High resolution spectroscopy of MgOH (X 2Σ+) in its V2 mode: Further evidence for quasilinearity

Article abstract of DOI:10.1063/1.480455

Pure rotational spectra of the MgOH and MgOD radicals have been recorded in the v₂ bending vibration of their X ²Σ⁺ ground electronic states using millimeter-wave direct absorption spectroscopy. Multiple rotational transitions arising from the v¹₂= 1¹, 2², 2⁰, 3¹, 3³, 4², and 4⁴ substates have been measured in the frequency range 240-520 GHz for these species. Both the spin-rotation and l-type doubling interactions have been resolved in the spectra. The complete data sets for MgOH and MgOD have been analyzed using a linear model for the Hamiltonian which takes into account higher order (l=±4) l-type interactions. The global analyses were adequate, but anomalous behavior was apparent in both molecules. In particular, the B_v vs v₂ relation was found to be highly nonlinear, large variations in the l-type doubling constant q were observed with vibrational level, and r₀, r_s, and r_e structures determined differed substantially. Such findings suggest that MgOH is highly quasilinear, comparable to HNCO. The competition between ionic and covalent bonding is therefore becoming apparent in the lighter alkaline earth hydroxide species.

Full text of DOI:10.1063/1.480455

High resolution spectroscopy of MgOH (X 2 Σ + ) in its V 2 mode: Further evidence for
quasilinearity
A. J. Apponi, M. A. Anderson, and L. M. Ziurys
Citation: The Journal of Chemical Physics 111, 10919 (1999); doi: 10.1063/1.480455
View online: http://dx.doi.org/10.1063/1.480455
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 111, NUMBER 24
22 DECEMBER 1999
2
؉
High resolution spectroscopy of MgOH „X ⌺ … in its V mode: Further
2
evidence for quasilinearity
A. J. Apponi,a) M. A. Anderson,b) and L. M. Ziurysc)
Department of Chemistry, Department of Astronomy, and Steward Observatory, University of Arizona,
9
33 North Cherry Avenue, Tucson, Arizona 85721
Received 26 August 1999; accepted 27 September 1999͒
Pure rotational spectra of the MgOH and MgOD radicals have been recorded in the v bending
͑
2
2
ϩ
vibration of their X ⌺ ground electronic states using millimeter-wave direct absorption
spectroscopy. Multiple rotational transitions arising from the v ϭ1 , 2 , 2 , 3 , 3 , 4 , and 4
l
1
2
0
1
3
2
4
2
substates have been measured in the frequency range 240–520 GHz for these species. Both the
spin-rotation and l-type doubling interactions have been resolved in the spectra. The complete data
sets for MgOH and MgOD have been analyzed using a linear model for the Hamiltonian which
takes into account higher order (lϭϮ4) l-type interactions. The global analyses were adequate, but
anomalous behavior was apparent in both molecules. In particular, the B vs v relation was found
v
2
to be highly nonlinear, large variations in the l-type doubling constant q were observed with
vibrational level, and r , r , and re structures determined differed substantially. Such findings
˜
0
s
suggest that MgOH is highly quasilinear, comparable to HNCO. The competition between ionic and
covalent bonding is therefore becoming apparent in the lighter alkaline earth hydroxide species.
©
1999 American Institute of Physics. ͓S0021-9606͑99͒00648-0͔
I. INTRODUCTION
bration. Later pure rotational studies conducted for the
lighter alkali species KOH and NaOH showed even more
pronounced anomalous behavior. For example, Kuijpers,
Extensive high resolution studies of metal monohydrox-
ide molecules have been conducted in the past 30 years, in
particular of alkali and alkaline earth species, revealing some
unique aspects of their bonding characteristics and dynamic
1
2
Torring, and Dymanus had to use fourth-order corrections
to fit the rotational spectra of the vibrational satellite lines of
KOH, while Pearson, Winnewisser, and Trueblood13 could
only do a state-by-state analysis of their KOH data. In the
¨
1
–4
motions. The bonding for these species is expected to be
ϩ
Ϫ
Ϫ
1
4
ionic (M OH ), with the OH ligand behaving as a halide
ion. Because of this ionic nature, the structure of these spe-
cies is predicted to be linear.5 As covalent bonding begins
to play a role, however, the structure changes, becoming
bent, in analogy to water. Such a structure has been recently
¨
case of NaOH, Kuijpers, Torring, and Dymanus were not
able to confidently assign many of the vibrational satellite
,6
0
lines of this species, including the ͑02 0͒ state. To our
knowledge, the pure rotational spectrum of NaOH has never
been fully analyzed. While the irregularities in the KOH
spectra are thought to again arise from the large amplitude v2
bending motions, those of NaOH are far more extreme and
could be an indication that the molecule is quasilinear.
The alkaline earth monohydroxides are another class of
molecules where the competition between bonding types is
becoming evident. Studies of the pure rotational spectra of
7
observed in the F excited state of CaOH, as well as in the
ground states of CuOH and AgOH. The MOH bond angles
for the two transition metal species, in fact, were found to be
8
110° and 108°, respectively. Because the formation of
M–OH bonds is thought to be important in the corrosion of
9
metal surfaces, examining the structural trends in the mono-
hydroxides is of interest.
2
ϩ
these species in their X ⌺ electronic states were first con-
The competition between ionic and covalent bonding,
however, does not always produce a clearly linear or bent
molecule. Subtle deviations from linearity were first ob-
served in the pure rotational spectra of CsOH and RbOH.
