Nuclear Spin Symmetry Conservation and Relaxation in Water

Article pubs.acs.org/JPCA

Nuclear Spin Symmetry Conservation and Relaxation in Water (1H216O) Studied by Cavity Ring-Down (CRD) Spectroscopy of Supersonic Jets Carine Manca Tanner, Martin Quack,* and David Schmidiger Laboratorium für Physikalische Chemie, ETH Zürich, CH-8093 Zürich, Switzerland ABSTRACT: We report high resolution near-infrared laser spectra of water seeded in a supersonic jet expansion of argon probed by cavity ring-down spectroscopy (CRDS) in the R branch of the 2ν3 band (above 7500 cm−1) at several effective temperatures T < 30 K. Our goal is to study nuclear spin symmetry conservation and relaxation. For low mole fractions of water in the gas mixture, we obtained the lowest rotational temperatures and observed nuclear spin symmetry conservation, in agreement with theoretical expectation for inelastic collisions of isolated H2O molecules with Ar and similar to a previous series of experiments with other small molecules in supersonic jet expansions. However, for the highest mole fractions of water, which we used (xH2O < 1.6%), we obtained slightly higher rotational temperatures and observed nuclear spin symmetry relaxation, which cannot be explained by the intramolecular quantum relaxation mechanism in the monomer H2O. The nuclear spin symmetry relaxation observed is, indeed, seen to be related to the formation of water clusters at the early stage of the supersonic jet expansion. Under these conditions, two mechanisms can contribute to nuclear spin symmetry relaxation. The results are discussed in relation to claims of the stability of nuclear spin isomers of H2O in the condensed phase and briefly also to astrophysical spectroscopy.

1. INTRODUCTION More than 80 years ago, experiments by Bonhoeffer and Harteck showed that hydrogen exists in two forms, which differ by their total nuclear spin of the two hydrogen nuclei (each with spin 1/2), ortho-hydrogen, which has a total nuclear spin I = 1, and para-hydrogen with I = 0.1 Taking the generalized Pauli principle into account, the rotational states characterized by odd values of rotational angular momentum J are those of the ortho-hydrogen, while the states with even J belong to parahydrogen. Because of the large energy difference between the first two ortho and para states (J = 0 and J = 1) of H2, it is possible to separate the ortho and para forms by cooling H2 down to its boiling point (20.4 K) in the presence of activated charcoal as a catalyst for interconversion of the two forms. After equilibration, 99.8% of H2 is in its para form, which can be then warmed up. para-Hydrogen can be kept stable for many months in the absence of catalysts and thus can be treated as a nuclear spin isomer of hydrogen and similarly for ortho-hydrogen. These experiments were considered to be an important test of quantum mechanics and the related underlying symmetry principles.2−4 More generally, molecules with several identical nuclei exhibiting a nonzero nuclear spin exist in several forms called nuclear spin isomers. Inelastic collisions usually do not interconvert nuclear spin isomers5 nor do ordinary spectroscopic transitions, resulting thus in selection rules due to approximate nuclear spin symmetry conservation.4,6 Quite a few cases of conservation of nuclear spin symmetry in inelastic collisions have been studied in supersonic jet expansions, and © 2013 American Chemical Society

we may mention, as examples, studies of methane and some of its isotopomers (see7−13 and references cited therein), which could be extended also to low temperature flow cell conditions.14 However, different from hydrogen, on longer time scales under room temperature conditions, methane has been shown to exhibit interconversion between nuclear spin isomers on time scales of hours and less.15 It is now generally accepted that many polyatomic molecules show relatively fast interconversion between nuclear spin isomers (see reviews in refs 3 and 16). The concept of intramolecular nuclear spin symmetry relaxation in polyatomic molecules induced by collisions, which prepare doorway states for conversion, originally developed by Curl et al.15 has successfully been applied to 12CH3F and 13CH3F;16,17 it relies on the so-called quantum relaxation, which occurs if states of different nuclear spin isomers mix. Indeed intra- and intermolecular spin relaxation has been demonstrated on long time scales for a number of molecules, among them fluoromethane and some of its isotopomers,16,17 ethylene and some of its isotopomers,18,19 formaldehyde,20,21 and ammonia22 to cite a few (see also ref 3). In contrast to the mechanism of nuclear spin symmetry relaxation mentioned, which may be called a unimolecular Special Issue: Oka Festschrift: Celebrating 45 Years of Astrochemistry Received: January 28, 2013 Revised: May 13, 2013 Published: May 13, 2013 10105

dx.doi.org/10.1021/jp400958f | J. Phys. Chem. A 2013, 117, 10105−10118

The Journal of Physical Chemistry A

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symmetry conservation and relaxation can be investigated by high resolution spectroscopy in a supersonic expansion. In section 3, we briefly describe our experimental setup and conditions. The results are shown and discussed in section 4 in the context of nuclear spin symmetry relaxation under specific experimental conditions, with formation of water clusters in the supersonic jet. A preliminary report of our work was given in ref 49. In a historical context we can mention here also the early work on the nuclear spin isomers of water, dating back to the early days of quantum mechanics.50−52

process in its essential step, one may generally also have apparent nuclear spin symmetry relaxation in bimolecular reactive processes such as H + H2 → H2 + H

(1)

where the product H2 molecule may have another nuclear spin symmetry than the reactant H2. This effect is in fact subtle as there may be an underlying selection rule with nuclear spin symmetry conservation still valid for the reactive bimolecular collision process, which may not be immediately apparent for a reaction such as eq 1. However, as predicted in ref 6, even in reactions with possibilities of exchange of identical nuclei, such as in the reaction important in astrophysics: H 2+ + H 2 → H3+ + H

2. SYMMETRY AND THEORY 2.1. Rovibrational Spectroscopy and Nuclear Spin Isomers of Water. Water is an asymmetric top molecule that belongs to the C2v point group in its equilibrium geometry (see Figure 1). Using the Longuet-Higgins group of permutation

(2)

there can be remaining selection rules, and this prediction was confirmed experimentally.23,24 The importance of this reaction in the formation of H3+ under a variety of astrophysical conditions is well established as is also the crucial role of H3+ itself.25−27 Another molecule of great astrophysical interest is H2O. The role of nuclear spin symmetry conservation in this molecule has attracted recent interest with the claim that ortho- and paraH2O can be separated, being stable without interconversion in the gas phase and could be stored for months at 255 K even in the condensed phase.28 In careful attempts to reproduce and extend these experiments, these results could not be confirmed neither in our work29 nor by others.30 Of course, in principle, the failure to reproduce the existence of stable ortho- and paraH2O might be due to catalytic impurities or heterogeneous interconversion at catalytic surfaces, which might have been absent in the original experiments.28 Although this seemed unlikely for a number of experimental and theoretical reasons, we decided to study this question under different conditions in supersonic jets, where catalytic impurities and wall effects should be unimportant. There seem to exist no previous studies of nuclear spin symmetry conservation and interconversion in H2O molecules in supersonic jets in spite of its astrophysical interest. The anomaly of intensities in H2O+ spectra relevant for astrophysics has been pointed out but not assigned to nuclear spin symmetry relaxation31 (see also refs 32−39, as well as the discussion in refs 40 and 41). The relaxation of nuclear spin isomers of water has recently been investigated in the condensed phase in rare gas matrixes.42−46 A brief note on terminology may be useful here. We distinguish the process of nuclear spin symmetry conversion, which transforms one nuclear spin isomer into another from the process of nuclear spin symmetry relaxation, which corresponds to a relaxation toward an equilibrium population of the nuclear spin isomers. In the present work, we report observations of the latter process. Although the two processes are obviously (and simply) related, the terms are not exactly synonymous. We can refer here to the similar situation in reactions between enantiomers of chiral molecules, where we have carefully discussed the distinction between the processes of stereomutation or enantiomerization (a transformation from one enantiomer into another) and racemization (a relaxation toward equilibrium47,48). We investigate in the present work nuclear spin symmetry conservation and relaxation in the gas phase in a supersonic jet expansion of water seeded in argon. In section 2, we review the symmetry selection rules for water and how nuclear spin

