On long and short hydrogen-bonds

Journal of Molecular Liquids, 46 (1990) 305-321

305

Elsevier Science Publishers B.V., AmsterdAm

ON LONG AND SHORT HYDROGEN-BONDS"

Hubertus KLEEBERG t, Veneta VIDENOVA-ADRABIgSKA + and Thomas WESS t

tDept, of Phys. Chem., Unlverslty of Marburg Hans-Meerwelnstr., D-3550 Marburg (FRG) +Inst. of Inorg. Chem. & Metallurgy Rare Elements, Techn. Unlverslty of Wroclaw, Smoluchowsklego 23; 50-372 Wroclaw

(Poland)

(Received 15 March 1990)

SUMMARY Experimental results of OH-stretching frequencies, 0-0and O - H - d i s t a n c e s a r e c o m p a r e d w i t h e a c h o t h e r and a r e d i s c u s s e d I n c o n n e c t i o n w i t h results of t h e same c h a r a c t e r i s t i c p a r a m e t e r s as w e l l as t h e l r c o m p l e x a t l o n energles as d e t e r m i n e d on t h e b a s l s o f t h e t h e o r e t i c a l ab i n l t l o calculations o f Alm15f for [C1.--H..C 1 ] - complexes. T h e comparison of the various results shows that the devlatlon of the X-H-distance Ar and Ar c s' respectively, from the central posltlon seems to b e a helpful tog~ in order to dlstlngulsh between asymmetrlc H-bond pot entlals and potentials in whlch the lowest energy level Is above the potential barrler (more or less symmetrlc H-bonds). T h e theoretlcal results support the Idea that the v -R correlatlon is n o t continuous at R ffi 2.44 A - the O-O-distance where °~he°~trongest H-bonds a r e to be expected. O0 T h e theoretical results indicate, that the correlatlon of the H-bond energy A E ( v = O ) wlth the XH-frequency (or frequency shift) is not linear and is d l f f e r e n t for asymmetrlc and more or less symmetric H-bonds. However, for re I a t l v e frequency shifts of more than approximately 30~ the change in H-bond energy Is expected to be of the order of kT. This Indlcates, that the influence of the surroudlng of a H-bond wlll become very important for c o m p a r a t l v e l y strong H-bonds (approx. -22kcal/mol H-bond for CIH-complexes). INTRODUCTION In the course of Investigation i n H-bond f o r m a t i o n

it

occurred,

complex between a proton the interaction

of

A13+...O-H..-Pyrldlne

"Dedicated

effects

a comparatively

a cation

C+ ( r e f s .

1-5)

transfer

or F-H..-F-H...N(CH3) 3 (refs.

(ref.

Y was s t r e n g t h e n e d

occurred; 8,

Luck

© 1990 - - Elsevier Science Publishers B.V.

1) i n v o l v e d

weak H-bond o f a X H . - . Y

d o n o r )fl{ and a H-bond a c c e p t o r

t o P r o f e s s o r W.A.P.

0167-7322/90/$03.50

on t h e c o o p e r a t i v e that

9).

for

example

by in

306 Many

investigations

chemlcal (refs.

reactions

18-23).

are concerned

(refs. 10-17)

The situation,

wlth

or

the proton

in biological

where the proton

transfer

structures

Is transfered

mechanism like

in

enzymes

"half way",

is

discussed in more or less symmetric (X...H..-Y) complexes (refs. 24-27), which may be of technical

interest with respect

to their superlonlc

conductivity

(ref. 25), for example. In order to increase our knowledge of long and weak, shorter and very short H-bonds, we reexamined the general spectroscopic and structural properties of H-bond

complexes.

experimental

We

results

expected would

that

the comparlson

increase

our

of

ab

understanding

Inltlo

of

and

the physical

principles involved.

THE DEVIATION OF THE PROTON POSITION FROM THE SYMMETRIC CASE For a varlety of compounds O-H...O complexes with known O.-.H

(ros} distances

(hydrates,

acids and acldlc salts},

(mostly from neutron diffraction}

(refs. 26-43),

we

calculated

containing

0-0

(Roe} and

the deviation

Ares

of

the proton posltlon from the symmetric position:

Ar

OH

= R

O0

/2-r

(1)

OH

Only H-bonds, approx. In

whlch are linear or at least nearly linear

(i.e. OHO angle

180±10 degrees) have been included. Flg. 1,

the hr

values

are

compared

with

the corresponding

OH

frequency VOH (refs. 24, 27-30, 44-59} of the O-H stretching vibration. obvious

that

the correlation

crystallographic

Is

discontinuous.

For

O.05~Ar

It is

OH

as well as spectroscopic data seem to be very rare.

~0.14]t It Is

an open question whether H-bonds wlth O.05-~AroH~O, 14A do not exist or whether thls

group

of

compounds

has

not

the frequency reglon 2000>vOH>6OOcm-1, Ar

been

sufficiently

some very small

Investlgated.

In

(usually about O.02A}

values have been found. OH

As It wlll be discussed below (Fig. 9), for the case of HCI the change In H-bond

energy

in

the region

2000cm-I~SPcIH~O

is

quite

small.

Consequently,

small changes In the structure surroundlng the H-bond may lead to siglnlflcant changes of Its geometry. Thus,

we

may

distinguish

between

asymmetric

(AroH>O.14A)

and

closely

symmetric H-bonds (Ar
the CI-H

we wanted to compare thls result wlth theory. stretching

frequencies

(see

Appendix)

from

Thus, we

the

energy

307

~

IA!

