Infrared spectra of water. II : Dynamics of H2O(D2O) molecules

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Infrared spectra of water. II : Dynamics of H2O(D2O) molecules

Y. Maréchal

To cite this version:

Y. Maréchal. Infrared spectra of water. II : Dynamics of H2O(D2O) molecules. Journal de Physique

II, EDP Sciences, 1993, 3 (4), pp.557-571. �10.1051/jp2:1993151�. �jpa-00247854�

Classification

Physics

Abstracts 61.25E

Infrared spectra ^of water. II

_:

Dynamics of H~O(D~O)

molecules

Y. Mardchal

D£partement

de Recherche Fondamentale _sur la Matikre Condens£e, SESAM/PCM, Centre d'Etudes Nucl£aires, 85X, F-38041 Grenoble Cedex, France

(Received 9 October J992, accepted ²² December J992)

Abstract.

Spectra

of e" (imaginary ^dielectric constant) of _water in the IR region, ^obtained as

described in _a

previous

article

by using

attenuated total reflection (ATR)

techniques,

_are

analyzed.

Criteria _are presented which allow _{us to} define, _on the basis of

spectroscopical

_arguments

only,

the low temperature spectrum

e"(T~)

and the

high

temperature spectrum

e"(T~)

on which any spectrum at temperature T, in the range 5 °C to 80 °C, _may be

decomposed.

These spectra display novel features their v~ bands (intramolecular stretch) have

shapes

which have great similarities in both spectra ^the 8 band (intramolecular bend) of the high temperature spectrum

e"(T~),

has _a

simple shape

with _no apparent structure, which may be approximated, ^with a

good precision, by

_a Lorentzian _curve. A discussion of the

origin

of these features reveals _{a new}

picture

of _{water at a} molecular level _: it is made of

H~O

molecules which either

perform

rotations of _a

vibrational character (librations) around their three _axes and appear in

e

"(T~)

_or

perform

rotations around their C2 symmetry ^axis z of _a diffusional (relaxational) character. H20 molecules of the latter type appear in

e"(T~).

Their concentration reaches =35fb _at 0°C (I atm.) and

m 90 fb at 100 °C (I atm.). They ^{have rotational} energies ^around z greater ^than the maximum of the potential _energy

goveming

this rotation. Around their other two axes they perform librations which

qualitatively

do not differ from those

performed

by ^molecules

appearing

in _e

"(T~).

^{The estimated}

correlation time, _{or average} time

during

which

phase

coherence of 8 vibrations in these molecules is

kept,

falls in the range 10~ ~~-10~~~

s, as deduced from the Lorentzian

shape

^{of the} 8 band in

e"(TH).

The

analysis

of these spectra ^{also indicates that the} « 8 ₊ v~ » band borrows its

intensity

from v~ ^via a cubic _term in the vibrational potential.

1. Introduction.

Water is _a

species

which exhibits many

paradoxes.

^Its constituent molecule,

H~O,

for

instance, is _one Of the

simplest

and most stable molecules. Yet it has _a very

particular

electronic _structure which looks

quite ordinary

but has far

lying

consequences : it has _as many

non-bonding

orbitals _as valence orbitals. This is at the

origin

of an

extremely high density

of H- bonds in water, which makes it _an

exceptional liquid.

A

part

^{of the}

paradox

is that _we

certainly

better understand how this

exceptional density

of H-bonds is _at the

origin

of

exceptional

properties

of _water

[I]

than how

H20

molecules manage, with these _numerous directional H-

bonds,

to

keep

water _a

liquid,

_even if _a

complex liquid [2].

Another

paradox

is

that, although

one of the most familiar

species

which has been studied

by

all available

techniques,

its IR

spectra

were up ^to

recently poorly

known and _no

systematic dependence

of these spectra upon such parameters as

temperature

or

H/D isotopic composition

_were

reported. Using

_an ATR

cell,

_we have been able _to obtain

good quality

IR

spectra

^of water, which _are described in _a

preceding

article

[3] (which

will be denoted I in the

following)

and to

study

their

dependence

upon these _two parameters. ^Let us stress that ATR

spectra

^{in the IR}

region

_are

spectra

^{of bulk} water, as it consists of

making absorption

_on the evanescent _wave

only

which

gets

out of _a

crystal.

As this _{evanescent wave} extends _{over a}

region

of the size of the

wavelength,

that

is,

several microns in _{our case,} ATR spectra are spectra of _a film of this

thickness,

with

negligible

surface effects which

disappear

at a distance of the order of I _nm

[4].

The aim of this article is _to

analyze

these IR

spectra

^of water, in view of

getting

_some

insight

into the

disposition

and

dynamics

of

H~O

molecules in _water. One of the main results described in I is that any

spectrum e"(T) (

5 °C

~ T

~ 80 °C _; e" is the

imaginary

dielectric constant of

water)

_may be

decomposed

into _any two

spectra

e

"(To )

and

e"(Ti) following

the

equation

_:

e"(T)

=

e"(To) a(T, To, Ti)

x

ie"(To) e"(Ti)i (1)

In these

equations

_we have not

explicited,

for

simplicity,

wavenumbers

P,

but _we shall

keep

in mind that the

e"(T) represent spectra.

^{This form}

implies

the presence of several isosbectic

points

ⁱⁿ various bands of the

spectra

^which appear ^at all wavenumbers P where

e

"(To)

=

e"(Ti).

