Terahertz laser spectroscopy of the water dimer intermolecular ...

JOURNAL OF CHEMICAL PHYSICS

VOLUME 112, NUMBER 23

15 JUNE 2000

Terahertz laser spectroscopy of the water dimer intermolecular vibrations. II. „H2O…2 L. B. Braly, K. Liu,a) M. G. Brown,b) F. N. Keutsch, R. S. Fellers,c) and R. J. Saykallyd) Department of Chemistry, University of California, Berkeley, California 94720

共Received 24 January 2000; accepted 6 March 2000兲 Terahertz VRT laser spectra of four 共H2O兲2 intermolecular vibrations consisting of 362 transitions have been measured between 87 and 108 cm⫺1 with ca. 2 MHz precision. The results differ both qualitatively and quantitatively from the predictions of dimer potentials tested. The spectra also reveal an ordering of the intermolecular vibrations which differs dramatically from that predicted by normal mode analysis. Strong coupling is indicated between the low barrier tunneling motions and the intermolecular vibrations as well as among different vibrations. In particular the 102.1 cm⫺1 共H2O兲2 vibration assigned as the acceptor wag ( ␯ 8 ) exhibits two types of perturbations. In one of these a component of K a ⫽1 coupling with a tunneling component of K a ⫽0 in the 108 cm⫺1 acceptor twist ( ␯ 11) vibration. There is also an indication that the 103.1 cm⫺1 共H2O兲2 band assigned as the donor in-plane bend ( ␯ 6 ) is coupled to the acceptor wag resulting in a lower of the in-plane bend frequency and a higher acceptor wag frequency. Detailed analysis of the VRT levels confirms the extreme nonrigidity of this complex, indicating that the use of approximate models with reduced dimensionality to calculate its properties are likely to fail. © 2000 American Institute of Physics. 关S0021-9606共00兲00821-7兴

I. INTRODUCTION

In the accompanying paper 共paper I兲 describing our spectroscopic studies of the intermolecular vibrations of 共D2O兲2, the background, requisite group theory, and experimental details are given. Here the results of our corresponding terahertz laser spectroscopy measurements of four intermolecular vibrations of 共H2O兲2 are presented and discussed. Both the measurement and the assignment of 共H2O兲2 spectra are far more difficult than for the case of 共D2O兲2. ⫺ ⫹ ⫺ Every other line is missing from the A ⫹ 1 /B 1 and B 1 /A 1 spectra due to the zero statistical weights of B 1 levels. This, along with the larger rotational constants, produces much more sparse spectra that are more difficult to identify within a dense data set. Moreover 共H2O兲2 exhibits much larger tunneling splittings, such that the spectra of a single intermolecular vibration may require several different FIR lasers to be fully characterized. Intermolecular vibrations of 共H2O兲2 occur at higher frequencies than 共D2O兲2, where strong FIR laser lines are more sparse. Finally, the higher nonrigidity of 共H2O兲2 allows the intermolecular vibrations to be more closely spaced. This, along with the larger tunneling splittings, results in vibrational spectra that are overlapping. As will be seen, four intermolecular vibrations have been measured in this work, but they are not as completely characterized as the four corresponding 共D2O兲2 intermolecular vibrations also reported, and three of them occur very close in frequency. a兲

Department of Chemistry, University of Southern California, Los Angeles, CA. b兲 Department of Chemistry, University of Oregon, Eugene, OR. c兲 Lawerence Livermore National Lab, Livermore, CA. d兲 Author to whom correspondence should be addressed. 0021-9606/2000/112(23)/10314/13/$17.00

There is no experimental determination of the acceptor switching splitting for 共H2O兲2 like that for the 共D2O兲2 performed by Paul et al.1 Only the sum of the K a⬙ ⫽0 and K a⬙ ⫽1 ground state splittings is known to be ⬃411 GHz from the work of Zwart et al.2 This is because the K a⬙ ⫽1 levels of the ‘‘1’s’’ are not populated in rotationally cold molecular beams. These levels are more than 13 cm⫺1 above the K a⬙ ⫽0 levels. Therefore only the change in the acceptor switching can be determined from the following data. The acceptor switching splitting for K a⬙ ⫽0 was estimated using the Local IAM model of Coudert and Hougen to be ⬃280 GHz.2,3 However, from the well-characterized ground state it is found that there is a Coriolis coupling in the ‘‘2’s’’ between K a⬙ ⫽0 and the upper asymmetry component of K a⬙ ⫽1 which makes the combination differences very different for each tunneling component. This makes unambiguous assignment for each tunneling component and K a value possible if most of a VRT spectrum has been observed, unlike the case of 共D2O兲2. Moreover, for the ‘‘1’s’’ the B 1 levels are absent due to a zero nuclear spin statistical weight, providing a unique spectral signature. II. SPIN STATISTICS AND PERTURBATIONS

For the subsequent discussion, it is necessary to give additional group theoretical details specific to 共H2O兲2. The product of the four I⫽1/2 proton nuclear spin functions of 共H2O兲2 generate a (2I⫹1) 4 dimensional representation of ⫹ ⫹ G 16 . This reduces to the direct sum 6A ⫹ 1 ⫹3B 1 ⫹B 2 ⫹3E ⫹ . 共H2O兲2 must have a total wave function which is antisymmetric for odd permutations of protons and symmetric for even permutations; this requires that the total wave ⫺ function has symmetry of B ⫹ 2 or B 2 in G 16 . From this, Dyke4 obtained the statistical weights for the 共H2O兲2 rovi-

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© 2000 American Institute of Physics

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J. Chem. Phys., Vol. 112, No. 23, 15 June 2000

Spectroscopy of the water dimer. II

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⫺ ⫹ ⫺ ⫹ ⫺ bronic species as A ⫹ 1 /A 1 (1), B 1 /B 1 (0), A 2 /A 2 (3), ⫹ ⫺ ⫹ ⫺ ⫹ ⫺ B 2 /B 2 (6), E /E (3); the B 1 ,B 1 energy levels will not be observable, thus generating spectra with ‘‘missing’’ lines. It has been found that A 2 /E 2 /B 2 states with K a ⫽0 and 1 in the ground state are perturbing one another 共within the ‘‘pseudodiatomic approximation’’ each K a level is treated separately兲. A model was proposed by Hu and Dyke5 which coupled the vibrational angular momentum with the overall rotation of the complex, resulting in a b-type Coriolis interaction. Since K a is not a good quantum number, the K a ⫽0 and K a ⫽1 states are allowed to mix if they have the same overall symmetry and same J. This model has the form

W⫾⫽

冋

J 共 J⫹1 兲 关 W 0 ⫹W 1 兴 关 W 1 ⫺W 0 兴 2 ⫾ ⫹␰2 2 4 2

册

1/2

,

where W 0 and W 1 are the unperturbed, conventional energy level expressions W⫽⌬⫹

共 B⫹C 兲 共 B⫺C 兲 J 共 J⫹1 兲 ⫺ J 共 J⫹1 兲 2 4

⫹D j J 2 共 J⫹1 兲 2 . Although a complete deperturbation is still not achieved, this model is effective in that it was possible to obtain rotational constants which were in much better agreement with those of the other unperturbed states. However, a review of the correlation matrix still shows a strong correlation between (B ⫹C)/2, (B⫺C)/4, and ␨, due to the similarity in the dependence on J(J⫹1) for the rotational constants and J 2 (J ⫹1) 2 of the Coriolis interaction constant. Similar perturbations have been observed within the 103.1 cm⫺1 band corresponding to the acceptor wag, and the same model was used to treat these.6 III. RESULTS AND DISCUSSION A. The 87 cmÀ1 band: Donor torsion „ ␯ 12…

Forty-seven perpendicular b-type transitions from the K a⬙ ⫽0 ground state to the K a⬘ ⫽1 upper state have been measured for the three tunneling components of the ‘‘1’s.’’ The stick spectrum is shown in Fig. 1, and the transitions are listed in Table I. Combination differences verified the tunneling assignment, and the presence of Q(1) where possible and in one case the presence of R(1) verified the K a⬘ assignment. A pronounced increase 共⬃50%兲 in the K a⬘ ⫽1 interchange splitting is observed relative to the ground state K a ⫽0. K a ⫽0→I. The 47 measured transitions were fit to a band origin of 2 630 747.8 MHz 共87.7 cm⫺1兲. Table II lists the fitted parameters and Fig. 2 shows the VRT energy level diagram. This vibration has A ⬙ symmetry and is the lowest energy vibration observed thus far for 共H2O兲2. The lowest expected vibration is that corresponding to the donor torsion ( ␯ 12), and the 共D2O兲2 analog was measured near 65 cm⫺1. The interchange splitting was found to be 33.3 GHz as compared to the K a⬙ ⫽0 value of 22.5 GHz. The bifurcation shift was determined to be 538 MHz, a change of 163 MHz 共43%兲 from K ⬙a ⫽0. Since the K a⬘ ⫽1 ‘‘2’s’’ have not yet been observed it is not possible to estimate the change in the