VO~

o.E

o.~

DO

3000

2000

" ~Ol.i[¢m4 ~~00 " ~ "

Fig. I. Comparison of the devlatlon of the central proton position Ar with the OH-stretchlng frequency in hydrates (refs. 26-34), acids and acld~ H salts (refs. 27, 37-43).

~H, [A] 1.5,

/ \

1.C

-~" 1

o exptI. x R >3,2

o ~'0oo" 20'00 °'1o0o~" o

~HlCm-~]

Fig. 2. Comparison of the deviation of the central proton position Ar with ClH. the theoretical CiH-stretchlng frequency in [CI-..H...CI]complexes; experimental polnts (open clrcles (refs. 49, 62-64) are Indlcated as well).

308 values of for

[Cl...H...Cl]--complexes,

a variety

of CI-CI-

study of Alml~f Before

we

= R

C1H

describe

and v eqn.

/2-r

ClC1

1).

the potential

(Fig. are

I).

(ref. 65),

an ab Inltlo

curves

in

detail,

we

should

look

at

(2}

i n eqn.

[C1-..H...C1]--complexes, and the shape

Two well

known

very carefully

In

C1H:

2 (the abbreviation

For

discontinuous

(rcIH),

C1H

in fig.

C1H

CI-H-dlstances

(ref. 61).

the correlation between Ar

~r

whlch have been calculated

(RClCl) and

to

Is the same as

established

belong

to

are included

2 has the analogous meaning as in

too,

t h e Arcls-Vcl H

experlmental

two

different

correlation

in the case of O-H...O points

types

(refs.

of

in Fig. 2 (open clrcles).

is

complexes

49, 62-64),

which

[CI. • -H. • .Cl]--complexes

Both these polnts

lle very

nicely on the two parts of the correlatlon found. We have found even more experimental (refs.

65, 71, 72)

the possibility [F,*,H---F]-

(refs.

of

two

groups

of

present very

structures

73, 74).

All

these

slmllarltles

discussed

our

qualitatively

to be

different

true

In Figs.

as

speak

however,

purposes.

similar

as

general,

of

-

with

[CI..-H..-Cl]-

In the system

in favour

without

In

behavlour

well

for H-bonds

and theoretical

(N.-.H...N)

the generallty

of

1 and 2.

POTENTIALAND THE CL-H STRETCHINGFREQUENCIES

the potential

energy

functions

of

[CI...H-..CI]-

complexes

for

R ( i n d i c a t e d by n u m b e r s (A) i n t h e f i g u r e } , a r e shown. The f u l l c1c1 correspond to the energies of the [C1..-H...C1]complexes minus

points

the energy

of

energy

connecting according ab

"Cl-lon".

the infinitely difference

these

separated

AE i s

points,

as

lnltio

is

t h e same

For R

AE=0 a t

potentials

well

CICI

barrier

close

For to

decreases

as

C1--lon or

I n more d e t a i l In

the proton 3},

Is

H

the "C1--ton"

levels,

cases

at

CICI

in

energy.

(ref.

61).

The

lines

were

drawn

model

since

i n the Appendix.

all

in

the left

the potential

decreasing

in height.

given

H-bond

the vibrational

symmetric

=~ ( t o p o f F i g .

t h e minimum

the potential

are

whether

t h e mlnlmum.

C1H and

the interaction

to the procedure outlined

the energy

3.2A,

a

for

seems

In Fig. 3

with

show

9, 49, 66-70)

[F.,-H-**F]--complexes, data

same

THE [CL'" "H'" "CL]

The

for these

The

the correlations

This

use

complexes

the presence complexes.

data

to

(refs.

or

of the free

between

shifts

this

to

at

the right

C1H i s shown,

infinity larger

and r

C1H

about and

20

"t~... ,.t%.o, =,

,

,'

/ 4 7 6 ~

309 ',

.~ 0 ~-10 -20 ;

~

3.70

-10

-20 0

-10

~

3/.9

-20 3.28 -20 3c

2C lO

0

-10 -20

~

3.07 2

CI I

I

H .....

3

rOH[A] ",

CI-

rClH [~,ICI

I

Fig. 3. Theoretical CI-H potentials (calculated points taken from (ref. 61)) for different CI--.CI distances R (A} (indicated by numbers} in [CI"'H...CI]- complexes, clcl

310 For R

ClCl

z3. TA the three lowest vlbratlonal

levels are below the barrier; v:

this means the fundamental vibrational transition (wlth Av=l;

vlbratlonal

quantum number) and the flrst overtone (Av=2) wlll be observed-wlth gradually Increasing

anharmonlclty

(Flg. 4)

for

decreasing

RClCl.

In

the frequencies of the CIH stretching vibration and its overtones to

the calculation;

see

Appendix},

are

compared

for

Fig. 4

(according

the different

CI-CI

distances. In the case of R (V=2) Just

iS

forbidden

above

ClCl and

=3.49A {centre of Fig. 3), the third vlbratlonal level the forth

the potential

c o m p l e x e s we e x p e x t them t o f l n d that

and

barrler. at

t h e C1-H f u n d a m e n t a l f r e q u e n c y ,

will

be

observable

an o v e r t o n e

and

between

1800

the closeness

the spectrum corresponding

of

flfth

With

levels

unusually

is

a very

just low

could not

above

and

vlbratlonal

other

be c a l c u l a t e d

I000 cm-I a s w e l l . wlll be

be p o p u l a t e d found

close

to

with

in this

this

the potential

together, of

Fig.

accidental

is

level

expected

these

4 shows

overtone, absence

to

of

Fig.

complicate

considerably.

