Infrared spectra of H216O , H218O and D2O in the liquid phase by single-pass attenuated total internal reflection spectroscopy

Spectrochimica Acta Part A 60 (2004) 2611–2619

Infrared spectra of H2 16O, H2 18O and D2 O in the liquid phase by single-pass attenuated total internal reflection spectroscopy Simon E. Lappi, Brandye Smith, Stefan Franzen∗ Department of Chemistry, North Carolina State University, Raleigh, NC 27695, USA Received 16 June 2002; received in revised form 22 December 2003; accepted 29 December 2003

Abstract Mid-infrared attenuated total internal reflection (ATR) spectra of H2 16 O, H2 18 O and D2 16 O in the liquid state were obtained and normal coordinate analysis was performed based on the potential energy surface obtained from density functional theory (DFT) calculations. Fits of the spectra to multiple Gaussians showed a consistent fit of three bands for the bending region and five bands for the stretching region for three isotopomers, H2 16 O, H2 18 O and D2 16 O. The results are consistent with previous work and build on earlier studies by the inclusion of three isotopomers and mixtures using the advantage of single-pass ATR to obtain high quality spectra of the water stretching bands. DFT calculation of the vibrational spectrum of liquid water was conducted on seven model systems, two systems with periodic boundary conditions (PBC) consisting of four and nine H2 16 O molecules, and five water clusters consisting of 4, 9, 19, 27 and 32 H2 16 O molecules. The PBC and cluster models were used to obtain a representation of bulk water for comparison with experiment. The nine-water PBC model was found to give a good fit to the experimental line shapes. A difference is observed in the broadening of the water bending and stretching vibrations indicative of a difference in the rate of pure dephasing. The nine-water PBC calculation was also used to calculate the wavenumber shifts observed in the water isotopomers. © 2004 Published by Elsevier B.V. Keywords: IR; Attenuated total reflection; H2 16 O; H2 18 O; D2 16 O; Density functional theory calculations

1. Introduction The strong intermolecular interactions in water have a profound effect on all its properties including its vibrational spectrum. Although infrared spectra of water are often considered an undesirable background in spectra of biological molecules, these bands themselves may contain information. A method for extracting that information requires a very short path length because of the intense absorbance of the water stretching bands. Since the desired path length is less than 1 ␮m which is difficult to obtain in the transmission geometry. For this reason many recent studies of water spectra have been carried out by Fourier-transform infrared attenuated total reflection (FTIR-ATR) spectroscopy [1–8]. Although, there has been great interest in FTIR-ATR spectroscopy of aqueous solutions [1,3,4,9–13] there has been little work on the spectroscopy of the isotopomers of liquid water [4,10,14,15]. The majority of infrared ATR spectroscopy studies of liquid water has been conducted using multipass ATR accessories, which are primarily of ∗

Corresponding author. E-mail address: stefan [email protected] (S. Franzen).

1386-1425/$ – see front matter © 2004 Published by Elsevier B.V. doi:10.1016/j.saa.2003.12.042

two geometry types: the rectangular bar and the cylindrical circle [2,4,16,17]. These types of ATR accessories have several problems. They are difficult to assemble and require special gaskets to prevent leaks and contamination. They often must be modified to prevent large absorbance that results in non-linear detector response (primarily in the stretching region). They must be calibrated for the number of bounces in order that the correct intensities to be determined. On the other hand the single-pass ATR accessories suffer from none of these problems, which makes them ideal for studies of biopolymers where a holistic approach to the analysis of the spectra includes the water spectrum [18]. This follows from the fact that waters of hydration may be significantly different from bulk water and are hence part of the measured absorption due to a protein or polynucleotide sample [3,12,19–22]. There are a number of specific features that need to be considered for single-pass FTIR-ATR applications. First, the overall features of the spectrum, including the relative intensities of different bands may differ in single-pass and multipass ATR configurations due to the number of reflections and differing penetration depth of the radiation. The penetration of the infrared radiation due to the evanescent wave

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Table 1 The experimental wavenumbers and absorbance intensity of liquid H2 16 O, H2 18 O and D2 16 O Normal mode

