Water dimer hydrogen bond stretch, donor ... - cchem.berkeley.edu
JOURNAL OF CHEMICAL PHYSICS
VOLUME 119, NUMBER 17
1 NOVEMBER 2003
Water dimer hydrogen bond stretch, donor torsion overtone, and ‘‘in-plane bend’’ vibrations Frank N. Keutsch Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138
Linda B. Braly Intel Corporation Technology and Manufacturing Group, Rio Rancho, New Mexico 87124
Mac G. Brown Los Alamos National Laboratory, Los Alamos, New Mexico 87545
Heather A. Harker and Poul B. Petersen Department of Chemistry, University of California, Berkeley, California 94720
Claude Leforestier Laboratoire de Structure et Dynamique des Syste`mes Mole´culaire et Solides (UMR 5636), CC014, Universite´ des Sciences et Techniques du Langue-doc, 34095 Montpellier Ce´dex 05, France
Richard J. Saykallya) Department of Chemistry, University of California, Berkeley, California 94720
共Received 11 June 2003; accepted 8 August 2003兲 We report the measurement and analysis of 64 new K a ⫽0←0,1 and K a ⫽1←0,1 transitions of (H2 O) 2 and 16 new K a ⫽0←0 transitions of (D2 O) 2 by terahertz laser vibration–rotation– tunneling spectroscopy of a planar supersonic expansion between 140.5 and 145.5 cm⫺1. The transitions in both isotopomers correspond to A ⬘ vibrations assigned to the hydrogen bond stretch 共translational兲 and donor torsion overtone vibrations. The interchange splitting is 56.3 GHz in K a ⫽0 of the excited state of (H2 O) 2 , nearly 3 times the value of the ground state, and the bifurcation tunneling splitting is 1.8 GHz, over 2 times the value of the ground state. We compare the existing experimental spectra with calculations on state-of-the-art intermolecular potential energy surfaces and critically review the vibrational assignments reported in the literature. We show that the discrepancy between theory and experiment regarding the assignment of the feature near 103 cm⫺1 can be resolved by considering E 2 →E 1 transitions, which had not been considered previously. © 2003 American Institute of Physics. 关DOI: 10.1063/1.1614774兴
I. INTRODUCTION
determination of a rigorously accurate water dimer potential is the most important step towards the construction of an accurate ‘‘universal’’ force field model for liquid water. Toward this end, a large collection of intermolecular vibration– rotation–tunneling 共VRT兲 spectra of the dimer have been acquired, sampling both ‘‘high-lying’’ 共⬎20 cm⫺1兲 rotational and ‘‘low-lying’’ 共⬍1000 cm⫺1兲 intermolecular vibrational states, which are of central importance for testing of intermolecular potential energy surfaces 共IPSs兲. Concurrently, much progress has been made in the actual development of such intermolecular potentials. In particular, three potentials of spectroscopic accuracy have now been determined from the combination of ab initio and spectroscopic data, VRT共ASP-W兲III,7 SAPT-5st,8 and MCY-5f.5 A detailed comparison of calculated VRT energy states with new experimental results provides a further test of these new IPSs. Furthermore, there has been some confusion regarding assignments of certain intermolecular vibrations; in particular, the feature near 103 cm⫺1 assigned to the K a ⫽0 levels of the in-plane-bend 共IPB兲 vibration by Braly et al.9 has represented a troubling discrepancy between theory and experiment.
Water clusters have been objects of intense scrutiny by both modern theory and experiment, serving as paradigms for systematically untangling intricate details of the hydrogen bond network that underlies the remarkable properties of liquid and solid water.1,2 The systematic investigation of pure water clusters by the combination of laser spectroscopy and theory has characterized the most stable arrangements of two through six water molecules in detail and those of larger clusters more qualitatively.1 The principal goal in these studies of small water clusters has been to develop an exact description of the intricate details of the hydrogen bond network and its dynamics. This objective is close to realization in the case of the dimer, wherein complete descriptions of both the intermolecular and intramolecular dynamics have been incorporated into a theoretical formalism which was subsequently used to fit the spectroscopic data3–5 in terms of highly detailed potential energy surfaces. Two-body forces account for ⬃75% of the total interaction energy of water clusters larger than the dimer6 and liquid; accordingly, the a兲
Author to whom correspondence should be addressed.
0021-9606/2003/119(17)/8927/11/$20.00
8927
© 2003 American Institute of Physics
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
8928
Keutsch et al.
J. Chem. Phys., Vol. 119, No. 17, 1 November 2003
FIG. 1. Equilibrium structure of the water dimer as determined from the VRT共ASP-W兲III surface. The calculation used fixed monomers with ⬔HOH⫽104.52° and R OH⫽0.9572 Å. The structure has C S symmetry and the calculated interoxygen distance is R OO⫽2.978 Å 共Ref. 20兲. One water molecule acts as a single hydrogen bond donor and the other as a single hydrogen bond acceptor. The distinctly nonrigid structure undergoes a number of large-amplitude vibrations and tunneling motions that exchange the protons of the acceptor 共AS兲, donor 共BT兲, or interchange the roles of the acceptor and donor molecules 共I兲.
II. BACKGROUND: SPECTROSCOPY OF THE WATER DIMER
The water dimer is a highly nonrigid near-prolate top 共Fig. 1兲, and high-resolution spectra of the dimer reveal splittings of each rotation–vibration transition that result from large-amplitude tunneling motions 共Fig. 2兲,9–15 which connect eight degenerate minima on the six-dimensional IPS via three low-barrier tunneling motions. A correlation diagram for the VRT levels of the water dimer and transitions reported here is shown in Fig. 3.9,10,13,15 These tunneling motions, which manifest themselves in spectral splittings and shifts, reflect the overall topography of the IPS and not just the minima in which the vibrational wave functions are primarily localized. Thus they provide a very sensitive test of a given potential energy surface.
FIG. 3. Ground-state energy level diagram of (H2 O) 2 is shown together with the observed transitions. The dashed arrows represent c-type transitions 共or possibly b-type in the case of the E 1 states兲 and the solid arrows a-type transitions. The solid arrowheads represent unambiguous assignments and the open arrowheads correspond to the 4295-GHz band, which has two possible assignments. Note the close vicinity of the ground-state K a ⫽0 and K a ⫽1 levels of the 2s. This is also the case for the lowest tunneling level of the 2s in the excited state.
A. Tunneling dynamics
1. Acceptor switching
Acceptor switching 共AS兲 consists of a tunneling motion that exchanges the hydrogens in the acceptor molecule. This motion does not break the hydrogen bond and has the lowest barrier of all tunneling pathways, estimated at 154 cm⫺1 by Goldman et al.7 on the VRT共ASP-W兲III surface and 222 cm⫺1 by Groenenboom et al.4 on the SAPT-5st surface. This motion splits each (H2 O) 2 /(D2 O) 2 rovibrational level by ca. 140–280 GHz/18 –53 GHz into two levels labeled A 1 /B 1 , and A 2 /B 2 共Fig. 2兲. 2. Interchange
FIG. 2. Correlation diagram for the rotation–tunneling states of (H2 O) 2 are shown for K a ⫽0. The magnitudes of the tunneling splittings are not to scale. Acceptor switching tunneling, AS, splits each rovibrational level by ca. 280 GHz into two levels labeled A 1 /B 1 and A 2 /B 2 . This tunneling splitting has not been directly determined from experimental observations. Interchange tunneling I splits each of these levels into 4, the E states being degenerate. Bifurcation tunneling, BT, shifts the energy levels and is ca.⫻100 larger than for (D2 O) 2 . The difference between the band origin of the 1s, (1s), and the band origin commonly used in the literature ¯ (1s) is indicated. The latter band origin has been used, as the E states usually have not been calculated.
Tunneling along this pathway interchanges the role of the donor and acceptor monomers and is the second most facile tunneling motion, with a barrier estimated at 229 cm⫺1 on VRT共ASP-W兲III 共Ref. 7兲 and 248 cm⫺1 on SAPT-5st 共Ref. 4兲. For J⫽0, K a ⫽0, this motion splits each of the A 1 /B 1 and A 2 /B 2 levels of (H2 O) 2 /(D2 O) 2 by ca. 11–23 GHz/0.5–1.2 GHz into three states labeled A 1 /E 1 /B 1 共henceforth referred to as 1s) and A 2 /E 2 /B 2 共henceforth referred to as 2s) 共Fig. 2兲. It should be pointed out that from a group theoretical point of view there is no distinction between E 1 and E 2 levels, and these act merely as labels. Participation of tunneling along both a geared 共G兲 and antigeared 共AG兲 interchange 共I兲 tunneling pathway was suggested by Coudert and Hougen.16 This could account for the observed difference between the interchange splittings of the A 1 /B 1 and A 2 /B 2 levels. However, the importance of the antigeared tunneling pathway is unclear as it was not found on the VRT共ASP-W兲 surface, even though the difference in the A 1 /B 1 and A 2 /B 2 interchange splittings are reproduced.3
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
J. Chem. Phys., Vol. 119, No. 17, 1 November 2003
3. Bifurcation
Bifurcation tunneling 共BT兲 involves the exchange of the hydrogens/deuteriums of the donor molecule and corresponds to the pathway with the highest barrier and smallest effect on the spectrum. The barrier has been calculated to be 430 cm⫺1 on the VRT共ASP-W兲III 共Ref. 7兲 and 685 cm⫺1 on SAPT-5st 共Ref. 4兲. The result of this tunneling motion 共see Fig. 2兲 is a shift of each energy level by ca. 690–750 MHz/ 6 –7 MHz in the ground state of (H2 O) 2 /(D2 O) 2 , and for the latter the shifts are beyond the precision of current calculations. B. Coriolis interactions
In the vibrational ground state of (H2 O) 2 , the 2s of K a ⫽1 are very close in energy to the 2s of K a ⫽0. As K a is not a good quantum number, states with the same overall symmetry are allowed to mix if they have the same J rotational quantum number. A model was proposed which couples the vibrational angular momentum with the overall rotation of the complex.9 This Coriolis perturbation results in characteristic shifts of all the transitions involving the 2s of K a ⫽0 of (H2 O) 2 and half of the asymmetry doublets of the 2s of K a ⫽1. Although the spectra are complicated by the Coriolis interaction, the characteristic appearance of the perturbation can aid in the identification and assignment of (H2 O) 2 spectra. C. Group theory considerations
The group theoretical treatment and selection rules of the tunneling water dimer have been described in detail and the ⫺ ⫹ ⫺ ⫹ ⫺ allowed transitions are A ⫹ 1 ↔A 1 , A 2 ↔A 2 , B 1 ↔B 1 , ⫹ ⫺ ⫹ ⫺ 10–16 From the selection rules, it B 2 ↔B 2 , and E ↔E . follows that tunneling results in a splitting of each rovibrational transition into six components, which typically appear as two sets (1s and 2s) of three more closely spaced transitions 共e.g., A 1 /E 1 /B 1 ). The relative intensities are determined by the nuclear spin weights, which for ⫺ ⫹ ⫺ ⫹ ⫺ (D2 O) 2 /(H2 O) 2 are A ⫹ 1 /A 1 共21/1兲, A 2 /A 2 共3/3兲, B 1 /B 1 ⫹ ⫺ 9,15 ⫹ ⫺ 共15/0兲, B 2 /B 2 共6/6兲, and E /E 共18/3兲. There exist vibrations of two different (C S) symmetries: symmetric (A ⬘ ) vibrations and antisymmetric (A ⬙ ) vibrations, which correspond to vibrations that break the plane of symmetry of the dimer. The symmetry of the states with a given J and K a in an A ⬘ vibration are the same as in the vibrational ground state 共GS兲 共see Fig. 3兲. The symmetry label 共e.g., A ⫹ 1 ) of the states with a given J and K a in an A ⬙ vibration are the same as those for J(A ⬙ )⫽ 兩 J(GS)⫺1 兩 共odd and even J兲 of the GS. Vibrational transitions from the GS to an excited state with A ⬘ symmetry have allowed a-type (⌬K a ⫽0) and c-type (⌬K a ⫽⫾1) components, whereas those to an excited state with A ⬙ symmetry only have b-type (⌬K a ⫽⫾1) components. From a practical point of view, the (H2 O) 2 spectra have proved more difficult to identify and assign. In the ⫺ ⫹ ⫺ A⫹ 1 /B 1 and B 1 /A 1 spectra of (H2 O) 2 every other line is missing due to the zero statistical weights of B 1 levels. These sparse spectra are more difficult to identify within a dense data set. (H2 O) 2 also exhibits much larger tunneling splittings, such that the spectra of a single intermolecular vibra-
Water dimer
8929
tion may require measurements with several far-infrared 共FIR兲 lasers to be fully characterized. Finally, intermolecular vibrations of (H2 O) 2 occur at higher frequencies than (D2 O) 2 , where strong FIR laser lines are more sparse. III. EXPERIMENT
The Berkeley terahertz spectrometer used in the observations of the water dimer transitions reported here has been described previously and, thus, only a brief summary of the experiment will be presented here. A high-power 共85 W兲, line-tunable, infrared CO2 laser coaxially pumps a fixedfrequency FIR molecular gas laser, the output of which is coupled onto a 1T24 Schottky barrier diode. The two lasers used for the work described here were the 70-m 共4.251 676 36 THz兲 CH3 OH and 72-m 共4.158 915 8 THz兲 13 CH3 OH lasers. The fundamental, first, or second harmonic of a HP8367B microwave synthesizer is coupled via an antenna onto the Schottky barrier diode and the nonlinear properties of the diode mix the microwave and THz radiation, creating tunable sidebands with frequencies of (laser) ⫾ (microwave). The sidebands, which are tunable ⫾2 cm⫺1 around each laser, are separated from the carrier frequency, multipassed in the throat of a pulsed planar supersonic expansion and detected on an unstressed germanium/ gallium photoconductive detector. The pulsed molecular beam is produced by expanding pure argon saturated with H2 O or D2 O through a 101.6-mm-long slit at a repetition rate of 33 Hz while maintaining the vacuum chamber at approximately 35 mTorr with a Roots blower 共Edwards EH4200兲 backed by two rotary pumps 共Edwards E2M275兲. IV. RESULTS AND DISCUSSION A. Rotation tunneling assignments and fit
1. (H2O)2
Altogether, 137 new H2 O cluster transitions were observed, and 64 of these were assigned 共see Fig. 4 and Table I兲 to parallel a-type, K a ⫽0←0, K a ⫽1←1, and perpendicular c-type, K a ⫽0←1, K a ⫽1←0, bands of the dimer. P(1) transitions obviously only occur in K a ⫽0←1, and K a ⫽0←0 subbands and the former have no R(0) transitions, whereas the latter have no Q branches. Together with the known energy differences of transitions of K a ⫽0 and K a ⫽1 levels terminating in the identical upper states 共combination differences兲, this suffices to verify the assignment of ⫹ ⫺ ⫹ the A ⫺ 2 /B 2 and B 2 /A 2 K a ⫽0←1 and K a ⫽0←0 subbands. Unfortunately, no K a ⫽0←0 transitions of the E 2 states were observed and the P P 1 (1) transition of the 4261-GHz K a ⫽0←1 subband of the E 2 levels is located in a gap of the scanning range of the spectrometer. However, the assignment is consistent, as combination differences demonstrate that the 4261-GHz subband involves K a ⫽1 E 2 states and the band is located between the corresponding A- and B-state subbands, which is expected. The only other E-state subband, at 4295 GHz 共identified via the characteristic intensity pattern兲 is located at higher energy than the A- and B-state subbands, which is possible but not common. The assignment of the 4212-GHz K a ⫽1←0 Q branch is verified by the characteristic Coriolis shifts that are the fin-
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
8930
Keutsch et al.
