JOURNAL OF CHEMICAL PHYSICS
VOLUME 121, NUMBER 23
15 DECEMBER 2004
The rotational spectrum and dynamical structure of LiOH and LiOD:
A combined laboratory and ab initio study
Kelly J. Higgins, Samuel M. Freund,a) and William Klemperer
Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138
Aldo J. Apponi and Lucy M. Ziurys
Departments of Chemistry and Astronomy, The University of Arizona, Tucson, Arizona 85721
共Received 30 June 2004; accepted 20 September 2004兲
Millimeter wave rotational spectroscopy and ab initio calculations are used to explore the potential
energy surface of LiOH and LiOD with particular emphasis on the bending states and bending
potential. New measurements extend the observed rotational lines to J⫽7←6 for LiOH and J
⫽8←7 for LiOD for all bending vibrational states up to (033 0). Rotation-vibration energy levels,
geometric expectation values, and dipole moments are calculated using extensive high-level ab
initio three-dimensional potential energy and dipole moment surfaces. Agreement between
calculation and experiment is superb, with predicted B v values typically within 0.3%, D values
within 0.2%, q l values within 0.7%, and dipole moments within 0.9% of experiment. Shifts in B v
values with vibration and isotopic substitution are also well predicted. A combined theoretical and
experimental structural analysis establishes the linear equilibrium structure with r e (Li–O)
⫽1.5776(4) Å and r e (O–H)⫽0.949(2) Å. Predicted fundamental vibrational frequencies are v 1
⫽923.2, v 2 ⫽318.3, and v 3 ⫽3829.8 cm⫺1 for LiOH and v 1 ⫽912.9, v 2 ⫽245.8, and v 3
⫽2824.2 cm⫺1 for LiOD. The molecule is extremely nonrigid with respect to angular deformation;
the calculated deviation from linearity for the vibrationally averaged structure is 19.0° in the 共000兲
state and 41.9° in the (033 0) state. The calculation not only predicts, in agreement with previous
work 关P. R. Bunker, P. Jensen, A. Karpfen, and H. Lischka, J. Mol. Spectrosc. 135, 89 共1989兲兴, a
change from a linear to a bent minimum energy configuration at elongated Li–O distances, but also
a similar change from linear to bent at elongated O–H distances. © 2004 American Institute of
Physics. 关DOI: 10.1063/1.1814631兴
I. INTRODUCTION
Molecular structure plays a fundamental role in chemical
reactions. The understanding of chemical bond lengths is
learned essentially from the potential energy function for a
radial coordinate and thus may be readily obtained from a
variety of diatomic examples. Furthermore, the relatively
small variation in internuclear distance generally encountered in a particular elemental pair reduces the incentive for
detailed understanding with predictive power. Evaluation of
the angular geometry and with it the potential energy function for angular coordinates is both more important and probably much more difficult. Since virtually all molecular geometries can be summarized by an angle of 135°⫾45°, it is
clear that for a predictive utility, theories of angular potential
functions must be accurate to a few degrees. It is indeed the
angular geometry of stereochemistry that has been the target
of numerous ad hoc models.1
The explanations for the geometry of the water molecule
play an important role in the development of the nature of
directed valence. The H2 O molecule is the simplest stable,
readily studied polyatomic molecule. Since the general explanations of the 104° angle of HOH holds equally for
a兲
Present address: Los Alamos National Laboratory, Los Alamos, New
Mexico 87545.
0021-9606/2004/121(23)/11715/16/$22.00
XOX ⬘ , with X and X ⬘ arbitrary monovalent ligands, the
similarity in angular geometry of a wide variety of molecules
is used to establish the validity and power of the presented
explanation. Clearly, it is equally useful to examine the instances in which the geometry of XOX ⬘ is very different than
that of water. There are many systems in which the angle
around oxygen is linear or near linear. For example, this is
the most common angular geometry of Si–O–Si units in
silicate crystals and Li–O–Li molecules in the gas phase.2
The system just between bent H2 O and linear Li2 O is
LiOH. The LiOH molecule was first studied in the gas phase
by Freund,3 who directly measured the l-type doubling transitions for v 2 ⫽1, 2, and 3 in the microwave region. McNaughton et al.4 later studied LiOH and several isotopically
substituted species at millimeter wavelengths by measuring
its rotational spectrum in the ground state and in a number of
the bending modes, but only included data for J⭐5 and v 2
⭐2. These authors found LiOH to be linear at least to a first
approximation. They also showed the difficulty in establishing the linearity of the minimum energy configuration from a
pure rotational spectrum for systems suspected of having
large amplitude oscillations.
Previous computational studies of LiOH range from geometry optimizations and harmonic frequency calculations5–10 to more complete potential energy surfaces and
rotation-vibration state calculations.4,11 Early work by Pople
11715
© 2004 American Institute of Physics
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11716
Higgins et al.
J. Chem. Phys., Vol. 121, No. 23, 15 December 2004
and co-workers6,7 calculated geometries as a means to evaluate theoretical methods and basis sets. Gurvich et al.12 have
summarized computational and experimental work through
1996. Most recently, several groups have separately calculated various properties of LiOH, including its structure and
heat of formation using high-level methods, large basis sets,
and several levels of core electron correlation.9,10,13,14 McNaughton et al.4 performed limited ab initio calculations of
the bending potential, determining the optimal bond lengths
for six LiOH bond angles at the MP3/6-311G** level of
theory. The most extensive calculations were performed by
Bunker et al.,11 who calculated the potential energy at 166
geometries using the average coupled pair functional 共ACPF兲
method, fit the results to an analytic expression, and calculated the rotation-vibration energies using Jensen’s morse
oscillator-rigid bender internal dynamics 共MORBID兲 variational approach on the full three-dimensional analytic surface. They also discovered that there is a large Li–O stretchbend interaction that results in an optimal LiOH structure
that is bent when the Li–O bond is stretched.
The methodology of the present research is to generate
an extensive data set of reliable experimental and fully ab
initio results. In this paper, we present a combined laboratory
and ab initio study of LiOH to further investigate its potential energy surface, paying particular attention to the bending
potential and excited bending states. The experimental measurements were extended to include v 2 ⫽3 for both LiOH
and LiOD, and J⫽7 for LiOH and J⫽8 for LiOD. The
computational approach utilizes extensive coupled-cluster
electronic structure calculations with core electron correlation and a large basis set to calculate the potential. The
rotation-vibration energy levels of LiOH, LiOD, Li 18 OH,
and 6 LiOH for the generated three-dimensional potential are
calculated using the DVR3D package of Tennyson and
co-workers.15 The resulting energy levels are then compared
to experiment through fitted molecular constants as a means
to assess the accuracy of the potential.
II. EXPERIMENT
A. Experimental method
The rotational spectra of LiOH and LiOD were measured using one of the millimeter wave spectrometers of the
Ziurys group that has been used to detect more than 70 new
metal containing species. Detailed descriptions of these instruments have been given previously.16 Briefly, the absorption experiment consists of a Gunn oscillator/Schottky diode
multiplier source operating in the range of 65– 650 GHz, a
gas cell incorporating a Broida oven, and an InSb hot electron bolometer detector. Phase sensitive detection is achieved
by FM modulation of the tunable radiation source followed
by demodulation with a lock-in amplifier.
The LiOH and LiOD species were generated in a dc
discharge reaction of Li vapor and the appropriate precursor:
50% H2 O2 for LiOH and D2 O for LiOD. Lithium vapor was
produced by resistive heating of solid Li in an alumina crucible lined with a steel sleeve. Without the sleeve, the experiment would not have been possible because Li reacts readily
with the alumina crucible at high temperature. Although co-
pious amounts of both LiOH and LiOD were produced without the aid of a dc discharge, the signals were even stronger
in the presence of one, where the optimal conditions were
typically 500–1000 mA and 3–20 V. A variable amount of
Ar carrier gas was introduced to further optimize the signals
as required. This production technique is quite different to
those used by either McNaughton et al.4 or Freund,3 where
Li2 O was heated to 1400 K and then reacted with H2 O or
D2 O and resulted in weak signals. In the work presented
here, high signal to noise was achieved for all the modes
observed, and with that, complete spectral coverage was possible across the entire working band pass of the instrument,
which allowed for the collection of a more complete data set.
B. Experimental results
The rotational transitions measured for LiOH and LiOD
in the X 1 ⌺ ⫹ ground state are listed in Tables I and II. As
these tables show, seven transitions were recorded for LiOH
and eight transitions for LiOD in the frequency range 70–
504 GHz starting from the lowest possible transition (J lower
⫽l) in each case. This approach allowed the unambiguous
assignment of the rotational spectrum in each vibrational
mode because J must be greater than or equal to l. The lines,
for example, associated with the (033 0) mode disappear in
the J⫽3←2 transition. The same effect was observed for the
(022 0) and the (011 0) modes as well. Moreover, this restriction verified the position of the (020 0) mode because its
lines have a similar intensity to those of the (022 0) mode
and they are seen all the way through the J⫽1←0 transition.
Spectra for v 2 ⫽0, 1, 2, and 3 were measured for both LiOH
and LiOD.