Assignment

H2 16 O (cm−1 )

Intensity absorbance

H2 18 O (cm−1 )

Intensity absorbance

D2 16 O (cm−1 )

Intensity absorbance

ν2 ν2+R ν1 ν3

Bending Combination Symmetrical stretching Asymmetrical stretching

1639 2134 3261 3351

0.075 0.015 0.15 0.16

1632 2130 3241 3337

0.08 0.02 0.15 0.16

1206 – 2407 2476

0.08 – 0.16 0.18

Normal mode assignments are the accepted assignments [14,15,27,35,48–50].

is wavelength-dependent in ATR spectroscopy. It is also important to consider the linearity of the detector response, which may be improved in single-pass ATR relative to multipass ATR or transmission methods. For example, the maximum absorbance is ca. 0.15 for intense water stretching vibrations in a single bounce mode (see Table 1). For a typical multipass ATR configuration consisting of eight bounces the corresponding absorbance would be 8 × 0.15 = 1.2. Second, comparisons of H2 16 O and D2 16 O are important because of the utility of D2 16 O exchange studies [14,15,23–27]. However, there are well-known effects on spectra including the appearance of an H–O–D band at intermediate concentrations. Third, contributions to the spectra from temperature, salts, buffering components, and the final solution pH should all be considered thoroughly [2,8,14,28,29]. In this study we have combined consideration of these aspects with an analysis of the H2 16 O normal modes of vibration in solution based on 18 O and deuterium isotope effects. The normal mode analysis has been furthered by use of density functional theory (DFT) calculation of the vibrations to simulate bulk water in free clusters and periodic bound clusters. Building on previous studies of water and its isotopomers (H2 16 O, D2 16 O and H16 OD) [27,30–36], we report the spectrum of liquid H2 18 O compared to that of liquid H2 16 O. Although there is no doubt concerning the assignment of water bending and stretching vibrations, the nature of the complex bands observed in liquid samples is approached through the study of the three isotopomers H2 18 O, H2 16 O and D2 16 O. In this study we present DFT calculations that show that the distinction between symmetric and asymmetric water stretching bands is not applicable to liquid water. Instead, the stretching bands of liquid water are collective normal modes comprised of linear combinations of the well-known symmetry and asymmetric normal modes of individual water molecules. This finding is not surprising since liquid water lacks the C2v symmetry of isolated water molecules. However, it does influence the interpretation of spectra as illustrated below.

2. Experimental: chemicals Deionized water (H2 16 O) was freshly prepared (18 M) as dispensed from a BARNSTEAD E-PURE, water

purification system, Barnstead International (Dubuque, IA) and stored in a stoppered clean glass container until use. Isotopic water (H2 18 O) (purity was not provided) was obtained from the Stable Isotope Resource at Los Alamos National Laboratory, New Mexico and storied in a secondary container purged with dry nitrogen until use. Deuterium oxide (D2 16 O) 99.9% (D) was purchased from Aldrich (Milwaukee, WI) and stored in the original shipping container until use. All samples were placed in contact with the ATR element by a Hamilton 25 ul gas tight syringe (Model 1760). 2.1. Infrared measurements All spectra were collected using a Bio-Rad-Digilab FTS-6000 Fourier-transform infrared (FTIR) spectrometer with an attached infrared microscope (model #UMA-500) using a mounted crystalline germanium, attenuated total internal reflection (ATR) sampling attachment. The infrared light reflected back through the objective to a liquid nitrogen-cooled, narrow band mercury–cadmium–telluride (MCT) detector. There is nominally one reflection with a spot size of approximately 30 ␮m. The entire microscope was incased in a dry nitrogen glove bag, which reduces the possibility of atmospheric water or CO2 contamination of the spectra and samples. Each spectrum is the average of 10 accumulations of 64 scans each. All spectra were recorded at room temperature, approximately 25 ± 2 ◦ C with a resolution of 2 cm−1 . The spectra were converted into absorbance units by taking the negative of the log ratio of a sample spectrum to that of an air spectrum. The resulting absorbance spectra were also converted to molar extinction coefficient using the following relationship: A = cLε, where A is the absorption, c the concentration (55.39 mol/l, H2 16 O), ε the molar extinction coefficient and L the path length as determined by the depth of penetration equation. The depth of penetration is
given by the following equation: L = Dp = λnm /2πn1 sin2 θ − (n2 /n1 )2 , where n1 = 4.00, n2 = 1.30 [4,10,37–39] and θ = 25◦ . The data was then transferred to data processing programs (MicrocalTM Origin® , v7.0, Microcal Software Inc., Northampton, MA or Igro-Pro, v3.12, Wavemetrics, Lake Oswego, OR), where numerical treatment and final graphs were prepared.

