Anharmonicity and hydrogen bonding. III. Analysis of the near infrared spectrum of water trapped in argon matrix

Chemical Physics 273 (2001) 217±233

www.elsevier.com/locate/chemphys

Anharmonicity and hydrogen bonding. III. Analysis of the near infrared spectrum of water trapped in argon matrix J.P. Perchard * LADIR/Spectrochimie Mol eculaire, UMR 7075, Universit e Pierre et Marie Curie, B^ atiment F 74, case courrier 49, 4 Place Jussieu, 75252 Paris Cedex 05, France Received 30 May 2001; in ®nal form 11 September 2001

Abstract The infrared spectra of H2 16 O and H2 18 O trapped in solid argon were recorded in the range 8000±15 cm 1 at Ar/H2 O molar ratios between 2000 and 20. At low concentration in water the quasifreely rotating monomer predominates, giving rise to relatively narrow rovibrational signals for the transitions involving exclusively the J ˆ 0 and 1 rotational levels, i.e. the R(0)-, Q(1)- and P(1)-type transitions. For the dimer most of the one and two quanta transitions of both proton acceptor (PA) and proton donor (PD) subunits were identi®ed on the basis of 16 O=18 O isotopic substitution and of the results previously obtained in nitrogen matrix [Chem. Phys. 266 (2001) 109]. A new assignment for m3 of PA is proposed, involving the internal rotation of PA around its symmetry axis, as observed in the gas phase and in He clusters. As in N2 matrix the 2m1 band of PD has not been observed, which con®rms the intensity weakening of the ®rst overtone of a hydrogen-bonded OH oscillator (OHb ). The same phenomenon occurs for larger polymers (H2 O)n , n > 2. The data analysis is focused on three points: rovibrational analysis and determination of the rotational parameters of some A1 vibrational levels; role of Fermi resonance as shaping mechanism of the mOHb band of water polymers; determination of electrooptic parameters from intensity measurements for both monomer and dimer. Ó 2001 Elsevier Science B.V. All rights reserved.

1. Introduction In this series of matrix isolation studies devoted to the e€ect of hydrogen bonding on the anharmonicity of OH oscillators we have successively examined the near infrared spectra of methanol and water trapped in solid nitrogen [1,2]. The main conclusion is the astonishing intensity weakening of the ®rst overtone of an OH oscillator engaged in a hydrogen bond with respect to a free oscillator.

*

Fax: +33-01-44273021. E-mail address: [email protected] (J.P. Perchard).

The absence of gas phase data on the near infrared spectra of free water aggregates to con®rm these observations prompted us to extend our work to the case of a more inert matrix, argon, which is supposed to cause less perturbations than N2 on the band intensities. Replacing N2 by Ar introduces a noticeable intricacy tied to the quasifree rotation of monomeric water, which gives rise to a multiplicity of rovibrational signals for each vibrational transition, with possible overlaps with polymeric bands. A detailed analysis of the near infrared spectrum of water is proposed in this paper. It follows a publication from Jacox and coworkers [3] describing the spectrum of water trapped in solid

0301-0104/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 ( 0 1 ) 0 0 4 9 6 - 7

218

J.P. Perchard / Chemical Physics 273 (2001) 217±233

neon in the range 8000±700 cm 1 . The smallness of the matrix shifts in neon compared to those in the heavier rare gases allows an easy interpretation of the monomer spectrum from the gas phase data but the absence of data on the pure rotational spectrum prevents the determination of the rovibrational parameters of the various fundamentals or overtones transitions. Furthermore the large neon/water molar ratios, between 400 and 3200, used in this study precludes the observation of the overtones of the aggregates. These two limitations were overcome in the present work by extending the range of Ar/water molar ratio down to 20 and the spectral range down to 15 cm 1 . Thus one may hope a comprehensive spectral analysis for both monomer and dimer. 2. Experimental Experimental details have been described in Refs. [1,2] referred to as I and II. The argon solution of water was deposited at 19 K and the spectra were recorded using a Bruker 120 FTIR spectrometer in the conditions reported in I. Data acquisition in the range 14±100 cm 1 was carried out at 0.2 cm 1 resolution, using a 23 lm thick mylar beam splitter, a globar source and a bolometer as detector. As shown below, the analysis of the spectra of H2 O monomer is partly based on nuclear spin conversion which spontaneously occurs in the matrix [4±6]. We observed that this process, which probably implies paramagnetic O2 molecules present as impurity traces in the matrix, is noticeably enhanced by UV±VIS irradiation of the sample. Accordingly irradiations were carried out with the full light of a 150 W xenon lamp. Isotopic water samples (18 O enriched from YEDA, Rehovoth, Israel) as well as those of natural water were degassed in a vacuum line. Argon (Air Liquide, 99.999% purity) was used without puri®cation. 3. Results The description of the spectra is divided in three parts respectively devoted to monomer, dimer and

aggregates larger than the dimer which are generally easily distinguishable from each other by concentration and annealing e€ects. In particular it is worth noting that, as already reported in II, annealing of heavily doped matrices (Ar/H2 O molar ratio less than 100) leads to nearly complete disappearance of the dimer bands correlated to the growth of those of larger polymers. 3.1. Monomer As discussed by Engdahl and Nelander [7] two kinds of water molecule are spectroscopically distinguishable in rare gas matrices: the rotating monomer and the non-rotating monomer (hereafter referred to as nrm). The ®rst kind, which by far predominates at low concentration, gives rise for each vibrational transition to several rovibrational lines starting from J ˆ 0 or 1 levels of the vibrational ground state. The second kind, for which the rotation is hindered either by matrix inhomogeneity or by weak interactions between non-nearest neighbors, induces signals close to the pure vibrational frequencies, whose intensity decreases upon temperature increase. Our observations for H2 16 O are comparable with those reported in previous works in the mid-infrared [4± 9] as well as in the far infrared [10±12]. They also agree for H2 18 O with the data of Ayers and Pullin [13] but, for both molecules, we were able to observe weak features, especially at high temperature, due to transitions from excited rotational levels, not reported before. Such is the case of the lines at 3622.7 and 3606.8 (m1 ), 3124.8 and 3108.7 cm 1 (2m2 ) of H2 16 O (Table 1). Above 4000 cm 1 , to our knowledge, none of the bands reported in Tables 1 and 2 had been previously described. The pure rotational spectra (B-type band selection rules) are characterized for H2 16 O by two narrow lines (0.8 cm 1 bandwidth at low concentration) at 32.4 and 16.1 cm 1 , 1.3 and 0.9 cm 1 red shifted upon 16 O=18 O isotopic substitution, respectively, which have been assigned to the 00 0 ! 11 1 and 10 1 ! 11 0 rotational transitions [10±12]. The increase of their intensity ratio after irradiation with the Xe lamp, due to ortho ! para conversion, con®rms this assignment. Other broader bands are observed between 40 and 100

J.P. Perchard / Chemical Physics 273 (2001) 217±233

219

Table 1 Frequenciesa (cm 1 ) and RIb of type-B bandsa of H2 16 O and H2 18 O (in parantheses) trapped in solid argon at 10 K Rot

m2

2m2

m1

11 1 ! 00 0

1556.7 (1551.4)

3108.7 (3097.3)

3606.8 (3600.4)

11 0 ! 00 1

1573.1 (1567.4)

3124.8 (3113.2)

3622.7 (3616.0)

5193.2

nrmc

1589.2 (1582.7)

3141.2

3638.3 (3631.0)

5208.8

7163.2

m1 ‡ m2

2m1

10 1 ! 11 0

16.1 (15.2)

1607.9 (1600.6)

3163.2 (3150.1)

3653.5 (3645.5)

5227.9

7178.4

00 0 ! 11 1

32.4 (31.1)

1623.8 (1616.1)

3178.8 (3165.2)

3669.7 (3661.2)

5243.9

7194.7

10 1 ! 21 2

46.5 br (43.6) br

1636.5

11 1 ! 22 0

67.5 br (66.5) br

1657.2 br (1649.4) br

11 0 ! 22 1

71.5 br (70.8) br

1661.4 br (1654.8) br

95 br (94) br

1687.6 br

0.25

4.8

0.03

0.37

RI

350

1699.9 br 100

a

br: broad. Intensities of the 00 0 ! 111 lines normalized to that of m2 . c nrm: band of non-rotating monomer, characterized by intensity increase with concentration and by intensity decrease upon temperature increase. b

cm 1 . According to Kn ozinger and Wittenbeck [11] they could occur from activation of matrix phonons by the molecular impurity. However one observes a striking correlation between the far infrared spectrum of H2 O and the part of the m2 band above the frequency of the pure vibrational transition (Fig. 1). This correlation is con®rmed by comparable behaviors upon temperature change and irradiation. On the one hand the very weak doublets around 100 cm 1 (far infrared) and 1690 cm 1 (100 cm 1 shifted with respect to the m2 vibrational frequency) are better observed at high temperature. On the other hand the intensity ratio between the components of the doublets 67.5±71.5 and 1657.2±1661.4 cm 1 (70 cm 1 shifted from the m2 vibrational frequency) experiences the same decrease after irradiation with the full light of the Xe lamp. So both spectra have to be interpreted in the same way.