FIG. 1. The 87 cm⫺1 band stick spectrum, donor torsion ( ␯ 12). Forty-seven b-type transitions with K a ⫽0→1 observed. Maximum signal-to-noise ⬃100:1, linewidth ⬃2 MHz.

acceptor switching splitting or to dissect the interchange splitting into geared and antigeared components. The ‘‘2’s’’ are expected to lie above the ‘‘1’s’’ because this is an A ⬙ vibration. Such was the case for the 共D2O兲2 donor torsion. A search of the recorded VRT data has not yet revealed these subbands. It may be that these subbands lie at a frequency which is in an inaccessible laser gap. Examination of the (B⫹C)/2 rotational constant reveals a change of ca. ⫺30 MHz 共⫺0.48%兲 in each of the three tunneling components of the ‘‘1’s’’ from the corresponding ground state K a⬙ ⫽0 values. There is a small decrease 共⬃⫺6 kHz, ⫺12%兲 in the distortion constants (D j ). The asymmetry constants (B⫺C)/4, were found to have values of 11.3, ⫺ ⫹ ⫺ ⫹ ⫺ 10.3, and 11.1 MHz for A ⫹ 1 /B 1 , E 1 /E 1 , and B 1 /A 1 , respectively. These values are quite different from the slightly negative values for the ground state K ⬙a ⫽1. (B⫺C)/4 is dependent on the light out-of-plane hydrogens and is contaminated with tunneling information. The asymmetry-associated distortion constants (d j ) are small and negative 共ca. ⫺2.7 kHz兲, as are the ground state values. This vibrational motion is expected to couple to the acceptor switching and bifurcation tunneling pathways. Observation of the ‘‘2’s’’ with K a ⫽0→1 should reveal a very different interchange splitting from that observed for the ‘‘1’s’’ and approximately a doubling of the acceptor switching splitting, indicating that the ‘‘2’s’’ should be found near 2900 GHz. While the 共H2O兲2 vibration is expected to behave similarly to the 共D2O兲2 analog, it is important to remember that the mass difference in the hydrogen and deuterium atoms will affect the amount of change in the tunneling split-

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TABLE I. 87 cm⫺1 共H2O兲2 band: donor torsion ( ␯ 12) transition frequencies 共MHz兲. 1␴ uncertainties in italics. ⫺ A⫹ 1 ,B 1

Transition 8 18←9 09 7 17←8 08 6 16←7 07 5 15←6 06 4 14←5 05 3 13←4 04 2 12←3 03 1 11←2 02 1 10←1 01 2 11←2 02 3 12←3 03 4 13←4 04 5 14←5 05 6 15←6 06 7 16←7 07 8 17←8 08 9 18←9 09 1009←10010 11010←11011 1 11←0 00 2 12←1 01 3 13←2 02 4 14←3 03 5 15←4 04 6 16←5 05 7 17←6 06 9 19←8 08 10110←9 09

E ⫹ ,E ⫺

Obs–Calc

A⫹ 1

2 550 889.9

⫺0.42

A⫹ 1

2 576 934.7

0.88

A⫹ 1

2 602 564.9

⫺3.26

A⫹ 1

2 652 338.7

0.65

A⫹ 1

2 651 858.3

⫺1.44

A⫹ 1

2 651 111.9

0.98

A⫹ 1

2 650 095.1

⫺0.23

A⫹ 1

2 664 759.3

0.81

A⫹ 1

2 688 847.7

1.80

A⫹ 1

2 735 633.8

0.24

E⫺ E⫹ E⫺ E⫹ E⫺ E⫹ E⫺ E⫹ E⫺ E⫹ E⫺ E⫹ E⫺ E⫹ E⫺ E⫹ E⫺ E⫹ E⫺

K a ⫽0→1 2 509 775.7 2 522 837.0 2 535 818.3 2 548 709.5 2 561 509.5 2 574 213.9 2 586 828.4 2 599 347.9 2 624 031.1 2 623 913.9 2 623 737.3 2 623 503.1 2 623 209.7 2 622 860.1 2 622 453.5 2 621 990.7 2 621 474.1 2 620 901.1 2 620 275.1

⫺0.32 ⫺3.26 ⫺0.50 0.27 0.17 ⫺3.14 ⫺2.07 ⫺0.01 1.07 1.36 0.75 0.78 ⫺0.52 ⫺0.63 ⫺0.90 0.82 0.19 ⫺0.22 0.05

E⫺ E⫹ E⫺ E⫹ E⫺

2 648 431.1 2 660 447.9 2 672 360.1 2 684 176.6 2 695 882.6

1.66 0.73 ⫺2.10 2.59 0.36

E⫹ E⫺

2 730 390.6 2 741 675.3

tings as will the position of the energy level relative to the tunneling barriers. The interchange splitting for the same tunneling components and K a value in 共D2O兲2 is more than three times the ground state value, while in 共H2O兲2 it has increased by 50% of the K ⬘a ⫽0 value. B. The 102.8 cmÀ1 band: Acceptor wag „ ␯ 8 …

Two hundred thirty-four, parallel a-type and perpendicular c-type transitions originating from both K a⬙ ⫽0 and 1 and terminating in K a⬘ ⫽0 or 1 of the excited vibration have been observed for all six tunneling components near 103 cm⫺1. The measured data for 21 subbands were fit to an A ⬘ symmetry vibration and assigned to the acceptor wag ( ␯ 8 ), analogous to the 83 cm⫺1 共D2O兲2 vibration. These transitions

⫺ B⫹ 1 ,A 1

Obs–Calc

Obs–Calc

A⫺ 1

2 482 788.2

A⫺ 1

2 508 669.8

⫺0.1

A⫺ 1

2 534 244.9

⫺0.4

A⫺ 1

2 559 492.5

0.25

A⫺ 1

2 596 663.7

0.15

A⫺ 1

2 596 432.9

⫺1.1

A⫺ 1

2 596 021.7

⫺0.8

A⫺ 1

2 595 433.5

A⫺ 1

2 594 667.1

A⫺ 1

2 621 069.5

1.03

A⫺ 1

2 668 675.5

0.05

0.04

1.28

⫺0.4

are represented by a stick spectrum in Fig. 3 and the frequencies listed in Table III. The fitted constants are in Table IV and the resulting VRT energy level diagram is in Fig. 4. Combination differences for the ground state were used to assign the J, K a , and K c values of the spectra as well as to determine the overall symmetry of the vibration. There are a number of perturbations to this vibrational state which can be explained by Coriolis interactions. There is a Coriolis interaction between K a⬘ ⫽0 and K ⬘a ⫽1 for two tunneling components which is similar to that observed in the ground state. There is also a Coriolis interaction between one K a⬘ ⫽1 tunneling component of this vibration and a K a⬘ ⫽0 tunneling component of the acceptor twist vibration ( ␯ 11) discussed below.

TABLE II. 87 cm⫺1 共H2O兲2 band, donor torsion ( ␯ 12) fitted parameters 共MHz兲. 1␴ uncertainties in italics. ⫺ A⫹ 1 /B 1

(B⫹C)/2 Dj (B⫺C)/2 dj

6124.008 0.0430 11.251 ⫺0.0039

Band origin 2 630 747.8 Interchange 33273.9 Bifurcation ⫺163.2 Number of transitions ␴ 共standard deviation of fit兲

⫺ E⫹ 1 /E 1

0.080 0.0010 0.050 0.0007 1.0 1.9 1.3 47 0.39

K ⬘a ⫽0 6120.775 0.0446 10.333 ⫺0.0016

⫺ B⫹ 1 /A 1

0.038 0.0003 0.023 0.0002

rms error of residuals

6118.453 0.0441 11.106 ⫺0.0026

0.125 0.0018 0.070 0.0013

1.62

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J. Chem. Phys., Vol. 112, No. 23, 15 June 2000

FIG. 2. 87 cm⫺1 共H2O兲2, donor torsion ( ␯ 12) energy level diagram. J⫽0 →J⫽1, K a ⫽0→K a ⫽1 transitions are shown.