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2.2. Computational methods: molecular geometries

0.20 0.18

3. Results and discussion 3.1. Infrared spectra The uncorrected FTIR spectra obtained for H2 16 O, H2 18 O and D2 16 O in terms of absorbance are shown in Fig. 1A and in terms of molar extinction coefficient are shown in Fig. 1B. The effect that the depth of penetration has on the resulting absorbance spectra is clearly apparent from the marked decrease in the bending mode and corresponding increase in the stretching mode of these spectra. In the H2 16 O spectrum there are three bands in the region between 600 and 1 Figures of the Gaussian fits, the fitting parameters, calculated spectra of all the DFT models, and the nine-water PBC model are provided in the supplemental for this publication and have been deposited with the British Library Boston Spa, Wetherby, West Yorks, UK as supplementary Publication No. “SUP. . . (. . . pages)”. Persons wishing to obtain copies of deposited material should contact Service Enquiries, British Library Boston Spa, Wetherby, West Yorks LS23 7BQ, UK citing the SUP number. Tel.: +44-1937-546-060; fax: +44-1937-546-333. [email protected].

1631

18

H2 O 16

D2 O

0.14 Absorbance

16

H2 O

1638

0.08

0.16

0.06

0.12

1600

1625 1650

1675

0.10 0.08 0.06 0.04 0.02 0.00 1000 1500 2000 2500 3000 3500 4000 4500 5000 -1

(A)

Wavenumbers (cm )

100 16

Molar Extinction Coefficient (L / mole*cm)

Seven molecular assemblies of water were constructed. Five different models consisted of 4, 9, 19, 27 and 32 individual waters in close association, without the constraint of periodic boundaries and two models consisted of four and nine individual waters, respectively, with the constraint of periodic boundary conditions (PBC). The optimized ground state geometries were obtained using the generalized gradient approximation (GGA) of Perdew [40] as implemented in DMol3 [41] using a numerical double-␨ basis with polarization functions (DNP) [42]. All calculations were carried out on the SGI/Cray Origin 2400 or the IBM SP RS/6000 supercomputers at the North Carolina Supercomputer Center (NCSC). The geometry optimizations were carried out until the energy difference was less than 10−6 a.u. on subsequent iterations. Upon optimization of the geometry a frequency calculation was then done by the finite difference method as implemented in DMol3. The results of the frequency calculation were √ then converted into Gaussian waveforms [G(ν) = 1/ 2πσ exp{−(ν − ν0 )2 /2σ 2 }, using σ = 50 cm−1 , for the bending region]. The stretching region was also modeled using σ ∼ 60–75 cm−1 for the Gaussian broadening function. The resulting Gaussian and stick spectra for the non-boundary models are shown in the Supporting Information1 and the PBC models are presented below. Isotopic mass change was also performed selectively on the hydrogen and oxygen atoms of the PBC nine-water model as implemented in InsightII (Accelrys, Burlington, MA). Evaluation of isotopic shifts was carried out by recalculations of the reduced mass of the molecule and the frequencies using the Hessian matrix obtained from the DMol3 vibrational frequency calculation.