J. Chem. Phys., Vol. 119, No. 17, 1 November 2003
FIG. 4. Overview of all observed (H2 O) 2 transition together with the assigned transitions. The symmetry labels correspond to the label of the ground-state levels that the transitions are originating from. The left middle ⫹ inset shows the R Q 0 B ⫺ 2 /A 2 Q branch and the left top inset shows an experimental scan of the R Q 0 (3) and R Q 0 (4) transitions of this subband. The right middle inset shows the ⫹ P Q1 A⫺ 2 /B 2 Q branch and the right top inset shows an experimental scan of the P Q 1 (3) transition.
⫹ gerprint of the GS B ⫺ 2 /A 2 levels. It is highly unlikely that transitions exhibiting the exact 共in this case to within 1 MHz兲 shifts of the vibrational ground state could arise as a result of a combination of perturbations in ground and excited states. This assignment is further verified by observation of combination differences with K a ⫽1←1 transitions terminating in identical upper states. From the relative intensities of the transitions of the Q branch of the 4295-GHz subband, it is clear that it has E symmetry. Furthermore, the fact that it is free from any perturbation shows that it either is a E 1 K a ⫽1←0 subband or a E 2 K a ⫽1←1 subband arising from the lower 共unperturbed兲 component of the asymmetry doublet. It is unlikely that the transitions correspond to a E 2 K a ⫽0←1 band, as this would require the existence of an additional vibrational level. It should also be noted that transitions arising from the K a ⫽1 states of the 1s are never observed in our THz experiments, as they have very low intensities due to their low population. Unfortunately, no combination differences, which could easily distinguish the two cases mentioned above, were observed. All water dimer transitions were fit with the following energy expressions typical for near prolate rotors:
K a ⫽0: 0兲 ⫹B 共 0 兲 J 共 J⫹1 兲 E 共 A ⫾ /B ⫾ 兲 ⫽⫾ 21 共I 0 兲 ⫺ 共BT
⫺D 共 0 兲 关 J 共 J⫹1 兲兴 2 , 0兲 ⫹B 共 0 兲 J 共 J⫹1 兲 ⫺D 共 0 兲 关 J 共 J⫹1 兲兴 2 ; E 共 E ⫾ 兲 ⫽ 共BT
K a ⫽1: 1兲 ⫹B 共 1 兲 关 J 共 J⫹1 兲 ⫺1 兴 E 共 A ⫾ /B ⫾ 兲 ⫽ 共 1 兲 ⫾ 21 共I 1 兲 ⫺ 共BT
⫺D 共 1 兲 关 J 共 J⫹1 兲 ⫺1 兴 2 ⫾ 关共 B⫺C 兲 共 1 兲 /4 ⫺d 共 1 兲 J 共 J⫹1 兲兴 J 共 J⫹1 兲 , 1兲 ⫹B 共 1 兲 关 J 共 J⫹1 兲 ⫺1 兴 ⫺D 共 1 兲 关 J 共 J⫹1 兲 E 共 E ⫾ 兲 ⫽ 共 1 兲 ⫹ 共BT
⫺1 兴 2 ⫾ 关共 B⫺C 兲 共 1 兲 /4⫺d 共 1 兲 J 共 J⫹1 兲兴 J 共 J⫹1 兲 ,
(1) ⫽band origin of the K a ⫽1 states, I(0,1) ⫽interchange tunneling splitting in K a ⫽0,1, (0,1) BT ⫽bifuraction tunneling splitting in K a ⫽0,1,
B (0,1) ⫽the average of the B and C rotational constants in K a ⫽0,1, D (0,1) ⫽the average of the D 共distortion兲 rotational constant in K a ⫽0,1, d (1) ⫽the average of the d 共distortion兲 rotational constant in K a ⫽1. For the vibrational ground state of (H2 O) 2 , the K a ⫽0 levels and upper asymmetry components of the K a ⫽1 levels of the 2s are very close in energy, resulting in a Coriolis perturbation between levels with identical symmetries. The energy level expression for these states is E⫽ 关 E 共 0 兲 ⫹E 共 1 兲 兴 /2⫾ 关共 E 共 1 兲 ⫺E 共 0 兲 兲 2 /4⫹ 2 J 共 J⫹1 兲 /2兴 1/2, where the E (n) are the conventional unperturbed energy levels given above and is the Coriolis interaction constant. For the fits reported here, the values of of the GS were fixed to the previously determined values, as they could not be fit
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
J. Chem. Phys., Vol. 119, No. 17, 1 November 2003
Water dimer
8931
TABLE I. Assigned transitions of (H2 O) 2 reported here are shown together with the difference between observed and calculated frequencies 共all values are in MHz兲. The symmetry labels correspond to those of the states the transitions are originating in 共also in Fig. 4兲. The symmetry labels of the upper states can be determined form the selection rules. The fits for the two possible assignments of the 4295-GHz subband (E 2 K a ⫽1←1 or E 1 K a ⫽1←0) are both shown in the lowest part of the table 共see Sec. IV A兲. K a ⫽0←0 Transition 4 04←5 05 2 02←3 03 1 01←2 02 0 00←1 01 3 03←2 02 4 04←3 03 5 05←4 04 6 06←5 05 K a ⫽0←1 Transition 4 04←5 14 3 03←4 13 2 02←3 12 1 01←2 11 0 00←1 10 1 01←1 11 2 02←2 12 3 03←3 13 4 04←4 14 5 05←5 15 6 06←6 16 7 07←7 17 8 08←8 18 9 09←9 19 2 02←1 10 3 03←2 11 4 04←3 12 5 05←4 13 6 06←5 14 7 07←6 15 K a ⫽1←0 Transition 1 11←1 01 2 12←2 02 3 13←3 03 4 14←4 04 5 15←5 05 6 16←6 06 7 17←7 07 8 18←8 08
Frequency
⫹ A⫺ 2 /B 2
⌬
4244069.3 4270732.5 4283560.0 4296051.5
B⫹ 2 B⫹ 2 A⫺ 2 B⫹ 2
1.5 ⫺3.2 3.3 1.9
Frequency
⫹ A⫺ 2 /B 2
⌬
4223988.5 4238804.5
B⫹ 2 A⫺ 2
0.4 ⫺2.9
4266803.0 4279920.0 4292009.5 4291200.5 4289989.5 4288396.5 4286439.3 4284116.1
A⫺ 2 B⫹ 2 A⫺ 2 B⫹ 2 A⫺ 2 B⫹ 2 A⫺ 2 B⫹ 2
⫺1.0 ⫺0.2 ⫺0.7 1.7 ⫺1.4 ⫺1.2 5.3 ⫺2.3
Frequency
⫹ B⫺ 2 /A 2
4212700.6 4212922.0 4213220.9 4213565.9 4213927.0 4214277.6 4214594.1 4214860.4
A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2
Frequency
⫹ B⫺ 2 /A 2
⌬
4270654.0 4283797.5 4297008.0 4310212.9
B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2
0.5 ⫺1.3 ⫺1.9 ⫺1.4
Frequency
⫹ E⫺ 2 /E 2
⌬
4222725.5 4235876.0
E⫹ 2 E⫺ 2
1.5 ⫺0.4
4261185.0 4261011.5 4260748.5 4260387.5 4259924.7
E⫺ 2 E⫹ 2 E⫺ 2 E⫹ 2 E⫺ 2
0.4 ⫺0.5 0.1 ⫺0.9 0.0
4285299.5 4296808.5 4308009.0
E⫹ 2 E⫺ 2 E⫹ 2
⫺1.0 0.0 0.8
⌬ 2.0 ⫺0.4 ⫺1.4 ⫺1.2 ⫺0.3 0.5 ⫺0.3 ⫺0.1
K a ⫽1←1 Transition 2 12←2 11 2 12←1 11 3 13←2 12 5 15←4 14
K a ⫽1←1 Frequency
Transition
⫹ E⫺ 2 /E 2
Transition
4295669.4 4295723.5 4295801.6 4295903.5 4296032.7 4296187.8 4296368.5 4296572.2
1 10←1 11 2 11←2 12 3 12←3 13 4 13←4 14 5 14←5 15 6 15←6 16 7 16←7 17 8 17←8 18
E⫺ 2 E⫹ 2 E⫺ 2 E⫹ 2 E⫺ 2 E⫹ 2 E⫺ 2 E⫹ 2
1 11←1 01 2 12←2 02 3 13←3 03 4 14←4 04 5 15←5 05 6 16←6 06 7 17←7 07 8 18←8 08
without correlation. A similar Coriolis term was introduced to the energy expression of the excited vibrational state ⫹ A⫺ 2 /B 2 levels. Table I shows the assigned transitions and the difference between observed and calculated frequencies, and Table II shows the molecular constants determined in the fits.
Frequency
⫹ B⫺ 2 /A 2
⌬
4194867.0 4207416.0 4220134.5 4220497.5 4220979.0 4221521.5 4222073.9 4222592.9 4223039.2 4223388.5 4223616.5 4244795.5 4257077.0 4269209.5 4281175.3
B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2
⫺2.0 ⫺2.0 2.1 1.7 1.7 0.3 ⫺0.9 0.2 0.0 1.7 ⫺0.9 ⫺1.3 2.1 0.4 1.2
4304523.8
B⫺ 2
5.0
Frequency
⫹ B⫺ 2 /A 2
⌬
4199342.8 4224606.5 4236843.5 4261250.7
B⫺ 2 B⫺ 2 A⫹ 2 A⫹ 2
⫺1.1 ⫺0.8 1.6 1.5
K a ⫽1←0 ⫹ E⫺ 1 /E 1 E⫺ 1 E⫹ 1 E⫺ 1 E⫹ 1 E⫺ 1 E⫹ 1 E⫺ 1 E⫹ 1
⌬ ⫺1.2 1.0 1.2 ⫺0.6 ⫺0.7 ⫺0.2 0.7 ⫺0.2
The quality of the fit is demonstrated by the 共1兲 root-meansquare deviation of 1.53 MHz for the 2s, smaller than the experimental linewidth of ca. 3 MHz. For the 1s, a 共1兲 root-mean-square deviation of only 0.79 MHz was observed. The interchange splitting is 56.3 GHz in K a ⫽0 of the ex-
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
8932
Keutsch et al.
