Millimeter-wave rotational spectroscopy of MgOD and CaOD ( X 2 S 1 )
B. P. Nuccio,a) A. J. Apponi,a) and L. M. Ziurysb)
Department of Chemistry, Arizona State University, Tempe, Arizona 85287-1604
~Received 31 May 1995; accepted 29 August 1995!
Pure rotational spectra of CaOD and MgOD have been recorded in the range 200–390 GHz using
millimeter/sub-mm direct absorption spectroscopy. Transitions arising from the ~000!, ~010!, ~020!,
and ~100! modes have been measured for the 2 S 1 ground electronic states of these free radicals. The
data were analyzed successfully using a linear 2 S 1 model for CaOD; for MgOD, only the ~000! and
~010! states could be fit with this Hamiltonian. Moreover, the ~010! data required the addition of a
substantial p P term to account for contamination of excited 2 P electronic states. For both species,
the a2 vibration–rotation term was found to be negative, in contrast to MgOH and CaOH,
suggesting a less anharmonic contribution to the bending potential in CaOD and MgOD. These
measurements also indicate a shorter O–H bond in MgOH than the other alkaline earth hydroxide
radicals, which likely results because this species is quasilinear. © 1995 American Institute of
Physics.
I. INTRODUCTION
Metal monohydroxide species are of interest because
they may be linear, bent, or quasilinear, depending on the
nature of the metal–OH bond. Ionic bonding results in a
linear structure, while a bent geometry indicates a covalent
bond. Some mixture of these two bond types causes a molecule to be quasilinear. The geometry of the monohydroxides
is thus an indication of the nature of the metal–ligand bond.
Such structure can readily be deduced from high resolution
spectroscopy.
To date, only a small fraction of metal monohydroxide
molecules have been studied at high spectral resolution.
These include the earlier works of Lide and collaborators,1– 4
who recorded the microwave spectrum of KOH, RbOH, and
CsOH, as well as the deuterium isotopomers of the latter two
species. They also measured many vibrational satellite lines
of these molecules, from which they deduced that there was
a large anharmonic contribution to the bending mode in both
CsOH and RbOH. More recent work has been carried out for
the alkaline earth hydroxide series. Harris and
collaborators5–7 and the Bernath group8 –11 have done extensive visible spectroscopy of CaOH, SrOH, and BaOH, particularly the A 2 P – X 2 S 1 and B 2 S 1 – X 2 S 1 systems. An
optical study by Ni and Harris has also been carried out for
MgOH.12 These investigations showed that the alkaline earth
hydroxide radicals are linear molecules, with the exception
of MgOH, which appeared to be quasilinear.12
Very recent experiments have included the measurement
of the millimeter-wave pure rotational spectra of the electronic 2 S 1 ground states of the alkaline earth hydroxide series by this group,13–16 which confirmed their linear geometry. In fact, in its ground electronic and vibrational state, the
data of Barclay, Anderson, and Ziurys14 showed that even
MgOH is, on average, linear. Other new studies on these
hydroxide radicals include optical experiments probing the
vibrationally excited levels ~010! and ~020! of SrOH and
a!
NASA Space Grant Fellow.
NSF Presidential Faculty Fellow.
b!
J. Chem. Phys. 103 (21), 1 December 1995
CaOH by Coxon and collaborators17–21 and by Jarman and
Bernath.22 In addition, Fletcher et al.23 have measured pure
rotational spectra of MgOH, CaOH, SrOH, and BaOH in
their ~010!, ~020!, ~030!, and ~100! vibrational modes. A linear model fit these data quite well, with the exception of
MgOH, and is further evidence that this species is quasilinear.
Studies have also been carried out for the deuterated
forms of many of these molecules. As mentioned, Lide and
collaborators investigated the pure rotational microwave
spectrum of CsOD2 and RbOD.3 These authors found that
the anharmonic contribution to the bending mode slightly
decreased with the deuterium substitution. The
B 2 S 1 – X 2 S 1 and C 2 D – X 2 S 1 system of CaOD have
been investigated Hailey et al.11 and by Jarman and
Bernath22 at high resolution, who determined very accurate
rotational constants for the ~000!, ~010!, and ~020! modes of
the X 2 S 1 state. Coxon, Li, and Presunka19 and Li and
Coxon21 measured the A 2 P – X 2 S 1 system of CaOD as
well, and determined ground state B v values for the ~000!,
~010!, ~020!, and several quanta of the ~100! vibrational
modes. In fact, Li and Coxon21 found that the ~020! level of
the excited A state is substantially perturbed by Fermi resonance.