2613

1631

H2 O

1638

18

H2 O

80

16

D2 O 20 18

60

16 14

1600

1625

1650

1675

40

20

0

1000 1500 2000 2500 3000 3500 4000 4500 5000

(B)

-1

Wavenumber (cm )

Fig. 1. (A) The uncorrected ATR-FTIR spectra for H2 16 O, H2 18 O, and D2 16 O are shown for the spectral range of 650–5000 cm−1 . The inset graph shows the clear peak separation for the bending modes of H2 16 O and H2 18 O. The baseline offset observed in the H2 16 O spectrum decreases in the H2 18 O spectrum and is absent in the D2 16 O spectrum can be attributed to unresolved overtone and combination band of the large liberation band, of which the tail end can be observed in the spectra of H2 16 O and H2 18 O starting at <1000 cm−1 . (B) The ATR-FTIR spectra for H2 16 O, H2 18 O, and D2 16 O are shown for the spectral range of 650–5000 cm−1 , but have been converted to molar extinction coefficient.

5000 cm−1 , a narrow band at 1638 cm−1 , a weak, broad band centered at approximately 2134 cm−1 and a prominent, unresolved multiple band centered at approximately 3350 cm−1 . In the H2 18 O spectrum there are three bands in the region between 600 and 5000 cm−1 , a narrow band at 1631 cm−1 , a weak, broad band centered at approximately 2130 cm−1 and a prominent, unresolved multiple band centered at approximately 3337 cm−1 . In the spectrum of D2 16 O there are five bands in the region between 600 and 5000 cm−1 , a narrow band at 1205 cm−1 , a broad, unresolved double band with centers at approximately 1490 and 1610 cm−1 , a prominent, unresolved multiple band centered at approximately

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2450 cm−1 , a weak, broad band centered at approximately 3420 cm−1 and a weak, unresolved double band with centers at approximately 3860 and 4220 cm−1 . The spectrum of D2 16 O clearly shows the presence of H16 OD and H2 16 O contamination with a set of unresolved peaks centered at approximately 1490 cm−1 (H16 OD) and 3420 cm−1 (H2 16 O) [14]. Table 1 summarizes the peak positions and observed intensities of the principal experimental bands. Gaussian fitting was preformed on the classical bending and stretching peaks of H2 16 O, H2 18 O and D2 16 O, the results can be found in the Supporting Information along with the fitting parameters. The high wavenumber band peaked at 3350 cm−1 in H2 16 O has long been assigned to the symmetric and asymmetric stretch of water [14,32,34,35]. The width and asymmetry of the band has hampered efforts to observe the individual frequencies of the underlying normal modes. Although the 18 O isotope difference spectrum (see Supporting Information) provides evidence for two unique bands in the stretching region, a fit of the bands for either H2 16 O or H2 18 O to two Gaussian bands is poor. A good fit to the observed broad, stretching peak is obtained when five Gaussian bands are used [11,43] (see Supporting Information). We found that it was not possible to associate these bands with the asymmetric or symmetric stretching normal modes because of severe mixing of these types of displacement for all of the normal modes throughout the stretching region. For the nine-water PBC calculation there are 18 modes in the stretching region. While a few of those modes have predominantly asymmetric character it was not possible to identify modes that had only symmetric displacements of the nine-water molecules. Instead, these modes had a collective character with some mixture of symmetric and asymmetric displacements for individual water molecules. The gas phase symmetric (ν1 ) and asymmetric (ν3 ) stretching frequencies are relatively close in energy, ν1 = 3651.7 cm−1 and ν3 = 3755.8 cm−1 , respectively [44]. It is perhaps not surprising, but not generally recognized, that strong hydrogen bonding does not permit the separation of the liquid water stretching bands into the two different symmetry types. A comparison of spectral bands for D2 16 O, H2 16 O and for the 50:50 mixture of D2 16 O/H2 16 O is shown in Fig. 2. It is quite interesting that a new band, which can be unambiguously attributed to H16 OD, appears in the bending region of the spectrum, but not in the stretching region. The H–O–H bend centered at 1640 cm−1 shifts to a D–O–D bend at 1200 cm−1 in D2 16 O. In solvent mixtures a H–O–D bending band centered at ≈1450 cm−1 appears. The wavenumber of the H–O–D bending band is increased as the mole fraction of either H2 16 O or D2 16 O approaches zero [14,15]. The increase relative to the wavenumber of 1450 cm−1 is (+2.0% at [H2 O < 5%] and +0.5% at [H2 O > 95%]) and is indicative of intermolecular interactions as discussed below. The behavior of the stretching bands is quite different. The stretching band is comprised of at least five