Figures 1 and 2 are stick diagrams illustrating the progression of the vibrational modes as a function of frequency
within the J⫽5←4 rotational transition of LiOH and LiOD
near 352 and 317 GHz, respectively. As these figures illustrate, the line intensities drop off considerably with increasing v 2 quantum number. Using the calculated vibrational energies listed in Table XI, a vibrational temperature of about
400 K is typically found under normal experimental conditions. In LiOH, the v 2 progression occurs towards lower frequency of the ground 共000兲 state, indicating that the rotationvibration term ␣ 2 ⬎0, and it is fairly regular for the states
with v 2 ⫽l. The l-type splitting is sufficiently large in the
(011 0) and (031 0) modes that the upper l-type component in
these cases lies to the high frequency side of the 共000兲 line.
The (022 0) mode is split by a much smaller amount, and the
l-type doubling could not be resolved in the (033 0) mode for
any of the measured transitions. The (020 0) mode is shifted
by over 1 GHz higher in frequency from that of the centroid
of the (022 0), indicating some degree of anharmonicity in
the potential. The rotational constant decreases essentially
linearly with v 2 , indicating a strong cross anharmonicity between v 2 and v 3 . The (022 0) state is bent more than the
(020 0) state. For LiOD, the vibrational progression begins at
the higher frequency of the 共000兲 state, indicating a small
negative value for ␣ 2 , but reverses at the (033 0) mode owing to high-order terms in the vibration-rotation interaction.
The l-type doubling in the (011 0) state is large enough to
place the lower component of the doublet on the low fre-
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J. Chem. Phys., Vol. 121, No. 23, 15 December 2004
Rotational spectrum of LiOH
TABLE I. Observed transition frequencies 共in MHz兲 for LiOH (X̃ 1 ⌺ ⫹ ).
( v 1 , v l2 , v 3 )
Transition
Frequency
observed
ObservedCalculated
共000兲
J⫽1←0
J⫽2←1
J⫽3←2
J⫽4←3
J⫽5←4
J⫽6←5
J⫽7←6
70 684.827
141 364.458
212 033.641
282 687.165
353 319.812
423 926.405
494 501.678
(011c 0)
J⫽2←1
J⫽3←2
J⫽4←3
J⫽5←4
J⫽6←5
J⫽7←6
(011d 0)
(020 0)
(022c 0)
(022d 0)
(031c 0)
(031d 0)
(033cd 0)
11717
TABLE II. Observed transition frequencies 共in MHz兲 for LiOD (X̃ 1 ⌺ ⫹ ).
( v 1 , v l2 , v 3 )
Transition
Frequency
observed
ObservedCalculated
⫺0.007
0.007
0.008
0.001
⫺0.014
0.003
0.002
共000兲
J⫽1←0
J⫽2←1
J⫽3←2
J⫽4←3
J⫽5←4
J⫽6←5
J⫽7←6
J⫽8←7
62 954.770
125 905.882
188 849.733
251 782.599
314 700.981
377 601.122
440 479.411
503 332.199
0.009
0.001
0.015
⫺0.031
0.005
0.007
0.006
⫺0.005
140 187.606
210 268.260
280 333.188
350 377.172
420 394.917
490 381.183
0.024
⫺0.002
⫺0.018
0.001
0.005
⫺0.001
(011c 0)
J⫽2←1
J⫽3←2
J⫽4←3
J⫽5←4
J⫽6←5
J⫽7←6
J⫽8←7
125 412.870
188 110.215
250 796.581
313 468.386
376 121.958
438 753.630
501 359.776
⫺0.013
0.008
⫺0.009
0.000
0.010
0.002
⫺0.005
J⫽2←1
J⫽3←2
J⫽4←3
J⫽5←4
J⫽6←5
J⫽7←6
141 370.558
212 042.371
282 698.008
353 332.096
423 939.221
494 514.055
0.000
0.006
0.001
0.003
⫺0.015
0.008
(011d 0)
J⫽1←0
J⫽2←1
J⫽3←2
J⫽4←3
J⫽5←4
J⫽6←5
J⫽7←6
70 331.918
140 655.765
210 963.418
281 246.754
351 497.638
421 707.929
491 869.362
⫺0.054
⫺0.065
⫺0.043
0.005
0.055
0.081
⫺0.067
J⫽2←1
J⫽3←2
J⫽4←3
J⫽5←4
J⫽6←5
J⫽7←6
J⫽8←7
126 607.559
189 901.644
253 184.114
316 451.142
379 698.854
442 923.353
506 120.702
0.019
0.004
⫺0.022
⫺0.018
0.010
0.032
⫺0.019
(020 0)
J⫽3←2
J⫽4←3
J⫽5←4
J⫽6←5
J⫽7←6
210 104.778
280 114.958
350 103.961
420 066.612
489 997.487
0.134
0.060
⫺0.058
⫺0.059
0.037
J⫽1←0
J⫽2←1
J⫽3←2
J⫽4←3
J⫽5←4
J⫽6←5
J⫽7←6
J⫽8←7
63 194.510
126 378.475
189 541.556
252 673.077
315 762.480
378 799.147
441 772.409
504 671.774
⫺0.107
⫺0.223
⫺0.151
⫺0.033
0.111
0.198
0.094
⫺0.157
(022c 0)
J⫽3←2
J⫽4←3
J⫽5←4
J⫽6←5
J⫽7←6
210 114.728
280 140.236
350 154.806
420 155.730
490 140.466
⫺0.058
⫺0.030
⫺0.005
⫺0.012
0.019
J⫽3←2
J⫽4←3
J⫽5←4
J⫽6←5
J⫽7←6
J⫽8←7
189 049.044
252 047.741
315 031.378
377 996.187
440 938.337
503 854.004
0.196
0.119
0.012
⫺0.084
⫺0.118
0.088
(022d 0)
J⫽3←2
J⫽4←3
J⫽5←4
J⫽6←5
J⫽7←6
208 802.505
278 373.373
347 918.473
417 431.349
486 905.749
⫺0.021
0.021
0.023
⫺0.039
0.014
J⫽3←2
J⫽4←3
J⫽5←4
J⫽6←5
J⫽7←6
J⫽8←7
189 074.709
252 112.145
315 160.430
378 222.454
441 301.003
504 398.794
0.041
⫺0.041
⫺0.121
⫺0.072
0.056
0.024
(031c 0)
J⫽3←2
J⫽4←3
J⫽5←4
J⫽6←5
J⫽7←6
212 463.497
283 252.183
354 013.067
424 738.861
495 422.623
⫺0.112
⫺0.057
0.114
⫺0.094
⫺0.081
J⫽3←2
J⫽4←3
J⫽5←4
J⫽6←5
J⫽7←6
J⫽8←7
188 115.134
250 789.440
313 437.571
376 053.064
438 629.728
501 161.510
0.077
⫺0.021
⫺0.054
⫺0.033
0.070
⫺0.021
(031d 0)
J⫽4←3
J⫽5←4
J⫽6←5
J⫽7←6
278 489.120
348 080.687
417 651.727
487 198.260
0.003
0.012
⫺0.024
0.010
J⫽3←2
J⫽4←3
J⫽5←4
J⫽6←5
J⫽7←6
J⫽8←7
191 893.843
255 824.349
319 725.313
383 588.945
447 407.040
511 171.102
⫺0.063
0.004
0.052
0.042
⫺0.073
0.021
(033c 0)
J⫽4←3
J⫽5←4
J⫽6←5
J⫽7←6
J⫽8←7
251 938.141
314 914.894
377 886.567
440 851.625
503 808.614
a
⫺0.001
0.002
⫺0.002
0.000
(033d 0)
J⫽4←3
J⫽5←4
J⫽6←5
J⫽7←6
J⫽8←7
251 938.141
314 916.569
377 891.090
440 861.953
503 829.481
a
0.001
⫺0.002
0.001
0.000
quency side of the 共000兲 line. The l-type splitting of (022 0)
is again much smaller, but in this case the (033 0) doublet is
resolved in all the observed transitions; these features are
shown in the inset. Like LiOH, the (020 0) line for LiOD is
shifted by more than 1 GHz from the centroid of the (022 0)
doublet.
a
Unresolved doublet not included in the fit.
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11718
J. Chem. Phys., Vol. 121, No. 23, 15 December 2004
FIG. 1. A stick figure showing the progression of the vibrational modes in
the J⫽5←4 rotational transition of LiOH. The heights of the sticks indicate
the observed relative intensity as compared to the ground vibrational mode.
Figures 3 and 4 show typical spectra obtained for LiOH
and LiOD. Figure 3 shows a portion of the spectrum of the
J⫽5←4 transition of LiOH near 353.3 GHz. The ground
vibrational state and the upper l component of the (011 0)
mode are shown. The scan width is 100 MHz and the acquisition time is ⬇1 min. The signal to noise ratio in this spectrum is greater than 200:1 for the strongest feature present.
Figure 4 shows sections of the spectrum of the J⫽8←7
transition of LiOD near 503 GHz. The panel on the left
shows the ground vibrational mode while that on the right
shows the lower l component of the (022 0) state and the
l-type doublet of the (033 0) mode. The intensity of the lines
decreases exponentially with increasing v 2 . This is consistent with a Boltzmann distribution, as expected under the
conditions of this experiment.