Figure 1. Schematic representation of the water molecule and its symmetry elements in the C2v point group, including axes definitions.

and inversion operations,53 water belongs to the group MS4 or S2*, isomorphous to C2v, which is the direct product of the S2 group containing the identity E and the permutation of the two protons (1 2), with the inversion group S* = {E,E*}. Table 1 Table 1. Character Table of the C2v and MS4 = S2* Groups

C2v A1 A2 B1 B2

MS4 A+ A− B− B+

C2v

E

C2

σyz

σxz

MS4

E

(1 2)

E*

(1 2)*

1 1 1 1

1 1 −1 −1

1 −1 −1 1

1 −1 1 −1

Tz Rz Tx, Ry Ty, Rx

shows how the irreducible representations A1, A2, B1, and B2 in the C2v point group are related to the parity and permutation symmetry in the MS4 permutation-inversion group, while retaining the “spectroscopic notation” A for symmetric and B for antisymmetric species, and using the notation of ref 6, which makes parity (positive or negative, + or −) explicit as an exponent in the notation. As mentioned in the introduction, water exists in two forms with different total nuclear spins I because of the presence of two identical nuclei of spin IH = 1/2: the form with I = 1 has the highest statistical weight of 3 (MI = 0, ±1) and is called conventionally ortho-H2O, while the form with I = 0 has a 10106



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statistical weight of 1 and is called para-H2O, analogous to the hydrogen molecule. Because of the generalized Pauli principle, the total wave function for H2O should be antisymmetric with respect to the permutation (1 2) of the protons because the protons are fermions; as a consequence the ortho and para isomers do not have the same rotational levels. Indeed, the symmetry species of a JKa,Kc rotational state of an asymmetric top molecule depends on whether Ka and Kc , the projections of total angular momentum J ⃗ on the z-axis in the limiting cases of a prolate symmetric top and an oblate symmetric top, respectively, are even (e) or odd (o); the results are summarized in Table 2 for the case of the totally symmetric Table 2. Symmetry Species of a JKa,Kc Rotational State of Water in the Totally Symmetric Vibrational Ground State in the C2v and MS4 Groups, as Well as the Allowed Combinations with Nuclear Spin Symmetry Γns and the Statistical Weights g; “o” Stands for Odd and “e” Stands for Even Γrot Γns g

Ka,Kc

e,e

o,e

e,o

o,o

C2v MS4 MS4

A1 A+ B+ 1

B2 B+ A+ 3

B1 B− A+ 3

A2 A− B+ 1

Figure 2. Energy level diagram of H2O with the lowest rotational energy levels up to 800 cm−1 of the para nuclear spin isomer (left, in blue) and of the ortho nuclear spin isomer (right, in red) as indicated in Table 3. The symmetry of the rotational species are indicated for the MS4 molecular symmetry group.

54

ground vibrational state of water. The rotational states of water with symmetrical representation (A+ or A−, and Ka,Kc e,e or o,o) combine with the antisymmetric nuclear spin wave function of the two protons B+, while the rovibrational states with antisymmetric representation (B+ or B−, and Ka,Kc o,e or e,o) combine with a symmetric nuclear spin wave function A+. In other words, the ortho or para character of a rotational state can be defined by the sum Ka + Kc . A state JKa,Kc is an ortho state with nuclear spin species Γns = A+ if Ka + Kc is odd, and it is a para state with Γns = B+ if Ka + Kc is even. In addition to the selection rule for electric dipole transitions ΔJ = 0, ±1 for J ≠ 0, and ΔJ = ±1 for J = 0

Geff (J ′Ka′ , Kc′ ← JK , K , Γns, Trot) = a

=C×

B+ ↔ B−

(5)

c

(7)

where α(Trot,ν̃) = L−1 ln(I0/I) is the absorption coefficient at temperature Trot and wavenumber ν̃, L being here the absorption path length, I0 the effective incident intensity, and I the transmitted intensity. In practice, we report the results for CRD spectra in terms of the absorbance per pass App = α × L. σ(Trot,ν̃) is the corresponding absorption cross-section with C the density of the absorbing species. Following the work of Amrein et al.,8 G(J′Ka′,Kc′ → JKa,Kc,Γns,Trot) depends on the rotational temperature and can be approximately related to the relative population p(JKa,Kc,Γns,Trot) of the initial state JKa,Kc of the radiative transition as follows:

leading to ΔKa = ±1, ±3, ±5... and ΔKc = ±1, ±3, ±5...

∫line σ(Trot , ν)̃ ν−̃ 1dν ̃ a

which defines the P, Q, and R branches of a vibrational band, the conservation of nuclear spin symmetry (A↮ B) and change of parity (+ ↔ −) for an electric dipole transition allows the following rovibrational transitions only: (4)

∫line α(Trot , ν)̃ ν−̃ 1dν ̃

= C × G(J ′Ka′ , Kc′ ← JK , K , Γns, Trot)

(3)

A+ ↔ A−

c

(6)

G(J ′Ka′ , Kc′ ← JK , K , Γns, Trot) a

which corresponds to b-type transitions (see also ref 54). Figure 2 provides a survey of the rotational energy levels and their symmetries for H2O in the vibrational ground state. 2.2. Line Intensities and Nuclear Spin Symmetry Conservation or Relaxation in Water. The effective integrated absorption cross-section Geff(JK′ a′Kc′← JKa,Kc, Γns, Trot) at temperature Trot of the rovibrational line corresponding to the transition JK′ a′Kc′ ← JKa,Kc of the nuclear spin isomer Γns (in our case, Γns is implicitly defined by the sum Ka + Kc as mentioned above) is defined by

c

∝ p(JK , K , Γns, Trot)A(JK , K , J ′Ka′ , Kc′ ) a

c

a

c

(8)

where A(JKa,Kc, J′Ka′,Kc′) is the rotational line strength factor for the J′Ka′,Kc′ ← JKa,Kc transition. If the nuclear spin symmetry is conserved (indexed “c”) during the cooling process of the supersonic expansion, the ortho and para isomers keep their relative populations set at room temperature (T0) before the expansion and one should observe a superposition of two Boltzmann distributions. More 10107



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Table 3. Lowest Rotational Levels JKa,Kc of Water up to (E/ hc) = 800 cm−1 as Listed in ref 71; the Symmetry of the Rotational Species Γrot are Indicated for the MS4 Group as Well as the Nuclear Spin Statistical Weight gI

generally, the relative population of rotational level JKa,Kc of the nuclear spin isomer Γns at rotational temperature Trot can then be written as follows: pc (JK , K , Γns, T0 , Trot) = a

c

x(Γns, T0)(2J + 1) Q rot(Γns, Trot)

⎛ E (J , Γns) − E0(Γns) ⎞ Ka , K c ⎟ × exp⎜⎜ − ⎟ kBTrot ⎠ ⎝

JKa,Kc 00,0 10,1 11,1 11,0 20,2 21,2 21,1 22,1 22,0 30,3 31,3 31,2 32,2 32,1 33,1 33,0 40,4 41,4 41,3 42,3 42,2 43,2 43,1 44,1 54,0 50,5 51,5 51,4 52,4 52,3 53,3 53,2 54,2 54,1 55,1 55,0 60,6 61,6 61,5 62,5 62,4 63,4 63,3 64,3 64,2 70,7 71,7 71,6 72,6 72,5 80,8 81,8

