Isotope effects in liquid water by infrared spectroscopy. III. H 2 O and D 2 O spectrafrom 6000 to 0 cm 1Jean-Joseph Max and Camille Chapados

Citation: The Journal of Chemical Physics 131, 184505 (2009); doi: 10.1063/1.3258646 View online: http://dx.doi.org/10.1063/1.3258646 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/131/18?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Energy-dependent dynamics of large- E collisions: Highly vibrationally excited azulene ( E = 20 390 and 38 580cm 1 ) with C O 2 J. Chem. Phys. 129, 014303 (2008); 10.1063/1.2943668 Diode-pumped 188 fs mode-locked Yb 3 + : Y 2 O 3 ceramic laser Appl. Phys. Lett. 90, 071101 (2007); 10.1063/1.2476385 The 5 f 2 5 f 1 6 d 1 absorption spectrum of Cs 2 Ge F 6 : U 4 + crystals: A quantum chemical and experimentalstudy J. Chem. Phys. 125, 074511 (2006); 10.1063/1.2336427 Potential-energy surface for the electronic ground state of N H 3 up to 20 000 cm 1 above equilibrium J. Chem. Phys. 123, 134308 (2005); 10.1063/1.2047572 High-resolution absorption spectrum of jet-cooled C H 3 Cl between 70000 and 85 000 cm 1 : New assignments J. Chem. Phys. 123, 104302 (2005); 10.1063/1.1950671

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Isotope effects in liquid water by infrared spectroscopy. III. H2O and D2Ospectra from 6000 to 0 cm−1

Jean-Joseph Maxa� and Camille Chapadosb�

Département de Chimie-Biologie, Université du Québec à Trois-Rivières, Trois-Rivières,Quebec G9A 5H7, Canada

�Received 20 July 2009; accepted 15 October 2009; published online 11 November 2009�

The infrared spectra �IR� of pure liquid light �H2O� and heavy �D2O� water were obtained withattenuated total reflection �ATR� and transmission measurements in the mid-IR and far-IR. Withthese and with other values obtained from the literature, the real �n� and imaginary parts �k� of therefractive index were meticulously derived in the complete IR region from 6000 to 0 cm−1. Thereliability of the results resides in the critical comparison of our experimental data with that obtainedfrom other laboratories and between calculated and experimental spectra, obtained by ATR andtransmission techniques. The new optical properties �n and k� can now be used as standards forliquid H2O and D2O. To these we have added the water �H and D� absorption coefficients �K� thatare derived from the k values. These can be used as references for spectra obtained by transmissionwith an absorbance intensity scale because they are almost the same. © 2009 American Institute ofPhysics. �doi:10.1063/1.3258646�

I. INTRODUCTION

What is the structure of (liquid) water was listed in Sci-ence 125 anniversary issue �2005� as one of the 125 un-solved questions that the scientific community has toaddress.1 Fundamental questions on liquid water are unex-plained. One of these questions is the presence of “free” OHgroups. Here free OH indicates that the water OH groups arenot hydrogen bonded �H-bonded� to adjacent molecules. Inour 2002 paper on light and heavy water mixtures we foundthat bulk liquid water �hereafter liquid water or water� formsa close network of hydrogen bonds with no free OH group.2

However, recent papers consider that this highly inter-mingled hydrogen bonding system has a small amount offree OH.3,4 In our infrared �IR� studies of water H2O–D2Omixtures, that of pure light and heavy waters at differenttemperatures, and that of water-acetone mixtures we foundnone.2,5 Furthermore, our recent study of methanol-acetonemixtures where free OH groups could exist showed no evi-dence of them.6 Even in the methanol-hexane mixture sys-tem, only a few ppm of free OH is present at very lowmethanol concentrations.7 There, 99.9%+ of the methanolOH groups form H-bonds. Water and methanol moleculesshare their labile H atoms as soon as a few neighboring ac-ceptors are available. Nevertheless, diluted in organic solu-tions of strong H-bond acceptors the water and alcohols OHstretch bands blueshift from the position of the pureliquid5,6,8 but much less than that of the free OH position.7

This comes from a strengthening of the valence OH bond asthe number of H-bonds accepted by the oxygen atom de-creases.

Near infrared �NIR� spectroscopy is sometimes used toobtain structural information on liquid water.9–11 The analy-sis of the NIR bands arrives at the conclusion that free OH ispresent in liquid water. The NIR region contains the waterharmonics and combination bands which are situated in the7500–5000 cm−1 region.9 An adequate assignment of thebands in this region is a prerequisite to the spectral analysis.The water fundamental bands come from the stretching��1 ,�3� and deformation ��2� modes that appear in mid-IR�MIR�. To these internal modes, frustrated rotational �libra-tions, �L� and translational modes produce some absorptionin the far IR �FIR�. The internal and external modes cancombine together. Some unambiguous ones are the ��1+�2�and ��3+�2� bands in the 5200–5000 cm−1 region, �2�1� and�2�3� in the 7200–6700 cm−1 region and ��2+�L� in the2115 cm−1 region. Many other combination bands are over-looked or ill defined because they overlap with fundamentaland other combination bands. One example is the overtoneof the deformation band �2�2� that cannot easily be identifiedin the massive �1 and �3 absorption region.12 In aqueousacetone5 and acetonitrile where water �1 and �3 bands arestrong and well resolved while the 2�2 band appearing in thevicinity is very weak. However, this intensity relation cannotbe extrapolated to that of pure liquid where Fermi resonancemay influence a part of the massive band. Another particu-larity in the water spectrum is the “plateau” in the1500–900 cm−1 region.2,13 This region is often neglectedand, worse, sometimes brought to the base line. However,this absorption is genuine and we have assigned the absorp-tion to several bands �combination and difference� implyinglibrations, other FIR bands, and �2.2 Since combinationbands are observed in the 2200–900 cm−1 region and, inparticular, in the 2100 cm−1 band, others may be present inthe �1 and �3 absorption region.2 In this reference the assign-ment of some of these was tentative since they were estab-

a�Present address: ITF Labs, 400 Montpellier, Montréal, QC, CanadaH4N 2G7. Electronic mail: jjmax@itfoptical.com.

b�Author to whom correspondence should be addressed. FAX: 819-376-5084. Electronic mail: camille.chapados@uqtr.ca.

THE JOURNAL OF CHEMICAL PHYSICS 131, 184505 �2009�

0021-9606/2009/131�18�/184505/13/$25.00 © 2009 American Institute of Physics131, 184505-1

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lished with ill defined FIR bands. Thus the assignment of allthe components in the massive �OH band spanning almost1000 cm−1 �full width at half height �FWHH� �400 cm−1� isincomplete. To complete the assignment is far from simplebecause the band enhancement techniques �second deriva-tives and Fourier self-deconvolution� are useless on thesebroad bands. However, all that is known of light and heavywater in the NIR, MIR, and FIR regions must be put togetherto obtain flawless spectra of both waters.

The liquid water �H2O� spectrum covering the8000–0 cm−1 region was last updated in 1996.13 That ofD2O was updated in 1989 for the region of 8000–700 cm−1.Since the H2O and D2O spectra are very similar when theisotopic factor is taken into account2 the D2O spectrum canaid in the assignment of the H2O components in conflictingsituations. For this we need a high quality D2O spectrumcovering the complete region from 0 to at least 6000 cm−1.