Finally, recently the pure rotational spectrum the ~000!
mode of SrOD,15 BaOD,16 and MgOD15 were recorded in
this group. The substitution of deuterium, as well as the less
abundant metal isotopes of Sr, Ba, and Mg, enabled r 0 and
partial substitution r s structures to be calculated. These computations suggested that the O–H bond length in MgOH was
unusually short in comparison to BaOH and SrOH ~;0.8 Å
vs 0.9 Å!. This difference could arise from a quasilinear,
floppy structure in MgOH, where the hydrogen atom spends
a large fraction of time bent off-axis. This bending motion
could result in a shortened bond length projected along the
internuclear axis. Clearly, establishing the O–H bond length
in CaOH would be useful for comparison, which requires
isotopic substitutions.
Here, we present measurements of the pure rotational
spectrum of CaOD in its ~000!, ~010!, ~0220!, ~0200!, and
0021-9606/95/103(21)/9193/7/$6.00
© 1995 American Institute of Physics
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Nuccio, Apponi, and Ziurys: Rotational spectroscopy of MgOD and CaOD
~100! vibrational modes. We also reexamined the rotational
spectrum of MgOD in its ~000! state, and obtained data for
the ~010!, ~0200!, and ~0220! modes as well for this radical.
These measurements were carried out using millimeter/
sub-mm direct absorption spectroscopy in the frequency
range 206 –390 GHz. Part of the motivation behind recording
these spectra was to establish accurate constants for the ~020!
modes of CaOD, which were somewhat unreliable from optical data because of severe perturbations in the A excited
state.21 After assigning the CaOD data, we found an error in
our assignment of the ~000! mode of MgOD, which turned
out to actually be the (01 1d 0) state. In this paper we give
very accurate rotational constants for the ground vibrational
state and several excited modes of both molecules. We also
give estimates of the O–H bond lengths in CaOH and MgOH
and discuss the harmonic vs anharmonic contributions to the
bending vibration in these two species.
II. EXPERIMENT
The rotational spectra of CaOD and MgOD were measured using a direct absorption millimeter wave spectrometer
operating in the frequency range of 65– 400 GHz. This instrument is described in detail elsewhere.24 Briefly, the spectrometer consists primarily of three parts: the sample cell, the
radiation source, and the detector. To generate the radiation,
two tunable Gunn oscillators were used, operating from 65–
115 GHz. The oscillators were phase locked to a signal generator operating near 2 GHz. A frequency multiplier was
used to achieve the higher frequencies mentioned. The Gunn
source is frequency modulated at a rate of 25 kHz for phase
sensitive detection. The radiation from the source is transmitted quasioptically using teflon lenses and scalar feed horns.
The sample cell is a 0.5 m metal tube 4 in. in diameter with
teflon lenses sealing both ends. The radiation makes a double
pass through the cell via a rooftop reflector affixed to one
end, which imparts a 90° phase change to the signal which
then can be separated from the original radiation using a
polarizing grid. The radiation then is focused into a InSb
detector, which is cooled to 4.2 K with liquid helium.
The MgOD and CaOD molecules were produced by two
different methods. Originally, the molecules were created in
the cell by reacting metal vapor with a deuterated hydrogen
peroxide. The vapor was generated by heating solid metal in
a Broida-type oven. The deuterated hydrogen peroxide was
made by combining D2O and H2O2 in a small sealed container, which was then pumped on to remove H2O, thereby
forming a concentrated solution of D2O2 via hydrogen exchange. Later, an easier and more effective production
method was found by reacting metal vapor with pure D2O
while running a dc discharge of ;250 mA. This technique
gave stronger signals. The metal vapor was typically combined with about a 50 mTorr of D2O2 or D2O, and 20–30
mTorr flow of argon carrier gas, using either method.
The rotational transition frequencies were measured using scans 3 MHz in frequency coverage, with linewidths of
;900 kHz. The estimated accuracies of the measurements
are 6100 kHz for the ~000! modes, while the remaining
modes likely have an error of about 6250 kHz. The most
probable source of uncertainty is in determining the center of
any given line, which was done by fitting the spectra with
Gaussian profiles. An additional error is the intrinsic stability
of the 2 GHz signal generator.
III. RESULTS
The rotational transitions measured for CaOD are shown
in Table I. As the table illustrates, eleven rotational transitions from the ground vibrational mode were recorded, and
four transitions were observed for the excited modes ~0110!,
~0200!, ~0220! and ~100!. For every transition, spin–rotation
doublets were resolved, and l-type doublets were recorded
for the bending modes.
Figure 1 shows the progression of the vibrational modes
as a function frequency within a given rotational transition
for CaOD. The lines observed, in this case for the N519 –
20 transition, are drawn as stick figures. The strongest set of
doublets are assigned to the ~000! mode, as expected. The
next strongest lines observed belong to the ~010! bending
mode. Because of l-type doubling, two sets of doublets occur
in this state, and for CaOD each respective pair occurs on
either side of the ~000! lines. Their centroid lies at the higher
frequency side of the ground state doublets, resulting in a
negative vibration–rotation term a2 , which is not very large.
