Rotational spectra and hyperfine constants of ZrO and ZrS

Article abstract of DOI:10.1063/1.479014

The pure rotational spectra of ZrO and ZrS have been recorded using cavity Fourier transform microwave spectroscopy in the frequency range 9-26 GHz. The molecules were generated by laser ablation of a solid Zr rod in the presence of 0.05% of O₂ or H₂S, respectively, in either argon or neon. Rotational spectra of five previously unobserved isotopomers of ZrO in the X¹∑⁺ state have been measured. Spectra for all five Zr³²S isotopomers and for the ⁹⁰Zr³⁴S isotopomer in natural abundance have also been measured; this is the first report of pure rotational transitions for ZrS. Transitions in several excited vibrational states were also measured for the most abundant isotopomers of both species. Atomic mass-dependent Born-Oppenheimer breakdown correction terms were determined by fitting the data obtained for each molecule to a Dunham-like expression. Values for the equilibrium bond lengths of the two species were also calculated from the results of these fits. For both the ⁹¹Zr³²S and ⁹¹Zr¹⁶O isotopomers, nuclear hyperfine structure due to the zirconium nucleus was observed and values for eQq₀(⁹¹Zr) and C₁(⁹¹Zr) have been determined. A rotational transition in the low lying a ³Δ state of ZrS has also been observed.

Full text of DOI:10.1063/1.479014

Rotational spectra and hyperfine constants of ZrO and ZrS
Sara A. Beaton and Michael C. L. Gerry
Citation: The Journal of Chemical Physics 110, 10715 (1999); doi: 10.1063/1.479014
View online: http://dx.doi.org/10.1063/1.479014
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/110/22?ver=pdfcov
Published by the AIP Publishing
Articles you may be interested in
Rotational spectra of rare isotopic species of fluoroiodomethane: Determination of the equilibrium structure from
rotational spectroscopy and quantum-chemical calculations
J. Chem. Phys. 137, 024310 (2012); 10.1063/1.4731284
Internuclear distance and effects of Born–Oppenheimer breakdown for PtS, determined from its pure rotational
spectrum
J. Chem. Phys. 121, 3486 (2004); 10.1063/1.1769365
Rotational spectrum of jet-cooled HfO 2 and HfO
J. Chem. Phys. 117, 9651 (2002); 10.1063/1.1516797
Fourier transform microwave rotational spectra of the Ne 2 –N 2 O and Ar 2 –N 2 O van der Waals trimers
J. Chem. Phys. 111, 3919 (1999); 10.1063/1.479695
Fourier-transform microwave spectrum, structure, harmonic force field, and hyperfine constants of sulfur chloride
fluoride, ClSF
J. Chem. Phys. 106, 10037 (1997); 10.1063/1.474061
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
141.209.100.60 On: Tue, 23 Dec 2014 04:43:46

JOURNAL OF CHEMICAL PHYSICS
VOLUME 110, NUMBER 22
8 JUNE 1999
Rotational spectra and hyperfine constants of ZrO and ZrS
Sara A. Beaton and Michael C. L. Gerrya)
Department of Chemistry, The University of British Columbia, 2036 Main Mall, Vancouver,
British Columbia, Canada V6T 1Z1
͑Received 9 November 1998; accepted 5 March 1999͒
The pure rotational spectra of ZrO and ZrS have been recorded using cavity Fourier transform
microwave spectroscopy in the frequency range 9–26 GHz. The molecules were generated by laser
ablation of a solid Zr rod in the presence of 0.05% of O2 or H2S, respectively, in either argon or
neon. Rotational spectra of five previously unobserved isotopomers of ZrO in the X 1⌺ϩ state have
been measured. Spectra for all five Zr32S isotopomers and for the 90Zr34S isotopomer in natural
abundance have also been measured; this is the first report of pure rotational transitions for ZrS.
Transitions in several excited vibrational states were also measured for the most abundant
isotopomers of both species. Atomic mass-dependent Born–Oppenheimer breakdown correction
terms were determined by fitting the data obtained for each molecule to a Dunham-like expression.
Values for the equilibrium bond lengths of the two species were also calculated from the results of
these fits. For both the 91Zr32S and 91Zr16O isotopomers, nuclear hyperfine structure due to the
zirconium nucleus was observed and values for eQq0(91Zr) and CI(91Zr) have been determined. A
rotational transition in the low lying a 3⌬ state of ZrS has also been observed. © 1999 American
Institute of Physics. ͓S0021-9606͑99͒00121-X͔
I. INTRODUCTION
astrophysical importance. Many transition metal oxides and
hydrides ͓e.g., TiO ͑Ref. 2͒, LaO ͑Ref. 3͒, and FeH ͑Ref. 4͔͒
have been detected via their electronic spectra in cool, car-
bon rich stars ͑M and S type͒. However, recent calculations
have predicted that in such environments where the C:O ratio
is close to unity, certain metal monosulphides including ZrS
may be more abundant than the corresponding metal
monoxides.5 More detailed knowledge of the composition of
the atmospheres of these stars is required to further the un-
derstanding of stellar evolution. The absorption bands of ZrO
were first detected in S-type stars in 1922,6 and now consti-
tute a defining characteristic of such stars. Consequently ZrO
has received a vast amount of spectroscopic attention includ-
ing optical ͑for example Refs. 7, 8͒ and microwave9 studies,
ab initio calculations,10,11 lifetime studies,12 and rotational
line strength analyses.13 In contrast, it is only in the last
decade that ZrS has been identified as the carrier of the
Keenan bands ͓three red degraded bands first observed in
1950 ͑Ref. 14͒ in the spectra of certain S-type stars͔, thus
confirming its presence in these stellar atmospheres. This
was largely due to the fact that when ZrS was first proposed
as the carrier of the Keenan bands in 1980 ͑Ref. 5͒ there
were no laboratory spectroscopic data available for this mol-
ecule.
In general, the transition metal monosulphides have been
less well characterized than the analogous monoxides.
Chemically, both species are models for understanding tran-
sition metal bonding involving d electrons. Measuring the
spectroscopic properties of these molecules, particularly hy-
perfine parameters, can therefore give valuable insight into
their electronic structures and the nature of the chemical
bonds involved. The majority of the work to date on these
species has been electronic spectroscopy. However, these di-
atomic molecules often have surprisingly complicated elec-
tronic spectra, and the analysis may be far from
straightforward.1 Such molecules typically have a large num-
ber of low lying electronic states with high spin multiplicities
and perturbed excited electronic states; in addition many
transition metal nuclei have nuclear spins. To add to this, the
molecules can be difficult to generate in the gas phase be-
cause of the refractory nature of many transition metals and
their compounds. In terms of theoretical calculations, elec-
tron correlation effects become important when there are
many unpaired electrons and so these molecules also provide
a challenge for ab initio techniques. Spectroscopic data can
therefore be used to calibrate these calculations for such sys-
tems. The combination of the above considerations with the
fact that only a handful of these molecules have ⌺ ground
states has resulted in only a few transition metal monoxides
and no monosulphides having been studied by Fourier trans-
form microwave ͑FTMW͒ spectroscopy.
Zr has five naturally occurring isotopes: 90Zr(51.45%),
91Zr(11.22%),
92Zr(17.15%),
94Zr(17.38%),
and
96Zr(2.80%). Only the 91Zr nucleus has nuclear spin, with
Iϭ5/2. Accurate spectroscopic constants for the X 1⌺ϩ state
of ZrO are known from a variety of studies. Be , ␣e , and ␥e
were determined for 90Zr16O in an extensive analysis of the
vibrationally excited bands of the B 1⌸–X 1⌺ϩ electronic
transition by Philips and Davis.7 More recently, Simard
et al.15 re-examined the C 1⌺ϩ –X 1⌺ϩ transition via laser
induced fluorescence using a laser ablation/supersonic ex-
In addition to fundamental spectroscopic interest in these
species, both ZrO and ZrS are molecules of considerable
a͒
Author to whom correspondence should be addressed; electronic mail:
mgerry@chem.ubc.ca
0021-9606/99/110(22)/10715/10/$15.00
10715
© 1999 American Institute of Physics
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
141.209.100.60 On: Tue, 23 Dec 2014 04:43:46

10716
J. Chem. Phys., Vol. 110, No. 22, 8 June 1999
S. A. Beaton and M. C. L. Gerry
pansion technique. Rotational constants for all five Zr16O
isotopomers were obtained in this work. Also, the FTMW
spectra of 90Zr16O, 92Zr16O, and 94Zr16O have been measured
by Suenram et al.9 by ablating a rod of ZrO2 and using pure
Ne backing gas. The authors stated in Ref. 9 that the signals
obtained were not strong enough to permit measurements of
the two remaining minor isotopomers.
excitation frequency. A pulsed nozzle is mounted near the
center of the other, fixed mirror. All measured lines appear as
doublets due to the Doppler effect, since the molecular jet
and the axis of microwave propagation are parallel. Operat-
ing the spectrometer in this ‘‘parallel configuration’’ pro-
vides high sensitivity and very narrow linewidths, the latter
on the order of 9–10 kHz full width at half maximum
͑FWHM͒. The measurement accuracy is estimated to be bet-
ter than Ϯ1 kHz.