In particular, the variation of the effective rotational constant
ducted by our group, which carried out measurements of the
ground vibrational state lines of MgOH, CaOH, SrOH, and
15–18
BaOH.
These data were successfully analyzed assuming
1
0,11
the molecules to be linear. Recording the spectra of the less
25
137
abundant MgOH and BaOH isotopomers of these radi-
cals enabled the metal hyperfine structure to be investigated,
which indicated that the unpaired electron in these species
resides primarily on the metal nucleus. Such data supported
B with respect to v , the quantum number for the degener-
v
2
ate bending mode, was strongly nonlinear with an initial
negative slope. These inconsistencies were attributed to large
amplitude motions ͑LAM͒ of the low frequency bending vi-
ϩ
Ϫ
the M OH ionic ͑and therefore linear͒ structure proposed
for these molecules.5 Subsequent studies of the vibra-
,6
a͒Current address: Division of Engineering and Applied Science, Harvard
University, 29 Oxford St., Cambridge, MA 02138.
tionally excited states, in contrast, revealed additional com-
19–21
plications, particularly in the v bending mode.
The v2
b͒
2
Current address: Neste Resin Corp., 475 N. 28th St., Springfield, OR
ϭ1, 2, and, in certain cases, 3, states of CaOH and its deu-
terium isotopomer, SrOH, and BaOH were readily analyzed
9
7477.
c͒
Electronic mail: lziurys@as.arizona.edu
0021-9606/99/111(24)/10919/7/$15.00
10919
© 1999 American Institute of Physics
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1

10920
J. Chem. Phys., Vol. 111, No. 24, 22 December 1999
Apponi, Anderson, and Ziurys
with a linear model, with small corrections to account for
contamination of the ⌸ and ⌬ vibronic levels by excited
electronic states of the same symmetry. For MgOH and
conditions were optimized to obtain maximum signal to
noise. Typical settings used were 500–1000 mA at 3–20 V.
In the case of MgOH, H O was sufficiently reactive that no
2
2
MgOD, however, only the v ϭ1 state could be fitted with
dc discharge was required.
2
this model with comparable residuals. Moreover, many of
Initially, scans covering 100 MHz in frequency were re-
corded to sort out the various spectral features. Part of this
process included measurements of the relative intensities of
spectral features. Because the spectrometer source power
varies in a nonuniform manner as a function of frequency,
intensity calibration was conducted on the basis of signal-to-
noise ratio per spectral line. An accurate baseline removal
was carried out to obtain such ratios. Also, when possible,
spectra were recorded that had several features on one single
scan. Then, when going to a nearby frequency, one of the
‘‘calibrated’’ lines was left in the new spectrum for scaling
purposes. Actual transition frequencies were measured using
scans 3–4 MHz in coverage, depending on the linewidth.
The linewidths were typically 700–1000 kHz over the range
240–520 GHz. The estimated error on the measurements is
Ϯ50 kHz.
the v Ͼ1 states for the magnesium species could not be
2
confidently assigned, unlike the other hydroxides.
In an effort to aid in these identifications, Bunker et al.22
used the MORBID ͑Morse oscillator rigid bender for internal
dynamics͒ Hamiltonian to derive a full ground state potential
surface for MgOH. The surface was optimized to fit some of
the rotational data ͑0° and six vibrationally excited substates
1
d
1c
2d
2c
0
1d
1
, 1 , 2 , 2 , 2 , 3 ), as well as vibrational energies
of several quanta of the bend deduced from laser induced
fluorescence ͑LIF͒ measurements. This study showed that
MgOH is linear at equilibrium with a flat, quartic bending
Ϫ1
potential. A small barrier to linearity of ϳ10 cm could not
be excluded, however, given the precision of the fitting.
Hence, the calculations of Bunker et al. suggested that
MgOH is indeed quasilinear.
The modeling of the potential surface by Bunker et al.
enabled predictions of rotational constants for the vibra-
tionally excited states of MgOH. Additional predictions by
III. RESULTS
The data obtained for MgOH and MgOD in their ground
2
2
Bunker were also carried out for MgOD, which were sub-
sequently followed by further laboratory measurements on
both species in our group. In this paper we present our com-
plete pure rotational data set for MgOH and MgOD with
accurate vibrational satellite assignments. For MgOH, the
2
ϩ
24
electronic ⌺ state are given in the EPAPS database. To
summarize, rotational transitions arising from nine excited
vibrational substates of MgOH in the degenerate v
2
l
2
0
2c 2d 1c 1d
bending mode were recorded (v ϭ2 , 2 , 2 , 3 , 3 ,
3c 3d 2c 2d
3
, 3 , 4 , 4 ). Multiple substates per quantum v arise
0
2
1
3
2
2
2
, 2 , 3 , 3 and 4 states were investigated, and for
because of the effects of l-type doubling and l-type reso-
nance ͑e.g., Refs. 25–27͒, where lϭv , v Ϫ2, v Ϫ4,...
0
2
1
3
4
MgOD the 2 , 2 , 3 , 3 and 4 states. These data extend
1
19
2
2
2
the 1 measurements published in Fletcher et al. and Nuc-
cio, Apponi, and Ziurys.21 The pure rotational satellite spec-
tra have been analyzed assuming both molecules to be linear
but accounting for l-type doubling, l-type resonance, and an-
harmonicity effects. Rotational, spin–rotation, and l-type
doubling constants have been determined for each vibra-
tional state. Anomalies have been found in the spectra that
are consistent with MgOH and MgOD being quasilinear.