Flg.

4).

given,

3).

The

This

leads

overtones,

means, a c c o r d i n g

may b e e x p e c t e d

t o kT,

Arcls~1.39A)

below level

some p r o t o n s and

to

which

not only the lowest vlbratlonal

mlnlmum ( a t

of

i s b e l o w and t h e n e x t one

(mlddle

the energy values

case;

close

under discussion,

(290 cm-1;

At room t e m p e r a t u r e ,

The

overtones

barrier

frequency

very

the overtones

low wave n u m b e r s .

3000 cm- I .

to the potential

the potential

to

a s w e l l a s t h e s e c o n d and t h i r d

F o r Rclcl=3.28A o n l y t h e l o w e s t v l b r a t l o n a l (v=l)

are

respect

will

a considerable

extent will be In a more or less central position. For thls potentlal we will expect broad vibrational bands and large corrections for thermal motion at room temperature and consequently smaller values at low temperatures. For R

ClCI

s3.2A only one found

single minimum,

potential,

was

decreasing

Rclcl, the H-bond

for

in an apparently quite harmonic

the [C1...H.-.C1]energy

becomes

complexes

more

positive

{Fig. 3). (Fig. 3),

Wlth and

the stretching frequencies increase approximately linearly (Fig. 4). According to the method of calculatlon used, with

decreasing

Rclc1<3.0A

{Figs. 3

and

4).

the CI-H-dlstance decreases It

may

be

argued

whether

this sltuatlon will be found in real systems because of the strong influence of the surroundlng on the H-bond. These results point to some reasons,

why the interpretation of vibrational

spectra may become very dlfflcult for Rclcl~3.2A or correspondingly R0o~R. SA {see below}.

In addition,

combination vibrations may have to be taken into

account (ref. 73), which may further complicate the Interpretatlon.

311

THE CORRELATION BETWEEN RXH AND Rxy Until

now,

the c o m p a r i s o n

o£

theoretical

complexes and the e x p e r i m e n t a l r e s u l t s

results

of

[CI..*H...CI]

o£ O - H . . . O c o m p l e x e s , s e e m s r e a s o n a b l e

BOO0

~Jcm"} 6000

+ o a

AV I 2

E]

3

I

,

I

'

~

I

I

I

0 /

]

I

1

I I

0

I

I

I

I I

i i

i

I I

t I

t I

I

i i

4

I

4000

I \\1

I

+ \

I

*, [

2000

~

i

I I i J ..__----4 ---------*

94. / ,

,\: :/: .

I ,,, 'M I

,

~1%" \1/ i .

I

I I '

.,,~

,

3

5 RUO

co [ Al

Fig. 4. The f u n d a m e n t a l C I H s t r e t c h i n g f r e q u e n c y (+) as well as the f r e q u e n c y of the first o v e r t o n e (o) s h o w s a dlscuntlnulty, if p l o t t e d a g a i n s t the CI-CI d i s t a n c e at R ~3.2A. S o m e second (a) and 3 rd o v e r t o n e s (x) are also ClCl indicated.

{A] 1.6

o exptl. x COIC.

X

____ X

•

2

3

i

IJ

,

Raa [A]

Fig. 5. C o m p a r i s o n of the C I - H d i s t a n c e [CI - - -H - - 4=1 ] - complexes,

r

with cls

the CI-CI

distance R

in clcl

312 and it seems worth for the picture therefore,

to look In for further

emerging

compared r

For O-H...O

with R

C1H

support

from the [CI-..H-..CI]-

complexes,

- or for contradlcltons

calculations.

C1CI"

similar

correlations

between

r

and R OH

known

(refs.

28, 29, 40-42).

qualitatively 40-42).

very

However,

slmllar

for

short

Fig. 5),the curvature

The as

result

the one

for for

asymmetric

O-H..-O

complexes

are well O0

[CI...H...CI]-

complexes

complexes

(refs.

(Rclcl~3.1A;

is usually not drawn as steep for O-H...O

probably be due to the dlfflcultles due

supports

to the low potential

the qualitative

quantitative

barrier

(see above).

of

this

agreement with the experimental

as

This wlll

Fig. 5 also

which

is

in

points for [CI-- .H...CI)-.

COMPARISON OF THE XH-STRETCHING FREQUENCY AND THE X-Y DISTANCE The comparlson of the CI-H stretchln8 frequency and the Ci-Cl-dlstance Fig. 6,

demonstrates

the two

[Cl...H...Cl]--complexes

very

separatln 8 both reglons, the case of

reglons

for

clearly.

asymmetrlc

There

is

whlch - to our knowledge

[CI..-H...CI]-

close to those calculated

complexes.

Agaln

In

of the proton

However,

comparison,

llne

complexes

of the precise determination

usefulness

looks 28, 29,

dashed

we expect it from Fig. 5 by the connection of the calculated values.

position

-

In Fig. 5 we,

and

closely

an obvious

In

symmetrlc

dlscontlnulty

- has not been dlscussed

the experlmental

polnts

In

are very

theoretlcally.

compounds

In Fig. 7

we plotted v agalnst R for a large varlety of dlfferent OH O0 includln 8 hydrates, hydroxldes (refs, 76-84), acids and salts (see

also ref.

of FIg.

been

plotted

and

1). Thls kind of diagram replotted

(refs.

is known for a long tlme and has

24, 44-46,

50, 51, 90),

but

two

features

seem important to be stressed with respect to Flg. 6: I). Surprlslngly

enough all these dlfferent

or at least very slmllar - correlatlons.

compounds

seem to obey the same -

This Is especially

(O-H)- will be expected to have a dlfferent

surprlslng,

charge dlstrlbutlon

(refs.

since 85-87),

as H 0 and as carboxyllc OH-groups, for example. Furthermore, It is not only 2 the OH-group whlch is conslderably different but In hydroxldes the OH--lon Is

more

or

less

polarized

(refs.