The presence ^{of such} isosbectic

points

has been

previously recognized

in v~ Raman bands

[5-7]

_{or 2 v~} ^NIR

(near infrared)

bands

[8-10].

In the range of

temperatures considered,

the variations of

a(T, To, Ti)

with T _are well described

by

_a

quadratic approximation.

^When

To

^{is taken}

equal

_to 0 °C and

Ti

to 75

°C,

which

we shall suppose in the _rest

of

the

article, a(T, To, Ti),

which _we shall

simply

write

a(T)

then

obeys

the

equation

_:

a

(T)

= a

(T, 0,75 )

₌

[(T

_TOY

(Ti To )]

x

(1

^0.2

^{[(T Ti )/(Ti} To II (2)

These

equations (I)

and

(2)

are valid whatever the

H/D isotopic composition,

under the condition that all

e"(T)

in

equation (I)

stand for

spectra having

the _same

H/D composition.

The choice of

To

= 0 °C and

Ti

= 75 °C is well suited _to describe

experimental

results.

These

temperatures

^and

corresponding

spectra

e"(To)

^and

e"(Ti) have,

however, no

special physical meaning.

In view of

obtaining

a

description

of the _structure and

dynamics

^of

H~O(D~O)

molecules in water, we shall instead of these spectra ^take as a basis for the

decomposition

of

spectra

at

temperature

^T

(Eq. (I)) spectra e"(T~)

and

e"(T~)

which _are the

spectra

^{which would be observed} at very low and very

high

temperatures

respectively

^if

phase

transitions did not occur before such

temperatures

^{could be}

experimentally

reached. These

spectra e"(T~)

and

e"(T~),

which then have _a

physical meaning,

_are defined

by

their

decomposition

on the

experimentally

known spectra e

"(To )

and

e"(Ti ) (Eq. (I)),

that is,

by

their

a(T~)

=

a(T~, To, Tj)

and

a(T~)

=

a(T~, To, Ti ).

With such _a

basis,

_we have _:

e"(T)

=

e"(T~)

_a

(T)

x

ie"(T~) e"(T~)1 (3)

with the concentration of _« defect _»

molecules,

that is the

proportion

of molecules

contributing

to

e"(T~) given by

a

(T)

= a

(T, T~, T~)

₌

la (T)

a

(T~)i/ ia(T~)

_a

(T~)1 (4)

Let _us mention that

a does not

only depend

on temperature ^{T but also}

depends

on pressure,

as pressure has been shown _to have _an effect similar to that of temperature

[I I].

As spectra described in article I _were obtained _at I _atm, this p

dependence

of _a will _not be considered in this article. Let _us also note that the

quadratic development

of

a(T)

ⁱⁿ

equation (2)

is of _{no use} to define _a

(T~)

and _a

(T~ ),

and

consequently

_e

"(T~ )

^and _e

"(T~ ),

as this

development

is

largely

insufficient for

extrapolations

_{to very} low and very

high

temperatures. ^The

problem,

which will be discussed in section 2, I will then be to find criteria which will allow _{us to} define these

quantities.

Once defined _a

spectroscopic analysis

of various bands of

e"(T~)

and

e"(T~)

will be

performed

in

subsequent

subsections. In section 3a

dynamical description

for the arrangement ^of

H~O(D~O)

molecules in water, which

incorporates

novel features revealed

by

this

analysis,

will be

proposed.

2.

Analysis

of

e"(T~)

and

e"(T~).

2, I DETERMINATION. The

decomposition

of the 2 v~

band,

as obtained in the NIR

region,

into several Gaussian bands has been

proposed by

Luck and Ditter

[8]

and constituted the first

quantitative attempt

to

analyze

this band and

get

a

picture

of water at the molecular level. The

decomposition

_on a Gaussian basis

is, however,

at the

origin

of _a lack of

flexibility

which makes it hard to use when _one wishes to

improve

the

precision.

Some

attempts

to

directly

define the low

temperature

^and

high temperature components

^{of Raman} _v~ ^{bands from}

experimental

_spectra have been later

proposed [6, 12].

Such _a

procedure

avoids

decomposition

on bands

having

_a

predetermined

form. As described

previously (Eqs. (1)-(4))

IR

spectroscopy

is

particularly

well

adaptated

to

it, and,

in order to define _e

"(T~)

and _e

"(T~ )

we shall be able to

use

spectroscopic

criteria

only, discarding thermodynamical

_ones which _{seem to} be less

precise.

The first criterion which _we shall _use is that these

spectra

have _no

negative

_parts. It

implies a(T~)

_~ l. I and _a

(T~

~ 2, I for spectra ^of _any

isotopic composition.

With the latter

value the v~ band

(Fig, I)

of

e"(T~)

has nevertheless

quite

an unfamiliar

dip

at

3 150 cm~ which makes it unreasonable. The absence of this

dip requires a(T~)

_~ l.7. We may furthermore

reasonably postulate

that the

decomposition

of any spectrum

e"(T)

_on

e"(T~)

and

e"(T~)

is valid up ^to 100°C

(we

^{have checked} it up to

80°C).

It

implies a(T~)~

l.25

by extrapolating equation (2)

_up to T=100°C. In order _to have _a better

determined value for this

quantity,

_{we may}

appeal

_to Raman spectra ^{which exhibit}

strongly decreasing

_v~

(libration)

bands when the

temperature

is raised

[5].