Here we present the data and its analysis, and discuss the
interesting behavior of these unusual species.
Ϫv ͑c and d indicate substates with respect to Ϯl). Five
2
transitions consisting of two spin–rotation components were
2
measured for each state ͑except for the 4 level, where only
1c
four transitions were recorded͒. Previously, only the 1 and
1d
19,20
1
and the v ϭ1 data had been reported,
in addition to
1
the ground (vϭ0) state. The same set of vibrationally ex-
cited states were observed for MgOD, with the exception of
2
l
2
4c
4d
the substate 4 . In addition, lines from the v ϭ4 and 4
levels were recorded as well. For MgOD, six to nine transi-
tions were observed for each vibrational state, all which con-
sist of spin–rotation doublets. Similarly, measurements of
II. EXPERIMENT
1
only the ground and 1 states for MgOD had been previously
The rotational spectra of MgOH and MgOD were re-
corded using one of the quasioptical millimeter-wave spec-
trometers of the Ziurys group, which are described in detail
published.21
Assignment of the spectra of MgOH and MgOD was not
trivial. Although harmonic relationships were readily estab-
lished between features arising from different rotational tran-
sitions, careful intensity studies, as described previously,
were critical for proper identifications. Also, predictions of
rotational constants for MgOH from Bunker et al.22 and for
MgOD from separate calculations aided in the assignments.
Stick figures illustrating the final vibrational assignments and
observed relative intensities are shown in Figs. 1 and 2. Fig-
ure 1 presents data for the Nϭ11→12 transition of MgOH
near 353 GHz. ͑The spin–rotation splittings have been omit-
ted for simplicity.͒ The inset panel shows a close-up view of
2
3
elsewhere. The instrument consists of a Gunn oscillator/
varacter multiplier source operating in the range 65–530
GHz, a gas cell incorporating a Broida-type oven, and an
InSb detector.
MgOH and MgOD were synthesized in the gas phase by
the reaction of metal vapor with the appropriate precursor.
About 50% H O in H O was used as the precursor for
2
2
2
MgOH, and pure D O for MgOD. Magnesium was heated in
2
the oven and the vapor entrained in 10–20 mTorr of argon
carrier gas and flowed into the gas cell. Approximately 50
mTorr of the reactant material was then added to the metal
vapor/argon mixture over the top of the oven. For MgOD, a
dc discharge was run continuously through these gases using
a cathode placed above the grounded oven. The discharge
a cluttered region near 352 GHz. Because ␣ is positive for
2
2
5
MgOH, unlike most linear triatomic molecules, the vibra-
tional satellite lines lie to lower frequency relative to the
ground state, as Fig. 1 illustrates. Also, while the centroids of
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J. Chem. Phys., Vol. 111, No. 24, 22 December 1999
Spectroscopy of MgOH
10921
FIG. 1. A stick diagram showing the vibrational progression in the Nϭ11
→
12 transition of MgOH near 353 GHz and the approximate relative inten-
sities. The magnitude of the spin–rotation interactions is sufficiently small
to be neglected here. The inset panel is a close-up view of the region near
52 GHz. The large shifts of the 2 , 3 , and 4 substates relative to the 22
0
1
2
3
3
and 3 states suggests that MgOH is quasilinear.
l
1
2
3
the v ϭ1 , 2 , and 3 states are spaced at somewhat regular
2
0
frequency intervals relative to the 0 state, as expected for a
linear molecule, the 2 , 3 , and 4 states are shifted consid-
erably from their v counterparts, in the direction of the 0
line. For example, the 2 satellite line lies almost 2 GHz to
higher frequency relative to the 2 and 2 features, while
the centroid of the 3 state is shifted ϳ2.5 GHz to higher
frequency from the 3 lines. Similarly, the 4 features lie to
0
1
2
0
2
0
FIG. 3. Representative satellite line spectra of the Nϭ11→12 transition of
MgOH and the Nϭ16→17 transition of MgOD near 352 and 456 GHz,
respectively. The magnitude of the spin rotation vs l-type interactions is
clearly illustrated in the spectra. The MgOH figure is a composite of two
separate 110 MHz scans, each with an acquisition time of 1 min, the MgOD
data are from a single 100 MHz scan with a 1 min duration. Baselines were
removed from each spectrum.
2
c
2d
1
3
2
much higher frequency relative to where the v ϭ4 state is
expected in the vibrational progression. For a strictly linear
2
molecule, the l-type substates of a given v quantum number
2
2
5
should occur relatively close to each other in frequency.
Fermi resonance cannot account for such frequency shifts,
either, as the v ϭ1 and v ϭ1 stretching modes are at suf-
ficiently higher ͑and different energies͒ relative to the v2
states, as predicted by Bunker et al.
The vibrational progression for the Nϭ12→13 transi-
tion of MgOD near 350 GHz is shown in Fig. 2. Again the
effects of spin–rotation interactions are suppressed for clar-
ity, and the inset at the upper right magnifies a congested
1
2
region of the spectrum. Similarly, the centroids of the 1 , 2 ,
1
3
3
4
3
, and, in this case, 4 states lie at fairly regular spacings
relative to the ground state ͑except for MgOD, ␣ is small
2
0
and negative͒. However, the 2 lines and the centriod of the
1
2
3
3
features are shifted relative to their 2 and 3 counter-
2
parts. ͑The 4 state was never confidently assigned in
MgOD.͒ In Fig. 3, representative vibrational spectra for
MgOH and MgOD are presented. The top panel shows the
2
c
2d
spin–rotation doublets for the 2 , 2 , and v ϭ1 states and
1
one fine structure component of the 42 level for the
c
Nϭ11→12 transition of MgOH. The l-type doubling inter-
2
action for the 2 state is significantly larger than that arising
from spin–rotation, as is generally the case for most sub-
3
states observed for MgOH except the 3 level. These data
cover 210 MHz in frequency space. The lower panel shows a
part of Nϭ16→17 transition of MgOD near 456 GHz, span-
ning nearly 100 MHz. The spin–rotation components of the
2
c
, 3 , and 3 levels are visible in these data. For the 33
3c
3d
2
lines, the spin–rotation and l-type doubling splittings are
comparable in magnitude.