87-89)

by

the strong

interaction

with

the corresponding catlon. 2).

The d i v i s i o n

asymmetric (full increases H-bonds

of the experlmental points line),

the quality into

theoretlcal

these

and c l o s e l y s y m m e t r i c H-bonds ( d a s h e d l i n e of the correlatlon.

two

quantltles

i n t o two r e g i o n s c o r r e s p o n d i n g t o

groups, are

to

decide to which group a c e r t a i n ,

seems

be

This indicates to

compared.

be

necessary

Furthermore,

newly i n v e s t i g a t e d

In Fig.

7),

that

a separation

of

if

experimental

or

7 may h e l p

to

Flg.

compound b e l o n g s .

313

For the real O...H.--O systems wlth strong H-bonds

(around 2.45A),

propose a correlation corresponding to the (steep) dashed llne

we

{Fig. 7).

4000

~C,H

\

Icm-1]

o

2000 x calc.

o /

/ \ 6 I

3

4 RCICl

[.~]

Fig. 6. Comparison of the CI-H stretching frequency distance R in [CI.-.H...CI]- complexes.

Pc]s with

the CI-CI

ClCl

t.O00 vop

lem~l

n d

*OH-

300C

I

200(

°* o •

2~

I l

o o

i

=

a hydroxides • h~ro~es

Z~

2~

30

%0 IA132

3~

Flg. 7. Comparison of the O-H stretching frequency Vo (ref. 29)} wlth the 0-0 distance R in O-H-..O complexes o~ (refs. 76-84), hydrates, acids and a c l ~ c salts {refs. 26-43).

(OH-{vap}: hydroxides

314 However,

this should not be considered as contradictory

to the statement of

Joswlg, Fuess and Ferrarls (ref. 41): that for a glven very short O-O-dlstance dlfferent OH-frequencles may exist.

COMPARISON BETWEEN THE INTERACTION ENERGY AND THE CL-CL-DISTANCE In

FIg. 8

the lowest

the calculated

vibrational

level)

interaction

energy

is

with

compared

AE{v=O)

(referring

the CI-Cl-dlstance.

to

Three

points are worth mentioning: i).

For

asymmetrlc

H-bonds

thls

correlation

Is

nearly

linear

between

approximately 3.6 and 5A. This result may help In practlcal cases, where an estimation of the H-bond energy is desired. 2).

The

shallow

energy

minimum

lles

In

the region

of

3.2A,

where

a non-monotonous behavlour was observed in the other correlations. This shows, that from the energetlcal polnt of view, from asymmetric With

there Is a very gradual

to symmetric H-bond complexes with decreasing

AE (v=O) ~-22kcal/mol,

the agreement

between

the

transition

X-Y-distance.

theoretical

and

experimental results is very good (refs. 62, 91). Taking

a CI-H

-22kcal/mol

bond

for

energy

of

the Interactlon

the [CI- • .H. • .CI]-

-complex

the complex becomes

is

symmetric

-103.2kcal/mol

energy, held

we

together

in the region

(ref. 92)

come

of

to

and

adding

the conclusion,

by

-125.2kcal/mol.

the energy

minimum

that Slnce

{compare

Figs. 3 and 8) thls means that the H-bond - or the bond of either slde of this complex corresponds to -62.6kcal/mol.

This shows very clearly that the energy

of

CIH

the CI-H

the formation

bond of

The cancellation

in

the isolated

the symmetric of energy

molecule

complex

on

contributions

is

account

involved

of

reduced

by

the other

in H-bond

40Z

on

(H-)bond.

formation,

has

been discussed in detail from a theoretical polnt of view (refs. 93,94). 3. ) Although

the interactlon

energy

becomes

more

positive

CI-Cl-dlstances below 3.2A, it is still negatlve untlll R

CIC1

for

decreasing

~2.8A. This means

that the formation of a very short (CI...H...CI)- complexes {with considerable repulslon of the Cl-lons;

van der Waals radius:

I.SA (ref. 92), still may be

a favourable process (see below).

COMPARISON OF INTERACTION ENERGY AND XH STRETCHING FREQUENCY Fig. 9 demonstrates that the complexatlon energy correlates wlth

the CIH

frequency.

Badger-Bauer-Rule However,

This

Is

(refs. 95, 96),

dlsperslon

interactlons,

In

opposition

whlch whlch

to

predlcts may

nonllnearly

the frequently

a llnear

increase

used

correlatlon.

the experlmental

interaction energles for weak H-bonds (i.e. in the reglon of O>AE>-5kcal/mol),

315

AE(v=0)

[ mok~!] 10-

-10

-20 ¸

2

J

:)

¼

5

""&> Roo [A]

Flg. 8. The calculated complexatlon energy AE(v=O] o£ [Cl.-.H...Cl]- complexes shows a shallow minimum at 3.2A.