The first published spectroscopic study of ZrS was by
Simard et al. in 1988.16 They observed the E 1⌺ϩ –X 1⌺ϩ
transition in the visible region of the spectrum by laser in-
duced fluorescence. The molecule was made by laser abla-
tion of a zirconium rod with a few percent of OCS in a
helium backing gas. A vibrational analysis of the main iso-
topomer was given; however the resolution of the spectrum
did not permit a rotational analysis. Also in 1988, Jonsson,
Lindgren, and Taklif17 reported in a letter that they had ob-
served two singlet bands and several triplet bands ͑including
the b 3⌽–a 3⌬ transition which gives rise to the Keenan
bands͒ in emission at high resolution. In this case, they used
a microwave discharge through ZrCl4 and sulphur in argon
to make ZrS. A preliminary bond length for the ground state
was given in Ref. 17, and rotational analyses of three triplet
bands for the main isotopomer were subsequently published
in 1995.18,19 Since then, a full rotational analysis of the sin-
glet bands has also been perfomed,20 although we were un-
aware of the results of that work at the outset of this study.
There is also a very recent lifetime study of the singlet states
of zirconium sulphide.21 In addition, there has been an ab
initio study performed by Langhoff and Bauschlicher on sev-
eral transition metal oxides and sulphides which included
both ZrS and ZrO.10
In this article we report the observation of the pure ro-
tational spectra of the X 1⌺ϩ states of ZrO and ZrS, mea-
sured using cavity pulsed FTMW spectroscopy. Previous
work on ZrO has been extended and rotational transitions
have been measured for a further five isotopomers. For ZrS,
this is the first observation of the rotational spectrum; tran-
sitions have been observed for six isotopomers in natural
abundance. The data obtained for ZrO and ZrS have been fit
to a Dunham-like expression and Born–Oppenheimer break-
down correction terms have been determined in each case.
Equilibrium bond lengths have been calculated for both mol-
ecules. For both the 91Zr32S and 91Zr16O species, nuclear
hyperfine structure in the ground state has been observed for
the first time, and the nuclear quadrupole coupling constants
for 91Zr have been determined. In addition, a rotational tran-
sition in the low lying a 3⌬ state of ZrS has been observed
and is discussed.
The laser ablation source used to generate gas phase ZrO
and ZrS samples has also been described previously.24
A
stainless steel nozzle cap was used to hold a 5 mm diam Zr
rod ͑Goodfellow, 99.8ϩ%͒ approximately 5 mm from the
orifice of a General Valve Series 9 nozzle. The rod was
continuously rotated and translated to expose a fresh area of
the surface to each laser pulse. The second harmonic of a
Q-switched Continuum Surelite I ͑Nd:YAG͒ laser was used
to ablate the zirconium rod ͑ϳ5 mJ per pulse @ 532 nm͒.
The laser pulse was timed to coincide with a gas pulse of a
suitable reactant molecule in a buffer gas which then under-
went supersonic expansion into the microwave cavity. The
nozzle typically operated with a backing pressure of 4–6
atm. The repetition rate of the experiment was 1 Hz.
Strong ZrO signals ͑which did not become weaker over
time͒ could be readily observed using pure argon as a back-
ing gas; such experimental conditions for making metal ox-
ides have been observed before.25 Adding small amounts of
O2 to the argon produced, at best, a 50% increase in signal
strength. The signals were such that the Jϭ1–0 transition of
the main isotopomer could be observed in two averaging
cycles. It is likely that ZrO arises from ZrO2 present in the
rod as an impurity, but also that a small amount forms from
O2 ͑not H2O͒ as an impurity in the backing gas sample. The
latter is supported by two qualitative observations: ͑a͒ using
0.05% O2 ͑50% 18O͒ in the argon backing gas produced
‘‘strong’’ Zr18O signals, ͑b͒ using 0.05% H2O ͑40% 18O͒
produced only ‘‘very weak’’ Zr18O signals. The Zr16O and
Zr18O ϭ0 spectra reported here were measured using con-
v
ditions similar to ͑a͒ above. ZrS was produced by reacting
ablated metal plasma with 0.05% H2S in argon backing gas.
This was found to give about four to five times better signal
to noise than using OCS in argon as a source of sulphur. The
best ZrS signals obtained were approximately five times
weaker than the corresponding ZrO signals. In order to ob-
serve rotational transitions in excited vibrational states for
both species, neon was used as the backing gas instead of
argon. This produced a higher vibrational temperature in the
expansion without significantly reducing the rotational cool-
ing; see later for details. Neon was also used in the measure-
ment of transitions in the a 3⌬ excited electronic state of
ZrS.
II. EXPERIMENT
A Balle–Flygare-type Fourier transform microwave
spectrometer22 was used to measure the spectra of ZrO and
ZrS. This instrument has been described in detail elsewhere23
and only a brief description will be given here. The micro-
wave cavity consists of two spherical aluminum mirrors 24
cm in diameter, with a radius of curvature of 38.4 cm, placed
approximately 30 cm apart. One of the mirrors is movable so
that the cavity can be tuned into resonance at the microwave
III. RESULTS
A. ZrO „X 1⌺؉ state…
As was mentioned in the introduction, microwave spec-
tra of the Jϭ1–0 transition in the X 1⌺ϩ state have been
measured previously for the three most abundant ZrO
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
141.209.100.60 On: Tue, 23 Dec 2014 04:43:46

J. Chem. Phys., Vol. 110, No. 22, 8 June 1999
S. A. Beaton and M. C. L. Gerry
10717
TABLE I. Measured frequencies for the Jϭ1–0 transition of ZrO in the
1
ϩ
X
⌺
state.
Frequency
͑MHz͒
obsϪcalc
͑kHz͒
a
Isotopomer F –F
Ref. 9
Ј
Љ
v
b
90Zr16O
0
1
2
3
0
0
0
0
1
2
0
1
2
0
0
1
2
0
1
0
25 339.2837
25 222.2487
25 104.7648
24 986.8280
25 278.9800
25 290.6416
25 318.1075
25 256.0960
25 139.6384
25 022.7348
25 176.4150
25 060.5094
24 944.1609
25 100.0336
22 946.9756
22 846.1562
22 744.9696
22 863.7702
22 763.4997
22 784.0724
Ϫ0.05
0.02
Ϫ0.18
0.01
25 339.290͑2͒
3
5
91Zr16O
92Zr16O
94Zr16O
–
–
–
0.08c
Ϫ0.17c
0.13c
0.07
2
2
7
5
2
5
2
2
5
2
25 256.093͑4͒
25 176.414͑4͒
0.18
Ϫ0.05
Ϫ0.03
Ϫ0.05
Ϫ0.12
0.20
0.03
0.05
0.39
FIG. 1. Power spectrum of the Jϭ1–0 ϭ0 transition of 90Zr16O measured
96Zr16O
90Zr18O
v
in 100 averaging cycles. The excitation frequency was 25 339.2820 MHz. 4
K data points were recorded and the power spectrum is shown as a 4 K
transformation. For this measurement the backing gas used was pure argon.
92Zr18O
94Zr18O
Ϫ0.03
Ϫ0.32
Ϫ0.11
isotopomers.9 This was also the only rotational transition
available in the frequency range of our spectrometer. The
frequencies of these three transitions remeasured in the
present work are reported for completeness. A typical spec-
trum is shown in Fig. 1. The transition frequencies for the
other isotopomers were predicted by mass scaling the rota-
tional constant and the literature value of D0 for the main
isotopomer ͑see Table IV͒. For 91Zr16O, the only guide to the
magnitude of the hyperfine splitting was that it had not been
resolved in the laser induced fluorescence study,15 in which
linewidths of 120 MHz were obtained. All three hyperfine
aFrom least squares fit of data ͑excluding 91Zr16O data͒ to Eq. ͑2͒.
bNumbers in parentheses are the quoted experimental uncertainties.
cFrom least squares fit of 91Zr16O data only using SPFIT ͑Ref. 33͒.
hypothesis that the splittings would be comparable to those
in the spectrum of 91Zr16O, which proved to be the case.