IV. ANALYSIS
FIG. 2. A stick figure showing the progression and relative intensities of the
vibrational satellites in the Nϭ12→13 transition of MgOD. ͑The effects of
spin–rotation here are negligible and hence not shown.͒ The region near 349
GHz is shown in detail in the upper right-hand corner. Because MgOD has
Despite the irregularities in the spectrum, the data were
analyzed assuming both molecules to be linear. Hence, the
following Hamiltonian was used:
a small negative ␣ value, the pattern is different from that of MgOH, where
2
ϳ100 MHz, but large frequency shifts are still seen in the 2 and 31
0
␣2
substates.
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ˆ
ˆ
ˆ
ˆ
ˆ
ld
HϭH ϩH ϩH ϩH .
͑1͒
rot
cd
sr
1

10922
J. Chem. Phys., Vol. 111, No. 24, 22 December 1999
Apponi, Anderson, and Ziurys
The first two terms are simply those for molecular frame
rotation and its centrifugal distortion corrections, which need
no further comment. The other two terms, which concern
spin–rotation and l-type interactions, are more complicated
and will be discussed briefly. The l-type interactions for the
et al. ͑10.5 cmϪ1͒ while 11.8 cmϪ1 was used for MgOD, also
based on calculations by Bunker. These energy separations
gave reasonable fits for both molecules.
For the v ϭ3 state, the l-type interactions are expressed
2
by a 4ϫ4 matrix of the form
v ϭ1, 2, and 3 states were analyzed using the matrix ele-
ments formulated by Amat and Nielsen, but considering
2
2
7
E⌽
W31
W3-1
0
the differences in parity of the two spin rotation levels F
W31
E⌸ W1-1 W3-1
1
2
8
,
͑6͒
and F , as outlined by Presunka and Coxon. In the Amat
2
W3-1
W1-1
W3-1
E⌸
W31
ͯ
ͯ
and Nielsen representation, the most general form of l-type
interactions is l-type resonance with l-type doubling being a
special case occurring only in ⌸ vibronic states i.e., for lϭ
Ϯ1). The l-type interactions appear in the energy matrix
only as off-diagonal terms of the form:
0
W31
E⌽
where W1 and W31 represent l-type interactions linking
states varying by lϭϮ2 ͑q parameter͒. W
term for states differing by lϭϮ4 ͑␳ parameter͒. Again, this
matrix had to be separated into F and F parity blocks, and
the energy splitting between the 3 and 3 substates had to
be estimated, also using values of Bunker et al. In these
cases, the higher order l-type resonance term ␳ had to be
used to account for splittings in the 3 states.
The v ϭ1, 2, and 3 data were analyzed in a single,
global fit using these representations. For the 4 and 4 sub-
states of MgOH and MgOD, respectively, other v ϭ4 levels
were not securely identified. Hence, l-type interactions with
the other sublevels were not considered, and the data were fit
-1
is the energy
3
-1
ˆ
1
2
͗
͗
vЈ,l
͉
͉
H
͉
͉
v,lϮ2
v,lϮ4
͘
͘
,
,
͑2͒
͑3͒
1
3
ˆ
vЈ,l
H
3
ˆ
where H is the perturbing Hamiltonian. The first matrix ele-
ment here characterizes the l-type doubling parameter qv ,
2
2
4
and the second element, the higher order constant, ␳ . Ex-
v
plicit expressions for these elements can be found in Maki
2
2
9
and Lide. In addition, the diagonal terms for the unper-
2
turbed energies need to include g l , the contribution of the
ll
separately with an effective l-type doubling term q , ac-
angular momentum l to the vibrational energy, where gll is
the anharmonicity constant. Differences between these fac-
tors characterize the splitting between l substates of a given
eff
cording to the following equation:27
1
2
⌬
El typeϭϮ qeff͕͓N͑Nϩ1͒Ϫl͑lϩ1͔͒
0
2
v bending mode. For example, the 2 and 2 states will be
2
ϫ͓N͑Nϩ1͒Ϫ͑lϩ1͒͑lϩ2͔͒ 1
/2.
