High-Resolution IR Spectroscopy of the N2O–H2O and N2O–D2O van der Waals Complexes

Journal of Molecular Spectroscopy 216, 315–321 (2002) doi:10.1006/jmsp.2002.8687

High-Resolution IR Spectroscopy of the N2 O–H2 O and N2 O–D2 O van der Waals Complexes G. Gimmler and M. Havenith Lehrstuhl f¨ur Physikalische Chemie II, Ruhr-Universit¨at Bochum, Universit¨atsstr. 150, 44780 Bochum, Germany E-mail: [email protected] Received March 26, 2002; in revised form August 22, 2002

We report high-resolution infrared vibrational–rotational spectra of the weakly bound complexes N2 O–H2 O and N2 O–D2 O in the higher frequency N2 O stretching mode region (ν3 = 2223.756693(124) cm−1 ). The measurements were carried out using a free jet expansion in combination with a lead salt diode laser spectrometer. Rotational constants, quartic centrifugal distortion constants, and band origins have been derived for both isotopomers. The geometrical structure is determined using isotopic substitution. The deduced structure shows evidence for a second hydrogen bond interaction within the complex. The nonrigidity of the complexes gives rise to an internal rotation of the water molecule around its own C2v symmetry axis. For N2 O–H2 O, a tunneling splitting arising from this internal motion has been observed in the spectra. According to symmetry considerations, the observed splitting in the spectrum of N2 O–H2 O corresponds to the difference between the tunneling frequencies in the ground C 2002 Elsevier Science (USA) and vibrationally excited states. 

I. INTRODUCTION

Research on van der Waals and hydrogen bond systems containing water has grown substantially over the past two decades. The infrared spectra of these species provide information on their structures and potential energy surfaces. Potential energy surfaces as deduced from the spectra of different inter- and intramolecular modes can help to develop a deeper insight into the theory of intermolecular forces. A more detailed knowledge of these forces is still needed to understand phenomena like water solvation on a microscopic level. Moreover, data on watercontaining complexes have turned out to be of atmospheric relevance (1). Before the interactions in a whole ensemble of water molecules can be understood, binary systems and higher order complexes need to be studied to gain insight into the different contributions to the total interaction. Weakly bound complexes containing water can show tunneling splittings due to internal proton exchange motions. Quite a few infrared studies on water-containing complexes can be found in the literature, e.g., (H2 O)2 (2–5), Ar–H2 O (6–9), CO– H2 O (10, 11), CO2 –H2 O (12). However, despite its atmospheric relevance no infrared work on N2 O–H2 O has yet been reported. In this paper we report the first infrared spectrum of this complex. The only previous measurements on N2 O–H2 O were carried out by Zolandz et al. in the microwave region (13). They recorded rotational spectra of N2 O–H2 O, N2 O–D2 O, and N2 O– HDO and derived rotational and centrifugal distortion constants. For N2 O–H2 O they observed a tunneling splitting due to the internal rotation of the water subunit exchanging the bound and free proton and calculated the tunneling barrier height to be

about 235(10) cm−1 . Based upon the rotational constants they deduced the geometric structure in terms of the distance of the centers of mass of the two subunits Rcms and the angle of the N2 O subunit and the N–O weak bond. From their dipole moment measurements they derived the in-plane tilt of the water molecules’ C2v axis toward the N–O weak bond. They also measured the quadrupole coupling constants for the two nitrogen nuclei. The only theoretical predictions on N2 O–H2 O have been published by Sadlej and Sicinski (14) performing geometric optimization by SCF theory as well as harmonic vibrational frequency calculations with two different basis sets. The predicted structures show a stronger hydrogen bond character than the structure determined by the experimental microwave work. Compared to the experimental results the H2 O molecule is further tilted toward the O-atom of the N2 O (see Fig. 4). The calculated vibrational frequency of the ν3 -band of the complex differs by more than 10% from the experimental value which is presented in this work.