1. K a Ä 0 and 1\0 subbands

Parallel a-type transitions for all six tunneling components with K a ⫽0→0 were observed as well as c-type tran-

FIG. 3. 102.8 cm⫺1 共H2O兲2 stick spectrum, acceptor wag ( ␯ 8 ). Two hundred thirty-four a- and c-type transitions with K a ⫽0→0, K a ⫽0→1, K a ⫽1→0, and K a ⫽1→1. Maximum signal-to-noise ⬃50:1 for c-type and 20:1 for a-type, linewidth ⬃2 MHz.

Spectroscopy of the water dimer. II

10317

sitions for the three tunneling components corresponding to the ‘‘2’s’’ with K a ⫽1→0. It is unlikely that the K a ⫽1 →0 levels for the ‘‘1’s’’ can be observed since the K ⬙a ⫽1 levels are more than 13 cm⫺1 above the K ⬙a ⫽0 levels. These levels are not significantly populated in the molecular beam (T rot⬃5 K) with argon as the carrier gas. These assignments were verified by the absence of a Q branch for the K a ⫽0→0 transitions, the presence of a Q branch for the K a ⫽1→0 transitions and the presence of P(1) transitions in both cases. The band origin for the ‘‘1’s’’ was determined to be 3 235 539.5 MHz, and for the ‘‘2’s’’ the band origin is 2 929 212.8 MHz. The fitted parameters for all subbands are in Table IV. As stated earlier, only the change in the acceptor switching can be calculated in 共H2O兲2. For K a⬘ ⫽0 it has decreased by 306.3 GHz from K a⬙ ⫽0 if the same ordering is assumed about the acceptor switching splitting. A fit using the IAM high barrier model to ground state data estimated the acceptor switching splitting to be ⬃280 GHz in K a⬙ ⫽0, and the sum of the acceptor splittings in the K a⬙ ⫽0 and K a⬙ ⫽1 ground state levels was determined to be 411.5 GHz 共13.7 cm⫺1兲.2 If the value determined by Zwart et al.2 is close to the correct value then there is a reordering of the energy levels about the acceptor switching splitting. If observation of the K a ⫽1→0 transitions for the ‘‘1’s’’ were possible, then these should lie near 2824 GHz. The interchange splitting in the ‘‘1’s’’ was determined to be 88.5 GHz, almost four times the ground state K ⬙a ⫽0 value of 22.5 GHz. For the ‘‘2’s’’ the interchange splitting was determined to be only ⬃500 MHz, nearly 39 times less than the ground state K ⬙a ⫽0 value of 19.5 GHz. Decomposition of the interchange splitting into geared and antigeared components as suggested by the IAM model3 results in a geared interchange value of 44.5 GHz and an antigeared component of 45.0 GHz, indicating that the geared and antigeared tunneling pathways are equally important contributing ⬃50% each to the total interchange splitting, as compared to the ground state where the antigeared component is only 5% of the total interchange splitting. In the 共D2O兲2 analog the antigeared component is 10% in the excited state K a⬘ ⫽0. The bifurcation shift is ⬃⫺2.3 GHz, a decrease of 2.7 GHz from the ground state K a⬙ ⫽0 value in the ‘‘1’s’’ and ⬃⫹6.0 GHz in the ‘‘2’s’’ a decrease of 5.0 GHz. There is a ⫹ substantial reordering in the energy levels. The E ⫺ 2 /E 2 lev⫺ ⫹ ⫺ ⫹ els are significantly lower than the A 2 /B 2 and B 2 /A 2 lev⫹ ⫺ ⫹ els. The A ⫺ 2 /B 2 and B 2 /A 2 levels are very close together 共see Fig. 5兲. Also the ‘‘1’s’’ are now most likely above the ‘‘2’s’’ which is opposite of what is seen in the ground state. This drastic reordering of the states suggests a strong coupling between the vibration and both the acceptor tunneling and donor tunneling pathways. Examination of the acceptor tunneling motion shows an initial ‘‘flip’’ of the acceptor monomer before rotation of the donor and overall rotation of the complex. The flip is similar to the acceptor wag motion which could result in strong coupling. The bifurcation tunneling pathway also requires a flip of the acceptor as part of the total motion.7 The K ⬘a ⫽0 and 1 levels for the ‘‘1’s’’ are very close together. Two of the tunneling components experience a Co-

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J. Chem. Phys., Vol. 112, No. 23, 15 June 2000

TABLE III. 103 cm⫺1 共H2O兲2 band, acceptor wag ( ␯ 8 ) transition frequencies 共MHz兲. Residuals 共observed–calculated兲 in italics. ⫺ A⫹ 1 ,B 1

Obs–Calc

A⫹ 1

3 190 243.0

⫺4.9

A⫹ 1

3 215 887.3

⫺1.4

Transition 7 07←8 08 6 06←7 07 5 05←6 06 4 04←5 05 3 03←4 04 2 02←3 03 1 01←2 02 2 02←1 01 3 03←2 02 4 04←3 03 5 05←4 04 6 06←5 05 7 07←6 06

A⫹ 1

3 266 314.5

⫺0.8

A⫹ 1

3 327 531.8

1.5

A⫹ 1

3 351 426.5

0.4

A⫹ 1

3 374 998.0

5.0

⫺ A⫹ 2 ,B 2

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 0 00←1 01 1 01←0 00 2 02←1 01 3 03←2 02

E ⫹ ,E ⫺ K a ⫽0→0 a-type transition 3 130 385.2 E⫹ E⫺ 3 143 573.5 3 156 690.2 E⫹ E⫺ 3 169 715.2 E⫹ 3 182 624.8 E⫺ 3 195 412.2 3 208 054.7 E⫹ E⫺ 3 257 016.2 3 268 860.5 E⫹ E⫺ 3 280 570.8 3 292 155.8 E⫹ E⫺ 3 303 636.5 3 315 031.2 E⫹ E ⫹ ,E ⫺

Obs–Calc

⫺ B⫹ 1 ,A 1

Obs–Calc 0.4 ⫺0.1 ⫺0.2 ⫺0.2 ⫺4.5 ⫺1.9 0.3 3.1 1.0 2.5 0.5 ⫺0.7 ⫺0.2

A⫺ 1

3 096 182.4

0.0

A⫺ 1

3 120 125.5

2.1

A⫺ 1

3 205 153.3

0.0

A⫺ 1

3 230 933.5

⫺2.1

⫺ B⫹ 2 ,A 2

Obs–Calc

B⫹ 2 A⫺ 2

2 855 971.9 2 867 669.9

⫺3.9 1.8

A⫺ 2

2 891 191.2

1.6

A⫺ 2 B⫹ 2 A⫺ 2

2 914 994.1 2 927 047.9 2 951 531.5

⫺2.4 ⫺3.7 ⫺3.8

3 317 175.0 3 330 534.5 3 343 795.8

0.5 ⫺0.4 ⫺1.3

3 369 961.0 3 382 823.0 3 408 028.8 3 408 069.5 3 408 130.0 3 408 209.3

1.3 2.1 4.1 4.1 4.4 5.1

B⫹ 2 A⫺ 2 B⫹ 2 A⫺ 2

3 432 386.8 3 442 283.5 3 456 002.8 3 467 557.2

⫺4.1 ⫺4.9 ⫺3.4 ⫺5.0

A⫺ 2 B⫹ 2 A⫺ 2 B⫹ 2 A⫺ 2 B⫹ 2

3 300 410.5 3 311 997.8 3 323 691.8 3 335 481.0 3 347 362.0 3 359 341.1 3 371 395.2 3 383 527.0 3 407 854.8 3 407 561.2

⫺4.9 5.4 8.9 4.6 ⫺2.4 1.9 0.5 0.8 3.1 3.6

3 432 755.0 3 445 240.1 3 457 803.3

⫺6.4 ⫺6.7 ⫺3.9

Obs–Calc

A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2

2 859 579.6 2 871 333.7 2 883 147.9 2 895 048.7

0.0 0.6 1.1 0.9

E⫺ E⫹ E⫺

2 876 297.1 2 888 089.4 2 899 965.6

0.8 0.3 0.4

B⫺ 2 A⫹ 2 B⫺ 2

2 931 488.0 2 943.929.2 2 956 501.9

⫺1.6 ⫺0.7 0.5

E⫹ E⫺

2 948 837.4 2 961 437.0

⫺1.5 1.4

7 16←8 17 6 15←7 16 5 14←6 15 4 13←5 14 3 12←4 13 2 11←3 12 1 10←2 11 1 10←1 11 2 11←2 12 3 12←3 13 4 13←4 14 6 15←6 16 2 11←1 10 3 12←2 11 4 13←3 12 5 14←4 13 6 15←5 14 7 16←6 15 8 17←7 16