(9)

x(Γns, T0) is the mole fraction of nuclear spin isomer Γns at temperature T0 before the expansion, where the isomers are assumed to be equilibrated: x(Γns, T0) = g (Γns)

Q rot(Γns, T0) r Q rot (T0)

⎛ E (Γ ) ⎞ × exp⎜ − 0 ns ⎟ ⎝ kBT0 ⎠

(10)

E0(Γns) is the energy of the lowest level of the nuclear spin isomer Γns and E(JKa,Kc, Γns) in eq (9) is the energy of the rotational level JKa,Kc of the same nuclear spin isomer. g(Γns) is the nuclear spin statistical weight factor; g(A+) = 3 and g(B+) = 1 in the case of water. The rotational partition function of the nuclear spin isomer Γns at temperature T, Qrot(Γns, T), is defined as follows: Q rot(Γns, T ) =

∑ (2J + 1) J

⎡ ⎛ E (J , Γ ) − E0(Γns) ⎞⎤ ⎢ ∑ exp⎜ − Ka , Kc ns ⎟⎥ ⎜ ⎟⎥ ⎢⎣(K , K ) ∈Γ k T B ⎝ ⎠⎦ a c ns (11)

Qrrot(T0)

in eq 10 is the relaxed rotational partition function including nuclear spin at temperature T0 and is defined as follows: r Q rot (T0) =

⎛ E0(Γns) ⎞ ⎟ ⎝ kBT0 ⎠

∑ g(Γns)Q rot(Γns, T0) × exp⎜− Γns

(12)

However, in the case of nuclear spin symmetry relaxation (indexed ″r″), the nuclear spin states are allowed to change during the collisional process of the expansion and the relative populations should represent a global thermal equilibrium among all the states at low temperature. In this case, the relative population of rotational state JKa,Kc of nuclear spin isomer Γns at rotational temperature Trot can be written as follows: p r (JK , K , Γns, Trot) a

=

c

⎛ E (J , Γns) ⎞ g (Γns)(2J + 1) Ka , K c ⎟ × exp⎜⎜ − r ⎟ Q rot(Trot) kBTrot ⎠ ⎝

(13)

Table 3 lists the rotational levels of the vibrational ground state of water up to 800 cm−1 that were used in our calculations to estimate the relative populations p(JKa,Kc, Γns, Trot) for rotational levels with J ≤ 2 (the populations of rotational levels with J ≥ 3 are too small to be relevant for our measurements as discussed below). Figure 3 shows the calculated changes in the relative populations as a function of the rotational temperature Trot in the case of nuclear spin symmetry conservation (with T0 = 298 K no longer mentioned in the notations to simplify the

gI 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3

Γrot +

A B− A− B+ A+ B+ A− B− A+ B− A− B+ A+ B− A− B+ A+ B+ A− B− A+ B+ A− B− A+ B− A− B+ A+ B− A− B+ A+ B− A− B+ A+ B+ A− B− A− B+ A− B− A+ B− A− B+ A+ B− A+ B+

(E/hc)/cm−1 00.00000 23.794350 37.137118 42.371743 70.090805 79.49636 95.175932 134.90162 136.16390 136.76165 142.27848 173.36580 206.30144 212.15635 285.21939 285.41939 222.05276 224.83839 275.49706 300.36232 315.77957 382.51691 383.84254 488.10781 488.13428 325.34794 326.62551 399.45754 416.20876 446.51070 503.96820 508.81214 610.11451 610.34131 742.07315 742.07640 446.69657 447.25239 542.90582 552.91146 602.77350 648.97877 661.54897 756.72491 757.78029 586.24364 586.47921 704.21413 709.60824 782.40993 744.06374 744.16276

expression) and nuclear spin symmetry relaxation. Depending on the sensitivity of the experiment, one might determine if nuclear spin symmetry relaxation occurs already at Trot = 45 K; 10108



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when a resonance occurs in the cavity. Because of perturbations mostly from mechanical vibrations and hysteresis effects in the piezoelectric transducer, the resonances do not occur strictly periodically, but with small jitters. Therefore, a time window TS of 200 μs is defined around the time for the expected resonance; the solenoid valve controlling the opening of the supersonic expansion is activated before the expected resonance to ensure the overlap between the gas expansion and the laser beam. The resonances occurring while the nozzle is not activated are collected separately to obtain the spectral baseline during the same scan and will be referred as “background”. The resonances occurring in the time window TS, after the nozzle has been activated are also collected separately and will be referred to as “signal”. Each recorded decay is analyzed and fitted to estimate the ring-down (RD) constant kRD = τRD−1 according to I(t ) = I(t = 0)exp( −t /τRD) = I(t = 0)exp( −kRDt ) (14)

Figure 3. Relative population of some of the lowest rotational states of water labeled JKa,Kc (up to J = 2) as a function of the rotational temperature Trot (in K) in the case of nuclear spin symmetry conservation (full line) or relaxation (dotted line).

where I(t) is the intensity of the transmitted light through the cavity at time t. More details of the mathematical treatment of the exponential fit are given in ref 10. Typically 50 decays are accumulated for resonances with molecular beam for the signal and about 600 for the background (without molecular beam); the two series of kRD are averaged, and the difference of the two averaged k̅RD values constitute one point of a CRD spectrum, which is obtained by scanning the laser wavelength. The latter is measured at each data acquisition point with the wavemeter. For a relative calibration, the etalon fringes of a 500 MHz etalon are recorded simultaneously and used to linearize the spectrum (the free spectral range of the etalon is known with great precision, and the frequency drift is 1 MHz per day). The difference of k̅RD for signal and background is directly proportional to the absorption coefficient α. The minimum observable absorption coefficients with the sensibility of our setup can therefore be estimated by

however, for Trot < 30 K, the results should be unambiguous with any reasonable sensitivity of the experiment.

3. EXPERIMENTAL SECTION 3.1. Experimental Setup. The improved experimental setup of our cavity ring-down supersonic jet laser spectroscopy has been described in detail previously.10 In the following, we briefly describe the main components. A near-infrared InGaAsP laser diode (Radians Innova) emits up to about 1 mW between 7510 and 8000 cm−1 in single-frequency mode. Minor parts of the laser output are diverted to a 500 MHz external monitor etalon and a wavemeter composed of a scanning Michelson interferometer with a built-in stabilized HeNe laser (Burleigh, WA-1500-NIR) for calibration. The main part of the laser output is led through an acousto-optical modulator AOM (Isomet 1205C-2); the first-order deflection is transferred through a single-mode optical fiber and coupled into an optical cavity using a lens to match the geometry of the laser beam to the single transversal cavity mode TEM00. The cavity is composed of two highly reflective concave mirrors with 1 m radius (Newport, R > 99.97%) mounted on an optical bench (Newport mirror holders and Spindler and Hoyer, Mikrobank) at a distance of about 33 cm. The cavity is set up in a vacuum chamber, the vacuum with residual pressure of typically about 10−7 mbar being maintained by a 8000 L/s oil diffusion pump backed by a combination of a vacuum blower pump and a mechanical roughing pump. The absorption path is crossed at a right angle by a supersonic jet produced by a pulsed slit nozzle. The 33 × 0.1 mm2 slit of the solenoid pulsed nozzle is aligned along the optical axis of the cavity and has a probe distance of less than 1 cm to the axis. After switching-off the laser output via the AOM, the transmitted decaying light intensity is detected by a fast InGaAs photodiode (NewFocus, 125 MHz). An elaborate timing and trigger scheme allows the cavity length to match the laser wavelength during the gas expansion in the cavity.10 It includes a method for matching the cavity length to the wavelength of the laser using a periodic wobble of the cavity length and a switch off of the laser light via the AOM