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II. EXPERIMENTAL SETUP

The computer-controlled lead salt diode laser spectrometer and the vacuum apparatus containing the free jet expansion have been described previously (15–18). The appropriate gas mixture to form the complexes was expanded through a 5 cm × 50 µm slit nozzle. To compensate for the huge gas load the vacuum chamber was pumped by an Edwards EH 2600 roots blower, a Leybold Ruvac 501 roots blower, and a Leybold S65 rotary vane pump. 0022-2852/02 $35.00  C 2002 Elsevier Science (USA)

All rights reserved.

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FIG. 1.

Spectra of the ν3 bands of N2 O–H2 O and N2 O–D2 O.

The production of the complexes was achieved by blowing a mixture of less than 1% N2 O in 600 Torr through a bubbler containing H2 O or D2 O at room temperature. The gas mixture was optimized to suppress signals from (N2 O)2 and maximize the signals from N2 O–water at the same time. The gas was blown over the water surface and the bubbler was mounted as close to the nozzle as possible to avoid condensation of the picked up water vapor. The resulting background pressure from these expansion conditions was 1.5 × 10−1 mbar. The laser radiation from standard lead salt diodes mounted on the cold head of a closed-cycle helium cryostat was passed 40 times through the expansion zone using a new Herriott-type multipass cell recently constructed in our lab (19). This corresponds to an absorption length of approximately 80 cm. The lateral distance of the nozzle to the center of the Herriott cell was optimized for the best signal-to-noise ratio (5–7 mm). The laser radiation detected by a HgCdTe and frequency modulated at 7 kHz. In order to increase the sensitivity to I = 10−5 –10−6 , I0 phase sensitive demodulation of the detector signals using lockin amplifiers was used. Relative frequency calibration was provided by the interference fringes of a Fabry–Perot e´ talon with a free spectral range of 0.01 cm−1 . The background gas in the vacuum chamber contained suitable concentrations of monomeric N2 O, so the monomer absorptions could be used for absolute frequency calibration of the spectra. III. EXPERIMENTAL RESULTS

The spectra of the N2 O–H2 O and N2 O–D2 O complexes have been recorded between 2229.7 and 2242.1 cm−1 in the region

of the N2 O–monomer higher frequency stretching vibration (see Fig. 1). Two different diodes have been used which covered most of the interesting frequency range. For N2 O–H2 O the coverage is complete, while for N2 O–D2 O two gaps between 2231.5 and 2233.75 cm−1 and between 2239.65 and 2240.05 cm−1 appear in the spectrum. The latter spectrum was recorded a few weeks after the N2 O–H2 O spectrum. Intermediate warming of the diodes to room temperature changed the emission characteristics of one of the diodes drastically. In consequence the frequency coverage for N2 O–D2 O is incomplete. The final assignment of the spectra was facilitated by the observation of R-branches at the high-frequency part of the spectra. All lines could be attributed to b-type transitions (K a = ±1, K c = ±1). The highest J -value observed in the spectra was J = 21 for the K a : 1 ← 0 subband. Transitions up to K a : 11 ← 10 have been observed. No a-type transitions could be observed in the spectra. This is in agreement with the assumption that the N2 O axis lies almost perpendicular to the a-axis of the complex. The lack of c-type transitions confirms the planarity of the complex, as was already, found in the microwave experiments (13). For N2 O–H2 O a doubling of the lines was found, with one line being decreased in intensity by a factor of 2–4 compared to the blue-shifted component. Figure 2 shows a sample spectrum representing this splitting. The doublets are due to the tunneling motion of the water subunit inside the complex. Since the hydrogen nuclei are fermions, the total wavefunction of the complex must be antisymmetric upon their exchange. Therefore, the spatially symmetric A-tunneling state requires an antisymmetric spin wave function while the antisymmetric B-tunneling state

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FIG. 2. and K c .