Figure 2 illustrates the similar sizes of the nuclear hyperfine
splittings for ZrO and ZrS. In the process of measuring the
spectrum of 91Zr32S, the Jϭ1–0 ϭ1 transition of 90Zr32S
v
components of the Jϭ1–0 ϭ0 transition of 91Zr16O were
v
v
was also found, only 1 MHz from the most intense hyperfine
component observed, as shown in Fig. 2. The zirconium sul-
phide signals were sufficiently strong that transitions in sev-
eral excited vibrational states of the three most abundant
Zr32S isotopomers could be measured, to confirm the identity
of this transition. Moreover, the resulting value of ␣e for the
X 1⌺ϩ state is within 5% of the value of ␣e reported for the
very low lying a 3⌬ state,18 which is also the case for the
observed, as well as Jϭ1–0 ϭ0 transitions of 96Zr16O and
three Zr18O isotopomers. From the molecular constants in
Ref. 7, the frequencies of the Jϭ1–0 rotational transitions
in excited vibrational states for a number of isotopomers
were predicted. With neon as the backing gas, the signals
were sufficiently strong and the vibrational temperature of
the expansion sufficiently high (Tvibϳ650 K) that transitions
up to ϭ3 were measured for the main isotopomer and up to
v
ϭ2 for several other isotopic species. Table I gives the
v
complete list of the measured transition frequencies for ZrO.
B. ZrS „X 1⌺؉ state…
Only the Jϭ1–0 and Jϭ2–1 transitions in the X 1⌺ϩ
state of ZrS were available in the frequency range of the
spectrometer. Using the preliminary bond length of 2.156 Å
reported by Jonsson, Lindgren, and Taklif17 an initial predic-
tion for the Jϭ1–0 transition frequency for the main isoto-
pomer was made. The transition was found within 20 MHz
of this frequency. Its identity was confirmed by observing
transitions for the four other Zr32S isotopomers and the
90Zr34S isotopomer in natural abundance. The frequencies of
Jϭ1–0 transitions of the minor isotopomers were predicted
by simply mass scaling B0 for the main isotopomer, and all
the unsplit transitions were found within 500 kHz of the
predictions. For the 91Zr32S isotopomer, hyperfine structure
due to the zirconium nucleus was observed. The spectral
searches for the hyperfine components were based on the
FIG. 2. Two composite spectra showing the nuclear hyperfine structure due
to the 91Zr nucleus in the Jϭ1–0 transition of 91Zr16O ͑upper spectrum͒ and
91Zr32S ͑lower spectrum͒. The horizontal scales on the two spectra are the
same and the hypothetical unsplit frequencies of the Jϭ1–0 transitions are
shown with dotted lines. The transition marked with an asterisks in the
lower spectrum is the Jϭ1–0 ϭ1 transition of the main isotopomer
v
90Zr32S.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
141.209.100.60 On: Tue, 23 Dec 2014 04:43:46

10718
J. Chem. Phys., Vol. 110, No. 22, 8 June 1999
S. A. Beaton and M. C. L. Gerry
TABLE II. Measured frequencies for the Jϭ1–0 and Jϭ2–1 transitions of
1
ϩ
ZrS in the X
⌺
state.
a
Isotopomer F –F
J –J
Ј
Frequency ͑MHz͒ obs-calc ͑kHz͒
Ј
Љ
Љ
v
90Zr32S
1–0
2–1
1–0
2–1
1–0
2–1
2–1
1–0
1–0
1–0
2–1
2–1
1–0
2–1
1–0
2–1
1–0
2–1
1–0
2–1
1–0
2–1
1–0
2–1
1–0
2–1
1–0
2–1
0
0
1
1
2
2
3
0
0
0
0
0
0
0
1
1
2
2
0
0
1
1
2
2
0
0
0
0
9 198.3007
18 396.5661
9 166.9932
18 333.9513
9 135.6110
18 271.1872
18 208.2696
9 155.5073
9 165.9156
9 190.4134
18 338.9723
18 340.9603
9 145.8320
18 291.6295
9 114.7928
18 229.5510
9 083.6788
18 167.3246
9 095.5750
18 191.1161
9 064.7917
18 129.5497
9 033.9345
18 067.8360
9 047.3995
18 094.7644
8 800.0135
17 599.9947
0.23
Ϫ0.05
Ϫ0.05
Ϫ0.40
0.00
Ϫ0.01
0.04
3
5
91Zr32S
–
–
–
–
–
0.01b
Ϫ0.01b
0.00b
Ϫ0.08b
0.08b
0.12
2
2
7
5
2
5
2
5
3
2
7
5
2
9
2
2
7
2
92Zr32S
FIG. 3. Power spectrum of the Jϭ2–1 ϭ0 transition in the 3⌬ spin-orbit
0.15
0.19
0.18
Ϫ0.39
0.62
Ϫ0.10
Ϫ0.07
Ϫ0.07
0.18
Ϫ0.61
Ϫ0.19
0.33
Ϫ0.28
0.17
Ϫ0.11
v
1
component of the a 3⌬ electronic state of 90Zr32S measured in 5000 averag-
ing cycles. The excitation frequency was 17 855.3340 MHz. 4 K data points
were recorded and the power spectrum is shown as a 4 K transformation.
94Zr32S
electronic spectrum it was initially assumed to be negligible.
Now, the magnetic moment of a molecule, ␮, is given by
96Zr32S
90Zr34S
␮ϭ ⌳ϩg⌺͒␮ ,
͑1͒
͑
B
where ␮Bϭ the Bohr Magneton and gϳ2. Therefore, al-
3
though both ⌳ and ⌺ are nonzero in the ⌬1 component,
aFrom least squares fit of data ͑excluding 91Zr32S data͒ to Eq. ͑2͒.
bFrom least squares fit of 91Zr32S data only using SPFIT ͑Ref. 33͒.
since ⌳ϭ2 and ⌺ϭϪ1, ␮ is almost zero. Any Zeeman split-
ting of the rotational transitions caused by the Earth’s mag-
netic field26 was thus expected to be very small.
A transition was found within 500 kHz of the predicted
frequency; it is shown in Fig. 3. The linewidth ͑ϳ50 kHz
FWHM͒ is consistent with a very small, though nonzero,
magnetic moment and the intensity is comparable to that of
the excited vibrational states, which is consistent with a tran-
sition in a low lying electronic state. The assignment of this
line was unambiguously confirmed by the observation of the
values of B0 and ␻ for the two states. The measured tran-
sition frequencies for ZrS are given in Table II.
e
C. ZrS „a 3⌬ state…
The electronic energy of the a 3⌬ state has been pre-
dicted by an ab initio study10 to be only 500Ϯ200 cmϪ1
above that of the X 1⌺ϩ ground state; there is no experimen-
tal value for this at present. However, accurate molecular
constants for this excited state ͑for the main isotopomer
only͒ are available from the rotational analyses of the triplet
systems of zirconium sulphide.18,19 Therefore, since rota-
tional transitions in excited vibrational states up to ϳ1500
Jϭ2–1 transition in the ϭ1 level for the main isotopomer
v
and the Jϭ2–1 ϭ0 transition in the 92Zr32S and 94Zr32S
v
isotopomers. The frequencies of the transitions in the minor
isotopomers were predicted by mass scaling the effective
molecular constants for 90Zr32S. Again, each of these transi-
tions was found within 500 kHz of the prediction and each
line had the characteristic broadened line shape shown in
Fig. 3. The line positions of all observed transitions are given
in Table III.
cmϪ1 above ϭ0 were observed easily, a search was also
v
made for rotational transitions in the a 3⌬ electronic state of
ZrS.