αmin =

Δτ 1 L τ cτ0 Leff

(15)

where Δτ/τ is the precision of the determination of the ringdown time, L is the cavity length, and Leff is the effective absorption length, corresponding to the part of the supersonic expansion probed by the laser. Accumulating 50 decays as signal and 600 decays as background, the distribution of ringdown times is a narrow Gaussian centered at 7.14 ± 0.03 μs, and the resulting minimum observable absorption is therefore about 2 × 10−7 cm−1, which requires only 1% of absorbing molecules in the gas mixture of a supersonic jet for adequate spectroscopic detection of weak lines (absorption cross-section of about 10−21 cm2). 3.2. Investigation of Nuclear Spin Symmetry Conservation or Relaxation. For a spectroscopic investigation of nuclear spin symmetry conservation or relaxation, two criteria have to be fulfilled:13 (i) at least one transition associated with each nuclear spin isomer has to be measured in order to estimate the relative populations of the isomers and (ii) at least one extra transition associated with one of the nuclear spin isomers has to be measured to determine the rotational temperature. In the case of water, a minimum of three transitions is therefore required. Other criteria arise from the experimental conditions. For example, using a supersonic expansion guarantees low temperatures and a rovibrational 10109



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transition with J > 2 should be hardly observable, which reduces the number of rovibrational transitions which can be measured. The type of laser used for the excitation and the wavelengths available also reduce the number of possible candidates for observed lines. The best conditions for a semiquantitative analysis in a supersonic jet expansion are reached when all the transitions can be measured in a single laser scan to allow almost identical experimental conditions for all transitions. This is unfortunately not possible in the case of water because of the large rotational constants and the corresponding low density of spectral lines. Nevertheless, our previous investigation of methane has shown that our supersonic jet expansion can be considered as uniform during a day.10 Taking the spectral range available with our 1.3 μm laser and the criteria mentioned previously, Table 4 summarizes the water transitions of the 2ν3

simplified notation: GJKa,Kc is the integrated absorption crosssection of the transition in the R branch originating from the state JJKa,Kc. Therefore, (i) G11,0 is the integrated absorption crosssection of the J = 2, Ka = 2, Kc = 1 ← 1,1,0 transition of the ortho isomer, (ii) G11,1 is the integrated absorption cross-section of the 2,2,0 ← 1,1,1 transition of the para isomer, and (iii) G21,2 is the integrated absorption cross-section of the 3,2,1 ← 2,1,2 transition of the ortho isomer. Using a supersonic jet expansion prevents us from knowing the total concentration of the probed species. In recent work,10 we have shown that we can circumvent this problem by working with relative effective integrated absorption crosssections of one line to another assuming that the supersonic jet expansion remains uniform during a day. The estimation of the line strength (Hönl−London) factor indicated in eq (8) remains an issue. Indeed, the expression of A(JKa,Kc,JK′ a′,Kc′) is not known as simply for an asymmetric top as for the other types of rotors. The usual way is to use the formulae for the “nearest” symmetric top.55 Indeed, intensity formulae have been derived for J values up to J = 3 for water within this approximation.56 Another solution would be to circumvent the estimation of the line strength factors. Since this factor is the only term that does not depend on the temperature in eq (8), the ratio of the integrated absorption cross-section of a given line at two different temperatures T1 and T2 is equal to the ratio of corresponding populations:

Table 4. Assigned Transitions with J ≤ 2 of the 2ν3 Band of 16 H2O in the Region Reachable with the 1.3 μm Diode Laser; the Symmetry of the Nuclear Spin Isomer Γns is Indicated (“o” Stands for Ortho and “p” for Para) ν̃/cm−1

J′

7479.6355 7497.14015 7498.4767 7511.92596 7528.09182 7534.7981 7567.5814

1 2 3 3 2 2 3

K′a 1 1 0 1 2 2 2

K′c 1 2 3 3 1 0 1

←

J 0 1 2 2 1 1 2

Ka 0 0 1 0 1 1 1

Kc

Γns

0 1 2 2 0 1 2

+

B A+ A+ B+ A+ B+ A+

(p) (o) (o) (p) (o) (p) (o)

GJ

(T1)

GJ

(T2)

Ka , K c

band, which might be observable with our experimental setup. They are all from the R branch and too far from each other to be recorded in one scan only. Furthermore, the adjustment and stabilization of the diode laser below 7508 cm−1 requires a significant amount of time, preventing us to systematically record all these lines in one day. In the results presented below, the last three transitions in Table 4 have been systematically investigated, which is the minimum required to investigate a possible nuclear spin symmetry conservation and relaxation. Whenever possible, the line at 7498.4767 cm−1 was also measured and confirmed the results (both the estimation of the rotational temperature and the efficiency of nuclear spin symmetry relaxation) deduced from the analysis of the three other lines. Since there is no ambiguity between the transitions of the 2ν3 band investigated systematically, from now on, we use a

Ka , K c

=

p(JK , K , Γns, T1) a

c

p(JK , K , Γns, T2) a

(16)

c

The three selected lines have already been investigated at 296 K; their line strength SJKa,Kc(296 K), defined as SJ

Ka , K c

(296 K) =

̃ ν̃ ∫line σ(ν)d

(17)

can be related to GJKa,Kc(296 K) according to GJ

Ka , K c

(296 K) ≃

SJ

Ka , K c

(296 K) ν0̃

(18)

where ν̃0 is the position of the line in cm−1. Therefore, we can estimate GJKa,Kc(T) with the following relationship:

Table 5. Experimental Position and Line Strength of the Five Selected Transitions; All the Line Strengths Found in the Literature Have Been Converted in the Same Unit for Comparison; Standard Deviations Are Indicated in Parentheses in Units of the Last Digit Given line strength S/(10−23 cm molecule−1)

transition J′Ka′Kc′ ← JKa,Kc

ν̃/cm−1

ref 72

ref 58

ref 59

ref 57

Avg. exp.a

ref 73b

from fitc

← ← ← ← ←

7497.14015 7528.09182 7534.79810 7511.92556 7567.58137

3.855

3.836 5.405 1.678 1.061 3.114

4.17(125) 6.83(205) 1.707(512) 1.094(328) 3.801(114)

4.276 6.172 1.856 1.190 3.590

4.03(22) 6.13(71) 1.73(9) 1.12(7) 3.42(33)

3.73 5.46 1.64 1.01 3.16

6.78 6.13 1.77 2.58 2.92

21,2 22,1 22,0 31,3 32,1

10,1 11,0 11,1 20,2 21,2

1.660 3.184

a

Average from all experimental values in the literature for comparison, one standard deviation being given in parentheses. bTheory supplementary, data being made available by J. Tennyson and L. Lodi. cRelative intensities obtained from a simulated spectrum with the spectroscopic constants of ref 74 and scaled to the 22,1 ← 11,0 transition as 6.13 × 10−23 cm molecule−1, including rovibrational couplings as given therein. The fitted wavenumbers are 7528.7; 7537.5; 7513.1, 7568.1 cm−1 in this model. 10110


The Journal of Physical Chemistry A GJ

Ka , K c

(T ) ≃

SJ

Ka , K c

(296 K) ×

ν0̃

Article

before the expansion, and dynamical pressure in the cavity) so that the spectra were always recorded under the same conditions. The only parameter that was changed between two measurements was the composition of the gas mixture and more specifically the concentration of water. The gas composition was generated by sending the carrier gas (Ar with pAr = 2 bar) through a bubbler filled with distilled water and maintained at θbath. Table 6 lists the values of θbath used for our measurements and therefore the expected partial pressure and mole fraction of water in the gas mixture before the expansion.

