The nature of the hydrogen bond in the bifluoride ion

HAL Id: jpa-00205810

https://hal.archives-ouvertes.fr/jpa-00205810

Submitted on 1 Jan 1964

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

The nature of the hydrogen bond in the bifluoride ion

James A. Ibers

To cite this version:

James A. Ibers. The nature of the hydrogen bond in the bifluoride ion. Journal de Physique, 1964,

25 (5), pp.474-477. �10.1051/jphys:01964002505047400�. �jpa-00205810�

THE NATURE OF THE HYDROGEN BOND IN THE BIFLUORIDE ION (1) By ^{JAMES A.} IBERS,

Chemistry Department, Brookhaven National Laboratory, Upton, Long Island, ^New York, ^{U. S. A.}

Résumé.

Les intensités de diffraction neutronique ^de monocristaux de NaHF2 ^{et de} NaDF2

ont été analysées ^{sur la base de} plusieurs ^modèles proposés pour la géométrie ^de l’ion bifluorure.

Dans le fluorure acide de sodium, l’ion bifluorure doit être linéaire et les deux atomes F doivent être équivalents. ^La distance F-H-F est 2,264 ^± 0,003 A, la distance F-D-F est 2,265 ± 0,007 Å.

Les données de diffraction neutronique obtenues par Peterson et Levy ^{dans leur étude d’un}

monocristal de KHF2 ont été raffinees pour essayer de résoudre le problème ^{de la} géométrie ^de

l’ion bifluorure dans KHF2. La distance F-H-F est 2,277 ± 0,006 Å.

Ni dans le fluorure acide de sodium, ^{ni dans celui de} potassium, ^{il n’est} possible ^de distinguer ^sur

la seule base de données de diffraction, ^{entre un} modele symétrique ^de l’ion bifluorure et un modèle dans lequel le potentiel ^de l’hydrogène (ou ^de deutérium) ^le long de la liaison aurait deux minima égaux ^de chaque ^{côté du} centre, ^{même si ces minima sont à une distance de l’ordre de} 0,15 A du centre.

Cependant, ^en comparant ^les différences, _pour ^{H et} F, ^de leurs carrés moyens d’amplitude ^de

vibration ^le long ^{de la} liaison, déduites soit de l’analyse des données de diffraction, ^{soit des fré-}

quences spectroscopiques, ^{on conclut dans les deux cas} que l’ion bifluorure ^est symetrique.

Abstract.

Neutron diffraction data, obtained from single crystals ^{of NaHF2 and NaDF2, have}

been analyzed in terms of several models for the bifluoride ion geometry. In sodium acid fluoride the bifluoride ion must be linear and the two fluorine atoms equivalent. The F-H-F distance is 2.264 ± 0.003 Å, the F-D-F distance is 2.265 ± 0.007 Å.

The neutron diffraction data obtained by ^{Peterson and} Levy from a single crystal ^of KHF2 ^have

been refined in an attempt ^{to settle the} question ^{of the} geometry ^{of the} bifluoride ion in KHF2.

The F-H-F distance is 2.277 ± 0.006 Å.

In neither sodium acid fluoride nor potassium ^{acid fluoride is it} possible ^{from the} diffraction data alone to distinguish ^{between a} symmetric ^{model for the} bifluoride ion and one in which the poten- tial for the hydrogen (or deutérium) along the bond has two equal ^{minima on} either side of the center, ^even when these minima are 0.15 Å or so from the center. However, ^{in both cases from a} comparison ^between the differences in mean-square amplitudes of vibration along ^{the bond of} hydrogen (or deuterium) ^{and fluorine as obtained from the} analysis ^{of the} diffraction data and as

calculated from the spectroscopic frequencies ^{it is} concluded that the bifluoride ion is indeed _sym- metric.

PHYSIQUE 25, 1964,

Introduction.

The literature on the F-H-F iun in KHF2 ^{is extensive} ~1]. ^The principal

reason for this is the interest in strong hydrogen bonds ; the F-H-F ion contains one of the stron-

gesL hydrogen ^{bonds kno.wn.} Although ^{the sim-} plest interpretation ^{of the} spectroscopic ^{and bulk}

measurements on the bifluoride ion in KHF2 ^is

that the ion is linear and symmetric, ^{there remain}

certain difficulties involving ^the divergence ^{of the}

energy levels and the isotropic dependence ^{of the} frequencies which Blinc [2] ^has called attention to.