C. Experimental analysis
The rotational data in all of the observed vibrational
states for LiOH and LiOD were analyzed using a standard
linear molecule Hamiltonian consisting of rotation, centrifugal distortion, and l-type interactions 共see Ref. 17兲. The re-
FIG. 2. A stick figure showing the progression of the vibrational modes in
the J⫽5←4 rotational transition for LiOD. The vibrational modes shown
are 共000兲, (011 0), and (022 0). The heights of the sticks indicate the observed relative intensity as compared to the ground vibrational mode.
Higgins et al.
FIG. 3. Spectrum of the J⫽5←4 transition of LiOH in its ground vibrational and first excited modes near 353 GHz. The scan width is 100 MHz
and the acquisition time is ⬇1 min. The signal to noise ratio of this spectrum
is ⬎200:1, illustrating the improvement of this method over those used in
the past.
sulting spectroscopic constants are given in Table III. The
data for both molecules in their respective 共000兲 and (020 0)
modes were fit with only two parameters, B and D, while the
remaining vibrational modes also required two l-type doubling parameters, q and q D . In addition, several high-order
centrifugal distortion terms were necessary to obtain an acceptable fit for LiOD.
Using the rotational constants determined for each bending vibration, the vibrational progression was modeled with
the following expression:
B 共 0,v 2 ,0兲 ⫽B̃ e ⫺ ␣ 2 共 v 2 ⫹1 兲 ⫹ ␥ 22共 v 2 ⫹1 兲 2 ⫹ ␥ ll l 2 ,
共1兲
where B (0,v 2 ,0) is the rotational constant per v 2 state, B̃ e
⫽B e ⫺ 12 ( ␣ 1 ⫹ ␣ 3 ) is the effective equilibrium rotational constant, ␣ 2 and ␥ 22 are the vibration-rotation interaction constants, and ␥ ll is the l-dependent vibration-rotation interaction constant. The ␣ 2 , ␥ 22 , and ␥ ll parameters determined
from Eq. 共1兲 are given in Table IV, as well as theoretical
FIG. 4. The spectrum of the J⫽8←7 transition of LiOD near 503 GHz; a
baseline has been removed. The panel on the left shows the ground vibrational mode while the panel on the right shows the lower l component of the
(022 0) mode and both l components of the (033 0) mode. The y scale for the
left panel is ten times larger than that on the right. Each spectrum is a 100
MHz scan with an acquisition time of ⬇1 min.
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J. Chem. Phys., Vol. 121, No. 23, 15 December 2004
Rotational spectrum of LiOH
11719
TABLE III. Experimental and theoretical values of molecular constants 共in MHz兲 for LiOH and LiOD.
LiOH
LiOD
Theoretical
( v 1 , v l2
, v 3)
Experimental
Current PES
Ref. 11 PESa
35 016.604
0.214 18
31 477.684共4兲
0.151 73共5兲
31 391.313
0.151 46
31 211.351
0.150 11
35 088.089
0.221 05
⫺293.804
0.005 927
⫺149.479
34 868.876
0.217 63
⫺308.271
0.006 332
⫺147.727
31 503.492共3兲
0.156 56共3兲
⫺298.738共6兲
0.009 21共7兲
25.808
31 414.508
0.156 24
⫺296.890
0.009 05
23.193
31 242.106
0.154 72
⫺315.481
0.010 346
30.756
35 166.662共5兲
0.338 08共7兲
⫺176.190
35 055.707
0.335 85
⫺181.861
34 850.049
0.370 51
⫺166.554
31 598.186共4兲
0.438 99共5兲
120.502
31 506.259
0.436 94
114.946
31 342.270
0.583 64
130.919
B
D
qef f
q Def f
⌬B
35 019.956共4兲
0.167 01共6兲
0.1056共1兲
1.6(3)⫻10⫺7
⫺322.896
34 909.869
0.167 33
0.1043
1.2⫻10⫺7
⫺327.699
34 692.885
0.143 84
0.1418
2.4⫻10⫺7
⫺323.718
31 510.511共3兲
0.021 79共4兲
0.268 94共8兲
1.6(1)⫻10⫺7
32.827
31 419.126
0.022 19
0.267 48
1.6⫻10⫺7
27.813
31 249.947
⫺0.054 12
0.414 12
2.4⫻10⫺7
38.597
B
D
H
q
qD
qH
⌬B
35 109.982共4兲
0.279 41共6兲
34 996.234
0.277 81
34 791.941
0.287 57
⫺610.591共8兲
0.0228共1兲
⫺606.044
0.0225
⫺611.923
0.0235
⫺232.870
⫺241.334
⫺224.663
31 672.034共6兲
0.2885共2兲
⫺2.4(2)⫻10⫺5
⫺630.37共1兲
0.031共2兲
7.3(2)⫻10⫺7
194.350
31 577.333
0.2869
⫺2.4⫻10⫺5
⫺625.85
0.031
7.2⫻10⫺7
186.020
31 412.579
0.3481
⫺6.5⫻10⫺5
⫺641.197
0.038
1.8⫻10⫺6
201.228
B
D
H
qef f
q Def f
qH
⌬B
rms
34 813.529共4兲
0.170 68共7兲
31 492.82共1兲
0.0405共4兲
2.6(3)⫻10⫺5
0.003共9兲
⫺3(2)⫻10⫺4
3.4(2)⫻10⫺5
15.135
0.071
31 399.367
0.0409
2.4⫻10⫺5
0.002
⫺3⫻10⫺4
3.4⫻10⫺5
8.054
0.076
31 231.924
⫺0.0249
6.6⫻10⫺5
0.008
⫺7⫻10⫺4
8.3⫻10⫺5
20.573
0.137
Constant
Experimental
Current PES
Ref. 11 PES
共000兲
B
D
35 342.852共5兲
0.217 38共7兲
35 237.568
0.216 96
(011 0)
B
D
q
qD
⌬B
35 196.097共4兲
0.221 53共5兲
⫺295.792共8兲
0.0060共1兲
⫺146.755
(020 0)
B
D
⌬B
(022 0)
(031 0)
(033 0)
a
Theoretical
From
DVR3D
34 701.940
0.171 16
Unresolved
Unresolved
⫺529.323
0.045
34 491.611
0.152 68
⫺0.126
4.5⫻10⫺4
⫺535.628
0.034
a
⫺0.022
7.8⫻10⫺4
⫺524.993
0.067
calculations using the PES of Ref. 11.
values obtained from computations described below. The
terms ␥ 22 and ␥ ll are exceptionally high, suggesting that
LiOH and LiOD exhibit large amplitude oscillations. The
nature of the large amplitude motions become clear after the
comparison of the spectroscopic constants obtained from
electronic structure theory is made.
III. COMPUTATIONAL
A. Computational methods
The three-dimensional potential energy surface 共PES兲
for LiOH was calculated at the coupled-cluster level with
single and double excitations and perturbative contributions
of connected triple excitations 关CCSD共T兲兴. Preliminary
CCSD共T兲 geometry optimization calculations were performed to determine the optimal basis set to use, the effect of
core electron correlation, and the effect of basis set superposition error 共BSSE兲 on the computed geometries and energies
of LiOH. A three-dimensional dipole moment surface was
also calculated using second-order Møller-Plesset perturbation theory 共MP2兲. Electronic structure calculations were
performed using MOLPRO2000.18,19 To gauge the quality of the
PES by making comparisons to the current and previous ex-
TABLE IV. Vibrational dependence of B v 共values quoted are in MHz兲 from states in the current study.
LiOH
Constant
B̃ e a
␣2
␥ 22
␥ ll
LiOD
Experimental
Theoretical
Experimental
Theoretical
35 497.50共1兲
176.86共1兲
22.291共2兲
⫺36.9937共6兲
35 395.28共3兲
179.98共2兲
22.332共4兲
⫺36.7183共16兲
31 451.28共1兲
⫺14.467共8兲
11.543共2兲
⫺22.2339共8兲
31 368.07共3兲
⫺11.43共2兲
11.591共4兲
⫺22.1639共16兲
1
B̃ e ⫽B e ⫺ 2 ( ␣ 1 ⫹ ␣ 3 ).
a
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11720
Higgins et al.
J. Chem. Phys., Vol. 121, No. 23, 15 December 2004
TABLE V. Geometry optimization results 共in Å and cm⫺1 unless noted兲 and a sampling of previous results.
Basis
r(LiO)
r(OH)
E tot (hartree)
De
D e (CPC) a
CPC%
CCSD共T兲
Frozen core
avqz
av5z
acvqz
1.5954
1.5945
1.5947
0.9490
0.9486
0.9491
⫺83.262 878
⫺83.269 810
⫺83.264 447
⫺73 546
⫺73 849
⫺73 548
⫺73 276
⫺73 726
⫺73 328
0.37
0.17
0.30
CCSD共T兲
Full electron
correlation
cvqz
acvqz
1.5759
1.5805
0.9477
0.9483
⫺83.365 913
⫺83.369 319
⫺73 634
⫺74 014
⫺73 196
⫺73 781
0.59
0.31
Hartree-Fock
acvqz
1.5743
0.9300
⫺82.959 498
⫺47 350
⫺47 318
0.07
b
6-311G**
6-311⫹⫹G(2d f ,2pd)
e
1.5857
1.5732
1.587
1.5802
0.9499
0.9446
0.948
0.9510
⫺83.266 532
⫺82.938 316
⫺83.268 74
⫺83.284 58
Method
ACPFb
MP3c
CCSD共T兲d
CCSD共T兲e
Counterpoise correction 共CPC兲 applied to noncounterpoise corrected optimized geometry.