A small difference in the spin–rotation splittings in the two
~010! modes was additionally observed. As also shown in the
figure, the ~0220! lines lie approximately twice the frequency
spacing from the ~000! lines to the ~010! centroid. Again, the
~0220! state is split by l-type doubling such that two sets of
doublets are present. However, the l-type doubling in this
case is much smaller. To higher frequency are doublets for
the ~0200! mode, spit away from ~0220! lines because of
l-type resonance. Finally, spin–rotation pairs of the ~100!
mode ~the heavy-atom stretch! occur far to the low frequency
side of the ~000! lines, almost 2 GHz away in the N519 – 20
transition. In contrast to the bending vibration, the heavyatom stretch for CaOD has a positive vibration–rotation
term.
Table II lists the data taken for MgOD. For this molecule, only ~000! and ~010! data are presented. Seven rotational transitions for the ~000! state and four transitions for
each l-type component of the ~010! bending mode were recorded. Again, spin–rotation splittings were resolved in every transition.
The pattern for the rotational transitions of the ~000! and
~010! modes of MgOD is very similar to that of CaOD. The
l-type doublets are split to either side of the ground state
lines, with a negative a2 value such that the ~010! centroid
lies on the higher frequency side of the ~000! mode. Also, the
fine structure splittings differ between the (01 1c 0) and
(01 1d 0) modes and this difference is noticeably larger
~;1–2 MHz! than in CaOD. After that, however, the pattern
for MgOD deviates from that of CaOD. The ~0200! mode
appears to be shifted unexpectedly high in frequency relative
to the ~000! lines, and other doublet pairs were observed
which could not be identified. Furthermore, the ~020! states
could not be fit with the linear model used in the analysis
~see Sec. IV!. The vibrational satellite lines of MgOH presented a similar problem ~see Fletcher et al.23!. Assignment
of many of the vibrational modes and successful analysis for
J. Chem. Phys., Vol. 103, No. 21, 1 December 1995
Nuccio, Apponi, and Ziurys: Rotational spectroscopy of MgOD and CaOD
TABLE I. Observed transition frequencies for CaOD (X 2 S 1 ).
N→N 8
TABLE I. ~Continued.!
J→J 8
nobs ~MHz!
nobs2ncalc. ~MHz!
N→N 8
9.5→10.5
10.5→11.5
10.5→11.5
11.5→12.5
11.5→12.5
12.5→13.5
12.5→13.5
13.5→14.5
13.5→14.5
14.5→15.5
14.5→15.5
15.5→16.5
15.5→16.5
16.5→17.5
16.5→17.5
17.5→18.5
17.5→18.5
18.5→19.5
18.5→19.5
19.5→20.5
19.5→20.5
20.5→21.5
199 766.521
199 798.046
217 918.780
217 950.289
236 068.507
236 099.976
254 215.464
254 246.996
272 359.435
272 391.012
290 500.287
290 531.785
308 637.702
308 669.199
326 771.527
326 803.016
344 901.511
344 933.016
363 027.477
363 059.004
381 149.166
381 180.697
0.006
0.016
20.003
20.008
0.002
20.043
20.005
0.013
20.029
0.034
0.010
20.006
0.007
20.011
0.018
20.007
0.007
20.002
0.010
0.021
20.025
20.008
(02 2d 0)
17→18
16.5→17.5
17.5→18.5
17.5→18.5
18.5→19.5
18.5→19.5
19.5→20.5
19.5→20.5
20.5→21.5
324 766.053
324 797.015
342 784.299
342 815.568
360 798.825
360 830.085
378 809.157
378 840.365
0.113
0.005
20.131
0.001
20.056
20.005
0.075
0.000
16.5→17.5
17.5→18.5
17.5→18.5
18.5→19.5
18.5→19.5
19.5→20.5
19.5→20.5
20.5→21.5
326 433.326
326 465.303
344 544.407
344 576.488
362 651.057
362 682.927
380 753.725
380 785.474
20.072
20.092
0.097
0.231
20.082
20.106
0.056
20.034
16.5→17.5
17.5→18.5
17.5→18.5
18.5→19.5
18.5→19.5
19.5→20.5
19.5→20.5
20.5→21.5
327 258.425
327 290.199
345 414.948
345 446.620
363 567.235
363 598.921
381 715.115
381 746.833
20.018
20.034
0.056
20.012
0.025
0.024
20.064
0.022
16.5→17.5
17.5→18.5
17.5→18.5
18.5→19.5
18.5→19.5
19.5→20.5
19.5→20.5
20.5→21.5
327 108.595
327 140.451
345 252.891
345 284.822
363 392.519
363 424.393
381 526.877
381 558.874
0.014
20.078
0.006
0.009
0.084
0.053
20.104
0.015
16.5→17.5
17.5→18.5
17.5→18.5
18.5→19.5
18.5→19.5
19.5→20.5
19.5→20.5
326 878.395
326 910.522
345 013.302
20.024
20.037
20.167
363 144.400
363 176.522
381 270.963
0.058
0.041
0.144
~000!