Relative band intensities were obtained from the intensities of the strongest rovibrational lines. The intensity of one jo; n00 i ! jv; n0 i transition, where o ! v and n00 ! n0 characterize respectively the changes of vibrational and rotational states is written as [14]: Io;n00 !v;n0 ˆ

8p3 N m…1 exp… hm=kT ††gn00 3hc exp… En00 =kT † 2 2 …hOjljvi† hn00 j/jn0 i ;  Zrot …T†

where En00 is the energy of the initial state, gn00 its weight factor, N the number of molecules per volume unit, m the frequency of the transition, Zrot the rotational partition function; hOjljvi and 2 hn00 j/jn0 i are the transition dipole moment and the line strength, respectively. According to this equation the intensity ratio between two transitions

220

J.P. Perchard / Chemical Physics 273 (2001) 217±233

Table 2 Frequencies (cm 1 ) and RIa of type-A bands of H2 16 O and H2 18 O (in parentheses) trapped in solid argon at 10 K m3

m2 ‡ m3

2m2 ‡ m3

m1 ‡ m3

10 1 ! 00 0

3711.3 (3698.3)

5280.6 (5258.0)

6815.2

7186.9 (7166.2)

11 0 ! 11 1

3724.9 (3711.1)

5295.4 (5274.7)

nrm

3736.0 (3721.7)

5308.2 (5287.4)

11 1 ! 11 0

3739.0 (3725.4)

5310.5 (5290.6)

00 0 ! 10 1

3756.6 (3742.2)

5325.4 (5304.7)

6859.8 (6833.1)

7231.9 (7211.5)

10 1 ! 20 2

3776.4 (3761.9)

5345.9 (5325.3)

6881.1

7252.1 (7232.0)

RI

85

9.4

0.39

3.7

7208.3

3.2. Dimer

a

Intensities of the 00 0 ! 10 1 lines normalized to the 00 0 ! 11 1 line of m2 , as in Table 1.

Fig. 1. Comparison of the rotational and rovibrational (m2 transition) spectra of water trapped in solid argon (Ar/ H2 16 O ˆ 800) at 10 K (: HDO isotopic impurity).

issuing from the same rovibrational level jo; n00 i is written as: Ion00 !v1 n0

1

Ion00 !v2 n0

2

2

ˆ

Tables 1 and 2 gathers the measurements carried out on the R(0)-type transitions of H2 16 O (00 0 ! 11 1 and 00 0 ! 10 1 for vibrational transitions A1 and B2 , respectively) for which the line strengths are equal [14]. The R(0) line of m2 has been chosen as the reference for two reasons: it is the strongest line of the whole rovibrational spectrum and the m2 mode is expected to be weakly sensitive to molecular interactions (vide infra).

2 m1 jhOjljv1 ij jn00 j/jn01 ij : m2 jhOjljv2 ij2 jhn00 j/jn0 ij2 2

…1†

The mid-infrared spectrum of the open chain water dimer trapped in argon matrix has been reported by several authors [7,9,15,16]. The three fundamentals of the proton donor (PD) molecule were identi®ed but only m1 and m2 of the proton acceptor (PA) one were con®dently assigned. Indeed m3 of PA has been identi®ed neither by Ayers and Pullin [15] nor by Nelander [16] while Bentwood et al. [9] assigned a weak band at 3726 cm 1 to this mode together to the monomeric rovibrational 11 0 ! 11 1 transition. As previously noted by Engdahl and Nelander [7] all the dimer bands are split into doublets whose relative intensity of the components varies with temperature. The problem of the missing fundamental, m3 of PA, measured at 3715 cm 1 in N2 , has been examined by performing a series of experiments at relatively large Ar/H2 O molar ratios (between 2000 and 300) in order to get rid of band broadening. Fig. 2 displays the spectrum at 10 and 25 K of an Ar/H2 O ˆ 800 sample in the domain where m3 is expected. At 10 K bands are measured at 3737.8, 3736.0, 3724.9, 3715.7, 3711.3 and 3708.5± 3707 cm 1 (ill-de®ned doublet). Those at 3724.9 and 3711.3 cm 1 have been assigned to rovibrational transitions of the monomer [4±6] and the 3708.5±3707 cm 1 doublet to m3 of PD [7,9,15]. The nearly complete disappearance of the 3724.9 cm 1 feature at low temperature excludes an accidental band overlap with m3 of PA which has thus to be searched around 3737 or 3715 cm 1 . At 25 K the absorption around 3737 cm 1 is signi®cantly modi®ed since its maximum is shifted to 3739.0 cm 1 while the narrow band at 3736.0 cm 1 vanishes. Engdahl and Nelander [7] assigned this band to nrm while the temperature-induced blue shift

J.P. Perchard / Chemical Physics 273 (2001) 217±233

Fig. 2. Temperature e€ect for an Ar/H2 16 O ˆ 800 matrix sample in the m3 region. Spectra recorded at 25 (a) and 10 K (b). M: quasifreely rotating monomer; nrm: non-rotating monomer; PA, PD: dimer.

arises from the growth a Q(1)-type rovibrational line. And ®nally, the two remaining absorptions at 3737.8 and 3715.7 cm 1 , which are both due to aggregates on the basis of concentration e€ects, are possible candidates for m3 of PA. Note however that they are much weaker than m3 of PD at 3708.5 cm 1 , typically I3708 =I3715 =I3736  4=1=1. In the 2m2 region, concentration and temperature e€ects allow a straightforward identi®cation of the dimer signals at 3182.3 and 3150.8 cm 1 , the ®rst one four times stronger than the second (Fig. 3), which suggests a stronger m1 =2m2 Fermi resonance for the high frequency component. In the stretching ‡ bending combination region 5400±5100 cm 1 , experiments at various concentrations and temperatures enable the four dimer transitions to be identi®ed. Fig. 4 displays the m2 ‡ m3 domain recorded at two Ar/H2 O molar ratios, 800 (trace a, rotating monomer alone), 80 (traces b and c, dimer main aggregate). On trace b recorded at 10 K the three rovibrational lines observed in a are accompanied by weaker bands at 5309, 5308.2, 5301, 5295 and 5288 cm 1 . Upon temperature increase to 25 K (trace c) two Q(1)type rovibrational lines at 5310.5 and 5295.4 cm 1 grow up while the signal of nrm at 5308.2 cm 1 vanishes. The other main features at 5309 and 5301 cm 1 , not sensitive to temperature, are assignable to the dimer. In the m1 ‡ m2 region, 5250± 4950 cm 1 , weaker features are observed (Fig. 5),

221

Fig. 3. Temperature and concentration e€ects for water trapped in argon in the 2m2 region. Ar/H2 16 O ˆ 800 (a), 80 (b, c). Spectra recorded at 25 (a) and 10 K (a, b), 20 K (c). M: quasifreely rotating monomer; nrm: non-rotating monomer; PA, PD: dimer; Tr: trimer; P: polymers larger than the trimer.