B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 A⫹ 2 B⫺ 2 A⫹ 2 A⫹ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2

3 186 066.0

⫺5.9

3 212 398.0 3 225 497.0

⫺5.2 ⫺5.0

3 251 481.5 3 264 310.0

1.7 ⫺0.4

3 289 689.0

0.7

3 290 089.8 3 290 708.0

1.4 0.7

3 325 957.2 3 337 777.0 3 349 469.8 3 361 067.8 3 372 579.0 3 384 020.0

⫺0.9 0.6 ⫺0.7 4.1 3.8 0.9

8 18←9 19 7 17←8 18 6 16←7 17 5 15←6 16 4 14←5 15 3 13←4 14 2 12←3 13 1 11←2 12 1 11←1 10 2 12←2 11 3 13←3 12 4 14←4 13 5 15←5 14 6 16←6 15 2 12←1 11 3 13←2 12 4 14←3 13

B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2 B⫺ 2 A⫹ 2 B⫺ 2

3 178 505.0 3 190 884.8 3 203 261.2 3 215 626.8 3 227 977.5

⫺0.2 ⫺5.9 ⫺4.7 ⫺3.1 ⫺4.0

3 252 643.8 3 264 951.2 3 289 252.2 3 288 741.5 3 288 009.0 3 287 080.8 3 285 989.8 3 284 747.2 3 314 002.5 3 326 217.3 3 338 407.0

0.7 0.2 0.3 0.7 1.4 0.2 3.6 0.9 ⫺0.9 1.3 0.9

Obs–Calc

K a ⫽1→1 a-type transitions E⫹ E⫺ E⫹ E⫺ E⫹ E⫺ E⫺ E⫹ E⫺ E⫹

3 271 408.8 3 284 848.5 3 298 198.8 3 311 443.5 3 324 559.3 3 337 515.0 3 362 828.0 3 362 853.0 3 362 890.5 3 362 939.8

9.6 1.7 ⫺3.4 ⫺5.2 ⫺4.3 ⫺3.0 2.3 1.7 1.7 3.1

E⫹ E⫺ E⫹

3 387 141.8 3 398 950.3 3 410 559.5

2.2 1.6 2.7

E⫹ E⫺

3 433 284.5 3 444 459.8

⫺3.1 3.5

E⫺ E⫹ E⫺ E⫹ E⫺ E⫹ E⫺ E⫹ E⫹ E⫺ E⫹ E⫺ E⫹ E⫺ E⫺ E⫹ E⫺

3 288 756.5 3 301 161.5 3 313 543.0 3 325 901.0 3 338 229.8 3 362 526.0 3 361 967.3 3 361 170.5 3 360 169.0

3.0 ⫺3.4 ⫺5.9 ⫺4.8 ⫺5.8 2.2 1.6 1.6 3.3

3 387 275.0 3 399 458.0 3 411 607.0

1.6 1.4 1.2

B⫹ 2 A⫺ 2

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J. Chem. Phys., Vol. 112, No. 23, 15 June 2000

Spectroscopy of the water dimer. II

10319

TABLE III. 共Continued.兲 Transition 5 15←4 14 6 16←5 15 7 17←6 16

A⫹ 2 B⫺ 2 A⫹ 2

Transition 8 17←9 09 7 16←8 08 6 15←7 07 5 14←6 06 4 13←5 05 3 12←4 04 2 11←3 03 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 9 19←9 09 11111←11011 1 10←0 00 2 11←1 01 3 12←2 02 4 13←3 03 5 14←4 04 6 15←5 05 7 16←6 06 8 17←7 07

3 350 569.8 3 362 722.0 3 374 835.0

⫺2.9 7.7 5.0

⫺ A⫹ 1 ,B 1

Obs–Calc

3 282 479.2

2.4

A⫹ 1

3 306 910.5

0.1

A⫹ 1

3 331 411.0

⫺2.1

A⫹ 1

3 380 485.8

A⫹ 1

3 380 162.5

A⫹ 1

3 379 657.2

⫺0.2

A⫹ 1

3 378 977.0

0.0

⫺0.3 0.3

A⫹ 1

3 392 967.0

⫺0.7

A⫹ 1

3 417 693.3

3.6

A⫺ 1

3 442 446.8

⫺1.0

A⫹ 1

3 467 219.8

⫺2.2

⫺ A⫹ 2 ,B 2

Obs–Calc

B⫺ 2 A⫹ 2 B⫺ 2

3 302 318.2 3 302 595.0 3 302 914.5

⫺1.0 ⫺0.3 0.5

B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2

3 339 536.6 3 352 363.2 3 365 309.2 3 378 329.8 3 391 409.8

0.1 ⫺1.0 5.4 2.1 ⫺2.5

⫺ A⫹ 2 ,B 2

Obs–Calc

Transition 4 13←5 14 3 12←4 13 2 11←3 12 1 10←2 11 1 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

Obs–Calc

A⫹ 1

Transition 4 13←5 05 2 11←3 03 1 10←2 02 1 11←1 01 2 12←2 02 3 13←3 03 4 14←4 04 5 15←5 05 6 16←6 06 2 11←1 01 3 12←2 02 4 13←3 03 5 14←4 04 6 15←5 05 7 16←6 06

⫺ A⫹ 2 ,B 2

E ⫹ ,E ⫺ K a ⫽1→1 a-type transitions E⫹ 3 435 788.2 E⫺ 3 447 825.2 E⫹ E ⫹ ,E ⫺ K a ⫽0→1 c-type transitions E⫺ 3 164 688.2 3 175 802.5 E⫹ E⫺ 3 187 006.0 3 198 327.5 E⫹ E⫺ 3 209 777.2 3 221 375.0 E⫹ E⫺ 3 233 134.5 E⫺ 3 269 592.8 3 269 719.0 E⫹ E⫺ 3 269 906.7 3 270 152.8 E⫹ E⫺ 3 270 452.9 3 270 805.4 E⫹ E⫺ 3 271 204.6 3 271 647.5 E⫹ E⫺ 3 272 128.2 E⫺ 3 273 194.6 3 282 042.5 E⫹ E⫺ 3 294 740.8 3 307 610.0 E⫹ E⫺ 3 320 634.0 3 333 797.8 E⫹ E⫺ 3 347 073.2 3 360 453.8 E⫹ E⫺ 3 373 904.5 ⫺ E⫹ 2 ,E 2

Obs–Calc

⫺3.7 2.1 Obs–Calc

⫺2.9 ⫺0.7 ⫺3.7 ⫺1.4 ⫺1.7 ⫺2.4 ⫺6.1 ⫺1.6 ⫺0.3 1.8 3.5 3.2 2.7 0.3 ⫺2.3 ⫺5.5 2.7 ⫺1.1 1.3 2.4 2.2 4.1 ⫺0.1 4.0 1.7

E⫹ E⫺ E⫹ E⫺ E⫹ E⫺ E⫹ E⫺

3 374 086.0 3 374 290.5 3 374 557.8 3 374 852.0 3 375 143.8 3 375 411.8 3 398 703.0 3 411 275.5