10→11
11→12
12→13
13→14
14→15
15→16
16→17
17→18
18→19
19→20
20→21
~100!
17→18
18→19
19→20
20→21
(01 1c 0)
17→18
18→19
19→20
20→21
(01 1d 0)
17→18
18→19
19→20
20→21
~0200!
17→18
18→19
19→20
20→21
(02 2c 0)
17→18
18→19
19→20
20→21
9195
18→19
19→20
20→21
J→J 8
nobs ~MHz!
nobs2ncalc. ~MHz!
20.5 → 21.5
381 302.890
20.068
16.5→17.5
17.5→18.5
17.5→18.5
18.5→19.5
18.5→19.5
19.5→20.5
19.5→20.5
20.5→21.5
326 905.271
326 937.363
345 045.325
345 077.216
363 181.190
363 213.261
381 313.523
381 345.642
20.022
0.013
0.215
0.069
20.096
20.040
20.109
0.022
MgOH required use of a quasilinear model, as carried out by
Bunker et al.25 A similar analysis of the MgOD spectra is
currently being performed and will be published in a later
paper.26
Typical spectra obtained in this work are shown in Figs.
2 and 3. In Fig. 2, the N513→14 rotational transition in the
~000! state of MgOD near 376 GHz is displayed. The spinrotation doublets of this molecule, separated by about 33.6
MHz, are clearly resolved. Figure 3 is the spectra of the
l-type doublets of the ~0220! mode in the N520→21 rotational transition of CaOD near 363 GHz. The two pairs of
doublets are labeled by (02 2c 0) and (02 2d 0), respectively.
The fine structure splitting here is 32.1 MHz.
IV. DATA ANALYSIS
The data analysis for MgOD and CaOD was done using
a conventional Hund’s case~b! 2 S Hamiltonian. The data
were fit separately for each vibrational mode recorded. The
details of the analysis are described in Fletcher et al.,23 and
hence will only be summarized here.
Briefly, the two spin–rotation energy levels for each rotational level N are given by27
F 1 ~ N ! 5B v @ N ~ N11 ! 2l 2 # 2D v @ N ~ N11 ! 2l 2 # 2
11/2 g V N11/2 g D N 2 ~ N11 ! ,
~1!
FIG. 1. A stick figure illustrating the vibrational progression in the
N519→20 rotational transition of CaOD near 363 GHz. The heights of the
sticks qualitatively indicate the observed relative intensities. Transitions
arising from ~000! state, l-type doublets of the ~0110! mode, and l components of the ~0220! and ~0200! vibrations and ~100! stretching mode are
present.
J. Chem. Phys., Vol. 103, No. 21, 1 December 1995
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Nuccio, Apponi, and Ziurys: Rotational spectroscopy of MgOD and CaOD
TABLE II. Observed transition frequencies for MgOD (X 2 S 1 ).
N→N 8
J→J 8
nobs ~MHz!
nobs2ncalc. ~MHz!
5.5→6.5
6.5→7.5
6.5→7.5
7.5→8.5
7.5→8.5
8.5→9.5
8.5→9.5
9.5→10.5
9.5→10.5
10.5→11.5
11.5→12.5
12.5→13.5
12.5→13.5
13.5→14.5
188 094.847
188 128.587
214 958.413
214 992.079
241 818.156
241 851.798
268 673.605
268 707.207
295 524.252
295 557.872
349 209.358
349 242.969
376 042.759
376 076.442
20.020
0.050
20.006
20.006
0.006
20.014
0.020
20.033
0.008
20.021
0.031
0.007
20.037
0.019
7.5→8.5
8.5→9.5
9.5→10.5
10.5→11.5
11.5→12.5
12.5→13.5
12.5→13.5
13.5→14.5
241 053.319
241 088.836
294 590.555
294 625.651
348 107.014
348 141.873
374 856.272
374 891.113
20.059
0.015
0.077
20.030
0.037
20.019
20.057
0.031
7.5→8.5
8.5→9.5
9.5→10.5
10.5→11.5
11.5→12.5
12.5→13.5
12.5→13.5
13.5→14.5
242 864.123
242 901.323
296 801.335
296 838.152
350 716.238
350 752.822
377 664.144
377 700.624
20.043
0.022
0.058
20.019
20.002
20.025
20.014
0.022
~000!