We undertook the present diffraction study ^of

the bifluoride ion in sodium acid fluoride and the

present refinement of the earlier data [3] ^on potas-

sium acid fluoride with the hope ^of obtaining ^more

accurate information not only ^{on the} position ^of

the hydrogen atom, ^{but also on} the vibrations of the ion. We felt that it would be through ^the

combination of information on the motions of the

system from diffraction and spectroscopic ^studies

(1) ^Work performed under the auspices of the U. S.

Atomic Energy Commission.

that the question ^{of the} symmetry ^{of the iron could}

be settled. In this paper ^we summarize briefly [4]

the results of our diffraction study and show that these data, in combination with the spectroscopic data, provide ^{new, and we feel} convincing, ^evi-

dence that the F-H-F ion is linear and symmetric.

Unit cells and possible space groups.

In a

series of precession ^and Weissenberg photographs

taken with MoKoc radiation it was confirmed that

NaHF 2 ^and NaDF 2 ^{have Laue} symmetry 31n,

with systematic absences of the hexagonal ^in-

dices [5] corresponding ^{to the} trigonal system.

The cell dimensions, ^{based on}

^{5.6402 at}

27 oC, ^are

-NaHF2 a ^{= 3 .476} ± 0.002 A,

= 13 . 76 ± ^0.01 A,

= 3.474 ± ^0.002 A,

^{13.75 ± 0.01 A.}

The density calculated for three molecules of

KaHF 2 ^{in the} triply primitive hexagonal ^{cell is}

2.14 g/CM2 ^versus that of 2.08 g/CM2 ^measured by Andersen and Hassel [6].

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01964002505047400

475 The space groups consistent with the diffraction

symbol ^{R3rra are} Dga-R3¡n, C-5,-R3m 3 ^and D¡-R32.

As ^a result of calculations described elsewhere [4]

models for these structures based on the non-

equivalence of the fluorine atoms (i.e., ^are improbable. Accordingly ^{we shall consider} only

two possible models for the NaHF2 structure : Na at (0, 0, 0), ^{F at} 1 (0, 0, ZF) ^{with ZF ~ 0.41} f 6],

and 1/2 ^H (or 1/2 D) at + (0, 0, zH). ^{If ZH}

1.~2,

the H atom is centered (model 1) ; ^if zil 1/2,

the H atom is distributed randomly ^but symme-

trically ^on either side of the center (model 2, ^a symmetric ^{double minimum} potential ^{well with}

the ground ^{level below the} barrier).

From both _x-ray studies and the neutron dif- fraction study [3] ^it is known that KHF2 ^{is tetra-} gonal, ^{with four molecules in a cell} of dimensions

a

5.67, ^c

^{6.81 A.} The space group ^is The potassium ^atoms occupy the

positions (4a) ^{~ (0, 0,} 1/4) (+ body centering).

The fluorine atoms occupy ^the positions (8h) ± (x, 1/2 + x, 0), + (1I2 + x, x~ 0)

with 0.1.4 [7]. Half-hydrogen ^{atoms also}

occupy position (8h) ; ^{for x}

^{0 we} obtain model 1,

we obtain model 2.

Collection and reduction of the neutron diffrac- tion data. - D ata were collected at room tempera-

ture from single crystals ^of NaHF2 ^and NaDF2 ^on

one of the Brookhaven single crystal spectrometers.

The neutron wavelength ^{was 1.073 A. The values}

of I and a(1) ^were reduced in the usual _way to values of F5 ^and Estimated standard deviations

a(l) ^were obtained from a combination of the usual

errors based on the counting statistics with the factor (0.05 ^X 1) ^which attempts ^{to allow for}

errors inherent in the crystals, ^for example ^for

those factors which give ^{rise to} differences between the intensities of hkl and hkl. In all there ^were 52

non-zero independent F20 values ^for NaHF2 ^{and 44}

for NaDF2. ^For KHF 2 ^{the values of} F~ ^and cr(F 0) given by Peterson and Levy [3] ^were used without further modification, except ^for rescaling. ^There

were 43 non-zero values of F O.

Analysis of the diffraction data.

Because of the limited number of data, ^{the reliable error esti-}

mates for these data, ^{and our desire to obtain} easily the thermal parameters ^{of the} atoms, ^we

chose to analyze ^{the data} by least-squares ^rather

than by ^Fourier techniques. ^All least-squares ^cal-

culations were carried out on an IBM 7094 com-

puter, using ^{the local} modification of the Busing- Levy ^ORFLS program. For sodium acid fluoride refinements were carried out on F2 ; ^for potassium

acid fluoride refinements were carried out on F.