Theoretical calculations are also used to unravel thestructure of liquid water. For this, molecular dynamics simu-lation �MDS� is a powerful analytical tool that tackles smallmolecules such as water with incessant increasing computerpower. However, MDS is limited by the capability of theempirical potentials to reproduce the real watersituation.14–17 In liquid water, the H-bond is ill defined whichleads to contradictory conclusions.16,18,19 Chemical bondinghas a large effect on the valence electronic structure anddifferent H-bonding configurations will produce variations inthe local water molecular orbital structure.17 In their MDScalculations, authors frequently consider that the water �OH

stretch massif absorption is the result of a continuous distri-bution of H-bonding strength �related to O–O distance� anddo not consider the contribution from �1, �3, and the associ-ated combination bands.20 Following these results, somespectroscopists applied the simplification and neglected thepresence of the two OH vibrations of water and the couplingbetween them.21 This is irreconcilable with the experimentaldata where well-defined pairs of bands have been observedin different water situations that have different H-bondingarrangements.5,8,22–24 Furthermore, the simulations do not in-clude the proton hopping between neighboring water mol-ecules at the fast rate of 0.1–10 ps.25,26 The phenomenon ofproton mobility due to proton hopping, H-bonding, or bothare necessary premises in the water network model organi-zation. Notwithstanding this uncertainty the short lived OHstretch vibrations will have a broadening effect on the ab-sorption band.

Considering that the two water OH stretch modes ��1

and �3� form a sea of indiscernible OH absorption in liquidwater leads MDS authors to separate the water OH absorp-tion massif into three �sometimes more� different groups ofH-bonded water molecules identified as strongly bonded,medium bonded, and weakly bonded �and sometimes freeOH�.3,21,27 Other authors consider this absorption as the re-sult of a continuous distribution of H-bonds with no discern-able components.3,28 These two patterns although differentcannot be related to experimental IR results of isotopic mix-tures where many discernable components are observed.2

This comparison questions the hypothesis made in the MDSstudies.

Therefore, the description of liquid water at the molecu-lar level requires the knowledge of the intra- and intermo-lecular movements. These include the fundamentals and alsothe numerous combination and harmonic bands that liquidwater has. This knowledge is a prerequisite for a comprehen-sive determination of the molecular organization. IR spec-troscopy, being a mild technique, is adequately suited for thetask. Although several studies were made by IR and by othertechniques to unravel the water molecular organization, noneso far is completely satisfactory.29

Part I of this IR study of mixtures of H2O in D2O �100%to 0%� was made at room temperature to obtain the numberof species present in the mixtures.2 For this we preparedsome 60 odd solutions from pure light water to pure heavywater and obtained their IR spectra by attenuated total reflec-tion �ATR�. Through factor analysis �FA� we obtained, forthe solutions, five multiplying factors �MFs�: spectra andabundances. Recall that the MFs are related to the speciesconcentrations. To assign these to specific molecular organi-zations we made a statistical evaluation of the molecules’tribology �neighboring assembly of molecules�. Sixteen or-ganizations of equal probability surround a target molecule.Because of symmetry some of these are equivalent which weregrouped into nine different spectroscopic species. Theabundance of these as a function of mole fraction was ob-tained. These curves indicated that some organizationsevolved concomitantly and we added them. The comparisonof these with the IR experimental curves obtained by FA wasa perfect match. This indicated that the IR spectra were good,the FA was adequate, and the statistical evaluation wellsuited. The five spectroscopic factors retrieved were assignedto OH4, OH3D, OH2D2, OHD3, and OD4. The identity of thefactors was obtained from the solution compositions and thefactor spectral signatures. The solutions are made of H2O,HDO, and D2O in the following proportions: in OH4 it is1:0:0; in OH3D it is 1:1:0; in OH2D2 it is 1:4:1; in OHD3 itis 0:1:1; and in OD4 it is 0:0:1. Reference 2 gives the proce-dure details. The governing factors in the solutions are thetwo covalent bonds and the two accepted hydrogen bonds.To these, proton hopping that exchange at a fast rate mixescovalent and H-bonds.25,26

Since the statistical model of liquid light and heavy wa-ter mixtures gave nine different evolving species and FA ofthe experimental IR spectra gave five factors, the secondpaper �Part II� was an attempt to untangle the factor degen-eracy observed in I.2 Several IR studies made on water atvarying temperatures were interpreted differently.9,11 The dif-ferences come mainly from the interpretation of the OH ab-sorption of water. Some authors consider that in liquid waterthe amount of free OH increases with temperature. Othersconsider that it is the amount of weakly bonded water mol-ecules that increase with temperature. This fundamentalquestion is still unsolved.

To address the free OH question and the weak bondsituation and to compare adequately H2O and D2O spectra,we need high quality spectra from 6000 to 0 cm−1

at several temperatures. With our ATR-IR measurements�6000–650 cm−1� of pure light and heavy water from roomtemperature to 95 °C, we covered a part of the region. FA of

184505-2 J.-J. Max and C. Chapados J. Chem. Phys. 131, 184505 �2009�

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the spectra indicated that pure water is composed of only twofactors whose concentrations vary inversely with tempera-ture. We coined them as cold and hot factors. Orthogonaliza-tion of these gave us their spectra and abundances and estab-lished their temperature limit as −20 and +120 °C,respectively.2 None of these factors could be ascribed to freeOH.

FIRs of pure H2O and pure D2O at different tempera-tures are available in the 25–460 cm−1 region.30 FA of thesegave results that well matched the abundance curves ob-tained in MIR.2 However, the extrapolation technique thatthe author used to fill the gap30 between 450 and 1000 cm−1

did not follow it. Since no obvious reason could explain sucha disparity we decided to look at it closely. Although this iseasily said it is not easily done since the MIR spectra wereobtained by ATR and the FIR ones by transmission measure-ments through silicon windows. The spectra coming from thetwo techniques cannot be concatenated because of opticalincompatibilities: �1� ATR spectra are not true absorbancespectra although they look alike;31 and �2� transmission mea-surements are perturbed by multiple internal reflections gen-erated by the windows and sample refractive index �RI� mis-matches. Since the concatenation of the different spectralregions is a necessity to have complete spectra we have totransform our ATR-IR spectra, the FIR spectra, and the di-electric measurements �we need them� of pure H2O and pureD2O into the real and imaginary parts of the RI. This is donethrough the Kramers–Kronig �KK� relations by integratingthe numerical data since the analytical form is impossible.32

Iterative procedures are used to optimize the output.The objective of this paper is to obtain, at room tempera-

ture, the complete spectra of pure light and heavy water from0 to 6000 cm−1. Also, we want to correct the mismatchesmentioned above, complete the heavy water FIR spectrum,and select the proper terahertz data to fill the data fromaround 100 to 0 cm−1. Furthermore, we want to ensure thatall the spectral regions are properly orchestrated since any ofthe previous steps will result in a sinusoidal train followingthe KK relation. The comparison between light and heavywater spectra will permit the evaluation of the assemblageand validate the resulting spectra.