6→ 7
7→ 8
8→ 9
9→10
10→11
12→13
13→14
1c
(01 0)
8→ 9
10→11
12→13
13→14
(01 1d 0)
8→ 9
10→11
12→13
13→14
FIG. 3. Spectrum of the N520→21 rotational transition of CaOD in its
~0220! excited vibrational mode near 363 GHz. This transition consists of
l-type doublets, which are labeled by (02 2c 0) and (02 2d 0), each which are
additionally split due to spin–rotation interactions. The spin–rotation splitting of g'32.2 MHz is readily apparent for each pair. This spectrum is an
average of four scans, each with ;3 min scan time.
F 2 ~ N ! 5B v @ N ~ N11 ! 2l 2 # 2D v @ N ~ N11 ! 2l 2 # 2
21/2 g V ~ N11 ! 21/2 g D N ~ N11 ! 2 .
In this equation g v is the spin–rotation constant and g D is its
centrifugal distortion correction. The constant g D was used
only for MgOD and for the ~010! and ~100! modes of CaOD.
Additional terms were added to the Hamiltonian to account
for l-type doubling interactions in the bending modes. For
the ~010! levels, the l-type doubling term, taken from Presunka and Coxon,20 is
2
DE l-type561/2q v N ~ N11 ! 61/2q D
v @ N ~ N11 !# .
FIG. 2. Spectrum of the N513→14 rotational transition of MgOD in its
ground vibrational and electronic ~000! state near 376 GHz. The two spinrotation components of this transition are clearly resolved. This spectrum,
covering 100 MHz in scan range, represents an average of four scans, each
with a scan time of ;3 min.
~2!
~3!
In this expression, q V is the l-type doubling constant and q D
V
is the centrifugal distortion correction to this doubling; the
1sign in the equation refers to the F 1 (c) and F 2 (d) levels
and the negative sign to the F 1 (d) and F 2 (c) states. For the
~020! modes, the interaction between the l50 and l52 components must be represented by a 333 matrix, which is described in detail by Larzilliere and Jungen28 and Jungen, Hallin, and Merer.29 The matrix representation requires
knowledge of the ~0200! and ~0220! energy separation, which
is equal to four times g 22 . The value of g 22 for CaOD was
taken from Coxon, Li, and Presunka.19 It was found that the
exact value of the energy splitting did not affect the fit very
much.
In addition to these parameters, a p P term had to be
added to the Hamiltonian to account for the different spin–
rotation splittings in the ~010! modes of both molecules. As
discussed by Fletcher et al.,23 this p P constant has the same
functional form as the lamba-doubling term in a 2 P electronic state, and was originally used to fit vibrational data for
C2H.31,32 For CaOD, this parameter was found to be
p P ;20.2 MHz, but was almost 1.7 MHz for MgOD.
In Table III the spectroscopic constants determined for
the ~000! and vibrationally excited modes of CaOD and
MgOD are listed. Errors quoted for the parameters are 3s,
and the overall rms of the fit for each molecule is also given.
In addition, the constants for CaOD determined from the
J. Chem. Phys., Vol. 103, No. 21, 1 December 1995
Nuccio, Apponi, and Ziurys: Rotational spectroscopy of MgOD and CaOD
TABLE III. Molecular constants for CaOD and MgOD (X 2 S 1 ).a
This work ~MHz!
( v 1v 2v 3)
CaOD
~000!
~01 0!
1
~0220!
~100!
~0200!
rms of fit:
Bv
Dv
gv
Bv
Dv
gv
gD
qv
q Dv
pP
Bv
Dv
gv
qv
Bv
Dv
gv
gD
Bv
Dv
gv
0.068
MgOD
~000!
Bv
Dv
gv
gD
~010!
Bv
Dv
gv
gD
qv
q Dv
pP
rms of fit: 0.026
9083.151 2~32!
0.008 838 3~51!
31.514~64!
9085.316 8~86!
0.009 010~11!
32.33~66!
20.000 45~57!
222.983~17!
0.000 104~22!
20.21~15!
9086.2643~87!
0.009 159~11!
32.139~78!
223.425~25!
9027.444~12!
0.008 852~16!
30.48~93!
0.000 61~81!
9093.536~12!
0.009 255~16!
32.03~11!
TABLE V. l-Type doubling constants for MgOH and CaOH.a
Optical ~MHz!
9079.4~3.6!,b 9082.28~59!c
0.008 80~17!c
28.6~2.2!c
9084.78~62!,c 9085.81~14!d
0.009 07~24!,c 0.009 156~45!d
36.9~4.5!,c 33.7~1.1!d
222.878~49!,c 222.847~36!d
13 438.500 1~54!