Fig. 4. Temperature and concentration e€ects for water trapped in argon in the m2 ‡ m3 region. Ar/H2 16 O ˆ 1500 (a), 100 (b, c). Spectra recorded at 10 K (a, b), 20 K (c). M: quasifreely rotating monomer; nrm, PA, PD: same symbols as for Fig. 3; P: polymers larger than the dimer.

with frequencies decreasing with increasing polymer size. The rovibrational lines of the monomer are located between 5250 and 5200 cm 1 , the nrm one at 5208.8 cm 1 close to the dimer signal at 5210.9 cm 1 . Another dimer band at 5169.5 cm 1 is stronger than the ®rst one by more than one order of magnitude. At last several broader bands below 5150 cm 1 develop at low Ar/H2 O molar ratio and are assignable to larger aggregates.

222

J.P. Perchard / Chemical Physics 273 (2001) 217±233

Fig. 5. Concentration e€ect for water trapped in argon in the m1 ‡ m2 region. Spectra recorded at 10 K at Ar/H2 16 O ˆ 100 (a) and 20 (b). M, PA, PD, Tr, P: same symbols as for Fig. 3.

In the 2mOH region dimer bands were identi®ed only in the domain 7280±7120 cm 1 . This is shown in Fig. 6 which displays the e€ect of concentration for H2 16 O. At Ar/H2 O ˆ 100 (trace a) ®ve rovibrational lines at 7252.1, 7231.9, 7194.7, 7186.9 and 7178.5 cm 1 are assignable to m1 ‡ m3 and 2m1 . At Ar/H2 O  60 (trace b) one notes the strengthening of a doublet at 7208.6±7206.3 and the appearance of weak features at 7163.2 and 7152.1±7151.0 cm 1 . Furthermore a shoulder develops on the

Fig. 6. Concentration e€ect for water trapped in argon in the 2mOH region. Spectra recorded at 10 K at Ar/H2 16 O ˆ 100 (a), 60 (b), 20 (c). M and M : m1 ‡ m3 and 2m1 transitions of quasifreely rotating monomer; nrm, PA, P: same symbols as for Fig. 4.

high frequency side of the rovibrational line at 7186.9 cm 1 . At Ar/H2 O  20 all the bands are broadened but the two low frequency signals at 7163.2 and 7152 cm 1 are clearly enhanced. On the other hand spectral recordings at various temperatures show that the bands at 7208.6 and 7163.2 cm 1 have the characteristic temperature dependence of nrm, decreasing reversibly upon temperature increase. Finally the absorptions at 7206.3, 7188 and 7152 cm 1 are assignable to the dimer. Besides these absorptions located in the spectral ranges expected for one or two quanta intramolecular transitions, other weak features have been identi®ed in unexpected domains, at 1885.6, 3877.1, 5449.8 cm 1 (H2 16 O) and 1879.8, 3862.8 cm 1 (H2 18 O). Their growth is correlated to that of dimers, which is con®rmed by their narrow bandwidth, of the order of a few wave numbers, excluding their assignment to larger aggregates. 3.3. Polymers The spectra of (H2 O)n , n > 2, aggregates in solid argon are characterized [9] by two groups of OH stretching bands, one in the range 3700±3680 cm 1 due to proton acceptors (OHf ), the other widely spread between 3530 and 3200 cm 1 due to PD (OHb ). The spectral analysis has been limited to the trimer [16,17] characterized by one main mOHb band at 3514 cm 1 and weaker features at 3700, 3695, 3616, 1620, 1602 cm 1 according to Barnes and Suzuki [17] or 3707.2, 1602.3 cm 1 according to Engdahl and Nelander [18]. Our results globally agree with the previous ones. At low Ar/H2 O molar ratio the bending region displays ®ve main overlapping bands peaked at 1625, 1611, 1602, 1593 and 1590 cm 1 , those at 1611±1593 cm 1 characterizing the dimer and the one at 1590 cm 1 the nrm. The broad and strong band at 1625 cm 1 cannot be exclusively assigned to the rotating monomer. In the mOHb region, besides the 3516 cm 1 band with a shoulder at 3528 cm 1 assigned to the trimer, three groups of absorptions around 3380, 3330 and 3210 cm 1 are well separated (Fig. 7). The ®rst one displays a main component at 3372 cm 1 with high frequency

J.P. Perchard / Chemical Physics 273 (2001) 217±233

223

Fig. 7. Concentration e€ect for water trapped in argon in the mOH and 2mOH regions. Spectra recorded at 10 K at Ar/H2 16 O ˆ 60 (a), 20 (b).

shoulders at 3418, 3409 and 3391 cm 1 and the second two components at 3332 and 3325 cm 1 . The low frequency weaker group displays several ill-de®ned submaxima between 3230 and 3205 cm 1 . A band decomposition has not been undertaken since the components are broad and too close to each other; the only reliable observation is that the maximum shifts to lower frequency as the water concentration increases. At last one narrower and weaker band at 3174 cm 1 , not assigned to monomer and dimer, is a possible candidate for the ®rst overtone of the m2 band at 1602 cm 1 . In the mOHf region two submaxima close to 3700 and 3695 cm 1 emerge from a broad absorption appearing as a shoulder to the strong dimer band at 3708 cm 1 . We also observed a weak feature at 3611.6 cm 1 which disappears after annealing. It could be due to a metastable aggregate but, in the absence of any other band with the same behavior, it will not be discussed any more.

As in N2 matrices the two quanta transitions of the polymers above 4000 cm 1 are dicult to observe and the scarce identi®ed bands dicult to assign to one speci®c species. The best situation is that of the mOH ‡ m2 combinations for which one well de®ned band at 5292 cm 1 involves mOHf (3690 ‡ 1610) while four bands at 5137, 5114.8, 5072 and 5001 cm 1 involve mOHb . The ®rst overtones of mOHf and mOHb are expected in well separated domains, close to 7200 cm 1 for OHf , below 6800 cm 1 for OHb . Two polymeric bands, not assigned to the dimer, at 7201 and 7188.5 cm 1 , correspond to 2mOHf . As for 2mOHb , we were unable to detect any absorption in the expected domain, despite the strong absorption of the mOHb bands (Fig. 7). The same absence was reported in I and II and thus seems to be a general property of the OH


O systems involving a medium strength hydrogen bonding, at least at low temperature.

224

J.P. Perchard / Chemical Physics 273 (2001) 217±233

4. Spectral analysis The assignments of the …0 0 0† ! …v1 v2 v3 ) transitions are based on the comparison with the N2 matrix data and, for the monomer, with the gas phase data, and on the 16 O=18 O isotopic substitution. The frequency shifts follow the relationship: X vi Dmi ; …2† D…v1 v2 v3 † ˆ iˆ1;3

where D stands for the Ar/N2 , gas/Ar or 16 O=18 O frequency shifts, D…v1 v2 v3 † and Dmi relating to the multiquanta and fundamental transitions, respectively. For the monomer the determination of the vibrational frequencies requires a preliminary analysis of the rotational structure of the bands. Once this problem solved, the anharmonicity coecients xij and the harmonic frequencies xi de®ned by expansion of vibrational energy:   X  X  1 1 G v1 v 2 v 3 ˆ xi vi ‡ xij vi ‡ ‡ 2 2 iˆ1;3 i 6 jˆ1;3   1  vj ‡ …3† 2 can be deduced. However their determination requires corrections for vibrational resonances which involve cubic and quartic terms of the potential energy V written as: X 1X 2 V ˆ xi qi ‡ Kijk qi qj qk 2 iˆ1;3 i 6 j 6 kˆ1;3 X ‡ Kijkl qi qj qk ql ; …4† i 6 j 6 k 6 lˆ1;3

where q stands for a dimensionless normal coordinate, the harmonic frequencies and the anharmonic constants K being expressed in cm 1 . 4.1. Rovibrational analysis The assignment of the rovibrational transitions, based on the selection rules of the asymmetric rotor, is straightforward but the quantitative analysis is plagued by the perturbation of the rotational levels induced by the anisotropy of the crystal ®eld. The method used in this paper for the determination of the energy of the J ˆ 1 levels

stems from the model proposed by Manz [19]. It consists in introducing e€ective rotational constants, which are supposed to account for the synchroneous displacements of the matrix atoms surrounding the rotating molecule. The energies of the J ˆ 1 levels are then simply written as [14]: E…10 1 † ˆ Bv ‡ Cv ; E…11 1 † ˆ Av ‡ Cv ; E…11 0 † ˆ Av ‡ Bv ; where Av , Bv , Cv are the e€ective rotational constants (smaller than those of the free molecule) in the vibrational state v. These three constants are not independent from each other but are tied by the inertia defect D de®ned as D ˆ IC IA IB , where I stands for any moment of inertia, whose theoretical formulation has been developed by Oka and Morino [20]. These authors have shown that the main contribution to D, Dvib , occurs from vibration±rotation interaction; in the case of water this contribution only depends on the harmonic frequencies and on the Coriolis constants f23 and f13 which are not signi®cantly modi®ed from the gas to the Ar matrix. From Eq. (40) of Ref. [20] and from the inequality f23  f13 [21] one gets: 