^{It is} then reasonable to

assume that the v~ band in the Raman

equivalent

_spectrum of

e"(T~ )

has _a very weak

intensity

which is

equivalent

to

assuming

that the intensities of v~ Raman bands

mainly originate

from

« lattice _water molecules _», which appear in

e"(T~)

in IR spectra. ^The concentration of these

molecules is I

-a(T) (Eq.(3)). Taking

the intensities of these Raman v~ bands _at

To

₌ 0 °C and

Ti

₌ 75 °C to be

proportional

to 0.225 and 0.076

[5] respectively,

we have

using equations (2)

and

(4)

_:

[1 _a

(To)]/[I

_a

(Ti)]

=

0.225/0.076

= a

(T~)/[a(T~) 1]. (5)

It

gives a(T~)

₌ ^1.5 which is the value which _we shall

adopt.

Let _{us note} that with this value

(and

with any

higher value) e"(T~)

has a very weak

negative part

^{in the}

region

2 350- 2 700 cm~ It may be due _{to some} small temperature

dependence

of

e"(T~)

which remained up ^{to now}

undetected,

and which introduces

negative

values

originating

from _a derivative of this

bandshape

_or,

equivalently,

to a

(small) temperature dependence

of the centers of

« 3 ₊ v~ »

(the

bands which fall in this

region)

in

e"(T~).

In

(I)

_we have indicated that

a(T~)

^should be less than 0.6. For values of

a(T~)

less than I,I

negative

values localized _on the

high frequency

side of the v~ band appear which _can

~

Uj

o ~~

to

,,

I

_+~~,,

o o

WRVENUMBER

Fig. I.

Spectra

e"(T~) of ordinary water calculated

using equation(I)

with

a(T~)=

a(T~,

_To,

Tj)

= 1.25 (thick line),

a(T~)

= 2.05 (thin line), To = 0 °C and Tj ₌ 75 °C. Denominations of bands _are indicated.

hardly

be

justified,

_even with the

assumption

that

e"(T~)

has _a hidden temperature

dependence,

because

they

_are too localized _{to come} from _a derivative

bandshape.

We shall choose

a(T~)

=

0.8 _as the most

representative.

An

argument supporting

the choice of this value will be

given

ⁱⁿ section 2.3. As may be _seen in

figure

² variations of

a(T~) modify

the

intensity

of the v~ band without

changing

its

position

and

shape significantly.

In the

following,

_spectra

E"(T~)

and

e"(T~)

will

correspond,

unless otherwise

indicated,

to these values

a(T~)

= 0.8 and _a

(T~)

=

1.5. The latter value for

a(T~)

^relies on

quantitative

arguments. ^{That for}

a(T~)

is

only

the most reasonable. It

consequently

does not

preclude choosing,

if

justified,

other values. As will be _seen these

will, nevertheless,

_not

modify

_our

conclusions in _a

significant

_manner. With these values _we

find, using equation (4),

that the concentration _a of

H~O

defect molecules,

represented by

their

spectra e"(T~),

at the temperature ^{of fusion}

T~

₌ ^{0 °C is} :

a

(T~)

=

0.35

(6)

In the _same way

(Eq. (4))

the concentration

a loo of defect molecules at loo °C is found to be

equal

to 0.89. The

adoption

of different values for

a(T~)

would lead _{to no}

significant changes

for these

values, especially

for

a(100),

_as

long

as

they

_stay within the limits

compatible

with the absence of

negative

parts ⁱⁿ

e"(T~)

and

e"(T~).

2.2 v~ ^BANDS. These

correspond

to

stretching

vibrations

o-fi---O

_{which have been}

extensively

studied in Raman and NIR

spectroscopies.

One novel

point

_appears in IR

spectra

ⁱⁿ

>

lU

=

Uj

m

to

d4

Dz

oJ

Fig.

3. v~ bands in

e"(T~)

for ordinary and

heavy

water (thick lines). Thin lines _are v~ bands in

e"(T~) multiplied

by 2 and shifted toward lower

frequencies

of 100 cm~ ^' for normal _water

and 80cm~' _for heavy water. Wavenumbers _are for

e"(T~).

The _arrow

points

the

position

of the 2 8 band of

e"(T~)

of heavy water.

energies conceming

_v~ vibrations situated _on two different

H~O

molecules which _are H- bonded. It nevertheless remains

that,

with the

exception

of small variations in _curvatures which may be attributed _to Fermi resonances, the

shape

of v~ in

e"(T~)

is _not much different from that in

e"(T~),

which is _an

important point

in this article.

2.3 3 BANDS. These _are bands which

correspond

to the

bending

vibration within _an

H~O

molecule

(the

_v~ band in the gas

phase). They

have been

scarcely

studied up ^to now, except ⁱⁿ

some Raman spectra ^{where it has been noted that}

they

become _narrower when the temperature is raised

[5].

This effect appears in _{a more}

quantitative

_manner in IR spectra

(Figs.

4 and

5)

where

e"(T~)

and

e"(T~)

_are drawn in the

region

P _w 2 000 cm~ ^' We may then _see that the most

striking

feature is found in

e"(T~)

where 3 bands have Lorentzian

shapes

of the form _:

£H(?)

₌

PH/"RH(i

₊

j(P PH)/RHI~) (7)

with

P~

=

40 _cm~

', _P~

=

637 _cm and R~ =

34 _cm~ for

ordinary

water and

P~

=

29 _{cm~ ~,} P~ ₌ 206 cm~ and R~ =

21 cm~ for

heavy

water.