Sample spectrum of some lines of N2 O–H2 O exhibiting the tunneling splitting. The quantum numbers are the asymmetric for quantum number J1 K a ,

requires a symmetric spin wave function (the notation of the tunneling states follows that from (13)). An intensity ratio of 3 : 1 (B : A) is predicted, which is in general good agreement with our experimental observations. However, due to the overlap of distinct lines the measured intensities are sometimes distorted and do not represent the true 1 : 3 relation (Fig. 2). For D2 O–N2 O, the tunneling splitting was beyond our spectral resolution, apparently because the heavier mass of the deuterons decreases the tunneling frequency. In the case of CO–H2 O and CO–D2 O the tunneling splitting decreases by a factor of 15 (10). Assuming a similar factor in our case would already explain our observations.

IV. FIT OF THE EXPERIMENTAL CONSTANTS

The transitions were fit using a nonlinear least-squares fitting program containing a Watson S-reduction asymmetric rotor Hamiltonian in I r -representation (20) of the form    B +C 2 B +C 2 B −C 2 H = J + A− Ja + Jb − J2c 2 2 2 − D J J4 − D J K J2a J2 − D K J4a + d1 J2 (J2+ + J2− ) + d2 (J4+ + J4− ),

[1]

TABLE 1 Spectroscopic Constants for N2 O–H2 O: All Values Except for the Inertial Defect Are in cm−1 Ground state (present work)

A (B + C)/2 B −C B C DJ DK DJ K d1 d2 δK ν0 ❛ /[amu A2 ]

A-state

B-state

0.421020(8) 0.128450(2) 0.039121(3) 0.148011(3)∗ 0.108890(3)∗ 8.3(12) · 10−7 −1.1(4) · 10−5 9.0(6) · 10−6 −2.5(3) · 10−7

0.420440(5) 0.1284593(7) 0.039120(2) 0.1480193(7) 0.1088993(7) 8.0(5) · 10−7 −6.5(20) · 10−6 9.2(2) · 10−6 −2.9(2) · 10−7 −1.1(2) · 10−7

0.879

0.817

Data from MW-spectroscopy Ref. [11] A-state

B-state

0.42104393(677)

0.42045696(257)

0.14801625(157) 0.10890725(157) 1.03(4) · 10−6 1.167 · 10−5 8.11(11) · 10−6 −2.9(1) · 10−7

0.14803479(107) 0.10888523(107) 1.03(4) · 10−6 1.167 · 10−5 8.11(11) · 10−6 −2.9(1) · 10−7

7.48(25) · 10−6

7.48(25) · 10−6 0.859

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Excited state (present work) A-state

B-state

0.41801(5) 0.127989(7) 0.03909(3)

0.41740(3) 0.127993(3) 0.03911(1)

8.7(10) · 10−7 −9.6(29) · 10−6 9.2(5) · 10−6 −2.0(4) · 10−7

8.7(4) · 10−7 −6.6(16) · 10−6 9.2(2) · 10−6 −2.4(2) · 10−7

2232.3720(3) 0.819

2232.3831(1)

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TABLE 2 Spectroscopic Constants for N2 O–H2 O: All Values Except for the Initial Defect Are in cm−1

A B + C/2 B − C/2 B C DJ DK DJ K d1 d2 δK ν0 ❛ /[amu A2 ]

Ground state (present work)

Ground state MW-data from [11]

Excited state (present work)

0.414244(2) 0.1173556(1) 0.0331571(5) 0.1330341(3)∗ 0.10095701(3)∗ 6.7(1) · 10−7 9.9(4) · 10−6 6.5(1) · 10−6 −2.21(4) · 10−7 −7.6(3) · 10−8

0.41424737(207)

0.411675(7) 0.116945(1) 0.033118(4)

0.13394974(87) 0.10076256(87) 9.4(2) · 10−7 1.167(37) · 10−5 6.80(47) · 10−6 −2.9(2) · 10−7 6.07(17) · 10−6

0.716

6.9(1) · 10−7 7.6(3) · 10−6 6.4(1) · 10−6 −2.10(7) · 10−7 −8.0(6) · 10−8 2232.47435(8) 0.709

∗ These constants were calculated from (B − C)/2 and (B − C)/2 for comparison.