0.019 897~19!
33.69~19!
20.000 1~5!
13 446.403 6~62!
0.020 263~19!
36.78~25!
20.002 0~6!
2100.883~12!
0.001 463~39!
1.69~15!
9063.6~3.6!b
9024.3~1.8!b
9197
Mode
MgOHb
MgOD
CaOHb
CaOD
~0110!
~0220!
285.123~18!
2100.883~12!
221.649~10!
221.131~51!
222.983~17!
223.425~25!
a
In MHz.
From Ref. 23.
b
optical spectroscopy of Coxon, Li, and Presunka,19 Li and
Coxon21 and Jarman and Bernath22 are presented.
Because several bending modes of CaOD were analyzed,
the vibrational dependence of the rotational constant B v can
be considered. Such a dependence was modeled by Lide and
collaborators2,3 for RbOH and CsOH, and is described by the
following equation:
B v 5B̄ e 2 a 2 ~ v 2 11 ! 1 g 22 ~ v 2 11 ! 2 1 g ll l 2 .
9067~11!,b 9092.03~66!c
0.010 03~21!c
30.0~6.0!c
13,470~21!e
0.018~18!e
Errors are 3s.
Reference 19.
c
Reference 22.
d
Reference 21.
e
Reference 12.
a
~4!
Here, B̄ e 5B e 21/2 a 1 21/2 a 3 5B̃ e 21/2 a 1 . The terms in
this equation were determined from the experimentally derived rotational constants for the ~000!, ~010!, ~0200!, and
~0220! modes of CaOD and are given in Table IV. For comparison, the parameters found for CsOH and RbOH are also
presented.
Table V presents the experimentally determined l-type
doubling constants for MgOH, MgOD, CaOH, and CaOD.
In Table VI, estimates of bond lengths for CaOH are
given, as well as revised values for MgOH. For CaOH, r 0
values are only determined, but both r s and r 0 bond distances are listed for MgOH. The r s numbers were calculated
from a partial substitution structure using the 24 MgOH,
26
MgOH, and 25 MgOH data of Barclay et al.14 and the deuterium measurements here. Also listed in the table for comparison are the bond distances determined for SrOH15 and
BaOH.16
b
V. DISCUSSION
As shown in Tables I and II, the derived constants for
CaOD reproduce the observed frequencies to nobs – ncalc&43
kHz for the ~000! mode and nobs – ncalc<250 kHz for the vibrationally excited states. Similarly, for MgOD,
nobs – ncalc<80 kHz for the ~000! and ~010! modes. Hence, a
2
S Hamiltonian does appropriately describe CaOD and at
least the ground vibrational state of MgOD. However, as for
TABLE IV. Vibrational dependence of B v .a
B̃ e
a1
a2
g22
g ll
CaODb
CaOHc
RbODd
RbOHd
CsODe
CsOHe
9109.440~25!
55.707~25!
20.357~20!
1.209~5!
21.818~5!
10 085.12~10!
66.725~4!
31.518~3!
2.849~3!
23.361~1!
5750.00
38.3
11.16
1.08
21.15
6343.42
43.7
33.38
1.905
22.05
5013.88
29.3~0.2!
3.08
0.642
20.830
5535.39
33.3~0.2!
18.95
1.207
21.615
In MHz, errors are 3s.
This work.
c
From Ref. 23.
d
From Ref. 3.
e
From Ref. 2.
f
B̃ e 5B e 21/2 a 3 .
a
b
J. Chem. Phys., Vol. 103, No. 21, 1 December 1995
9198
Nuccio, Apponi, and Ziurys: Rotational spectroscopy of MgOD and CaOD
TABLE VI. Estimated bond lengths for MgOH and CaOH.a
r 0b
M–O
c
MgOH
CaOHc
SrOHe
BaOHf
1.780
1.985
2.111
2.200
rs
O–H
M–O
0.871
0.922
0.922
0.927
d
0.825d
2.109
2.196
0.924
0.930
1.784
O–H
a
In Å.
Determined from MOH/MOD.
c
Using MgOH data from Refs. 13 and 14.
d
Calculated from a partial substitution structure using
26
MgOH, and MgOD data Ref. 14.
e
Values from Ref. 15.
f
Values from Ref. 16.