E⫺ E⫹ E⫺

3 436 672.8 3 449 442.2 3 462 221.8

⫺6.1 ⫺5.4 ⫺3.2

E ⫹ ,E ⫺

Obs–Calc

2 855 498.3 2 868 558.6

⫺1.4 ⫺0.4

A⫹ 2

2 894 192.6

0.4

Obs–Calc

3 470 438.0

⫺9.1

⫺ B⫹ 1 ,A 1

Obs–Calc

A⫺ 1

3 066 648.4

0.0

A⫺ 1

3 145 516.0

⫺0.6

A⫺ 1 A⫺ 1

3 166 227.2 3 200 981.5

3.5 0.3

A⫺ 1

3 201 381.2

⫺0.1

A⫺ 1 B⫹ 1 A⫺ 1

3 202 096.5

⫺0.1

3 203 119.2

0.1

A⫺ 1

3 204 436.8

0.0

A⫺ 1

3 227 796.5

⫺3.7

A⫺ 1

3 256 329.5

0.7

⫺ B⫹ 2 ,A 2

Obs–Calc

Obs–Calc

B⫹ 2 B⫺ 2 A⫺ 2

3 363 879.8 3 387 606.5 3 399 575.8

9.1 1.7 1.4

A⫺ 2 B⫹ 2 A⫺ 2 B⫹ 2 A⫺ 2

3 461 038.8 3 473 649.0 3 486 324.0 3 499 052.0 3 511 798.2

⫺5.9 ⫺2.2 ⫺2.0 3.7 ⫺0.9

⫺ B⫹ 2 ,A 2

Obs–Calc

B⫹ 2 A⫺ 2 B⫹ 2 A⫺ 2

2 859 325.9 2 872 424.1 2 885 401.9 2 898 240.2

⫺2.0 ⫺1.6 ⫺1.6 ⫺0.1

A⫺ 2 B⫹ 2 A⫺ 2 B⫹ 2 A⫺ 2 B⫹ 2 A⫺ 2 B⫹ 2 A⫺ 2

2 923 447.8 2 923 512.0 2 923 607.4 2 923 735.1 2 923 893.1 2 924 081.5 2 924 299.6 2 924 545.7 2 924 819.6

3.8 2.8 1.1 0.1 ⫺1.2 ⫺1.7 ⫺0.9 0.9 5.1

⫺1.0 ⫺0.3 0.5

2.6 2.9

K a ⫽1→0 B⫺ 2 A⫹ 2

B⫹ 2

⫺ B⫹ 2 ,A 2

E⫺

2 887 640.6

⫺0.7

E⫺ E⫹ E⫺ E⫹ E⫺

2 912 950.0 2 912 990.5 2 913 051.3 2 913 135.7 2 913 242.7

1.0 0.6 ⫺0.5 0.1 0.2

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10320

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J. Chem. Phys., Vol. 112, No. 23, 15 June 2000

TABLE III. 共Continued.兲 Transition 2 02←1 10 3 03←2 11 4 04←3 12 10010←9 18

A⫹ 2 B⫺ 2 A⫹ 2

⫺ A⫹ 2 ,B 2

Obs–Calc

2 931 068.8 2 942 923.1 2 954 590.1

0.4 0.2 0.0

E ⫹ ,E ⫺ E⫹ E⫺ E⫹

K a ⫽1→0 2 937 276.6 2 949 112.3 2 960 754.4

⫺ B⫹ 2 ,A 2

Obs–Calc

⫺1.5 0.6 ⫺1.3

Obs–Calc

B⫹ 2 A⫺ 2

2 947 839.4 2 959 772.9

4.7 3.7

B⫹ 2

3 039 619.5

⫺2.8

TABLE IV. 108 cm⫺1 共H2O兲2, acceptor wag ( ␯ s ) fitted constants 共MHz兲. 1␴ uncertainties in italics.a ⫺ A⫹ 1 /B 1

(B⫹C)/2 Dj Band origin Interchange Bifurcation

6435.847 0.0535 3 235 539.5 88 472.9 ⫺2305.1

⫺ E⫹ 1 /E 1

0.592 0.014

6146.332 0.0484

Band origin 2 929 212.8 Interchange 498.3 Bifurcation 5957.8 Igc 44485.6 I共a.g.兲c 44983.9 Acceptor switchc

⫹ E⫺ 2 /E 2

0.540 0.0251

6279.693 2.5194 86.247 ⫺2.4595 2893

Band origin 3 296 982.3 Interchange 157 043.4 Bifurcation ⫺20 876.4 ␴ 共stand, deviation of fit兲

6146.279 0.0537 19.214 ⫺0.0061

Band origin 3 369 365.0 Interchange 102 298.8 Bifurcation 22 122.9 ␴ 共stand, deviation of fit兲 Igc 12 9671.1 I共a.g.兲c 27372.3 Acceptor switchc A rotational constantc

0.230 0.0036

6147.466 0.0303

⫹ B⫺ 2 /A 2

0.398 0.0131

b

6153.491 0.0425

0.081 0.0008

AS共gs兲⫺306 GHz ⫺ E⫹ 1 /E 1

0.167 0.0034 0.112 0.0031

1.4 2.9 1.9 0.56

⫹ A⫺ 2 /B 2

(B⫹C)/2 Dj (B⫺C)/4 dj

6121.907 ⫺0.0292

1.3 2.7 2.7

⫺ A⫹ 1 /B 1

(B⫹C)/2 Dj (B⫺C)/4 dj ␨, coriolisc

0.180 0.0030

3.1 6.2 3.7

⫹ A⫺ 2 /B 2

(B⫹C)/2 Dj

K ⬘a ⫽0 6127.966 ⫺0.0147

⫺ B⫹ 1 /A 1

K a⬘ ⫽1 6199.128 0.0995 7.282 ⫺0.0212 1914

⫺ B⫹ 1 /A 1

0.071 0.0008 0.045 0.0007

rms error of fit ⫹ E⫺ 2 /E 2

0.095 0.0014 0.0513 0.0010 0.9 1.7 1.5 0.70

6133.278 0.058 10.507 ⫺0.0014

6155.835 0.0541 15.294 ⫺0.0088

0.162 0.0023 0.0892 0.0016

2.28 ⫹b B⫺ 2 /A 2

0.121 0.0023 0.067 0.0016

rms error of fit

6159.566共6141.660兲 0.0134共0.0575兲 ⫺12.167共5.581兲 ⫺0.0348共0.0040兲

0.110 0.0019 0.0650 0.0014

3.21

AS共gs兲⫹72 GHz 240 GHz

a

Number of transitions⫽234. Values in parentheses are coriolis corrected. c Constant not fit. b

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J. Chem. Phys., Vol. 112, No. 23, 15 June 2000

Spectroscopy of the water dimer. II

10321

FIG. 4. 102.8 cm⫺1 共H2O兲2 stick spectrum, acceptor wag ( ␯ 8 ) energy level diagram. A- and c-type transitions with K a ⫽0→0, K a ⫽0→1, K a ⫽1→0, and K a ⫽1→1 are shown.

FIG. 5. Perturbation to the 102.8 cm⫺1 acceptor wag vibration.

riolis interaction similar to that in the ground state between the K ⬙a ⫽0 and 1 levels of the ‘‘2’s.’’ The observed interaction is treated in the same manner and is discussed below. ⫺ The B ⫹ 1 /A 1 levels are not perturbed, and the (B⫹C)/2 rotational constant was found to be 6122.0 MHz. For the ⫺ E⫹ 1 /E 1 states the deperturbed (B⫹C)/2 is 6128.0 MHz and ⫹ the A 1 /B ⫺ 1 levels which are the most perturbed have a value of 6435.8 MHz. A satisfactory deperturbation was not possible for this tunneling component most likely because the K a⬘ ⫽0 and 1 levels are too close together and interact too strongly to use a simple single perturber theory. Loeser7 had the same frustrating problem in her analysis of the 共NH3兲2 intermolecular vibrations. A more complete description of the interaction is necessary. Use of an asymmetric rotor Hamiltonian which explicitly contains the coupling between different K a values within a vibration would treat this problem correctly. But due to the large tunneling splittings in the water dimer this is not possible. ⫺ From the unperturbed component B ⫹ 1 /A 1 it is observed that the (B⫹C)/2 for this state has decreased by ⬃35 MHz 共⫺0.57%兲. It will be assumed that a similar decrease would be observed in the other two tunneling components if no perturbation existed. The distortion constants (D j ) are also contaminated with Coriolis interaction information after deperturbing, making it difficult to assign them any physical meaning. The values range from ⫺14.7 to ⫹53.5 kHz compared with an average value of 47 kHz for the ground state K ⬙a ⫽0 values.