͑7͒
separated by the energy 4g22 . Consequently, the energy
splittings between the different l substates for a given level
͖
The spectroscopic constants derived from this analysis
are listed in Table I. The rms given in Table I applies to the
global fit of the v ϭ1, 2, and 3 data. For both molecules, the
observed spectra are relatively well described by B, D, H, ␥,
␥D ͑the centrifugal distortion correction to ␥, the spin–
rotation constant͒, and, when l-type doubling is involved, the
corresponding constant q, its centrifugal distortion correction
v must be known to explicitly solve for the l-type param-
2
1
eters. Therefore, while l-type interactions for the 1 state are
simply described by
2
1
2
⌬
EϭϮ q N͑Nϩ1͒,
͑4͒
v
not including centrifugal distortion corrections, those for the
v2ϭ2 and 3 states must be expressed in matrix form. For the
1
q , and, in the case of the 3 substate, q as well. As men-
D
H
v2ϭ2 state, the matrix representation is
tioned, ␳, the l-type resonance parameter, was needed to fit
3
1
1
the 3 data. Finally, the 1 and 3 states required the con-
E⌬ W20 W22
stant p , to account for the differences in spin–rotation
⌸
W20 E⌺ W20
,
͑5͒
splittings between the l-type doublets. This parameter has the
same functional form as the lambda-doubling constant p in a
ͯ
ͯ
W22 W20 E⌬
2
⌸
electronic state, and probably arises from the mixing of
2
where E indicates the energy of the lϭ2 states and E , the
low-lying ⌸ electronic states with the v ϭ1 ⌸ vibronic
level. The constant was needed to fit the 1 and 3 data for
CaOH, SrOH, and BaOH. Similar p and p⌫ terms were
also necessary in the 4 MgOH and 4 MgOD analyses, of
identical vibronic origins. The rms of the global MgOH fit is
274 kHz, with residuals to the fit as high as 900 kHz—above
the estimated experimental uncertainty of Ϯ100 kHz. The
rms of the MgOD global analysis was similar: 257 kHz, with
comparable residuals. Some systematic errors were present
⌬
⌺
2
1
1
lϭ0 state. The W off-diagonal term in this matrix involves
2
2
1
9
the higher order constant ␳ , which was not needed to fit the
v
⌬
4
2
v2ϭ2 data set and therefore was set to zero in the analysis.
This matrix becomes further simplified as a result of
parity selection rules, which play a role because the spin–
rotation interaction separates out every rotational level into
F and F components. The lϮ2 levels also have F and F
1
2
1
2
parities, and only states of the same parity can interact. Con-
1
sequently, the F and F states become separated into two
in the 3 data as well, which cannot be accounted for by the
1
2
parity blocks ͑e.g., see Refs. 19 and 28͒, each which loose
half of their off-diagonal terms. Moreover, diagonalization of
these final matrices can only be done with knowledge of the
l-type, spin–rotation, and vibronic interactions modeled here.
Clearly the quality of these analyses are not nearly as good
as those carried out for comparable data sets for CaOH,
SrOH, and BaOH, where the rms of the fits were 15–35
kHz.19
0
2
separation between the 2 and 2 levels, namely 4g . For
2
2
MgOH, this separation was set to that derived by Bunker
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J. Chem. Phys., Vol. 111, No. 24, 22 December 1999
Spectroscopy of MgOH
10923
2
ϩ
a
TABLE I. Molecular constants for MgOH and MgOD (X ⌺ ).
˜
1
2
where B ϭB Ϫ (␣ ϩ␣ ). This expression was used by
e
e
1
3
1
1
l
Lide and Matsumura to describe the nonlinear behavior of
B with respect to v for RbOH and CsOH. This equation
has also been used to model the spectra for MgOH and
MgOD using the v ϭ0, 1, 2, and 3 states, not including the
level. The resulting ␣ , ␥ , and ␥ parameters are given
in Table II, along with those determined for CaOH, CaOD,
and NaOH. It is interesting to note that ␣ is positive for
MgOH, unlike most linear triatomic molecules. Positive ␣2
(
v ,v ,v )
MgOH
MgOD
1
2
3
v
2
1
͑
01 0͒
B
D
␥
14 757.1807͑66͒
0.026 546͑25͒
42.23͑27͒
13 446.4037͑51͒
0.020 263͑17͒
36.76͑22͒
Ϫ0.002 01͑52͒
Ϫ100.885͑10͒
0.001 468͑34͒
Ϫ1.68͑12͒
2
1
3
␥D
q
qD
p⌸
Ϫ0.004 10͑72͒
Ϫ85.134͑13͒
0.000 413͑49͒
Ϫ2.16͑13͒
2 22 ll
2
0
values have been routinely found for alkali and alkaline earth
(
(
02 0)
B
14 771.018͑15͒
0.026 860͑57͒
¯
13 483.435͑11͒
0.021 470͑50͒
¯
hydroxide species,1
0,11,19
and have been thought to arise from
D
H
␥
substantial anharmonic terms in the bending potential. The
␣2 constant for MgOH, however, is unusually large ͑110.5
MHz͒, indicating a severe degree of anharmonicity. Values
for ␣ of less than 50 MHz have been measured for CaOH,
SrOH, BaOH, KOH, CsOH, and RbOH. On the other hand,
40.15͑39͒
0.0008͑10͒
35.68͑59͒
0.0013͑17͒
␥D
2
02 0)
B
14 698.0383͑87͒
0.026 346͑33͒
¯
13 444.6864͑89͒
0.020 106͑44͒
2
D
H
␥
Ϫ8
Ϫ6.5(6.5)ϫ10
40.51͑15͒
the MgOH value is comparable to that of NaOH (␣ ϭ97),
2
50.60͑27͒
another species whose vibrational satellite pattern is complex
and not completely understood.14 The ␣2 parameter for
MgOD, in contrast, is small and negative (␣2
ϭϪ5.43 MHz), and follows the trend of alkali/alkaline earth
hydroxide species on deuterium substitution ͑e.g., Ref. 21͒.