~E(v=0) [m~o°[ ] -2t ///I//

/

-I(

/

/r l

IC

/

/'

x R>3.2 • o R
/

I/I

I

I

/I I I I

I I

4000

2000

'

'

0

%1CIH [cm -1]

Flg. 9. The calculated H-bond energy AE[v=O) does not correlate llnearly wlth the CIH stretching frequency P of [C1...H.-.Cl]- complexes. CIH

316 have not been taken into account In the theoretlcal calculatlon, dlscusslon

(ref. 61).

Therefore

we

expect

that

used in thls

experlmental

interaction

energies may be slightly more negative than the ab Inltlo values. agreement

wlth

non-llnear

Badger-Bauer-correlatlons

for

weak

Thls Is in

Interactlons,

which have been assigned to van der Waals (dlsperslon) forces (refs. Plotting (teEs.

the experimentally

observed

linear

1, 97).

Badger-Bauer-correlatlons

1, 95, 97) for O-H.-.O complexes Into Fig. 9 would give a straight llne

which approxlmately Thls indicates,

tangentially

touches the correlation for

[CI...H---CI]-.

that at least the order of maEnltude of the frequently used

Badger-Bauer-Rule Is not too Incorrect. Other correlations put forward on the grounds of the charge transfer theory (l.e.

correlatlon

more linearly,

of

~E

with

({v~am-vzcomplex}l/Z (refs. 98, 99))

correlate

but systematic devlatlons in the reglon of small and positive

AE(v=O) of [CI.-.H...CI]- complexes are still present. As

one

of

the most

important

results

of

thls

dlscusslon

we

conslder

the fact, that the most stable complex formed within ±kT corresponds to a CI-H stretchlng

frequency

of

approxlmately

1800cm-1(correspondlng

to

a relatlve

frequency shift of 40~). This means, complexes which show dlfferences at large frequency

shifts

experlmental: dlfferences

with

2885cm-1; In energy.

respect

may

vary

the Isolated 2998cm -I)

In other words:

example different solvents, frequency

to

calculated:

temperature,

conslderably

by

osclllator

are

not

changes

pressure,

(between

in

of

large

the surroundlng

etc.),

approx.:

(VClH(free):

Indlcatlve

(for

the X-H stretchlng

2000

and

300cm-1;

see

Fig. 9) wlth hardly any change In Its energy. This concluslon is supported by the large

frequency

comparatively dlstant

shlfts

strong

nelEhbours

found

H-bonded on

H-bonds

in dependence

complexes In

of

different

(refs. 100, 101).

crystals

has

been

An

solvents

for

influence

of

stressed

for

strong

that

proton

H-bonds as well (refs. 88, 102). Another transfer proton expected

result

polntlng

Is observed afflnltles

of

In

In noble 0.2

the same gas

dlrectlon

matrices

(ref. 103),

for

although

is

the fact

complexes proton

with

normalized

transfer

would

to occur only for H-bond donors and acceptors with about

be

the same

proton afflnlty (l.e. normallzed proton afflnltles of O; see also (ref. 91)). Furthermore, vlbratlons,

may

the temperature dependence of the half wldth of X-H stretching be

explalned

by

the

strong

curvature

of

the ~E-v CtH

correlation for H-bond of intermedlate strength (Fig. 9). In view of Fig. 9, we have

to conclude,

that

the dlvlslon

of dlfferent

H-bonds into long, intermediate and short ones (ref. I04), Is to be preferred over weak,

intermediate and strong

(ref. 27), however,

havlng

the potentlal

317 (Fig. 3) in mind, we think a separation

energy curves strong

-

asymmetric

and

closely

symmetric

Into, posslbly- weak and

H-bond

to

be

sufficient

for

the purpose of a qualitative descrlptlon.

APPENDIX The potential

curves

For the calculatlon method

of

potential

of the energy levels,

quantlzatlon

(ref.

curve is necessary,

moves in the different

-

ConsequentZy, the potential

it

(see

according

below),

to the Bohr-Sommerfeld

the knowledge

in which the oscillator

of

the total

- in our case the proton

states of quantlzatlon.

was

values,

105}

necessary

which

to

where

1:

supplement

calculated

for

the mirror

certain

image

of

C1-H-dlstances


/2 by AlmlSf (ref. 61), and 2. to combine the polnts calculated by ClCl polynomials. As the zero point of the energy scale of the potential curves we took the potential minimum of the free HC1 molecule. The

symmetric

contlnuatlon

of

the potential

the framework of ab Inltlo calculations, whether

the H-atom

orlglnally belonged the answer

to

(proton)

in

too.

reality

curves

question

does

not

correct

It is an open question, "knows",

to

in the course of its osclllatlons

this

is

seem

to

which

however,

"Cl-lon"

across R m m / 2 .

be

relevant

in

to

it

However,

the results

dlscussed. Adjacent polynomlal

polnts

of

the potential

curve

were

combined

by

a

3 rd

order

of the form y=ax3+bx2+cx.