p(JK , K , Γns, T ) a

c

p(JK , K , Γns, 296 K) a

c

(19)

The relative population of one state labeled “1” compared to another labeled “2” can be expressed as GJ

(T )

1K , K a1 c1

GJ

2K

(T ) a2 , Kc 2

≃

p(J1

Ka1, Kc1

, T ) p(J2

Ka2 , K c 2

p(J2

Ka2 , K c 2

, T ) p(J1

Ka1, Kc1

, 296 K) ν ̃

0,2

SJ

(296 K)

1K , K a1 c1

, 296 K) ν0,1 ̃ SJ

2K

(296 K)

Table 6. Experimental Conditions (θbath, Estimated p(H2O) and xH2O) Used for Our Series of Experiments with H2O:Ar Supersonic Jet Expansion, and Rotational Temperature Trot Obtained from the Ratios of Integrated Absorption CrossSections

a2 , Kc 2

(20)

where ν̃0,i is the position of the transition arising from the state labeled “i” in cm−1. It turns out that several measurements already published lead to significantly different values of line strength as indicated in Table 5. The line strength of the transitions can differ by 11% to 26% depending on the work. Figure 4 shows the resulting G-

θbath/°C

p(H2O)/mbar

xH2O/%

G11,1/G11,0

G21,2/G11,0

Trot/K

2.0(1) 5.0(1) 10.0(1) 14.0(1) 16.0(1) 20.0(1) 20.0(1) 25.0(1)

7.06(7) 8.72(8) 12.27(14) 15.98(13) 18.17(17) 23.37 23.37 31.66

0.35 0.44 0.61 0.80 0.91 1.2 1.2 1.6

0.23(2) 0.31(2) 0.27(2) 0.30(3) 0.50(4) 0.46(3) 0.43(3) 0.43(5)

0.10(2) 0.11(2) 0.11(2) 0.14(3) 0.16(2) 0.21(3) 0.22(3) 0.25(3)

19(1) 22(1) 21(1) 23(1) 25(1) 27(1) 29(1) 31(1)

The overlap of the supersonic expansion and the laser beam is the main issue of our trigger scheme since the measurement is not performed at a given time but during the time window TS (see section 3.1). We have measured the effective pulse profile of the supersonic expansion to obtain the best experimental conditions available for our semiquantitative investigation. Figure 5 shows the intensity of the CRD signal recorded at the maximum of the R(11,0) transition as a function of the delay between the beginning of the electric signal activating the opening of the nozzle, and the beginning of the measurement window TS. This latter window is a constraint determined by

Figure 4. Ratios of effective integrated absorption cross-section (G) of the R(11,1) and R(21,2) transitions compared to that of the R(11,0) transition as a function of the rotational temperature, Trot. The Gratios are calculated according to eq (20) and experimental data available in the literature at room temperature in the case of nuclear spin symmetry conservation (full line) or relaxation (dotted line).

ratios G11,1/G11,0 and G21,2/G11,0 as a function of the rotational temperature Trot calculated from the experimental data found in the literature.56−59 Our own approximate measurements with a 50 cm path cell at room temperature agree with those from ref 59. However, if one wants to rigorously use eq (16), the integrated absorption cross-section of the 3,2,1 ← 2,1,2 transition is too small in our direct absorption measurements to definitely rely on our own result only. This difficulty is probably also the main reason of the discrepancy between the different measurements. Therefore, in a first estimation, we will not simply consider one value of the relative integrated absorption cross-section in order to determine Trot, but a range taking all the experimental results published into account, as shown in Figure 4. This does not prevent us from obtaining our qualitative answer on nuclear spin symmetry relaxation of water as will be shown below. It only increases the uncertainty in the rotational temperature. 3.3. Measurements. We chose not to change the gas expansion parameters (i.e., nozzle time opening, delay between the nozzle opening and the laser, pressure of the gas mixture

Figure 5. CRD signal at the maximum of the R(11,0) transition for the H2O:Ar supersonic jet expansion (a) as a function of the delay between the electric signal activating the opening of the nozzle and the beginning of the measurement window of the trigger system (b). 10111



Article

0.0067 cm−1. We used the most intense line, assigned as R(11,0), as reference to calculate the relative integrated absorption cross-section of the two other transitions. These G-ratios are independent of the total concentration but proportional to the ratio of relative populations as discussed in section 3.2. Figure 7 shows the estimation of the G-ratios from the R(11,1) and R(21,2) transitions compared to that of the R(11,0)

the cavity and the frequency of the piezoelectric transducer mounted on one of the mirrors of the cavity (see section 3.1); we have optimized the delay between the nozzle opening and the time window TS as well as the expansion parameters (duration of the pulse, pressure of the gas mixture before the expansion) so that the absorption measured from the CRD signal is maximal and constant during the time window TS, without keeping the nozzle opened for an unnecessarily long time in order to optimize the pumping efficiency in the cavity. Figure 5 shows a typical pulse profile of an H2O:Ar expansion with a width of ∼500 μs; it exhibits a plateau of at least 200 μs where the measurement can occur.

4. RESULTS AND DISCUSSION 4.1. Determination of the Rotational Temperature. Figure 6 shows the CRD spectra of the three selected

Figure 7. Ratios of integrated absorption cross-section (G) of the R(11,1) and R(21,2) transitions compared to that of the R(11,0) transition as function of the rotational temperature, Trot. The uncertainty indicated for the experimental points from the various H2O:Ar expansions arises from the Gaussian fit of each line measured with the jet-CRD setup only. For the ratio G21,2/G11,0, there is no visible difference between the models of conservation or relaxation (as expected). The triangle symbols represent measurements with xH2O > 0.9% with cluster formation; the square symbols represent measurements with xH2O < 0.9% without cluster formation.

transition, i.e., G11,1/G11,0 and G21,2/G11,0 with the help of eq (20) as a function of the rotational temperature (see Figure 4), as well as the values obtained from our experimental measurements. The G21,2/G11,0 ratio of the two lines both arising from an ortho state is used to estimate the rotational temperature, while the G11,1/G11,0 ratio allows us to investigate nuclear spin symmetry relaxation. One might think that three lines only, i.e., the minimum required, is hardly sufficient to determine the rotational temperature and furthermore to investigate the ortho/para ratio of water monomer. Before we discuss the results regarding nuclear spin symmetry conservation or relaxation, we would like to provide some further observations from our work performed on methane in order to support our results on water. In our most recent investigation of methane with the supersonic jet/cavity ring-down setup,10 21 transitions of the ν2 + 2ν3 band were investigated between 7 and 48 K; we have observed an excellent agreement between our experimental measurements and the predictions of temperature based on the assumption that the populations follow a Boltzmann distribution as described in ref 8, except for nuclear spin symmetry effects. Moreover, we have changed our experimental conditions of the supersonic jet expansion between the two series of measurements using a larger pressure of argon and a lower partial pressure of water compared to the measurements

Figure 6. Jet-CRD spectra as absorbance per pass App of the R(11,0), R(11,1), and R(21,2) transitions of water (from left to right) for various H2O:Ar gas mixtures: 0.35% at 19 K, 0.44% at 22 K, 0.8% at 23 K, 0.91% at 25 K, and 1.2% at 29 K in argon (from top to bottom). The rotational temperature has been determined using Figure 7.