b
24
MgOH,
25
MgOH,
the alkaline earth monohydroxide series, MgOD is clearly
different from CaOD. As discussed, its vibrational pattern
varies substantially from that of CaOD, with modes that cannot be fit with a linear model—identical to the behavior of
MgOH.23 Moreover, as for its hydroxide counterpart, the
~010! data of MgOD requires a large p P term ~1.69 MHz! for
a reasonable fit, i.e., the respective spin–rotation splittings in
the (01 1c 0) and (01 1d 0) modes vary significantly from each
other. The corresponding p P term in CaOD is much smaller
~20.21 MHz!. The p P parameter arises from perturbing excited electronic 2 P states. The A 2 P state of CaOD lies
closer in energy to the X 2 S state than in MgOD.12,19 Hence,
the p P constant is expected to be larger in the calcium molecule than in the magnesium species. The fact that it is quite
the opposite can be attributed to the quasilinear nature of
MgOD. An identical effect is seen in MgOH.23
The derived mm-wave spectroscopic constants agree
well with those derived from optical data for CaOD19,21,22 for
the ~000!, ~010!, and ~100! modes. There is some disagreement between our constants and the optically derived ones
from Coxon, Li, and Presunka19 for the ~020! modes for
CaOD, but, as noted by Li and Coxon,21 these differences are
not unexpected. As described by these authors, the ~020!
results from Ref. 19 are not completely reliable because of
severe perturbation by Fermi resonance of the upper A state
~020! level, and the lack of an accurate representation at that
time for this level. In fact, the a2 value for CaOD from Li
and Coxon21 of 22.56 MHz, determined from
B v (000) – B v (010), agrees well with our value of
a2522.17 MHz, calculated by the same method.
For MgOD, the only data for comparison is that of Ni,12
who estimated B v and D v constants for the ~000! state. There
is a noticeable difference between our B v value @13 438.5001
~54! MHz# and the optical number of B v 513 470(21)
MHz. This discrepancy in the optical rotational constant contributed to a misassignment of the vibrational states in our
original work on MgOD by Barclay, Anderson, and Ziurys.14
In this analysis we incorrectly assigned the (01 1d 0) mode of
MgOD to the ~000! state. Our previously published constant
of B v 513 496 MHz is incorrect, and the actual value is
B v 513 438.5001 ~54!, as shown in Table III.
The vibrational dependency of B v for CaOD, as shown
in Table IV, appears to be unusual. Using the expansion in
Eq. ~4!, a2 for CaOD has the value 20.357 MHz. This number is over an order of magnitude smaller than a2531.518
MHz for CaOH, and the sign is negative. Moreover, the
higher order terms in the expansion have larger values than
a2 , with g2251.209 MHz and g ll 521.818 MHz. This effect differs in CaOH, where the a2 constant is larger than
either g22 or g ll in the vibrational expansion ~see Table IV!.
In contrast, for RbOH and RbOD, the a2 value stays
positive and only decreases in value by a factor of three,3
when substituting D for H. Also, as in CaOH, the a2 term for
these species dominates the vibrational expansion ~again, see
Table IV!. However, as shown in Table IV, in going from
CsOH to CsOD, a2 decreases by a factor of 6. Moreover, the
a2 , g22 , and g ll terms are much closer in value for CsOD,
approaching what is found for CaOD, although a2 still remains positive.
Unfortunately, the vibrational dependence of MgOD
could not be determined. Comparing simply B(000) and
B(010), however, a2 for MgOD is roughly 27.9 MHz, vs
a2'65 MHz for MgOH. Again, as for CaOD, a2 becomes
negative with the deuterium substitution.
The sign of a2 is determined by three contributions, according to Lide,4 who expressed them in the following equation:
a 2 5 ~ a 2 ! h1 1 ~ a 2 ! h2 1 ~ a 2 ! anh .
~5!
The first contributing term ( a 2 ) h1 , is the Coriolis contribution and is equal to ( a 2 ) h1 51/2 u q v u . The second term is the
‘‘pseudoanharmonic’’ component, and the third is the anharmonic contribution; mathematical expressions for these two
latter terms, which involve bond force constants, can be
found in Lide and Matsumura.4 The ( a 2 ) h2 term is always
negative, while ~a2!anh is positive, and usually these two contributions dominate the overall a2 value in a molecule, provided the l-type doubling is small. In normal linear triatomic
molecules, a2 is usually negative because the ( a 2 ) h2 contribution is quite large. As Lide and Matsumura4 discuss, a2.0
for CsOH and RbOH because of a large anharmonic contribution, which arises from the floppy O–H bond. Also the
l-type doubling is not large in these molecules, such that
( a 2 ) h1 '4 – 5 MHz. Substitution of heavier deuterium atom
in CsOD and RbOD appears to lessen the anharmonic contribution, but not enough to change a2 to a negative value.
