atom may introduce some additional repulsion, which
also contributes to the lengthening of the metal–sulfur bond
distance.
Chan and Hamilton24 have performed ab initio calculations on SrSH and have determined an equilibrium structure
for this radical. Their calculations suggest r SrS⫽2.744 Å,
r SH⫽1.355 Å, and ␪ Sr–S–H⫽97.87°. These bond lengths are
quite close to the r 0 values determined here, but the bond
angle is significantly larger 共⬃7%兲. Large differences between the ab initio and the r 0 experimental values have been
seen before in CaSH.11 Chan and Hamilton predicted the
angle to be 94.35°, Ortiz39 estimated it to be 100.0°, while
Taleb-Bendiab et al.22 suggested the value was 97.1°. The
experimental r 0 bond angle was measured to be 91.0共5.4兲°.
The zero-point inertia defects, ⌬ 0 , derived from the observed rotational constants for SrSH and SrSD, are 0.2303共6兲
amuÅ2 and 0.3146共3兲 amuÅ2, respectively. This is somewhat
higher than normal as compared to most planar asymmetric
top molecules.40 For example, ⌬ 0 for MgSH is 0.158共4兲21
and for CaSH is 0.212共6兲.22 ⌬ 0 has been found to have contributions from harmonic and Coriolis terms of vibrationrotation interactions:40
⌬ 0 ⫽⌬ harm
⫹⌬ cor
0
0 .
共3兲
The Coriolis contribution is thought to be small for small
molecules.40 Therefore, the most important contribution to
the inertial defect for the hydrosulfides is the harmonic term.
term can be calculated from the centrifugal distorThe ⌬ harm
0
tion constants, using the centrifugal distortion tensor.41 This
calculation, however, requires knowledge of D K , which can
only be obtained from b-type transitions. Therefore, to carry
out this computation for SrSH, this constant had to be estiterm
mated by scaling the optical value for CaSH. The ⌬ harm
0
was then determined to be 0.196, close to the actual inertial
defect. Thus, vibrations are distorting the molecule, and may
signify a trend toward a more floppy structure. Competition
between covalent and ionic bonding 共or bent versus linear
geometry兲 may be causing this effect.
Determination of the spin-rotation parameters for SrSH
allows for calculation of the g tensor, which gives some insight into the distribution of the unpaired electron in a molecule. Using Curl’s formula,42 the g tensor takes the form
Downloaded 17 Jan 2002 to 128.196.209.95. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp
11136
Halfen et al.
J. Chem. Phys., Vol. 115, No. 24, 22 December 2001
TABLE III. Spin rotation parameters for alkaline-earth hydroxides and
hydrosulfides.a
M
␥ 共M–OH兲
(␧ bb ⫹␧ cc )/2 共M–SH兲
A SO(M–OH:A 2 ⌸)
Mg
Ca
Sr
Ba
37.602共72兲b
34.765共57兲c
72.774共48兲d
71.325共81兲e
55.34共19兲f
41.93共17兲g
57.45共10兲
-
2 002 000h
7 900 000i
19 040 000i
a
In MHz.
Reference 14.
c
Reference 12.
d
Reference 13.
e
Reference 15.
f
Reference 21.
g
Reference 22.
h
Reference 9.
i
Reference 10.
j
Reference 11.
b
FIG. 4. An energy level diagram showing the J⫽53.5 through J⫽55.5
levels of SrSH for the K a ⫽0 and 1 components. The spin-rotation splitting
is negligible on this scale. The K a ⫽0, J⫽N⫺1/2 and the K a ⫽1, J⫽N
⫹1/2, K c ⫽N⫺1 levels cross around J⫽54.5, reversing their respective
energy ordering. This crossing results in a slight shift of these levels, which
is accounted for by the off-diagonal term of the spin-rotation interaction.
g ␣␣ ⫽g e ⫺
␧ ␣␣
,
2B ␣
共4兲
where ␣ is a molecule-fixed axis, B ␣ is the associated rotational constant, and g e ⫽2.002 32. Using this expression, the
g tensor for SrSH 共SrSD兲 was calculated to be g aa
⫽2.002 23 共2.002 20兲, g bb ⫽1.992 56 共1.992 56兲, and g cc
⫽1.992 00 共1.991 96兲. As mentioned, the unpaired electron
in the alkaline-earth hydrosulfides primarily resides on the
metal atom, predominantly in a spherically symmetric a ⬘
orbital. To a first approximation, therefore, the g factors
should be close to the free-electron spin value of 2.002 32.