transitions, i.e., R(11,0), R(11,1), and R(21,2), of the 2ν3 band of water recorded in a H2O:Ar supersonic expansion with a water mole fraction of 0.35% up to 1.6%. The spectra are shown as absorbance per pass (App = αL) since we can not estimate the concentration of the supersonic expansion. We made no special effort to calibrate these lines, and the position reported in the Hitran database for these transitions57 is considered as adequate for the present purpose. Each row of Figure 6 corresponds to the three spectral regions that were systematically investigated in one day with the same experimental conditions. Each column corresponds to one spectral region recorded on different days with different partial pressures of water in the gas mixture, other parameters of the supersonic expansion being kept the same (see section 3.3). All the lines were fitted with a Gaussian profile, and they exhibit a full width at half-maximum (FWHM) ranging from 0.0055 to 10112



Article

translational temperatures is frequently satisfied, including hydrides such as HF and (HF)2 and their isotopomers60,61 and CH4.10,62 For all these reasons, we believe that even if only three lines were used, the reproducibility of our setup and robustness of our approach is adequate as shown by our previous measurements. 4.2. Investigation of Nuclear Spin Symmetry Conservation and Relaxation. In Figure 7, the measurements can be classified into two groups, regarding nuclear spin symmetry. For measurements with the lowest mole fractions of water (i.e., xH2O < 0.9%), the G-ratios indicate that the nuclear spin symmetry is fully conserved, analogous to what has been found for methane,8 also with the same experimental setup,10 and in agreement with what theory predicts for inelastic collisions.5,6 This result differs from what has been observed in the condensed phase, especially when water is trapped in rare gas matrixes.42,44 In this case, the time for relaxation of some hundreds of minutes is due to the interaction with the matrix and results from the coupling between the water molecule and its Argon cage; the relaxation in Xenon matrixes is considered to be enhanced by the high natural abundance of Xenon isotopes with nuclear magnetic moments. Surprisingly, for the highest mole fractions of water that we used (xH2O > 0.9%), the G-ratios indicate an unambiguous nuclear spin symmetry relaxation. For xH2O = 0.91%, the ortho− para population ratio is estimated to be of 2.1:1, while it is 3:1 in the case of nuclear spin symmetry conservation. This is, to our knowledge, the first time that nuclear spin symmetry relaxation in a supersonic expansion is observed in the case of water. Several mechanisms can be considered to understand the nuclear spin symmetry relaxation observed in the gas phase. The first one usually assumed for small polyatomic molecules is the so-called quantum relaxation mechanism. It was first suggested by Curl et al.15 and further used by Chapovsky et al. in the case of fluoromethane for example.16 This mechanism relies on the existence of close lying states of different nuclear spin isomers that can mix because of nuclear spin−rotation interaction; it also requires these states to be populated by collisions. In the case of water, at least a pair of states (one ortho and one para) has to show such a mixing by spin− rotation interactions. This mechanism is therefore strongly connected to the energy gap between the states, i.e., the density of states. The question whether ortho−para transitions can be observed for water has been discussed recently,63 and ab initio calculations have shown that the hyperfine nuclear spinrotational coupling constants are quite small, about 30 kHz. The authors have also tried to determine the most strongly coupled states (separated by less than 0.1 cm−1), which have to be investigated in order to observe nuclear spin symmetry relaxation. It turns out that none of them can be significantly populated under our experimental conditions at low temperatures, the lowest pair being around 3300 cm−1. Hence, this mechanism has to be excluded under our experimental conditions. Another possible mechanism for nuclear spin symmetry relaxation is that intermolecular interactions through collision with a partner would modify energetically close lying levels of the water molecule. In that case, it seems highly improbable that Argon would lead to collision induced nuclear spin symmetry relaxation because it is an inert gas with neither orbital nor spin contribution to the total angular momentum;

with methane. Therefore, the collision rate of a probed molecule with argon at 300 K increased (from about 8 × 109 s−1 for methane, up to 2 × 1010 s−1 for water), which we believe might compensate for a reduced cooling efficiency of water, if any. For the series of measurements with water, the rotational temperature was estimated between 19 and 31 K. Moreover, Figure 8 shows the estimated rotational temperature as a

Figure 8. Rotational temperature Trot (in K) deduced from the jetCRD spectra of water shown in Figure 6 as a function of mole fraction of water xH2O.

function of the mole fraction of water in the gas mixture (xH2O). The approximately linear relationship observed is obviously not derived from a model and is just a guide for the eyes. Nevertheless, it confirms that the lower the mole fraction of water, the lower the rotational temperature, in agreement with the corresponding result obtained for methane measurements.10 It also provides an indication of the reproducibility and the reliability of the measurements as well as the stability of the experimental setup: the two measurements performed with θbath = 20 °C exhibit rotational temperatures that differ by 2 K, i.e., (28 ± 1) K, which includes both the standard deviation from the Gaussian fit of the lines and the uncertainty on the rotational temperature Trot discussed in section 3.2. As mentioned above, whenever possible, further lines listed in Table 4 were measured in addition to the three systematically investigated, for instance, the J′ = 2, Ka′ = 1, Kc′ = 2 ← J = 1, Ka = 0, Kc = 1 transition; its effective integrated absorption cross-section does not indicate any sizable nonBoltzmann effect and confirms our estimation of the rotational temperature when this test was possible.49 Finally, we estimated the transversal translational temperature of the expansion from the FWHM of the lines measured using a fit with a Gaussian profile. Depending on the concentration of water in the gas mixture, we found a Doppler width ranging from 0.0055 to 0.0067 cm−1, which corresponds to an effective translational temperature of about 22 K up to 30 K, in good agreement with our estimation of the rotational temperature. Here again, we found consistent behavior: (i) the Doppler width decreases as the estimated rotational temperature decreases, and (ii) the translational temperature of water is similar to that estimated in the case of methane measurements. While the apparent translational temperature derived from the Doppler line shape need not be identical to the rotational temperature and, indeed, the line shape need not be Gaussian in principle, we have found that for our expansion conditions the simple relation of apparent rotational and 10113



Article

In Figure 9, we observe a deviation from the linear model for the highest mole fractions of water that we used. This is clear evidence that water clusters are present in the supersonic jet

no strong intermolecular interactions are expected. Furthermore, if the nuclear spin relaxation observed experimentally originated from collisions with Argon, it could not explain why it was not observed for the lowest concentrations of water. However, collision with another water molecule may induce intermolecular interactions strong enough to fulfill the criteria. One can expect the formation of water clusters and changes in the symmetry of the system as well as in the energy level distribution. Indeed, once clusters are formed, there arise two important mechanisms for nuclear spin symmetry relaxation. 4.3. Nuclear Spin Symmetry Relaxation in (H2O)n Clusters. A direct measurement of the concentration of water clusters by spectroscopy was impossible under our conditions and in this spectral region. Nevertheless, we can get an estimation of the proportion of the water monomer. Figure 9 shows the ratio of the effective integrated absorption cross-

expansion for mole fractions of water 0.9% < xH2O < 1.6%. We use the values of the line strength of the three transitions at 296 K published in the Hitran database57 to estimate the relative density of the water monomer at temperature T: pJ (296 K) G Jeff (T ) Cmonomer(T ) K ,K Ka , K c = eff a c × Cmonomer(296K) p J (T ) G J (296 K) Ka , K c

Ka , K c

(21)

Figure 10. Estimated proportion of water in the monomer form in the supersonic expansion χmonomer (in %) from the R(11,0), R(11,1), and R(21,2) transitions and nuclear spin symmetry relaxation efficiency estimated from Figure 7 as a function of the expected mole fraction of water in the gas mixture xH2O (in %). Figure 9. Ratios of effective integrated absorption cross-section of the R(11,0), R(11,1), and R(21,2) transition over the corresponding relative population of the initial rotational level p11,0, p11,1, and p21,2, respectively, as a function of mole fraction of water xH2O.