For the alkaline earth monohydroxides MgOH through
BaOH, a2 is positive, as described by Fletcher et al.23 Furthermore, for CaOH, SrOH, and BaOH, u q v u is &22 MHz,
such that the ( a 2 ) h1 contribution is likely not to be large for
these species. Consequently, the anharmonic term must again
determine the sign of a2 . In contrast, ( a 2 ) h1 '42.5 MHz for
MgOH, because q v for this molecule is quite large, as shown
in Table V. Hence, a2 is positive in this case because of both
the anharmonic and Coriolis terms. Unlike the alkali metal
compounds, however, substitution of D for H in CaOH and
MgOH changes the a2 value from positive to negative. For
CaOD, a2 is very small ~20.4 MHz!, but in MgOD,
a2'27.9 MHz. Again, ~a2!anh must decrease with substitution of the heavier mass. For MgOD, ( a 2 ) h2 must also be
large, because ( a 2 ) h1 '50 MHz ~q v 52100.9 MHz; see
Table V!.
J. Chem. Phys., Vol. 103, No. 21, 1 December 1995
Nuccio, Apponi, and Ziurys: Rotational spectroscopy of MgOD and CaOD
The change of a2 to a negative value on deuterium substitution in MgOH and CaOH, but not in CsOH and RbOH,
may be related to the force constant of the M–O bond. The
two alkali metals occur lower in the periodic table than Mg
or Ca, and have additional inner electron shells. Hence, the
bond of Cs and Rb to oxygen may be weaker than to magnesium or calcium. This weaker bond results in a larger
change in the moment of inertia when the MOH molecule
bends, which manifests itself as a larger anharmonic term.
The quasilinear nature of MgOH and MgOD is again
suggested in Table V. As the table shows, the l-type doubling
constants for MgOH and MgOD are substantially larger than
for their calcium counterparts. Also, they increase more in
value in going to the deuterated form, i.e., q v ~MgOH!585.1
MHz to q v ~MgOD!52100.9 MHz, as opposed to q v '221
MHz for CaOH and 223 MHz for CaOD. The ‘‘floppiness’’
of MgOH results in enhanced l-type interactions. Since
q v }1/ v 2 ,27 another way to view it is that the molecule can
easily be bent, and hence v2 is relatively small.
The quasilinear nature of the magnesium molecule also
may result in an apparent shortening of the O–H bond
length. As shown in Table VI, the r 0 structures result in an
r O–H50.922 Å for CaOH, while for MgOH, r O–H50.871
Å—considerably shorter. The O–H bond lengths in SrOH
and BaOH are also r 050.92–0.93 Å.15,16 The partial substitution structure for MgOH, using the MgOD data presented
here and the 24 MgOH, 25 MgOH, and 26 MgOH measurements of Barclay et al.,14 give an r O–H50.825 Å—even
shorter than the others. In contrast, similar substitution structures for SrOH and BaOH yield r O–H50.924 and 0.930 Å,
respectively. The smaller O–H bond distance in MgOH is
likely due to large amplitude bending motions, which results
in an average linear geometry but a shortened projected bond
length. A similar effect is seen in quasilinear AlOH.32
VI. CONCLUSION
Millimeter-wave pure rotational spectra have been recorded for CaOD and MgOD in their ~000! and ~010! modes,
as well as in its ~0200!, ~0220!, and ~100! states for CaOD.
These data were successfully analyzed using a linear 2 S
Hamiltonian, but anamolous differences occur in the spectra
of MgOD. First of all, the vibrational pattern, after assignment of the ~000! and ~010! modes, differed considerably
from that of CaOD and could not be readily analyzed, as has
been found for MgOH. Moreover, differences in the spin–
rotation splittings of the (01 1c 0) and (01 1d 0) levels resulted
in the need of a large p P term in fitting the MgOD data. The
parameter, which arises from contamination of excited 2 P
electronic states, should have been negligible, in comparison
with that determined for CaOD. The l-type doubling in the
~010! state was also considerably larger in MgOD than in
CaOD. Both these effects arise in MgOH as well, when comparing this molecule to CaOH, SrOH, and BaOH. However,
both MgOD and CaOD have a2,0, in contrast to their hydroxide counterparts, which all have a2.0. The reversal of
sign likely results from a decrease in the anharmonic contri-
9199
bution to a2 on substitution of the heavier deuterium mass.
Finally, these measurements have resulting in a determination of r 0 bond lengths for CaOH, and a refinement of both
r s and r 0 bond lengths for MgOH. In comparison with
CaOH, SrOH, and BaOH, the O–H bond distance for MgOH
does appear to be significantly shorter, likely resulting from
the species’ quasilinear structure, which likely accounts for
the other anomalous effects observed.
ACKNOWLEDGMENTS
This research was supported by NSF Grant No. AST
92-53682 and NASA Grant No. NAGW 2989. A. J. A. and
B. P. N. thank the NASA Space Grant Program for their
fellowships. We also thank D. A. Fletcher for comments on
the manuscript.
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J. Chem. Phys., Vol. 103, No. 21, 1 December 1995