0.14

16

H2 O 16

H OD 16 D2 O

0.12 0.10 Absorbance

2614

0.08 0.06 0.04 0.02 0.00 1000

1500

2000

2500

3000

3500

4000

-1

Wavenumbers (cm )

Fig. 2. A comparison of spectral bands for D2 16 O, H2 16 O and for the 50:50 mixture of D2 16 O/H2 16 O is shown. The presence of H16 OD is clearly evident with the appearance of bands centered approximately at 1450 cm−1 .

components; the symmetric and asymmetric stretching bands, a combination band 2ν2 bending and the effects of weak and strong hydrogen bonding to the O–H oscillators [45]. The unresolved double band centered at 3300 cm−1 in H2 16 O shifts to a slightly better resolved double centered at 2450 cm−1 in D2 16 O. In D2 16 O/H2 16 O mixtures each of these bands more clearly resembles a single band and in each case the wavenumber is shifted significantly higher as the mole fraction approaches zero. In other words, the isolated O–H and O–D oscillator frequencies appear resolved at higher wavenumber than the symmetric and asymmetric normal modes. The improvement in the resolution of the isolated O–H and O–D oscillator frequencies results from an uncoupling of the isolated O–H or O–D oscillator from its neighbors, and from a decrease in the coupling of the combination bending band 2ν2 (D2 16 O and H2 16 O) with the corresponding symmetric and asymmetric stretching bands. This decrease can be inferred from the corresponding intensity increase in the combination bending band 2ν2 (H–O–D) centered at 2900 cm−1 and clearly evident as a prominent shoulder in the 50%:50% D2 16 O/H2 16 O mixture (Fig. 2). The H–O–D bending band wavenumber shows a remarkably consistent pattern as a function of H2 16 O mole fraction. There is a shift from higher wavenumber (at 99% D2 16 O) to a minimum (at 25% D2 16 O) and back to higher wavenumber at 1% D2 16 O. The results from fitting the O–H, O–D and H–O–D bands to a single Gaussian are shown in Table 2. 3.2. Modeling of vibrational spectra The density functional calculations for water clusters (4, 9, 19, 27 and 32 molecules, respectively) and water with periodic boundary conditions, i.e. (water in a box with four and nine molecules) are summarized in the Supporting

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Table 2 The results from a single Gaussian peak fitting for various H2 16 O:D2 16 O ratios Centera

±STD

Widtha

–OH stretching region 1 99 3 97 5 95 10 90 25 75 50 50

3401.5 3397.7 3397.5 3393.0 3381.0 3365.1

0.4842 0.3062 0.2183 0.2657 0.3151 0.1715

193.77 209.67 214.70 217.53 236.37 259.01

–OD stretching region 50 50 75 25 90 10 95 5 97 3 99 1

2485.4 2494.5 2499.3 2498.7 2498.2 2488.9

0.1499 0.1442 0.1788 0.2805 0.2280 0.4186

HOD bending peak 1 3 5 10 25 50 75 90 95 97 99

1473.8 1467.3 1463.1 1457.4 1452.6 1448.5 1447.8 1449.1 1451.2 1452.8 1456.8

0.3747 0.2828 0.2304 0.1373 0.0555 0.1105 0.1706 0.1740 0.2026 0.2312 0.4168

H2 16 O (%)

D2 16 O (%)