The (B⫹C)/2 values for the ‘‘2’s’’ range from 6146.3 to 6153.5 MHz, an average decrease of ⬃17 MHz 共⫺0.28%兲 from the ground state K ⬙a ⫽0 values. The distortion constants range from 30.3 to 48.4 kHz. The average D j value for K ⬙a ⫽0 is ⬃47 kHz. These energy levels show no evidence of perturbation. 2. K a Ä 0 and 1\1 subbands

Perpendicular c-type transitions for all six tunneling components with K a ⫽0→1 were observed as well as a-type transitions for the three tunneling components corresponding to the ‘‘2’s’’ with K a ⫽1→1. These assignments were verified by the presence of Q branches in each case starting with Q(1) and the fact that there were two sets of transitions with K a ⫽1→1 for each tunneling component. The band origin for the ‘‘1’s’’ was found to be 3 296 698.2 MHz and for the ‘‘2’s’’ the band origin is 3 369 065.0 MHz the acceptor switching splitting has increased by 72 GHz compared to K a⬙ ⫽0. As in the 共D2O兲2 analog, the energy levels for the ‘‘1’s’’ are lower in energy than the ‘‘2’s,’’ which is opposite of what is expected for an A ⬘ vibration. The interchange splitting for the ‘‘1’s’’ is determined to be 157.0 GHz, and for the ‘‘2’s’’ it is 102.3 GHz. The geared interchange component is determined to be 129.7 GHz and

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10322

Braly et al.

J. Chem. Phys., Vol. 112, No. 23, 15 June 2000

TABLE V. 103.1 cm⫺1 共H2O兲2 band. In-plane bend ( ␯ 6 ) transitions frequencies 共MHz兲. Residuals 共observed–calculated兲 in italics. ⫺ E⫹ 2 ,E 2

Transition 2 02←1 01 1 10←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 3 03←2 11 4 04←3 12 6 06←5 14 FIG. 6. 103.1 cm⫺1 共H2O兲2 stick spectrum, in-plane bend ( ␯ 6 ). Thirty-nine a- and c-type transitions with K a ⫽0→0, K a ⫽0→1, K a ⫽1→0, and K a ⫽1→1. Maximum signal:noise ⬃20:1, linewidth ⬃2 MHz.

the antigeared component is 27.4 GHz, composing about 18% of the total interchange splitting if the IAM picture is assumed compared to 29% in the 共D2O兲2 analog. The bifurcation shift for the ‘‘1’s’’ is ca ⫺20.9 GHz, and for the ‘‘2’s’’ it is ca ⫹22.1 GHz. This is a decrease of 21.5 GHz 共⬃40 times the ground state value兲 for the ‘‘the 1’s’’ and an increase of 11 GHz for the ‘‘2’s’’ 共⬃2 times the ground state value兲. The (B⫹C)/2 rotational constants vary greatly within the multiplet of the ‘‘1’s.’’ The deperturbed value for the ⫺ A⫹ 1 /B 1 levels which are the most perturbed is 6279.7 MHz. ⫺ ⫺ ⫹ For the E ⫹ 1 /E 1 levels it is 6199.1 MHz and for the A 1 /B 1 it is 6155.8 MHz 共not perturbed兲. The distortion constants are just as abnormal, ranging from ⬃5 to 2519 kHz. Clearly, there is still considerable Coriolis contamination of these constants. It is also possible that these two states are being perturbed by some other as yet unobserved vibrational state of the same symmetry which is slightly lower in energy. This would account for the fact that both (B⫹C)/2 rotational constants for K a ⫽0 and 1 are larger than the ground state value. A Coriolis constant 共␨兲 was employed in a manner similar to that used in the ground state in an attempt to deperturb ⫺ these states. The ␨ value for E ⫹ 1 /E 1 states is 1914 MHz and ⫹ ⫺ for A 1 /B 1 is 2893 MHz. The Coriolis interaction mixes the K a⬘ ⫽0 states with the upper asymmetry component of the K a⬘ ⫽1 which have the same overall J. The result is that the two sets of energy levels shift further apart. The K ⬘a ⫽0 levels are lowered. The upper asymmetry component of K ⬘a ⫽1 is pushed up 共see Fig. 5兲. The (B⫺C)/4 asymmetry constants from the ‘‘deperturbed’’ fit range from 7.3 to 86.2 MHz. The accompanying distortion constants (d j ) have values from ⫺2460 to ⫺8.8 kHz. Again complete deperturbation is not achieved, particu⫺ larly for the A ⫹ 1 /B 1 constants. ⫹ One of the tunneling components of the ‘‘2’s’’ (B ⫺ 2 /A 2 ) is slightly perturbed by the K a⬘ ⫽0 level of the acceptor twist ( ␯ 11) vibration with the same tunneling label. This perturba-

E⫹ 2

K a ⫽1→0 c-type transitions 3 057 223.1 E⫺ 2 3 069 767.2 E⫺ 2 3 082 529.0 E⫺ 2 3 082 991.0 E⫹ 2 3 083 678.8 E⫺ 2 3 084 586.6 E⫹ 2 3 085 730.0 E⫺ 2 3 087 095.0 E⫹ 2 3 088 689.0 E⫺ 2 3 119 735.4 E⫹ 2 3 132 209.2 E⫺ 2 3 157 327.1 E⫺ 2 ⫺ A⫹ 2 ,B 2

Transition 4 13←5 05 3 12←4 04 2 11←3 03 1 10←2 02 1 11←1 01 2 12←2 02 3 13←3 03 4 14←4 04 5 15←5 05 7 17←7 07 8 18←8 08 9 19←9 09 10110←10010 1 10←0 00 2 11←1 01 3 12←2 02 4 13←3 03

K a ⫽0→1 c-type transitions 3 635 995.5 A⫹ 2 3 647 822.0 B⫺ 2 3 659 693.0 A⫹ 2 3 671 626.2 B⫺ 2 3 695 982.2 A⫺ 2 3 696 337.5 B⫺ 2 3 696 834.5 A⫹ 2 3 697 443.0 B⫺ 2 3 698 138.5 A⫹ 2 3 699 693.8 A⫹ 2 3 700 517.0 B⫺ 2 3 701 353.5 A⫹ 2 3 702 190.2 B⫺ 2 3 708 070.5 B⫺ 2 3 720 477.0 A⫹ 2 3 732 994.8 B⫺ 2 3 745 602.2 A⫺ 2 ⫹ B⫺ 2 /A 2

Transition 2 12←3 13 1 11←1 10 2 12←2 11 3 13←3 12 4 14←4 13 5 15←5 14 4 14←3 13 3 12←4 13

K a ⫽0→0 3 118 839.0

K a ⫽1→1 a-type transitions 3 646 653.2 B⫺ 2 3 683 114.2 A⫹ 2 3 682 752.2 B⫺ 2 3 682 238.2 A⫹ 2 3 681 601.8 B⫺ 2 3 680 868.5 A⫹ 2 3 732 933.5 B⫺ 2 B⫹ 2

3 631 989.5

Obs–Calc 0.04

⫺0.1 ⫺0.3 ⫺1.8 2.5 1.2 ⫺1.9 0.6 ⫺1.4 0.7 0.5 0.3 0.2 Obs–Calc

⫺3.6 ⫺3.1 ⫺0.1 ⫺0.3 ⫺1.8 2.5 1.2 ⫺1.9 0.6 ⫺1.4 0.7 0.5 0.3 0.9 1.5 0.7 4.5 Obs–Calc

⫺3.5 ⫺3.8 ⫺2.7 ⫺4.0 ⫺4.4 ⫺2.1 0.5 ⫺1.1

tion will be discussed in the section dealing explicitly with the acceptor twist vibration. In Table IV, the first value for ⫹ the parameters of the B ⫺ 2 /A 2 K ⬘ a ⫽1 levels is from the uncorrected fit. The values in parentheses are from a deperturbed fit using a Coriolis coupling constant as was done for the 共D2O兲2 83 cm⫺1 ‘‘2’s’’ which were similarly perturbed by the acceptor twist. The other two tunneling components are not perturbed due to the large interchange splitting in the acceptor twist. The (B⫹C)/2 rotational constants range from 6133.3 to 6146.2 MHz, a small decrease 共⬃25 MHz, 0.04%兲 from the

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10323

TABLE VI. 103.1 cm⫺1 共H2O兲2 band, donor in-plane bend (n 6 ) transition frequencies 共MHz兲. 1s uncertainties in italics. K ⬘a ⫽0 (B⫹C)/2 Dj Band origin ␴ 共standard deviation of fit兲 rms error of residuals K ⬘a ⫽1 (B⫹C)/2 Dj (B⫺C)/4 dj Band origin Number of transitions in fit ␴ 共standard deviation of fit兲 rms error of residuals