J. Chem. Phys., Vol. 119, No. 17, 1 November 2003 TABLE II. Molecular constants and tunneling splittings determined in the fit of the (H2 O) 2 bands reported here are shown 共all values in MHz兲. Also shown are the ground-state constants and tunneling splittings used in the fit 共Ref. 19兲. The value of the band origin determined for K a ⫽1 of the 2s can only be rigorously determined if all tunneling splittings have been determined. Furthermore, the value determined in the fit depends on the value of the bifurcation tunneling splitting in the ground state, which has not been determined directly by experiment. The values used here for the latter correspond to the average of the splitting in K a ⫽0 and 1 in the ground state. The value given in the table for the vibrational band origin of the K a ⫽1 of the 2s assumes that the 4295-GHz band corresponds to E 2 transitions. If the latter band corresponds to E 1 transitions, only the lowest of the three tunneling components of the K a ⫽1 of the 2s is known and the band origin cannot be estimated. 1 uncertainties of fitted constants in parentheses. rms 1.53 MHz 2s/0.79 MHz 1s. ⫺ E⫹ 1 /E 1
K ⬙a ⫽0
K ⬙a ⫽1
K ⬘a ⫽0
K ⬘a ⫽1
I⬙ (0) ⬙BT(0)b B ⬙ (0) D ⬙ (0)
679.3a 6160.600a 0.04995a
⫹ A⫺ 2 /B 2
6167.736a 0.03824a
⫹ E⫺ 2 /E 2
⫹ B⫺ 2 /A 2
19530.91a 746.65a 6166.652a 0.03649a
6164.746a 0.03788a
⬙ (1) I⬙ (1)
18805.14a 16204.84a
⬙BT(1)b B ⬙ (1) D ⬙ (1) d ⬙ (1) ⬙ (B ⬙ ⫺C ⬙ ) (1) /4
⫺746.65a 6153.433a 0.05396a ⫺0.00631a 1594.100a 15.7321a
6152.279a 0.05403a ⫺0.00682a 1508.674a 14.899a
6151.129a 0.05419a ⫺0.00594a 1538.377a 14.459a
⬘ (0) I⬘ (0) ⬘ (0) BT B ⬘ (0) D ⬘ (0)
4271376.2 共0.7兲 56274.7 共1.2兲 1799.9 共0.8兲 5998.9 共0.1兲 0.501 共0.001兲
6094.9 共0.2兲 0.124 共0.007兲
5933.7 共0.1兲 ⫺0.107 共0.003兲
⬘ (1) I⬘ (1)
⬘ (1) BT B ⬘ (1) D (1) d ⬘ (1) ⬘ (B ⬘ ⫺C ⬘ ) (1) /4
4302512.4 共0.7兲
6188.51 0.0517 共0.0008兲 0d 15.0d
4313686.1 共1.3兲c 171884 共3兲c 0/not determinable 6146.4 共0.1兲 0.084 共0.001兲 0d ⫺3078 15.0d
6135.4 共0.1兲 0.0490 共0.001兲 0d 15.0d
a
Fixed from Ref. 19. ⬙ (0,1) determined as the average of the splitting in K a⬙ ⫽0 and 1. BT c If the 4295-GHz subband corresponds to E 2 transitions, otherwise not determinable. d Fixed. b
cited state of (H2 O) 2 , nearly 3 times the value of the ground state, and the bifurcation tunneling splitting is 1.8 GHz, over 2 times the value of the GS. If the 4295-GHz subband corresponds to E 2 transitions, the interchange splitting is 171.9 GHz, ca. 9 times that of the GS. ⫹ It should be noted that the upper-state A ⫺ 2 /B 2 levels of K a ⫽1 are slightly lower in energy than those of K a ⫽0. The ⫹ Coriolis shift of the K a ⫽0 A ⫺ 2 /B 2 levels towards higher energy, reflected in the sign of , is consistent with the existence of a perturbing level at slightly lower energy, almost certainly the presently unobserved higher-energy component ⫹ of the asymmetry doublet of the K a ⫽1 A ⫺ 2 /B 2 levels. 2. (D2O)2
Altogether, 25 (D2 O) 2 transitions between 140.5 and 145.5 cm⫺1 were identified. These weak (D2 O) 2 VRT transitions overlap with a very intense (D2 O) 4 and weak (D2 O) 3 vibrational band, making the spectral region very congested. Together with the fact that dimer spectra are comparatively sparse, no further assignments and positive identification of
(D2 O) 2 transitions were possible, although experiments with mixtures of D2 O with increasing H2 O content indicate that several other transitions also arise from (D2 O) 2 . In the entire spectral region between 140.5 and 145.5 cm⫺1, only one (D2 O) 2 Q branch was observed at ca. 4115 GHz. The intensity pattern of the Q branch indicates that it has E symmetry; however, no combination differences were observed and thus no assignment is currently possible. Two a-type K a ⫽0←0 subbands were observed and fit 共see Table III兲. Although no P(1) transitions were observed, we are certain of the assignment of both the rotational quantum numbers and assignment to an a-type K a ⫽0←0 transitions, as we will briefly explain here. For (D2 O) 2 subbands 关and unperturbed (H2 O) 2 subbands兴, the second differences between observed transitions „e.g., 关 R(J⫹2)⫺R(J⫹1) 兴 ⫺ 关 R(J⫹1)⫺R(J) 兴 … are a very good estimate of 2⌬B⫽2(B (n) ⬘ ⫺B (n) ⬙ ). As the GS B (0) ⬙ and B (1) ⬙ constants are all close to 5432 MHz, this allows a good estimate of B ⬘ even without knowledge of the rotational assignments. The first difference can be estimated as R(J)⫺R(J⫺1)⫽2B ⬙ ⫹2(J⫹1)⌬B and P(J⫺1)⫺ P(J)
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
J. Chem. Phys., Vol. 119, No. 17, 1 November 2003
Water dimer
8933
TABLE III. Assigned transitions of (D2 O) 2 reported here are shown together with the differences between observed and calculated frequencies 共all values are in MHz兲. The assignment of the tunneling symmetry is based on relative intensities and the results of the fit, but remains uncertain. As a result of this uncertainty, the determination of tunneling splittings and other molecular constants is not rigorous. The range of values of ⌬B ⬘ is also shown. K a ⫽0←0 Transition 6 06←7 07 5 05←6 06 4 04←5 05 3 03←4 04 2 02←3 03 1 01←2 02 1 01←0 00 2 02←1 01 3 03←2 02 4 04←3 03 5 05←4 04 7 07←6 06 ⌬B ⬘
Frequency 4204749.48 4215403.00 4226094.84 4236822.00 4247584.20 4290973.12 4301902.68 4312862.64
4356980.76 7.0–7.1
⫹ E⫺ 2 /E 2
⌬
E⫹ 2 E⫺ 2 E⫹ 2 E⫺ 2 E⫹ 2 E⫺ 2 E⫺ 2 E⫹ 2 E⫺ 2
1.3 ⫺0.9 ⫺0.1 0.7 1.3
E⫺ 2
⫺0.5
⫽2B⬙⫺2(J⫺1)⌬B. With ⌬B determined from the second differences, this allows an assignment of the rotational J quantum number from the first difference, which can easily be verified. Thus we are readily able to identify R(0) transitions, which, together with combination differences, rules out that transitions are originating in K a ⫽1. The assignment to a-type K a ⫽0←0 rather than c-type or b-type K a ⫽1←0 transitions is consistent with the lack of Q branches, which would have been easily observable. Unfortunately, we are unable to assign the symmetry labels of the tunneling components for the two subbands. However, even without these, we can estimate ⌬B⫽7.0– 7.1 MHz for the 4267-GHz band and ⌬B⫽15.8– 16.5 MHz for the 4290-GHz subband. Similarly, the less reliable fit of the 4115-GHz Q branch also yields ⌬B of roughly the same magnitude. B. Vibrational assignment
The observation of K a ⫽1←0 and K a ⫽0←1 bands terminating in the same upper states as the a-type K a ⫽0←0 and K a ⫽1←1 transitions shows that the excited vibrational states of (H2 O) 2 reported here have A ⬘ symmetry. The only subband, which could be an exception, is the 4295-GHz subband, as it could be either b type or c type if it corresponds to E 1 transitions. Similarly, the symmetry of the excited vibrational state of the (D2 O) 2 band reported here is A ⬘ , as proved by the observation of a-type K a ⫽0←0 transitions. The assignment of specific vibrational modes beyond this has to rely on the interpretation of relative intensities, changes in rotational constants and tunneling splittings, and comparison with theoretical calculations. In the following, the importance of such a comparison for the validation of existing IPS models will be evident. Traditionally, the intermolecular vibrational modes of the dimer had been assigned following the normal-mode picture first introduced by Reimers and Watts.17 Following this approach, there exist three normal modes of A ⬘ and A ⬙ symmetry each for a total of six intermolecular modes 共see Table IV兲. The limitations of such a normal-mode picture for the water dimer with its large amplitude vibrations is apparent
⫺0.3 ⫺0.5 ⫺1.0
Frequency
⫹ B⫺ 2 /A 2
⌬
4212949.00 4223764.80 4234598.32 4267190.88 4278081.16 4288988.08 4299906.00 4310836.92
B⫺ 2 A⫹ 2 B⫺ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2
⫺0.3 ⫺0.3 0.1 0.7 ⫺1.1 0.7 0.3 ⫺0.2
15.8 –16.5
and the assignment of the vibrational modes until recently has employed the modes in Table IV merely as labels. Leforestier et al.5 and Smit et al.,8 who used a careful analysis of the nodal patterns of the vibrational wave functions, have shown that vibrational overtone and combination bands have to be considered. Figure 5 and Table V show a comparison of the (H2 O) 2 vibrational levels calculated on the VRT共ASPW兲III, SAPT-5st, and VRT共MCY-5f兲 surfaces with the experimentally determined ones. Theoretical calculations generally agree well on the ordering of the vibrational and tunneling levels. Differences in assignments remain only in the labeling and Goldman et al.7 关VRT共ASP-W兲III兴 assigned the second A ⬘ mode of the 2s of K a ⫽0 to the IPB, whereas Smit et al.8 共SAPT-5st兲 assigned it to the donor overtone 共DT兲2 and Leforestier et al.18 关VRT共MCY-5f兲兴 assigned it to the hydrogen bond stretch 共S兲. Here we will follow the labeling by Smit et al. for the experimental levels. A comparison shows that the agreement of the calculated levels with experiment is good for all three models 共see Table V兲. The VRT共ASP-W兲III values are generally too high and the 2s of K a ⫽0 of the DT are in worse agreement with experiment TABLE IV. Harmonic frequencies of the water dimer normal modes calculated on the SAPT-5st surface 共Ref. 8兲.
Mode Donor torsion 共DT兲 Acceptor twist 共AT兲 Acceptor wag 共AW兲 Hydrogen bond stretch 共S兲 In-plane bend 共IPB兲 Out-of-plane bend 共OPB兲 a
Frequency 关cm⫺1兴a (H2 O) 2 /(D2 O) 2 121.01/88.07 143.70/102.87 157.87/118.52 186.83/172.84 369.99/274.76 564.70/406.11
From Ref. 8.
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
8934
Keutsch et al.
J. Chem. Phys., Vol. 119, No. 17, 1 November 2003
FIG. 5. Comparison of all experimentally observed vibration–tunneling levels 共in cm⫺1兲 together with those calculated by Goldman et al. 共Ref. 7兲 on the VRT共ASP-W兲III surface, Smit et al. 共Ref. 8兲 on SAPT-5st, and Leforestier et al. 共Ref. 5, 18兲 on the VRT共MCY-5f兲 surface. The experimental levels are shown for J⫽1 共to show where Coriolis resonances can occur兲, whereas the calculated ones are for J⫽0 for K a ⫽0 and J⫽1 for K a ⫽1. Solid lines correspond to A ⬘ vibrational levels and dashed lines to A ⬙ vibrational levels. The nomenclature of the vibrational modes follows Table V, and 共DT兲2 refers to the donor torsion overtone transition. UK 共labeled with solid circles兲 refers to the vibration–tunneling level previously assigned to the K a ⫽0 IPB by Braly et al. 共Ref. 9兲. The two levels corresponding to the two possible vibrational assignments of the 4295-GHz band are labeled with solid diamonds. The theoretical calculations have the same ordering of vibration tunneling levels and also agree well with the experimental ones, except for the UK level, as discussed in the text.
than those of the other potentials, as are the 2s of K a ⫽0 reported here 关Fig. 5: labeled as IPB for VRT共ASP-W兲III兴. The acceptor wag 共AW兲 共best agreement of the three potentials兲 and acceptor twist 共AT兲 levels agree very well with the experimental ones. The levels calculated on SAPT-5st are also generally too high, but also agree well with experiment except for the AW K a ⫽0 levels, which are higher in energy than the experimental and other calculated ones. The
VRT共MCY-5f兲 values have the best agreement with experiment and do not show a clear trend of being either too high or too low. For all (H2 O) 2 subbands reported here, except for the 4295-GHz one, comparison with the calculated vibrational tunneling levels argues that the levels reported here correspond to the 2s of K a ⫽0 of 共DT兲2 共following the mode assignments by Smit et al.兲 and the 2s of K a ⫽1 of S. If the
TABLE V. Comparison between experimental and calculated energy levels 共in cm⫺1兲 shows that the calculated VRT共MCY-5f兲 energies have the best agreement with experiment. K a ⫽0 energy levels were chosen as K a ⫽1 levels are not available for some of the potentials. ⌬ is the difference between calculated and experimental band origins. The band origins are defined as the average of the energy difference between the excited vibrational state and GS A 1 /B 1 or A 2 /B 2 pairs. The difference between that definition and the one given in Table II is indicated in Fig. 2. The value of AS cannot be determined experimentally and thus the calculated values were subtracted for the 2s. 共Note that errors of the VRT共MCY-5f兲 are close to the error of using v ⫽300 000 km/s for the speed of light in vacuum兲. Band origin 2s of 1s of 2s of 2s of 2s of rmsa
K a ⫽0 DT K a ⫽0 AW K a ⫽0 AW K a ⫽0 AT K a ⫽0 共DT兲2
Experiment 53.34b 107.93c 97.71c 109.01c 142.44d
VRT共ASP-W兲III 共⌬兲e 62.61共9.27兲 108.17共0.24兲 99.93共2.22兲 110.35共1.34兲 152.65共10.21兲 6.3
SAPT-5st 共⌬兲f 53.17共⫺0.17兲 113.39共5.46兲 110.57共12.86兲 109.79共0.78兲 145.28共2.84兲 6.4
VRT共MCY-5f兲 共⌬兲g 51.95共⫺1.36兲 104.32共⫺3.61兲 96.94共⫺0.77兲 109.93共0.92兲 142.63共0.19兲 1.8
rms⫽ 冑1/N ⌺( obs⫺ calc) 2 . From Ref. 21. c From Ref. 9. d This work. e From Ref. 7. f From Ref. 22. g From Ref. 18. a
b
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
J. Chem. Phys., Vol. 119, No. 17, 1 November 2003
4295-GHz band corresponds to E 1 transitions, the excited level of this subband would correspond to the 1s of K a ⫽1 of 共DT兲,2 and if it corresponds to E 2 transitions, the excited state would correspond to the 2s of K a ⫽1 of S. Figure 5 shows that a comparison with the calculated energy levels does not aid in distinguishing which of these assignments is correct. Commonly, the analysis of rotational constants and tunneling splittings is used to aid in the analysis of the vibrational motions. However, the rotational constants of the 2s of K a ⫽0 reported here are severely Coriolis contaminated and thus do not allow structural interpretations. Comparison of the nuclear displacements of a specific vibration with the tunneling pathways can allow estimates of the expected change in tunneling splitting on excitation of this vibration. For example, the motion of the donor water molecule in the AS tunneling pathway resembles the DT vibrational displacements, consistent with dramatic increase of the AS splitting in the DT vibrational state. Similarly, the motion of the acceptor water in the AS tunneling pathway resembles the AW vibrational displacements. However, experimentally, a significant decrease of the AS splitting is observed on excitation of the AW vibration. Furthermore, the I tunneling splitting of the 1s of the 共DT兲2 vibration on the SAPT-5st surface is very different from that of the 2s. This demonstrates that for the water dimer, observed changes in tunneling splittings can only assist in vibrational assignment through comparison with theoretical results, rather than deductions based on nuclear displacements. Last, the observed relative intensities can aid in the vibrational assignment. The experimental c-type K a ⫽0←1 (DT兲2 transitions are significantly stronger than the a-type K a ⫽0←0 共DT兲2 transitions. Table VI shows a comparison of calculated transition dipole moments for the observed vibrations. The results of Smit et al.8 and Leforestier18 agree well with the biggest difference 共⬃50%兲 observed for K a ⫽1←0 transitions of the 2s. Smit et al. do not calculate intensities for transitions originating in K a ⫽1, but the results of Leforestier—like the experiment—show that the c-type K a ⫽0←1 共DT兲2 transitions are significantly stronger than the a-type K a ⫽0←0 共DT兲2 transitions. The experimental intensity of the 4295-GHz subband is only a little lower than that of the c-type bands discussed above. As mentioned earlier, the unperturbed appearance of this band only allows it to be either a E 1 K a ⫽1←0 subband or a E 2 K a ⫽1←1 subband arising from the lower component of the asymmetry doublet. For the latter case, it is reasonable to assume that the band terminates in the same vibrational state 共S兲 as the observed K a ⫽1←0 transitions. Table VI shows that these are calculated to be very weak—comparable to the K a ⫽0←0 transitions of the 2s of 共DT兲2. In contrast, the E 1 K a ⫽1 ←0 共DT兲2 transitions have a magnitude between the 共both experimentally and calculated兲 strong K a ⫽0←1 and weak K a ⫽0←0 transitions transitions of the 2s of 共DT兲2. This would argue that it is more likely that the 4295-GHz subband corresponds to E 1 K a ⫽1←0 共DT兲2 transitions. A new and expanded perspective can now be employed to reevaluate the nature of the levels previously referred to as ⫹ IPB by Braly et al.9 The A ⫺ 2 /B 2 K a ⫽1 states, the lowestenergy tunneling component of the 2s, and the only pres-