water. Furthermore we state that the monomer structures are unchanged upon complex formation based on the experiences in other weakly bound systems. Therefore the structure of the N2 O– H2 O complex can be described by only three parameters: The distance Rcms between the centers of mass of the two subunits, the angle θ of the N2 O molecular axis against the intermolecular axis, and the angle φ of the water C2v -axis against the intermolecular axis. In order to calculate the dependency of the rotational constants on these three parameters a coordinate system (x, y, z) different from the principal axis system is chosen, in which the molecule lies in the x z-plane. The x-axis and the molecular aaxis coincide. Within this coordinate system the elements of the inertial tensor can be written as    2 2  θHOH θHOH 2 Ix x = m HrOH sin + φ + sin −φ 2 2 2 − m H2 O dO–cms sin2 φ + IN2 O sin2 θ 2 I yy = µRcms + IN2 O + IHC2 O

where J and Ja are the total angular momentum and its component along the a-axis and J± are the raising and lowering operators, J± = Jb ± iJc . The infrared transitions were fit simultaneously with the microwave data of reference (13). As expected, the results for the ground state is in excellent agreement with the result of the fit of the rotational constants in the previous microwave study with the only exception that the distortion constants could be improved due to the increased number of transitions involving higher J levels. For N2 O–D2 O 369 infrared transitions could be assigned to the b-type spectrum of the ν3 -band. A full set of rotational and quartic centrifugal distortion constants for the ground and excited state was obtained. For N2 O–H2 O each tunneling state was fit separately. For the A-tunneling state of N2 O–H2 O 134 lines were included into the fit. For the B-tunneling component 262 transitions could be assigned. The ground state and excited state D K constants have negative values. This is at first glance surprising since centrifugal forces around the a-axis are expected to decrease the A-rotational constant. However, J = K a corresponds to a rotation around the a-axis. The same has been observed by Fraser et al. (21). The standard deviation of the fit is 0.0005 cm−1 for N2 O–D2 O and 0.001/0.0008 cm−1 for the A/B-components of N2 O–H2 O. All values are less than or equal to the experimental uncertainty of 0.001 cm−1 of our apparatus. The constants derived from the fits are shown in Table 1 and Table 2.

[2] [3]

  2 2   θHOH θHOH 2 Izz = m HrOH cos + φ + cos −φ 2 2

Ix z

2 2 − m H2 O dO–cms cos2 φ + IN2 O cos2 θ + µRcms     θHOH θHOH 2 = m HrOH cos + φ sin +φ 2 2     θHOH θHOH 2 − m HrOH cos − φ sin −φ 2 2 2 − m H2 O dO–cms cos φ sin φ + IN2 O cos θ sin θ

Ix y = I yx = I yz = Izy = 0,

[4]

[5] [6]

with µ, IN2 O , IHC2 O , m H , m H2 O , dO–cms , θHOH being the pseudoatomic reduced mass of the complex, the moment of inertia of nitrous oxide, the moment of inertia of the water molecule along its own c-principal axis, the masses of hydrogen and water, the distance between the center of mass of the water molecule and its O-atom, and the intramolecular angle of the water molecule, respectively. The principal moments of inertia of the complex can be obtained by diagonalizing the inertial tensor formed by the elements stated above. Using the I r -representation we obtain 1 1 (Ix x + Izz ) − (Ix x − Izz )2 + 4Ix2z 2 2 1 1 I B = (Ix x + Izz ) + (Ix x − Izz )2 + 4Ix2z 2 2 IA =

V. STRUCTURAL ANALYSIS

Based on the lack of c-type transitions in our spectra, as well as the analysis of the dipole moments and rotational constants in the microwave work (13), we assume a planar structure for N2 O–  C 2002 Elsevier Science (USA)

2 IC = µRcms + IN2 O + IHC2 O .

[7] [8] [9]

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TABLE 3 Comparison of Geometrical Parameters and Vibrational Frequencies Vib. state Isotope ❛