Reference 11. See reference for details of the basis set.
c
Reference 4.
d
Reference 14.
e
Reference 9. See reference for details of the basis set.
a
b
perimental results, the energy levels, transition frequencies,
and various expectation values for LiOH, LiOD, Li 18OH,
and 6 LiOH were calculated using the DVR3D package of Tennyson and co-workers.15
The atomic basis sets used for the preliminary calculations were the correlation-consistent polarized valence,
cc-pVnZ共vnz) and correlation-consistent polarized corevalence, cc-pCVnZ共cvnz), 20 basis sets of Dunning and
co-workers,21,22 and these sets augmented with diffuse functions for O and H, aug-cc-pVnZ共avnz) or aug-ccpCVnZ共acvnz). For the core-valence basis sets cvnz and
acvnz, calculations were performed using sets of double-,
triple-, and quadruple-zeta 共the highest available兲 quality,
while for the vnz and avnz basis sets the quality ranged from
double to quintuple zeta. Because there are no diffuse functions available for the Dunning basis sets for Li and no corevalence sets for H the total basis used for LiOH in each case
is labeled by the set used for the O atom with the understanding that Li and H used the closest available basis set.
CCSD共T兲 calculations were performed at the frozen-core
approximation and with all electrons correlated. In addition,
a single geometry optimization at the Hartree–Fock/acvqz
level was performed to determine the effect of completely
ignoring electron correlation has on the geometry and binding energy of LiOH. Binding energies for the optimized geometries were calculated relative to the ground state atoms
by subtracting the atomic energies calculated in the atomic
basis from the molecular energy. The energetic effect of
BSSE was calculated by using the counterpoise 共CP兲
method23 with the non-CP optimized geometry.
Selected geometry optimization results are listed in
Table V along with results from previous studies for comparison. Frozen-core results using the avnz basis sets illustrate the convergence of the geometry and binding energy as
a function of basis set size, with the avqz results differing
from the av5z results by just 0.0009 Å for the Li–O bond
length, 0.0004 Å for the O–H bond length, and 0.41% in the
binding energy. The effect of core-electron correlation can be
seen by comparing the results for the acvqz basis sets using
full electron correlation to those using the frozen-core approximation. There is very little difference for the binding
energy and the O–H distance 共0.63% and 0.0008 Å, respectively兲, but the Li–O bond distance shrinks considerably
共0.0142 Å兲. This shrinkage proved vital to getting the correct
rotational constants in the rovibrational calculations presented below. Comparing the acvqz results with the cvqz
results shows that the inclusion of diffuse functions on the O
and H result in a lengthening of the Li–O bond by 0.0046 Å
and of the O–H bond by 0.0006 Å, and an increase in the
binding energy of 0.51%. Also note in Table V the effect of
BSSE as estimated using the CP correction, which for the
acvqz basis set amounts to just 0.31% of the total binding
energy. The best calculations using the acvqz basis yield an
equilibrium Li–O bond length of 1.5805 Å and an equilibrium O–H bond length of 0.9483 Å. These results are in
good agreement with the most recent reported LiOH
calculations.9,10 Included in Table V are results for Hartree–
Fock level calculations using the acvqz basis set. These calculations result in a binding energy that is 64% of the
CCSD共T兲 binding energy as well as Li–O and O–H bond
lengths that are somewhat shorter.
Based on the results of the preliminary calculations, the
full three-dimensional CCSD共T兲 potential energy surface
was calculated with the acvqz basis set utilizing full electron
correlation with no counterpoise correction. The potential
was calculated in a Jacobi coordinate system with R the distance from Li to the center of mass of OH, r the OH bond
length, and ␪ the angle between R and r with ␪⫽0 defined as
the linear Li–OH arrangement. Calculations were performed
on a grid of points with ten values of r ranging from 0.6 to
1.8 Å, eight values of R from 1.1 to 3.0 Å, and ␪ ranging
from 0° to 180° in increments of 15° for a total of 1040
geometries.24 As with the optimized geometry binding energies, the potential at each point is taken as the difference
between the LiOH energy and the ground state energies of
the individual atoms calculated with the atom’s basis set.
Interpolation of the potential was performed using a
three-dimensional cubic spline routine.25 To ensure a smooth
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J. Chem. Phys., Vol. 121, No. 23, 15 December 2004
Rotational spectrum of LiOH
11721
TABLE VI. Morse oscillator parameters 共in bohr and hartree兲 for the basis sets used in DVR3DRJZ.
LiOH
LiOD
Li 18 OH
6
LiOH
r 1⫽
r(OH)
re
De
␻e
2.064 197 3
0.169
3.245 356 1⫻10⫺2
2.046 788 6
0.169
1.992 938 8⫻10⫺2
2.062 770 5
0.169
3.234 628 2⫻10⫺2
2.064 197 3
0.169
3.245 356 1⫻10⫺2
r 2 ⫽R
re
De
␻e
3.919 755 3
0.168
2.696 256 8⫻10⫺3
4.014 451 2
0.168
2.654 322 3⫻10⫺3
3.917 075 7
0.168
2.620 228 5⫻10⫺3
3.920 488 9
0.168
2.994 541 7⫻10⫺3
and accurate interpolation in the R coordinate additional
points were generated by fitting the ab initio points for each
r and ␪ combination to an analytical potential function in R,
6
V 共 R, 关 r, ␪ 兴 兲 ⫽A exp共 ⫺ ␤ R 兲 ⫺
兺
n⫽1
C n R ⫺n ⫺V OH共 r 兲 , 共2兲
where V OH(r) is the potential energy of OH calculated in the
same manner as the LiOH potential energy, and then using
this function to produce points on a finer spacing over the
range R⫽0.9– 3.0 Å. 26 Additional points at r⫽0.5 Å were
generated by fitting the r dependence of V(R,r, ␪ ) for each
关 R, ␪ 兴 combination to a simple quadratic expression using
the r⫽0.6, 0.7, and 0.8 Å points as input. The spline routine
uses a natural spline at both ends of the r range and the outer
end of the R range, a constraint that the slope of the potential
be zero in the ␪ direction for ␪⫽0° and 180°, and a constraint
that the slope in the R direction at the inner end of the R
range be determined by fitting the inner two points to an
exponential expression in R, A exp(⫺␤R), and taking its
slope at R⫽0.9 Å. Because a square grid of potential points
was used, some of the input geometries were in areas of
tremendous atomic repulsion with correspondingly high potential energies, and these points caused problems with the
cubic spline interpolation, therefore any potential energy
greater than 5⫻105 cm⫺1 was scaled on input to lie between
5 and 10⫻105 cm⫺1 using the formula V scaled⫽5
⫻105 (1 – 5⫻105 /V unscaled)⫹5⫻105 . The potential subroutine also shifts the center of mass used for OD or 18OH in
their respective calculations.
The dipole moment surface was calculated at the MP2
level using the acvqz basis set on the same grid of points as
the ab initio potential calculation with all electrons
correlated.24 A fixed orientation with the z axis directed along
the OH bond was used in the MP2 calculations, although for
the dipole expectation value calculations described later the
calculated dipole components were rotated into the inertial
frame by diagonalizing the moment of inertia tensor for each
geometry calculated. The dipole surface was interpolated using the same cubic spline routine as the potential, but this
time a natural spline was used for both ends of the r and R
range while the same constraint of zero slope at ␪⫽0° and
180° was used. No extra points were necessary because the
dipole surface is smooth enough for a cubic spline to interpolate accurately on the calculated grid.
Rovibrational energy levels of LiOH, LiOD, Li 18OH,
and 6 LiOH for the CCSD共T兲 potential surface were calculated using the DVR3D program suite.15 This package uses a
discrete variable representation 共DVR兲 method in all three
coordinates to calculate the energy levels, wave functions,
and expectation values of triatomic molecules. It employs a
two-step process in which the program DVR3DRJZ solves the
pure vibrational (J⫽0) or Coriolis-decoupled vibrational
(J⭓0) problem and then the program ROTLEV3 uses the results of DVR3DRJZ as a basis to solve the full rovibrational
problem. The basis functions for DVR3DRJZ consist of Morseoscillator-like functions for the radial coordinates and Legendre polynomials or associated Legendre polynomials for
the angular coordinate.