⫺ E⫹ 2 /E 2

6251.871 0.0499 309 3462.8

0.08 0.0021 0.4 0.18 0.79

⫹ A⫺ 2 /B 2

6151.174 0.0737 ⫺13.319 0.0037 3 701 945.2

0.114 0.0094 0.160 0.0088 1.0 39 0.53 2.4

ground state K ⬙a ⫽0 values. The distortion constants range from 53.7 to 58 kHz, approximately a 10 kHz 共18%兲 increase from the ground state. The asymmetry constant 关 (B⫺C)/4兴 ⫹ for the perturbed B ⫺ 2 /A 2 levels is negative for the uncorrected fit indicating that the lower asymmetry component is pushed above the upper asymmetry component 共see Fig. 5兲. The deperturbed value is 5.6 MHz. The (B⫺C)/4 value for the other two tunneling components are 19.2 and 10.5 MHz ⫹ ⫺ ⫹ for A ⫺ 2 /B 2 and E 2 /E 2 , respectively. It is likely that the deperturbation was not complete. The associated distortion constants (d j ) range from ⫺1.4 to ⫹4.0 kHz, close to the average value of ⫺5 kHz for the ground state. The A rotational constant can be estimated as in paper I. Using the band origins given in Table IV, A was determined to be 240 GHz compared with 227.6 GHz for the ground state.2 The assignment of this vibration was made difficult by the many perturbations. Comparing the data with what is already known about the analogous vibrations in 共D2O兲2 has made this assignment possible. There are three possible A ⬘ intermolecular vibrations. After attempts to deperturb this vibration it can be seen that the (B⫹C)/2 rotational constants decrease on average from those of the ground state value. This was also the case for the 83 cm⫺1 共D2O兲2 analog. The 104 cm⫺1 共D2O兲2A ⬘ vibration showed on average an increase in the (B⫹C)/2 value and was assigned to the inplane bend ( ␯ 6 ). Observation of two components of another A ⬘ band near 103.1 and 123 cm⫺1 共discussed later兲 also exhibit an increased value for the rotational constant. The third A ⬘ vibration possible is the O–O stretch which is predicted to be near 150 cm⫺1 in the pseudodiatomic approximation using the ground state centrifugal distortion constants. This vibration should be characterized by a large decrease in the rotational constants (B⫹C)/2 due to the change in the separation of the heavy oxygen atoms. There is evidence for this vibration near 141 cm⫺1 which will be reported in a future paper. With this knowledge it is reasonable to assign the present band to the acceptor wag ( ␯ 8 ). There is a sharp deviation from the IAM picture evident

FIG. 7. 103.1 cm⫺1 共H2O兲2, in-plane bend ( ␯ 6 ) energy level diagram. Aand c-type transitions with K a ⫽0→0, K a ⫽0→1, K a ⫽1→0, and K a ⫽1 →1 are shown.

in this vibration. It is difficult even to discuss what has been observed in terms of the IAM model. The most notable deviation is the inversion about the acceptor switching splitting in both K a⬘ ⫽0 and 1, the opposite of what is expected for an A ⬘ vibration. Another deviation is that the geared and antigeared interchange components are nearly equal in K a⬘ ⫽0, but make up roughly 18% and 82% of the total interchange splitting for the antigeared and geared components, respectively, in K a⬘ ⫽1 if one uses the IAM model. Furthermore the magnitude of the bifurcation shift exceeds the magnitude of interchange splitting in K a⬘ ⫽0 for the ‘‘2’s’’ resulting in the

FIG. 8. 108 cm⫺1 共H2O兲2 stick spectrum, acceptor twist ( ␯ 11). Forty-seven b-type transitions with K a ⫽1→0. Maximum signal-to-noise ⬃30:1.

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TABLE VII. 108 cm⫺1 共H2O兲2 band, acceptor twist ( ␯ 11) transition frequencies 共MHz兲. Residuals 共observed–calculated兲 in italics. ⫺ A⫹ 2 ,B 2

Transition 9 09←101,10 8 08←9 19 7 07←8 18 6 06←7 17 4 04←5 15 3 03←4 14 2 02←3 13 1 01←2 12 0 00←1 11 1 01←1 10 2 02←2 11 3 03←3 12 4 04←4 13 5 05←5 14 6 06←6 15 7 07←7 16 8 08←8 17 9 09←9 18 2 02←1 11 3 03←2 12 4 04←3 13 5 05←4 14 6 06←5 15 7 07←6 16

B⫺ 2 A⫹ 2 B⫺ 2 A⫹ 2 B⫺ 2

⫺ E⫹ 2 ,E 2

3 045 560.8 3 057 036.0 3 068 708.0 3 080 582.0 3 092 656.4

⫺2.80 0.55 ⫺0.59 ⫺0.26 ⫺0.56

B⫺ 2 A⫹ 2 B⫺ 2

3 130 069.2 3 142 935.0 3 155 991.0

⫺0.22 2.42 2.00

B⫺ 2 A⫹ 2

3 182 672.0 3 196 296.8

⫺1.18 0.64

E⫺ 2 E⫹ 2 E⫺ 2 E⫹ 2 E⫺ 2 E⫹ 2 E⫺ 2 E⫹ 2 E⫺ 2 E⫹ 2 E⫺ 2 E⫹ 2 E⫺ 2 E⫹ 2

⫺ B⫹ 2 ,A 2

K a⬘ ⫽0 3 117 141.8 3 128 005.0 3 139 052.8 3 150 274.5 3 161 671.3 3 173 244.2 3 184 988.8 3 196 913.5

2.38 ⫺4.01 ⫺0.52 1.30 2.10 2.60 ⫺1.57 ⫺1.72

3 221 203.0 3 221 049.0 3 220 858.8 3 220 666.5 3 220 496.8

3 246 362.5 3 259 150.8 3 272 109.5 3 285 233.2 3 298 523 3 311 968.5

E⫺ 2 E⫹ 2 E⫺ 2 E⫹ 2 E⫺ 2 E⫹ 2

reordering of the energy levels. It is clear that there is considerable coupling between the tunneling motions and this intermolecular vibration. The tops of the tunneling barriers are being approached and the high barrier limit is no longer valid. C. The 103.1 cmÀ1 band: In-plane bend „ ␯ 6 …

Thirty-nine parallel a-type and perpendicular c-type ⫹ transitions have been measured for E ⫺ 2 /E 2 tunneling states ⫺ ⫹ with K a ⫽0 and 1→0 and for B 2 /A 2 states with K a ⫽0 and 1→1. The data are represented in the stick spectrum of Fig. 6 and the transitions are listed in Table V. There are few data for this vibration due to the lack of FIR lasers to complete the higher frequency data set and a lack of sensitivity when the lower frequency data were measured. By process of elimination and comparison to 共D2O兲2 results this vibration is assigned to the in-plane bend ( ␯ 6 ).

⫺0.92 ⫺1.37 ⫺1.91 ⫺0.92 ⫺1.85

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

3 353 785.2 3 365 988.5 3 378 210.5 3 390 457.0 3 402 538.0 3 402 155.0 3 401 597.2 3 400 877.0 3 400 009.5 3 399 007.5 3 397 877.5 3 396 626.0 3 395 261.2

⫺4.14 ⫺0.67 ⫺1.50 ⫺3.31 0.63 3.46 6.85 7.62 6.31 4.17 0.03 ⫺3.31 2.34

3.33 1.06 0.99 0.04 1.91 ⫺0.91

B⫹ 2 A⫺ 2 B⫹ 2 A⫺ 2

3 439 692.0 3 452 049.0 3 464 408.8 3 476 763.5

⫺4.94 ⫺2.48 ⫺3.61 ⫺7.63

1. K a Ä 0 and 1\0

The band origin of the K a ⫽0 and 1→0 subband is 3 093 462.8 MHz. All parameters are listed in Table VI, and the energy level diagram is shown in Fig. 7. Attempts to locate the other two symmetry components of this fork have been unsuccessful so far. The (B⫹C)/2 rotational constant is 6251.9 MHz, a 1.4% increase above the K ⬙a ⫽0 ground state value. This band is analogous to the 104 cm⫺1 band in 共D2O兲2 which also exhibits an increase in the K a⬘ ⫽0 rotational constant. The distortion constant (D j ) is 49.9 kHz, an increase of 2.7 kHz 共5.7%兲 above the K ⬙a ⫽0 value. 2. K a Ä 0 and 1\1 ⫹ The band origin for the K a ⫽0,1→1 B ⫺ 2 /A 2 subband is 3 701 945.2 MHz. This band is at the end of the 123 cm⫺1 laser and there is a large laser gap 共123–139 cm⫺1兲 which follows. If this is the lowest frequency K ⬘a ⫽1 subband of the