Water dimer
8935
TABLE VI. Calculated transition dipole moments 共in ea 0 ) of Smit et al. 共Ref. 8兲 and Leforestier 共Ref. 18兲 are shown for observed vibrational energy levels of (H2 O) 2 including the proposed E 2 →E 1 transitions of the DT 共UK兲 band. A comparison with experimental work is not shown due to the large variation of experimental conditions such as the intensity of the FIR laser line. Most of the experimental intensities reported by Braly et al. 共Ref. 9兲 were measured with older pulsed source technology. The bands reported here were observed with the new pulsed source on a weak laser line. The UK band was observed under more sensitive conditions with the new pulsed source technology and a strong laser line by Braly et al. 共Ref. 9兲 and at the time reported as IPB. Vibration
AW
共DT兲2
DT AW
共DT兲2
S
DT 共UK兲
State
Smit et al.a
Leforestierb
Leforestierb
⫹ A⫺ 1 ←A 1 ⫹ A 2 ←A ⫺ 2 ⫺ B⫹ 2 ←B 2 ⫺ A⫹ ←A 2 2 ⫹ B 2 ←B ⫺ 2
J⫽1, K a ⫽0← J⫽0, K a ⫽0 0.212 0.237 0.258 0.023 0.023
J⫽1, K a ⫽0← J⫽0, K a ⫽0 0.206 0.229 0.252 0.035 0.029
J⫽1, K a ⫽0← J⫽1, K a ⫽1 0.168 0.247 0.220 0.073 0.085
J⫽1, K a ⫽1← J⫽0, K a ⫽0 0.228 0.191 0.147 0.074 ⬍c ⬍c 0.221
J⫽1, K a ⫽1← J⫽0, K a ⫽0 0.191 0.192 0.180 0.177 0.056 0.030 0.158
J⫽1, K a ⫽1← J⫽1, K a ⫽1 0.068 0.233 0.263 0.286
0.073 0.077
0.041 0.036
⫹⫺ A⫺ 1 ←A 1 ⫺ A 1 ←A ⫹ 1 ⫺ A⫹ 2 ←A 2 ⫹ B 2 ←B ⫺ 2 ⫹ E⫺ 1 ←E 1 ⫹ E⫺ 2 ←E 1 ⫹ B 2 ←B ⫺ 2 ⫺ E⫹ 2 ←E 2 ⫹ E 1 ←E ⫺ 2 ⫺ A⫹ 2 ←A 2 ⫹ B 2 ←B ⫺ 2 ⫹ E⫺ 1 ←E 2 ⫺ E⫹ 1 ←E 2
P(1) R(1) R(0)
⬍ 0.037 0.024 0.089 0.083
K a ⫽0←K a ⫽0 K a ⫽0←K a ⫽1 0.023 0.030 0.053 0.017 0.007 0.057
a
From Ref. 8. From Ref. 18. c The A 1 and B 1 tunneling symmetries had very small dipole moments; no E states were calculated. b
ently observed K a ⫽1 states of the IPB are consistent with the K a ⫽1 energy level structure calculated on all three model IPSs, and the overall agreement between experiment and theory for K a ⫽1 is quite good. We have accordingly reassigned these levels to the 共DT兲2 mode rather than IPB in light of the vibrational mode analysis by Smit et al. In con⫹ trast, the E ⫺ 2 /E 2 K a ⫽0 states, labeled as UK in Fig. 5 共and previously assigned to IPB by Braly et al.兲, are a cause of concern. All calculations disagree with the assignment of this level to IPB, and the vibrational assignment of this subband has therefore been cast in doubt. Disagreement goes beyond this though 共IPB was being used largely as a label, and thus the disagreement was largely semantic兲, as theoretical calculations do not yield any unassigned level with the correct symmetry. In fact hitherto the lowest unassigned level of the correct symmetry corresponded to the ones we assigned to the new bands reported here, which lie at significantly higher energy. In contrast, the new experimental levels agree well with calculated energy levels 共see Fig. 5兲, and it seems unlikely that instead the UK level corresponds to one of these and the new levels reported here to some vibration that has a
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
8936
Keutsch et al.
J. Chem. Phys., Vol. 119, No. 17, 1 November 2003
much higher calculated energy 共which implies that all calculations are in considerably worse agreement then apparent in Table V or Fig. 5兲. This disagreement thus questions the entire vibration–tunneling level structure of (H2 O) 2 and also the correctness of all model surfaces as they would appear to ‘‘miss’’ a level. However, it is unlikely that the calculations on all three highly sophisticated surfaces with different methods all ‘‘miss’’ a level. The theoretical work would therefore rather imply a misidentified symmetry, as indeed there exist some presently unobserved or at least unassigned vibration– tunneling levels. The only unassigned K a ⫽0 levels are the 1s of DT and of AT, and the only unassigned levels of the 2s are the K a ⫽1 DT levels. The characteristic Coriolis shifts and combination differences of the vibrational ground state observed by Braly et al.9 for this band prove that it is extremely unlikely that the transitions terminating in the UK level do not originate in E 2 K a ⫽1 states. The observation of a P(1) transition similarly proves that the transitions terminate in K a ⫽0 共we have also verified the assignments of all other vibration–tunneling states兲. K a is not a good quantum number and various cases of Coriolis mixing of K a ⫽0 and K a ⫽1 states have been observed. However, no mixing with a K a ⫽0, J⫽0 state is allowed as the mixing levels must have identical J (J⫽0 does not exist for K a ⫽1). In addition, Fig. 5 shows that the only possible E 2 candidate for mixing or even direct transitions is the currently unobserved K a ⫽1 DT level, which is calculated at much lower energy. In a previous section, we have mentioned that symmetry allows transitions between E 1 and E 2 states, but these have never been observed or identified, even though they are of considerable importance, since they would give a direct measure of the acceptor switching splitting. From group theory, it is clear that for this case the UK transitions could only be terminating in K a ⫽0 E 1 states of an A ⬙ vibration. Interestingly, the 1s of DT are calculated to lie close in energy to the observed transition. As the experimental results are unambiguous, we speculate that the spectrum actually corresponds to transitions from K a ⫽1 and 0 E 2 levels of the vibrational ground state to K a ⫽0 E 1 states of DT or, possibly, states which are a mix of K a ⫽0 E 1 DT and K a ⫽1 E 2 DT states 共even though we do not observe a Coriolis perturbation for the excited state, which would be required for a mixed state兲. Leforestier18 has calculated the intensities for all (H2 O) 2 transitions from J⫽0,1 and K a ⫽0,1 up to 200 cm⫺1 and up to K a ⫽2 for all tunneling symmetries 共see some results in Table VI兲. The intensities of the E 2 →E 1 transitions vary significantly depending on the excited vibrational level. However, many of the transitions originating in E 2 states and terminating in E 1 states—in particular of K a ⫽0 of DT—have intensities that are comparable or stronger than those of the donor torsion overtone reported here 共recorded with a weaker laser line兲 and circa 401 of the strongest of all calculated vibrational transitions 共as judged by the line strength, which is proportional to the square of the transition dipole moment兲. As the strongest experimentally observed dimer transitions have a signal-to-noise ratio Ⰷ103 with pulsed source technology, the explanation suggested above for the UK energy level is quite probable. This also agrees well with the fact that despite intense experimen-
tal efforts, no A or B symmetry components, which otherwise would have to be in the vicinity of the E-state transitions, have been observed.9 The fact that no other E 2 →E 1 transitions have yet been reported may appear troubling. However, it is likely that other such transitions have indeed been observed, but so far not identified, and remain as unassigned transitions, as the assignments proposed here had never before been considered. If we accept the new solution offered above, the assignment of the bands reported here and shown in Fig. 5 is consistent with the theoretical calculations. The vibrational assignment of the (D2 O) 2 bands is more difficult due to the small available data set. The lowest unassigned K a ⫽0 levels of an A ⬘ vibration are the 2s of 共DT兲2 and the hydrogen bond stretch (1s and 2s). The former are predicted to have very low intensity. Furthermore, they are calculated to occur at significantly lower energy on VRT共ASP-W兲III, which otherwise agrees quite well with experiment, and at a little lower energy on SAPT-5st, which also agrees well with experiment except that it produces somewhat higher energies than the experimental ones. The increased B (0) in the upper state, indicative of slight decrease in size, could be expected for the IPB vibration. However, for the DT the 1s show a positive ⌬B and the 2s a negative ⌬B, which highlights the dangers of vibrational assignments based on a structural interpretation of the molecular constants. We therefore tentatively assign the (D2 O) 2 transitions to upper states of the hydrogen bond stretch vibration. Finally, we want to mention that we have also observed some (H2 O) 2 Q-branch transitions at ca. 575 cm⫺1. Although we are certain of the carrier of the transitions, our current experiment does not permit assignment of these extremely weak spectra. It is possible that they belong to the out-of-plane liberation, although the large density of states at these energies requires a detailed analysis before any assignments could be made, even with a complete dataset.
V. CONCLUSIONS
We report the highest-frequency intermolecular vibrational bands of the water dimer observed to date. We assign the (H2 O) 2 bands to an overtone of the donor torsion (K a ⫽0) and the hydrogen bond stretch of the 2s acceptor tunneling states (K a ⫽1). One (H2 O) 2 subband at 4295 GHz either corresponds to E-state transitions to the 2s of the hydrogen bond stretch (K a ⫽1) or E-state transitions of the 1s of the donor torsion overtone (K a ⫽1). We tentatively assign the (D2 O) 2 transitions to K a ⫽0 of the hydrogen bond stretch with currently unknown tunneling symmetry. The observation of the K a ⫽0 levels of the 2s reported here raises the question as to which vibrational level the experimental UK 共IPB of Braly et al.兲 level corresponds to. This problem had not been addressed appropriately before 共even though it is crucial for achieving consistency between experiment and theory兲, and we suggest that it arises from transitions originating in E 2 levels and terminating in E 1 levels of K a ⫽0 of DT. These transitions had not been considered in previous work, but the verification of the symmetry label assignments, the newly available calculated transi-
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
J. Chem. Phys., Vol. 119, No. 17, 1 November 2003
tion dipole moments, and the fact that no accompanying Aor B-state transitions have been observed in the spectra are strong evidence in favor of this argument. However, it is apparent that further investigation is still necessary, and its importance cannot be overstated. The assignment of UK to the 1s of DT requires further verification 共via observation of transitions originating in the 1s), which simultaneously would give a direct measurement of the AS splitting. We hope that this work will stimulate further collaboration between theoretical and experimental groups. Further experimental efforts are also necessary to identify the missing tunneling components of the vibrational bands reported here to complete the characterization of the (H2 O) 2 and (D2 O) 2 hydrogen bond stretching and donor torsion overtone vibrations. The spectral regions where these transitions are expected are inaccessible with the present THz VRT spectrometer. Implementation of new microwave and millimeter wave sources is required for accessing these regions.
ACKNOWLEDGMENTS
This work was supported by the Experimental Physical Chemistry program of the National Science Foundation. The authors thank Professor Ad van der Avoird for many helpful discussions.
Water dimer
8937
1
F. N. Keutsch and R. J. Saykally, Proc. Natl. Acad. Sci. U.S.A. 98, 10 533 共2001兲. 2 A. J. Huneycutt and R. J. Saykally, Science 299, 1329 共2003兲. 3 R. S. Fellers, C. Leforestier, L. B. Braly, and M. G. Brown, and R. J. Saykally, Science 284, 945 共1999兲. 4 G. C. Groenenboom, E. M. Mas, R. Bukowski, K. Szalewicz, P. E. S. Wormer, and A. van der Avoird, Phys. Rev. Lett. 84, 4072 共2000兲. 5 C. Leforestier, F. Gatti, R. S. Fellers, and R. J. Saykally, J. Chem. Phys. 117, 8710 共2002兲. 6 M. P. Hodges, A. J. Stone, and S. S. Xantheas, J. Phys. Chem. A 101, 9163 共1997兲. 7 N. Goldman, R. S. Fellers, M. G. Brown, L. B. Braly, C. J. Keoshian, C. Leforestier, and R. J. Saykally, J. Chem. Phys. 116, 10 148 共2002兲. 8 M. J. Smit, G. C. Groenenboom, P. E. S. Wormer, A. van der Avoird, R. Bukowski, and K. Szalewicz, J. Phys. Chem. A 105, 6212 共2001兲. 9 L. B. Braly, K. Liu, M. G. Brown, F. N. Keutsch, R. S. Fellers, and R. J. Saykally, J. Chem. Phys. 112, 10314 共2000兲. 10 T. R. Dyke, J. Chem. Phys. 66, 492 共1977兲. 11 T. R. Dyke, K. M. Mack, and J. S. Muenter, J. Chem. Phys. 66, 498 共1977兲. 12 J. T. Hougen, J. Mol. Spectrosc. 114, 395 共1985兲. 13 G. T. Fraser, Int. Rev. Phys. 10, 189 共1991兲. 14 L. B. Braly, Ph.D. thesis, University of California at Berkeley, 1999. 15 L. B. Braly, J. D. Cruzan, K. Liu, R. S. Fellers, and R. J. Saykally, J. Chem. Phys. 112, 10293 共2000兲. 16 L. H. Coudert and J. T. Hougen, J. Mol. Spectrosc. 130, 86 共1988兲. 17 J. R. Reimers and R. O. Watts, Chem. Phys. 85, 83 共1984兲. 18 C. Leforestier 共personal communication兲. 19 F. N. Keutsch, H. A. Harker, N. Goldman, E. Karyakin, and R. J. Saykally 共unpublished兲. 20 N. Goldman 共personal communication兲. 21 R. J. Saykally 共personal communication兲. 22 G. C. Groenenboom, P. E. S. Wormer, A. van der Avoird, E. M. Mas, R. Bukowski, and K. Szalewicz, J. Chem. Phys. 113, 6702 共2003兲.