By default DVR3D takes as input the number of DVR
points and the Morse parameters r e , D e , and ␻ e describing
the basis for each radial coordinate and determines the points
to use for that coordinate. To test convergence in terms of
range and/or number of DVR points, D e was held fixed
while r e and ␻ e were chosen so that the inner and outer
radial limits for a given number of DVR points matched the
values desired. Convergence characteristics were determined
by performing extensive calculations in which the number of
DVR points in each coordinate and the inner and outer limits
for the radial coordinates were varied. In addition, the number of basis functions in the final Hamiltonian for DVR3DRJZ
and the number of energy levels to be kept and used as input
to ROTLEV3 were varied. Results for J⫽0, 1, and 2 were used
to determine B and D for the 共000兲 and (020 0) states to
gauge the convergence of predicted spectroscopic constants
in addition to the convergence of absolute energy levels.
Convergence to 0.0003 cm⫺1 in absolute energy, 10 kHz in
B, and 0.3 kHz in D was achieved using a DVR grid of 50
points in R between 1.1 and 3.0 Å, 40 points in r between 0.6
and 1.5 Å, and 40 points in ␪ between 0° and 180°. Because
the center of mass of OD is shifted ⬇0.05 Å away from the
O atom the DVR grid in R for LiOD is between 1.15 and
3.05 Å. Parameters for the Morse-oscillator-like basis functions for the four isotopomers are listed in Table VI. For
DVR3DRJZ the z axis was embedded along the R coordinate,
the intermediate one-dimensional solutions were truncated at
0 cm⫺1, the final basis size was 2000 functions, and the
resulting lowest 200 states were used as input to ROTLEV3.
Expectation values of various geometric coordinates and the
dipole moment function were calculated with the program
XPECT3 using the wave function output from DVR3DRJZ for
J⫽0 and from ROTLEV3 for J⭓0. The dipole moment component along the a inertial axis, ␮ a , is calculated by taking
the expectation value of the instantaneous projection of the
dipole moment along the a axis. For comparison purposes,
rovibrational energy levels for LiOH and LiOD were calcu-
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11722
J. Chem. Phys., Vol. 121, No. 23, 15 December 2004
Higgins et al.
FIG. 5. Contour plot of the LiOH CCSD共T兲 potential energy surface for
r(OH) held fixed at 0.9489 Å. The origin is at the OH center of mass and
contours are labeled in 104 cm⫺1 .
lated using the PES from Bunker et al.11 in exactly the same
manner described above for the current PES.
B. Computational results
Although the PES and rotation-vibration calculations use
a Jacobi coordinate system, for discussion of the results it is
physically clearer to use the LiOH valence coordinates
r(LiO), r(OH), and ¯␳ , the deviation from linearity for the
Li–O–H bond angle.27 The global minimum on the spline
interpolated surface is ⫺74 014 cm⫺1 and occurs at r(LiO)
⫽1.5805 Å, r(OH)⫽0.9489 Å, and ¯␳ ⫽0°. This is an OH
bond length 0.0006 Å longer than the optimized structure
listed in Table V. This slight structural difference amounts to
only a 3 MHz difference in rotational constant for a static
structure. A contour diagram of the CCSD共T兲 PES as a function of Li position relative to the center of mass of OH for
r(OH) held fixed at its equilibrium distance of 0.9489 Å is
shown in Fig. 5. The minimum in the potential occurs in the
linear Li–O–H configuration and there is a wide, flat trough
in the bending potential about this linear configuration.
Details of the minimum energy path as a function of ¯␳
are presented in Fig. 6. Figure 6共a兲 shows the energy along
the minimum energy path and illustrates the monotonic increase in the potential from ¯␳ ⫽0° to 180° as well as the
flatness of the potential from ¯␳ ⫽0° to 90°. The value of
r(LiO) stays roughly the same from ¯␳ ⫽0° to 120° but
r(OH) lengthens dramatically over this same range and then
decreases dramatically as ¯␳ approaches 180°. Note the minimum energy configuration for ¯␳ ⫽180° is O–H–Li, which
calculations show is 44 994 cm⫺1 lower in energy than the
configuration O–Li–H. Figure 7 shows a comparison with
the calculations of Refs. 4 and 11 over the range ¯␳
⫽0° – 90° and it can be seen that the current PES falls between the previous two in terms of the bending potential and
structure over this range. The analytic PES of Ref. 11 was
derived from ab initio calculations over the range 1.41
⭐r(LiO)⭐1.81 Å, 0.78⭐r(OH)⭐1.18 Å, and 0°⭐¯␳
⭐90°, which is a smaller range than the current calculations
but the analytic form allows for extrapolation. Extrapolating
beyond ¯␳ ⫽90° results in good agreement in terms of energy,
which at ¯␳ ⫽180° is 3.5% higher relative to equilibrium than
the current PES; however, it results in disagreement in terms
FIG. 6. Values of the 共a兲 potential energy, 共b兲 Li–O bond distance, and 共c兲
O–H bond distance along the minimum energy path of the CCSD共T兲 potential energy surface as functions of ¯␳ , the deviation from linearity for the
Li–O–H angle.
of the optimal bond lengths, with r(LiO) decreasing to
1.5540 Å and r(OH) increasing to 0.9930 Å at ¯␳ ⫽180°.
The interesting effects of stretching r(LiO) or r(OH) are
shown in Figs. 8 and 9, respectively, where it is shown that
the minimum energy structure of LiOH becomes bent as either r(LiO) or r(OH) is stretched. The effect for r(LiO) was
first reported by Bunker et al.11 but this is the first report of
a similar effect for r(OH). The molecule stays linear until
r(LiO)⫽1.7259 Å and then approaches a tetrahedral angle
as r(LiO) approaches 3.0 Å. The difference in energy between the linear configuration and the bent configuration is
shown in Fig. 8共b兲. By r(LiO)⫽3.0 Å the bent form is 2636
cm⫺1 more stable than the linear form. Figure 8共c兲 shows
that the optimal value of r(OH) changes as well, rising from
0.9489 Å at equilibrium to 0.9643 Å at r(LiO)⫽3.0 Å. The
latter value is quite close to the r e value of 0.9644 Å calculated for OH⫺ using the same basis and method as LiOH.
The analytic PES of Ref. 11 is in good agreement in all
aspects with the current PES, even in the extrapolated region
with r(LiO)⬎1.8 Å, with the change from linearity occurring 0.0177 Å earlier and the bent structure being 2660 cm⫺1
lower in energy than the linear structure at r(LiO)⫽3.0 Å.
The effect of stretching r(OH), shown in Fig. 9, differs
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J. Chem. Phys., Vol. 121, No. 23, 15 December 2004
FIG. 7. Comparison with previous LiOH potentials of 共a兲 potential energy
relative to equilibrium value, 共b兲 Li–O bond distance, and 共c兲 O–H bond
distance along the minimum energy path as a function of ¯␳ . Dashed line is
PES of Ref. 11 and filled circles are from Ref. 4.
from that of r(LiO). A local minimum on the PES develops
in the bent configuration at r(OH)⫽1.2900 Å while the linear minimum persists until r(OH)⫽1.3939 Å, so for a short
distance there are two minimums. The change from linearity
occurs at r(OH)⫽1.3095 Å, when the bent minimum becomes lower in energy than the linear minimum and it is
seen as a discontinuous jump in Fig. 9. By r(OH)⫽1.8 Å the
optimal ¯␳ value is 103°, the optimal r(LiO) is 1.6894 Å, and
the bent configuration is 2940 cm⫺1 lower in energy than the
linear configuration. The PES of Ref. 11 predicts qualitatively similar behavior even though the change from linearity
begins well beyond their calculated r(OH) region.
To gauge the quality of the PES a comparison is made to
the experimentally determined molecular constants by determining theoretical constants using the same program and
same transitions used to determine the experimental constants. This approach is favored over a direct comparison of
transition frequencies because even a slight difference in rotational constant can lead to a systematic disagreement between experiment and computation that masks the true quality of the PES. In addition, the fitted constants each probe a
different aspect of the PES, with the rotational constant probing structural agreement and the distortion constants probing
the stiffness of the PES. Table III lists the experimentally and
Rotational spectrum of LiOH
11723
FIG. 8. Effects of stretching the Li–O bond in terms of 共a兲 ¯␳ for the minimum energy configuration, 共b兲 potential energy difference between the minimum energy configuration and the linear configuration, and 共c兲 the variation
of the optimal O–H bond distance. CCSD共T兲 values are represented by the
solid lines and Hartree–Fock values are represented by dashed lines.
computationally determined rotational, distortion, and effective l-doubling constants for the current experiment. The
agreement is excellent, with the computed rotational constants typically 0.3% too low and the computed distortion
constants typically 0.2% too low. Also listed is the shift in B
with vibrational level, ⌬B. The computed values are within
8.5 MHz of the experimental values. The l-doubling constants are also well predicted, with the computed values typically within 0.75% of the experimental values. Larger relative discrepancies start to appear for the higher-order
constants that have values in the kHz range, which is pushing
the limits of the current calculations’ numerical convergence.
The l doubling in the (033 0) state of LiOH is unresolved in
the current experiment but was measured directly by Freund
for J⫽6 – 12.3 Table VII lists the observed and predicted
transition frequencies of this state as an illustration of how
well the current calculation can predict these small splittings.