II. THEORETICAL

A. The use of the KK relation

ATR and transmission spectra depend on the samplecomplex RI, real �n� and imaginary �k� parts. These are re-lated to the dielectric constants �� and �� by the equationn*2=�* �with * indicating complex terms�.13 ATR is a mea-surement of reflections involving n and k that are functionsof wavelength. Transmission measurements are also depen-dent on RI but differently than ATR. The absorption coeffi-cient K �sometimes called the Beer–Lambert absorption co-efficient or Lambert absorption coefficient� which is the termof interest is directly related to k: K �cm−1�=4���̃�k,where �̃ is the wave number in cm−1.13

The refractive indices of the cell windows and that of thesample differ. Because of this, unavoidable reflections at the

window-sample interfaces are obtained. These cause fringeswhose intensities depend on the difference between windowsand sample RI: a big difference causes high interferencefringes. The choice of IR windows will try to minimize thesefringes but is dependent on their transmission regions. TheATR technique does not generate fringes but is subject to thecrystal transmission region and to the anomalous dispersioneffect.31,33 Hence, the knowledge of either k or K is not suf-ficient for calculating the spectra needed for the comparisonto the experimental ones, knowledge of n is also necessary.Fortunately, in linear optics, n and k are related through KKrelation.32,34 This relation permits the calculation of one formto the other provided that the whole spectrum is known �thatis from 0 to ��: in practice, since infinity is not an option, itis the region where bands absorb. However, the limit is noteasy to determine and depends on the operator ability whichnecessitates numerical verifications.35 For pure liquid water,the influence of integration frequency ranges and the choiceof other parameters are illustrated in Supplement A.36 Animportant parameter is the anchor value of n at “infinite”frequency n�. The choice of this is not easy since it is relatedto a finite frequency which limits the integration range.

The KK relation is used to transform k into n. Proce-dures that use fast Fourier transform �FFT� can be used butwith caution since it is prone to generate irregularities.31,34

Although, the use of the KK procedure spreads any datadisturbances �noise, step function error, data discontinuitiesin the original, or derivative traces� between k and n, thesedisturbances are not eliminated. Hence, care must be taken toavoid them in the input data since they will cause irregulari-ties in the end spectra.

B. Data concatenation 0–7901 cm−1

Available experimental data by different measurementmethods were obtained from several sources. The KK trans-formation requires the input spectrum to be complete fromnull to infinite frequency.32,34 Since this is not possible it isnecessary, in practice, to put the integration limit far awayfrom strong bands.13,31 These in liquid water are located be-low 4000 cm−1.9,37 Since the water electronic absorption ishigher than 15 000 cm−1,38 we decided to settle the KK inte-gration in the 7901–0 cm−1 range. However, the effects ofthis truncation need evaluation since the accuracy of the KKtransformation is less reliable close to the integration limit.This is important in FFT since this procedure uses periodicfunctions �one period equal the integration range�. However,FFT can be used successfully for liquid water if the neces-sary conditions are followed. These are given in SupplementA which gives also an example of truncation.36

Concatenation of available data is required before apply-ing the KK relation. Special care is needed to avoid junctiondiscontinuities which are steps in the input and first deriva-tive spectra. Such mismatches were seen in the reportedspectrum of water.13 Although these errors are minimal theymust be removed to obtain a reference spectrum that can beused as a standard. Gaussian fittings were used to overcomesuch problems in the FIR of 700–100 cm−1 of water where

184505-3 Complete H2O–D2O IR spectra J. Chem. Phys. 131, 184505 �2009�

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experimental data are scarce and show inconsistencies be-tween authors.30,39 The water Gaussian components charac-teristics �number, position, and FWHH� are discussed inSec. IV B 2 and Sec. IV C 4. The arguments are based on thereported k data for H2O and D2O in the temperature rangefrom −6 to 80 °C.30 Supplement B gives the details.36

C. Matching calculated and experimental spectra

The best way to ensure the validity of the resulting wateroptical properties is to compare several experimental datasets with the results from calculations that use the water op-tical properties. In the present work, experimental data wereobtained by ATR and transmission measurements.

1. ATR spectra

The equations given for ATR calculations13 were modi-fied to take into account the general case where the “total”number of reflection is not an integer. The justification forthis is given in Supplements C and D �Ref. 36� where n2 isthe RI of the ATR crystal �nonabsorbing medium�, � theangle at the reflection interface, and p the number of reflec-tion that part a of the light beam overcomes. The remainingpart of the light �1−a� overcomes �p+1� reflections, where pis an integer and a is a real number � �0,1�. With the real �n�and imaginary �k� parts of the sample RI, the ATR spectrumis �see also Supplement C�36

ATR��� = 12 ��1 − a��Rp + R2p� + a�Rp+1 + R2�p+1��� , �1�

with

�R =n2

2 cos2 � − 2Xn2 cos � + Y

n22 cos2 � + 2Xn2 cos � + Y

Y = ��n2 − k2 − n22 sin2 ��2 + 4n2k2

X = �12 �n2 − k2 − n2

2 sin2 � + ��n2 − k2 − n22 sin2 ��2 + 4n2k2�

� .�2�

Equation �1� is valid if the coherence of light is lost fromone reflection to the next.13,40 With the optical property spec-tra, the angle �, and parameters p and a, the ATR spectra canbe calculated with Eqs. �1� and �2�. An iterative procedure isused to insure the proper match between calculated and ex-perimental spectra.13,31

2. Transmission spectraWe recently developed the equations that calculate, in an

analytical form, a sample �m1� transmission spectrum ofthickness �1 between two windows not perfectly parallel.33

These are made of the same nonabsorbing material �m2� withreal RI �n2�. An absorbing sample has a complex RI �n

1*

=n1+jk1� generating, at the window/sample interface, a com-plex reflection coefficient �r

2*�,

�r2* =

n2 − n1*

n2 + n1*

=n2 − �n1 + jk1�n2 + �n1 + jk1�

= r2R + jr2I,

r2R =n2

2 − n12 − k1

2

�n2 + n1�2 + k12 ,

r2I = − 2n2k1

�n2 + n1�2 + k12 .

� �3�

We assume that the sample thickness varies uniformlyfrom ��1−�� to ��1+�� over the area where the near normalbeam strikes. The beam transmission is given by33