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
VOLUME 119, NUMBER 17
1 NOVEMBER 2003
Water dimer hydrogen bond stretch, donor torsion overtone, and ‘‘in-plane bend’’ vibrations Frank N. Keutsch Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138
Linda B. Braly Intel Corporation Technology and Manufacturing Group, Rio Rancho, New Mexico 87124
Mac G. Brown Los Alamos National Laboratory, Los Alamos, New Mexico 87545
Heather A. Harker and Poul B. Petersen Department of Chemistry, University of California, Berkeley, California 94720
Claude Leforestier Laboratoire de Structure et Dynamique des Syste`mes Mole´culaire et Solides (UMR 5636), CC014, Universite´ des Sciences et Techniques du Langue-doc, 34095 Montpellier Ce´dex 05, France
Richard J. Saykallya) Department of Chemistry, University of California, Berkeley, California 94720
共Received 11 June 2003; accepted 8 August 2003兲 We report the measurement and analysis of 64 new K a ⫽0←0,1 and K a ⫽1←0,1 transitions of (H2 O) 2 and 16 new K a ⫽0←0 transitions of (D2 O) 2 by terahertz laser vibration–rotation– tunneling spectroscopy of a planar supersonic expansion between 140.5 and 145.5 cm⫺1. The transitions in both isotopomers correspond to A ⬘ vibrations assigned to the hydrogen bond stretch 共translational兲 and donor torsion overtone vibrations. The interchange splitting is 56.3 GHz in K a ⫽0 of the excited state of (H2 O) 2 , nearly 3 times the value of the ground state, and the bifurcation tunneling splitting is 1.8 GHz, over 2 times the value of the ground state. We compare the existing experimental spectra with calculations on state-of-the-art intermolecular potential energy surfaces and critically review the vibrational assignments reported in the literature. We show that the discrepancy between theory and experiment regarding the assignment of the feature near 103 cm⫺1 can be resolved by considering E 2 →E 1 transitions, which had not been considered previously. © 2003 American Institute of Physics. 关DOI: 10.1063/1.1614774兴
I. INTRODUCTION
determination of a rigorously accurate water dimer potential is the most important step towards the construction of an accurate ‘‘universal’’ force field model for liquid water. Toward this end, a large collection of intermolecular vibration– rotation–tunneling 共VRT兲 spectra of the dimer have been acquired, sampling both ‘‘high-lying’’ 共⬎20 cm⫺1兲 rotational and ‘‘low-lying’’ 共⬍1000 cm⫺1兲 intermolecular vibrational states, which are of central importance for testing of intermolecular potential energy surfaces 共IPSs兲. Concurrently, much progress has been made in the actual development of such intermolecular potentials. In particular, three potentials of spectroscopic accuracy have now been determined from the combination of ab initio and spectroscopic data, VRT共ASP-W兲III,7 SAPT-5st,8 and MCY-5f.5 A detailed comparison of calculated VRT energy states with new experimental results provides a further test of these new IPSs. Furthermore, there has been some confusion regarding assignments of certain intermolecular vibrations; in particular, the feature near 103 cm⫺1 assigned to the K a ⫽0 levels of the in-plane-bend 共IPB兲 vibration by Braly et al.9 has represented a troubling discrepancy between theory and experiment.
Water clusters have been objects of intense scrutiny by both modern theory and experiment, serving as paradigms for systematically untangling intricate details of the hydrogen bond network that underlies the remarkable properties of liquid and solid water.1,2 The systematic investigation of pure water clusters by the combination of laser spectroscopy and theory has characterized the most stable arrangements of two through six water molecules in detail and those of larger clusters more qualitatively.1 The principal goal in these studies of small water clusters has been to develop an exact description of the intricate details of the hydrogen bond network and its dynamics. This objective is close to realization in the case of the dimer, wherein complete descriptions of both the intermolecular and intramolecular dynamics have been incorporated into a theoretical formalism which was subsequently used to fit the spectroscopic data3–5 in terms of highly detailed potential energy surfaces. Two-body forces account for ⬃75% of the total interaction energy of water clusters larger than the dimer6 and liquid; accordingly, the a兲
Author to whom correspondence should be addressed.
0021-9606/2003/119(17)/8927/11/$20.00
8927
© 2003 American Institute of Physics
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
8928
Keutsch et al.
J. Chem. Phys., Vol. 119, No. 17, 1 November 2003
FIG. 1. Equilibrium structure of the water dimer as determined from the VRT共ASP-W兲III surface. The calculation used fixed monomers with ⬔HOH⫽104.52° and R OH⫽0.9572 Å. The structure has C S symmetry and the calculated interoxygen distance is R OO⫽2.978 Å 共Ref. 20兲. One water molecule acts as a single hydrogen bond donor and the other as a single hydrogen bond acceptor. The distinctly nonrigid structure undergoes a number of large-amplitude vibrations and tunneling motions that exchange the protons of the acceptor 共AS兲, donor 共BT兲, or interchange the roles of the acceptor and donor molecules 共I兲.
II. BACKGROUND: SPECTROSCOPY OF THE WATER DIMER
The water dimer is a highly nonrigid near-prolate top 共Fig. 1兲, and high-resolution spectra of the dimer reveal splittings of each rotation–vibration transition that result from large-amplitude tunneling motions 共Fig. 2兲,9–15 which connect eight degenerate minima on the six-dimensional IPS via three low-barrier tunneling motions. A correlation diagram for the VRT levels of the water dimer and transitions reported here is shown in Fig. 3.9,10,13,15 These tunneling motions, which manifest themselves in spectral splittings and shifts, reflect the overall topography of the IPS and not just the minima in which the vibrational wave functions are primarily localized. Thus they provide a very sensitive test of a given potential energy surface.
FIG. 3. Ground-state energy level diagram of (H2 O) 2 is shown together with the observed transitions. The dashed arrows represent c-type transitions 共or possibly b-type in the case of the E 1 states兲 and the solid arrows a-type transitions. The solid arrowheads represent unambiguous assignments and the open arrowheads correspond to the 4295-GHz band, which has two possible assignments. Note the close vicinity of the ground-state K a ⫽0 and K a ⫽1 levels of the 2s. This is also the case for the lowest tunneling level of the 2s in the excited state.
A. Tunneling dynamics
1. Acceptor switching
Acceptor switching 共AS兲 consists of a tunneling motion that exchanges the hydrogens in the acceptor molecule. This motion does not break the hydrogen bond and has the lowest barrier of all tunneling pathways, estimated at 154 cm⫺1 by Goldman et al.7 on the VRT共ASP-W兲III surface and 222 cm⫺1 by Groenenboom et al.4 on the SAPT-5st surface. This motion splits each (H2 O) 2 /(D2 O) 2 rovibrational level by ca. 140–280 GHz/18 –53 GHz into two levels labeled A 1 /B 1 , and A 2 /B 2 共Fig. 2兲. 2. Interchange
FIG. 2. Correlation diagram for the rotation–tunneling states of (H2 O) 2 are shown for K a ⫽0. The magnitudes of the tunneling splittings are not to scale. Acceptor switching tunneling, AS, splits each rovibrational level by ca. 280 GHz into two levels labeled A 1 /B 1 and A 2 /B 2 . This tunneling splitting has not been directly determined from experimental observations. Interchange tunneling I splits each of these levels into 4, the E states being degenerate. Bifurcation tunneling, BT, shifts the energy levels and is ca.⫻100 larger than for (D2 O) 2 . The difference between the band origin of the 1s, (1s), and the band origin commonly used in the literature ¯ (1s) is indicated. The latter band origin has been used, as the E states usually have not been calculated.
Tunneling along this pathway interchanges the role of the donor and acceptor monomers and is the second most facile tunneling motion, with a barrier estimated at 229 cm⫺1 on VRT共ASP-W兲III 共Ref. 7兲 and 248 cm⫺1 on SAPT-5st 共Ref. 4兲. For J⫽0, K a ⫽0, this motion splits each of the A 1 /B 1 and A 2 /B 2 levels of (H2 O) 2 /(D2 O) 2 by ca. 11–23 GHz/0.5–1.2 GHz into three states labeled A 1 /E 1 /B 1 共henceforth referred to as 1s) and A 2 /E 2 /B 2 共henceforth referred to as 2s) 共Fig. 2兲. It should be pointed out that from a group theoretical point of view there is no distinction between E 1 and E 2 levels, and these act merely as labels. Participation of tunneling along both a geared 共G兲 and antigeared 共AG兲 interchange 共I兲 tunneling pathway was suggested by Coudert and Hougen.16 This could account for the observed difference between the interchange splittings of the A 1 /B 1 and A 2 /B 2 levels. However, the importance of the antigeared tunneling pathway is unclear as it was not found on the VRT共ASP-W兲 surface, even though the difference in the A 1 /B 1 and A 2 /B 2 interchange splittings are reproduced.3
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
J. Chem. Phys., Vol. 119, No. 17, 1 November 2003
3. Bifurcation
Bifurcation tunneling 共BT兲 involves the exchange of the hydrogens/deuteriums of the donor molecule and corresponds to the pathway with the highest barrier and smallest effect on the spectrum. The barrier has been calculated to be 430 cm⫺1 on the VRT共ASP-W兲III 共Ref. 7兲 and 685 cm⫺1 on SAPT-5st 共Ref. 4兲. The result of this tunneling motion 共see Fig. 2兲 is a shift of each energy level by ca. 690–750 MHz/ 6 –7 MHz in the ground state of (H2 O) 2 /(D2 O) 2 , and for the latter the shifts are beyond the precision of current calculations. B. Coriolis interactions
In the vibrational ground state of (H2 O) 2 , the 2s of K a ⫽1 are very close in energy to the 2s of K a ⫽0. As K a is not a good quantum number, states with the same overall symmetry are allowed to mix if they have the same J rotational quantum number. A model was proposed which couples the vibrational angular momentum with the overall rotation of the complex.9 This Coriolis perturbation results in characteristic shifts of all the transitions involving the 2s of K a ⫽0 of (H2 O) 2 and half of the asymmetry doublets of the 2s of K a ⫽1. Although the spectra are complicated by the Coriolis interaction, the characteristic appearance of the perturbation can aid in the identification and assignment of (H2 O) 2 spectra. C. Group theory considerations
The group theoretical treatment and selection rules of the tunneling water dimer have been described in detail and the ⫺ ⫹ ⫺ ⫹ ⫺ allowed transitions are A ⫹ 1 ↔A 1 , A 2 ↔A 2 , B 1 ↔B 1 , ⫹ ⫺ ⫹ ⫺ 10–16 From the selection rules, it B 2 ↔B 2 , and E ↔E . follows that tunneling results in a splitting of each rovibrational transition into six components, which typically appear as two sets (1s and 2s) of three more closely spaced transitions 共e.g., A 1 /E 1 /B 1 ). The relative intensities are determined by the nuclear spin weights, which for ⫺ ⫹ ⫺ ⫹ ⫺ (D2 O) 2 /(H2 O) 2 are A ⫹ 1 /A 1 共21/1兲, A 2 /A 2 共3/3兲, B 1 /B 1 ⫹ ⫺ 9,15 ⫹ ⫺ 共15/0兲, B 2 /B 2 共6/6兲, and E /E 共18/3兲. There exist vibrations of two different (C S) symmetries: symmetric (A ⬘ ) vibrations and antisymmetric (A ⬙ ) vibrations, which correspond to vibrations that break the plane of symmetry of the dimer. The symmetry of the states with a given J and K a in an A ⬘ vibration are the same as in the vibrational ground state 共GS兲 共see Fig. 3兲. The symmetry label 共e.g., A ⫹ 1 ) of the states with a given J and K a in an A ⬙ vibration are the same as those for J(A ⬙ )⫽ 兩 J(GS)⫺1 兩 共odd and even J兲 of the GS. Vibrational transitions from the GS to an excited state with A ⬘ symmetry have allowed a-type (⌬K a ⫽0) and c-type (⌬K a ⫽⫾1) components, whereas those to an excited state with A ⬙ symmetry only have b-type (⌬K a ⫽⫾1) components. From a practical point of view, the (H2 O) 2 spectra have proved more difficult to identify and assign. In the ⫺ ⫹ ⫺ A⫹ 1 /B 1 and B 1 /A 1 spectra of (H2 O) 2 every other line is missing due to the zero statistical weights of B 1 levels. These sparse spectra are more difficult to identify within a dense data set. (H2 O) 2 also exhibits much larger tunneling splittings, such that the spectra of a single intermolecular vibra-
Water dimer
8929
tion may require measurements with several far-infrared 共FIR兲 lasers to be fully characterized. Finally, intermolecular vibrations of (H2 O) 2 occur at higher frequencies than (D2 O) 2 , where strong FIR laser lines are more sparse. III. EXPERIMENT
The Berkeley terahertz spectrometer used in the observations of the water dimer transitions reported here has been described previously and, thus, only a brief summary of the experiment will be presented here. A high-power 共85 W兲, line-tunable, infrared CO2 laser coaxially pumps a fixedfrequency FIR molecular gas laser, the output of which is coupled onto a 1T24 Schottky barrier diode. The two lasers used for the work described here were the 70-m 共4.251 676 36 THz兲 CH3 OH and 72-m 共4.158 915 8 THz兲 13 CH3 OH lasers. The fundamental, first, or second harmonic of a HP8367B microwave synthesizer is coupled via an antenna onto the Schottky barrier diode and the nonlinear properties of the diode mix the microwave and THz radiation, creating tunable sidebands with frequencies of (laser) ⫾ (microwave). The sidebands, which are tunable ⫾2 cm⫺1 around each laser, are separated from the carrier frequency, multipassed in the throat of a pulsed planar supersonic expansion and detected on an unstressed germanium/ gallium photoconductive detector. The pulsed molecular beam is produced by expanding pure argon saturated with H2 O or D2 O through a 101.6-mm-long slit at a repetition rate of 33 Hz while maintaining the vacuum chamber at approximately 35 mTorr with a Roots blower 共Edwards EH4200兲 backed by two rotary pumps 共Edwards E2M275兲. IV. RESULTS AND DISCUSSION A. Rotation tunneling assignments and fit
1. (H2O)2
Altogether, 137 new H2 O cluster transitions were observed, and 64 of these were assigned 共see Fig. 4 and Table I兲 to parallel a-type, K a ⫽0←0, K a ⫽1←1, and perpendicular c-type, K a ⫽0←1, K a ⫽1←0, bands of the dimer. P(1) transitions obviously only occur in K a ⫽0←1, and K a ⫽0←0 subbands and the former have no R(0) transitions, whereas the latter have no Q branches. Together with the known energy differences of transitions of K a ⫽0 and K a ⫽1 levels terminating in the identical upper states 共combination differences兲, this suffices to verify the assignment of ⫹ ⫺ ⫹ the A ⫺ 2 /B 2 and B 2 /A 2 K a ⫽0←1 and K a ⫽0←0 subbands. Unfortunately, no K a ⫽0←0 transitions of the E 2 states were observed and the P P 1 (1) transition of the 4261-GHz K a ⫽0←1 subband of the E 2 levels is located in a gap of the scanning range of the spectrometer. However, the assignment is consistent, as combination differences demonstrate that the 4261-GHz subband involves K a ⫽1 E 2 states and the band is located between the corresponding A- and B-state subbands, which is expected. The only other E-state subband, at 4295 GHz 共identified via the characteristic intensity pattern兲 is located at higher energy than the A- and B-state subbands, which is possible but not common. The assignment of the 4212-GHz K a ⫽1←0 Q branch is verified by the characteristic Coriolis shifts that are the fin-
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
8930
Keutsch et al.