For the treatment

of the potential

curves with Hclcl=4.34A,

H

=m, it was necessary to add the following polnts ClCl (I. 137A, 0 kcal/mol), (1, I16A, 5 kcal/mol) and

respectlvely,

at

the slde of the H-bonded

to the potential (I. 518A;

points were obtained by comparison

curves

those

=4.02A

for

of R

=4.34

and 4.76A

curves

15 kcal/mol),

"Cl-lon °' (indicated

Fig. 3). These addltlonal of R

IRclm--4.76A and

by

clrcles

in

of the potential

and of

the R =4.76 ClCl CICI CIC1 -=m. Evaluation of the senslvlty of the CIH stretching frequency cIc! change of the points of the potentlal curve in the rcl H dlrectlon by

curve for R to

a

+O.05A

ylelded

a varlatlon

stretchlng frequency.

of

Gulssanl

57, in

the fundamental

CIH

points,

will not influence our results markedly.

of the energy levels and

the electrlcal

RataJczak

(ref.

and mechanlcal

frequencies

of H-bonded systems. to

considering

I06)

thoroughly

anharmonlclty

be

reduced

approximately

This shows that the cholse of the few additional

necessary for our calculation,

Calculation

only

calculated

on the posltlon

the effect

of

of X-H stretching

These authors showed that the calculation may

a one-dimenslonal

quantummechanical

oscillator

in

318

an average

force

the Cl-atoms In

fleld.

we

model,

the periodic

two turning

points

r

periodic

movement

Bohr-Sommerfeld §pdr = (v+I/2)h we

r

2 write

consider

the positions

of

movement

of

of

the H-atom

the potential

the phase

curve

takes

V(r).

integral,

place

For

this

according

to

105}:

(v=0,1,2 .... }

quantlze

oscillator,

1

can

we

(ref.

and

may

as fixed.

the classical

between

if

Simplifying,

in [Cl---H...C1]--complexes,

the zero

(p=Impulse

(AI)

point

of

vibration

the oscillating

analogously

mass,

to

r=coordlnate

the harmonic of

movement,

h=Plancks constant and v--vlbrational quantum number}. In our case one osclllatlon corresponds r (v) 2S 2 pdr = (v+l/2)h r (v) 1 With

(v=0,1,2 .... )

the connection

the oscillator determine

between

in the quantum

E(v)

{ref.

107}.

given by the condition, SchiSberg are

(ref.

exactly

to:

(A2}

the impulse

p

and

the energy

state v as given by the potential

Doing

this,

the turning

points

are

of

we may

slmultanously

that V(r1(v}} = E(v) = V(r2{v}).

107) showed for the most important potential

soluble

E(v)

V(r},

by

wave

mechanlcs,

coincide exactly with the corresponding

that

the energy

curves,

nlveaus

which

obtained,

energy elgen values of the Schr~dlnger

equation. In

the sence

potentlal

of

our

barrier,

the phase integral

we

"seml-classlcal" have

considered

for

quantum

potential

state

as

curves

with

°'forbldden",

if

in equation AI or A2 was too small on the one hand to raise

the corresponding

energy

level above

the potential

hand too large to permit an oscillation wells.

ansatz a

Consequently,

we

have

barrier,

and on the other

only within one of the two potential

excluded

tunneling

of

the H-atom

through

the potential barrier. If we

consider

both potential

the phase

integral

for

the vibrational

(ref.

I08).

the free

This

HCI.

localization

(I.e.

we permit

frequency

wells

(if present)

tunneling}, Po_I(CIH)

is about half of the value This

makes

tunneling

in

we get

(Fig. 6)

for as

the integration the limiting

only

about

of the fundamental

the sence

of wave mechanics not very probable.