The a 3⌬ state is well described by Hund’s case ͑a͒ cou-
18
3
pling and is a regular ⌬ state. The spin-orbit components
3
3
3
are therefore ⌬1 , ⌬2 , and ⌬3 in order of increasing en-
ergy. In each of these spin-orbit components Jу⍀ and
hence the lowest frequency pure rotational transition is J
ϭ(⍀ϩ1)Ϫ⍀. Since B0 for the a 3⌬ state is approximately
4 500 MHz, only the Jϭ2–1 transition in the 3⌬1 spin-orbit
component at ϳ18 GHz is in the frequency range of our
spectrometer. Using the effective molecular constants deter-
3
TABLE III. Measured frequencies for the Jϭ2–1 transition in the
component of the a 3⌬ state of ZrS.
⌬
1
Isotopomer
90Zr32S
Frequency
v
a
0
1
0
0
17 855.326 9͑50͒
17 795.697͑15͒
17 753.564͑15͒
17 656.070͑15͒
92Zr32S
94Zr32S
3
mined for the ⌬1 spin-orbit component in Ref. 18 a predic-
tion was made for the Jϭ2–1 ϭ0 transition of 90Zr32S.
aThe uncertainties have been estimated based on the line shape and relative
intensities of the transitions.
v
Since no lambda-type doubling had been observed in the
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
141.209.100.60 On: Tue, 23 Dec 2014 04:43:46

J. Chem. Phys., Vol. 110, No. 22, 8 June 1999
S. A. Beaton and M. C. L. Gerry
10719
1
ϩ
TABLE IV. Molecular parameters in megahertz for isotopomers of ZrO in the X
⌺
state.
O
01
Y01
Be
103Y02
Y11
103Y21
103␥e
103Y31
103⑀e
Zr
01
␦
␦
parametera
90Zr16Oc
Ϫ103De
Ϫ␣e
re (Å)b
d
12 698.836 387͑350͒
12 699.4f
Ϫ9.563e
Ϫ9.56f
Ϫ58.295 47͑78͒
Ϫ58.58f
Ϫ110.4͑5͒
Ϫ99f
Ϫ0.39͑8͒
2.696 1͑11͒
0.378͑3͒
1.711 952 42͑73͒
91Zr16Og
92Zr16O
94Zr16O
96Zr16O
90Zr18O
92Zr18O
94Zr18O
12 677.721 745
12 657.098 557
12 617.120 477
12 578.797 937
11 498.639 979
11 456.900 385
11 416.920 615
Ϫ9.531
Ϫ9.500
Ϫ9.440
Ϫ9.383
Ϫ7.840
Ϫ7.784
Ϫ7.729
Ϫ58.150 11
Ϫ58.008 25
Ϫ57.733 58
Ϫ57.470 69
Ϫ50.227 69
Ϫ49.954 41
Ϫ49.693 11
Ϫ110.0
Ϫ109.7
Ϫ109.0
Ϫ108.3
Ϫ90.5
Ϫ0.39
Ϫ0.39
Ϫ0.38
Ϫ0.38
Ϫ0.30
Ϫ0.30
Ϫ0.30
1.711 952 13
1.711 951 86
1.711 951 33
1.711 950 82
1.711 932 18
1.711 931 63
1.711 931 10
Ϫ89.9
Ϫ89.2
Correlation coefficients from least squares fit ͑isotopomer 1 is 90Zr16O͒
1
Y01
Y11
Y21
Ϫ0.917
0.869
Ϫ0.832
0.245
0.419
1
rms of residualsϭ0.15 kHz
no. of data pointsϭ17
no. of isotopomersϭ7
Ϫ0.986
0.958
Ϫ0.032
Ϫ0.164
1
Y31
Ϫ0.991
0.020
0.143
1
O
Ϫ0.034
Ϫ0.151
1
␦
␦
01
Zr
01
0.312
1
aSpectroscopic parameter to which the Yk1 is approximately equal, where Ev,JϭJ(Jϩ1) B ϪD J(Jϩ1)Ϫ␣ ( ϩ1/2)ϩ␥ ( ϩ1/2)2ϩ⑀ ( ϩ1/2)3 ; see
͓
v
v
v
e
͔
e
e
e
e
Ref. 26.
2
bCalculated from Y01 using Y01ϭh/8␲ ␮re where ␮ is the atomic reduced mass.
2
cParameters for this isotopomer are the results of the least squares fit of all the isotopic data ͑excluding 91Zr16O data͒ to Eq. ͑2͒. The parameters for all other
isotopomers presented in this table are calculated from these using Eq. ͑5͒.
dNumbers in parentheses are 95% confidence limits in units of the last significant figure except those for the bond length re , which are one standard deviation
in units of the last significant figure ͑also see text͒.
eConstrained to this value (D0 from Ref. 30͒ in the fit. The uncertainty quoted is 0.081ϫ10Ϫ3 MHz; if Y02 is constrained to values at the limits of this
uncertainty in the fit then Y01 varies by less than half the 95% confidence limit given above and the other parameters are unchanged.
fSpectroscopic parameters from Philips and Davis ͑Ref. 7͒. No uncertainties in the parameters are quoted in this reference.
gData for this isotopomer were not included in the fit and the predicted parameters for this species ignore nuclear spin effects.
lϩk/2
IV. ANALYSIS
␮
1
1
k
l
E␣ ,J͒ϭ
͑v
Ykl ϩ1/2͒ J Jϩ1͒
͑v ͓ ͑
͔
ͩ ͪ
͚
␮
A. Vibrational data
͑kl͒Þ͑00͒
␣
The analyses of the X 1⌺ϩ state data for the spin-free
(Iϭ0) isotopomers of ZrO and ZrS were essentially parallel.
Initially, the data for each isotopomer were fit separately to
spectroscopic constants (Be , De , ␣e , etc͒. Equilibrium
bond lengths were then calculated for each isotopomer using
the normal relation Beϭh/8␲ ␮re. Significantly, the results
from this showed that the bond length for the 90Zr18O isoto-
pomer differed from the value obtained from the 90Zr16O
isotopomer by 30 times the calculated uncertainty ͑for ex-
ample, see Table IV͒. Such an observation is an indication of
breakdown of the Born–Oppenheimer approximation; this
effect has been treated by Watson.27 The fact that such a
discrepancy in the equilibrium bond lengths of different iso-
topomers was apparent in the analysis of very accurate yet
M␣AϪM1A
lϩk/2
␮
1
A
kl
ϩ
␦
ͩ ͪ
ͫ
ͩ
ͪ
͚
MA␣
␮
͑kl͒у͑00͒
␣
M␣BϪM1B
B
k
ϩ
␦
ϩ1/2͒ J Jϩ1͒ l, ͑2͒
͑v
͓ ͑
͔
ͩ
ͪ
ͬ
MB␣
kl
2
2
where the sub/superscript 1 refers to the main isotopomer,
the sub/superscript ␣ refers to any given isotopomer, ␮ is the
reduced mass of the atoms, and M is the atomic mass. Now,
experimentally the largest data set is usually obtained for the
most abundant ͑main͒ isotopomer. One advantage of the
above treatment is that the parameters for this isotopomer,
rather than a set of Ukl’s, now become the reference point for
further corrections. In other words, fitting the data in this
way directly produces a set of molecular constants that are
relevant to a real system, rather than to the hypothetical po-
tential minimum in the Born–Oppenheimer approximation.
The mass-independent parameters describing the latter situ-
ation are, of course, directly calculable from the constants
obtained using Eq. ͑2͒. Furthermore, the atomic mass-
dependent Born–Oppenheimer breakdown terms now appear
as additive and not multiplicative corrections, and Eq. ͑2͒ is
therefore linear in the parameters to be determined. The ␦kl’s
have the same units as the Ykl’s and obey the relationship
low J and low data pointed to the possibilty of fitting the
v
FTMW data to a Dunham-like expression.
For this, the program DSParFit, which was kindly pro-
vided by Dr. Robert J. Le Roy, was used. This program takes
a new approach:28 instead of fitting to a ‘‘standard’’
Dunham-type expansion involving Ukl’s and ⌬kl’s,29 the
data are fit to a rearranged form of this expression, from
which Ykl and ␦kl parameters for the main isotopomer are
determined. The explicit expression used for a diatomic AB
in a X 1⌺ϩ state is
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
141.209.100.60 On: Tue, 23 Dec 2014 04:43:46

10720
J. Chem. Phys., Vol. 110, No. 22, 8 June 1999
S. A. Beaton and M. C. L. Gerry
1
ϩ
TABLE V. Molecular parameters in megahertz for isotopomers of ZrS in the X
⌺
state.