 Dvib ˆ 134:6 0:00075 v2 ‡ 12 0:000059 v3 ‡ 12 ; …5† where Dvib is in amu A2 . The consequences of Eq. (5) are: (i) For the ground state and the (v1 0 0) levels, Dvib is of the order of 0.047. (ii) Within the (0 v2 0) sequence, Dvib increases as (2v2 ‡ 1). (iii) Within the (0 0 v3 ) sequence, Dvib slightly decreases when v3 increases. These assessments are correctly veri®ed for the gas phase (Table 3). Each vibrational state is characterized by three rotational constants and by its pure vibrational frequency which can be deduced from the R(0), Q(1) and P(1)-type transitions if the rotational constants A0 , B0 , C0 of the ground state are known from the rotational spectra.

J.P. Perchard / Chemical Physics 273 (2001) 217±233

225

Table 3 Vibrational frequencies (m0 , cm 1 ), rotational constants (cm 1 ) and inertia defect (D, amu A2 ) of some vibrational levels of H2 16 O and H2 18 O (in parentheses) in the gas phasea and trapped in argon matrix (0 0 0)

(0 1 0)

(0 2 0)

(1 0 0)

(0 0 1)

(0 1 1)

(0 2 1)

(1 0 1)

1594.75 (1588.27) 1589.1 (1582.5)

3151.63 (3139.05) 3141.1 (3128.4)

3657.05 (3649.68) 3639.2 (3631.5)

3755.93 (3741.57) 3732.2 (3718.8)

5331.28 (5310.47) 5301.5 (5278.5)

6871.55

7249.83

6836.1

7207.8 (7186.7)

27.88 (27.53) 24.25 (23.15)

31.13 (30.73) 26.70 (25.80)

35.69 (35.00) 30.00 (29.25)

27.12 (26.79) 22.60 (22.00)

26.85 (26.32) 22.21 (21.15)

14.52 (14.52) 12.71 (12.53)

14.69 (14.68) 12.86 (12.78)

14.84 (14.81) 12.96 (12.93)

14.30 (14.31) 12.56 (12.48)

14.43 (14.41) 16.99 (16.57)

9.28 (9.24) 8.15 (7.95)

9.13 (9.09) 8.00 (7.80)

8.97 (8.96) 7.70 (7.55)

9.10 (9.06) 7.90 (7.70)

9.14 (9.11) 7.45 (6.85)

0.051 (0.051) 0.047b (0.047)b

0.157 (0.158) 0.165 (0.188)

0.271 (0.262) 0.320 (0.352)

0.052 (0.053) 0.046 (0.072)

0.048 (0.040) 0.511 (0.647)

m0 Gas Matrix A Gas Matrix B Gas Matrix C Gas Matrix D Gas Matrix a

Gas phase values: (0 0 0) and (0 1 0), Ref. [22] (26); (0 2 0), (1 0 0) and (0 0 1), Ref. [23] (27,28); (0 1 1), Ref. [24] (29); (0 2 1) and (1 0 1), Ref. [25]. b Value of D used for the determination of the rotational constant B0 .

Pure rotational spectra: The identi®cation of the transitions 00 0 ! 11 1 and 10 1 ! 11 0 enables A0 and C0 to be determined. The B0 value is then obtained assuming a value of D close to that measured in the gas phase (item (i) above). These values are reported in Table 3. Note that the molecular symmetry requires that the rotational constant B0 should remain invariant upon 16 O/18 O isotopic substitution. Rovibrational spectra: The four parameters of three rovibrational B-type bands (m2 , 2m2 and m1 ) of H2 16 O and H2 18 O have been deduced from the frequencies of the four transitions involving J ˆ 0 and 1 states (Table 3). The rotational constants are typically 12±16% smaller than in the gas but follow the same evolution according to the vibrational state: for H2 16 O A varies as 1/1.117/1.280/0.973 in

the gas [22±25] and as 1/1.101/1.237/0.932 in Ar matrix in the (0 0 0)/(0 1 0)/(0 2 0)/(1 0 0) states while B and C remain nearly unchanged in both cases. On the other hand the values of D are close to those in the gas and correctly ®t the theoretical prediction (Eq. (5)). For H2 18 O comparable results are obtained but the D values are generally greater than in the gas phase [26±29]. The same procedure applied to the analysis of the rovibrational A-type bands leads to values of the rotational constants incompatible with the expected matrix e€ect and with the theoretical D values. For the m3 band, as example, use of the four frequencies involving only the transitions between J ˆ 0 and 1 levels, whose assignments reported in Table 3 agree with those given in Refs. [5,7,9], leads to values of rotational constants and of D for

226

J.P. Perchard / Chemical Physics 273 (2001) 217±233

Table 4 Frequenciesa (cm 1 ) and RI (in parentheses) of the bands of H2 16 O and H2 18 O dimer trapped in argon at 10 K Transitionb

(H2 16 O)2 PA

PD

PA

PD

1593.1 (1 0 0) 1885.6 (1.3) 3150.8 (0.67) 3633.1 (5.4)

1610.6 (87)

1586.5

1604.3

3182.3 (2.7) 3574.0 (220)

3138.3

3171.3

3625.7

3565.3

3715.7 (25) 3737.8 (25)

3708.0 (130)

3724.0

3694.6

m1 ‡ m2

5210.9 (0.03)

3877.1 (1.8) 5169.5 (2.0)

m2 ‡ m3

5288 (0.4) 5309 (1.4)

5301.0 (5.2)

m2 m2 ‡ IM 2m2 m1 m3

m3 ‡ IM

2m1 m1 ‡ m3

2m3 a b

(H2 18 O)2

1879.8

3862.8 5154.5

5288

5282.3

5449.8 7151.5 (0.7) 7188 7207.1 (2.0) 7235.9 (3.3)

In most cases mean frequency of a doublet. IM: intermolecular modes.

the (0 0 1) state inconsistent with the gas phase data (Table 4): 17% increase of B and D greater by one order of magnitude. This result is of course inconsistent with the model proposed by Manz and will be discussed in a forthcoming publication devoted to the rovibrational analysis of monomeric D2 O trapped in argon, for which this inconsistency does not exist. 4.2. Vibrational assignments Monomer: Use of Eq. (2) leads to a straightforward assignment of the vibrational transitions