Figure 10 shows the relative proportion of water in the monomer form χmonomer (χmonomer = xmonomer/xH2O) estimated from the effective integrated absorption cross-sections of the three transitions as a function of the mole fraction of water in the gas mixture (xH2O). The difference between the estimations from the three lines arises from the uncertainty of the effective integrated absorption cross-sections, that of the rotational temperature, and the accuracy of the line strength at 296 K (see section 3). The proportion of monomers decreases as the mole fraction of water in the gas mixture increases. In Figure 10, we also show the nuclear spin symmetry relaxation efficiency as a function of the mole fraction of water. This is estimated from Figure 7 with the assumption that for a given rotational temperature a certain fraction of water follows the nuclear spin symmetry conservation model and the other fraction follows the nuclear spin symmetry relaxation model. The nuclear spin symmetry relaxation efficiency clearly correlates the decrease of the relative proportion of monomer and the formation of water clusters (see Figure 10) . We believe that excited water clusters can be formed in a supersonic jet expansion via two-body collisions. They can redissociate or the additional collisions with the carrier gas might lead to the dissociation or the stabilization of the briefly formed clusters according to the following simplified mechanism:

sections over the expected relative population determined from Figure 7 that we will note pJKa,Kc from now on to simplify the equations, as a function of the mole fraction of water xH2O in the gas mixture. According to eqs 7 and 8, the ratio Geff JKa,Kc/pJKa,Kc is independent of Trot but should be proportional to the concentration of the absorbing species, i.e., that of the water monomer. For low mole fractions of water, we observe a roughly linear dependence of GJeff /pJKa,Kc for the three Ka,Kc transitions investigated systematically. Assuming that the water vapor is in the monomer form, it is possible to get an estimation of the ratio of the line strength factors (i.e., A11,1/A11,0 and A21,2/A11,0) that are used in Figure 7 for a refined version of Figure 4. One might argue that Geff JKa,Kc/pJKa,Kc obviously depends on pJKa,Kc from our estimation of Trot. Taking the uncertainty of 2 K of the rotational temperature into account, we have checked that the Geff JKa,Kc/pJKa,Kc ratios and slopes found in Figure 9 do not change by more than 10%; therefore, we consider the Figure 7 as a valid representation of our results. 10114



Article

H 2O + (H 2O)n − 1 → (H 2O)*n

(22)

(H 2O)*n → (H 2O)n − 1 + H 2O

(23)

(H 2O)*n + Ar → H 2O + (H 2O)n − 1 + Ar

(24)

(H 2O)*n + Ar → (H 2O)n + Ar

(25)

happens in stabilized (H2O)n clusters or in excited clusters (H2O)*n .

5. CONCLUSIONS Our supersonic jet cavity ring-down near-infrared laser spectroscopy of H2O seeded in Ar allows us to reach effective rotational temperatures well below 30 K and thereby to study the possibilities of nuclear spin symmetry conservation or relaxation. The most important experimental conclusion from our study is that effective nuclear spin symmetry conservation is valid under conditions of high dilution for H2O in Ar, where monomers dominate in the experiments: the high (room) temperature ratio of ortho and para H2O is essentially maintained. However, at somewhat higher concentration of H2O in Ar, when the formation of (H2O)n is possible and evident from the mass balance, we find interconversion with ortho and para isomers relaxing essentially to a Boltzmann equilibrium at the relevant low temperature in the jet. The conclusion on nuclear spin symmetry conservation under conditions where H2O monomer collisions with Ar dominate the cooling process is in agreement with expectations for such inelastic collisions and the short time scale of the supersonic jet expansion, including quantitative estimates for interconversion rates for nuclear spin isomers of H2O.3−5,63,75 However, the observation of nuclear spin symmetry relaxation under conditions where (H2O)n clusters are present in the jet allows for interpretations of this phenomenon by different mechanisms. Disregarding less likely interpretations of the results, two different main mechanisms can be mentioned (i) de facto and (ii) de lege symmetry breaking of nuclear spin symmetry. (i) In the de facto nuclear spin symmetry breaking, the nuclear spin symmetry of the monomer H2O appearing as reactant in the collision with (H2O)n−1 in eq (22) is different from the nuclear spin symmetry of the H2O product in the dissociation of the intermediate complex (H2O)*n in eq (23). This can happen with conservation of nuclear spin symmetry in the overall process, eq (22) followed by eq (23), if there is possibility of exchange of protons between the H2O monomer units in the intermediate complex (H2O)*n . For example, even in the case of the dimer (H2O)2 as intermediate, one can have de facto a change from two ortho to two para isomers following the discussion of ref 6 (see Table 6 therein).

The relative concentrations of water clusters (H2O)n in a pulsed slit-jet supersonic expansion has already been investigated by several groups under various conditions.64−66 Clusters from the dimer to pentamer range have been observed for low concentrations of water in H2O:He and H2O:Ar gas mixtures.64,65 It has been also shown that, for higher concentrations of water, the contribution of larger clusters from hexamer to decamer range is not negligible.66 We then think that there exists substantial evidence for cluster formation under the relevant conditions in our experiments. The water molecules resulting from the formation/ dissociation mechanism according to Reactions 22−24 would then exhibit monomer components on the spectrum but would also retain the information of the cluster lifetime where (i) protons could have been exchanged, (ii) symmetry could have been changed, and (iii) energy level distribution could have been modified, all of these processes being able to lead to nuclear spin symmetry relaxation. Proton transfer has been investigated in small (charged) clusters of water both experimentally67,68 and theoretically.69,70 It is not clear yet whether the transfer of protons occurs in successive steps in a Grotthuss-like mechanism or in a concerted reaction mechanism; nevertheless, apparent nuclear spin symmetry relaxation may occur in the monomer when a proton is transferred in the complex. For small neutral clusters, proton transfer may appear less likely, but it cannot be excluded for large clusters. However, when a water molecule is hydrogenbonded in a water cluster, it can no longer freely rotate but exhibits a barrier to rotation, which becomes an internal rotation with tunneling. This obviously greatly changes possibilities for close degeneracies and nuclear spin symmetry relaxation by the unimolecular mechanism with nuclear spin− rotation interactions. For water clusters there exist no detailed theoretical results on this mechanism, but we can refer to the work of Limbach et al.40 who have discussed quite an analogous situation in the case of the hydrogen molecule bound to a transition metal: the barrier to rotation increases with the H−H bond length and the quantum rotation is not immediately quenched but converted into a “rotational tunneling splitting”. The energy difference between the two lowest states (ortho and para) decreases as the H−H bond length increases, and therefore, the time scale for the nuclear spin symmetry relaxation decreases. The same kind of mechanism has been applied to understand the ortho/para relaxation in ice:41 while in the water monomer, the energy splitting between the lowest ortho and para states is of 4 × 1011 Hz, in an ice crystal hydrogen bonding and other intermolecular interactions quench the ortho/para energy difference to some 10−2 Hz. We believe that the same kind of mechanism can apply here: as the water clusters are formed, the O−H bond length involved in a hydrogen bond increases, and the rotation is converted into a rotational tunneling splitting, reducing the energy difference between pairs of ortho and para states. We cannot distinguish, however, whether the nuclear spin symmetry relaxation

(H 2O)ortho + (H 2O)ortho → (H 2O)*2 → (H 2O)para + (H 2O)para

(26)