S
01
Y01
Be
103Y02
Y11
Ϫ␣e
103Y21
103␥e
103Y31
103⑀e
Zr
01
␦
␦
Parametera
90Zr32Sc
Ϫ103De
re(Å)b
d
4 606.966 120͑320͒
4 607.26͑16͒
Ϫ1.45͑2͒
Ϫ1.463 0͑54͒
Ϫ15.616 85͑67͒
Ϫ15.705 5͑50͒
Ϫ18.17͑40͒
Ϫ0.13͑7͒
0.516͑3͒
0.150͑2͒
2.156 676 49͑92͒
e
e
e
91Zr32Sf
92Zr32S
94Zr32S
96Zr32S
90Zr34S
4 593.660 694
4 580.664 958
4 555.472 701
4 531.323 683
4 407.319 808
Ϫ1.44
Ϫ1.43
Ϫ1.42
Ϫ1.40
Ϫ1.33
Ϫ15.549 23
Ϫ15.483 29
Ϫ15.355 72
Ϫ15.233 76
Ϫ14.612 63
Ϫ18.07
Ϫ17.96
Ϫ17.77
Ϫ17.58
Ϫ16.63
Ϫ0.13
Ϫ0.13
Ϫ0.13
Ϫ0.12
Ϫ0.12
2.156 676 10
2.156 675 73
2.156 675 00
2.156 674 29
2.156 669 40
correlation coefficients from least squares fit ͑isotopomer 1 is 90Zr32S͒
1
Y01
Y11
Y21
Y31
Ϫ0.855
0.810
Ϫ0.771
Ϫ0.375
0.368
1
rms of residualsϭ0.26 kHz
no. of data pointsϭ23
no. of isotopomersϭ5
Ϫ0.987
0.959
Ϫ0.032
Ϫ0.251
Ϫ0.176
1
Ϫ0.991
0.042
0.172
0.167
1
Y02
Ϫ0.054
Ϫ0.155
Ϫ0.178
1
S
Ϫ0.029
Ϫ0.014
1
␦
␦
01
Zr
01
0.370
0.399
1
aSpectroscopic parameter to which the Ykl is approximately equal, where Ev,JϭJ(Jϩ1) B ϪD J(Jϩ1)Ϫ␣ ( ϩ1/2)ϩ␥ ( ϩ1/2)2ϩ⑀ ( ϩ1/2)3 ; see
͓
v
v
v
e
͔
e
e
e
e
Ref. 26.
2
bCalculated from Y01 using Y01ϭh/8␲ ␮re where ␮ is the atomic reduced mass.
2
cParameters for this isotopomer are the results of the least squares fit of all the isotopic data ͑excluding 91Zr32S data͒ to Eq. ͑2͒. The parameters for all other
isotopomers presented in this table are calculated from these using Eq. ͑5͒.
dNumbers in parentheses are 95% confidence limits in units of the last significant figure except those for the bond length re , which are one standard deviation
in units of the last significant figure ͑also see text͒.
eSpectroscopic parameters from Jonsson et al. ͑Ref. 20͒
fData for this isotopomer were not included in the fit and the predicted parameters for this species ignore nuclear spin effects.
Ϫ͑lϩk/2͒
1
Y1klϭ␮
UklϪ␦AklϪ␦Bkl ,
͑3͒
are given in Tables IV and V, respectively; the residuals are
given in Tables I and II, respectively. It can be seen that the
parameters obtained from these fits are all well deter-
hence in general giving a more obvious picture of the mag-
nitude of the mass-dependent corrections to the Y1kl’s. It
should be noted that ␦kl parameters have an implicit depen-
dence on the choice of isotopomer 1. This is best illustrated
for the special case of kϭ0, lϭ1 by the relation of the ␦01’s
to the isotopically independent Watson-type ⌬01’s
␦
01
mined and are not highly correlated with any other param-
eters. This indicates that using FTMW data alone, a break-
down in the Born–Oppenheimer approximation for these two
molecules can be observed. In particular, for ZrO, even mea-
surement of only the Jϭ1–0 transition has demonstrated
that the effect is real and that it can be quantified.
meU01⌬A01
␮1M1A
␦A01ϭϪ
,
͑4͒
It should be noted that the above analysis fitted the data
to well within the experimental uncertainty without the in-
clusion of the nuclear field effects described by Schlembach
and Tiemann.31 These had been found to be significant for
metal atoms low in the periodic table, notably Tl and Pb,31 in
several diatomics. Since DSParFit is not yet programmed to
include these effects, the program used in the initial fitting
was modified and extended to check that the nuclear field
effects could be ignored. Only the effect of the Zr nucleus
was included. It was found that the inclusion of the field
effect did not improve the rms of the residuals, and futher-
more produced a fitting constant that was indeterminate and
where me is the mass of the electron, and the analogous
equation for atom B. Further advantages are discussed by Le
Roy.28
Initially, the FTMW data from this work were least
squares fit to Eq. ͑2͒ with all the ␦kl terms constrained to
zero. Since only the Jϭ1–0 transition was measured for the
ZrO isotopomer, Y102 was constrained to the value of the
centrifugal distortion parameter ϪD0 for the main isoto-
pomer given by Balfour and Tatum,30 which is essentially
the same as ϪDe given by Philips and Davis7 ͑see Table IV͒.
For both molecules, the residuals in the resulting fits had
unacceptably large root-mean-square ͑rms͒ values: 258 kHz
for ZrO and 23 kHz for ZrS. This demonstrates that, particu-
larly in the case of ZrO, simple mass scaling of the Ykl
parameters is completely inadequate to model the data. Only
was essentially perfectly correlated with ␦0Z1r . A fit was also
01
Zr
tried in which the field effect was included but ␦ was ig-
nored, following the procedure of Ref. 31. In this case the
rms of the residuals was ten times worse, and greater than the
experimental uncertainty, and systematic isotopically depen-
dent residuals were found. We thus conclude that the nuclear
field effects can be ignored with the present data, though a
larger data set might possibly reveal them. The following
discussions are based on this assumption.
O/S
01
Zr
01
the inclusion of both the ␦ and ␦ terms reduced the rms
of the residuals below the estimated measurement uncer-
tainty ͑Ϯ1 kHz͒; no other ␦kl or Ykl terms could be deter-
mined for either molecule. The parameters and correlation
coefficients resulting from these fits of the ZrO and ZrS data
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
141.209.100.60 On: Tue, 23 Dec 2014 04:43:46

J. Chem. Phys., Vol. 110, No. 22, 8 June 1999
S. A. Beaton and M. C. L. Gerry
10721
TABLE VI. Molecular constants in megahertz for 91Zr16O and 91Zr32S.
TABLE VII. Watson-type ⌬01 terms for several diatomics.
B
103D0
9.531a
eQq0(91Zr)
A
CI(91Zr)
⌬
Molecule͑AB͒
Ref.
⌬
Molecule
B0
01
01
b
a
12 648.619 15a
130.549 9͑46͒ Ϫ0.014 15͑23͒
ZrO
ZrS
Ϫ4.872͑39͒
Ϫ5.325͑82͒
Ϫ6.188 8͑25͒
Ϫ6.523͑39͒
this work
this work
91Zr16O
91Zr32S
4 585.881 68͑41͒ 1.455͑66͒ 116.460 9͑47͒ Ϫ0.011 03͑24͒
CO
Ϫ2.054 5͑12͒
Ϫ1.505͑87͒
Ϫ2.62͑35͒
Ϫ0.26͑20͒
Ϫ2.098 2͑13͒
Ϫ1.86͑14͒
Ϫ4.218 1͑13͒
0.126 2͑8͒
34
35
36
37
aConstrained to these values; see text.
b
b
GeSe
GaH
ClH
bNumbers in parentheses are one standard deviation in units of the last
significant figure.
aThe numbers in parentheses are one standard deviation in units of the last
significant figure.
For both species, Ykl’s were determined for the main
isotopomers directly in the least squares fits, the results of
which are given in Tables IV and V. Ykl’s for the minor
isotopomers have been calculated using the results of the fit
and
bThese numbers are actually ⌬B terms determined from a fit to Dunham
potential parameters, but only differ from ⌬01 terms in that they do not
contain a contribution from the Dunham correction, which is expected to be
small.