Another irregularity in the vibrational dependence of MgOH
␥D
q
qD
Ϫ0.014 20͑72͒
Ϫ79.96͑12͒
0.002 39͑54͒
Ϫ0.003 77͑23͒
Ϫ84.601͑39͒
0.001 015͑94͒
1
(
03 0)
B
D
H
␥
␥D
q
qD
qH
p⌸
14 744.7103͑68͒
0.020 136͑25͒
¯
13 498.7655͑81͒
0.021 271͑37͒
Ϫ7
Ϫ1.31(52)ϫ10
37.35͑14͒
43.15͑28͒
͑and MgOD͒ is the unusually large values of the higher order
Ϫ0.003 81͑72͒
Ϫ65.859͑30͒
0.002 22͑24͒
0.000 016 28͑63͒
6.14͑36͒
Ϫ0.000 81͑19͒
Ϫ78.2716͑82͒
0.001 073͑38͒
¯
terms ␥22 and ␥ . For MgOH, the constants are ␥
ll
22
ϭ21.18 MHz and ␥ ϭϪ18.27 MHz. To our knowledge,
ll
these are the highest values of these parameters found in the
literature for any molecule, and deviate from the trend of the
3.94͑30͒
other alkaline earth monohydroxides, where ␥22
3
(
(
03 0)
B
14 644.3711͑61͒
0.033 143͑24͒
¯
13 439.0084͑83͒
0.020 380͑40͒
19
ϭ1.3–2.8 MHz and ␥ ϭϪ1.5 to Ϫ3.6 MHz. They are
ll
D
H
␥
␥D
␳
Ϫ8
also much larger than most alkali monohydroxide values,
Ϫ6.9(5.9)ϫ10
47.16͑24͒
Ϫ0.009 02͑51͒
Ϫ0.000 332͑54͒
which are typically a few megahertz or less.1
3,21
The only
64.08͑28͒
Ϫ0.032 71͑71͒
0.032 686͑59͒
molecule that has remotely similar constants is NaOH, where
1
4
␥22
ϭ9(2) MHz and ␥ ϭϪ10(2) MHz.
ll
2
04 0)
B
D
␥
qeff
qD,eff
qH,eff
qI,eff
14 679.9365͑88͒
0.029 672͑38͒
43.389͑75͒
¯
¯
¯
¯
¯
¯
¯
¯
V. DISCUSSION
0.9236͑38͒
Many molecular species undergo large amplitude mo-
tions ͑LAM͒, which result in peculiarities in their spectra.
Only a subset of such molecules are truly quasilinear, i.e.,
have a potential with a minimum at other than linearity. Fur-
thermore, the energy required to access the linear configura-
tion for a quasilinear species is lower than the zero point
energy of the bending vibration.
Ϫ0.008 922͑71͒
0.000 041 00͑48͒
Ϫ8
Ϫ7.42(11)ϫ10
p⌬
3.188͑75͒
4
(
04 0)
B
D
H
␥
␥D
qeff
qD,eff
p⌫
¯
¯
¯
¯
¯
¯
¯
¯
13 430.1957͑77͒
0.032 673͑41͒
1.920(61)ϫ10
52.53͑14͒
Ϫ6
The millimeter-wave studies of MgOH presented here
provide very good experimental evidence that this molecule
is indeed a quasilinear species. First of all, assignment of the
vibrational satellite states proved extremely difficult, even
when aided by careful intensity studies and theoretical pre-
dictions. In fact, there are several rotational progressions of
lines with the typical spin–rotation splittings for both MgOH
and MgOD whose identity cannot be confidently established.
Of the assignments made, the substates that appear shifted
Ϫ0.011 30͑19͒
Ϫ5
Ϫ5.01(93)ϫ10
2.45(19)ϫ10
Ϫ0.003͑28͒
Ϫ7
rms of fitb
0.274
0.257
a
In MHz. Errors are 3␴ and apply to the last quoted decimal places.
Excludes v ϭ4 mode.
b
2
0
1
2
relative to their expected positions (2 , 3 , and 4 states͒ are
those that correlate with excited vibrational levels in the bent
The vibrational dependence of B with respect to v for
v
2
0
1
2
limit. In fact, the 2 , 3 , and 4 levels become the K ϭ0, 1,
linear triatomic molecules exhibiting large amplitude mo-
a
1
1
and 2 levels of the first vibrationally excited state (v ϭ1) of
tions is given by
2
1
2
the bent molecule ͑see, e.g., Ref. 26͒. In contrast, the 1 , 2 ,
˜
2
2
ll
B ϭB Ϫ␣ ͑v ϩ1͒ϩ␥ ͑v ϩ1͒ ϩ␥ ,
͑8͒
3
4
v
e
2
2
22
2
3 , and 4 substates, which follow a fairly regular pattern for
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10924
J. Chem. Phys., Vol. 111, No. 24, 22 December 1999
Apponi, Anderson, and Ziurys
TABLE II. Vibrational dependence of B .a
v
Parameter
MgOH
MgOD
CaOHd
CaODd
NaOHe
˜
˜
B
e
␣1
␣2
b
c
BЈ
15 036.85͑10͒
14 911.76͑10͒
250.17͑5͒
110.47͑5͒
21.18͑3͒
¯
13 428.65͑10͒
¯
10 085.12͑10͒
¯
9109.440͑25͒
¯
¯
12 654͑22͒
¯
e
66.725͑4͒
31.518͑3͒
2.849͑3͒
Ϫ3.361͑1͒
55.707͑25͒
Ϫ0.357͑20͒
1.209͑5͒
Ϫ5.43͑5͒
4.28͑3͒
97͑20͒
9͑2͒
␥22
␥ll
Ϫ18.27͑3͒
Ϫ9.80͑3͒
Ϫ1.818͑5͒
Ϫ10͑2͒
a
Values quoted are in MHz.
b
˜
BЈϭB Ϫ1/2␣ .
e
e
3
c
d
e
˜
B ϭB Ϫ1/2(␣ ϩ␣ ).
e
e
1
3
From Refs. 19 and 21.