reported in Table 3. As examples, for H2 16 O, the Ar/N2 matrix shifts of 2m2 , m2 ‡ m3 , 2m2 ‡ m3 , m1 ‡ m3 calculated according to Eq. (2) are 16.0, 3:3, 10:3, ‡9:0 cm 1 , respectively, to be compared to the experimental values 17.1, 2:4, 10:6, ‡8:5 cm 1 ; for the same transitions the gas/Ar matrix shifts are 11.3, 29.4, 35.0, 41.6 (calculated) against 10.5, 29.8, 35.4, 42.0 (observed). Dimer: The ®rst problem to solve is the localization of m3 of PA. For that purpose two kinds of informations have to be taken into account: the results of theoretical calculations and those obtained in molecular beam experiments. The numerous post HF and DFT calculations on the water dimer [30±39] lead to consistent conclusions on the harmonic frequencies and intensities of the intramolecular modes. The PD±PA splittings of m2 , m1 , m3 are respectively calculated close to 25, 90, 20 cm 1 and the corresponding PD/PA intensity ratios 0.65, 25, 0.9. On the other hand, in molecular beam experiments (H2 O)2 has been identi®ed either as a free dimer [40] or embedded in He [41] or formed on Ar [40] clusters. The m3 mode of PD is characterized by a well de®ned band around 3730 (free dimer or dimer in He cluster) or 3714 cm 1 (dimer on argon cluster), in this last case close to the matrix signal. On the contrary m3 of PA exhibits a complex pattern which has been rotationaly resolved for the free dimer [42]. The band origin is located at 3745.48 cm 1 , and the widely separated subbands spread from 3779 to 3735 cm 1 arise from a tunneling splitting involving the internal rotation of PA. In He clusters the subbands are still identi®ed while on Ar clusters they merge into an ill-de®ned absorption in the range 3755±3720 cm 1 appearing as a shoulder to the strong and narrow m3 PD line at 3714 cm 1 . At the light of these data we suggest that the tunneling motion which exchanges the two protons of PA still occurs in Ar matrix, giving rise to subbands, two of them centered at 3715.5 and 3736.8 cm 1 . Note that the splitting of m3 into several components has also been observed [43] in the case of the H2 O±HX (X ˆ Cl, Br, I) complexes trapped in argon matrix. The m3 multiplets have been better interpreted considering the complexes as axial rotors (C2v symmetry) performing a hindered rotation around their A2 axis. Finally we propose to

J.P. Perchard / Chemical Physics 273 (2001) 217±233

locate m3 PA at 3723  1 cm 1 on the following grounds. Assuming the same (monomer±PA) frequency shift of m3 as in the gas …‡10:45 cm 1 † one gets 3722 cm 1 ; assuming the same (PA±PD) m3 frequency shift as in the gas (‡15:5 cm 1 ) one gets 3724 cm 1 . Of course these two assumptions are consistent with the fact that the (monomer±PD) m3 shifts in the gas and in Ar matrix are close to each other (25.5 and 23.7 cm 1 , respectively). The two quanta transitions involving m2 are easily assigned on the basis of the Ar/N2 frequency shifts. For PD the calculated shifts of 2m2 , m1 ‡ m2 , m2 ‡ m3 , are 16:8, ‡15:3, ‡0:2 cm 1 , respectively, against 16.7, ‡14:7, ‡6:0 cm 1 observed. The discrepancy for m2 ‡ m3 is probably tied to the overlap of the m2 ‡ m3 signals of PA and PD in N2 matrix which makes the measurements inaccurate. For PA the calculated shifts of the same transitions are 16.6, 2:2, ‡14:1 cm 1 against 15.9, 6:0, ‡14:0 cm 1 observed (the high component of m3 and m2 ‡ m3 in Ar being considered). In the 2mOH region the behavior of PA is expected to be close to that of the monomer, with one relatively strong m1 ‡ m3 absorption and much weaker 2m1 and 2m3 overtones; for PD the decoupling of the two oscillators gives rise to a di€erent pattern, the absorption of 2m3 around 7200 cm 1 prevailing over that of m1 ‡ m3 and 2m1 which have not been identi®ed in N2 matrix. For PA, the high frequency component of m1 ‡ m3 and 2m1 are observed at 7207.1 and 7151.5 cm 1 , respectively, which corresponds to Ar/N2 shifts of ‡14:6 and ‡26:8 cm 1 (against ‡10:8 and ‡27:8 cm 1 calculated); for PD only 2m3 is identi®ed at 7235.9 cm 1 (Ar/N2 shift of ‡15:9 cm 1 , calculated ‡17:2 cm 1 ). At last two extra features at about 3877 and 1886 cm 1 for H2 16 O and 3863 and 1880 cm 1 for H2 18 O assignable to the dimer correspond to combinations involving one fundamental and one 18 intermolecular mode. Since the 16 O= O frequency shifts are expected to be small for the intermolecular modes the observed 3877 3863 ˆ 14 cm 1 shift implies that the fundamental involved in the high frequency combination is m3 . Because of the splitting of m3 of PA into several components, it seems more realistic to assign this band to the combination of m3 PD with an intermolecular

227

mode at 3877 3708 ˆ 169 cm 1 . The combination at 1886 cm 1 requires another intermolecular mode either at 1886 1610 ˆ 276 or at 1886 1593 ˆ 293 cm 1 according as PD or PA is involved in the combination. For H2 16 O another dimeric signal at 5450 cm 1 , whose 18 O counterpart has unfortunately not been identi®ed implies an intermolecular mode at 149, 239 or 280 cm 1 according as the coupled internal level is m2 ‡ m3 of PD, m1 ‡ m2 of PA or m1 ‡ m2 of PD, respectively. Polymers: Recent calculations [39 and references cited therein] on (H2 O)n , n > 2, aggregates conclude that their most stable structure is cyclic for n ˆ 3, 4, 5 and tridimensional (3D) for n > 6, the transition between bidimensional (2D) and 3D structures occurring in the hexamer region. For 2D aggregates, which probably predominate in our experiments, each molecule plays simultaneously the role of PD and PA, with one hydrogen-bonded (OH


, or OHb ) and one nonhydrogen-bonded (


OH, or OHf ) oscillator. These two kinds of oscillators are characterized by frequencies localized in the monomer region for OHf and, for OHb , at much lower frequencies which decrease when n increases. These predictions are well veri®ed in the photodepletion experiments carried out on free water clusters recently reviewed by Buck and Huisken [44]: from n ˆ 3 to 5 the mOHf frequencies are localized in the range 3726± 3714 cm 1 while the mOHb ones decrease from 3533 (n ˆ 3) to 3416 (n ˆ 4) and 3360 cm 1 (n ˆ 5). The Ar matrix spectra may be correlated to the gas phase data assuming comparable matrix shifts whatever the size of the aggregate. These shifts amount to 27 and 19 cm 1 for the dimer and the trimer, respectively, so that the tetramer and pentamer bands in argon are expected around 3400 and 3340 cm 1 , respectively. Accordingly the group of bands in the range 3420±3370 cm 1 is assigned to cyclic tetramers and the group around 3330 cm 1 to cyclic pentamers. Note that, as in the gas, the mOHb band of the tetramer in argon is noticeably broader than that of the other polymers (50 cm 1 against 20 and 10 cm 1 respectively for the trimer and the dimer). The last group of bands in argon around 3210 cm 1 correlates to a broad absorption peaked at 3220 cm 1 in the gas and

228

J.P. Perchard / Chemical Physics 273 (2001) 217±233

assigned by Paul et al. [45] to the hexamer. This interpretation will be discussed below. None of the remarkably strongly red shifted signals below 3150 cm 1 assigned to (H2 O)n , n P 7, were observed in our spectra, even at very low Ar/H2 O molar ratio and after annealing. 4.3. Vibrational resonances For H2 16 O molecules with C2v symmetry (monomer and PA) the determination of the energy levels requires corrections for Fermi resonances within the s ˆ 2±4 polyads (s ˆ 2v1 ‡ v2 ‡ 2v3 ) and for Darling±Dennison resonance between 2m1 and 2m3 . In the Fermi resonances the (v1 v2 v3 ) and (v1 1, v2 ‡ 2, v3 ) levels interact through the coupling element: hv1 v2 v3 jV jv1

1; v2 ‡ 2; v3 i

ˆ K122 ‰v1 …v2 ‡ 1†…v2 ‡ 2†=2Š

1=2

=2

…6†

while in the Darling±Dennison resonance the coupling element is: hv1 v2 v3 jV jv1 ˆ c‰ v1 … v1

2; v2 ; v3 ‡ 2i 1†…v3 ‡ 1†…v3 ‡ 2†Š1=2 =2;

