The rotational spectrum and dynamical structure of

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

Downloaded 25 Mar 2005 to 128.196.209.95. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

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-

Downloaded 25 Mar 2005 to 128.196.209.95. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

J. Chem. Phys., Vol. 121, No. 23, 15 December 2004

Rotational spectrum of LiOH

˜ 1 ⌺ ⫹ ). TABLE I. Observed transition frequencies 共in MHz兲 for LiOH (X ( 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

˜ 1 ⌺ ⫹ ). TABLE II. Observed transition frequencies 共in MHz兲 for LiOD (X ( 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.

Downloaded 25 Mar 2005 to 128.196.209.95. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

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: ˜ ⫺ ␣ 共 v ⫹1 兲 ⫹ ␥ 共 v ⫹1 兲 2 ⫹ ␥ l 2 , B 共 0,v 2 ,0兲 ⫽B e 2 2 22 2 ll

共1兲

where B (0,v 2 ,0) is the rotational constant per v 2 state, ˜B 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.

Downloaded 25 Mar 2005 to 128.196.209.95. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

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 ˜B a e ␣2 ␥ 22 ␥ ll a˜

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

B e ⫽B e ⫺ 2 ( ␣ 1 ⫹ ␣ 3 ).

Downloaded 25 Mar 2005 to 128.196.209.95. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

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

Downloaded 25 Mar 2005 to 128.196.209.95. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

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-

Downloaded 25 Mar 2005 to 128.196.209.95. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

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

Downloaded 25 Mar 2005 to 128.196.209.95. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

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

Downloaded 25 Mar 2005 to 128.196.209.95. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

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

Downloaded 25 Mar 2005 to 128.196.209.95. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

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.

Downloaded 25 Mar 2005 to 128.196.209.95. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

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

˜r 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. ˜ derived from Eq. 共1兲. Calculated from B e 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 ˜r 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 ˜B e values from Table IV are used for the determination ˜r 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 ˜r 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 ˜r 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 ˜r 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

Downloaded 25 Mar 2005 to 128.196.209.95. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

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

Downloaded 25 Mar 2005 to 128.196.209.95. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

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. 1

See, for example G. L. Miessler and D. A. Tarr, Inorganic Chemistry, 3rd ed. 共Pearson Prentice Hall, Upper Saddle River, NJ, 2004兲, Chap. 3. 2 A. Bu¨chler, J. L. Stauffer, W. Klemperer, and L. Wharton, J. Chem. Phys. 39, 2299 共1963兲. 3 S. M. Freund, Ph.D. thesis, Harvard University, Cambridge, MA, 1970. 4 D. McNaughton, L. M. Tack, B. Kleibo¨mer, and P. D. Godfrey, Struct. Chem. 5, 313 共1994兲. 5 ˇ a´rsky, and R. Zahradnı´k, Chem. Phys. 25, 19 共1977兲. H. Lischka, P. C 6 D. J. DeFrees, B. A. Levi, S. K. Pollack, W. J. Hehre, J. S. Binkley, and J. A. Pople, J. Am. Chem. Soc. 101, 4085 共1979兲. 7 J. S. Binkley, J. A. Pople, and W. J. Hehre, J. Am. Chem. Soc. 102, 939 共1980兲. 8 C. W. Bauschlicher, Jr. and S. R. Langhoff, J. Chem. Phys. 84, 901 共1986兲. 9 E. P. F. Lee and T. G. Wright, Chem. Phys. Lett. 352, 385 共2002兲. 10 M. B. Sullivan, M. A. Iron, P. C. Redfern, J. M. L. Martin, L. A. Curtiss, and L. Radom, J. Phys. Chem. A 107, 5617 共2003兲. 11 P. R. Bunker, P. Jensen, A. Karpfen, and H. Lischka, J. Mol. Spectrosc. 135, 89 共1989兲. 12 L. V. Gurvich, G. A. Bergman, L. N. Gorokhov, V. S. Iorish, V. Y. Leonidov, and V. S. Yungman, J. Phys. Chem. Ref. Data 25, 1211 共1996兲. 13 A. Schulz, B. J. Smith, and L. Radom, J. Phys. Chem. A 103, 7522 共1999兲. 14 P. Burk, K. Sillar, and I. A. Koppel, J. Mol. Struct.: THEOCHEM 543, 223 共2001兲. 15 J. Tennyson, J. R. Henderson, and N. G. Fulton, Comput. Phys. Commun. 86, 175 共1995兲; J. Tennyson, M. A. Kostin, P. Barletta, G. J. Harris, O. L. Polyansky, J. Ramanlal, and N. F. Zobov, Comput. Phys. Commun. 163, 85 共2004兲. 16 L. M. Ziurys, W. L. Barclay, Jr., M. A. Anderson, D. A. Fletcher, and J. W. Lamb, Rev. Sci. Instrum. 65, 1517 共1994兲.