1

2�

�1−�

�1+�

Td�1 = �1 − rs2�21 − r2

*22e−�1�1 +1

6��1

�

�1 2� 1

1 − �r2R2 + r2I

2 �2e−2�1�4�

�

⎩⎪⎨⎪⎧

1

+sin�400��̃n1��

200��̃n1�e−�1��r2R

2 − r2I2 �cos�2T1� + 2r2Ir2R sin�2T1��

+sin�800��̃n1��

400��̃n1�e−2�1���r2R

2 − r2I2 �2 − 4r2I

2 r2R2 �cos�4T1� + 4r2Ir2R�r2R

2 − r2I2 �sin�4T1��

+sin�1200��̃n1��

600��̃n1�e−3�1��r2R

2 − r2I2 ���r2R

2 − r2I2 �2 − 12r2I

2 r2R2 �cos�6T1�

+ 2r2Ir2R�3�r2R2 − r2I

2 �2 − 4r2I2 r2R

2 �sin�6T1� �+

sin�1600��̃n1��800��̃n1�

e−4�1���r2R2 − r2I

2 �4 + 16r2I4 r2R

4 − 24�r2R2 − r2I

2 �2r2I2 r2R

2 �cos�8T1�+ 8�r2R

2 − r2I2 �r2Ir2R��r2R

2 − r2I2 �2 − 4r2I

2 r2R2 �sin�8T1� �

+sin�2000��̃n1��

1000��̃n1�e−5�1��r2R

2 − r2I2 ���r2R

2 − r2I2 �4 − 40�r2R

2 − r2I2 �2r2I

2 r2R2 + 80r2I

4 r2R4 �cos�10T1�

+ 2r2Ir2R�5�r2R2 − r2I

2 �4 − 40�r2R2 − r2I

2 �2r2I2 r2R

2 + 16r2I4 r2R

4 �sin�10T1� �+

sin�2400��̃n1��1200��̃n1�

e−6�1���r2R2 − r2I

2 �6 − 60�r2R2 − r2I

2 �4r2I2 r2R

2 + 240�r2R2 − r2I

2 �2r2I4 r2R

4 − 64r2I6 r2R

6 �cos�12T1�+ �12�r2R

2 − r2I2 �5r2Ir2R − 160�r2R

2 − r2I2 �3r2I

3 r2R3 + 192�r2R

2 − r2I2 �r2I

5 r2R5 �sin�12T1� �

+ f�cos�2pT1�,sin�pT1�,p 6� , ⎭⎪⎬⎪⎫

184505-4 J.-J. Max and C. Chapados J. Chem. Phys. 131, 184505 �2009�

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with rs= �n2−1� / �n2+1� and

1 − r2*22 = 1 + r2R

4 + r2I4 − 2r2R

2 + 2r2I2 + 2r2R

2 r2I2 . �5�

The propagation term �Ex� of the electric field in me-dium x with optical properties nx and kx over the distance �x

is given by41

Ex = e−j�2��/c�nx�x � e−�2��/c�kx�x, �6�

where � is the frequency. The time delay �Tx� passingthrough the thickness �x of this medium is

nx�x2��/c = Tx. �7�

The analytical form of Eq. �4� gives rapid answerswhereas numerical integrations are long and tedious. Theimportant parameter in Eq. �4� is �, the maximum thicknessdeviation from the average value. This parameter was variedin a spreadsheet program to find the anchor value. Even withextremely flat window plates it is difficult to insure exactparallel faces of the sample cavity.42 Equation �4� takes careof any variations and gives the sample accurate optical prop-erties.

III. CHEMICALS, SOLUTIONS, AND IRMEASUREMENTS

A. Chemical and solutions

De-ionized freshly double distilled water was used forlight water. Heavy water �Aldrich Chemical Co., purity99.9 atom % D� was used without further purification.

B. IR measurements

The IR measurements were obtained with a model 510PNicolet FTIR spectrometer with a deuterium triglycine sul-fate detector. Two KBr windows isolated the measurementchamber from the outside. Samples were contained in trans-mission cells with Si, ZnSe, and BaF2 windows separated bydifferent spacer thicknesses. The lower transmission limits ofthese are 400, 500, and 700 cm−1, respectively. Several spac-

ers were used: 25 �m spacers made of inox steel, thinnerones of different thicknesses were made with a print of a18KT Gold leafing pen �Krylon�.

Other samples were contained in a Circle cell�SpectraTech� equipped with a ZnSe crystal rod �8 cm long�in an ATR configuration with an incident beam at a 45° angle�manufacturer’s value�. The spectral range of the ATR sys-tem is 6500–650 cm−1. The beam makes 11 internal reflec-tions in the crystal. Two ATR cylindrical cells with a differ-ent number of reflections in contact with the sample wereused. The ATR spectral intensities are presented in ATR ab-sorbance units �ATR AU�.

The spectra were taken under a nitrogen flow to ensurelow CO2 and water vapor residues in the spectrometer. Eachspectrum obtained at 27.1�1.2 °C is an accumulation of100 scans or more at 2 cm−1 resolution �0.9645 cm−1 sam-pling interval�. Since model 510P is a single-beam spectrom-eter, a background was taken before measuring each sample.

The data are transferred to a spreadsheet program fornumerical calculations. Compensation for the window ab-sorptions was made with the window spectra after removingtheir reflection losses. The determination of these was madein nonabsorbing regions.

IV. RESULTS AND DISCUSSION

A. Available data

The high limit of our spectrometer is around 6500 cm−1;the ATR accessory with a ZnSe crystal has a low limit ofaround 700 cm−1.43 Because of this we have to use data fromother sources to apply the KK relation since we need thevalues starting from 0 cm−1.

Numerous water IR spectra have been reported in thepast century. A screening of these was made to select the bestones outside our ATR range by considering the experimentalmethod used. We kept those that reduced the most thesources of error. Table I lists the data source retained for thecalculations of liquid water optical properties �k and n� at25 °C. The Lambert coefficients are reliable when no strong

TABLE I. Sources of optical properties of water used in the present work.

Method

Materialrod or

windows SampleRange�cm−1� First author Ref.

a Absorption coefficientBeer Lambert

H2O 16 000–5500 Kou �1993� 37

b ATR ZnSe H2O, D2O 5500–700 �650� Presentwork

c Transmission BaF2 H2O, D2O 5500–750ZnSe 5500–500 Present

workSi 5500–630, 590–400d Transmission Si H2O, D2O 450–100 Zelsmann �1995� 30e Absorption coefficient

Beer LambertPE H2O 130–10 Xu �2006� 44

f Absorption coefficientReflection

Si H2O, D2O 60–5 Rønne�1997, 1999, 2002�

45

g Dielectric constantInterferometry

H2O 10–0 Ellison �2007� 46

Buchner �1999� 47

184505-5 Complete H2O–D2O IR spectra J. Chem. Phys. 131, 184505 �2009�

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bands that give anomalous dispersions are present. The k��̃�water data in the 15 000–5500 cm−1 range in Ref. 37 meetthese criteria and were taken without modification. The K��̃�values were obtained directly from these.

The Lambert coefficient of liquid water near 25 °C ofXu et al. in the 118–10 cm−1 range were consideredreliable.44 These were interpolated and smoothed with a thirdorder polynomial function. The result was corroborated withRef. 45 data that were obtained by another method. Opticaldata in the 15–0 cm−1 range were calculated from dielectricones using the numerical equations in Refs. 46 and 47. Otherdata in Table I are experimental ATR and transmission re-sults.

To improve the reliability of our results, two ATR cellswith the same ZnSe crystal but with a different number ofreflections in contact with the sample were used to obtain thespectra.48 Several transmission spectra were obtained withdifferent path lengths and different windows �BaF2, ZnSe,and Si� in the range 6500–400 cm−1. Experimental spectra inthe 450–30 cm−1 range from Ref. 30 were used after correct-ing them for the Si window absorption �see Supplement E�.36

B. Method

An iterative procedure is used to fit the two ATR experi-mental spectra obtained from long and short cells to the cal-culated spectra. We first used the water recommendedspectrum13 to calibrate the ATR cell number of reflections.However, since the related ATR equations were improved�Supplement C�36 the reference spectrum was no longer sat-isfactory. Therefore, another calibration procedure was re-quired: the respective numbers of reflections of the two ATRcells were adjusted to minimize the standard deviations ob-tained for fitting the ATR spectra normalized to their numberof reflections. Starting from the experimental ATR spectrumof the first ATR cell, �i� the optical properties of water werederived, �ii� the ATR spectrum of the second cell was thencalculated using these results, �iii� the difference spectrumbetween calculated and experimental results was obtained,and �iv� the same procedure was used with the experimentalATR spectrum of the second cell. The respective numbers ofreflections �p and a� were adjusted to minimize the differ-ence spectra. Due to distortion and higher noise in the700–650 cm−1 region, the iterative fitting procedure was ap-plied in the 5500–700 and 5500–650 cm−1 ranges for H2Oand D2O, respectively.