…7†

where c is a function of the cubic Kijk and quartic K1133 constants and of the harmonic frequencies x1 and x3 . For an asymmetric molecule (PD case) the normal coordinates q1 and q3 can be identi®ed to the dimensionless stretching coordinates of the OHb and OHf oscillators, respectively, and the coupling elements involved in the Fermi resonances are derived from Eq. (6): · between (v1 v2 v3 ) and (v1 1, v2 ‡ 2, v3 ) levels: Wb ˆ kb22 ‰v1 …v2 ‡ 1†…v2 ‡ 2†=2Š1=2 =2; · between (v1 v2 v3 ) and (v1 , v2 ‡ 2, v3 1) levels: 1=2 Wf ˆ kf22 ‰v3 …v2 ‡ 1†…v2 ‡ 2†=2Š =2. This last one, which involves more spaced levels than the other, was neglected in II. Finally, for cyclic polymers (H2 O)n , with n coupled OHb stretchings and n coupled bendings, the discrete energy levels are replaced, as in con-

densed phases [45], by bands of energy, characterized by mean values of energy and of cubic anharmonicity constants kb22 and kf22 . Monomer: The m1 =2m2 Fermi resonance has been treated assuming that the coupling element W ˆ 0:5K122 keeps the value found in II for H2 O monomer trapped in N2 , namely 30.6 cm 1 . The unperturbed levels m01 and 2m02 are 1.9 cm 1 shifted with respect to the observed ones; the resonance is weak and 92% of the observed intensity of 2m2 arise from the intrinsic intensity of the overtone. The anharmonicity coecient x22 de®ned as 0.5…2m02 † m2 is found equal to 17:6 cm 1 . The …m1 ‡ m2 †=3m2 resonance has been calculated using the following data: unperturbed 3m02 level located at 3m2 ‡ 6x22 ˆ 4661:7 cm 1 , coupling element 0.866K122 ˆ 53:05 cm 1 and perturbed m1 ‡ m2 level observed at 0 5211.3 cm 1 . The unperturbed …m1 ‡ m2 † level is calculated at 5206.2 cm 1 , leading to x12 ˆ 21:2 cm 1 . At last, the treatment of the …m1 ‡ m3 †= …2m2 ‡ m3 † diad, characterized by perturbed levels at 7207.8 and 6836.1 cm 1 and by a coupling element 0.5K122 ˆ 30:6 cm 1 , leads to unperturbed levels at 7205.3 and 6838.6 cm 1 , 90% of the intensity of the (2m2 ‡ m3 ) band occurring from the corresponding transition dipole moment. From these values the x13 and x23 anharmonicity coecients are found equal to 164.2 and 19.6 cm 1 , respectively. Note that the x23 value agrees with the value 19.8 cm 1 deduced from the frequency of the (m2 ‡ m3 ) combination. In the treatment of the Darling±Dennison resonance, we have to ®t the observed 2m1 signal of nrm at 7163.2 cm 1 , in the absence of an accurate determination of the corresponding frequency for the rotating monomer. This resonance, characterized by a coupling term c ˆ 74 cm 1 (value used in II), has been calculated together with the 2m1 =…m1 ‡ 2m2 †, s ˆ 4, Fermi characterized by pdiad  the coupling element K122 = 2 ˆ 43:3 cm 1 and an 0 unperturbed …m1 ‡ 2m2 † level at m01 ‡ 2m02 ‡ 2x12 ˆ 6737:0 cm 1 (value for nrm). The unperturbed 2m01 and 2m03 levels are then found at 7189.3 and 7378.0 cm 1 , respectively, leading to x11 and x33 values of 44.0 and 47.0 cm 1 , respectively. Assuming that these last values are also those of the rotating monomer the harmonic frequencies are then calculated; all the terms involved in the expression of

J.P. Perchard / Chemical Physics 273 (2001) 217±233 Table 5 Anharmonicity coecients xij and harmonic frequencies xi of water monomer and dimer trapped in argon (all values in cm 1 ) x11 x22 x33 x12 x13 x23

x1 x2 x3 a b

Monomer

PA

44.0a 17.6 47.0a 20.2 164.2 19.7 3817.5 1644.2 3918.1

43.9 16.7 47.0 18.7 164.4 21.9 3810.5 1646.8 3910b

PD 8.4 21.6 21.5

Deduced from nrm frequencies. m3 frequency at 3723 cm 1 .

the vibrational spectral term Gv1 v2 v3 (Eq. (3)) are reported in Table 5. Dimer: The same procedure as for the monomer has been applied to PA, using the same values of the resonance parameters K122 and c, 61.2 and 74 cm 1 , respectively. The corrections for the m1 =2m2 Fermi resonance are weak: shift of 1.9 cm 1 on the frequencies, leading to a x22 value of 16.7 cm 1 , 97% of the intensity of the overtone band coming from the 0 0 0 ! 0 2 0 transition moment. The …m1 ‡ m2 †=3m2 diad, treated as the monomer one (3m02 at 4679.1, W ˆ 53:05 cm 1 ), leads to an un0 perturbed …m1 ‡ m2 † level at 5205.6 cm 1 and x12 ˆ 18:6 cm 1 . The …m1 ‡ m3 †=…2m2 ‡ m3 † resonance, calculated with a …2m2 ‡ m3 †0 level at 6846.7 0 cm 1 , leads to a corrected …m1 ‡ m3 † level at 7204.5 cm 1 , ®tting the observed one at 7207.1 cm 1 , and a x13 value of 164:4 cm 1 . At last the …0 0 2†= 0 …2 0 0†=…1 2 0† resonances, treated with a …m1 ‡ 2m2 † level at 6746.5 cm 1 , leads to unperturbed 2m01 and 2m03 levels at 7174.5 and 7350.0 cm 1 , respectively, and x11 and x33 coecients equal to 43:9 and 47:0 cm 1 , respectively. Table 5 gathers all the results obtained in these treatments together with the harmonic frequencies. For PD the intensity increase of 2m2 at 3182.3 cm 1 is interpreted as arising from the strengthening of the Fermi resonance with m1 and, to a lesser extent, with m3 . The calculations where carried out assuming that all the intensity of 2m2 is borrowed from m1 and m3 and that the values of Kb22 and Kf22 are not very di€erent from the K122 value of the monomer. This point has been dis-

229

cussed at length by Rice and coworkers [46] for water in its condensed phases and by Burneau and Corset [47] for H2 O complexed with organic bases in the liquid phase. In both cases Kb22 was found greater than K122 of the free molecule while Kf22 keeps a comparable value. Finally, with Kb22 and Kf22 values of 74 and 62 cm 1 , respectively, the experimental data are ®tted by unperturbed m03 =m01 =2m02 levels at 3706.1=3570.5=3187.7 cm 1 and relative intensities (RI) C0m3 =C0m1 =C02m2 ˆ 0:59=1=0. One deduces then a x22 value of 8.4 cm 1 . Note that the neglect of Kf22 , in the hypothesis that all the intensity of 2m2 is borrowed from m1 , would lead to a Kb22 value of 84.4 cm 1 and to unperturbed m01 =2m01 levels at 3569.4/3186.9 cm 1 . The s ˆ 3 triad involving the (0 3 0), (1 1 0) and (0 1 1) levels has been calculated using the Kb22 and Kf22 values drawn from the s ˆ 2 diad and an unperturbed (0 3 0) level at 3m2 ‡ 6x22 ˆ 4781:5 cm 1 . The experimental results are ®tted with unperturbed (1 1 0) and (0 1 1) levels at 5159.5 and 5295.2 cm 1 , respectively, leading to x12 and x23 values of 21:6 and 21:5 cm 1 , respectively. Polymers: The combined e€ects of the increase of Kb22 and of the decrease of the m0 OHb 2m02 frequency di€erence strengthen the Fermi resonance. Neglecting the m0 OHf =2m02 interaction, which plays already a minor role at the dimer level, and the contribution of the h0 0 0j~ lj0 2 0i transition dipole moment to the intensity of the 2m2 band, the intensity ratio CmOHb =C2m2 has been calculated as a function of the energy di€erence between the m01 and 2m02 unperturbed levels for Kb22 values in the range 80±100 cm 1 . Fig. 8 displays the results obtained for 3300 6 m0 OHb 6 3420 and 3220 6 2m02 6 3250 cm 1 which correspond to realistic domains for (H2 O)n , n > 3, aggregates. It is clear that the contribution of the perturbed 2m2 transition to the absorption around 3210 cm 1 cannot be neglected as soon as the m0 OH 2m02 splitting is less than 120 cm 1 . As example, for a value of 90 cm 1 , compatible with n ˆ 5 (m0 OHb  3310, 2m02  3220 cm 1 ) and Kb22 ˆ 90 cm 1 , mOHb and 2m2 are calculated around 3330 and 3200 cm 1 , respectively, in the intensity ratio 5.8. In line with this result the contribution of the 2m2 bands of (H2 O)n , n ˆ 3±5, polymers to the 3220±3200 cm 1 absorption has been estimated by taking into account the