Also listed in Table III are constants derived from DVR3D
calculations using the PES of Ref. 11. The B values are typically 0.9% too low and the ⌬B values are within 10.4 MHz
of experiment, but agreement for the other fitted constants is
much less consistent. Values for D range from within 1.5% to
greater than 13% of experiment while q values range from
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11724
Higgins et al.
J. Chem. Phys., Vol. 121, No. 23, 15 December 2004
TABLE VIII. Experimental and theoretical constants 共in MHz兲 for other
vibrational states and isotopomers.
Species
b
LiOH
( v 1 , v l2 , v 3 )
Constanta
共100兲
B
D
⌬B
B
D
⌬B
B
D
⌬B
B
D
⌬B
B
D
⌬B
(120 0)
共001兲
(020 1)
共101兲
34 887.76共5兲
455.09共5兲
34 723.44共10兲
619.41共10兲
35 240.8共5兲
102.0共5兲
34 836共1兲
507共1兲
Li OH
共000兲
B
D
⌬B
34 531.819共9兲
0.20940共26兲
811.033共9兲
LiOHd
共000兲
B
D
⌬B
39 244.82共25兲
18
6
LiOD
c
共000兲
共100兲
(120 0)
共001兲
FIG. 9. Effects of stretching the O–H bond in terms of 共a兲 ¯␳ for the minimum energy configuration, 共b兲 potential energy difference between the minimum energy configuration and the linear configuration, and 共c兲 the variation
of the optimal Li–O bond distance. The break in the ¯␳ and r(LiO) lines
indicates a jump between two competing minimums. CCSD共T兲 values only
shown.
Experimental
共101兲
(020 1)
B
D
⌬B
B
D
B
D
B
D
B
D
B
D
⫺3 901.97共25兲
31 477.684共4兲
0.15173共5兲
3 865.168共5兲
Theoretical
34 785.324
0.216 40
452.244
34 616.373
0.338 78
621.195
35 079.316
0.215 47
158.252
34 914.168
0.354 19
323.400
34 627.023
0.215 01
610.545
34 428.414
0.208 90
809.154
39 108.503
0.264 19
⫺3 870.935
31 391.313
0.151 46
3 846.255
31 021.686
0.157 96
31 158.391
0.478 66
31 224.538
0.149 66
30 876.508
0.036 47
31 357.573
0.459 85
⌬B values are calculated relative to the B (000) value of LiOH.
Experimental from Ref. 3.
c
Experimental from Table VI of Ref. 4.
d
Experimental from the J⫽1←0 transition frequency listed in Table III of
Ref. 4.
a
b
within 0.3% to greater than 30% of experiment for LiOH,
with the range for LiOD even greater.
Previous experimental studies3,4 of LiOH have reported
rotational lines for vibrational states and isotopomers not included in the current experimental work but useful for comparison with the current calculation. Table VIII lists the experimental and theoretical constants for these species and
vibrational states as well as for several vibrational states of
LiOH and LiOD that have not been observed experimentally
but are used in the structure determination below. Predicted
TABLE VII. l-doubling transition frequencies 共in MHz兲 for the (033 0) state
of LiOH.
a
J
Experimentala
Theoretical
6
7
8
9
10
11
12
1.040共5兲
2.555共5兲
5.635共5兲
11.323共5兲
21.255共5兲
37.260共5兲
62.555共5兲
0.987
2.481
5.481
11.028
20.608
36.300
60.934
Reference 3.
isotope shifts relative to LiOH for B (000) are within 0.8% of
the experimental values. The vibrational shifts for the 共100兲
and (120 0) states of LiOH are predicted to within 0.6%, but
those for the 共001兲 and 共101兲 states are too high by 55% and
20%, respectively. Given the level of agreement between experiment and theory up until this point, it is probable that the
experimental values for 共001兲 and 共101兲 are in error.28
Vibration-rotation interaction constants provide another
measure of the quality of the PES by probing the elasticity at
longer ranges than the distortion constants. Table IV lists the
experimental and theoretical constants determined using Eq.
共1兲 from the states studied in the current experiments. The
level of agreement is excellent, including the large change in
␣ 2 upon deuteration, indicating that the PES reproduces the
bending potential accurately even for the large amplitude vibrations in the (03l 0) states. Table IX lists constants determined using a variety of expanded data sets fit to
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J. Chem. Phys., Vol. 121, No. 23, 15 December 2004
Rotational spectrum of LiOH
11725
TABLE IX. Vibration-rotation constants 共in MHz兲 determined using data from the current and previous studies.
LiOH all experimental dataa
Constant
Be
␣1
␣2
␣3
␥ 22
␥ ll
␥ 12
␥ 13
␥ 23
Experimental
LiOH mixed datab
Theoretical
Experimental
LiOD mixed datac
Theoretical
Experimental
Theoretical
35 791.5共4兲
35 703.68共4兲
35 811.06共5兲 35 707.72共4兲
31 734.41共1兲 31 651.20共4兲
485.9共6兲
458.49共3兲
460.72共9兲
458.49共3兲
390.76
390.76共3兲
179.63共3兲
183.08共2兲
183.68共3兲
187.11共3兲
⫺4.781共8兲
⫺1.75共3兲
127.3共9兲
158.31共2兲
166.40
166.40共3兲
186.26
186.26共3兲
22.291共2兲
22.332共4兲
22.291共2兲
22.332共4兲
11.543共2兲
11.591共4兲
⫺36.9937共6兲 ⫺36.7183共16兲 ⫺36.9937共6兲 ⫺36.7183共16兲 ⫺22.2339共8兲 ⫺22.1639共16兲
5.54共6兲
6.182共9兲
5.54共6兲
6.182共9兲
10.582
10.582共9兲
50共1兲
0.008共20兲
0.008
0.008共20兲
21.53
21.53共2兲
8.083
8.083共9兲
8.790
8.790共9兲
Experimental values fit using B v values for 共000兲, (011 0), (020 0), (022 0), (031 0), and (033 0) from this work
and for 共100兲, (120 0), 共001兲, and 共101兲 from Ref. 3. Theoretical values fit using B v values from this work.
b
Theoretical values fit by adding the B v value for (020 1) to the ‘‘all experimental’’ data set. Experimental values
fit by removing the B v values for 共001兲 and 共101兲 from the all experimental data set and fixing ␣ 3 , ␥ 13 , and
␥ 23 at their theoretical values.
c
Experimental values fit using B v values from this work and fixing ␣ 1 , ␣ 3 , ␥ 12 , ␥ 13 , and ␥ 23 at their
theoretical values.
a
B v ⫽B e ⫺ ␣ 1 共 v 1 ⫹ 12 兲 ⫺ ␣ 2 共 v 2 ⫹1 兲
⫺ ␣ 3 共 v 3 ⫹ 12 兲 ⫹ ␥ 22 共 v 2 ⫹1 兲 2 ⫹ ␥ ll 共 l 兲 2
⫹ ␥ 12 共 v 1 ⫹ 21 兲共 v 2 ⫹1 兲 ⫹ ␥ 13 共 v 1 ⫹ 21 兲共 v 3 ⫹ 12 兲
⫹ ␥ 23 共 v 2 ⫹1 兲共 v 3 ⫹ 21 兲 .
共3兲
The first two columns list experimental and theoretical constants determined using B v values for all experimentally
measured vibrational states of LiOH. The disagreement for
the 共001兲 and 共101兲 states noted earlier is apparent in the
large differences between the experimental and theoretical
values for ␣ 1 , ␣ 3 , and ␥ 13 . Although the B v shift is well
predicted for the 共100兲 state, the value of ␣ 1 is quite far off
due to the influence of the large experimental ␥ 13 value. The
next four sets of constants presented in Table IX are determined from a mix of experimentally measured and theoretically predicted states for LiOH and LiOD and are used to
derive a semiexperimental equilibrium structure later in this
paper. The theoretical constants are fit using a data set that
includes the (020 1) state in order to determine the value of
␥ 23 . The experimental constants are fit by removing the
questionable states 共001兲 and 共101兲 from the experimental
LiOH data set and fixing the undeterminable constants for
either LiOH or LiOD to their theoretical values. The agreement between experiment and theory for ␣ 1 is much better
for this data set.
Finally we compare the charge distribution parameters
observed with the calculated values. Table X lists the experimentally determined dipole moments and quadrupole coupling constants as well as the calculated dipole moments of
several vibrational states. The calculated ␮ a dipole components show excellent agreement with experiment, falling
within 0.5% for LiOH and 0.9% for LiOD of the experimentally measured values. There is a slight increase in dipole
moment with the LiO stretching vibration but a significant
increase in the dipole moment with the bending vibration,
and as such this is an excellent test of both the calculated
dipole moment surface and the PES. This variation with vibrational state follows what is expected given the variation
of the calculated dipole moment with ¯␳ and r(LiO) presented in Fig. 10. Although the current calculation does not
include quadrupole coupling effects, it is interesting to note
the experimental 7 Li quadrupole coupling constant increases
significantly with bending vibration, indicating a dependence
of the electric field gradient at the 7 Li nucleus on the bending
angle.