1. First step H2O

In a first step, experimental ATR spectra in the6000–650 cm−1 range were used with the recommended datafrom Ref. 13 for the 649–0 cm−1 range and Ref. 37 for the7901–6000 cm−1 range in order to obtain a first set of k andn values for pure light liquid water. The iterativeprocedure13,31 was applied to fit the calculated and experi-mental ATR absorbance spectra by adjusting the k values inthe 6000–650 cm−1 range while keeping the k values stableoutside this range. This permitted to �i� adjust the number ofreflections �parameters p and a� for the ATR cells used, �ii�

adjust the n� parameter, and �iii� show that some defectswere present in the 650–0 cm−1 range of the recommendeddata �see Supplement F�.36

The first step gave k and n values very close to the finalresults in the 5500–900 cm−1 range. Values of k above thisrange are final because they were taken directly from Ref. 37since the original experimental data are not available. Valuesof k in the lower range � 900 cm−1� are sensitive to theadjustment of the Gaussian fitting operated in the650–0 cm−1.

2. Second step H2O

For the spectrum in the 900–100 cm−1 range we madeGaussian fittings of available experimental spectra that wereobtained by transmission measurements. Fine tuning wasmade by an iteration procedure. For the fitting we used eightGaussian components. The justification of this procedure isgiven in Supplement B.36

The 118–10 cm−1 H2O spectrum was determined by ob-taining the data of Xu et al., Rønne et al., and Ellison.44–46

Supplement G �Ref. 36� gives an evaluation of thesefrom which we obtained a third order polynomial function�y=7.23�10−3+5.60�10−4�̃−4.06�10−6�̃2+2.99�10−8�̃3,where �̃ is the wavenumber in cm−1� that we use for thewater spectrum in that FIR region. The values in the10–0 cm−1 region were obtained from dielectric constantequations.46,47

Due to sensitivity of the 900–650 cm−1 region to modi-fications at lower frequencies �650–0 cm−1� the iterativeprocedure required the recalculation and fitting of the ATRspectrum over the entire wavenumber range after any modi-fications in the low frequency region.

3. Third step H2O: Finishing touch

The ATR experimental spectra were corrected for pertur-bation of known sources: small amounts of CO2 and H2Ovapors in the background, small Teflon™ bands �near1150 cm−1� due to the O-rings used to secure the ZnSe rodinto the ATR cell.48 Then the spectra were smoothed using aquadratic-cubic algorithm with a 41 data points moving av-erage ��39.5 cm−1�.49 Finally, a small baseline adjustmentwas made �less than 3 ATR mAU� to match the ATRexperimental spectrum to the reference spectrum in the5800–5500 cm−1 region where water absorbs but verylittle.37

4. First step for D2O: Prelude

Although the D2O spectra were obtained in a similarfashion as that of H2O they were tainted with several genu-ine problems that had to be resolved before the procedure.

The first problem is that of a minute amount of H in theliquid heavy water used that contained 99.9% D. Althoughthe quantity of H is very small it nevertheless gives an an-noying OH band that was deemed necessary to remove inorder to have a 100% pure D2O spectrum. Since chemicalremoval is not easy we used our previous spectroscopicstudy of H2O–D2O mixtures to do the operation.2 There, wedetermined that five factors were present in the mixtures:

184505-6 J.-J. Max and C. Chapados J. Chem. Phys. 131, 184505 �2009�

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OH4, OH3D, OH2D2, OHD3, and OD4. These are related totwo hydrogen atoms �H or D� covalently bonded to a givenO while two others are H-bonded. Even if each species can-not be physically isolated one from the other their genuinespectrum can be retrieved.

Considering that in liquid D2O the amount of H atom isvery low � 0.1% �, we have to deal with only two species:pure D2O and a small amount of OHD3 �HOD–D2O�.2

Therefore, using a method similar to the one used foracetone-water mixtures that permitted the retrieval of thepure factors,5 we obtained the pure D2O spectrum �SOD4

� bythe following procedure. Taking two ATR spectra S1 and S2

from two D2O samples having low but different quantity ofH atoms �h1 and h2, respectively�, we have

�S1 = h1 � SOHD3+ �1 − h1� � SOD4

S2 = h2 � SOHD3+ �1 − h2� � SOD4

,� �8�

where SOHD3is the spectrum of HOD isolated in a D2O en-

vironment �HOD–D2O�: OHD3. From the condition h1

h2�1, we deduce that

�SOD4=

h2 � S1 − h1 � S2

h2 − h1

SOHD3=

�1 − h1� � S2 − �1 − h2� � S1

h2 − h1.� �9�

Therefore, a pure D2O spectrum devoid of H is obtainedby subtracting from a spectrum at H mol fraction h1�1 an-other one with H mol fraction h2 with h1 h2�1. If notknown, the coefficients h1 and h2 are varied taking care thatspectra SOD4

and SOHD3do not contain any negative band and

that the OH band near 3410 cm−1 �from OHD3� vanishesfrom SOD4

. The liquid D2O spectra from the literature are notthat of pure D2O.13,50 In these, the authors did not evaluatethe amount of H in their samples which is 0.2% and 0.1%,respectively. For this reason the literature spectra cannot beused as a reference for pure D2O devoid of H.

Using the procedure indicated above, one gets a pureD2O �100%� spectrum that can be used as reference. Thisprocedure also gives the OHD3 spectrum. With both purespectra one can determine the mixture composition in a D2Osample containing less than 5% H.

5. Second step D2O: Special concerns

Since above 6000 cm−1 the data are not available forD2O but are available for H2O, so we made the followingoperation to fill the gap since we needed the values for theKK relation. Because of the 1.35 factor between light andheavy water spectra,2 the D2O spectrum up to 5850 cm−1 isequivalent to that of H2O up to 7900 cm−1. Since the absorp-tion of water is very low in the 7900–20 000 cm−1 range, wecompleted the D2O ATR spectrum with zero filling from5850 to 7900 cm−1. Although these values are necessary forthe KK transforms it will not modify the optical properties ofliquid D2O in the 6000–0 cm−1 region. However, the imagi-nary part of the RI above 5500 cm−1 will be unreliable.

6. Third step D2O: Cleaning touch

Although a thorough nitrogen purge drives out most ofthe CO2 from the spectrometer, a minute quantity still per-sists. To get rid of it in the spectra we subtract it with areference spectrum. Since the �3 CO2 band at 2340 cm−1 isburied in the massive OD stretch of heavy water it cannot beused to monitor the subtraction as for the H2O spectra. Forthis we used the �2 CO2 band at 668 cm−1.