From Ref. 14.
1
1
MgOH and MgOD, correlate with the K ϭ1, 2, 3, and 4
a
ample, q(1 )ϭϪ85.13 MHz, while q(3 )ϭϪ65.86 MHz, a
1
levels in the bent molecule’s ground state (v ϭ0). In other
2
considerable decrease. In contrast, q(1 )ϭϪ11.85 MHz and
q(3 )ϭϪ12.48 MHz for SrOH. Such changes in the l-type
1
1
words, v (bent)ϭ 2 ͓v (linear)Ϫ͉l͉͔, and K (bent)
2
2
a
ϭl(linear). Therefore, the vibrational progressions of
MgOH and MgOD are those exactly expected for a molecule
whose structure is in between the linear and bent limits.
Other indications of quasilinear behavior are rotational
constant for the magnesium hydroxide species are compa-
rable to that of highly quasilinear HNCO in its v mode,
5
3
0
which are about 22% as well. Indeed, using the predictions
of Bunker et al.,22 MgOH and MgOD have quasilinear pa-
2
6
constants that do not depend linearly on v , as expected
2
rameters similar to HNCO ͑Ϫ0.72 and Ϫ0.71 vs Ϫ0.66 ͒.
Consequently, common trends in q for the lowest energy
bending modes of these molecules might be expected.
Another interesting effect found for MgOH is the large
from the usual definition of B , and large variations in q ,
v
v
2
the l-type doubling constant for the v mode.26 Both effects
2
are found in MgOH As previously discussed and shown in
Table II, the vibrational expansion of B in terms of v has
positive value of ␣ , which decreases to a small, negative
v
2
2
large nonlinear terms. The ␥22 and ␥ parameters established
for MgOH are significantly greater than any others found in
the literature. These values were derived by fitting the rota-
number for MgOD. As previously mentioned, this is a com-
mon pattern for metal monohydroxide species, as illustrated
ll
by KOH, CsOH, RbOH, CaOH, SrOH, and
0
1
0
2
3
10,11,13,19,21
tional constants of the 0 , 1 , 2 , 2 , and 3 substates for
both MgOH and MgOD. However, the fit as it stands does
BaOH.
Each of these species undergoes a large
isotope shift when replacing hydrogen with a deuterium,
1
2
not reproduce the 3 data for either species, or the 4 spectra
for MgOH, with reasonable accuracy. Even higher order
terms would be needed in these cases—additional evidence
for quasilinear behavior.
which decreases the value of ␣ . Only for the lighter species
2
1
1
does ␣2 actually become negative. Lide and Matsumura
have attributed this property as arising from a large ͑and
positive͒ anharmonic term in the bending potential, which is
particularly prominent in the OH species, but decreases with
deuterium substitution. The isotope shifts also become larger
with decreasing mass of the metal atom, as expected. For
cesium, rubidium, calcium, potassium, and magnesium, the
shifts are Ϫ16, Ϫ22, Ϫ32, Ϫ34, and Ϫ114 MHz, respec-
tively.
Large differences in the l-type doubling constants are
also apparent in MgOH and MgOD, as illustrated in Table
III. This table presents the l-type parameter q of the v ϭ1, 2,
2
and 3 states for these two molecules, as well as those for
CaOH, CaOD, SrOH, and HNCO. The percent charge in q in
1
2
going from the 1 to the 2 substate is less than 2.5% for
CaOH, CaOD, and SrOH. In comparison, the difference in
the MgOH and MgOD values are 6% and 16%, respectively.
An even more pronounced effect is observed in going from
v ϭ1 to v ϭ3, where the difference is 22% for MgOH and
The final evidence for quasilinear behavior in MgOH is
found in a comparison of the r , r , and re structures, which
˜
0
s
can be obtained because deuterium and two magnesium sub-
stitutions have been carried out, and because ␣ has been
2
2
2
MgOD, as opposed to 5% for SrOH. For MgOH, for ex-
determined. ͑The term r in this case corrects for ␣ but not
˜
e
2
␣1
or ␣ .) These structures are given in Table IV. The r0
3
structure does not account for zero-point vibrational energy.
TABLE III. Comparison of l-type doubling constants.a
TABLE IV. Structures for MgOH.a
Molecule
q(11)
q(22)
q(31)
Reference
MgOH
MgOD
CaOH
CaOD
SrOH
Ϫ85.134͑13͒ Ϫ79.96͑12͒
Ϫ100.885͑10͒ Ϫ84.601͑39͒ Ϫ78.2716͑82͒
Ϫ21.649͑10͒ Ϫ21.131͑51͒
Ϫ22.983͑17͒ Ϫ23.425͑25͒
Ϫ11.855͑12͒ Ϫ11.934͑48͒ Ϫ12.4840͑60͒
Ϫ65.859͑30͒
This work
This work
r0b
rsc
d
˜
r
e
¯
19
21
19
30
rMg–O
rO–H
1.780
0.871
1.777
0.873
1.767
0.940
¯
b
a
HNCO
34.6391͑3͒
¯
27.091 65͑12͒
In angstroms.
b
c
From Ref. 21.
a
Using Mg, 26Mg, and deuterium substitutions.
25
In MHz.
For v5 mode instead of v2 .
b
d
Corrected for ␣2 only.