TABLE VIII. 108 cm⫺1 共H2O兲2 band, acceptor twist ( ␯ 11). Fitted parameters 共MHz兲. 1␴ uncertainty in italics. ⫹ A⫺ 2 /B 2

(B⫹C)/2 Dj

6235.756 0.0568

⫹ E⫺ 2 /E 2

0.251 0.0044

Band origin 3 267 984.3 1.3 Interchange 281601.1 2.7 Bifurcation ⫺24451.3 2.2 Number of transitions in fit ␴ 共standard deviation of fit兲

K a⬘ ⫽0 6223.91 0.0478

47 0.39

⫹a B⫺ 2 /A 2

0.146 0.0021

6149.847共6185.742兲 0.0991共0.0280兲

rms error of residuals

0.107 0.0013

3.07

⫹ ⬘ ⫽1 manifold of the 108 cm⫺1 acceptor wag. The This tunneling component, A ⫺ 2 /B 2 , is perturbed by the K a value in parentheses is Coriolis corrected.

a

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J. Chem. Phys., Vol. 112, No. 23, 15 June 2000

‘‘2’s’’ for this vibration 共as for other A ⬘ vibrations兲, then the other two tunneling components are in the laser gap. Complete analysis of this vibration is impossible without identification of new FIR lasers in this region to cover this gap. Interestingly, the energy levels with K ⬘a ⫽1 appear to be ordered like those of an A ⬙ symmetry upper state. However, quantum mechanical selection rules do not allow a-type transitions to an A ⬙ vibrational state. If the vibration is fit assuming A ⬘ symmetry exhibiting both a- and c-type transitions, the result is a negative (B⫺C)/4 asymmetry constant, ⫺13.3 MHz. The (B⫹C)/2 rotational constant is 6151.1 MHz, almost identical to the ground state K a⬙ ⫽1 value. The distortion constant (D j ) is 73.7 kHz, an increase of 22.5 kHz 共43.3%兲 from K ⬙a ⫽0. The negative asymmetry constant could result from two effects. One is that there is another as yet unobserved vibration that is perturbing the K ⬘a ⫽1 states. This would be simi⫹ lar to the situation where the A ⫺ 2 /B 2 ,K ⬘ a ⫽1 component of ⫹ /B the acceptor was is perturbed by the A ⫺ 2 2 ,K a⬘ ⫽0 component of the acceptor twist in 共H2O兲2. The other reason could be the contamination of the asymmetry constant with tunneling information. A similar situation occurs in the ground state K a⬙ ⫽1 共H2O兲2 states of the ‘‘1’s’’ where (B⫺C)/4 was determined to be ⬃⫺1 MHz. Without additional data on the other tunneling components of the excited state these hypotheses and vibrational assignment remain tentative. It was observed that the a-type transitions were much weaker than the c-type transitions. In fact only one transition with K a ⫽0→0 was measured although the frequency range which would include other transitions with K a ⫽0→0 has been scanned. A possible explanation for this is as follows. For the in-plane bend, there is no displacement along the b inertial axis and only a small displacement along a. However, the displacement along c is expected to have an observable effect. One might expect large repulsive forces hindering the bending motion above the 共ab兲 plane due to the two free hydrogens in the acceptor monomer. This would lead to an average displacement below the 共ab兲 plane and an increase in the C constant.

Spectroscopy of the water dimer. II

10325

FIG. 9. 108 cm⫺1 共H2O兲2, acceptor twist ( ␯ 11) energy level diagram.

it impossible to determine the change in the acceptor switching splitting. E. K a Ä1\0

The band origin is 3 267 984.3 MHz. The fitted parameters are given in Table VIII. The rotational constants (B ⫹C)/2 for the upper state were found to have increased to ⫹ 6235.8 MHz 共1.2%兲 for A ⫺ 2 /B 2 states and to 6223.9 MHz ⫺ ⫹ 共1.0%兲 for E 2 /E 2 states indicating a decrease in the O–O

D. 108 cmÀ1 „H2O…2 band: Acceptor twist „ ␯ 11…

Forty-seven perpendicular b-type spectra were observed near 108 cm⫺1 with K a ⫽1→0 for the ‘‘2’s.’’ This A ⬙ vibration has been assigned to the ␯ 11 , acceptor twist. The stick spectrum is depicted in Fig. 8 and the frequencies are listed in Table VII. The interchange splitting was determined to be 282 GHz, more than 14 times are ground state K a⬙ ⫽0 value. Transitions corresponding only to the ‘‘2’s’’ have been observed so far for this vibration. This assignment was confirmed through use of combination differences and the observation of J ⬙ ⫽1→J ⬘ ⫽0 transitions. Since only b-type transitions are allowed for this vibration, transitions to K ⬘a ⫽0 of the ‘‘1’s’’ must originate from the ground state K a⬘ ⫽1. Recall that the K ⬙a ⫽1 levels of the ‘‘1’s’’ are about 13 cm⫺1 above the K a⬙ ⫽0 levels and are unlikely to be populated in the molecular beam. It is unlikely that the K a⬘ ⫽0 levels for the ‘‘1’s’’ will be observed for this 共H2O兲2 vibration making

FIG. 10. Summary of observed 共H2O兲2 intermolecular vibrations.

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separation. For the upper most component having symmetry ⫹ B⫺ 2 /A 2 an initial fit shows (B⫹C)/2 to have decreased by 0.2% relative to the ground state value. However, closer ⫹ analysis reveals that the K ⬘a ⫽1,B ⫺ 2 /A 2 tunneling component ⫺1 A ⬘ band is interacting with this band of the 103 cm through a Coriolis interaction. This is similar to the interaction observed between components of the 共D2O兲2 acceptor twist and acceptor wag vibrations. A fit was performed using a Coriolis coupling term to estimate the perturbation and obtain rotational constants that are similar to the other unperturbed components. A Coriolis constant 共␨兲 of ⬃600 MHz gives a (B⫹C)/2 value of 6185.7 MHz. Since the deperturbation was not complete this implies it has not been treated correctly. A more complete description is probably required using higher order interaction terms. This is the same problem experienced in 共D2O兲2 between the acceptor wag and acceptor twist. The distortion constants (D j ) increase by 0.6 to 14.6 ⫹ ⫺ ⫹ kHz for the unperturbed E ⫺ 2 /E 2 and A 2 /B 2 levels, respec⫺ tively, and an increase of 48 kHz for the B 2 /A ⫹ 2 component was determined. Using the above Coriolis constant of ⬃600 MHz this D j is calculated to be 28 kHz. The Coriolis coupling scheme is not believed to be correct for this particular interaction, but these numbers serve as an estimate of the perturbation. The interchange splitting has increased to 281.6 GHz 共⬃9.4 cm⫺1兲 in K a⬘ ⫽0 more than 14 times larger than K a⬙ ⫽0. An energy level diagram is depicted in Fig. 9. At first

glance this seems exceedingly large. However, referring back to the analogous splitting in the 共D2O兲2 acceptor twist vibration discussed in our accompanying paper, it was found that the interchange splitting was almost 13 times larger than the K a⬙ ⫽0 value. A comparable change has occurred in 共H2O兲2. The bifurcation shift has decreased by 24.5 GHz, approximately three times the K a⬙ ⫽0 ground state value. IV. SUMMARY

The spectra and analysis for four intermolecular vibrations of 共H2O兲2 were reported significantly increasing the measurements available for characterization of the water dimer. A summary energy level diagram of the measured intermolecular vibrations is given in Fig. 10. The spectra exhibit numerous perturbations and deviations from the local IAM model and are both qualitatively and quantitatively different from the predictions of popular pair potentials. 1

J. P. Paul, R. A. Provencal, and R. J. Saykally, J. Phys. Chem. 102, 3279 共1998兲. 2 E. Zwart, J. J. ter Meuen, W. L. Meerts, and L. H. Coudert, J. Mol. Spectrosc. 147, 27 共1991兲. 3 L. H. Coudert and J. T. Hougen, J. Mol. Spectrosc. 139, 259 共1990兲. 4 T. R. Dyke, J. Chem. Phys. 66, 492 共1977兲. 5 T. A. Hu and T. R. Dyke, Forty-third Symposium on Molecular Spectroscopy, Columbus, OH, 1988. 6 D. J. Wales, Adv. Mol. Vib. Collision Dynamics 3, 365 共1998兲. 7 J. G. Loeser, Ph.D. thesis, University of California at Berkeley, 1995, and references therein.

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