7. Fourth step D2O: Terahertz region

Reliable FIR data below 100 cm−1 for liquid D2O are notavailable except at null frequency.51 The static dielectric con-stants of liquid water and heavy water are very similar in the0–100 °C temperature range.51 This similarity is maintainedin the 60–0 cm−1 range except for a 7 °C shift between H2Oto D2O.45 Some data reported in the 1960s for the320–20 cm−1 range showed that the similarity between H2Oand D2O extends above 120 cm−1.39 Unfortunately these dataobtained by reflection measurements are not accurate enoughfor our purpose. Nonetheless, this general trend observed indifferent systems led us to take identical absorption coeffi-cient for D2O and H2O in the 118–0 cm−1 range for theroom temperature ��25 °C�. Experimental spectra fromRef. 30, as well those from our laboratory will be used tocomplete the spectrum in the 650–118 cm−1 range.

8. Fifth step D2O: n�

The selection of n� in the transformation of k into nthrough the KK relation needs special considerations becauseit can offset the value of n �following the KK relation�.32,34

Such an offset, even small, in the value of n will modify theevanescent wave penetration depth in an ATR configurationand therefore modify the measured intensity accordingly.This in turn will influence the amplitude of the imaginary RIk of the sample. It has been proposed that the same n� valuefor both H2O and D2O be used.13 However, since the isoto-pic ratio ��1.35� is maintained between the entire IR ab-sorption D2O spectrum and that of H2O, we assume that it isalso valid for the real part of the RI. Hence, we adjusted thevalue of n� so that the RI of D2O at 4445 cm−1 matches thatof H2O at 6000 cm−1 ��0.001�. An a posteriori justificationof this choice is obtained by comparing both n spectra afterapplying the frequency isotopic ratio.

9. Sixth step D2O: Weak bands

Finally, the D2O bands retrieved by ATR in the5400–4800 cm−1 range are very weak �harmonics of �1 and�3 of D2O�. Even with the long ATR cell used, the bandintensities are below 4 mAU. Furthermore, in this region theintensity of the source is weak. All this gives a noisy signal.To improve the situation and obtain a valuable D2O spectrumin this region, we used the transmission spectra of samplessandwiched between BaF2 windows separated by 25 �m.This gave an intensity of around 30 mAU which is an orderof magnitude higher than that of ATR. With these spectra, wemade Gaussian fittings to simulate the absorption in this re-gion to obtain a good quality spectrum. For this matter weused six Gaussian profiles of 350 cm−1 FWHH for the

184505-7 Complete H2O–D2O IR spectra J. Chem. Phys. 131, 184505 �2009�

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5400–4800 cm−1 region and added another one of 135 cm−1

to simulate the end of the D2O 3850 cm−1 combination band.The sum of the components gave the spectrum for the6000–3988 cm−1 region which replaced the ATR one in thatregion.

C. Results

Putting together all the previous explanations of the datawe present first the overall spectra for light and heavy liquidwaters. Thereafter, we give supplementary justifications andcomparison between calculated and experimental spectra.

1. Calibration of the ATR cells

The parameters p and a �where p, an integer, is the num-ber of reflection that part a of the light beam overcomes� ofthe two ATR cells were obtained by a procedure that fitssimultaneously the ATR spectra of water from both cells to aunique set of optical properties �k and n for H2O and D2O�.The p and a values for the short and long pathlength cells are3, 0.500 and 6, 0.765, respectively.

For the KK transforms in the 7901–0 cm−1 integrationrange we used, for the n�, the value of 1.3400 to compareour ATR spectra to previously reported k values.13 Recall thatthe n� value is strongly linked to the definition of infinity, �.For water it might be 7901, 15 802 cm−1, or any other limit-ing value. In such cases, the n� value would differ slightlyfrom 1.3400.

2. RI of liquid H2O

After all the considerations and transformations indi-cated in the previous section, Fig. 1 shows the resulting lightand heavy water spectra superposed one on top of the other.Frame �a� presents the real part of the RI �n� in the6000–10 cm−1 region. Below this region, n increases rapidlyto 8.85 at 0 cm−1 �dc value at 25 °C�.51 On the spectra, theanomalous dispersion effects is clearly observed in the re-gions of strong absorption.

Figure 1�b� illustrates the imaginary part of the RI �k�.The location of the absorption bands is well defined. Somenoise is apparent in 5450 and 4800 cm−1 regions in the �200expanded scales. This noise which is weak comes from thelow intensity bands and weak intensity of the source in the6000–4000 cm−1 region.

3. Extinction coefficient of liquid H2O, K„�̃…

Figure 1�c� shows the extinction coefficient of water,K��̃�. This function directly represents the sample energyabsorption. This excludes losses coming from the cell �ATRcrystal, transmission windows, O-rings, etc.�, the ATR char-acteristics, the spectrometer, and water and CO2 vapor re-siduals. Spectra in Fig. 1�c� are similar to absorbance spectraobtained by transmission measurements with the cell win-dow characteristics removed.

The blue symbols in Fig. 1�c� are data from transmissionmeasurements coming from Ref. 37. These correspond to theresults obtained from our ATR measurements in the5500–4000 cm−1 range �black line� except for a very smalldeviation in the 4800–4200 cm−1 region which is suitable

considering the expansion scale of 50. This indicates that ourmethod of extracting the water imaginary part of the RI fromthe ATR measurements is good. In the 6000–5500 cm−1 re-gion the ATR results were too noisy to be useful and werereplaced by the transmission data from Ref. 37.

Table II lists the water molar absorbance at four selectedfrequencies of this work and what Venyaminov et al. ob-tained from transmission measurements through CaF2

windows.50 Almost all the intensities are the same within theclaimed accuracies although ours are systematically slightlylower except the 3404 cm−1 which is slightly higher. The1550 cm−1 H2O absorbance has 3.3% intensity difference.Although these differences are not great they illustrate thedifficulties encountered with transmission spectra which arebothered with multiple reflections at the window-sampleinterfaces.33 These cause an interference pattern that can beminimized by a judicious selection of windows but cannot beentirely eliminated even with CaF2 windows.33 In low ab-sorption regions, the sensitivity to baseline error is increased.This problem caused deviations in results presented in Ref.52. In this, the absorption coefficient at 2600 cm−1 is verynear 0 cm−1, whereas we obtain a value of 45 cm−1 �Fig.1�c�, 4.5�10−3 �m−1�. Although this difference is not greatit will cause bad choices of band shapes in simulation pro-cesses which are very sensitive to this parameter. Note thatno spectral region of liquid H2O falls to zero absorbanceintensity between 6000 and 0 cm−1 except at the lower limititself.

realrefractiveindex,n

a

absorptioncoefficient,K

/�m–1

b×200

c

imaginaryrefractiveindex,k

×50

1

1

1

2

2

1

2

2

2

1

–1cm/ν~

1

2

0

0.5

0

1

0100020003000400050006000

FIG. 1. Complete IR spectra of liquid water at room temperature: �1� H2Oand �2� D2O. �a� Real part of the RI n; �b� imaginary part of the RI k; �c�absorption coefficient K �=4����k� with �̃ in cm−1. The values indicatedby the blue symbols come from Ref. 37.

184505-8 J.-J. Max and C. Chapados J. Chem. Phys. 131, 184505 �2009�

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4. FIR spectrum of liquid H2O

With the available FIR data and the considerations givenin Supplements B, E, F, and G,36 we obtained a good spec-trum for liquid light water in the 900–0 cm−1 range usingeight Gaussian profiles �Table III�. The characteristic of theseare given in Table III and the traces are presented in Fig. 2�a��see also supplement B �Ref. 36��. The interpretation of thesewill be made when the complete set of spectra at all tempera-tures are available. Previous analysis of experimental FIRspectra at different temperatures indicates that these aremade of two species similarly to that in the MIR and NIRregions.2,9 The simulation was made with eight componentswhereas four was previously used for each of the sixtemperatures.30 This gives a total of 24 components whereaswe used the same eight components throughout. This is animprovement by a factor of three �see also Supplement B�Ref. 36��.

5. RI of liquid D2O

From two experimental spectra of samples that had verylow H atom contents the 100% pure D2O ATR spectrum wasobtained by using the extrapolation method described in Sec.IV B 4. The numerical development and results are given in

Supplement H.36 With the pure ATR D2O spectrum, the ex-traction of the optical properties proceeded as for H2O.

The resulting D2O spectra are the curves labeled �2� inFig. 1. The real and imaginary parts of the RI �n and k� are inframes �a� and �b�, respectively. In frame �b� the D2O spec-trum shows one more band than that of H2O. This band near5100 cm−1 which contains the harmonics of �1 and �3 ofD2O corresponds to the H2O 6900 cm−1 band �see Ref. 9�which is outside the frame. The D2O spectra are a trifle lessnoisy than that of H2O because the bands are located in aregion where the IR source is more intense; the 5100 cm−1

D2O band is noise-free because this region was simulatedwith Gaussian profiles from our noisy ATR measurementsand our 25 �m transmission ones.

The present results give the complete refractive indicesof liquid D2O from 6000 to 0 cm−1 which are an upgrade ofthe reference publication that covered the region down to700 cm−1.13 We note that �1� there is no OH band, �2� there isno step in the k or n functions, �3� the gap between 800 and100 cm−1 is filled, and �4� the band shapes and maxima areclearly defined. Taking into account the isotopic ratio of H2Oand D2O, the real and imaginary parts of the refractive indi-ces are very similar. These considerations indicate that theentire D2O spectra are good reference spectra.

TABLE II. Comparison of liquid water molar absorption at selected IR frequencies.

Sample

Ref. 50This workintensity

�M−1 cm−1�

Intensitydifference

�M−1 cm−1�%

deviationFrequency

�cm−1�Intensity

�M−1 cm−1�a

H2O3404.0 99.9�0.8 100.61�0.02 −0.71 −0.72127.5 3.50�0.10 3.46�0.01 0.04 1.21643.5 21.8�0.3 21.65�0.07 0.1 0.51550 6.55�0.13 6.34�0.04 0.21 3.3

D2O3840.0 0.74�0.05 0.73�0.01 0.01 1.42504.0 71.5�0.4 69.68�0.01 1.8 2.61650 1.41�0.05 1.39�0.01 0.02 1.41555.0 1.91�0.05 1.88�0.01 0.03 1.61209.4 17.4�0.2 17.10�0.10 0.3 1.8

aM�mol /L.

TABLE III. FIR Gaussian characteristics of light and heavy water bands in the absorption coefficient spectra K�Fig. 2�.

BandNo.

H2O D2O

�̃�cm−1�

FWHH�cm−1�

K��m−1�

�̃�cm−1�

FWHH�cm−1�

K��m−1�

1 900 135 0.0302 938 185 0.077 780 135 0.0303 811 141 0.137 660 135 0.0304 700 185 0.293 548 178 0.1805 560 185 0.228 443 178 0.1356 432 160 0.115 342 140 0.0657 296 188 0.085 258 138 0.0588 177 115 0.068 186 101 0.0649 127 115 0.019 126 94 0.038

184505-9 Complete H2O–D2O IR spectra J. Chem. Phys. 131, 184505 �2009�

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6. Extinction coefficient of liquid D2O: K„�̃…

Figure 1�c� illustrates the extinction coefficient of D2O,K���. This is very close to an absorbance spectrum obtainedby transmission measurements. Table II lists the D2O molarintensities at five selected frequencies and compares them tothat of Venyaminov et al. from transmission measurementsthrough CaF2 windows.50 The present work intensities aresystematically lower than the reported ones by around 2%.Although this is a small difference it causes, as for H2O,difficulties in the band simulations. Note also that, as forH2O, no spectral region of liquid D2O falls to zero absor-bance intensity between 6000 and 0 cm−1 except at the end.

7. FIR spectrum of liquid D2O

The FIR: 900–0 cm−1 region was fitted with nine Gauss-ian profiles. The characteristics of these are given in Table IIIand the traces are presented in Fig. 2�b�. In this region theH2O spectrum was fitted with eight components �Fig. 2�a��because band 1 is outside the region �considering the fre-quency shift generated by the isotopic ratio�.2 Notwithstand-ing the extra component in D2O, the justification of the num-ber of components is the same as that of H2O �see alsoSupplement B �Ref. 36��. Taking into consideration the iso-topic shift, the component characteristics are similar.

8. Estimation of the result accuracy

The use of two ATR cells with different effective reflec-tion numbers in contact with the samples is used in a crossvalidation procedure to determine the integer number of re-

flection �p� and the portion of light �a� that is submitted tothe p reflections; the remaining part of light �1−a� is sub-mitted to p+1 reflections. The ATR absorbance spectra werereported for H2O and D2O: for pure species and mixtures atroom temperature2�a� and for pure species at differenttemperatures.2�b� The spectra for the two cells are illustratedin Fig. 3�a�: traces �1� and �2� are experimental ones while�3� and �4� are calculated with n and k for the short and longcells, respectively. The iterative procedure to obtain the bestfit between calculated and experimental ATR spectra isstopped when the difference between �3� and �1� traces andthat between �4� and �2� traces are lower than 2�10−6 in the6000–0 cm−1 range. The IR spectra obtained with the shortATR cell look like that from the long ATR cell except for theband intensities.2,22

The cross difference �the difference between the resultsfrom one ATR cell to calculate the ATR absorbance spectrumof the other cell� is shown in Fig. 3�b�. The gray line �1�represents the error obtained when calculating the ATR ab-sorbance spectrum with �p=6, a=0.765� reflections from the�p=3, a=0.500� k and n results. The black line �2� representsthe reverse. This is lower than the former because it comesfrom a lower number of reflections giving lower intensities.Considering the intensity scale of Fig. 3�b� in relation to thatof Fig. 3�a�, the difference between the two curves is small.

ν0 900 780 660 548 443 342 258 186FWHH 135 135 135 178 178 140 138 101

isotopic ratio 1.20 1.23 1.28 1.26 1.26 1.15 0.95

a

b

absorptioncoefficient,K

/�m–1

absorptioncoefficient,K

/�m–1

0.0

0.2

0.4

–1cm/ν~

0.0

0.2

0.4

020040060080010001200

FIG. 2. Simulated absorption coefficient spectrum �K� of liquid �a� light and�b� heavy waters in the FIR region. The components were simulated byGaussian profiles; the black curve is the sum of the components �see text�.

∆k

c

1

2

ATRabsorbance

a

∆ATRabsorbance

b

3

4

1 2

–1cm/ν~

0

1

2

-0.05

0

0.05

-0.01

0

0.01

0100020003000400050006000

FIG. 3. IR spectra of liquid H2O obtained with the short and long ATR cells.�a� Experimental �1� and �2� and calculated �3� and �4� spectra with shortand long cells, respectively. �b� Cross differences between calculated andexperimental spectra �see text� and �c� difference k spectrum between longand short cells. �See text for details.�

184505-10 J.-J. Max and C. Chapados J. Chem. Phys. 131, 184505 �2009�

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This validates the operation. Note also that part of the differ-ence may come from a slight temperature variation betweenthe two samples.2

Figure 3�c� displays the difference between the imagi-nary RI �k� obtained from the long and short ATR cells. Notethat long and short refer to the sample portion in contact withthe crystal. This curve is a measurement of the error levelassociated with the procedure. Figure 3�c� shows some noiseon the OH stretch band top because the intensity reached1.85 ATR AU �Fig. 3�a�� which is almost at saturation. Thenoise was slightly smoothed with the Savitzky and Golayalgorithm.49 The relative k differences stay within 3% in the3600–700 cm−1 range, whereas, in the high intensity re-gions, they are less than 0.3%.

Notwithstanding these small differences, the almost null�k values obtained indicate that the cross validation proce-dure that we developed is working adequately. Therefore, thecell constants retrieved by the procedure are correct. Theoperations made with the liquid H2O were also made withliquid D2O with similar results.

9. Comparison to experimental spectra obtain bytransmission measurements

The k values in the 118–0 cm−1 region were obtainedfrom several sources from the literature. A critical evaluationof these values lead to the ones proposed. Data in the800–118 cm−1 range coming from transmission measure-ments are compared to measurements that we made.

Figure 4, traces �2� are the Zelsmann’s experimental

spectra �450–30 cm−1� of H2O �a� and D2O �b� at 20.2 °C.30

These were obtained by transmission through Si windowswith a path length of 19.3 �m. We corrected the reportedspectra for windows’ absorption �see Supplement E �Ref.36��. The calculated spectra for transmission measurements�1� match the experimental spectra, except below 120 and150 cm−1 for H2O and D2O, respectively �Fig. 4�. These mis-matches, related to negative intensities in the 50–30 cm−1

region, were noted by the author.30 The residual spectra fromthe difference between experimental and our calculated spec-tra in the 450–120 cm−1 region �450–150 cm−1 for D2O��traces 3� indicate that the optical properties retrieved in thepresent work are valid.

Figure 5�a� shows the comparison between calculated�1� and experimental spectra �2� of a liquid H2O film be-tween two ZnSe windows ��1=8.9, �=3.5 �m, see Sec.II C 2�. The match is very good. Similarly, Fig. 5�b� displaysthe results of liquid H2O between Si windows ��1=9.5, �=1.2 �m�. Except in the 620–580 cm−1 region where the Siwindows absorb, the match is also very good. Figure 5shows an improvement in the top of the band compared toprevious report.13 See Supplement F for details.36

Finally, a 25 �m film of liquid D2O was obtained bytransmission. Figure 6 frames �a� and �b� show the calculated�1� and experimental �2� spectra between BaF2 and ZnSewindows, respectively. The match between calculated andexperimental spectra is very good except in the strong waterabsorption saturating regions �2720–2350 cm−1� and below750 and 550 cm−1 where BaF2 and ZnSe windows absorb,respectively. The other small mismatches are situated whereHOD absorbs in the 3400, 1470, and below 750 cm−1 re-gions. The respective differences between experimental and

aabsorbance

1

2

3

absorbance

b

3 2

1

-0.5

0.5

1.5

2.5

–1/cmν~

-0.5

0.5

1.5

2.5

0100200300400500

FIG. 4. FIR spectra of light �a� and heavy �b� liquid waters: �1� calculatedspectra and �2� spectra from Ref. 30 after removal of the of Si windows’absorbtion; �3� difference between calculated and experimental spectra.

2

1absorbance

b

absorbance

a

1

2

–1cm/ν~

0

1

0

1

02004006008001000

FIG. 5. Comparison between calculated �1� and experimental �2� FIR spec-tra of light liquid water sandwiched between: �a� two 4 mm ZnSe windowsand �b� two 4 mm Si windows �Si strongly absorbs between 620 and580 cm−1�.

184505-11 Complete H2O–D2O IR spectra J. Chem. Phys. 131, 184505 �2009�

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calculated spectra are shown in Fig. 6�c�. The intensity dif-ferences are low except at the HOD positions because thecalculated spectrum is for pure D2O without HOD whereasthe experimental ones contain some. On this frame we alsonote that the interference pattern �because of transmissionmeasurements� is slightly perturbed by the presence of HODin D2O. Notwithstanding these particularities, Fig. 6 con-firms that the optical properties of liquid D2O retrieved in thepresent work are accurate.

V. CONCLUSION

The optical properties �real �n� and imaginary �k� partsof the RI and the absorption coefficient �K�� of pure liquidH2O and D2O at 25�2 °C are reported in the entire IRrange of 6000–0 cm−1 �Fig. 1, see also Supplement I for thetabulated data�. The present results correct for imperfectionsobserved in earlier data13 and add the FIR of liquid D2Owhich was lacking �see also Supplement F �Ref. 36��. Exten-sive verification of the data was done by using ATR andtransmission spectra, evaluating the difference between ex-perimental and calculated results. In resumé the improve-ments are the following: �1� no step in the k and n traces; �2�the band characteristics �position, intensity, and shape� areimproved over those presently available; �3� the low fre-quency region from 1000 to 100 cm−1 for H2O and espe-cially for D2O are presented in corrected forms. Because of

shortcomings of the KK relations that bring the refractiveindices out of scale for values lower than 10 cm−1, we rec-ommend the use of the equations reported in Refs. 46 and 47.

The KK relation involves the value of n�. This value isnot easy to determine for finite frequency ranges although itinfluences the n and k values. Although the choice of n� thatwe have made is the best one possible it may require finetuning when better values are available.

Notwithstanding this small shortfall, the spectra of thereal and imaginary parts of the RI of liquid H2O and D2Othat we present are an improvement over that actually avail-able. These spectra show that over the entire IR spectro-scopic range of 6000–0 cm−1 the spectrum of liquid lightwater is very similar to that of liquid heavy water if we applythe constant isotopic ratio of near 1.347. Since this ratio isalmost the same as the square root of the inverse of thereduced masses �1.374� it indicates that the proton is thegoverning factor throughout the spectra. These completespectra that contain the valence, librations, and translationfundamental modes in a comprehensive manner will help inthe enduring task of determining the molecular organizationof this common liquid that water is.

ACKNOWLEDGMENTS

This work was supported in part by a grant from theNatural Sciences and Engineering Research of Canada�NSERC�.

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1

absorbance

a

12

×50

absorbance

b

∆absorbance

2

c1

1

2

–1cm/ν~

0

1

2

0

1

2

-0.1

0.4

0100020003000400050006000

FIG. 6. Comparison between calculated �1� and experimental �2� FIR spec-tra of heavy liquid water: sandwiched between �a� two 4 mm BaF2 win-dows, �=27.6�0.6 �m; �b� two 4 mm ZnSe windows, �=26.3�0.2 �m;and �c� difference spectra �1� from �a� and �2� from �b�. The strong D2Oabsorption in the 2730–2350 cm−1 region is masked.

184505-12 J.-J. Max and C. Chapados J. Chem. Phys. 131, 184505 �2009�

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184505-13 Complete H2O–D2O IR spectra J. Chem. Phys. 131, 184505 �2009�

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