The calculated ground state energies are ⫺71 240 cm⫺1
for LiOH and ⫺71 849 cm⫺1 for LiOD, giving zero-point
energies of 2774 and 2165 cm⫺1 for LiOH and LiOD, respectively. Table XI lists calculated energies and structural
parameters for the ground state, the bending states up to
(033 0), and the Li–O 共100兲 and O–H共D兲 共001兲 stretching
TABLE X. Observed 共Ref. 3兲 and calculated dipole moments 共in debye兲 and observed hyperfine constants 共in
kHz兲 of LiOH and LiOD in several vibrational states.
LiOH
( v 1 , v l2
, v 3)
共000兲
共100兲
(020 0)
(011 0)
(031 0)
LiOD
␮ a 共Experimental兲
␮ a 共Theoretical兲
eQq Li
␮ a 共Experimental兲
␮ a 共Theoretical兲
4.755共2兲
4.851共2兲
5.031共2兲
4.898共5兲
5.133共5兲
4.755
4.849
5.039
4.906
5.158
295.8共15兲
299.7共31兲
346.9共21兲
4.711共2兲
4.80共1兲
4.89共1兲
4.813共5兲
5.002共5兲
4.715
4.809
4.934
4.827
5.033
Downloaded 25 Mar 2005 to 128.196.209.95. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
11726
Higgins et al.
J. Chem. Phys., Vol. 121, No. 23, 15 December 2004
FIG. 10. Total dipole moment as a function of 共a兲 ¯␳ , the deviation from
linearity for the Li–O–H bond, 共b兲 the Li–O bond length, and 共c兲 the O–H
bond length. From the MP2 dipole moment surface, each with the remaining
two geometric parameters held fixed at their equilibrium values.
states. The calculated vibrational fundamental transition frequencies for LiOH and LiOD are v 1 ⫽923.2 and 912.9, v 2
⫽318.3 and 245.8,29 and v 3 ⫽3829.8 and 2824.2 cm⫺1. As
far as we know there are no direct gas phase measurements
of these vibrational frequencies and therefore no comparison
with experiment is possible, although a matrix IR study reported v 1 ⫽870.5, v 2 ⫽256.5 cm⫺1 for LiOH and v 1
⫽862.0 cm⫺1 for LiOD.30 Agreement between this work and
the work of Bunker et al.11 is excellent for LiOH for the two
stretching modes, which they predict to be 923 and 3832
cm⫺1, but poor for the bending mode which they predict to
be 289 cm⫺1. DVR3D calculations using the PES of Ref. 11
yield fundamental frequencies of v 1 ⫽921.0, v 2 ⫽293.0,29
and v 3 ⫽3809.5 cm⫺1 for LiOH, which is slightly worse
agreement for the two stretching modes. Given the much
better agreement overall with experiment for this later work,
it is likely the true bending frequency is closer to 318.3 than
to 289 cm⫺1. The angular floppiness of the molecule is illustrated by the calculated average deviation from linearity for
the Li–O–H angle ¯␳ , which is 19° in the ground state and
increases to 42° in the (033 0) state for LiOH, and by the
dispersion in this angle, which is 10° for both states. These
values approach those of two weakly bound helium complexes, HeClF and HeOCS, investigated previously by two
of the current authors.31,32
Also of interest in Table XI are the differences in the
energetics and structures for different l values of the same
v 2 . 29 For v 2 ⫽2 the ⌺-⌬ splitting is 32.6 cm⫺1 for LiOH and
15.9 cm⫺1 for LiOD, with the ⌺ state lower in both cases.
The bond lengths are essentially equal but ¯␳ is larger by 2.4°
for LiOH and 2.0° for LiOD in the ⌬ state. Similar results
are seen for v 2 ⫽3, where the ⌸ state is 60.3 cm⫺1 lower for
LiOH and 29.6 cm⫺1 lower for LiOD than the ⌽ state and ¯␳
is 2.6° and 2.0° larger for the ⌽ state for LiOH and LiOD,
respectively.
TABLE XI. Calculated energies, fundamental vibrational frequencies 共in cm⫺1兲, and structural expectation
values 共in Å and deg兲 for LiOH and LiOD.
LiOH
LiOD
( v 1 , v l2 , v 3 )
E
⌬E
v 0a
具 r(LiO) 典
具 r(OH) 典
具¯␳ 典
共000兲
(011 0)
(020 0)
(022 0)
(031 0)
共100兲
(033 0)
共001兲
⫺712 40.2
⫺709 20.8
⫺706 29.3
⫺705 94.3
⫺703 19.7
⫺703 17.0
⫺702 57.1
⫺674 10.4
0.0
319.5
611.0
645.9
920.5
923.2
983.1
3829.8
318.3
611.0
643.6
919.3
923.2
979.6
3829.8
1.6001
1.6101
1.6189
1.6194
1.6265
1.6184
1.6277
1.6007
0.9653
0.9671
0.9689
0.9690
0.9707
0.9656
0.9710
0.9974
19.0
28.8
33.6
36.0
39.3
19.5
41.9
19.4
共000兲
(011 0)
(020 0)
(022 0)
(031 0)
(033 0)
共100兲
共001兲
⫺718 48.8
⫺716 01.9
⫺713 71.4
⫺713 53.5
⫺711 33.4
⫺711 01.8
⫺709 35.9
⫺690 24.6
0.0
246.9
477.4
495.4
715.4
747.1
912.9
2824.2
245.9
477.4
493.3
714.3
744.0
912.9
2824.2
1.5977
1.6057
1.6130
1.6133
1.6197
1.6204
1.6160
1.5982
0.9606
0.9619
0.9632
0.9632
0.9645
0.9647
0.9608
0.9833
16.6
25.1
29.5
31.5
34.8
36.8
17.1
16.9
a
See Ref. 29.
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J. Chem. Phys., Vol. 121, No. 23, 15 December 2004
Rotational spectrum of LiOH
11727
TABLE XII. Estimated bond lengths 共in Å兲 of M OH species.k
r 0a
LiOH
NaOH
KOH
RbOH
CsOH
MgOH
r̃ e b
r ec
M–O
O–H
M–O
O–H
M–O
O–H
1.594
1.95d
2.212f
2.316g
2.403i
1.780j
0.921
1.584
0.953
0.912f
0.913g
0.920i
0.871j
2.200f
2.305g
2.395i
1.767j
0.968f
0.965g
0.969i
0.940j
1.5776共4兲
1.9435e
2.196共2兲f
2.301共2兲h
2.391共2兲h
0.949共2兲
0.9543e
0.960共10兲f
0.957共10兲h
0.960共10兲h
a
Determined from the rotational constants of the ground vibrational mode.
Calculated from B̃ e derived from Eq. 共1兲.
c
LiOH values calculated from experimental ‘‘mixed data’’ B e listed in Table IX.
d
Reference 34.
e
Ab initio values from Ref. 43.
f
Reference 35.
g
Reference 36.
h
Reference 41.
i
Reference 37.
j
Reference 17.
k
Uncertainties for LiOH as discussed in text, others listed when provided in reference.
b
IV. DISCUSSION
One particular interesting finding is that LiOH exhibits a
positive rotation-vibration interaction constant ␣ 2 for the respective bending modes, and the value for LiOD is negative;
a negative value is expected for linear polyatomic species.33
The usual negative value, however, does not seem to be typical of the M OH species. A positive ␣ 2 is consistent with the
alkali hydroxide species NaOH,34 KOH,35 RbOH,36 and
CsOH,37 the alkaline earth hydroxide radicals MgOH,17
CaOH,38 SrOH,38 and BaOH,38 as well as AlOH.39 Each of
these species undergoes a significant isotope shift when the
hydrogen is replaced by a deuterium. In every case the value
of ␣ 2 decreases, but only in the cases of CaOD,40 MgOD,17
AlOD,39 and LiOD does the value become negative as expected. Lide and Matsumura41 have attributed this large isotopic shift to an anharmonic contribution in the vibrationrotation interaction term ␣ 2 , which dominates for the light
M OH species. This is primarily attributed to the low mass of
the hydrogen atom and the relatively weak M – O bond. Additionally, there seems to be a trend moving up the periodic
table on the magnitude of the isotope shift. Comparing the
values in Table IV for LiOH/D with those previously reported for KOH/D, RbOH/D, and CsOH/D the isotope shifts
are ⫺191, ⫺34, ⫺22, and ⫺16 MHz, respectively, while for
MgOH/D and CaOH/D they are ⫺114 and ⫺32 MHz, respectively. In each case the value decreases with increasing
mass number on the metal atom. For the LiOH/D system the
experimental values of ␣ 2 are well reproduced theoretically,
as may be seen in Table IV.
Determination of the structure of LiOH is complicated
by the large amplitude bending motion exhibited in all vibrational states and by the differences in bending amplitude between LiOH and LiOD for the same vibrational state. Several different methods have been used to determine the
vibrationally averaged and equilibrium bond distances using
purely experimental and mixed experimental and theoretical
data. Both r 0 and r̃ e bond distances for LiOH/D have been
calculated using purely experimental data and are listed in
Table XII along with those for other M OH species for comparison. The r 0 bond lengths are calculated by using the
B (000) rotational constants, while the B̃ e values from Table
IV are used for the determination r̃ e . The r 0 calculation does
not account for zero-point vibrational motion; therefore the
values represent the average projection of the vibrating molecule onto the inertial axis. The r̃ e values account for some
of the zero-point vibrational motion. As the table illustrates,
there is a significant difference between these values for all
the M OH species listed. In the case of MgOH, the O–H r 0
bond length is 0.069 Å shorter than the r̃ e value 共0.940 Å兲.