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1

J. Chem. Phys., Vol. 111, No. 24, 22 December 1999
Spectroscopy of MgOH
10925
1
The r structure, which considers changes in center of mass
with isotopic substitution, is thought to be closer to the true
J. Nakagawa, R. F. Wormsbecher, and D. O. Harris, J. Mol. Spectrosc. 97,
7 ͑1983͒.
P. F. Bernath and S. Kinsey-Nielsen, Chem. Phys. Lett. 105, 663 ͑1984͒.
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W. T. M. L. Fernando, M. Douay, and P. F. Bernath, J. Mol. Spectrosc.
s
3
2
3
4
equilibrium structure than the r one. Because it takes out
0
the contribution of the low-lying bending mode, the r struc-
˜
e
ture is corrected for some of the zero-point vibrations, and is
nearest to the true r geometry. ͑For MgOH, the v ϭ1 level
144, 344 ͑1990͒.
5
6
e
2
C. W. Bauschlicher, Jr. and H. Partridge, Chem. Phys. Lett. 106, 65
͑1984͒.
C. W. Bauschlicher, Jr., S. R. Langhoff, and H. Partridge, J. Chem. Phys.
Ϫ1
22
lies ϳ160 cm above ground state. ͒ As can be deduced
from Table IV, there are significant differences between the
O–H bond length for the r , and r , and re structures. The
˜
84, 901 ͑1986͒.
0
s
7
8
R. Pereira and D. H. Levy, J. Chem. Phys. 105, 9733 ͑1996͒.
C. J. Whitham, H. Ozeki, and S. Saito, J. Chem. Phys. 110, 11109 ͑1999͒.
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O–H bond distance is rO–Hϭ0.871 Å for the r calculation
0
and 0.873 Å for the r structure, which is unusually short for
9
s
2
1
this bond, as noted by Nuccio, Apponi, and Ziurys. This
decrease in apparent bond length likely arises from the pro-
jection of the O–H bond of the bending molecule on the
10
1
1
1
2
P. Kuijpers, T. To
1975͒.
¨
rring, and A. Dymanus, Z. Naturforsch. A 30, 1256
˜
͑
equilibrium linear axis. In comparison, the r value is
e
13
E. F. Pearson, B. P. Winnewisser, and M. B. Trueblood, Z. Naturforsch. A
1, 1259 ͑1976͒.
rO–Hϭ0.94 Å. This number is more typical of O–H bond
lengths and similar to the distances of rO–Hϭ0.92–0.93 Å
3
14
15
P. Kuijpers, T. T o¨ rring, and A. Dymanus, Chem. Phys. 15, 457 ͑1976͒.
M. A. Anderson, W. L. Barclay, Jr., and L. M. Ziurys, Chem. Phys. Lett.
196, 166 ͑1992͒.
found for linear CaOH, SrOH, and BaOH from r and r
0
s
structure determinations.21 Obviously correcting for the zero-
point contribution of the bending motion makes a significant
change in the structure of MgOH.
1
1
1
1
2
2
2
2
6
7
8
9
0
1
2
3
W. L. Barclay, Jr., M. A. Anderson, and L. M. Ziurys, Chem. Phys. Lett.
1
96, 225 ͑1992͒.
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84, L63 ͑1992͒.
3
VI. CONCLUSION
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L. M. Ziurys, D. A. Fletcher, M. A. Anderson, and W. L. Barclay, Jr.,
Astrophys. J., Suppl. 102, 425 ͑1996͒.
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͑1995͒.
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See EPAPS Document No. E-JCPSA6-111-006948 for complete list of
measured transition frequencies of the vibrational satellite lines of MgOH
and MgOD. This document may be retrieved via the EPAPS homepage
Analysis of the pure rotational spectra of the v vibra-
2
tional satellite transitions of MgOH and MgOD indicates that
both molecules are quasilinear. This property is apparent in
several of the spectroscopic constants determined in this
study, as well as in structural calculations. Moreover, the
spectra themselves show deviations from patterns expected
for a linear molecule. Quasilinear behavior has already been
suggested by theoretical calculations,22 which predict that
MgOH has a quartic bending potential perhaps containing a
small barrier. The ionic bonding of the linear species CaOH,
SrOH, and BaOH obviously acquires a more significant co-
valent component with substitution of the lighter alkaline
and alkali metals Mg and Na. However, MgOH and NaOH
are not predominantly covalent compounds or they would be
bent like CuOH or AgOH. Clearly it would be interesting to
investigate other metal monohydroxides in order to examine
further structural trends.
24
͑
http://www.aip.org/pubservs/epaps.html͒ or from ftp.aip.org in the direc-
tory /epaps/. See the EPAPS homepage for more information.
C. H. Townes and A. L. Schawlow, Microwave Spectroscopy ͑Dover,
New York, 1975͒.
B. P. Winnewisser, in Molecular Spectroscopy: Modern Research, edited
by K. Narahari Rao ͑Academic, Orlando, 1985͒, Vol. III, p. 321.
G. Amat and H. H. Nielsen, J. Mol. Spectrosc. 2, 163 ͑1958͒.
P. I. Presunka and J. A. Coxon, Can. J. Chem. 71, 1689 ͑1993͒.
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M. Winnewisser and B. P. Winnewisser, J. Mol. Spectrosc. 41, 143
͑1972͒.
25
26
2
2
2
3
7
8
9
0
ACKNOWLEDGMENTS
This work was supported by NSF Grant No. CHE-
9817707 and NASA Grant No. NAG53785.
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1