The 3 band in

e"(T~) keeps

a marked

peak

at a somewhat

higher

wavenumber

(1650 cm~~

_for

ordinary

_water and 1210

cm~~

_for

heavy water)

but exhibits

asymmetric

features and is wider. This

tendency

is not

unexpected

_as, when

going

to ice _{an even} wider band appears with _no apparent

peak

at all

j20].

We may

suspect

^{this 3 band} in water to be

composed

of two

bands,

_as

clearly

_appears in the _case of HDO molecules

j19].

This is _on the limit of

detection,

however, in _our present case of

H~O

and

D~O

molecules.

m

to

d4

oJ

d

_I

I4RVENUMBER

Fig.

4.

e"(TL)

(thick line) and

e"(TH)

(thin line) of

ordinary

water. The dotted spectrum represents

e"(T~)

where Gaussian bands

(Eq.

(8))

simulating

2 v~ and _« 8 + v~ » have been subtracted. The thin line spectrum marked

by

_{an arrow} is the spectrum obtained after subtraction of the Lorentzian _curve

(Eq.

(7)) from

e"(T~).

This 3 band of

e"(T~)

is

superimposed

_{on an} overtone of v~ and also

overlaps

the

« 3 + v~ » band in

ordinary

water. In order _to obtain _a

rough approximate bandshape

for 3

(Fig. 4j

_we subtract from the

experimental

band in

e^"

(T~ )

^the two Gaussian bands of the form _:

G(P)

₌ P

(exp 1/2[(P P)/«]~)/« ^/~ ₍₈₎

with P

=

66 _cm

',

_P

=

300 _cm and _«

= 260 _cm for the overtone band and

P

=

22 cm~ ~, ^P =

2 165 cm~ and _«

=

170 cm~ for the _« 3 ₊ v~ » band. We do not

assign

any

special meaning

to these Gaussian bands. In _our present state of

knowledge, they simply

represent ^{the best}

simple empirical

simulation for these

overlapping

bands. The

resulting

spectrum is drawn in dotted line in

figure

4. Its

integrated intensity P~,

center of

intensity P~

^{and width} _«~

P~

^and _«~ are

respectively

the normalized first and second centered _moments of the

resulting

3

band,

while P

~ is its moment of order

zero)

_may then be measured and these

quantities represent

^the

rough

characterization of the 3

bandshape

in

e"(T~)

which is allowed

by

this

empirical procedure. They

_are then found to be

equal

to

P~= 42cm~~,

P~

= 625 cm~ ~, «~ = 98 cm~ ~. These estimated values of first moments of the 3 band in

e"(T~)

will be useful in section 3.

The _same

procedure

is

applied

to the band of

e"(T~)

in

heavy

water

(Fig. 5).

The

v~ overtone is then better

approximated by

an

empirical

band of the form _:

C

(P

₌ P/2 _« cosh

(w/2 [(P

P

)/« (9)

oJ

~

iii

ua

d4

m

oJ

.

'' '

I

Fig.

5. e"(T~) (thick line) and

e"(T~)

(thin line) of heavy _water. The dotted spectrum represents

e"(T~)

where the band

simulating

2 _vL

(Eq.

(9)) has been subtracted. The thin line marked

by

_{an arrow} is the spectrum ^{obtained after} subtraction of the Lorentzian _curve (Eq. (7)) from e"(TH).

which has _a character somewhat intermediate between _a Gaussian and _a Lorentzian

[21],

^while the _« 3 + v~ » band is not subtracted because of its smaller

overlap

with 3. The first _moments of the

remaining

3 band

(dotted

_spectrum in

Fig. 5),

from which _a constant baseline has been

subtracted _are then

P~

=

33 cm~ ~,

P~

₌ ¹⁹⁰ cm~ ~, «~ = 65 cm~ ~.

We _see that 3 bands in

e"(T~)

and

e"(T~)

have

comparable

intensities

P~

and

P~.

As

P~ slightly

varies when _a different

a(T~)

is chosen for the definition of

e"(T~),

this has been _a criterion for

taking a(T~)

m 0.8. The _reason is that the intensities of

these 3 bands _are

hardly

affected

by

the environment

[3, 19].

^It is then

logical

to think that

they

have the _same intensities in

e"(T~)

and

e"(T~).

The centers of intensities

P~

^and

P~

^{of 3 bands in}

e"(T~)

and

e"(T~)

differ

by

_some

lo _cm~ with

P~ being

^{smaller than}

P~.

^{This is somewhat}

surprising

_as 3 bands _are found at

higher

wavenumbers when the

strength

^of H-bonds increases

[22].

As H-bonds in

e"(TL)

are

certainly

not weaker than those in

e"(T~),

this effect is attributed to _a residual

component

of

the v~ ^overtone which is visible _on the low

frequency

side of the dotted spectra ⁱⁿ

figures

4 and

5. With this

rough procedure

it looks useless to go

deeper

^{into this}

analysis

but, as a conclusion of this subsection _we may retain

that,

^within an accuracy of lo cm~ ~, centers of

intensity

of 3

bands in

e"(T~)

and

e"(T~)

are the _same.