230

J.P. Perchard / Chemical Physics 273 (2001) 217±233

(monomer) and 4 (dimer). The absolute intensities C were deduced from the RI assuming that the C2m2 values for the monomer and PA keep the gas value (65 km mol 1 [48]). As discussed in I this assumption stems from nearly constant values of Cm2 either measured for liquid water [49,50] or theoretically predicted for (H2 O)2 [51,52]. It will be shown below that this value is also consistent with the intensity of the pure rotational spectrum. The transition dipole moment for the 0 0 0 ! v1 v2 v3 transition, deduced from the intensity of the 0 0 0 ! v1 v2 v3 band [53]: Fig. 8. E€ect of the mOHb =2m2 Fermi resonance on the intensity ratio CmOHb =C2m2 as a function of the frequency di€erence d between the unperturbed levels m0 OHb and 2m02 of (H2 O)n , n > 3. Kb22 ˆ 100 (a) and 80 cm 1 (b).

strengthening of the Fermi resonance when n increases and assuming that these 2m2 signals merge into a broad absorption with ill-de®ned maxima around 3210 cm 1 . With realistic values of the C2m2 …n† =CmOHb …n† intensity ratios, namely 0.02, 0.08 and 0.13 4; 5, respectively, the intensity P for n ˆ 3;P ratio I = 2m …n† 2 nˆ3;5 nˆ3;5 I2mOHb …n† , where I2m2 …n† ˆ …C2m2 …n† =CmOHb …n† †ImOHb …n† and ImOHb …n† the intensity of the band at 3520 (n ˆ 3), 3380 (n ˆ 4) or 3330 cm 1 (n ˆ 5), has been calculated. In the spectra where these bands are accurately measured, corresponding to Ar/H2 O molar ratios P between 100 and 40, it is found equal to the I3210 = nˆ3;5 ImOHb …n† ratio within a few percent. One thus concludes that in these experimental conditions the low frequency polymeric absorption around 3210 cm 1 is not assignable to another n-mer, n > 5, but simply stems from Fermi resonances. 4.4. Dipole moment function For water monomer and dimer some terms of the dipole moment function de®ned as: X X ~ ~ ~ l ˆ~ l0 ‡ l i qi ‡ lij qi qi ; iˆ1;3

i 6 jˆ1;3

where ~ li and ~ lij are the ®rst and second derivatives of the dipole moment with respect to the dimensionless coordinates, have been obtained from the intensity measurements reported in Tables 1, 2

2

ljv1 v2 v3 ij C0 0 0 ! v1 v2 v3 ˆ 22:62  1058 jh0 0 0j~  …v1 m1 ‡ v2 m2 ‡ v3 m3 †;

…8†

where C is expressed in km mol 1 and ~ l in C m, is related to li s and lij s according to relationships developed by Secroun et al. [54] and Yao and Overend [55]. For one fundamental transition mi , the neglect of the second order contributions leads to simpli®ed expressions involving only ~ li : p ljii ˆ ~ li = 2: …9† h0j~ For two quanta transitions the transition dipole moments involve cubic terms of the potential function (Eq. (4)) which have been taken from Smith and Overend [56] for monomer and PA. Monomer and PA: Because of the quadratic dependence of the intensities with the transition dipole moment there are two possible values for each li and lij derivative. The li values are deduced from the intensities of the fundamentals according to Eqs. (8) and (9). Their signs are chosen ‡ ‡ for i ˆ 1; 2; 3 respectively, following the theoretical predictions [51,57]. For the monomer the intensity ratio between the 00 0 ! 11 1 transitions of the rotational spectrum and of the m2 rovibrational spectrum is, according to Eqs. (1) and (9), equal to 64.8l20 =1589:1l22 . From the experimental ratio and the l2 value respectively reported in Tables 1 and 6 one gets l0 ˆ 5:6  10 30 C m, close to the gas value 6.17  10 30 C m. This good agreement justi®es the assumption about the invariance of Cm2 . The two possible values of the lij s deduced from the intensities of the two quanta transitions are reported in Table 6, that with the sign theoretically predicted [57] being underlined.

J.P. Perchard / Chemical Physics 273 (2001) 217±233

231

Table 6 First …li † and second …lij † derivatives of the dipole moment function of water monomer and dimer (PA subunit) with respect to dimensionless normal coordinates (in 10 30 C m) i

lij a

li

jˆ1 M

a

PA

1

0.087

0.10

2

0.60

0.60

3

0.36

0.28

Upper values: (‡ ‡), lower values: (‡

M

jˆ2 PA

0.050 0:018

0.070 0:034

M

jˆ3 PA

M

0.011 0:005

0.012 0:007

0.13 0:021

0.010 0:071

0.041 0:10

0:11 0.18

PA

0.018 ) combinations. The sign of the underlined values is that reported in Ref. [57].

PD and polymers: For PD the intensities of most of the two quanta transitions are signi®cantly di€erent from those measured for PA. Some of these di€erences occur from the mechanical decoupling between the two OH oscillators (cases of m1 ‡ m3 and 2m3 ) and from the strengthening of Fermi resonance (case of 2m2 ). The most remarkable observations concern the m1 ‡ m2 and 2m1 transitions, for which the PD/PA intensity ratios are about 70 and 0, respectively. These evolutions can only be interpreted in term of changes of electrooptical parameters upon hydrogen bonding. Unfortunately their calculations gets intricate due to the non-nullity of a large number of cubic constants Kijk and to the unde®ned orientation of the ~ li and ~ lij derivatives in the molecular plane. For the fundamentals and overtones of the OH oscillators considered as completely decoupled from each other, use of the simpli®ed formulas for an isolated oscillator (Eqs. (9) and (10) of II) with values of the cubic constant of 400 and 420 cm 1 for OHf and OHb [56,58], respectively, leads to li and lii values of 0.57 and 0.13 (unit: 10 30 C m) for OHb (i ˆ 1) against 0.45 and 0.01 for OHf (i ˆ 3). For the combination m1 ‡ m2 the calculation of l12 is necessarily oversimpli®ed by the lack of knowledge about its orientation. Assuming negligible contributions of ~ li s in Eq. (60) of [55], which is roughly justi®ed by K112 , K122 and K123 values relatively small, of the order of 100 cm 1 [47], one gets a l12 value of 0.072  10 30 C m, to be compared to 0:007  10 30 for PA. A comparable situation occurs for larger aggregates whose 2mOHb bands are also too weak to

be identi®ed. However no quantitative determination of the dipole moment derivatives was undertaken because of a poor de®nition of the corresponding m2 signals used as references. 5. Conclusion The rovibrational spectrum of monomeric water trapped in solid argon has been quantitatively investigated up to 8000 cm 1 . On the basis of the pseudorotating cage model developed by Manz a self-consistent analysis of the rovibrational transitions involving J ˆ 0 and 1 levels of B-type bands has been obtained after determination of the rotational constants of the ground state from the pure rotational spectrum. Excitation to J 0 ˆ 2 levels, more highly perturbed by the matrix, results in broad absorptions. After determination of the frequencies of one and two quanta vibrational 18 transitions assigned on the basis of 16 O= O, Ar/N2 or Ar/gas shifts and after corrections from Fermi and Darling±Dennison resonances the anharmonicity coecients and harmonic frequencies have been obtained. On the other hand the ®rst and second derivatives of the dipole moment with respect to the dimensionless normal coordinates were deduced from the relative band intensity measurements, assuming the same intensity for the m2 band and the same values of the cubic constants of the potential as in the gas phase. Dimer absorptions were identi®ed and assigned in the spectral range 8000±1000 cm 1 . The analysis of the PA moiety spectrum closely follows that of the