Thus, a change from ortho- to para-H2O monomers is possible in this process even if some de lege selection rules are maintained if one considers the combined overall quantum state of the compound system, due to the assumption of overall nuclear spin symmetry conservation. Similar considerations arise for larger clusters (H2O)n>2 but are more complex. (ii) If the de lege nuclear spin symmetry breaking is important, then this amounts to nuclear spin symmetry mixing in some of the intermediate (H2O)n complexes, which can happen even without exchange of the protons between the H2O monomer units. The mechanism is essentially the same as in the general quantum relaxation model of refs 15−18 for polyatomic molecules, the complex (H2O)n being treated as the polyatomic molecule. Although little is known about such processes in (H2O)n, they appear qualitatively much more likely than in the monomer H2O because of the much higher density 10115



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(6) Quack, M. Detailed Symmetry Selection Rules for Reactive Collisions. Mol. Phys. 1977, 34, 477−504. (7) Dübal, H. R.; Quack, M.; Schmitt, U. High Resolution Interferometric Infrared Spectroscopy of CO2 and CH4 Vapour at Low Temperatures Near 10 K: Collisional Cooling in Supersonic Jets and Nuclear Spin Symmetry Conservation. Chimia 1984, 38, 438− 439. (8) Amrein, A.; Quack, M.; Schmitt, U. High Resolution Interferometric Fourier Transform Infrared Absorption Spectroscopy in Supersonic Free Jet Expansions: Carbon Monoxide, Nitric Oxide, Methane, Ethyne, Propyne, and Trifluoromethane. J. Phys. Chem. 1988, 92, 5455−5466. (9) Niederer, H. M.; Albert, S.; Bauerecker, S.; Quack, M.; Seyfang, G. Non-Equilibrium Population of CH4 Nuclear Spin Species in the Gas Phase at 16 K. Chimia 2010, 64, 582. (10) Manca Tanner, C.; Quack, M. Reinvestigation of the ν2 + 2ν3 Subband in the Overtone Icosad of 12CH4 Using Cavity Ring-Down (CRD) Spectroscopy of a Supersonic Jet Expansion. Mol. Phys. 2012, 110, 2111−2135. (11) Horká-Zelenková, V.; Quack, M.; Seyfang, G. Test of Nuclear Spin Symmetry Conservation in Partially Deuterated MethaneIsotopomers in the Expansion of a Molecular Supersonic Jet. Chimia 2010, 64, 568. (12) Caviezel, M.; Quack, M.; Seyfang, G. High Resolution Diode Laser IR-Spectra Measured in a Pulsed Slit Nozzle Supersonic Jet Expansion. Chimia 2006, 60, 466. (13) Snels, M.; Horká-Zelenková, V.; Hollenstein, H.; Quack, M. High-Resolution FTIR and Diode Laser Spectroscopy of Supersonic Jets. In Handbook of High-Resolution Spectroscopy; Quack, M., Merkt, F., Eds.; Wiley: Chichester, U.K., 2011; Vol. 2, pp 1021−1067. (14) Niederer, H. M.; Albert, S.; Bauerecker, S.; Boudon, V.; Seyfang, G.; Quack, M. On Nuclear Spin Symmetry Conservation in Methane. Faraday Discuss. 2011, 150, 128−130. (15) Curl, R. F. J.; Kasper, J. V. V.; Pitzer, K. S. Nuclear Spin State Equilibration through Nonmagnetic Collisions. J. Chem. Phys. 1967, 46, 3220−3228. (16) Chapovsky, P. L.; Hermans, L. J. F. Nuclear Spin Conversion in Polyatomic Molecules. Annu. Rev. Phys. Chem. 1999, 50, 315−345. (17) Chapovsky, P. L. Hyperfine Spectra of CH3F Nuclear Spin Conversion. J. Phys. B: At., Mol. Opt. Phys. 2000, 33, 1001−1011. (18) Chapovsky, P. L.; Cosléou, J.; Herlemont, F.; Khelkhal, M.; Legrand, J. Separation and Conversion of Nuclear Spin Isomers of Ethylene. Chem. Phys. Lett. 2000, 322, 424−428. (19) Sun, Z.-D.; Takagi, K.; Matsushima, F. Separation and Conversion Dynamics of Four Nuclear Spin Isomers of Ethylene. Science 2005, 310, 1938−1941. (20) Peters, G.; Schramm, B. Nuclear Spin State Relaxation in Formaldehyde: Dependence of the Rate Constant on Pressure. Chem. Phys. Lett. 1999, 302, 181−186. (21) Chapovsky, P. L. Nuclear Spin Conversion in Formaldehyde. J. Mol. Struct. 2001, 599, 337−345. (22) Hepp, M.; Winnewisser, G.; Yamada, K. M. Collisional Nuclear Spin Intercombination in NH3 Observed in Supersonic Jet Expansion by Diode Laser Spectroscopy. J. Mol. Spectrosc. 1992, 153, 376−384. (23) Uy, D.; Cordonnier, M.; Oka, T. Observation of Ortho-Para H3+ Selection Rules in Plasma Chemistry. Phys. Rev. Lett. 1997, 78, 3844− 3847. (24) Cordonnier, M.; Uy, D.; Dickson, R. M.; Kerr, K. E.; Zhang, Y.; Oka, T. Selection Rules for Nuclear Spin Modifications in Ion-Neutral Reactions Involving H3+. J. Chem. Phys. 2000, 113, 3181−3193. (25) Oka, T. Observation of the Infrared Spectrum of H3+. Phys. Rev. Lett. 1980, 45, 531−534. (26) Oka, T.; Geballe, T. R.; Goto, M.; Usuda, T.; McCall, B. J. Hot and Diffuse Clouds near the Galactic Center Probed by Metastable H3+. Astrophys. J. 2005, 632, 882−893. (27) Oka, T. Spectroscopy and Astronomy: H3+ from the Laboratory to the Galactic Center. Faraday Discuss. 2011, 150, 9−22. (28) Tikhonov, V.; Volkov, A. Separation of Water into its Ortho and Para Isomers. Science 2002, 296, 2363.

of quantum states and thus higher likelihood of near degeneracies in (H2O)n. At the present time, our results cannot distinguish between the two mechanisms as we observe only the net effect on the monomer symmetry (ortho- or para-H2O). A relatively straightforward experiment investigating the possibility of exchange of protons in collisions of H2O with (H2O)n−1 would be possible by testing for isotope scrambling in collisions of, say, D2O with (H2O)n−1 in crossed molecular beams. Independent of which mechanism is at the origin of the ortho−para interconversion in our experiments on H2O, we have provided compelling evidence for fast interconversion once (H2O)n clusters are present. Wall effects and related catalysis, say, by paramagnetic impurities, can be excluded under our supersonic jet conditions, where we note that we have studied also expansions of H2O in O2 in independent experiments without substantially changed results. Thus, the present results seem impossible to reconcile with the claim of long-lived ortho and para isomers of H2O in the condensed phase,28 where either mechanism (i) or (ii) or both are expected to be at least as important as in (H2O)n clusters. Given the inability of our and other groups to reproduce the results of ref 28, one must probably look for nonstandard interpretations of the latter experiments. More generally, the possibility of interconversion of ortho and para nuclear spin isomers of H2O via the intermediate (H2O)n clusters opens a wide range of possible experiments relevant for astrophysical and other applications.

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AUTHOR INFORMATION

Corresponding Author

*(M.Q.) Phone: +41 44 632 44 21. Fax: +41 44 632 10 21. Email: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge helpful discussions with Sieghard Albert and Georg Seyfang as well as help on various aspects on our projects from Zoran Bjelobrk, Manfred Caviezel, Zohra Guennoun, and Veronica Horká-Zelenková. Jonathan Tennyson and Lorenzo Lodi provided us with their theoretical line intensities as cited in the table. Our work is supported financially by ETH Zürich, the Schweizerischer Nationalfonds, and the European Research Council, ERC.

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Nuclear Spin Symmetry Conservation and Relaxation in Water

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