J. Chem. Phys., Vol. 119, No. 17, 1 November 2003
FIG. 4. Overview of all observed (H2 O) 2 transition together with the assigned transitions. The symmetry labels correspond to the label of the ground-state levels that the transitions are originating from. The left middle ⫹ inset shows the R Q 0 B ⫺ 2 /A 2 Q branch and the left top inset shows an experimental scan of the R Q 0 (3) and R Q 0 (4) transitions of this subband. The right middle inset shows the ⫹ P Q1 A⫺ 2 /B 2 Q branch and the right top inset shows an experimental scan of the P Q 1 (3) transition.
⫹ gerprint of the GS B ⫺ 2 /A 2 levels. It is highly unlikely that transitions exhibiting the exact 共in this case to within 1 MHz兲 shifts of the vibrational ground state could arise as a result of a combination of perturbations in ground and excited states. This assignment is further verified by observation of combination differences with K a ⫽1←1 transitions terminating in identical upper states. From the relative intensities of the transitions of the Q branch of the 4295-GHz subband, it is clear that it has E symmetry. Furthermore, the fact that it is free from any perturbation shows that it either is a E 1 K a ⫽1←0 subband or a E 2 K a ⫽1←1 subband arising from the lower 共unperturbed兲 component of the asymmetry doublet. It is unlikely that the transitions correspond to a E 2 K a ⫽0←1 band, as this would require the existence of an additional vibrational level. It should also be noted that transitions arising from the K a ⫽1 states of the 1s are never observed in our THz experiments, as they have very low intensities due to their low population. Unfortunately, no combination differences, which could easily distinguish the two cases mentioned above, were observed. All water dimer transitions were fit with the following energy expressions typical for near prolate rotors:
K a ⫽0: 0兲 ⫹B 共 0 兲 J 共 J⫹1 兲 E 共 A ⫾ /B ⫾ 兲 ⫽⫾ 21 共I 0 兲 ⫺ 共BT
⫺D 共 0 兲 关 J 共 J⫹1 兲兴 2 , 0兲 ⫹B 共 0 兲 J 共 J⫹1 兲 ⫺D 共 0 兲 关 J 共 J⫹1 兲兴 2 ; E 共 E ⫾ 兲 ⫽ 共BT
K a ⫽1: 1兲 ⫹B 共 1 兲 关 J 共 J⫹1 兲 ⫺1 兴 E 共 A ⫾ /B ⫾ 兲 ⫽ 共 1 兲 ⫾ 21 共I 1 兲 ⫺ 共BT
⫺D 共 1 兲 关 J 共 J⫹1 兲 ⫺1 兴 2 ⫾ 关共 B⫺C 兲 共 1 兲 /4 ⫺d 共 1 兲 J 共 J⫹1 兲兴 J 共 J⫹1 兲 , 1兲 ⫹B 共 1 兲 关 J 共 J⫹1 兲 ⫺1 兴 ⫺D 共 1 兲 关 J 共 J⫹1 兲 E 共 E ⫾ 兲 ⫽ 共 1 兲 ⫹ 共BT
⫺1 兴 2 ⫾ 关共 B⫺C 兲 共 1 兲 /4⫺d 共 1 兲 J 共 J⫹1 兲兴 J 共 J⫹1 兲 ,
(1) ⫽band origin of the K a ⫽1 states, I(0,1) ⫽interchange tunneling splitting in K a ⫽0,1, (0,1) BT ⫽bifuraction tunneling splitting in K a ⫽0,1,
B (0,1) ⫽the average of the B and C rotational constants in K a ⫽0,1, D (0,1) ⫽the average of the D 共distortion兲 rotational constant in K a ⫽0,1, d (1) ⫽the average of the d 共distortion兲 rotational constant in K a ⫽1. For the vibrational ground state of (H2 O) 2 , the K a ⫽0 levels and upper asymmetry components of the K a ⫽1 levels of the 2s are very close in energy, resulting in a Coriolis perturbation between levels with identical symmetries. The energy level expression for these states is E⫽ 关 E 共 0 兲 ⫹E 共 1 兲 兴 /2⫾ 关共 E 共 1 兲 ⫺E 共 0 兲 兲 2 /4⫹ 2 J 共 J⫹1 兲 /2兴 1/2, where the E (n) are the conventional unperturbed energy levels given above and is the Coriolis interaction constant. For the fits reported here, the values of of the GS were fixed to the previously determined values, as they could not be fit
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
J. Chem. Phys., Vol. 119, No. 17, 1 November 2003
Water dimer
8931
TABLE I. Assigned transitions of (H2 O) 2 reported here are shown together with the difference between observed and calculated frequencies 共all values are in MHz兲. The symmetry labels correspond to those of the states the transitions are originating in 共also in Fig. 4兲. The symmetry labels of the upper states can be determined form the selection rules. The fits for the two possible assignments of the 4295-GHz subband (E 2 K a ⫽1←1 or E 1 K a ⫽1←0) are both shown in the lowest part of the table 共see Sec. IV A兲. K a ⫽0←0 Transition 4 04←5 05 2 02←3 03 1 01←2 02 0 00←1 01 3 03←2 02 4 04←3 03 5 05←4 04 6 06←5 05 K a ⫽0←1 Transition 4 04←5 14 3 03←4 13 2 02←3 12 1 01←2 11 0 00←1 10 1 01←1 11 2 02←2 12 3 03←3 13 4 04←4 14 5 05←5 15 6 06←6 16 7 07←7 17 8 08←8 18 9 09←9 19 2 02←1 10 3 03←2 11 4 04←3 12 5 05←4 13 6 06←5 14 7 07←6 15 K a ⫽1←0 Transition 1 11←1 01 2 12←2 02 3 13←3 03 4 14←4 04 5 15←5 05 6 16←6 06 7 17←7 07 8 18←8 08
Frequency
⫹ A⫺ 2 /B 2
⌬
4244069.3 4270732.5 4283560.0 4296051.5
B⫹ 2 B⫹ 2 A⫺ 2 B⫹ 2
1.5 ⫺3.2 3.3 1.9
Frequency
⫹ A⫺ 2 /B 2
⌬
4223988.5 4238804.5
B⫹ 2 A⫺ 2
0.4 ⫺2.9
4266803.0 4279920.0 4292009.5 4291200.5 4289989.5 4288396.5 4286439.3 4284116.1
A⫺ 2 B⫹ 2 A⫺ 2 B⫹ 2 A⫺ 2 B⫹ 2 A⫺ 2 B⫹ 2
⫺1.0 ⫺0.2 ⫺0.7 1.7 ⫺1.4 ⫺1.2 5.3 ⫺2.3
Frequency
⫹ B⫺ 2 /A 2
4212700.6 4212922.0 4213220.9 4213565.9 4213927.0 4214277.6 4214594.1 4214860.4
A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2
Frequency
⫹ B⫺ 2 /A 2
⌬
4270654.0 4283797.5 4297008.0 4310212.9
B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2
0.5 ⫺1.3 ⫺1.9 ⫺1.4
Frequency
⫹ E⫺ 2 /E 2
⌬
4222725.5 4235876.0
E⫹ 2 E⫺ 2
1.5 ⫺0.4
4261185.0 4261011.5 4260748.5 4260387.5 4259924.7
E⫺ 2 E⫹ 2 E⫺ 2 E⫹ 2 E⫺ 2
0.4 ⫺0.5 0.1 ⫺0.9 0.0
4285299.5 4296808.5 4308009.0
E⫹ 2 E⫺ 2 E⫹ 2
⫺1.0 0.0 0.8
⌬ 2.0 ⫺0.4 ⫺1.4 ⫺1.2 ⫺0.3 0.5 ⫺0.3 ⫺0.1
K a ⫽1←1 Transition 2 12←2 11 2 12←1 11 3 13←2 12 5 15←4 14
K a ⫽1←1 Frequency
Transition
⫹ E⫺ 2 /E 2
Transition
4295669.4 4295723.5 4295801.6 4295903.5 4296032.7 4296187.8 4296368.5 4296572.2
1 10←1 11 2 11←2 12 3 12←3 13 4 13←4 14 5 14←5 15 6 15←6 16 7 16←7 17 8 17←8 18
E⫺ 2 E⫹ 2 E⫺ 2 E⫹ 2 E⫺ 2 E⫹ 2 E⫺ 2 E⫹ 2
1 11←1 01 2 12←2 02 3 13←3 03 4 14←4 04 5 15←5 05 6 16←6 06 7 17←7 07 8 18←8 08
without correlation. A similar Coriolis term was introduced to the energy expression of the excited vibrational state ⫹ A⫺ 2 /B 2 levels. Table I shows the assigned transitions and the difference between observed and calculated frequencies, and Table II shows the molecular constants determined in the fits.
Frequency
⫹ B⫺ 2 /A 2
⌬
4194867.0 4207416.0 4220134.5 4220497.5 4220979.0 4221521.5 4222073.9 4222592.9 4223039.2 4223388.5 4223616.5 4244795.5 4257077.0 4269209.5 4281175.3
B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2
⫺2.0 ⫺2.0 2.1 1.7 1.7 0.3 ⫺0.9 0.2 0.0 1.7 ⫺0.9 ⫺1.3 2.1 0.4 1.2
4304523.8
B⫺ 2
5.0
Frequency
⫹ B⫺ 2 /A 2
⌬
4199342.8 4224606.5 4236843.5 4261250.7
B⫺ 2 B⫺ 2 A⫹ 2 A⫹ 2
⫺1.1 ⫺0.8 1.6 1.5
K a ⫽1←0 ⫹ E⫺ 1 /E 1 E⫺ 1 E⫹ 1 E⫺ 1 E⫹ 1 E⫺ 1 E⫹ 1 E⫺ 1 E⫹ 1
⌬ ⫺1.2 1.0 1.2 ⫺0.6 ⫺0.7 ⫺0.2 0.7 ⫺0.2
The quality of the fit is demonstrated by the 共1兲 root-meansquare deviation of 1.53 MHz for the 2s, smaller than the experimental linewidth of ca. 3 MHz. For the 1s, a 共1兲 root-mean-square deviation of only 0.79 MHz was observed. The interchange splitting is 56.3 GHz in K a ⫽0 of the ex-
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
8932
Keutsch et al.