Departure from this number demonstrates that the orbital in
which the unpaired electron inhabits deviates from spherical
symmetry. The most deviation in SrSH is seen in the g cc
value, which is associated with the ĉ axis, the axis perpendicular to the plane of the molecule; g bb is similar in
magnitude—only slightly larger than g cc . In contrast, the
g aa value is very close to the free-spin value. These differences in the g factors likely arise from mixing of the atomic
p y and p x orbitals of the metal atom with the a ⬘ orbital.
Contributions from these p orbitals shift electron density of
the unpaired electron away from the Sr–S bond, presumably
stabilizing the structure. There is little mixing of the p z orbital because it lies in the direction of the ␴ bond between
the Sr and S atoms.
Since SrSH has C s symmetry, the off-diagonal spinrotation term, (␧ ab ⫹␧ ba )/2, is nonzero. This parameter
arises from the operator N a S b ⫹N b S a , which introduces a
coupling when the J⫽N⫺1/2, K a ⫽0 energy level overtakes
the J⫽N⫹1/2, K a ⫽1, K c ⫽N⫺1 level, with ⌬J⫽0. A prediction can be made to find when this crossover occurs, using
the expression J⬇(A⫺B⫺C)/(B⫹C). 43 This relationship
suggests that this crossing will occur between the J⬇49.5
and 50.5 levels for SrSH, and at J⬇25.5 for SrSD. The actual crossing for SrSH, based on the determined constants, is
at J⫽54.5, as illustrated in Fig. 4. As shown, the N⫽54, J
⫽53.5, K a ⫽0 level initially lies lower in energy than the
N⫽53, J⫽53.5,K a ⫽1, K c ⫽52 level. However, around J
⫽54.5, the levels shift. Unfortunately, the lowest J level recorded for SrSH is J⫽56.5 共and J⫽58.5 for SrSD兲, i.e., not
low enough to observe the crossing of these levels. However,
a slight shift in energy was noticed in the N K a K c ⫽570,57 ,J
⫽56.5 level. If the (␧ ab ⫹␧ ba )/2 constant was not included
in the fit, the residual for the N⫽57→58, K a ⫽0, J⫽56.5
→57.5 transition increased in magnitude by ⬃0.2 MHz. This
effect steadily decreased as N and J increased, and was not
seen at all in SrSD because of the high J values observed for
this species. However, an analogous shift was observed in
the crossing of K a ⫽1 and K a ⫽2 levels at the N⫽66
→67,J⫽66.5→67.5 transition for SrSD.
It is also of interest to compare spin-rotation parameters
of the alkaline-earth hydrosulfides relative to their hydroxide
counterparts. A summary of the spin-rotation constants is
given in Table III, which includes ␥ for the linear hydroxides, and for MSH its approximate analog for asymmetric
tops, (␧ bb ⫹␧ cc )/2. To a first approximation, these constants
are strictly mass-dependent, and therefore, they should decrease in value as the mass of the alkaline-earth metal increases. However, as the table shows, there is a substantial
increase in both ␥ and (␧ bb ⫹␧ cc )/2 going from calcium to
strontium. The parameters increase from 34.765 MHz to
72.774 MHz for CaOH to SrOH, and from 41.93 MHz to
57.45 MHz for CaSH to SrSH. This increase can be explained by second-order spin-orbit coupling, whose contribution to the spin-rotation constant is27
␥⬇
⫽
␧ bb ⫹␧ cc
2
具 2 ⌺ ⫹ 兩 A SOL̂ ⫺ Ŝ ⫹ 兩 2 ⌸ 典 • 具 2 ⌸ 兩 BL̂ ⫹ Ŝ ⫺ 兩 2 ⌺ ⫹ 典
E ⌸ ⫺E ⌺
,
共5兲
where A SO is the spin-orbit constant for a given molecule in
the nearest 2 ⌸ state and B is the rotational constant of the
ground state. For the hydroxide species, the interpretation of
this perturbation is relatively simple, since they all have observed A 2 ⌸ states, and most of the respective spin-orbit
constants are known. However, as shown in Table III, there
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J. Chem. Phys., Vol. 115, No. 24, 22 December 2001
Rotational spectra of SrSH and SrS
11137
important role in the strontium species, where the spinrotation constant increases substantially relative to calcium.