The width of 3 bands in

e"(T~)

is _most

probably

the manifestation of _a modulation of the force constant

goveming

the 3 vibrations

by

_some low

frequency

intermolecular modes of the

same symmetry as 3 in _an

H~O (D~O)

molecule. Good candidates for such modes _are the O-O-O

bending

modes which fall in the 50 cm~

region [17, 23].

Such _a modulation leaves the

integrated intensity

^of the band unaltered

[24].

2.4 _« 3 + v~ » BANDS. These _are bands whose maxima in

e"(T~)

fall around 2 150 _cm~

for

ordinary

water and 6 lo cm~ for

heavy

water. There is _some

ambiguity

when

assigning

them _{as «} 3 ₊ v~ » bands in IR _or Raman spectra

[13, 25],

^{and it is the} aim of this subsection to examine it. The

possibility

that

they

_are a 3 _x v~ ^overtone band has been discussed in the

case of ice

[20].

^An argument

against

this attribution is that these bands have similar

shapes,

and

particularly comparable widths,

in

e"(T~)

and in the spectrum ^{of ice. The main but} not

significant

differences _are found in _a somewhat

larger intensity

in ice

accompanied by

a shift of

some 50 _cm~ towards

higher

wavenumbers. It does not reflect the situation of v~ bands whose maxima _are much _more

separated

_:

they

_are found at 650-700

cm~~

_in

e"(T~)

and at 850- 900 _cm~ in the _case of

ice,

which

implies

^{that the maxima} of 3 _x v~ differ

by

a

quantity

much

greater ^{than 50} cm~ ^' between

e"(T~)

and the

spectrum

^{of ice.}

The attribution to « 3 ₊ v~ » is not,

however,

_so

straightforward.

For symmetry reasons it

cannot be the consequence of _a mechanical

anharmonicity

such _{as a} modulation of the force

constant of the 3 mode

by

_terms linear in the coordinates for v~, as is usual for

v~ bands of H-bonded systems

[15, 24].

The _reason is that in _a tetrahedral symmetry, ^such as

experienced by

a

particular H~O

molecule in ice where such _a band

exists,

_none of the three

v~ librations of this molecule has _a symmetry

representation

which would make the

corresponding potential completely symmetrical.

A

complementary

_argument is that in this

case this band would get ^its

intensity

from the 3

band,

and would

correspond

to a 00

- 11

transition, while the 3 band itself would

correspond

to a 00

- lo transition

(the

set of bands 3 and _« 3 + v~ » is in this _case most

comparable

to electronic bands with Franck-Condon

structures

[24, 26] ).

The center of

intensity

of this 3 band is then that of all 00

- n transitions

and would

consequently

^fall at

1870cm~~

_for

ordinary

water. This is _{not a common}

value

[22], especially

when

compared

with that in the gas

phase

at

1595cm~~ _[27].

Furthermore it would then be hard _to understand how 3 bands

(00

- lo

transition)

fall at the

same

position

in

e"(T~)

and

e"(T~) (Sect. 2.3)

whereas the _« 3 ₊ v~» band

(00-11 transition)

is shifted

by

_some loo

cm~~

_{between these two}

_spectra

_and is

appreciably

less

intense in

e"(T~)

than in

e"(T~) (Fig. 5).

Another

possibility

would be that that this _« 3 ₊ v~ » band is _a consequence of _« electrical

anharmonicity» (presence

of non-linear _terms in vibrational coordinates in the

dipolar moment).

The presence of

qualitatively

similar bands in Raman spectra,

however,

makes this

assumption unlikely,

since then

polarizability derivatives,

instead of

dipolar

moment

derivatives, trigger

transitions.

The novel

point conveyed by

IR spectra ^{is that the ratio of the} intensities of these

« 3 + v~ » bands in

e"(T~)

and

e"(T~)

is of the _same order of

magnitude

_as that of their v~ bands

(Fig. 3).

It

strongly _suggests

that the

« 3 + v~» band is _a consequence of _a

mechanical

anharmonicity appearing

in the form of _a cubic _term

(the

lowest order anharmonic

term)

in the

potential coupling

the coordinates of the

3,

_{v~ and v~} modes. Such terms _are of the

same nature as those

responsible

for Fermi _resonances

[24, 26].

It

implies

that this

« 3 ₊ v~ » band borrows its

intensity

from v~ but that its

position

is

mainly

defined

by

the

position

of ₊ v~.

3.

Interpretation.

IR

spectra

are

compatible

with the _now standard

picture

of water which

emerged

from NIR

[8, 9]

^and Raman

spectra [5, 12, 17, 28-30]

and describes water as a mixture of _« basic water molecules _», that is

H20

molecules which _are at the

origin

of

e"(T~),

and _« defect _» molecules _at the

origin

of

e"(T~).

This

description

offers the

advantage

of

retaining

the

possibility

to

explain why

distances

typical

of _a tetrahedral

ordering

of O _atoms

(as

found in

ice)

_are

kept

in water, as shown

by X-ray

and neutron diffraction

techniques [31-35].

^These defect molecules _are here to _ensure that _water is _a

liquid,

as basic water molecules _are

thought

to

aggregate

^{and form}

patches

of rather

rigidly

bonded

molecules,

_as deduced from these diffraction

experiments

and from Raman spectra

[36]

in the

supercooled region,

while defect molecules _are

thought

to be less bonded. The usual

description

of the _nature of these defect

molecules,

_as deduced from Raman and NIR

spectroscopy,

however,

displays

some

incompatibilities

with novel features revealed

by

IR

spectrometry, particularly

^those concem-

ing

_v~ and 3 bands of

e"(T~).