J. Chem. Phys., Vol. 119, No. 17, 1 November 2003 TABLE II. Molecular constants and tunneling splittings determined in the fit of the (H2 O) 2 bands reported here are shown 共all values in MHz兲. Also shown are the ground-state constants and tunneling splittings used in the fit 共Ref. 19兲. The value of the band origin determined for K a ⫽1 of the 2s can only be rigorously determined if all tunneling splittings have been determined. Furthermore, the value determined in the fit depends on the value of the bifurcation tunneling splitting in the ground state, which has not been determined directly by experiment. The values used here for the latter correspond to the average of the splitting in K a ⫽0 and 1 in the ground state. The value given in the table for the vibrational band origin of the K a ⫽1 of the 2s assumes that the 4295-GHz band corresponds to E 2 transitions. If the latter band corresponds to E 1 transitions, only the lowest of the three tunneling components of the K a ⫽1 of the 2s is known and the band origin cannot be estimated. 1 uncertainties of fitted constants in parentheses. rms 1.53 MHz 2s/0.79 MHz 1s. ⫺ E⫹ 1 /E 1
K ⬙a ⫽0
K ⬙a ⫽1
K ⬘a ⫽0
K ⬘a ⫽1
I⬙ (0) ⬙BT(0)b B ⬙ (0) D ⬙ (0)
679.3a 6160.600a 0.04995a
⫹ A⫺ 2 /B 2
6167.736a 0.03824a
⫹ E⫺ 2 /E 2
⫹ B⫺ 2 /A 2
19530.91a 746.65a 6166.652a 0.03649a
6164.746a 0.03788a
⬙ (1) I⬙ (1)
18805.14a 16204.84a
⬙BT(1)b B ⬙ (1) D ⬙ (1) d ⬙ (1) ⬙ (B ⬙ ⫺C ⬙ ) (1) /4
⫺746.65a 6153.433a 0.05396a ⫺0.00631a 1594.100a 15.7321a
6152.279a 0.05403a ⫺0.00682a 1508.674a 14.899a
6151.129a 0.05419a ⫺0.00594a 1538.377a 14.459a
⬘ (0) I⬘ (0) ⬘ (0) BT B ⬘ (0) D ⬘ (0)
4271376.2 共0.7兲 56274.7 共1.2兲 1799.9 共0.8兲 5998.9 共0.1兲 0.501 共0.001兲
6094.9 共0.2兲 0.124 共0.007兲
5933.7 共0.1兲 ⫺0.107 共0.003兲
⬘ (1) I⬘ (1)
⬘ (1) BT B ⬘ (1) D (1) d ⬘ (1) ⬘ (B ⬘ ⫺C ⬘ ) (1) /4
4302512.4 共0.7兲
6188.51 0.0517 共0.0008兲 0d 15.0d
4313686.1 共1.3兲c 171884 共3兲c 0/not determinable 6146.4 共0.1兲 0.084 共0.001兲 0d ⫺3078 15.0d
6135.4 共0.1兲 0.0490 共0.001兲 0d 15.0d
a
Fixed from Ref. 19. ⬙ (0,1) determined as the average of the splitting in K a⬙ ⫽0 and 1. BT c If the 4295-GHz subband corresponds to E 2 transitions, otherwise not determinable. d Fixed. b
cited state of (H2 O) 2 , nearly 3 times the value of the ground state, and the bifurcation tunneling splitting is 1.8 GHz, over 2 times the value of the GS. If the 4295-GHz subband corresponds to E 2 transitions, the interchange splitting is 171.9 GHz, ca. 9 times that of the GS. ⫹ It should be noted that the upper-state A ⫺ 2 /B 2 levels of K a ⫽1 are slightly lower in energy than those of K a ⫽0. The ⫹ Coriolis shift of the K a ⫽0 A ⫺ 2 /B 2 levels towards higher energy, reflected in the sign of , is consistent with the existence of a perturbing level at slightly lower energy, almost certainly the presently unobserved higher-energy component ⫹ of the asymmetry doublet of the K a ⫽1 A ⫺ 2 /B 2 levels. 2. (D2O)2
Altogether, 25 (D2 O) 2 transitions between 140.5 and 145.5 cm⫺1 were identified. These weak (D2 O) 2 VRT transitions overlap with a very intense (D2 O) 4 and weak (D2 O) 3 vibrational band, making the spectral region very congested. Together with the fact that dimer spectra are comparatively sparse, no further assignments and positive identification of
(D2 O) 2 transitions were possible, although experiments with mixtures of D2 O with increasing H2 O content indicate that several other transitions also arise from (D2 O) 2 . In the entire spectral region between 140.5 and 145.5 cm⫺1, only one (D2 O) 2 Q branch was observed at ca. 4115 GHz. The intensity pattern of the Q branch indicates that it has E symmetry; however, no combination differences were observed and thus no assignment is currently possible. Two a-type K a ⫽0←0 subbands were observed and fit 共see Table III兲. Although no P(1) transitions were observed, we are certain of the assignment of both the rotational quantum numbers and assignment to an a-type K a ⫽0←0 transitions, as we will briefly explain here. For (D2 O) 2 subbands 关and unperturbed (H2 O) 2 subbands兴, the second differences between observed transitions „e.g., 关 R(J⫹2)⫺R(J⫹1) 兴 ⫺ 关 R(J⫹1)⫺R(J) 兴 … are a very good estimate of 2⌬B⫽2(B (n) ⬘ ⫺B (n) ⬙ ). As the GS B (0) ⬙ and B (1) ⬙ constants are all close to 5432 MHz, this allows a good estimate of B ⬘ even without knowledge of the rotational assignments. The first difference can be estimated as R(J)⫺R(J⫺1)⫽2B ⬙ ⫹2(J⫹1)⌬B and P(J⫺1)⫺ P(J)
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
J. Chem. Phys., Vol. 119, No. 17, 1 November 2003
Water dimer
8933
TABLE III. Assigned transitions of (D2 O) 2 reported here are shown together with the differences between observed and calculated frequencies 共all values are in MHz兲. The assignment of the tunneling symmetry is based on relative intensities and the results of the fit, but remains uncertain. As a result of this uncertainty, the determination of tunneling splittings and other molecular constants is not rigorous. The range of values of ⌬B ⬘ is also shown. K a ⫽0←0 Transition 6 06←7 07 5 05←6 06 4 04←5 05 3 03←4 04 2 02←3 03 1 01←2 02 1 01←0 00 2 02←1 01 3 03←2 02 4 04←3 03 5 05←4 04 7 07←6 06 ⌬B ⬘
Frequency 4204749.48 4215403.00 4226094.84 4236822.00 4247584.20 4290973.12 4301902.68 4312862.64
4356980.76 7.0–7.1
⫹ E⫺ 2 /E 2
⌬
E⫹ 2 E⫺ 2 E⫹ 2 E⫺ 2 E⫹ 2 E⫺ 2 E⫺ 2 E⫹ 2 E⫺ 2
1.3 ⫺0.9 ⫺0.1 0.7 1.3
E⫺ 2
⫺0.5
⫽2B⬙⫺2(J⫺1)⌬B. With ⌬B determined from the second differences, this allows an assignment of the rotational J quantum number from the first difference, which can easily be verified. Thus we are readily able to identify R(0) transitions, which, together with combination differences, rules out that transitions are originating in K a ⫽1. The assignment to a-type K a ⫽0←0 rather than c-type or b-type K a ⫽1←0 transitions is consistent with the lack of Q branches, which would have been easily observable. Unfortunately, we are unable to assign the symmetry labels of the tunneling components for the two subbands. However, even without these, we can estimate ⌬B⫽7.0– 7.1 MHz for the 4267-GHz band and ⌬B⫽15.8– 16.5 MHz for the 4290-GHz subband. Similarly, the less reliable fit of the 4115-GHz Q branch also yields ⌬B of roughly the same magnitude. B. Vibrational assignment
The observation of K a ⫽1←0 and K a ⫽0←1 bands terminating in the same upper states as the a-type K a ⫽0←0 and K a ⫽1←1 transitions shows that the excited vibrational states of (H2 O) 2 reported here have A ⬘ symmetry. The only subband, which could be an exception, is the 4295-GHz subband, as it could be either b type or c type if it corresponds to E 1 transitions. Similarly, the symmetry of the excited vibrational state of the (D2 O) 2 band reported here is A ⬘ , as proved by the observation of a-type K a ⫽0←0 transitions. The assignment of specific vibrational modes beyond this has to rely on the interpretation of relative intensities, changes in rotational constants and tunneling splittings, and comparison with theoretical calculations. In the following, the importance of such a comparison for the validation of existing IPS models will be evident. Traditionally, the intermolecular vibrational modes of the dimer had been assigned following the normal-mode picture first introduced by Reimers and Watts.17 Following this approach, there exist three normal modes of A ⬘ and A ⬙ symmetry each for a total of six intermolecular modes 共see Table IV兲. The limitations of such a normal-mode picture for the water dimer with its large amplitude vibrations is apparent
⫺0.3 ⫺0.5 ⫺1.0
Frequency
⫹ B⫺ 2 /A 2
⌬
4212949.00 4223764.80 4234598.32 4267190.88 4278081.16 4288988.08 4299906.00 4310836.92
B⫺ 2 A⫹ 2 B⫺ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2
⫺0.3 ⫺0.3 0.1 0.7 ⫺1.1 0.7 0.3 ⫺0.2
15.8 –16.5
and the assignment of the vibrational modes until recently has employed the modes in Table IV merely as labels. Leforestier et al.5 and Smit et al.,8 who used a careful analysis of the nodal patterns of the vibrational wave functions, have shown that vibrational overtone and combination bands have to be considered. Figure 5 and Table V show a comparison of the (H2 O) 2 vibrational levels calculated on the VRT共ASPW兲III, SAPT-5st, and VRT共MCY-5f兲 surfaces with the experimentally determined ones. Theoretical calculations generally agree well on the ordering of the vibrational and tunneling levels. Differences in assignments remain only in the labeling and Goldman et al.7 关VRT共ASP-W兲III兴 assigned the second A ⬘ mode of the 2s of K a ⫽0 to the IPB, whereas Smit et al.8 共SAPT-5st兲 assigned it to the donor overtone 共DT兲2 and Leforestier et al.18 关VRT共MCY-5f兲兴 assigned it to the hydrogen bond stretch 共S兲. Here we will follow the labeling by Smit et al. for the experimental levels. A comparison shows that the agreement of the calculated levels with experiment is good for all three models 共see Table V兲. The VRT共ASP-W兲III values are generally too high and the 2s of K a ⫽0 of the DT are in worse agreement with experiment TABLE IV. Harmonic frequencies of the water dimer normal modes calculated on the SAPT-5st surface 共Ref. 8兲.
Mode Donor torsion 共DT兲 Acceptor twist 共AT兲 Acceptor wag 共AW兲 Hydrogen bond stretch 共S兲 In-plane bend 共IPB兲 Out-of-plane bend 共OPB兲 a
Frequency 关cm⫺1兴a (H2 O) 2 /(D2 O) 2 121.01/88.07 143.70/102.87 157.87/118.52 186.83/172.84 369.99/274.76 564.70/406.11
From Ref. 8.
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
8934
Keutsch et al.
J. Chem. Phys., Vol. 119, No. 17, 1 November 2003
FIG. 5. Comparison of all experimentally observed vibration–tunneling levels 共in cm⫺1兲 together with those calculated by Goldman et al. 共Ref. 7兲 on the VRT共ASP-W兲III surface, Smit et al. 共Ref. 8兲 on SAPT-5st, and Leforestier et al. 共Ref. 5, 18兲 on the VRT共MCY-5f兲 surface. The experimental levels are shown for J⫽1 共to show where Coriolis resonances can occur兲, whereas the calculated ones are for J⫽0 for K a ⫽0 and J⫽1 for K a ⫽1. Solid lines correspond to A ⬘ vibrational levels and dashed lines to A ⬙ vibrational levels. The nomenclature of the vibrational modes follows Table V, and 共DT兲2 refers to the donor torsion overtone transition. UK 共labeled with solid circles兲 refers to the vibration–tunneling level previously assigned to the K a ⫽0 IPB by Braly et al. 共Ref. 9兲. The two levels corresponding to the two possible vibrational assignments of the 4295-GHz band are labeled with solid diamonds. The theoretical calculations have the same ordering of vibration tunneling levels and also agree well with the experimental ones, except for the UK level, as discussed in the text.
than those of the other potentials, as are the 2s of K a ⫽0 reported here 关Fig. 5: labeled as IPB for VRT共ASP-W兲III兴. The acceptor wag 共AW兲 共best agreement of the three potentials兲 and acceptor twist 共AT兲 levels agree very well with the experimental ones. The levels calculated on SAPT-5st are also generally too high, but also agree well with experiment except for the AW K a ⫽0 levels, which are higher in energy than the experimental and other calculated ones. The
VRT共MCY-5f兲 values have the best agreement with experiment and do not show a clear trend of being either too high or too low. For all (H2 O) 2 subbands reported here, except for the 4295-GHz one, comparison with the calculated vibrational tunneling levels argues that the levels reported here correspond to the 2s of K a ⫽0 of 共DT兲2 共following the mode assignments by Smit et al.兲 and the 2s of K a ⫽1 of S. If the
TABLE V. Comparison between experimental and calculated energy levels 共in cm⫺1兲 shows that the calculated VRT共MCY-5f兲 energies have the best agreement with experiment. K a ⫽0 energy levels were chosen as K a ⫽1 levels are not available for some of the potentials. ⌬ is the difference between calculated and experimental band origins. The band origins are defined as the average of the energy difference between the excited vibrational state and GS A 1 /B 1 or A 2 /B 2 pairs. The difference between that definition and the one given in Table II is indicated in Fig. 2. The value of AS cannot be determined experimentally and thus the calculated values were subtracted for the 2s. 共Note that errors of the VRT共MCY-5f兲 are close to the error of using v ⫽300 000 km/s for the speed of light in vacuum兲. Band origin 2s of 1s of 2s of 2s of 2s of rmsa
K a ⫽0 DT K a ⫽0 AW K a ⫽0 AW K a ⫽0 AT K a ⫽0 共DT兲2
Experiment 53.34b 107.93c 97.71c 109.01c 142.44d
VRT共ASP-W兲III 共⌬兲e 62.61共9.27兲 108.17共0.24兲 99.93共2.22兲 110.35共1.34兲 152.65共10.21兲 6.3
SAPT-5st 共⌬兲f 53.17共⫺0.17兲 113.39共5.46兲 110.57共12.86兲 109.79共0.78兲 145.28共2.84兲 6.4
VRT共MCY-5f兲 共⌬兲g 51.95共⫺1.36兲 104.32共⫺3.61兲 96.94共⫺0.77兲 109.93共0.92兲 142.63共0.19兲 1.8
rms⫽ 冑1/N ⌺( obs⫺ calc) 2 . From Ref. 21. c From Ref. 9. d This work. e From Ref. 7. f From Ref. 22. g From Ref. 18. a
b
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
J. Chem. Phys., Vol. 119, No. 17, 1 November 2003
4295-GHz band corresponds to E 1 transitions, the excited level of this subband would correspond to the 1s of K a ⫽1 of 共DT兲,2 and if it corresponds to E 2 transitions, the excited state would correspond to the 2s of K a ⫽1 of S. Figure 5 shows that a comparison with the calculated energy levels does not aid in distinguishing which of these assignments is correct. Commonly, the analysis of rotational constants and tunneling splittings is used to aid in the analysis of the vibrational motions. However, the rotational constants of the 2s of K a ⫽0 reported here are severely Coriolis contaminated and thus do not allow structural interpretations. Comparison of the nuclear displacements of a specific vibration with the tunneling pathways can allow estimates of the expected change in tunneling splitting on excitation of this vibration. For example, the motion of the donor water molecule in the AS tunneling pathway resembles the DT vibrational displacements, consistent with dramatic increase of the AS splitting in the DT vibrational state. Similarly, the motion of the acceptor water in the AS tunneling pathway resembles the AW vibrational displacements. However, experimentally, a significant decrease of the AS splitting is observed on excitation of the AW vibration. Furthermore, the I tunneling splitting of the 1s of the 共DT兲2 vibration on the SAPT-5st surface is very different from that of the 2s. This demonstrates that for the water dimer, observed changes in tunneling splittings can only assist in vibrational assignment through comparison with theoretical results, rather than deductions based on nuclear displacements. Last, the observed relative intensities can aid in the vibrational assignment. The experimental c-type K a ⫽0←1 (DT兲2 transitions are significantly stronger than the a-type K a ⫽0←0 共DT兲2 transitions. Table VI shows a comparison of calculated transition dipole moments for the observed vibrations. The results of Smit et al.8 and Leforestier18 agree well with the biggest difference 共⬃50%兲 observed for K a ⫽1←0 transitions of the 2s. Smit et al. do not calculate intensities for transitions originating in K a ⫽1, but the results of Leforestier—like the experiment—show that the c-type K a ⫽0←1 共DT兲2 transitions are significantly stronger than the a-type K a ⫽0←0 共DT兲2 transitions. The experimental intensity of the 4295-GHz subband is only a little lower than that of the c-type bands discussed above. As mentioned earlier, the unperturbed appearance of this band only allows it to be either a E 1 K a ⫽1←0 subband or a E 2 K a ⫽1←1 subband arising from the lower component of the asymmetry doublet. For the latter case, it is reasonable to assume that the band terminates in the same vibrational state 共S兲 as the observed K a ⫽1←0 transitions. Table VI shows that these are calculated to be very weak—comparable to the K a ⫽0←0 transitions of the 2s of 共DT兲2. In contrast, the E 1 K a ⫽1 ←0 共DT兲2 transitions have a magnitude between the 共both experimentally and calculated兲 strong K a ⫽0←1 and weak K a ⫽0←0 transitions transitions of the 2s of 共DT兲2. This would argue that it is more likely that the 4295-GHz subband corresponds to E 1 K a ⫽1←0 共DT兲2 transitions. A new and expanded perspective can now be employed to reevaluate the nature of the levels previously referred to as ⫹ IPB by Braly et al.9 The A ⫺ 2 /B 2 K a ⫽1 states, the lowestenergy tunneling component of the 2s, and the only pres-