99 97 95 90 75 50 25 10 5 3 1

±STD

Areab

±STD

2.6532 1.0772 0.7533 0.8587 1.0696 1.0163

0.57 1.56 2.50 5.01 11.96 22.91

0.0129 0.0111 0.0120 0.0265 0.0739 0.1544

187.73 145.65 131.55 114.64 133.79 190.55

0.4926 0.5952 1.0004 1.8826 2.4383 11.1483

20.05 8.17 3.32 0.78 1.12 0.89

0.0716 0.0498 0.0422 0.0225 0.0420 0.1306

70.65 75.42 67.85 64.04 66.61 69.31 66.72 64.88 57.03 55.11 48.06

1.2763 1.4825 1.0381 0.4927 0.1830 0.2985 0.5847 1.1816 2.1463 1.7024 3.3859

0.32 0.54 0.64 1.00 2.01 2.71 1.93 0.95 0.24 0.23 0.06

0.0083 0.0184 0.0159 0.0108 0.0074 0.0140 0.0231 0.0309 0.0181 0.0132 0.0086

The stretching bands for the –OH, and –OD regions and the bending band for H16 OD were fit using a single Gaussian peak. STD refers to the standard deviation of the respective quantity in the Gaussian fit to the line shape. a The unites for the peak center and peak width (fwhm) are cm−1 . b The units of area are absorbance-cm−1 .

Information and in Fig. 3, respectively. In each calculation involving two or more water molecules there are a number of vibrational modes in the stretching and bending regions, this can be seen graphically in the stick spectra of Fig. 3. For cluster calculations the modes represent an average of modes involving hydrogen bonding and those at the edge of the cluster that do not. Water molecules that are at the edge of the hydrogen bond network have their vibrational modes skewed to higher wavenumber. Calculations with periodic boundary conditions are intended to remedy this problem. However, there is no currently accepted method for determining the infrared intensities of vibrations in a periodic lattice. To estimate the infrared intensities we used the following method, the periodic boundary assemblies were geometry optimized and frequencies were calculated, as indicated above, then the boundary constraint was removed from the assembly and a new frequency calculation was performed without further optimization. Thus two sets of vibrational frequencies were obtained for the same molecular assembly, one for the periodic boundary condition lacking intensity information and one for the gas phase system for which the intensities were determined. The intensities obtained from the pseudo-gas phase system were used as the intensities of the PBC frequency calculation.

A comparison of the resulting spectra is presented in Fig. 4A and B. The overall effect of periodic boundary conditions is to decrease the wavenumber of the stretching modes and increase the wavenumber of the bending modes, this can be clearly seen in Fig. 4A and B. These wavenumber shifts arise from the better modeling of hydrogen bonding in the PBC calculation. More complete hydrogen bonding will result in a shift of the stretching modes to lower wavenumber due to the electrostatic interaction of O–H with the oxygen lone pair. The bending modes will shift to higher wavenumber because of the constraint imposed on bending from two hydrogen bonds, i.e. from the configuration O · · · H–O–H · · · O. The nine-water PBC model, the H2 16 O bending band at 1634 cm−1 and the peak of O–H stretching region at 3255 cm−1 agree well with the experimental data at 1638 and 3350 cm−1 , respectively, despite the lacking the inclusion of anharmonicity. In the gas phase calculations of the H2 16 O vibrational spectrum, the calculated bending and stretching bands are ∼40 cm−1 too low and ∼350 cm−1 too high in wavenumber, respectively, compared to the liquid water spectrum. The discrepancy between the isolated water calculation and the liquid is due to hydrogen bonding and anharmonicity. The nine-water PBC

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No Periodic Boundaries Periodic Boundaries Calculated Intensity

Calculated Intensity

PBC 4 H2O Gaussian PBC 4 H2O Stick

1000

1500

2000

2500

3000

3500

4000

-1

(A)

1600 1650 1700 1750

1000

Wavenumbers (cm )

1500

2000

2500

3000

3500

4000

-1

Wavenumbers (cm )

(A) PBC 9 H2O Gaussian PBC 9 H2O Stick

Calculated Intensity

Calculated Intensity

No Periodic Boundaries Periodic Boundaries

1000

(B)

1500

2000

2500

3000

3500

1550 1600 1650 1700 1750

4000

-1

Wavenumbers (cm )

Fig. 3. The Gaussian and stick spectra for the two PBC water models are presented for the spectral range of 1000–4000 cm−1 . (A) The spectrum for the four-water PBC model is shown. (B) The spectrum for the nine-water PBC model is shown. The stick spectra are provide only as an indicator of the distribution of individual molecular modes within the calculated model and thus do not convey any information about the intensity difference within a given band. The spectra have a Gaussian width of 50 cm−1 , for all bands shown.