For some reason, however, the effect substantially lessens for
barium, although A SO is far larger in the A 2 ⌸ state of BaOH
共635 cm⫺1兲11 than in SrOH 共263.5 cm⫺1兲.10 It would be interesting to see whether this trend is also present in BaSH.
Generation of spin-rotation couplings is obviously a combination of various subtle effects.
VI. CONCLUSION
FIG. 5. A diagram showing the correlation between the A 2 ⌸ electronic
state of SrOH and the first two excited electronic states 共2 A ⬘ and 2 A ⬙ 兲 of
SrSH. To explain the magnitude of the spin-rotation parameter in SrSH
relative to CaSH, fast rotation about the â axis must mix the 2 A ⬘ and 2 A ⬙ ,
effectively generating a 2 ⌸ state with orbital angular momentum. Secondorder spin-orbit coupling is then possible.
is only a qualitative correlation between the magnitudes of ␥
and A SO . For example, while A SO increases by 4 in the respective A 2 ⌸ states, ␥ increases only by a factor of 2 from
CaOH (X 2 ⌺ ⫹ ) to SrOH (X 2 ⌺ ⫹ ), even while the denominator E ⌸ ⫺E ⌺ decreases.
For the hydrosulfides, the situation is more complicated
because electronic states in the C s group are restricted to A ⬘
and A ⬙ symmetry, and, strictly speaking, neither term has
electronic orbital angular momentum that can generate spinorbit coupling. Nonetheless, this second-order effect must be
present in the spin-rotation constants for these species. It can
be explained by examining the correlation diagram of SrOH
and SrSH as seen in Fig. 5, which shows the respective energy levels of the X 2 ⌺ ⫹ and A 2 ⌸ states of SrOH and the
corresponding X̃ 2 A ⬘ , Ã 2 A ⬘ , and B̃ 2 A ⬙ states of SrSH. The
introduction of asymmetry in SrSH effectively splits the
A 2 ⌸ state in the linear limit into the à 2 A ⬘ and B̃ 2 A ⬙ states
of a bent molecule. Rapid rotation about the â axis in SrSH,
however, couples the A ⬘ and A ⬙ states and, hence, reintroduces net orbital angular momentum into the molecule,
which generates an effective spin-orbit constant.44 Because
this perturbation is not as direct as in SrOH, the increase in
the spin-rotation constant is not as pronounced in the hydrosulfides, as is evident in the data.
There is an obvious competition between the first-order
nuclear dependence and second-order spin-orbit coupling in
the spin-rotation interaction of these molecules. It is not clear
that the electronic contribution always dominates, as suggested by theory.29 The second-order term plays a particular
This study has produced the first measurements of the
spectrum of the SrSH and SrSD radicals at rotational resolution. Like MgSH and CaSH, SrSH is clearly bent with a
similar bond angle near 91°. The alkaline-earth hydrosulfides, therefore, appear to be covalently bonded with few
changes upon substitution of the metal atom. The diagonal
spin-rotation terms suggest that the a ⬘ orbital of the unpaired
electron, located primarily on the strontium atom, has some
p y 共out-of-plane兲 and p x 共in-plane兲 character. There appears
to be competition between the first-order mass-dependence
and the second-order spin-orbit coupling in the spin-rotation
interactions, as well, on comparison with the other alkalineearth hydroxides and hydrosulfides. The effects are less severe for the hydrosulfides because the perturbing states only
indirectly have orbital angular momentum. A study of BaSH
would certainly aid in establishing trends in these interesting
compounds.
ACKNOWLEDGMENTS
The authors would like to thank Dr. James K. G. Watson
and Dr. Robert McKellar for providing a manuscript of the
MgSH paper prior to publication. This research is supported
by NSF Grant No. CHE 98-17707.
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