Rotational spectrum of LiOH

11729

17

A. J. Apponi, M. A. Anderson, and L. M. Ziurys, J. Chem. Phys. 111, 10919 共1999兲. 18 MOLPRO is a package of ab initio programs written by H.-J. Werner and P. J. Knowles, with contributions from R. D. Amos, A. Bernhardsson, A. Berning et al. 19 C. Hampel, K. Peterson, and H.-J. Werner, Chem. Phys. Lett. 190, 1 共1992兲. 20 cc-pCVnZ and aug-cc-pCVnZ basis sets were obtained from the Extensible Computational Chemistry Environment Basis Set Database, Version 10/21/03, as developed and distributed by the Molecular Science Computing Facility, Environmental and Molecular Sciences Laboratory which is part of the Pacific Northwest Laboratory, P.O. Box 999, Richland, Washington 99352, USA, and funded by the U.S. Department of Energy. The Pacific Northwest Laboratory is a multiprogram laboratory operated by Battelle Memorial Institute for the U.S. Department of Energy under Contract No. DE-AC06-76RLO 1830. Contact David Feller or Karen Schuchardt for further information. 21 T. H. Dunning, Jr., J. Chem. Phys. 90, 1007 共1989兲. 22 D. E. Woon and T. H. Dunning, Jr., J. Chem. Phys. 103, 4572 共1995兲. 23 S. F. Boys and F. Bernardi, Mol. Phys. 19, 553 共1970兲. 24 See EPAPS Document No. E-JCPSA6-121-011446 for complete lists of ab initio energies and dipole moments and a Fortran subroutine to calculate the potential. A direct link to this document may be found in the online article’s HTML reference section. The document may also be reached via the EPAPS homepage 共http://www.aip.org/pubservs/ epaps.html兲 or from ftp.aip.org in the directory /epaps/. See the EPAPS homepage for more information. 25 Modified from W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing 共Cambridge University Press, New York, 1986兲, Chap. 3. 26 Certain unphysical geometries, such as O–Li–H, are included in the spline input for completeness and required special attention in fitting and generating extra points. 27 The use of ¯␳ to denote the deviation from linearity is from J. T. Hougen, P. R. Bunker, and J. W. C. Johns, J. Mol. Spectrosc. 34, 136 共1970兲 and is used in Ref. 11. 28 The J⫽1←0 lines for the 共001兲 and 共101兲 states of LiOH were measured in a molecular beam from an effusive source at 1400 K 共Ref. 3兲. A thermal distribution gives a population of 2.0% and 0.8% relative to the 共000兲 state for the 共001兲 and 共101兲 states, respectively, and it is unlikely that these states were observed under the reported experimental conditions. In addition, there are approximately 14 states that lie energetically between the reported (120 0) and 共001兲 states, although an alternate assignment of the observed transitions cannot be determined. 29 Fundamental vibrational frequencies and energy splittings for v 2 ⫽0 states are calculated by subtracting the rotational energy, hcB v 关 J(J⫹1)⫺l 2 兴 from the energy for the lowest J level of the state, in contrast to Ref. 11 wherein they use the hypothetical J⫽0 level of these states. 30 L. Manceron, A. Loutellier, and J. P. Perchard, Chem. Phys. 92, 75 共1985兲. 31 K. Higgins, F.-M. Tao, and W. Klemperer, J. Chem. Phys. 109, 3048 共1998兲. 32 K. Higgins and W. Klemperer, J. Chem. Phys. 110, 1383 共1999兲. 33 C. H. Townes and A. L. Schawlow, Microwave Spectroscopy 共Dover, New York, 1975兲. 34 P. Kuijpers, T. To¨rring, and A. Dymanus, Chem. Phys. 15, 457 共1976兲. 35 E. F. Pearson, B. P. Winnewisser, and M. B. Trueblood, Z. Naturforsch. A 31A, 1259 共1976兲. 36 C. Matsumura and D. R. Lide, Jr., J. Chem. Phys. 50, 71 共1969兲. 37 D. R. Lide, Jr. and R. L. Kuczkowski, J. Chem. Phys. 46, 4768 共1967兲. 38 D. A. Fletcher, M. A. Anderson, W. L. Barclay, and L. M. Ziurys, J. Chem. Phys. 102, 4334 共1995兲. 39 A. J. Apponi, W. L. Barclay, Jr., and L. M. Ziurys, Astrophys. J. Lett. 414, L129 共1993兲. 40 B. P. Nuccio, A. J. Apponi, and L. M. Ziurys, J. Chem. Phys. 103, 9193 共1995兲. 41 D. R. Lide and C. Matsumura, J. Chem. Phys. 50, 3080 共1969兲. 42 P. R. Bunker, M. Kolbuszewski, P. Jensen et al., Chem. Phys. Lett. 239, 217 共1995兲. 43 E. P. F. Lee and T. G. Wright, J. Phys. Chem. A 106, 8903 共2002兲. 44 R. D. Brown, P. D. Godfrey, B. Kleibo¨mer, and D. McNaughton, J. Mol. Struct. 327, 99 共1994兲. 45 D. Bellert and W. H. Breckenridge, J. Chem. Phys. 114, 2871 共2001兲; D. Bellert, D. K. Winn, and W. H. Breckenridge, Chem. Phys. Lett. 337, 103 共2001兲; 355, 151 共2002兲; J. Chem. Phys. 119, 10169 共2003兲.