This difference likely arises because MgOH is quasilinear,
and the shortened r 0 bond distance is thought to be a dynamic effect caused by a quartic potential with a low barrier
across the C ⬁v axis.17,42 For LiOH, the minimum on the potential energy surface corresponds to a linear configuration,
but owing to a nearly flat potential to 90°, LiOH exhibits
large amplitude oscillations that are consistent with its O–H
r 0 bond length being much shorter than its O–H r̃ e bond
length.
To determine an equilibrium structure for LiOH that is
not artificially contaminated by vibrational effects, data from
experiments and calculations have been combined and the
resulting r e values are listed in Table XII. These r e values
were calculated using the experimental B e values for LiOH
and LiOD from Table IX. As an internal check of consistency, r e values were calculated from the purely theoretical
B e values and then compared to the known r e values from
the PES. The resulting r e values are in excellent agreement,
with the B e -derived Li–O and O–H r e values 0.0003 and
0.0002 Å shorter, respectively, than the PES’s r e values.
Given this, the largest uncertainty in the equilibrium structure results from the use of the theoretical vibration-rotation
constants in the determination of the experimental B e values.
The estimated uncertainties listed in Table XII were determined by doubling the largest difference between experimental and theoretical ␣’s or ␥’s and varying the theoretical constants used by plus or minus this amount. The resulting
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11728
J. Chem. Phys., Vol. 121, No. 23, 15 December 2004
largest changes in r e values were used to determine the uncertainties listed.
The r e values determined from the mixed experimentaltheoretical analysis agree well with the PES values and with
several recent high-level ab initio calculations,9,10,13,14 as
well as with the original estimates by Freund,3 but disagree
with those published previously by McNaughton et al.4 In
particular, their O–H equilibrium bond length is 0.9691共21兲
Å and their Li–O equilibrium bond length is 1.5816共10兲 Å;
these are 0.02 and 0.004 Å longer, respectively, than those
determined in the current study. The Li–O discrepancy is not
major, but the O–H discrepancy is, particularly in light of
discussions on the nature of bonding in LiOH and the nature
of the OH fragment within LiOH. In addition, several recent
computational papers on LiOH have used the McNaughton
r e values as an experimental comparison for the calculated
LiOH structure, and in each case the calculated values have
been ⬃0.02 Å shorter than the McNaughton values.9,10,13,14
Although the McNaughton values are taken as experimental
values, it should be remembered that they were derived using
a semirigid bender model fit to the experimental data and
while adjustments were made to account for the different
vibrationally averaged O–H distance upon deuteration, no
adjustment was made for the different bending amplitude.
This may lead to significant error in the O–H equilibrium
bond length determined by this method. Also listed in Table
XII are r e values for other alkali hydroxide species determined from experiment for KOH,35 RbOH,41 and CsOH,41
and from ab initio calculations for NaOH.43 In each case the
O–H r e values are 0.02–0.03 Å shorter than the values determined using the semirigid bender method.44 Given this,
and the excellent agreement between theory and experiment
in the current study, we conclude the O–H equilibrium bond
distance in LiOH is 0.949共2兲 Å.
As mentioned in the Introduction, LiOH is the molecule
that lies between bent H2 O and linear Li2 O, and therefore it
is instructive to compare these three molecules in terms of
structure and bonding. Breckenridge and co-workers have
performed extensive spectroscopic studies45– 47 of Li2 O and
have found it to be a ‘‘very ‘floppy’ ionic molecule.’’46 Using
dispersed fluorescence and stimulated emission pumping47
they have determined its Li–O r 0 bond length to be 1.611共3兲
Å, 0.017 Å longer than the r 0 bond length determined here
for LiOH. They did not experimentally determine an r e bond
length, but Koput and Peterson48 calculated an r e for Li2 O at
the CCSD共T,Full兲/cc-pCVQZ level of 1.6159 Å, 0.040 Å
longer than the r e calculated for LiOH at the same level in
this study 共see Table V兲. This apparent discrepancy between
differences in r 0 and r e values is most likely due to dynamic
effects; r 0 is a measure of the Li–O bond’s projection onto
the inertial axis, and in the case of LiOH the inertial axis
closely follows the Li–O bond whereas for Li2 O the Li–O
bond would make a substantial angle with the inertial axis as
it undergoes large amplitude bending vibrational motion. The
O–H r e distance in H2 O is 0.958 Å,49 0.009 Å longer than
the r e determined here for LiOH. In fact, the O–H r e of
0.949 Å in LiOH is substantially shorter than either the hydroxyl radical, r e ⫽0.970 Å, 50 or the hydroxide anion, r e
⫽0.964 Å. 51 The O–H stretching frequency is blueshifted
Higgins et al.
FIG. 11. Minimum energy path as a function of 1/r(Li–H). Note the x axis
uses an inverse scale. Dashed line is a linear fit with slope⫽27 205 Å cm⫺1.
considerably from these as well, with the calculated fundamental frequency for LiOH equal to 3829.8 cm⫺1, while it is
measured to be 3755.8 cm⫺1 for the v 3 mode of H2 O, 52
3569.6 cm⫺1 for the hydroxyl radical,53 and 3555.6 cm⫺1 for
the hydroxide anion.51 These differences between the OH in
LiOH and the hydroxyl radical or the hydroxide anion challenge the simple view of LiOH as either an undistorted ionic
molecule comprising Li⫹ (OH) ⫺ , or of Li interacting with
some combination of OH between OH radical and OH⫺ .
Further evidence against the simple ionic view is the fact that
Hartree-Fock level calculations, which should do well for
electrostatic interactions, recover only 64% of the CCSD共T兲
binding energy.
In terms of angular rigidity, the valence field bending
force constant k ␦ /l 1 l 2 derived using the theoretical bending
vibrational frequency and theoretical 共000兲 structure for
LiOH is 2.98 N/m, and for Li2 O and H2 O k ␦ /l 2 is equal to
1.37 共Ref. 47兲 and 70.3 共Ref. 54兲 N/m, respectively. Comparing to other XY Z linear triatomic molecules, k ␦ /l 1 l 2 is
equal to 20 and 37 N/m for HCN and OCS, respectively.54
Clearly, LiOH is much closer in nature to Li2 O than H2 O and
is considerably more floppy than typical linear triatomic
molecules.
Excellent agreement is shown with the results of
rotation-vibration calculations using a three-dimensional ab
initio PES for vibrations involving up to three quanta in the
bending mode. Moreover, the charge distribution as seen by
the electric dipole moment is also in excellent agreement. We
may thus examine the origin of the potential. Perhaps the
simplest explanation of the linearity of LiOH is that of elementary electrostatic repulsion of Li⫹ and H⫹ . Figure 11
shows the calculated potential along the angular minimum
energy path as a function of 1/r(Li–H). It is noteworthy that
indeed the bending potential is a linear function of
1/r(Li–H) up to a bond angle of at least 90°. If the bending
potential is due to electrostatic repulsion between the partial
Li and H charges, the slope of this line would give the product of the partial charges. The value obtained by fitting the
slope is 0.23e 2 , which falls somewhere between the product
of partial charges calculated using either Mulliken or Natural
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J. Chem. Phys., Vol. 121, No. 23, 15 December 2004
population analysis at the MP2/acvqz level. For r(LiO)
greater than 1.72 Å and r(OH) greater than 1.30 Å, the configuration of minimum energy is no longer linear. This indicates that the view of the bending potential as due to the
electrostatic repulsion between Li and H is too simple. This
is perhaps the point at which the electrostatic repulsion no
longer dominates the orbital effects. Unfortunately, current
experiments do not sample the bond lengths at which this
structural change takes place, which is calculated to occur at
v 1 ⫽7, more than 6100 cm⫺1 above the ground state, or at
v 3 ⫽10, more than 31 000 cm⫺1 above the ground state.
V. CONCLUSION
In summary, there is excellent agreement between the
predictions of the proposed unadjusted potential energy surface from a high-level electronic structure calculation and the
observed rotational transitions of a number of bending vibrational levels of LiOH and LiOD. We have predicted vibrational transition frequencies which further will test the reliability of the potential energy surface. In particular, the
fundamental v 3 transition of LiOH is predicted to be almost
100 cm⫺1 above the v 3 transition of H2 O. This prediction is
essentially untested by the present experimental data. The
soft bending mode v 2 is predicted to be a factor of 5 below
that of H2 O. In simplest view the linearity and soft angular
rigidity of LiOH is fit by the model of Coulombic repulsion
between Li and H.
ACKNOWLEDGMENTS
The authors wish to thank Dr. Phil Bunker for valuable
comments and for supplying code for the calculation of the
PES in Ref. 11. This research is supported by the National
Science Foundation under NSF Grant Nos. CHE-98-17707
and CHE-01-38521.
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