M␣AϪM1A
M␣BϪM1B
lϩk/2
␮
1
B
kl
Y␣ ϭ Y1 ϩ
␦A ϩ
ͪ ͩ
kl
␦
,
both eQq0 and CI from the data the parameters in Table IV
were used to calculate values for the constants B0 and D0 for
the 91Zr16O isotopomer and these were constrained in the fit.
This is equivalent to calculating and constraining the hypo-
thetical unsplit transition frequency and modeling the hyper-
fine interaction only. In the resulting fit the residuals had a
rms of 0.13 kHz which is very satisfactory and illustrates the
quality of the results in Table IV.
ͩ ͪ
ͩ
ͪ
ͭ
ͮ
MA␣
MB␣
kl
kl
␮
␣
͑5͒
and are also given in Tables IV and V for the reader’s con-
venience. In addition, re values have been calculated from
the Y01 parameters to demonstrate the variation in ‘‘equilib-
rium bond lengths’’ between isotopomers of the same mo-
lecular species. As a note, the uncertainties in the re bond
lengths quoted here are dominated by the uncertainties in the
fundamental constants,32 not by those in the atomic masses
or Y01’s.
V. DISCUSSION
It should be borne in mind, however, that because of the
limited data set, the parameters obtained in the present work
are likely to model only the bottom of the potential well
effectively and that as a result their predictive powers for
A. Born–Oppenheimer breakdown „BOB… correction
terms
To our knowledge, the present work is the first time that
͑BOB͒ correction terms have been obtained for a transition
metal-containing diatomic; the results are particularly inter-
esting. In order to facilitate comparisons with other species,
the Watson-type ⌬01 terms have been calculated for ZrO and
ZrS from the constants in Tables IV and V and are given in
Table VII. This also provides the advantage of a comparison
of isotopically independent parameters for which there are
expressions already in the literature for the various contribu-
tions. The BOB terms determined in this work for both of the
atoms in the each of the zirconium species studied are large
when compared to those of other molecules for which this
type of analysis has been performed; several such results are
also given in Table VII. Many previous studies have been
concerned with either very light molecules or hydrides ͓since
the correction terms are proportional to 1/M as can be seen
from Eq. ͑2͔͒; however the present work shows that the ef-
fects of the breakdown of the Born–Oppenheimer approxi-
mation are also evident for the transition metal oxide and
sulphide studied here. Three previous studies of relatively
heavy metal oxides ͓BaO and SrO,38 SnO,39 and GeO ͑Ref.
40͔͒, which all combined infrared and microwave data, were
unable to determine rotational BOB parameters for either
atom. However, they have been determined for PbS and sev-
eral other group 13 and 14 diatomics; see Ref. 41.
higher J and
transitions are probably limited. Unfortu-
v
nately, no vibration–rotation spectra have been recorded for
either species to date to test this hypothesis. However, com-
bining the data obtained in the current study with existing
information on the X 1⌺ϩ state from electronic spectroscopy
and fitting them together to directly determine a potential
would be desirable.
B. Hyperfine structure
The spectroscopic constants for the 91Zr16O and 91Zr32S
isotopomers were determined using Pickett’s exact fitting
program SPFIT ͑Ref. 33͒ and are given in Table VI. This
program employs a Hamiltonian of the form
HϭHrotationϩHcent. distortionϩHnuc. quadrupoleϩHnuc. spin-rotation
͑2͒
͑2͒
ϭB0J2ϪD0J4ϩV –Q ϩCII–J.
͑6͒
For 91Zr32S a sufficient number of transitions were observed
so that all four constants given in Table IV could be deter-
mined directly in a least squares fit. By comparing Eq. ͑2͒
with the above Hamiltonian it can be seen that numerically
in this case B0ϭY01Ϫ 12Y11Ϫ 14Y21Ϫ 18Y31 and D0ϭϪY02
.
The B0 and D0 parameters determined for 91Zr32S in this
way are therefore in excellent agreement with the results of
the multi-isotopomer fit ͑Table V͒ which predict B0
ϭ4585.881 544 MHz and D0ϭ1.442ϫ10Ϫ3 MHz.
Following Tiemann et al.41 the ⌬01 correction terms may
be written
Dunham
01
⌬01ϭ⌬a0d1ϩ⌬0n1onadϩ⌬
,
͑7͒
In the case of 91Zr16O, however, only three hyperfine
components were measured. In order to determine values for
which for atom A, for example, becomes
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
141.209.100.60 On: Tue, 23 Dec 2014 04:43:46

10722
J. Chem. Phys., Vol. 110, No. 22, 8 June 1999
S. A. Beaton and M. C. L. Gerry
͑D͒
TABLE VIII. Calculation of bond lengths in angstroms for ZrO and ZrS.
␮⌬Y01
␮g ͒
͑
J
⌬A ϭ ⌬A ͒adϩ
B ϩ
,
͑8͒
͑
01
01
90Zr16O
90Zr32S
mp
meBe
a
where (⌬A01)ad is the adiabatic correction to the Born–
Oppenheimer approximation, (␮gJ)B is the isotopically in-
1.711 952 42͑73͒
1.711 745 27͑74͒
1.711 91b
2.156 676 49͑92͒
2.156 520 76͑92͒
2.156 61͑4͒
re
rBe O
rleit
c
dependent value of ␮gJ referred to nucleus B as origin, mp is
(D)
01
aThe numbers in parentheses are one standard deviation in units of the last
the mass of the proton and ⌬Y
is the Dunham correction
significant figure.
to Y01 . The last term in Eq. ͑8͒ can be calculated from avail-
able spectroscopic constants.27,26 It is found to be of the or-
der of 10Ϫ8 MHz for each term in both ZrO and ZrS, and
therefore negligible at the accuracy considered here. Hence
the experimentally determined values of the ⌬01’s in this
work can be viewed as simply the sum of the adiabatic and
nonadiabatic contributions. Unfortunately, the molecular ro-
tational gJ factor has not been measured for either species
and so the relative magnitude of these two contributions for
each atom cannot be quantified yet. However, considering
the electronic structures of these molecules ͑which are typi-
cal of transition metal species͒ it does seem likely that the
dominant contributions to these BOB terms for both the Zr
and the O and S atoms will be nonadiabatic in origin. In
addition to the second-order interaction of the X 1⌺ϩ state
with excited 1⌸ states treated by Watson,29 it is also possible
that other second order ͑e.g., spin orbit͒ and a number of
higher-order terms would be significant for these transition
metal compounds given the large number of low-lying elec-
tronic states that are present. For example, in ZrS there are
seven known electronic states ͑two single, five triplet͒ within
ϳ15 000 cmϪ1 of the ground state. In particular the very
low-lying ͑ϳ500 cmϪ1͒ a 3⌬ state could interact with the
ground state via the B 1⌸ state at around 10 000 cmϪ1. Since
the magnitude of the correction due to this interaction is
proportional to the inverse of the energy differences between
the states this might be expected to be significant. It will be
interesting to see if similar results are obtained for other
transition metal diatomic species.
bCalculated from Be given by Philips and Davis ͑Ref. 7͒ using the atomic
reduced mass.
cJonsson et al. ͑Ref. 20͒.
given by Bunker,42 since U01 is obtained from the constants
in Tables IV and V using Eq. ͑3͒. This number represents
what the bond length for a molecule would be if the first-
order Bohr–Sommerfeld quantization condition is assumed
to be exact and mass dependent corrections to the potential
energy function are ignored. It also given in Table VIII. It is
interesting to note that the values of rBe O for ZrO and ZrS
differ from those for re for the main isotopomer signifi-
cantly, by ϳ2ϫ10Ϫ4 Å in both cases. This is comparable to
the uncertainties in the literature values of the re bond
lengths determined by electronic spectroscopy for these iso-
topomers. This difference is, of course, a mass-dependent
effect; the corresponding differences for some other species
are found to be ϳ4ϫ10Ϫ5 Å for HCl,27 ϳ1ϫ10Ϫ4 Å for
CO,27 and ϳ2ϫ10Ϫ3 Å for GaH.36
As mentioned in Sec. V A, the nonadiabatic effects can-
not be calculated because of the lack of the molecular gJ
factor ͓see Eqs. ͑10͒ and ͑21͒ in Ref. 27͒. However, having
calculated rBe O , a very crude approximation for gJ may be
obtained with the assumption that nonadiabatic effects com-
pletely dominate and therefore raedϷreBO . The result is gJϭ
Ϫ0.44 for ZrO and Ϫ0.27 for ZrS.