Downloaded 25 Mar 2005 to 128.196.209.95. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

11730 46

Higgins et al.

J. Chem. Phys., Vol. 121, No. 23, 15 December 2004

D. Bellert, D. K. Winn, and W. H. Breckenridge, Chem. Phys. Lett. 348, 39 共2001兲. 47 D. Bellert, D. K. Winn, and W. H. Breckenridge, J. Chem. Phys. 117, 3139 共2002兲. 48 J. Koput and K. A. Peterson, J. Chem. Phys. 116, 9255 共2002兲. 49 P. Jensen, S. A. Tashkun, and V. L. G. Tyuterev, J. Mol. Spectrosc. 168, 271 共1994兲. 50 K. P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure, Constants of Diatomic Molecules 共Van Nostrand Reinhold, New York, 1979兲.

51

N. H. Rosenbaum, J. C. Owrutsky, L. M. Tack, and R. J. Saykally, J. Chem. Phys. 84, 5308 共1986兲. 52 G. Herzberg, Molecular Spectra and Molecular Structure, Electronic Spectra and Electronic Structure of Polyatomic Molecules 共Van Nostrand, Princeton, NJ, 1966兲. 53 T. Amano, J. Mol. Spectrosc. 103, 436 共1984兲. 54 G. Herzberg, Molecular Spectra and Molecular Structure, Infrared and Raman Spectra of Polyatomic Molecules 共Van Nostrand Reinhold, New York, 1945兲.

Downloaded 25 Mar 2005 to 128.196.209.95. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp