Spectroscopy of H-bonds in acetic acid crystals at 10K

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Spectroscopy of H-bonds in acetic acid crystals at 10K

J.L. Leviel, Y. Marechal

To cite this version:

J.L. Leviel, Y. Marechal. Spectroscopy of H-bonds in acetic acid crystals at 10K. Journal de Physique,

1978, 39 (11), pp.1169-1176. �10.1051/jphys:0197800390110116900�. �jpa-00208856�

SPECTROSCOPY OF H-BONDS IN ACETIC ACID CRYSTALS AT 10K(*)

J. L. LEVIEL (**) and Y. MARECHAL (***)

Département de Recherche Fondamentale, Section de Résonance Magnétique,

Centre d’Etudes Nucléaires de Grenoble, 85X, 38041 Grenoble Cedex, France

(Reçu ^{le 28 mars} 1978, accepté ^le 12 juillet 1978)

Résumé.

Nous décrivons dans cet article les résultats d’une étude sur les bandes vs (O-H ... O)

dans les cristaux d’acide acétique CH3COOH à 10 K ainsi que dans ^ses analogues ^deutériés CD3COOH, CH3COOD ^et CD3COOD. ^{Ces raies sont en effet la} principale ^source d’information

quantitative ^sur la liaison hydrogène. ^Par comparaison ^des probabilités de transition intégrées,

centres de gravité ^et variances de ces bandes dans les quatre composés isotopiques ^{nous déduisons}

que ^ces modes vs ont, ^en plus ^du couplage anharmonique fondamental avec v03C3 (O-H ... O) ^{et éventuel-}

lement des couplages ^de résonance, ^une anharmonicité propre, qui ^{traduit une} amplitude de vibration anormalement grande. ^{Des mesures} supplémentaires ^seront cependant nécessaires pour arriver à

une description théorique précise ^{de la forme de ces bandes.}

Abstract.

^{As most} quantitative information on H-bonds originates from studies on vs bands

(O-H ... O), ^we describe the shapes ^{of these} specific ^{bands at 10 K} in the acetic acid crystal CH3COOH

and in the isotopic analogs CD3COOH, CH3COOD ^and CD3COOD. ^{From a} comparison ^{of the} integrated transition probabilities, ^{centres of} gravity and variances of the bands of these four isotopic species, ^{we can} deduce that these vs ^{modes show,} besides their fundamental anharmonic couplings with v03C3 (O-H ... O) ^{and some resonant} couplings, ^a strong anharmonicity in 03BDs, indicating ^an impor-

tant amplitude vibration. A complete theoretical description ^{of the} shape of these bands will require further experimental ^results.

Classification

Physics ^Abstracts

33.20E - 35.20G - 78.30

1. Introduction.

Stretching vibrations _{vs s}

(0-H ... 0) ^{of H atoms} in H-bonded species ^show strongly marked features characteristic of H-bonds which make IR spectroscopy appear presently ^{as the}

most precise probe ^to study H-bonds and show the

necessity ^of building precise descriptions ^of these v ^s

modes if one wishes to gain ^some insight ^{into the}

nature of H-bonds. It is now generally established that the main characteristic features of vs ^{modes of weak}

or intermediate strength ^{H-bonds are due to an}

anharmonic coupling of vs ^{with low} frequency Va ^modes

(0-H ... 0) ^{of the same bond. The} physical reality ^of

this mechanism is demonstrated by the correlations which can be established between the shape of vs

in 0-H ... 0 and 0-D ... 0 bonds and also between this shape ^{and the} différence of 0...0 equilibrium

distances in 0-H... 0 and 0-D... 0 bonds [1].

(*) ^{This work is} part ^{of a thesis} registered ^{at the Université} Scientifique ^et Médicale de Grenoble.

(**) USMG.

(***) CNRS.

Vs ^can however, ^{also be} resonantly coupled ^{to other}

modes [2], and certain kinds of resonance couplings (Fermi resonances) ^{have been detected on} the basis of

empirical correlations of frequencies. ^{The deter-}

mination of the magnitude ^{of these} couplings ^{and their}

introduction in the theory, ^will require however,

a knowledge ^of vs bands more quantitative ^than only

the frequencies of the submaxima of these bands, which can be obtained from most of the experiments

which have been performed up ^{to now.}

In a preceding series of articles on formic acid

crystals [3]-[6] ^we have described more quantitative

studies. Formic acide molecules are small molecules which are good models of well defined H-bonds in

crystals. However, experimental spectra have shown us

that the proximity ^of C-H groups and H-bonds

complicate ^the spectra because of résonance ^inter- actions between vs ^and VCH vibrations (C-H), ^{so we}

decided to study crystals having ^as simple ^{a structure}

as formic acid crystals ^but having ^CH groups further apart from H-bonds. These conditions ^{are met} in acetic acid crystals ^{which we consider to be} good

models of well defined H-bonds in crystals ^with

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0197800390110116900

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precisely ^{known structure which are} sufficiently simple ^{and can therefore lead to more} quantitative experiments.

Quantitative experiments require measurable _para- meters which can be varied. Deuteration is one of these parameters, ^{as it is} equivalent ^to doubling ^{the mass of}

the H-atom, ^{which can be} easily ^{taken into account} by any theory. ^We shall therefore describe in this _paper

systematic comparisons ^{of the} spectra of the four

isotopic species CH3COOH, CD3COOH, CH3COOD

and CD3COOD. ^These spectra have been recorded at low temperature, ^{where it is} hoped ^to gain ^{the maxi-}

mum of information, ^{that is at 10 K} which is the lowest temperature easily attainable under IR irradiation.

IR and Raman spectra of these four isotopic species

of acetic acid crystals ^at 0 °C and - 180 OC have been

previously published [7], [8]. ^These spectra ^{allowed a} correlation of frequencies of the submaxima of the v.,

bands with sums of frequencies ^{of two other modes,}

which strongly suggested that these submaxima could be due to resonance couplings (called ^{Fermi reso-} nances) between v., ^{and these} combination modes [9].

This suggestion, ^{which is} quite reasonable, implicitly requires, however, ^{that the} Vs mode is also strongly coupled ^{to the low} frequency ^mode Va, which gives

the _vs band a broad contour where Fermi resonances

could be superimposed. ^{In order to} investigate ^this

vs - Va coupling, ^{which can be somewhat masked} by

these resonances if one only concentrates on the salient features of the shape of vs ^{bands, we have used} samples

several microns thick and have measured their thickness with precision. ^{In such} conditions the

intense vs ^{bands never} saturate, which does not alter their profiles and allows the measurement of their first moments, ^{or more} particularly ^{of their} integrated

transition probabilities, ^{their centre of} gravity ^and

their variances which will be most useful to determine the magnitude of these différent anharmonicities.

2. Experiment.

The different isotopic species

have been prepared using standard methods.

CH3COOH ^{was a} commercial product ^{from Merck} having ^a purity better than 99.9 %. CD3COOD ^was supplied by ^the Département ^des Radioisotopes,

Commissariat à l’Energie Atomique, France. Its effective deuteration was better than 99.6 %.

CH3COOD ^was prepared by ’flowing ^{DCI in} liquid CH3COOH. CD3COOH ^was prepared ^{in the same}

way by flowing ^{HCI in} liquid CD3COOD. ^{HCI and}

DCI were anhydrous ^{and were} obtained from

C6HSOCI ⁺ H20(D20). This avoided _any conta- mination of acetic acids by ^{water. The} purity ^{of these} samples ^was later checked on IR spectra ^{where no}

trace of CH3COOH (CD3COOD) could be found in the spectrum of CH3C00D (CD3COOH). As vs ^bands

are most intense, IR spectroscopy ^{is indeed the most} sensitive method to detect impurities.

Liquid acetic acids were introduced by capillarity

into an optical cell. As this cell has been already

described in detail [3] ^{we shall} only briefly ^{sketch its}

salient features in this article. It is composed ^{of two} high quality CaF2 windows which are kept separated using gold spacers of several microns. The parallelism

of the windows was checked before filling ^{the cell} by recording interferences in visible light ^{at différent} positions of the windows. After introduction of the

liquid acid, ^{the two windows were then} positioned ⁱⁿ

an hermetic stainless steel cell which was held fixed in

an Air Liquide cryostat. ^Water contamination was

minimized by performing ^{all these} operations ^{under a} dry nitrogen atmosphere.

Samples ^were then cooled down and crystallization

and absence of bubbles were tested by setting ^two polarizers outside the windows of the cryostat ^and

illuminating ^the sample ^{with visible} light. Occasionaly

the sample could also be observed with a microscope equiped ^with polarizers, ^which showed that the

samples consisted of a juxtaposition ^of apparently

disordered monocrystals. Complete ^{disorder in the} plane of the windows was confirmed by ^{the invariance}

of the spectra ^{after a} rotation of the cell keeping ^the planes of the windows invariant.

IR spectra ^{were recorded on a} Beckmann IR 4240

spectrophotometer ^{which was} coupled ^{with a mini-} computer allowing ^the spectra ^to be recorded on

magnetic ^discs. Optical ^{densities were recorded at}

every wavenumber, ^which gave ^a sufficient definition for the rather broad bands investigated.

3. Results.

We have recorded the spectra ^of the

four isotopic species of acetic acid at 10 K in the

region 1 000-4 000 cm-1. As the interpretation ^{of these}

spectra ^can hardly be achieved without the knowledge

of the structure of the species, ^{we shall} briefly ^discuss

this structure and some related problems ^of polari-

zation.

Crystals ^of acetic acid CH3COOH ^are orthorhombic and individual molecules are bonded together by

H-bonds and form zig-zag ^chains [10], [11] having

average directions in planes perpendicular ^{to the a axis.}

In these planes ^{chains are} alternatively ^directed along

two vectors having ^{b and c axes as} bisector lines. This structure, which has been recently ^refined by ^neutron

diffraction [12] ^is very similar to that of formic acid HCOOH crystals. ^{The structure} of deuterated

samples ^{has not} béen described, ^{but one can} reasonably

think that it is the same as that of CH3COOH crystals,

except ^{for a} slight change in 0...0 distances of some hundredths of an Angstrôm, ^{which has} been measured in formic acid dimers [13]. ^This change ^{seems indeed} quite specific of H-bonded species ^{and is a} consequence of the important vs - Va anharmonic couplings [1], [14], [17].

In our preceding study ^of formic acid crystals [5],

we have shown that for thin crystals (- 3 pm) ^the

arrangement of the différent monocrystals ^{was such}

that their a axes were always perpendicular ^{to the}

plane ^{of the} windows. This is equivalent ^{to a} partial

polarization ^of light, ^{as we} irradiate the samples ^with light having its electric field always ⁱⁿ b, ^c planes,

which are statistically disordered. This point ^has recently been confirmed for acetic acid crystals [18].

ln figures ^{1 to 4 we show} the vs bands of the four

isotopic species ^{at 10 K. Other bands} than vs ^{do not}

show _any marked différence with those reported previously [7]. ^{We shall not therefore show} these bands and will rather concentrate on the complex vs ^bands.

In order to analyse these bands we have decomposed

them into elementary sub-bands. This kind of

decomposition ^{is not} unique, ^{but we} looked for a

decomposition which needs a minimum of sub-bands.

This can be achieved by using elementary ^sub-bands

of the form h(co) ⁼ 1 /cosh (w/u) ^{which is a function}

whose Fourier transform is a function of the same

analytical ^{form and is} asymptotic ^{to a} gaussian

FIG. 1.

The Vs band of CH3COOH crystals ^{at 10 K} (full line).

Individual bands composing ^this spectrum ^{are shown} (dotted lines).

At the bottom of the spectrum ^the difference between experimental

and reconstituted spectrum ^{is drawn at the same} scale. The thickness of the sample ^{is 1 = 3.5} gm.

FIG. 2.

The _v. band of CD3COOH crystals ^{at 10 K} (full line).

Individual bands composing ^this spectrum ^{are shown} (dotted lines).

At the bottom of the spectrum ^the difference between experimental

and reconstituted spectrum ^{is drawn at the same} scale. The thickness of the sample is 1 = 3.8 _gm.

FIG. 3.

The v. ^{band of} CH3COOD ^{crystals at 10 K} (full line).

Individual bands composing ^this spectrum ^{are shown} (dotted lines).

At the bottom of the spectrum ^the différence between experimental

and reconstituted spectrum ^{is drawn at the same} scale. The thickness of the sample is 1 = 3.2 gm.

FIG. 4.

The v. ^{band of} CD3COOD crystals ^{at 10 K} (full line).

Individual bands composing ^this spectrum ^{are shown} (dotted lines).

At the bottom of the spectrum the difference between experimental

and reconstituted spectrum ^{is drawn at the same} scale. The thickness of the sample ^{is 1 = 3.5} ym.

function when t > 0 and asymptotic ^{to an} exponential

function when 1 t 1 -> ^oc [3]. ^The shape ^of h(w) ^is consequently intermediate between a Lorentzian and

a Gaussian shape. ^In figures ^{1 to 4 we show such a} decomposition, together ^with experimental spectra.

In the lower part ^{of the} figures ^{we have drawn at the}

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same scale the diRèrence between experimental spectra and the sum of elementary sub-bands. This gives ^an

idea of the fit of the decomposition ^with experimental

spectra.

In tables I-IV we give ^{the values of} the three para- meters Ai, roi and Mi defining ^{the ith} sub-band of the spectrum. ^The optical density f (to) ^is equal ^{to :}

This decomposition ^{will be} used later to reconstitute

theoretically ^the shape ^of vs. At the present ^{time it can} be used to transmit the experimental spectra ^of figures ^{1-4. We} shall also use it to calculate the first

TABLE 1

TABLE II

momenta of the vs ^{bands or more} precisely ^{to calculate}

their integrated transition probabilities P, ^{their centres}

of gravity 15 and their variances a, which are defined

by :

1 is the thickness of the sample ^{and means}

summation over vs.

TABLE III

TABLE IV

The transition probability ^is proportional ^to !(w)/w (the absorption coefficient at wavenumber w is equal

to w multiplied by ^this probability). The calculation

LE JOURNAL UE PHYSIQUE. - T. 39, N" I I, NOVEMBRE 1978

of these summations can be advantageously replaced by ^{sums over the} elementary sub-bands, neglecting

the widths of these sub-bands. This _way of calculating

moments has the further advantage ^of defining

without ambiguity the limits of summations, ^which correspond ^{to the limits of} decompositions ^of figures ^1-4 and tables I-IV. It introduces an error

which has been shown to be negligible ^when compared

to other experimental ^errors [5].

In table V, ^{we show the values of} P, ^{ro and 6 for the} four isotopic species calculated using ^the decompo-

sition. The values of the P’s are given ^{with a} precision

which is estimated to be better than 7 %. ^{The errors}

on the values of the Qj’s and a’s are thought ^{to be less}

than 5 cm-1 and 8 cm-1 respectively.

TABLE V

4. Discussion.

It is now well established [2], [16]

that the peculiar shape of vs ^{is due to the} fact that the

amplitude ^of oscillation ^{of the H-atom along the}

H-bond _may be particularly large. In consequence the

potential representing this motion is strongly ^anhar-

monic. It has been shown [19] ^{that for weak or inter-}

mediate strength H-bonds the first kind of anharmo-

nicity ^to be considered is that coupling vs>, ^with the

low frequency mode Va of the H-bond (O-H...Õ).

This coupling ^{can be viewed as a} dependence ^{of the} frequency ^of vs ^on the 0...0 distance, ^{that is on} v,,.

In addition to this predominant anharmonic coupling

other kinds of anharmonicities ^can also be present.

When all. atoms except ^{the H-atom} of the H-bond

are held fixed the v., ^{vibration can} depart ^{from an}

harmonic vibration (Morse-type ^or double-well type anharmonicity) [17] ^{and its} degree ^of anharmonicity

can also be dependent ^{on the} 0...0 distance. We shall see in the following ^{that this} type of anharmo-

nicity is indeed strong ^even if it does not give any

particular feature to. the shape ^of vS. Finally vs may be resonantly coupled ^to othér modes and two kinds of resonance couplings may exist .: v., ^{may be} coupled

either ^to the _vs mode of a neighbouring ^H-bond (harmonic coupling) ^{or to} combinations of modes of the same molecule having nearby frequencies (Fermi resonances). ^{The first} type ^{of resonance} coupling may be detected in Ui [19]. The second type ^{of, resonance}

côupling ^{has been the} object ^{of much} speculation ^and

it seems now well established that it can be detected

79

1174

by making correlations between frequencies ^{of sub-}

maxima of vs ^with frequencies of combination modes

[9], ^{and more} particularly ^with changes ^{of these}

submaxima when passing ^from CH3 ^to CD3 ^acids.

We shall now discuss how we can obtain information

on these different couplings ^{from our} experimental

results.

The first point ^{to be} considered concerns the diffe-

rences of the spectra ^of CH3 ^and CD3 acids. The

shapes ^{of these} spectra ^are slightly ^different (Figs. 1-4)

but the quantities P, c5 ^{and a are the same for} CH 3

and CD3 ^acids (Table V) ^which is therefore a simpli-

fication when compared ^to formic acid crystals,

where these quantities changed significantly ^when passing from CH acids ^to CD acids [3]-[5]. ^{Let us}

therefore label with an H these quantities ^{in H-bonded}

acids and by ^{a D these} quantities in D-bonded acids.

We see that the ratio PHI Pp falls in the vicinity ^of 1.5, which ^can be taken as li ^within experimental

errors. This is also a simplification ^{if we} compare this ratio to the ratio experimentally ^{found for} carboxylic

acid dimers, ^where PHIPD -- 2, ^{which can be due to}

the existence of a strong electrical anharmonicity [20].

The ratio presently ^obtained (,/2-) ^{strongly suggests}

that electrical anharmonicity ^{should be} weak, ^which

can be mathematically ^reflected by ^a variation of the

dipole ^{moment linear in} Vs.

This however implies ^{that the P’s should be almost} independent ^of temperature, ^which will later appear

as being experimentally ^verified [21].

In order to extract information’from the w’s and

7’s, ^we shall calculate these quantities ^{for one model}

H-bond. In the case of a crystal, nèighbouring ^H-bonds

may interact (harmonic ^resonance coupling), ^{but this}

interaction appears in S only ^when electrical anhar-

monicity ^is neglected [6]. ^We shall therefore add this interaction only ^{when we shall} consider the Qj’s.

Let then q ^be the coordinate ^{of the v., mode, Q that}

of the Va ^mode (0-e... 0) and qa ^{be any other coor-}

dinate of the CH3COOH molecule which can combine with other _qlJ, to give ^resonance couplings ^with v,.

q and Q ^are local coordinates which are also normal modes [22], [23] (they ^{are not therefore} mass-weighted).

The q,’s ^{are normal} coordinates. If JC is the general

Hamiltonian describing ^{such an} H-bond, ^the Fourier transform C(t) of the transition probability f (w)w

of the vs band will be [24] :

where ^means thermal average and qo is the

equilibrium position ^of q, which can depend ^on Q.

As electrical anharmonicity ^is neglected the linear

dependence only on q of the dipole ^{moment is consi-}

dered. In the _presence of resonance couplings ^the eigenfunctions ^{of JC can have} complicated ^{and gene-} rally ^{unknown forms.} However, ^as Vs has frequencies falling typically ^{in the} region 2 000-3 000 cm -1 ¹ and Va has frequencies falling ^{in the} region ^150-200 cm-1,

an adiabatic separation ^between rapid oscillations

(Vs ^{and resonant} modes) and slow oscillations (va) ^can

be performed when v. ^{and resonant modes are in their} ground ^{state. This is no} longer ^true when vs ^{is excited}

and interacting ^{with resonant} modes, ^as slow oscilla- tions will then be able ^to change ^the mixing of vs ^with

these resonance modes. When vs ^{is in its} ground ^state 03A6o(q, Q ) the v03C3 mode will be represented ^{by the func-}

tions au’(Q) ^{which are} eigenfunctions ^of Ho, ^such

that :

In (2) ^{we have not} written the functions of the

ground ^{states of} the q6 ^{modes, for} simplicity, ^{but we}

have indicated under the ket 1 > ^that integration

should be performed ^not only on q but also on qa

(in ^their ground state). ^{We can} then write :

With a good approximation 00(q, ^{Q ) can be} represented by ^the ground ^state function of an harmo- nic oscillator having ^its equilibrium position qo and

frequency ^(J) depending ^on Q [6], [16], [19]. ^{One can} develop C(t) in powers of (it)"/n ! ⁱⁿ (3) and Ui will be proportional ^to the coefficient of it. We can then

see that _any term linear in q ^{in JC will not contribute}

to w if we discard the unrealistic case of a very strong

dependence ^of qo in Q (typically dqo/dQ is always

much smaller than 0.5 for weak or intermediate

strength ^H-bonds [16]). ^{This means that resonance}

terms will not appear in 00, ^because they ^{are linear} in q (they destroy ^an excitation in q ^while creating

a resonant excitation of other modes). ^In these condi-

tions, ^{ro will} only depend ^on the Vs - Va coupling ^and

also on the one-dimensional anharmonicity ^of VS.

When this last anharmonicity ^{can be} neglected ^one

can write that part ^{of JC which} depends on Vs ^{as :}

where m is the reduced mass of the H(D) ^{atom. The}

term linear in q ^is thought ^{to describe} general ^resonant

interactions of Vg ^{with any} combinations of modes b and ô’. One has then Ho = H(Q) ⁺ 1/2hm(Q)

where H(Q) ^{is that} part of JC which depends ^on Q only. ^{We can then} easily calculate ro and find that [6] :

with

if we approximate ^the potentiel H(Q) by ^{that of an}

harmonic oscillator 1/2 ^{MQ 2} Q 2 (03A9 ^{is the} frequency ^of

the Va mode, ^M its reduced mass).

Labelling H-bonds and D-bonds by ^{H or D sub-} scripts, ^we find then that :

The ratio WH(O)/WD(O) ^is equal ^{to 0.97} j2 ^{if one}

takes into account the reduced mass of H and D atoms bound to 0 atoms. Taking bH ~ 1 ^{(we shall}

see in the following ^that bH 1 ) and consequently b D 1/B/2 ^{(Eq. 5), we} find that wH/wD ^{should be} roughly equal ^to 0.95 2 ^{with Q/WH(O) ~ 1/18}

(hQ = ^{160 cm-1 1} [7] ^and WH( 0) ^is greater than - (~ ^{2 800} cm-1)). ^{If one} introduces in (5) ^and (6),

terms describing ^resonance interactions between neigh-

bour H-bonds, this ratio will not be modified because the magnitude of this interaction (~ ^{100 cm -1} [ 19] )

will be divided by J2 ^{when passing from an H-bond}

to a D-bond [6]. This shows that one cannot neglect

the one dimensional anharmonicity of vs ^{if one wishes}

to approach ^the experimental ^value (0.91 /2) ^for

w’H/wD’ ^{If we take this} anharmonicity ^{into account} by replacing ^{the harmonic} potential in q ⁱⁿ (4) by

a Morse potential having ^{the same curvature at the} origin [6], [17],

where b(Q) ^{is the} Q dependent anharmonicity para- meter, ^we find that c5(0) should ^{be at least as large}

as 0.25 to obtain ^a ratio wH/wD equal ^{to 0.91} J2.

lfhe Morse potential should be taken as a model

only, ^{but the} high value found for à(0) shows that the

one dimensional anharmonicity in q ^{is indeed} impor-

tant for this type of H-bond and that it should not be

neglected.

From (3) ^and (4) ^{one can} calculate the variance a

of _VS. The contribution of the v., - Va coupling ^{is then}

hQ

equal ^to b 03A9.p2 2 kT ^{[6] where :}

In this expression ^resonant coupling ^{terms should}

however be added (they have been discarded in [6]),

which show that, ^as UH is experimentally equal ^to

160 cm-1 bH ^is certainly smaller than 1. At the present time we cannot evaluate the respective contributions of resonance couplings ^{and of} the vs, - Va coupling

in J. This last coupling has however a temperature

dependent contribution, and the evolution of a with T is therefore hoped ^{to allow the} separation ^{of these two}

contributions.

Resonance couplings have been considered on the

basis of correlations of frequencies of submaxima of Vs bands with sums of frequencies of fundamental modes. They ^{are claimed to be} general ^for H-bonds, which implies ^that they ^{have a common} origin ^{in all}

H-bonds. We will then suppose that this ^common

origin ^{is a} coupling ^of vs with the bending ^vibration bOH(O-H t...0) ^{of the H-bond} [25]. ^{This means that}

if qa represents this local boH vibration, there exists in J6 a term of the form qqâ, ^{which can be viewed as}

a dependence in q of the force constant of the oH vibration. q ^{is a} normal coordinate. This is not true

for q8 ^{which has} important components in various normal modes [22]. ^{The term} qqâ ^will consequently decompose ^{into several terms} of the form _{qq, qj,}

(Eq. 4) where qô ^and qa, ^are normal coordinates. We shall then expect ^{maxima or minima} (Evàn’s holes)

of the _Vs band at frequencies falling around the sum

mô ⁺ mô, of the frequencies of these normal modes.

If we take the decomposition ⁱⁿ normal modes of the vibrations in acetic acid monomers [22], ^{we then see}

that for CH3COOH molecules, qa ^has components ⁱⁿ

vc-o, bOH and PcH3 modes, which qualitatively justifies previous assignments [7] ^{if one} discards attributions of unimportant submaxima. For CD3COOH ^{we find}

that the broad band appearing ^{at 2 800 cm-’ 1 should}

be assigned ^{to 2} bOH and the other assignments ^are

those of [7]. ^For CH3COOD qô ^{can be} decomposed

into ÔODI PcH3, ^vc-c and bocr,. The presence of maxima attributed to pcH3 ⁺ boo ^{and 2} bop ^is consequently logical. ^For CD3COOD q,, decomposes ^into bCD3’

5oD ^and vc_c. The thin line at 2 170 cm-’ ¹ should then be rather attributed to boo ⁺ bcD, ^{instead of}

Vc-o ⁺ pcn3 and ^{some extremum} around 2 200 cm-1 ¹ should then be attributed to 2 bOD. ^{These are the} only ^{comments which can be} presently ^{made on}

resonance couplings.

5. Conclusion.

In this article ^we have been able to show from the spectra of the four isotopic species

of acetic acid crystals ^{at 10} K, that beside the Vs - Va

coupling ^an important ^one dimensional anharmoni-

city of v. ^is present ⁱⁿ these H-bonds. We particularly postulate ^{such a mechanism to} explain the value found for the ratio of the frequencies ^{of the centres of} gravity ^of vs bands in H-bonds and D-bonds. The

large ^{value found for this} anharmonicity (à = 0.25)

is indeed puzzling ^{and will} require verification. We have determined an upper value of the v. - va coupling (bH 1) ^{but we could not} determine its exact magni-

tude as its contribution to the variance 6 could not be separated from the contribution of resonance

couplings. ^We hope ^{to be able to} separate ^{these two} contributions when we know how a varies with temperature. Finally ^we have shown that electrical

anharmonicity ^{could be} neglected ^{in these} crystals.

These results therefore constitute extremely ^useful

information which will certainly be of much help ⁱⁿ

giving ^{a detailed} description of the motion of H atoms

in H-bonds. At the present ^{time we cannot} go deeper

1176

into this interprétation, and this shows the necessity

of completing ^our experiments by ^{further measure-}

ments on the variations of vs bands of acetic acid

crystals ^with temperature ^{and also} by isotopic ^dilu-

tions. This will be described in a subsequent publi-

cation [21].

Références

[1] MARECHAL, Y., Chem. Phys. ^Lett.13 (1972) ^237.

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