C. Quadrupole coupling constants
It is clear from Table VI that the 91Zr quadrupole cou-
pling constants for ZrS and ZrO have the same signs and are
very similar in magnitude. This is also true for the spin ro-
tation parameters for the two molecules. In order to under-
stand the various contributions to the eQq0(91Zr) parameter
for each species, a useful starting point is a qualitative mo-
lecular orbital diagram. Figure 4 shows such a diagram for
ZrO. In this picture10 the bonding is described in terms of
fully occupied 11␴ and 5␲ molecular orbitals largely local-
ized on the oxygen which arise primarily from the oxygen
2p and the zirconium 4d atomic orbitals. The remaining two
valence electrons occupy the 12␴ orbital, a zirconium-
centered 5s5p hybrid pointing away from the oxygen, thus
reducing electron–electron repulsion. It is possible to derive
an expression for eQq0(91Zr) in terms of the contributions
from unbalanced electrons ͑both p and d͒ using the Townes–
Dailey model43 and an extension of this model given by
Brown.44 The resulting expression in this case is
B. Bond lengths
The determination of BOB terms in this work leads to
the need for a clear definition of what is meant by a bond
length. The re values given in Tables IV and V were calcu-
lated directly from the Y01’s ͑which are strictly only approxi-
mately equal to Be͒ using the atomic reduced mass and will
be referred to as the ‘‘atomic equilibrium bond lengths.’’
When the Dunham correction can be neglected ͑as in this
case͒ then Y01ϭBe and so this bond length can also be
viewed as re(adϩnonad) . It differs between isotopomers because
both the adiabatic and nonadiabatic contributions to the
Born–Oppenheimer bond length are isotopically dependent.
The previous literature values of the bond lengths defined in
this way for the main isotopomers are presented for compari-
son in Table VIII.
The isotopically invariant Born–Oppenheimer bond-
length, rBe O , can be calculated for each molecule using
eQq0 91Zr ϭeQq510n5p
͑
͒
z
h
n
xzϩn4d
͒
yz
͑
4d
U01ϭ
,
2
͑9͒
8␲ rBO
͒
2
ϩeQq420
n
2ϩ
,
͑10͒
ͫ
ͬ
4d
͑
z
e
2
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
141.209.100.60 On: Tue, 23 Dec 2014 04:43:46

J. Chem. Phys., Vol. 110, No. 22, 8 June 1999
S. A. Beaton and M. C. L. Gerry
10723
limit for the first term on the right hand side of Eq. ͑10͒ and
hence a lower limit for the second term and consequently the
minimum populations for the 4d orbitals. By assuming that
the populations of all three orbitals are equal we have n4d
2
z
ϭn4d ϭn4dyzϭ0.18. By referring back to the molecular or-
xz
bital diagram in Fig. 4 it can then be calculated that the
maximum charge transfer from zirconium to oxygen on for-
mation of ZrO would then be approximately one and a half
electrons. In other words, the upper limit on the ionicity of
the molecule is in the region Zrϩ1.5OϪ1.5. It should be noted
that the ab initio study10 determined the net charge on Zr to
be ϩ0.36; however this calculation underestimated both the
dipole moment of ZrO ͓1.560 D compared to the experimen-
tal value of 2.551 ͑11͒ D ͑Ref. 9͔͒ and the degree of 5s5p
hybridization.
FIG. 4. Qualitative molecular orbital diagram for ZrO.
The size of eQq0(91Zr) is similar for ZrS and ZrO al-
though ab initio calculations predict ZrS to be appreciably
less ionic than ZrO.10 The magnetic hyperfine parameters for
the a 3⌬ state of ZrS have not been measured and so an
identical treatment for ZrS is not possible. However, the re-
sults can be rationalized in terms of the bonding because in
each case there are two effects which contribute to the mag-
nitude of eQq0(91Zr). Sulphur is less electronegative than
oxygen suggesting that there would be less charge transfer
on formation of an ionic bond. Thus the negative sulphide
ion would generate a smaller electrostatic field than the oxide
ion and so the Zr electron distribution would be less polar-
ized by it. Hence it seems likely that there would be less 5p
character in the sp hybrid on Zr in ZrS than in ZrO. This
would tend to decrease the experimentally determined value
of eQq0(91Zr). On the other hand, there would probably be
greater overlap of atomic orbitals between Zr and S than
between Zr and O because of the greater spatial extent of
sulphur orbitals. This would lead to a greater covalent com-
ponent in the bonding and increased zirconium 4d occu-
pancy, thus causing an increase in the observed value of
eQq0(91Zr). The former effect presumably dominates in this
case resulting in a slightly smaller value for eQq0(91Zr) in
ZrS than ZrO.
where eQq510 and eQq420 are the zirconium atomic quadru-
pole coupling constants for a single electron in a 5p or 4d
orbital, respectively, and ni is the number of electrons in the
zirconium i atomic orbital ͑the z axis being along the inter-
nuclear bond͒. Neither eQq510 nor eQq420 is available in the
literature; however, there is an experimental value of
rϪ3 4dϭ2.30aϪ3 for the 4d25s2 configuration.45 Using this
͗
͘
0
value and the expression
2l lϩ1͒
͑
eQqnl0 MHz͒ϭϪ2.353
͑
2lϩ3͒ 2lϪ1͒
͑
͑
3
ϫQ fm2͒ a /r͒
,
͘
͑11͒
͑
͑
0
͗
derived from Gordy and Cook26 a value of eQq420ϭ
ϩ63.7 MHz is obtained. The number of electrons in the zir-
conium 5pz orbital can be estimated if the degree of hybrid-
ization of the 12␴ orbital is known. While there is no direct
measure of this for the X 1⌺ϩ state, the magnetic hyperfine
parameter bF for the a 3᭝ state for ZrO has been used to
deduce the percentages of 5s ͑39%͒ and hence 5p ͑61%͒
character of the corresponding orbital in that electronic
state.8 If it is assumed that the degree of hybridization is the
same in both these electronic states and also that two elec-
trons occupy this orbital, this then gives a value for n5p of
z
D. a 3⌬ state of ZrS
1.21. This leaves as unknowns in Eq. ͑10͒ eQq510 and the
populations of the three 4d orbitals involved in bonding.
Here, two possible solutions of Eq. ͑10͒ are presented.
In the first, the 4d␴ and 4d␲ populations ͑0.75 and
0.92, respectively͒ calculated in the ab initio study by Lang-
hoff and Bauschlicher10 are substituted into Eq. ͑10͒ and
eQq510ϭϩ44.2 MHz is obtained. This leads to rϪ3
It is interesting to note that both ZrO and ZrS have a
1
ϩ
⌺
ground state while both TiO and TiS have a 3⌬ ground
3
state. The ⌬ state in all these species arises from the pro-
motion of one electron from the metal centered sp hybrid to
the vacant metal d␦ orbital. The reduction in electron–
electron repulsion offsets the energy required for electronic
promotion. In ZrS the electronic energy of the a 3⌬ state is
of the order of the vibrational interval and so it is not sur-
prising that transitions within this state could be observed in
this experiment. The relative strengths of the transitions ob-
served in the two electronic states in this work remove any
͗
͘
5p
ϭ1.14aϪ0 3, which is considerably smaller than the value for
rϪ3 4d . Such a result is qualitatively consistent with recent
͗
͘
results for Ti where rϪ3 3dϭ1.4aϪ3 from atomic
͗
͘
0
measurements46 and rϪ3 4pϭ0.4aϪ3 from Fletcher et al.47
͗
͘
0
A similar trend is also observed for Sc.48 Although this result
is not conclusive, it is at least consistent with the current
understanding of the bonding in transition metal diatomics.
A second approach involves making the assumption that,
based on the above discussion, an upper limit for the value of
doubt that the ground state of ZrS is indeed the ⌺ϩ state.
1
The line shape of the transitions observed in the a 3⌬
state suggests that there is some unresolved Zeeman splitting
of the Jϭ2–1 line. Unfortunately our Helmholtz coils are
not sufficiently well aligned to collapse down the structure of
such a small splitting. In addition to this, unresolved lambda-
rϪ3
for Zr is obtained by setting it equal to the experi-
͗
͘
5p
mental value for rϪ3 4d . This would then give an upper
͗
͘
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
141.209.100.60 On: Tue, 23 Dec 2014 04:43:46

10724
J. Chem. Phys., Vol. 110, No. 22, 8 June 1999
S. A. Beaton and M. C. L. Gerry
type doubling may also contribute to the broadening of the
9 R. D. Suenram, F. J. Lovas, G. T. Fraser, and K. Matsumura, J. Chem.
Phys. 92, 4724 ͑1990͒.
lines. A search of 30 MHz either side of the Jϭ2–1 ϭ0
v
10 S. R. Langhoff and C. W. Bauschlicher, Jr., J. Chem. Phys. 89, 2160
͑1988͒.
transition of the main isotopomer revealed no lambda-type
doubling partner to that transition. If the doubling were
larger than this, then it would certainly have been resolved at
higher J in the electronic spectrum, which was not the case.