I shall first discuss these

incompatibilities,

before

proposing

a new

picture

for these defect molecules which is

compatible

^{with bands in}

e"(T~).

Defect molecules have been described _as

H20(D20)

molecules

keeping

one strong ^H-bond

(of

the _same nature as H-bonds

linking

basic _water

molecules)

and _one weaker H-bond which

may be _{a «} bifurcated _» H-bond

[37, 38]

_{or even a} broken H-bond

[8, 9].

The

difficulty

with such

descriptions

is that there is not _one

type

^of

defects,

but there _are two which _are

complementary

and in

equal number,

_as

they

are created in

pairs,

a

point already

noted

[38].

In order _to illustrate this

point

let _us think of _a defect molecule

consisting

of _{one «} strong » H- bond and _one broken H-bond. Its

complementary

defect is _an

H20

molecule

establishing

two

« strong » H-bonds with its O-H groups but

accepting only

one H-bond _on its two

lone-pairs.

These

complementary

defects cannot contribute _to

e"(T~),

as this would

imply

_a

(T) (Eq. (3))

to be less than 0.5. This is _an

impossible

condition _to

satisfy

since _at

Tj

= 75 °C

(or a(Ti )

=

I)

it

implies a(TH)

+ a

(T~)

_~

2, using equation (4).

As _seen in section 2, I this cannot

be obtained with

a(TL)

and

a(T~) satisfying

_even the less _severe conditions

(

I,I

~ a

(T~)

_~ 0.6 and 1.25 _{~ a}

(T~

_~ 2,

I)

which _are necessary for _e

"(T~ )

and _e"

(T~ )

to

display

no

negative

_parts.

These

complementary

defects

consequently

should contribute to

e"(T~).

The presence of two kinds of

defects, however,

is in contradiction with what is _seen in IR

spectra

as the 3 band of

e"(TH)

is _{a narrow} band with _no structure. The

assumption

that both kinds of defects

give

the _{same narrow} 3 band at _same wavenumber is

untenable,

_as defects

consisting

of one strong

and _one weakened H-bond

give asymmetrical

3 bands

[39]

while

complementary

defects

which have _two

equivalent

_strong H-bonds

give symmetrical

3 bands _at

higher

_wavenum-

bers

[22].

Furthermore _we would then expect 3 bands in

e"(T~)

to be _at lower wavenumbers than 3 bands in

e"(TL)

which is _not what has been found in section 2.3.

Finally

_a

rapid interchange

of the _two kinds of

defects,

which

might explain

the Lorentzian

shape

of 3 in

8"(TH)

_can be

rejected

_on the basis that it

strongly depends

on the concentration _a of

defects,

which is in contradiction with

e"(T~) (and

also

e"(T~)) being temperature independent.

Similar difficulties arise with v~ bands for which it is hard to understand how bands due to two kinds of defect

molecules,

_as in

e"(T~),

have

shapes

similar

(Sect. 2.2)

to bands

originating

from _one kind of molecules

only,

_as in

e"(T~).

Another

difficulty

of such _a model is that it

predicts

_v~ librational bands to appear ^at

significantly

lower wavenumbers in

e"(T~)

than in

e"(T~).

This does not _seem to be what

happens

_as this difference is of 100 cm~ ^'

only (Fig. 4),

which is also visible _{as a} shift of this order of

magnitude

between maxima of _« 3 ₊ v~ » bands between

e"(T~

and _e

"(T~ (Fig. 3)

and is described in the literature _{as a} small shift

only

of these v~ bands with temperature

[25, 40].

3, I DYNAMICS _{OF DEFECT MOLECULES.} From this discussion it may be concluded that

only

one

type

^{of defect molecules exists and} appears in

e"(T~).

These defect molecules cannot be much different from basic _water molecules because their v~ bands

keep

_many features of the v~ bands of the basic water molecules. Furthermore the Lorentzian

shape

of their 3 bands

implies

that _some of their

vibrations,

in _some way

coupled

to

3,

has _a diffusional character.

The most

straightforward

_{way to} fulfill these

requirements

is _to suppose that these defect

H20

molecules _are molecules whose energy levels for their rotations around their axis _z

(z

is the bisector of the _two O-H directions in the

plane

of the

molecule)

_are above the maximum of the

potential

_energy

goveming

these rotations and

consequently display

a

diffusional character for their rotations around this _z

axis,

while

keeping

a vibrational character for their rotations around their _two other _axes

(they

still

perform

librations around _x and

y).

Basic _water molecules

have,

_on the contrary, ^rotational

energies (around z)

below this maximum and

consequently perform

librations around their three _axes, which is

certainly

_a

particularity

^of water. This

description adopts

the _same

physical

basic

picture

as that

proposed by

^{Robinson and coworkers}

^{[41, 42].}

^{It differs somewhat from it with the} identification of the rotation around _{z as}

being responsible

for the

apparition

of defect

molecules,

whereas

Robinson and coworkers

identify

it _as that of lower

frequency

with _no

particular

attribution.