calculation shows that hydrogen bonding is the dominant contribution. The nine-water PBC model was also used for modeling isotopic substitution as described in Section 2.2. The result of exchanging 18 O for 16 O in all nine-water molecules is shown in Fig. 5A for the bending region and Fig. 5B for the stretching region. The calculated isotope shift of 6 cm−1 for the bending mode agrees very well with the observed 7 cm−1 shift in the experimental spectrum. In the stretching region the calculated isotope shift is 16 cm−1 , which agrees well with the observed 14 cm−1 shift in the experimental spectrum. The bending mode results for the nine-water PBC model with nine H–O–D and or nine D–O–D deuterium substitutions are shown in Fig. 6A along with the H–O–H starting system. The wavenumber separation between the D2 16 O and H2 16 O bending mode in the experimental spectrum

1000

(B)

1500

2000

2500

3000

3500

4000

-1

Wavenumbers (cm )

Fig. 4. The calculated Gaussian-broadened spectra for the two periodic boundary condition (PBC) water models and the two non-PBC water models are presented for the spectral range of 1000–4000 cm−1 . (A) The four-water system; (B) the nine-water system. The inset graphs in both figures show the peak shift of the bending mode, which moves to higher wavenumber for both models. The spectra have a Gaussian width of 50 cm−1 , for all bands shown.

(Fig. 2) is 432 cm−1 . In the nine-water PBC calculated model the peak separation is 438 cm−1 . The nine-water PBC model yields frequencies for the D2 16 O isotopomer of 1196 cm−1 for the bending mode and 2398 cm−1 for the peak of the O–D stretching band compared to the experimental values of 1205 and 2475 cm−1 , respectively. The stretching region shows structure in the Gaussianbroadened nine-water PBC model spectrum that does not agree with the experimental line shape in the stretching region (Figs. 4 and 5). The line width is determined by the convolution of the relaxation time (T2 ) in the excited state with inhomogeneous broadening. Fig. 6B shows that a Gaussian line width of σ = 75 cm−1 gives the best overall fit to the stretching band of the experimental data. The general

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1634

1628

16

H2 O

16

100% H2 O

18

1500

Calculated Intensity

Calculated Intensity 1000

16

100% H OD 16 100% D2 O

1196

H2 O

1620

1640

2000

2617

1634

1424

2500

1250

1500

1750

-1

(A)

Wavenumbers (cm )

(A)

Wavenumbers (cm )

3255

3239

16

H2 O

-1

16

H2 0 16

PBC 9 (H2 0)

18

H2 O

16 D2 0 16

3150

2500

(B)

3000

3500

3225

3300

-OH

-OD 2500

Absorbance

Calculated Intensity

PBC 9 (D2 0)

3000

3500

3500

3750

4000 2250

-1

Wavenumbers (cm )

Fig. 5. (A) The calculated Gaussian-broadened spectra of the bending region of PBC nine-water model and the isotopic 18 O nine-water models for the spectral range of 1000–2500 cm−1 . The inset graph clearly shows the peak shift of the bending mode, which moves to lower wavenumber consistent with the experimental shift. The bending region has a Gaussian width of 50 cm−1 . (B) The stretching region of PBC nine-water model and the isotopic 18 O nine-water models for the spectral range of 2500–4000 cm−1 . The inset graph clearly shows the peak shift of the stretching region, which moves to lower wavenumber consistent with the experimental shift. The stretching region has a Gaussian width of 75 cm−1 .

appearance is very similar to the experimental data, with exception of a tail on the higher wavenumber side of the band. The√full-width at half maximum for this band is fwhm = 2 2 ln(2)σ, which corresponds to ∼175 cm−1 for this calculated model, which fits the O–H stretching region well, is substantially larger than the fwhm of 80 cm−1 observed in the H–O–H bending mode. In the O–D stretching region a Gaussian width of σ = 60 cm−1 (corresponding to fwhm ∼ 140 cm−1 ) gave the best fit to the experimental data for D2 16 O and the D–O–D bending mode is also significantly narrower. The final band shape for the D2 16 O