Hence it is concluded that for all the transitions observed in
this work, the lambda-type doubling is within our experi-
mental linewidth. In the limit of pure case ͑a͒ coupling and
the absence of any Zeeman splitting, this places an upper
11 S. R. Langhoff and C. W. Bauschlicher, Jr., Astrophys. J. 349, 369 ͑1990͒.
12 P. D. Hammer and S. P. Davis, J. Mol. Spectrosc. 78, 337 ͑1979͒.
13 J. E. Littleton and S. P. Davis, Astrophys. J. 296, 152 ͑1985͒.
14 P. C. Keenan, Astrophys. J. 55, 74 ͑1950͒.
15 B. Simard, S. A. Mitchell, M. R. Humphries, and P. A. Hackett, J. Mol.
Spectrosc. 129, 186 ͑1988͒.
16 B. Simard, S. A. Mitchell, and P. A. Hackett, J. Chem. Phys. 89, 1899
͑1988͒.
limit on the lambda-type doubling parameter o⌬ ͑Ref. 49͒ of
17 J. Jonsson, B. Lindgren, and A. G. Taklif, Astron. Astrophys. 246, L67
͑1991͒.
˜
approximately 6 kHz.
18 J. Jonsson, J. Mol. Spectrosc. 169, 18 ͑1995͒.
19 J. Jonsson and B. Lindgren, J. Mol. Spectrosc. 169, 30 ͑1995͒.
20 J. Jonsson, S. Wallin, and B. Lindgren, J. Mol. Spectrosc. 192, 198
͑1998͒.
VI. CONCLUSION
ZrO and ZrS have been generated using a laser ablation/
supersonic expansion technique and their rotational spectra
have been recorded using FTMW spectroscopy. Transitions
in six isotopomers of zirconium monosulphide and eight iso-
topomers of zirconium monoxide have been observed. The
data obtained in this work were fit to a Dunham-like expres-
sion and from the results Born–Oppenheimer breakdown
correction terms and equilibrium bond distances have been
determined. Not only has this work produced the determina-
tion of BOB terms for a transition metal-containing diatomic,
it has done so using only FTMW data. Hyperfine parameters
for the 91Zr32S and 91Zr16O species have also been deter-
mined and used to investigate the participation of d electrons
in the bonding of these molecules. A pure rotational transi-
tion in the a 3⌬ state of ZrS has also been observed provid-
ing some information on the lambda-type doubling in this
state.
21 L. Karlsson and C. Lundevall, J. Phys. B 31, 491 ͑1998͒.
22 T. J. Balle and W. H. Flygare, Rev. Sci. Instrum. 52, 33 ͑1981͒.
23
¨
Y. Xu, W. Jager, and M. C. L. Gerry, J. Mol. Spectrosc. 151, 206 ͑1992͒.
24 K. A. Walker and M. C. L. Gerry, J. Mol. Spectrosc. 182, 178 ͑1997͒.
25 L. Karlsson, B. Lindgren, C. Lundevall, and U. Sassenberg, J. Mol. Spec-
trosc. 181, 274 ͑1997͒.
26 W. Gordy and R. L. Cook, Microwave Molecular Spectra, 3rd ed. ͑Wiley,
New York, 1984͒.
27 J. K. G. Watson, J. Mol. Spectrosc. 45, 99 ͑1973͒.
28 R. J. Le Roy, J. Mol. Spectrosc. ͑submitted͒.
29 J. K. G. Watson, J. Mol. Spectrosc. 80, 411 ͑1980͒.
30 W. J. Balfour and J. B. Tatum, J. Mol. Spectrosc. 48, 313 ͑1973͒.
31 J. Schlembach and E. Tiemann, Chem. Phys. 68, 21 ͑1982͒.
32
˘
I. Mills, T. Cvitas, K. Homann, N. Kallay, and K. Kuchitsu, Quantities,
Units and Symbols in Physical Chemistry, 3rd ed. ͑Blackwell Scientific,
Oxford, 1993͒.
33 H. M. Pickett, J. Mol. Spectrosc. 148, 371 ͑1991͒.
34 N. Authier, N. Bagtland, and A. Le Floch, J. Mol. Spectrosc. 160, 590
͑1993͒.
35 T. Honno and H. Uehara, Chem. Phys. Lett. 247, 529 ͑1995͒.
36 J. M. Campbell, M. Dulick, D. Klapstein, J. B. White, and P. F. Bernath,
J. Chem. Phys. 99, 8379 ͑1993͒.
ACKNOWLEDGMENTS
37 G. Guelachvili, P. Niay, and P. Bernage, J. Mol. Spectrosc. 85, 271
͑1981͒.
This work has been supported by the Natural Sciences
and Engineering Research Council of Canada ͑NSERC͒. The
authors thank Dr. Robert J. Le Roy for the program DSParFit
and for valuable discussions and extensive comments on the
manuscript. They thank the authors of Ref. 20 for communi-
cating their results to them prior to publication. They also
acknowledge Drs. Anthony Merer, Kaley Walker, Richard
Suenram, and Dale Brugh for helpful discussions.
38 C. E. Blom, H. G. Hedderich, F. J. Lovas, R. D. Suenram, and A. G. Maki,
J. Mol. Spectrosc. 152, 109 ͑1992͒.
39 A. G. Maki and F. J. Lovas, J. Mol. Spectrosc. 98, 146 ͑1983͒.
40 E. G. Lee, J. Y. Seto, T. Hirao, P. F. Bernath, and R. J. Le Roy, University
of Waterloo Chemical Physics Research Report CP-636 ͑1998͒.
41
¨
E. Tiemann, H. Arnst, W. U. Stieda, T. Torring, and J. Hoeft, Chem. Phys.
67, 133 ͑1982͒.
42 P. R. Bunker, J. Mol. Spectrosc. 68, 367 ͑1977͒.
43 C. H. Townes and B. P. Dailey, J. Chem. Phys. 17, 782 ͑1949͒.
44 T. L. Brown, Acc. Chem. Res. 7, 408 ͑1974͒.
1 A. J. Merer, Annu. Rev. Phys. Chem. 40, 407 ͑1989͒.
2 H. Spinrad and R. F. Wing, Annu. Rev. Astron. Astrophys. 7, 249 ͑1969͒.
3 P. C. Keenan, Astrophys. J. 107, 420 ͑1948͒.
4 H. L. Nordh, B. Lindgren, and R. F. Wing, Astron. Astrophys. 56, 1
͑1977͒.
45
¨
¨
S. Buttgenbach, R. Dicke, H. Gebauer, R. Kuhnen, and F. Traber, Z. Phys.
A 286, 125 ͑1978͒.
46 R. Aydin, E. Stachowska, U. Johann, and J. Dembezczynski, Z. Phys. D
15, 281 ͑1990͒.
47 D. A. Fletcher, C. T. Scurlock, K. Y. Jung, and T. C. Steimle, J. Chem.
Phys. 99, 4288 ͑1993͒.
5 D. L. Lambert and R. E. S. Clegg, Mon. Not. R. Astron. Soc. 191, 367
͑1980͒.
48 T. C. Steimle, A. J. Marr, and D. M. Goodridge, J. Chem. Phys. 107,
10406 ͑1997͒.
6 P. W. Merril, Astrophys. J. 56, 457 ͑1922͒.
7 J. G. Philips and S. P. Davis, Astrophys. J. 229, 867 ͑1979͒.
8 B. Simard, S. A. Mitchell, L. M. Hendel, and P. A. Hackett, Faraday
Discuss. Chem. Soc. 86, 163 ͑1988͒.
49 J. M. Brown, A. S.-C. Cheung, and A. J. Merer, J. Mol. Spectrosc. 124,
464 ͑1987͒.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
141.209.100.60 On: Tue, 23 Dec 2014 04:43:46