Water dimer
8935
TABLE VI. Calculated transition dipole moments 共in ea 0 ) of Smit et al. 共Ref. 8兲 and Leforestier 共Ref. 18兲 are shown for observed vibrational energy levels of (H2 O) 2 including the proposed E 2 →E 1 transitions of the DT 共UK兲 band. A comparison with experimental work is not shown due to the large variation of experimental conditions such as the intensity of the FIR laser line. Most of the experimental intensities reported by Braly et al. 共Ref. 9兲 were measured with older pulsed source technology. The bands reported here were observed with the new pulsed source on a weak laser line. The UK band was observed under more sensitive conditions with the new pulsed source technology and a strong laser line by Braly et al. 共Ref. 9兲 and at the time reported as IPB. Vibration
AW
共DT兲2
DT AW
共DT兲2
S
DT 共UK兲
State
Smit et al.a
Leforestierb
Leforestierb
⫹ A⫺ 1 ←A 1 ⫹ A 2 ←A ⫺ 2 ⫺ B⫹ 2 ←B 2 ⫺ A⫹ ←A 2 2 ⫹ B 2 ←B ⫺ 2
J⫽1, K a ⫽0← J⫽0, K a ⫽0 0.212 0.237 0.258 0.023 0.023
J⫽1, K a ⫽0← J⫽0, K a ⫽0 0.206 0.229 0.252 0.035 0.029
J⫽1, K a ⫽0← J⫽1, K a ⫽1 0.168 0.247 0.220 0.073 0.085
J⫽1, K a ⫽1← J⫽0, K a ⫽0 0.228 0.191 0.147 0.074 ⬍c ⬍c 0.221
J⫽1, K a ⫽1← J⫽0, K a ⫽0 0.191 0.192 0.180 0.177 0.056 0.030 0.158
J⫽1, K a ⫽1← J⫽1, K a ⫽1 0.068 0.233 0.263 0.286
0.073 0.077
0.041 0.036
⫹⫺ A⫺ 1 ←A 1 ⫺ A 1 ←A ⫹ 1 ⫺ A⫹ 2 ←A 2 ⫹ B 2 ←B ⫺ 2 ⫹ E⫺ 1 ←E 1 ⫹ E⫺ 2 ←E 1 ⫹ B 2 ←B ⫺ 2 ⫺ E⫹ 2 ←E 2 ⫹ E 1 ←E ⫺ 2 ⫺ A⫹ 2 ←A 2 ⫹ B 2 ←B ⫺ 2 ⫹ E⫺ 1 ←E 2 ⫺ E⫹ 1 ←E 2
P(1) R(1) R(0)
⬍ 0.037 0.024 0.089 0.083
K a ⫽0←K a ⫽0 K a ⫽0←K a ⫽1 0.023 0.030 0.053 0.017 0.007 0.057
a
From Ref. 8. From Ref. 18. c The A 1 and B 1 tunneling symmetries had very small dipole moments; no E states were calculated. b
ently observed K a ⫽1 states of the IPB are consistent with the K a ⫽1 energy level structure calculated on all three model IPSs, and the overall agreement between experiment and theory for K a ⫽1 is quite good. We have accordingly reassigned these levels to the 共DT兲2 mode rather than IPB in light of the vibrational mode analysis by Smit et al. In con⫹ trast, the E ⫺ 2 /E 2 K a ⫽0 states, labeled as UK in Fig. 5 共and previously assigned to IPB by Braly et al.兲, are a cause of concern. All calculations disagree with the assignment of this level to IPB, and the vibrational assignment of this subband has therefore been cast in doubt. Disagreement goes beyond this though 共IPB was being used largely as a label, and thus the disagreement was largely semantic兲, as theoretical calculations do not yield any unassigned level with the correct symmetry. In fact hitherto the lowest unassigned level of the correct symmetry corresponded to the ones we assigned to the new bands reported here, which lie at significantly higher energy. In contrast, the new experimental levels agree well with calculated energy levels 共see Fig. 5兲, and it seems unlikely that instead the UK level corresponds to one of these and the new levels reported here to some vibration that has a
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
8936
Keutsch et al.
J. Chem. Phys., Vol. 119, No. 17, 1 November 2003
much higher calculated energy 共which implies that all calculations are in considerably worse agreement then apparent in Table V or Fig. 5兲. This disagreement thus questions the entire vibration–tunneling level structure of (H2 O) 2 and also the correctness of all model surfaces as they would appear to ‘‘miss’’ a level. However, it is unlikely that the calculations on all three highly sophisticated surfaces with different methods all ‘‘miss’’ a level. The theoretical work would therefore rather imply a misidentified symmetry, as indeed there exist some presently unobserved or at least unassigned vibration– tunneling levels. The only unassigned K a ⫽0 levels are the 1s of DT and of AT, and the only unassigned levels of the 2s are the K a ⫽1 DT levels. The characteristic Coriolis shifts and combination differences of the vibrational ground state observed by Braly et al.9 for this band prove that it is extremely unlikely that the transitions terminating in the UK level do not originate in E 2 K a ⫽1 states. The observation of a P(1) transition similarly proves that the transitions terminate in K a ⫽0 共we have also verified the assignments of all other vibration–tunneling states兲. K a is not a good quantum number and various cases of Coriolis mixing of K a ⫽0 and K a ⫽1 states have been observed. However, no mixing with a K a ⫽0, J⫽0 state is allowed as the mixing levels must have identical J (J⫽0 does not exist for K a ⫽1). In addition, Fig. 5 shows that the only possible E 2 candidate for mixing or even direct transitions is the currently unobserved K a ⫽1 DT level, which is calculated at much lower energy. In a previous section, we have mentioned that symmetry allows transitions between E 1 and E 2 states, but these have never been observed or identified, even though they are of considerable importance, since they would give a direct measure of the acceptor switching splitting. From group theory, it is clear that for this case the UK transitions could only be terminating in K a ⫽0 E 1 states of an A ⬙ vibration. Interestingly, the 1s of DT are calculated to lie close in energy to the observed transition. As the experimental results are unambiguous, we speculate that the spectrum actually corresponds to transitions from K a ⫽1 and 0 E 2 levels of the vibrational ground state to K a ⫽0 E 1 states of DT or, possibly, states which are a mix of K a ⫽0 E 1 DT and K a ⫽1 E 2 DT states 共even though we do not observe a Coriolis perturbation for the excited state, which would be required for a mixed state兲. Leforestier18 has calculated the intensities for all (H2 O) 2 transitions from J⫽0,1 and K a ⫽0,1 up to 200 cm⫺1 and up to K a ⫽2 for all tunneling symmetries 共see some results in Table VI兲. The intensities of the E 2 →E 1 transitions vary significantly depending on the excited vibrational level. However, many of the transitions originating in E 2 states and terminating in E 1 states—in particular of K a ⫽0 of DT—have intensities that are comparable or stronger than those of the donor torsion overtone reported here 共recorded with a weaker laser line兲 and circa 401 of the strongest of all calculated vibrational transitions 共as judged by the line strength, which is proportional to the square of the transition dipole moment兲. As the strongest experimentally observed dimer transitions have a signal-to-noise ratio Ⰷ103 with pulsed source technology, the explanation suggested above for the UK energy level is quite probable. This also agrees well with the fact that despite intense experimen-
tal efforts, no A or B symmetry components, which otherwise would have to be in the vicinity of the E-state transitions, have been observed.9 The fact that no other E 2 →E 1 transitions have yet been reported may appear troubling. However, it is likely that other such transitions have indeed been observed, but so far not identified, and remain as unassigned transitions, as the assignments proposed here had never before been considered. If we accept the new solution offered above, the assignment of the bands reported here and shown in Fig. 5 is consistent with the theoretical calculations. The vibrational assignment of the (D2 O) 2 bands is more difficult due to the small available data set. The lowest unassigned K a ⫽0 levels of an A ⬘ vibration are the 2s of 共DT兲2 and the hydrogen bond stretch (1s and 2s). The former are predicted to have very low intensity. Furthermore, they are calculated to occur at significantly lower energy on VRT共ASP-W兲III, which otherwise agrees quite well with experiment, and at a little lower energy on SAPT-5st, which also agrees well with experiment except that it produces somewhat higher energies than the experimental ones. The increased B (0) in the upper state, indicative of slight decrease in size, could be expected for the IPB vibration. However, for the DT the 1s show a positive ⌬B and the 2s a negative ⌬B, which highlights the dangers of vibrational assignments based on a structural interpretation of the molecular constants. We therefore tentatively assign the (D2 O) 2 transitions to upper states of the hydrogen bond stretch vibration. Finally, we want to mention that we have also observed some (H2 O) 2 Q-branch transitions at ca. 575 cm⫺1. Although we are certain of the carrier of the transitions, our current experiment does not permit assignment of these extremely weak spectra. It is possible that they belong to the out-of-plane liberation, although the large density of states at these energies requires a detailed analysis before any assignments could be made, even with a complete dataset.
V. CONCLUSIONS
We report the highest-frequency intermolecular vibrational bands of the water dimer observed to date. We assign the (H2 O) 2 bands to an overtone of the donor torsion (K a ⫽0) and the hydrogen bond stretch of the 2s acceptor tunneling states (K a ⫽1). One (H2 O) 2 subband at 4295 GHz either corresponds to E-state transitions to the 2s of the hydrogen bond stretch (K a ⫽1) or E-state transitions of the 1s of the donor torsion overtone (K a ⫽1). We tentatively assign the (D2 O) 2 transitions to K a ⫽0 of the hydrogen bond stretch with currently unknown tunneling symmetry. The observation of the K a ⫽0 levels of the 2s reported here raises the question as to which vibrational level the experimental UK 共IPB of Braly et al.兲 level corresponds to. This problem had not been addressed appropriately before 共even though it is crucial for achieving consistency between experiment and theory兲, and we suggest that it arises from transitions originating in E 2 levels and terminating in E 1 levels of K a ⫽0 of DT. These transitions had not been considered in previous work, but the verification of the symmetry label assignments, the newly available calculated transi-
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
J. Chem. Phys., Vol. 119, No. 17, 1 November 2003
tion dipole moments, and the fact that no accompanying Aor B-state transitions have been observed in the spectra are strong evidence in favor of this argument. However, it is apparent that further investigation is still necessary, and its importance cannot be overstated. The assignment of UK to the 1s of DT requires further verification 共via observation of transitions originating in the 1s), which simultaneously would give a direct measurement of the AS splitting. We hope that this work will stimulate further collaboration between theoretical and experimental groups. Further experimental efforts are also necessary to identify the missing tunneling components of the vibrational bands reported here to complete the characterization of the (H2 O) 2 and (D2 O) 2 hydrogen bond stretching and donor torsion overtone vibrations. The spectral regions where these transitions are expected are inaccessible with the present THz VRT spectrometer. Implementation of new microwave and millimeter wave sources is required for accessing these regions.
ACKNOWLEDGMENTS
This work was supported by the Experimental Physical Chemistry program of the National Science Foundation. The authors thank Professor Ad van der Avoird for many helpful discussions.
Water dimer
8937
1
F. N. Keutsch and R. J. Saykally, Proc. Natl. Acad. Sci. U.S.A. 98, 10 533 共2001兲. 2 A. J. Huneycutt and R. J. Saykally, Science 299, 1329 共2003兲. 3 R. S. Fellers, C. Leforestier, L. B. Braly, and M. G. Brown, and R. J. Saykally, Science 284, 945 共1999兲. 4 G. C. Groenenboom, E. M. Mas, R. Bukowski, K. Szalewicz, P. E. S. Wormer, and A. van der Avoird, Phys. Rev. Lett. 84, 4072 共2000兲. 5 C. Leforestier, F. Gatti, R. S. Fellers, and R. J. Saykally, J. Chem. Phys. 117, 8710 共2002兲. 6 M. P. Hodges, A. J. Stone, and S. S. Xantheas, J. Phys. Chem. A 101, 9163 共1997兲. 7 N. Goldman, R. S. Fellers, M. G. Brown, L. B. Braly, C. J. Keoshian, C. Leforestier, and R. J. Saykally, J. Chem. Phys. 116, 10 148 共2002兲. 8 M. J. Smit, G. C. Groenenboom, P. E. S. Wormer, A. van der Avoird, R. Bukowski, and K. Szalewicz, J. Phys. Chem. A 105, 6212 共2001兲. 9 L. B. Braly, K. Liu, M. G. Brown, F. N. Keutsch, R. S. Fellers, and R. J. Saykally, J. Chem. Phys. 112, 10314 共2000兲. 10 T. R. Dyke, J. Chem. Phys. 66, 492 共1977兲. 11 T. R. Dyke, K. M. Mack, and J. S. Muenter, J. Chem. Phys. 66, 498 共1977兲. 12 J. T. Hougen, J. Mol. Spectrosc. 114, 395 共1985兲. 13 G. T. Fraser, Int. Rev. Phys. 10, 189 共1991兲. 14 L. B. Braly, Ph.D. thesis, University of California at Berkeley, 1999. 15 L. B. Braly, J. D. Cruzan, K. Liu, R. S. Fellers, and R. J. Saykally, J. Chem. Phys. 112, 10293 共2000兲. 16 L. H. Coudert and J. T. Hougen, J. Mol. Spectrosc. 130, 86 共1988兲. 17 J. R. Reimers and R. O. Watts, Chem. Phys. 85, 83 共1984兲. 18 C. Leforestier 共personal communication兲. 19 F. N. Keutsch, H. A. Harker, N. Goldman, E. Karyakin, and R. J. Saykally 共unpublished兲. 20 N. Goldman 共personal communication兲. 21 R. J. Saykally 共personal communication兲. 22 G. C. Groenenboom, P. E. S. Wormer, A. van der Avoird, E. M. Mas, R. Bukowski, and K. Szalewicz, J. Chem. Phys. 113, 6702 共2003兲.
Downloaded 28 Apr 2006 to 169.229.32.135. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