In all refinements the thermal motions of the atoms were taken to be anisotropic. ^{For the}

sodium salt the appropriate form of the tempe-

rature factor (which ^{modifies the} scattering ampli-

tude bi of atom i) is, ^{for the} general ^harmonic

oscillator

where ul >i and >i ^are the mean-square

amplitudes ^{of vibration} of atom i normal to and

along ^the F-H-F bond. For the potassium ^{salt it}

is more convenient to write the temperature ^factor

as

The mean-square amplitudes ^{of vibration for}

each atom are then

where u211 > is normal to the bond in the plane

z

0 and ul~ > ^{is normal to the bond along c.}

For the potassium atomP12

0, by symmetry.

Least-squares refinements for both the sodium and potassium ^salts diverge ^{if the} position para- meter of the 1/2 H is allowed to vary. This is because as the models tend toward model 1 the matrix of normal equations ^is nearly singular ^and spurious ^{shifts occur.} Accordingly ^{it is most con-}

venient to carry out the least-squares refinements for fixed values of the 1/2 ^H parameters.

Thus with zH (or ^zD) constrained there are for

NaHF2 eight parameters, ^{the fluorine} positional parameter, ^{the two thermal} parameters ^{for each}

of the three atoms, ^and the scale factor to be deter- mined from the 52 observations. There is in addi- tion the deuterium scattering amplitude (i.e., ^the percentage deuteration) ^{to be} determined from the 44 observations for NaDF 2. We find for both

NaHFz ^and NaDF2 that there is no significant

FIG. 1.

The variation of > for H and D with

distance of H and D from the center of the bond in

NaHF2 ^and NADF..

change ^{in the} agreement ^between F20 ^{and as zH}

or zD ranges from 1/2 ^to 0 . 48, ^{that is as the} hydro-

gen ^or deuterium is allowed to move up ^to 0 . 2 A

from the center. Only ^the mean-square ampli-

tude of vibration along ^{the bond of the} hydrogen

or the deuterium changes significantly ^{as zH or zD}

is changed ( fig. 1) ; ^{the other} parameters ^{are vir-} tually independent ^{of the value of zH or zD. Thus}

it is impossible ^{in the} diffraction experiment ^{to dis-} tinguish between models 1 and 2.

With xg constrained there are for KH F 2 ^eleven parameters, ^{the fluorine} positional parameter, ^the

three thermal parameters ^for F, ^{the three thermal} parameters ^for H, ^{the two thermal} parameters

for K, ^{and two scale} factors, ^{to be determined}

from the 43 non-zero values of Fo. ^{As in the}

sodium problem ^{as the} hydrogen ^{is moved off}

center there is no change ^{in the} agreement ^between Fo ^{and ~~ and the} only variable which changes significantly ^{is the} mean-square amplitude ^{of vi-}

bration of the hydrogen along ^the bond, u; > H.

In figure ^{2 we show the} variation of uft > g

FIG. 2.

The variation of P12, ^{and derived} quantities

for KHF2 with distance of the hydrogen ^{atom from the}

center of the bond. Note that U 2 > H ^is proportio-

nal to ~11 + PIL2’

(proportional to B11 + B12) ^{with distance of H}

from the center. Again ^{we are forced to conclude}

that from ^{the neutron} diffraction data alone it is

impossible ^to distinguish ^{models 1} from ^{2 over a}

reasonable _{range of} values of xH.

Combination nf diffraction and spectroscopic ^data.

- The thermal vibrational amplitudes ^determined

from the neutron diffraction data are the sum of all motions undergone by ^{these atoms. In the}

absence of a complete analysis ^{of the} vibrations of

the crystal ^{it is an} impossible ^{task to calculate}

these amplitudes ^from theory. ^{If one makes the}

reasonable assumption ^that the vibrational ampli-

tude of hydrogen (or deuterium) along ^{the bond}

must be less than that of fluorine, ^{then the res-}

trictions indicated in figure ^{1 can be} placed ^{on the}

distance of the light ^{atom from the center of the}

bond. However, the differences in amplitudes ^of hydrogen ^{and fluorine} along the bond arise only

from those motions in which the hydrogen ^and

fluorine do not move together, ^{that is} only ^{from the} stretching vibrations along ^the bond, ^{and these are} essentially zero-point vibrations. Assume then the simple ^linear symmetric F-H-F ion. It is then easy ^to derive from a normal-coordinate treatment that

where _v3 is the asymmetric and V1 ^{the sym-}

metric stretching frequency. With the values

~(H) = 1 ^{577 and} v3(D)