Rcms /[A] θ/[◦ ] φ/[◦ ] ν0 /[cm−1 ]

a b

Present work ground

Zolandz (13) ground

H2 O

D2 O

H2 O

2.964(8) 84(1) 58(13)

2.992(6) 83(2) 57(13)

2.91

Oa

D2 O

H2

2.89

3.44 55.35 99.97 2566

81 20

H2

Ob

2.78 81.53 45.40 2503

Present work ν3 -excited state H2 O 2.971(5) 84(2) 59(7) A 2232.3720(3) B 2232.3831(1)

D2 O 2.998(3) 83(2) 59(7) 2232.47435(8)

Results using MINI-1 basis set. Results using 4-31G basis set.

The intermolecular distance Rcms can be directly calculated from Eq. [9], with

Rcms

Sadlej (14) ground

   k 1 1 1 , = − − µ C bN2 O C H2 O

[10]

where bN2 O corresponds to the rotational constant of N2 O (0.419 011 006(15) cm−1 in the ground and 0.415 559 512 (18) cm−1 in the ν3 -excited state (22)). CH2 O is the C-rotational constant of water in the ground state (9.27771(3) cm−1 (23)) and k corresponds to a conversion factor for Rcms in angstroms. For N2 O–D2 O a value CD2 O = 4.846 798(5) cm−1 (24) was used. The values of the intermolecular distance for the different states and isotopes are shown in Table 2. Since the values for the A- and B˚ states of N2 O–H2 O are almost identical (difference ≈ 10−4 A) their mean values are taken.

The Rcms -values from the microwave study differ from our ground state values despite the fact that we obtained nearly the same rotational constants (see Table 3). If we take their C-rotational constants and insert them into Eq. [10], we obtain ˚ and 2.992(6) A ˚ for N2 O–H2 O and N2 O– values of 2.964(8) A D2 O, which are identical with our values. Since in their paper they give neither any equation for their structural determination nor the constants N2 O and CH2 O they actually used we have no explanation for this discrepancy. The calculation of the angles θ and φ cannot be performed independently for each isotopic species since I A and I B are correlated through the planarity relation IC ≈ I A + I B . However, using the different values of Rcms for the two isotopic species and assuming the structure remains unchanged upon isotopic substitution the angle φ can be determined from elementary geometrical relations: If we form a triangle between the center of mass of the N2 O molecule, the oxygen atom, and the center of

FIG. 3. The horizontal lines correspond to the experimentally determined moments of inertia for the different isotopes. The other lines show the predicted moments of inertia in dependence of the angle θ . The actual structure is determined by choosing the angle θ for which I(θ ) agrees best with the measured value.

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mass of the water, we assume that the angle α remains constant upon deuteration. We can then use the following equations to determine α and d, H2 O–N2 O Rcms = d 2 + SH2 − 2d SH cos α

[11]

H2 O–D2 O Rcms = d 2 + S D2 − 2d S D cos α,

[12]