of

of

value

1500cm -1

frequency

the probability

of of

319 REFERENCES 1 H. K l e e b e r g ,

ln: I n t e r a c t i o n s o f Water I n I o n i c and N o n l o n l c H y d r a t e s (H. K l e e b e r g , e d . ) , S p r l n g e r V e r l a g , H e l d e l b e r g , p. 89 (1987). 2 H. K l e e b e r g , J. Mol. S t r u c t . , 177 (1988) 157. 3 H. K l e e b e r g and W.A.P. Luck, Z. phys. Chemle, L e i p z i g , 270 (1989) 613. 4 H. K l e e b e r g , G. H e l n J e and W.A.P. Luck, J. Phys. Chem., 90 (1986) 4427. 5 H. K l e e b e r g , G. H e l n J e , T. Kammer and W.A.P. Luck; ( i n p r e p a r a t i o n ) . 6 H. K l e e b e r g , D. K l e l n and W.A.P. Luck, J. Phys. Chem., 91 (1987) 3200. 7 H. K l e e b e r g , W.A.P. Luck and K. R a n g s r l v a t a n a n o n , ( i n p r e p a r a t i o n ) . 8 G.L. J o h n s o n and L. Andrews, J. Amer. Chem. S o c . , 104 (1982) 3043; L. Andrews, J. Phys. Chem., 88 (1984) 2940. 9 K.M. Harmon and R.R. L o v e l a c e , J. Phys. Chem., 86 (1982) 900. 10 S. S c h e l n e r , Acc. Chem. R e s . , 18 (1985) 174; S c h e l n e r S . , J. Hol. S t r u c t . , 177 (1988) 79. 1 1 J . Emsley and P.A. Hoyte, CS D a l t o n , (1976) 2219; J. FJnsley, P.A. Hoyte and R.E. O v e r l l l , JCS P e r k l n I f , (1977) 2079. 12 H. F o g l l z z o and A. Novak, J. Chem. P h y s . , 66 (1969) 1539. 13 F. H l b b e r t , Acc. Chem. R e s . , 17 (1984) 115. 14 G. Zundel and J. F r l t s c h , J. Phys. Chem., 88 (1984) 6295; G. Zundel J. Hol. S t r u c t . ; 177 (1988) 43. 15 P.V. Huong and G. Noel, S p e c t r o c h l m . A., 32 (1976) 831. 16 A. K o l l , H. Rospenk and L. Sobczyk, J. Chem. S o c . , F a r a d a y Trans. I, 77 (1981) 2309. 17 G.M. Barrow and E.A. Yerger, J. Amer. Chem. S o c . , 76 (1954) 5211; E.A. Y e r g e r and G.H. Barrow, J. Amer. Chem. S o c . , 77 (1955) 4474; G.M. Barrow, J. Amer. Chem. S o c . , 78 (1956) 5802; E.A. Y e r g e r and G.M. Barrow, J. Amer. Chem. S o c . , 77 ~1955) 6206. 18 A. Fersht et al., Enzyme Structure and Mechanisms, 2 na edltlon; Freeman & Co., New York (1985). 19 A. Fersht et at., Nature, 314 (1985} 235. 20 T. Alber et al., Nature, 330 (1986} 41. 2 1 A . Fersht et al., Nature, 322 (1986) 284. 22 P. Carter and J.A. Wells, Nature, 332 (1988} 564. 23 D. Had~l, J. Mol. Struct., 177 (1988} 1. 24 D. Hadzl, B. Orel and A. Novak, Spectrochlm. A., 29 (1973) 1745. 25 Ph. Colomban and A. Novak, J. Mol. Struct., 177 (1988) 277. 26 J.-O. Lundgren and I. Olovsson, in: P. Schuster et al. (Eds.), The Hydrogen Bond -Recent Developments In Theory and Experiments, North-Holland Publ. Co., Amsterdam, 1976, p. 471. 27 A. Novak, Structure and Bondlng, Vol. 69, p. 97, Springer Verlag, Berlin, 1989. 30 M. Falk and O. Knop, in: F. Franks (Ed.), Water, a Comprehensive Treatise Vol. 2, Plenum Press, New York, 1973, p. 55. 31 I.D. Brown, Acta. Cryst., A32 (1976} 24. 32 K.K. Wu and I.D. Brown, Acta Cryst., B31 (1975} 890. 33 A. Sequelra, I. Bernal, I.D. Brown and R. Fagglanl, Acta Cryst., B31 (1975} 1735. 34 I.D. Brown, Acta Cryst., A32 (1976) 786. 35 D.T. Cromer, M.I. Kay and A.C. Larsson, Acta Cryst., 22 (1967) 182. 36 T.M. Sablne, G.W. Cox and B.M. Carven, Acta Cryst., H25 (1969} 2437. 37 B. Berglund, J. Llndgren and J. Tegenfeldt, J. Idol. Struct., 43 {1978} 179. 38 A. Erlksson, M.A. Husseln, B. Berglund, J. Tegenfeldt and J. Llndgren, J. Mol. Struct., 52 (1979) 95. 39 A. Erlksson, B. Berglund, J. Tegenfeldt and J. Llndgren, J. blol. Struct., 52 {1979) 107. 40 G. Olovsson, I. Olovsson and M.S. Lehmann, Acta Cryst.; C40 (1984) 1521.