^{1150 cm--1 for} NaHF2 ^and NaDF2 [8], v3(H) == 1"450 ^{em-- for} KH F 2 [9] ^{and the} value v1 = ^{600 for} KH F 2 [10] (and assumed for NaHF2 ^and NaDF 2) ^we

obtain for the calculated values of A 0.0097, 0.0062, and 0.0106 A2 for NaHF2, N aD F 2, ^and KHFz. ^These calculated values are compared

with the experimentally derived values in figures ³

and 4. The agreement between the calculated

FIG. 3.

The differences in mean-square amplitude ^of

vibration along the bond of H or D and F versus the distance of H

D from the center of the bond in NaHF2

and NaDF2.

values (where ^{a linear} symmetric ^{bond is} assumed)

and those obtained from the neutron diffraction

data for model 1 is excellent. This agreement, ^we

feel, provides ^{the most} powerful evidence that the

F-H-F and F-D-F bonds are symmetric.

477

4.

The difference in mean-square amplitude ^of

vibration along the bond of H and F versus the dis- tance of H from the center in KHF2.

The final positional parameters ^{for F in}

these compounds ^are [0.41772 :t 0.00009, 0.41760 + 0.00024, ^{and 0.1420} ± ^{0.0003 and} lead to F-H-F lengths ^{of 2.264 ~} 0.003, 2.265 fi 0.007, ^and 2.277 ± ^0.006 k in NaH F NaDF2, ^and KHF2.

Discussion

Pr PosT.

Des mesures pl6zo6lectriques ^ont-

elles été faites sur ces fluorures ?

Dr IBERS.

Je ne suis _pas au courant de me- sures sp6eifiques, mais je suis raisonnablement ^cer- tain qu’elles ^ont été faites et qu’aucun ^effect pi6zo- 6lectrique n’a été trouv6.

Pr WALLACE. - Si la fonction potentiel ^{a deux}

minima avec un seul maximum intercalaire 16g6-

rement au-dessous de 1’6nergie ^{du niveau station-} naire, ^ne pourrait-on pas obtenir une difference dans le comportement des ions FHF et FDF ? Une telle différence a-t-elle été observ6e ?

Dr IBERS.

Blinc a envisag6 ^{une fonction} poten-

tiel intermediaire entre une fonction sym6trique

et une fonction a double minimum, ^{avec les deux}

minima legerement deplaces ^du centre, ^{et une} barrière de faible hauteur par rapport ^{au niveau}

fondamental. De la sorte, ^la premi6re ^{vibration est}

une transition 0A - Os, ^ou PlUt6t 0 --> I - J’ai mal cite Blinc lorsque j’ai ^dit que la barri6re etait juste ^en

dessous du niveau fondamental.

Dr ABRAHAMS. - Dans quelle ^{mesure le mou-}

vement vibratoire des atomes d’hydrog6ne ^est-il

du a une agitation ^{au zero absolu ?}

Dr IBERS.

Les vibrations sym6triques ^et assy-

metriques ^de translation, ^celles qui ^{nous int6res-}

sent sont essentiellement des vibrations au zero absolu puisqu’elles ^se produisent ^{aux environs de}

1 500 et 600 cm-1.

REFERENCES

[1] ^{Reference 2} contains references to many of ^these studies.

[2] ^BLINC (R.), Nature, 1958, 182, ^1016.

[3] ^PETERSON (S. W.) ^{and LEVY} (H. A.), ^{J. Chem.} Physics, 1951, 20, ^704.

[4] ^This work is described in greater ^detail in J. Chem.

Phys., 1964, 40, ^402.

[5] Throughout ^this paper ^we refer the structure of

NaHF2 ^{to the} triply primitive hexagonal ^cell.

[6] ^ANDERSEN (C. C.) and HASSEL (0.), ^Z. Krist., 1926, 123, 151.

[7] ^HELMHOLZ (L.) and ROGERS (M. T.), J. Am. Chem.

Soc., 1939, 61, ^2590.

[8] Unpublished ^{results of R. G. SNYDER.}

[9] ^COTÉ (G. L.) and THOMPSON (H. W.), ^Proc. Roy. Soc., 1951, A210, ^206.

[10] COUTURE-MATHIEU (L.) and MATHIEU (J. P.), ^{C. R}

Acad. Sc., 1950, 230, 1054.