with S describing the distance between the oxygen atom and the α center of mass. We then obtain φ = arcsin{ dRsin }. For a given cms value of φ, the angle θ can be determined from Eq. [7] or [8] for both isotopes. These equations have to be solved numerically for θ since they are not algebraically invertible. Figure 3 shows a plot of all the possible solutions. Each moment of inertia yields four different values for θ. Taking into account that the theoretical calculations predict a tilt of the O-atom of the N2 O molecule toward the water subunit rather than away from it, only the four values around θ ≈ 82◦ are physically meaningful and will be taken into consideration. The errors for φ result solely from the propagation of error from Rcms . The error in θ was calculated substituting the error boundary values of Rcms and φ into Eqs. [7] and [8] and then solving numerically for θ. Since the change of S due to isotopic substitution is very ˚ compared to the intermolecular distance small (S = 0.061 A) ˚ R(3.0 A) and requires a rigid molecule the final result is expected to have larger error bars. If we compare this structure with the structure as determined in the MW study we obtain a considerable deviation in the angle φ. Zolandz et al. deduced the angle φ = 20◦ from Stark effect measurements which yielded a large value for µa and a small value for µb . In addition, their measurements indicated large-amplitude motions in the φ coordinate, which implies severe difficulties in deriving the equilibrium structure and might explain the differences in the structural parameters. Since the dipole moment measurements require smaller tilt angles of the water submit than we obtained, we have performed a second calculation where we fixed the angle φ to 20◦ and calculated the tilt of the N2 O based upon Eqs. [7] and [8]. We obtained for θ a value of θ = 82◦ instead of θ = 84◦ , which indicates that θ is very insensitive to variations in φ. The variation in φ reflects the nonrigidity of this complex in respect to the water submit. In the analysis of the MW data by Zolandz et al. the angle θ was obtained by a comparison with the experimental Arotational constant. They obtained a tilt of 9◦ –11◦ of the N2 Omonomer from the b-axis (θ = 81◦ –79◦ ) which corresponds very well with our value (θ = 82◦ –84◦ ) when considering averaging effects. Figure 4 shows a comparison between the derived structures from the microwave, the theoretical, and the present study. Our first structure is in good agreement with the theoretical results, yet shows a larger value for φ. This may suggest a second hydrogen-bond interaction inside the complex.

FIG. 4. Structure of the N2 O–water complex: (a) from the microwave work (13), (b) from theoretical calculations (14), and (c) from this study.

VI. DISCUSSION

The inertial defects  = IC − I B − I A for all the measured species and states are given in Table 1.  amounts to a few ˚ 2 , accounting for Coriolis effects and vibrational tenths amu A averaging, and agrees very well with the picture of a planar molecule. The nonrigidity of the complex must, therefore, be restricted to in-plane motions. ˚ upon The intermolecular bond length increases by 0.004 A excitation of the ν3 vibration for both isotopes. The values

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obtained for the two angles describing the structure of the complex have to be treated very carefully due to the averaging by internal rotation and large amplitude motions occurring inside the complex. They have to be considered as effective values averaged over the intermolecular motions according to the potential energy surface. The band origins of the studied complexes are all blueshifted with respect to the N2 O-monomer ν3 vibration lying at 2223.756693(124) cm−1 (22). For N2 O–H2 O, we obtain a shift of ν = 8.6153(3) cm−1 for the A-state and ν = 8.6264(2) cm−1 for the B-state. The blue shift in the spectrum of N2 O–D2 O has a value of ν = 8.7177(1) cm−1 . These blue shifts indicate a decrease in the binding energy of the complex upon excitation of the N2 O asymmetric stretch corresponding to an increase in the intermolecular bond length upon vibrational excitation. This result is comparable to the blue shift of about 11 cm−1 observed for CO–H2 O (10). The band origin of the B-state lies 0.0111(3) cm−1 above that of the A-state. Neglecting the tunneling motion the appropriate molecular point group symmetry of the complex is Cs . Including the tunneling motion we have to choose the molecular symmetry group G 4 (25), which is the adequate group for an internal rotor of C2v symmetry attached to a molecular frame of Cs symmetry. Considering the selection rules arising from these symmetry considerations, the lines in the spectra are attributed to “bottom to bottom” and “top to top”-transitions. Therefore, the difference in the band origins of the two tunneling states accounts for the difference in the tunneling splittings of the ground and the excited state. Since the same selection rules apply for microwave transitions in the ground state of the molecule, unfortunately neither the ground state nor the excited state tunneling frequency can be independently extracted from the experimental data. We should add that despite an intensive search for signals from N2 O–H2 O in the region of the ν1 -monomer vibration in the range between 1250 and 1310 cm−1 no lines have been found. A DFT calculation of the band intensities predicts a five times smaller intensity for this band than for the ν3 -band. However, based on our search we can state that these calculations overestimate the expected intensities.

ACKNOWLEDGMENTS We thank Professor M. Suhm for providing us with FTIR data for N2 O–H2 O. The project has been supported by SFB 452 of the Deutsche Forschungsgemeinschaft.

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