(B)

2500

2750

3000

3250 -1

Wavenumbers (cm )

Fig. 6. (A) The calculated spectra of the bending region for H2 16 O, isotopic D2 16 O and H16 OD are presented for the spectral range of 1100–1800 cm−1 . The PBC nine-water model was used for the comparison. The peak separation for the D–O–D and H–O–H bending mode is consistent with the experimental results. (B) The experimental and calculated spectra of the stretching modes of H2 16 O and D2 16 O are presented for the spectral range of 2100–3900 cm−1 . The PBC nine-water model was used for the comparison. The absolute peak positions for the D–O–D and H–O–H stretching mode was scaled and shifted (+95 and +77 cm−1 for H2 16 O and D2 16 O, respectively) to better compare the model with the experimental results. The inset graph shows the unshifted bands for the model.

nine-water PBC model closely resembles that of the experimental O–D band, with the exception of the overall bandwidth, which is slightly wider on the lower wavenumber side of the band (≈40 cm−1 ) and the tail which, like the O–H band, is on the higher wavenumber side of the band. The fact that the stretching region requires a larger Gaussian line width than the bending region indicates that there is a vibrational lifetime difference between these regions.

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Vibrational energy relaxation lifetimes (T1 ) for the ν1 and ν3 stretching modes have been studied by ultra-fast spectroscopy and reported to be approximately 1 ps in H2 16 O and 2 ps for D2 16 O [45–47]. On the 1 ps time scale the width of the stretching bands was observed to be ∼35 cm−1 , which represents the convolution of a short excitation pulse, the lifetime broadened band and spectral diffusion on that time scale [45]. The experimental results suggests that the upper bound for Γ homo is 35 cm−1 . Using the approximation that the observed width (fwhm) is the geometric mean  Γobs = Γhomo + Γinhomo of the homogeneous width, Γ homo and the inhomogeneous width Γ inhomo , we conclude that the majority of the ∼175 cm−1 width for the stretching band region is attributable to inhomogeneous broadening.

4. Conclusion Although water has been studied by infrared spectroscopy for 50 years, the present study is the first complete analysis and comparison of liquid water (H2 16 O) and the three isotopomers (H2 18 O, D2 16 O and H16 OD). Single-pass FTIR-ATR spectroscopy was used to obtain spectra that are consistent with previous work, but have the advantage that effects due to non-linearity of the detector response are minimized because of the significantly lower absorbance of the sample. The comparison of the first spectrum of H2 18 O obtained by the ATR-FTIR method indicates that the bending band of water is comprised by one unique mode and that the stretching band contains at least two modes, which are consistent with the presence of a symmetric and asymmetric stretching vibration as expected based on vibrational analysis of the isolated water molecule [32,34,35,48,49]. Analysis of the vibrational spectrum of liquid water requires calculation of hydrogen bonding effects and intermolecular contributions. To include these effects we calculated the vibrational spectrum of seven systems of water molecules. Five of these systems were clusters consisting of 4, 9, 19, 27 and 32 molecules. Two models used periodic boundary conditions (four and nine molecule). The best system was determined to be the nine-water PBC model, which gave good agreement with the experimental results for H2 16 O and isotopic H2 18 O and D2 16 O in both the bending and stretching modes. The stretching band shapes were also examined for this model and found to agree quite well with the corresponding experimental data. An estimate of the contribution of inhomogeneous broadening for the stretching bands was made based on a comparison of the calculated and observed bandwidths. The agreement of the calculated model is sufficient to represent the important features of liquid water in detail. The remaining issue in the analysis is the correction for anharmonicity. The use of periodic boundary conditions and explicit modeling of isotopomers

in water permits a systematic approach to further address the anharmonic corrections and to arrive at a detailed understanding of the vibrational spectra of liquid water.

Acknowledgements We gratefully acknowledge support by the North Carolina Supercomputer Center through a Faculty Research Account. SF acknowledges support by the NSF (MCB-9874895).

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