This

particular

choice of the _z axis _comes from the fact that for any

H~O

molecule _a rotation of _w around this axis leaves the rotational

potential unchanged,

^{while it}

requires

_a rotation of 2 _w around the other _{two axes.} Furthermore when the

H20

^molecule considered

experiences,

as in

ice,

an environment of tetrahedral symmetry, ^{the force} constants for these three rotations

are the _same around

equilibrium (zero rotation),

because of the

linearity

of H-bonds. It

implies

that the curvatures of the three

potentials

are the _same around their

equilibrium positions

^{in that}

case. From these _two

properties

_we deduce

that,

in _a tetrahedral

environment,

the

potential

maximum for _a rotation of w/2 around _z is much lower than the

potential

maxima for rotations of _w around the other _{two axes.} When the environment of the molecule considered _no

longer keeps

_a tetrahedral symmetry, ^{these maxima} may be

strongly modified,

but the

periodicities

of the three rotations do _not

change,

and for the great

majority

of

molecules,

if not

all,

the maximum of the

potential

around _z remains much lower than the maxima of the

potentials

around the other two _axes. We may then have molecules with their rotational

energies

around _z above the maximum of the

potential goveming

this

rotation,

while the rotations around the other two _axes remain under the maxima of the

corresponding potentials,

thus

retaining

_a

vibrational character for these two rotations.

We may then

easily

^{understand the}

apparent discrepancy

^that _v~ ^bands exhibit between IR and Raman spectra

[43]

_: the IR bands

change only

little when the

temperature

^{is raised}

[25, 40],

while the Raman bands have their intensities which

dramatically

decrease

[5], keeping

their

shapes

and

positions unchanged.

The behavior of the IR v~ band may be understood when _one realizes that in _a tetrahedral

symmetry

^the

dipole

moment has _no linear

terms in coordinates

describing

rotations around _z, because of the

parity.

These bands _are

consequently

not very sensitive to rotations around _{z even} when the environment no

longer keeps

this tetrahedral

symmetry (in

the average it has this

symmetry). They consequently

do not suffer _an

abrupt change

when such rotations _are altered, as when

passing

from basic _water

molecules _to defect molecules.

They

are

consequently

not very sensitive _to the concentration of defect molecules, and

display

small

changes only

when the temperature ^{is varied. This is} not

true for Raman v~ bands where

polarizability

has terms linear in coordinates

describing

rotations around _z in _a tetrahedral

symmetry

^and are

consequently

much _more sensitive to the concentration of defect molecules.

3.2 DISCUSSION. From the

preceding

section it appears that basic _water molecules _are not so much characterized

by

the fact that

they

_are four-bonded but

by

the fact that

they experience

rotations of _a vibrational character, which may also in

principle

be achieved

by

^molecules held

by

three bonds instead of four. These molecules

certainly

have _a small contribution in the

fluidity

of _water.

They

have _some similarities with

H20

molecules in ice _as

e"(T~) displays

some similarities with the IR spectrum ^{of ice1}

[20, 44].

The main difference is that

they certainly

form much less

cyclic

structures of

H~O molecules,

and in that _sense

they

_may be closer to molecules found in

amorphous

solid water

[45],

where H-bonds _are

thought

to be

JOURNAL DE PHYSJQUE Jl T 3, N'4, APRIL 1993 23

more bent than in ice.

They

_may

aggregate

in clusters of finite size

[31-36].

Defect molecules

are those molecules which

display

^rotations around their _{z axes} of _a diffusional character.

They consequently

have

only part

of the

properties

of molecules of _a normal

liquid,

which

perform

diffusional rotations around their three _axes.

The

description presented

here is

strictly

valid in the range of

temperatures investigated,

that is between 5 °C and 80 °C. It is

likely

to remain valid in the

deep supercooled region

where

the

significant

mechanism

expected

in this

region

is the increase in structuration of basic water molecules

aggregates.

^At

temperatures higher

than 80 °C _we

expect

^the

validity

of this

description

to remain

justified

_{on a} shorter range of

temperatures,

^{because the} concentration of broken H-bonds, which may

display cooperative properties, certainly

becomes _more and _more

appreciable.

Such broken H-bonds _are

certainly

_present in the range -5

°C, 80°C,

in

e

"(T~ )

and also in

e"(T~),

but _not in _a

quantity

sufficient _to appear as the

major

feature.

They

have been detected in NIR

spectra [10, 46, 47]

which is _a

region

where

they

_can be detected with _a much greater

sensitivity

than in the conventional IR

region,

^{where the} intensities related to v~ vibrations _may be smaller

by

_one order of

magnitude

for broken H-bonds _as

compared

to

strong ^H-bonds.

From the

magnitude

of the width R~ of the Lorentzian _curve

describing

the 3 band in

e"(T~ ) (Sect. 2.3)

we may estimate the correlation time r~, or average time

during

which the coherence of the 3 vibrations in defect molecules is

kept.

Let «~ be the width

(second

centered

moment)

of this 3 band if _we could freeze all rotations and intermolecular vibrations of

molecules. It is

likely

that _some of these intermolecular

displacements

_are

responsible

for this width

(through

_a modulation of the force _constant of

3,

for

instance),

_as it _cannot be due to

resonance vibrational energy ^{transfers between vibrations situated} on

neighbour

molecules.

When

varying

the environment of

H~O

molecules

by isotopic dilution,

such bands appear in the form of derivative-like bands

[3, 19]

which _are characteristic of bands which

modify

their centers, ^but not their intensities and widths. In contrast, the effect of _resonance vibrational energy transfers would be to alter the widths of these bands _upon

isotopic dilution,

which is _not the effect observed. We may ^then

write, using

Kubo's

theory

of

lineshapes [48]

_:

I~H "

~ "Tc

~I~ (10)

with 2 _wr~ ~~ ^« l

(rapid

modulation condition the factor 2 _{w comes} from the fact that R~ and «~ are

expressed

in P instead of _w

).