232

J.P. Perchard / Chemical Physics 273 (2001) 217±233

monomer. The dicult identi®cation of m3 has been explained in term of internal rotation as in the gas phase. The PD spectrum proves to be very di€erent from the PA one for three reasons, mechanical decoupling between the two oscillators, Fermi resonance strengthening and changes in the dipole moment function. While the two ®rst contributions involve modest changes of the potential function, the third one implies huge variations of two second derivatives of the dipole moment function involving OHb , l11 and l12 , which increase by nearly one order of magnitude. These variations are at the origin of the two most remarkable properties of the near infrared spectrum of PD, the intensity collapse of 2mOHb and the intensity increase of mOHb ‡ m2 , and seem to be an intrinsic property of hydrogen bonding. Indeed they also explain the main features of the near infrared spectra of larger aggregates. One may hope that these results will prompt quantochemists to develop calculations of overtone spectra of water clusters, following the Kjaergaard's pionering work [58].

References [1] J.P. Perchard, Z. Mielke, Chem. Phys. 264 (2001) 221. [2] J.P. Perchard, Chem. Phys. 266 (2001) 109. [3] D. Forney, M.E. Jacox, W.E. Thompson, J. Mol. Spectrosc. 157 (1993) 479. [4] R.L. Redington, D.E. Milligan, J. Chem. Phys. 37 (1962) 2162. [5] R.L. Redington, D.E. Milligan, J. Chem. Phys. 39 (1963) 1276. [6] H.P. Hopkins, R.F. Curl, K.S. Pitzer, J. Chem. Phys. 48 (1968) 2959. [7] A. Engdahl, B. Nelander, J. Mol. Struct. 193 (1989) 101. [8] G.P. Ayers, A.D.E. Pullin, Chem. Phys. Lett. 29 (1974) 609. [9] R.M. Bentwood, A.J. Barnes, W.J. Orville-Thomas, J. Mol. Spectrosc. 84 (1980) 391. [10] J.A. Cugley, A.D.E. Pullin, Chem. Phys. Lett. 19 (1973) 203. [11] E. Kn ozinger, R. Wittenbeck, J. Am. Chem. Soc. 105 (1983) 2154. [12] H.A. Fry, L.H. Jones, B.I. Swanson, Chem. Phys. Lett. 105 (1984) 547. [13] G.P. Ayers, A.D.E. Pullin, Spectrochim. Acta 32A (1976) 1689.

[14] A.C. Allen, P.C. Cross, Molecular Vib-Rotors, Wiley, New York, 1963. [15] G.P. Ayers, A.D.E. Pullin, Spectrochim. Acta 32A (1976) 1629. [16] B. Nelander, J. Chem. Phys. 88 (1988) 5254. [17] A.J. Barnes, S. Suzuki, J. Mol. Struct. 70 (1981) 301. [18] A. Engdahl, B. Nelander, J. Chem. Phys. 86 (1987) 4831. [19] J. Manz, J. Am. Chem. Soc. 102 (1980) 1801. [20] T. Oka, Y. Morino, J. Mol. Spectrosc. 6 (1961) 472. [21] J. Hawkins, S.R. Polo, J. Chem. Phys. 24 (1956) 1126. [22] C. Camy-Peyret, J.M. Flaud, Mol. Phys. 32 (1976) 523. [23] J.M. Flaud, C. Camy-Peyret, J. Mol. Spectrosc. 51 (1974) 142. [24] C. Camy-Peyret, J.M. Flaud, J. Mol. Spectrosc. 59 (1976) 327. [25] Y.Y. Kwan, J. Mol. Spectrosc. 71 (1978) 260. [26] R.A. Toth, J. Opt. Soc. Am. B 9 (1992) 462. [27] P.E. Fraley, K.N. Rao, L.H. Jones, J. Mol. Spectrosc. 29 (1969) 312. [28] R.A. Toth, J. Opt. Soc. Am. B 10 (1993) 1526. [29] J.P. Chevillard, J.Y. Mandin, J.M. Flaud, C. Camy-Peyret, Can. J. Phys. 63 (1985) 1112. [30] K. Laasonen, M. Parrinello, R. Car, C. Lee, D. Vanderbilt, Chem. Phys. Lett. 207 (1993) 209. [31] S.S. Xantheas, T.H. Dunning Jr., J. Chem. Phys. 99 (1993) 8774. [32] V. Barone, L. Orlandini, C. Adam, Chem. Phys. Lett. 231 (1994) 295. [33] M.J. Packer, D.C. Clary, J. Phys. Chem. 99 (1995) 14323. [34] J. Kim, J.Y. Lee, S. Lee, B.J. Mhin, K.S. Kim, J. Chem. Phys. 102 (1995) 310. ~ez, J. Elguero, J. Mol. Struct. [35] L. Gonzalez, O. M o, M. Yan (Theochem) 371 (1996) 1. [36] C. Mun~ oz-Caro, A. Ni~ no, J. Phys. Chem. A 101 (1997) 4128. [37] G. Van der Rest, M. Masella, J. Mol. Spectrosc. 196 (1999) 146. [38] G.M. Chaban, J.O. Jung, R.B. Gerber, J. Phys. Chem. A 104 (2000) 2772. [39] H.M. Lee, S.B. Such, J.Y. Lee, P. Tarakeshwar, K.S. Kim, J. Chem. Phys. 112 (2000) 9759. [40] F. Huisken, M. Kaloudis, A. Kulcke, J. Chem. Phys. 104 (1996) 17, and references cited therein. [41] R. Fr ochtenicht, M. Kaloudis, M. Koch, F. Huisken, J. Chem. Phys. 105 (1996) 6128. [42] Z.S. Huang, R.E. Miller, J. Chem. Phys. 91 (1989) 6613. [43] A. Engdahl, B. Nelander, J. Chem. Phys. 84 (1986) 1981. [44] U. Buck, F. Huisken, Chem. Rev. 100 (2000) 3863. [45] J.B. Paul, C.P. Collier, R.J. Saykally, J.J. Scherer, A. O'Keefe, J. Phys. Chem. A 101 (1997) 5211. [46] M.G. Sceats, M. Stavola, S.A. Rice, J. Chem. Phys. 71 (1979) 983. [47] A. Burneau, J. Corset, J. Chim. Phys. Physico-Chim. Biol. 69 (1972) 153. [48] L.S. Rothman, R.R. Gamache, R.H. Tipping, C.P. Rinsland, M.A.H. Smith, D. Chris-Benner, V. Malathy Devi, J.M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman,

J.P. Perchard / Chemical Physics 273 (2001) 217±233

[49] [50] [51] [52] [53]

S.T. Massie, L.R. Brown, R.A. Toth, J. Quant. Chem. Radiat. Transfer 48 (1992) 469. C.A. Swenson, Spectrochim. Acta 24A (1968) 721. J.E. Bertie, M.K. Ahmed, H.H. Eysel, J. Phys. Chem. 93 (1989) 2210. B.A. Zilles, W.B. Person, J. Chem. Phys. 79 (1983) 65. G. Van der Rest, M. Masella, J. Mol. Spectrosc. 196 (1999) 146. K.G. Brown, W.B. Person, J. Chem. Phys. 65 (1976) 2367.

233

[54] C. Secroun, A. Barbe, P. Jouve, J. Mol. Spectrosc. 45 (1973) 1. [55] S.T. Yao, J. Overend, Spectrochim. Acta 32A (1976) 1059. [56] D.F. Smith, J. Overend, Spectrochim. Acta 28A (1972) 471. [57] B.J. Rosenberg, W.C. Ermler, I. Shavitt, J. Chem. Phys. 65 (1976) 4072. [58] G.R. Low, H.G. Kjaergaard, J. Chem. Phys. 110 (1999) 9104.