320 4 1 W . Joswlg, H. Fuess and G. Ferrarls, Acta Cryst., B38 {1982) 2798. 42 M. Ichlkawa, Acta Cryst., B34 (1978) 2074. 43 J.N. van Nlekerk., F.R.L. Schoenlng and J.H. Talbot, Acta Cryst., 6 (1953) 720. 44 G.C. Plmentel and C.H. Sederholm, J. Chem. Phys., 24 (1956} 639. 45 K. Nakamoto, M. Margoshes and R.E. Rundle, J. Am. Chem. Soc., 77 {1955) 6480. 46 L.J. Bellamy and A.J. (]wen, Spectrochlm. A., 25 (1969) 329. 47 B. Berglund, J. Lindgren and J. Tegenfeldt, J. Mol. Struct., 43 (1978) 169 48 S. Detonl, L. Diop, R. Gunde, D. Hadzl, B. Orel, A. Potler and J. Potler, Spectrochlm. A., 35 {1979} 443. 49 J. Emsley, Chem. Soc. Rev., 9 (1980) 91. 50 R.C. Lord and R.E. Merrlfleld, J. Chem. Phys., 21 (1953) 166. 5 1 R . E . Rundle and M. Parasol, J. Chem. Phys.,20 (1952} 1487. 52 D. Had~i and B. Ore1, J. Mol. Struct., 18 (1973) 277. 53 A. Nova/(, J. Chem. Phys., 72 (1975} 981. 54 A. le Navor, P. Saumage and A. Novak, J. Chem. Phys., 64 {1967} 1643. 55 V. Videnova-Adrabi~ska, J. Mol. Struct., 177 (1988) 477. 56 J. Baran, J. Mol. Struct, 172 (1988} 1. 57 J. Baran, J. Mol. Struct, 162 (1987) 211. 58 J. Baran, Spectrochlm. A., 42A (1986) 12, 1365. 59 L. Sobczyk, personal communication. 60 J. Baran, J. Mol. Struct, 162 {1987) 229. 6 1 J . Alm15f, J. Mol. Struct., 85 (1981} 179. 62 B.S. Ault and L. Andrews, J. Chem. Phys., 63 (1975) 2466. 63 D.E. Milllgan and M.E. Jacox, J. Phys. Chem., 53 (1970) 2034. 64 P.N. Noble and G.C. Pimentel, J. Chem. Phys., 49 (1968) 3165. 65 T. Saltoh and R. Itoh, J. Mol. Struct., 177 (1988} 449. 66 E.P. Westrum and K.S. Pitzer, J. Amer. Chem. Soc., 71 (1949) 1940. 67 I. Kurnlg, M.M. Szczc~nlak and S. Schelner, J. Phys. Chem., 90 (1986} 4253. 68 K.M. Harmon, S.L. Madeira and W. Carllng, Inorg. Chem., 13 {1974) 1260. 69 J.A.A. Ketelaar and W. Vedder, J. Chem. Phys., 19 (1951) 654. 70 S.A. McDonald and L. Andrews, J. Chem. Phys., 70 (1979} 3134. 7 1 A . StegArd, A. Strlch, J. Alm15f and B. Broos, Chem. Phys., 8 (1975) 405. 72 J. A1m15f, Chem. Phys. Lett., 17 (1972} 49. 73 E. Grech, Z. Malarskl and L. Sobczyk, Chem. Phys. Lett, 128 (1986} 259. 74 E. Grech, Z. Malarskl, M. Ilczyszyn, O. Czupl~skl, L. Sobczyk, J. Rozi~re, B. Bonnet and J. Potler, J. Mol. Struct., 128 (1985} 249. 75 G.V. Yukhnevich and E.G. Tarakanova, J. Mol. Struct., 177 {1988) 495. 76 O. Glemser and E. Hartert, Z. f. Anorg. u. Allgem. Chem., 283 (1956) 111. 77 R.A. Buchanan, J. Chem. Phys., 31 (1959) 870. 78 W.R. Busing and H.W. Morgan, J. Chem. Phys., 28 (1958) 998. 79 R.A. Buchanan, E.L. Kinsey and H.H. Caspers, J. Chem. Phys., 22 (1954) 217. 80 K.A. Wickershelm, J. Chem. Phys., 31 (1959} 863. 81 W.R. Busing and H.A. Levy, J. Chem. Phys., 26 (1957) 563. 82 B.A. Phlllps and W.R. Busing, J. Phys. Chem., 61 (1957} 502. 83 W.R. Busing, J. Chem. Phys., 23 {1955} 933. 84 H.D. Lutz, W. Eckers, G. Schneider and H. Haesler, Spectrochim. A., 37 (1981) 561. 85 I. 01ovsson, Proceedings from Symposium on Organic Crystal Chemistry, Kiekrz-Pozna~, 4-7 Sept. (1980). 86 K. Hermansson and S. Lune11, Chem. Phys. Lett., 80 {1981} 64. 87 K. Hermansson, I. 01ovsson and S. Lune11, Theoret. Chlm. Acta (Berl.); 64 (1984) 265. 88 M.P. Gupta, C. van Alsenoy and A.T.H. Lenstra, Acta Cryst., C40 (1984) 1526. 89 M. Falk, Spektrochlm. A., 40 (1984) 43.

321 90 H. Lln, in: H. Eyrlng (Ed.), Physical Chemistry - An Advanced Treatlse Vol. V, Academlc Press, New York, 1970, p. 439. 9 1 T h . Zeegers-Huyskens, Chem. Phys. Lett., 129 {1986) 172; J. Mol. Struct.; 177 (1988) 125. 92 R.C. Weast {Ed.}, Handbook of Chem. and Phys., 59th edn., CRC Press Inc., Florida, 1978. 93 P. Kollman, J. McKelvey, A. Johansson and S. Rothenberg, J. Am. Chem. Soc., 97 {1975) 955. 94 K. Morokuma, Acc. Chem Res., 10 {1977} 294; K. Kltaura and K. Morokuma, Int. J. Quant. Chem., X (1976} 325. 95 R.M. Badger and S.H. Bauer, J. Chem. Phys., 5 {1937} 839; R.M. Badger, J. Chem. Phys., 8 (1940) 288. 96 H. Kleeberg, W.A.P. Luck and H.Y. Zheng, Fluld Phase Equil., 20 (1985) 119. 97 H. Kleeberg, O. Kodak and W.A.P. Luck, J. Solution Chem., 11 (1982) 611. 98 H. Ratajczak, W.J. Orvllle-Thomas and C.N.R. Rao, Chem. Phys., 17 (1976) 197. 99 C.N.R. Rao, P.C. Dwlvedl, H. RataJczak and W.J. Orville-Thomas, JCS, Faraday Trans. II, 71 (1975) 955. 100 M. Rospenk and Th. Zeegers-Huyskens, Spectrochlm. A., 42A (1986) 499. 1 0 1 M . Rospenk and Th. Zeegers-Huyskens, J. Phys. Chem., 91 (1987) 3974. 102 I. Olovsson, in: P. Becker (Ed.}, Electron and Magnetization Densltles In Molecules and Crystals, Nato Advanced Study Set. B, Vol. 48; Plenum Press, New York, 1980, p. 879. 103 B.S. Ault, E. Stelnback and G.C. Plmentel, J. Phys. Chem., 79 {1975) 615. 104 J.C. Speakman, Struct. Bonding (Berlln), 12 (1972) 142. 105 A. Sommerfeld, Atombau und Spektralllnlen, Vol. 1; 8th edn., Harrl Deutsch-Thun, Frankfurt/Id., 1978, p. 87. 106 Y. Gulssanl and H. Ratajczak, J. Chem. Phys., 62 (1981) 319. 107 D. SchlSberg, Mabllltatlonsschrlft, University of Marburg, Marburg, FRG, 1986. 108 W.A.P. Luck and T. Wess, in preparation.