We deduce «~ ^» R _~. As it is reasonable _to

expect

«~ « «~, where «~ is the width of the band in

e"(T~)

which _we have _seen to be of the order of 3 R~

(Sect. 2.3)

for both

ordinary

and

heavy

water, we deduce that «~ has _a value

falling

between R~ and 3 R~. From these extreme values _we

deduce, using equation (10)

with

R~ m 35 cm~

10~ ~~/2 _w

< r~ ^« 10~ ~~/2 _w

(in seconds). (I1)

This

T~-type

correlation time is

certainly

too short to be measured

by

NMR

experiments [2].

In

principle

it falls into the

possibilities

of Raman

spectroscopy,

^but has

apparently

not been measured

using

this

technique.

It

corresponds

to 8

making

a small number of oscillations

only

before

loosing phase

coherence. It is

likely

to be in someway connected _to the diffusive _nature of rotations around _z. The

precise

mechanism

by

which it is

connected, however,

remains unknown.

Finally,

let _{us note} that _a

Tj-type

relaxation

mechanism, corresponding

to _a finite lifetime

1/(2 WRH)

^{for the first excited} state in 3 would

give

the _same order of

magnitude (

m 10~ ^'~

s)

for this lifetime. We think it less

likely

to occur as it would

imply

_a much smaller

«~(«~« R~)

_to obtain _a Lorentzian

shape,

which would be hard _to correlate with _a

P~ (the

center of the

band) unchanged

when

passing

from

e"(T~)

to

e"(T~).

4. Conclusion.

The

analysis

of IR spectra, ^obtained

using

ATR

techniques

and which

display

_a

good signal-to-

noise

ratio,

revealed novel features: the v~ bands

display

similar

shapes

between

e"(T~)

and

e"(T~)

the band of

e"(T~)

is _narrow with _no apparent structure. It has _a

Lorentzian

shape

centered _at the _same wavenumber _as the

unsymmetrical

band of

e"(T~).

The

interpretation

of these features allowed _{us to} propose a

description

for the

dynamics

of

H~O(D~O

or

HDO)

molecules in _water which _starts from the _same

physical

mechanism _as that

proposed by

Robinson and coworkers

[41, 42]

but differs somewhat from it in its

development.

^{It classifies molecules into} two types ^which are called basic _water

molecules and defect molecules. This does not differ from

previous spectroscopic

studies whose main conclusions _are

consequently adopted.

We _are,

however,

able to be _more

precise

for what _concems the nature and

dynamics

of both kinds of molecules. Basic water molecules

are those molecules which

perform

rotations around their three _axes

having

a vibrational character

(librations),

while rotations around the axis of

symmetry

z of defect molecules have _a diffusional

liquid-like

character. This

special

role attributed to the _z axis does _not appear in Robinson and coworkers' model. These

properties

also differ from those

proposed earlier, especially

for defect molecules which _were

thought

of _as

being

molecules

having

broken _or

strongly

weakened H-bonds. In the range of

temperatures

considered

(

5 °C _~ T

~ 80

°C)

broken or

strongly

weakened H-bonds do not seem to

play

_any

special

role. This

might, however,

not be the _{case at}

higher

temperatures or pressures.

Let _us note

that, although

_our central

arguments

concem intramolecular vibrational bands

which _we have obtained

using

ATR

techniques,

_we have invoked results

conceming

intermonomer bands such _as libration bands. As _our spectra were limited _to P _m 650 _cm ^' _we

saw

only

_part of these bands and have

consequently

been

obliged

to

appeal

to older

spectra

in the FIR

region.

Such spectra are scarce and

certainly

amenable to better

quality using

modem

equipment

which has made great progress. It will in

particular

be very useful to

verify

that the

decomposition

of intermonomer vibrations follow the _same

decomposition

_as that of intramonomer bands

(Eqs. (I)

and

(2)),

which is not a

priori

true, as parts ^of

e"(T~)

^and

e"(T~)

in the FIR

region might display

temperature variations. It will be the aim of

subsequent experiments

to look at this

point.

This article has been devoted to the

analysis

of the variations of IR

spectra

^of water with temperature. ^In

forthcoming

articles

[19, 49]

1 shall

analyze

their variations with deuterium

concentration. This will allow the determination of various mechanical parameters, ^such as

intra and intermolecular

coupling energies

_or Fermi _resonance

energies

of various vibrations.

Let _us

finally

note that the interest of

obtaining precise

IR spectra ^of water extends

beyond

that of

conveying

information _on the _structure and

dynamics

of

H20

molecules in pure water, as it

may allow to

apply

IR

spectroscopy

to the vast domain of aqueous

solutions, particularly

the domain of molecular

biology,

where IR spectroscopy ^has

scarcely

been used outside _narrow

spectral

windows where water does not absorb.

Acknowledgments.

I _am indebted to Professor J. E.

Bertie, University

of

Alberta,

for

highly

valuable comments

conceming

more

particularly

article I of this series but which had

repercussions

in this article.

I _am also

grateful

to Professor W. A. P.

Luck, University

of

Marburg,

for

helpful

discussions and _comments.