Crystal structure and low-temperature methyl-group dynamics of cobalt and nickel acetates

Crystal structure and low-temperature methyl-group dynamics of cobalt and

nickel acetates

B. Nicolaï, G. J. Kearley , M. R. Johnson , F. Fillaux , and E. Suard

Citation: J. Chem. Phys. 109, 9062 (1998); doi: 10.1063/1.477577

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JOURNAL OF CHEMICAL PHYSICS

VOLUME 109, NUMBER 20

22 NOVEMBER 1998

Crystal structure and low-temperature methyl-group dynamics of cobalt

and nickel acetates

B. Nicola ¨ı , G. J. Kearley, and M. R. Johnson

ILL, BP 156, 38042 Grenoble, Cedex 09, France

F. Fillaux

LASIR-CNRS, 2 rue Henry-Dunant, 94320 Thiais, France

E. Suard

ILL, BP 156, 38042 Grenoble, Cedex 09, France

͑

Received 22 June 1998; accepted 11 August 1998͒

The crystal structures of cobalt and nickel acetate tetrahydrate have been determined at

room-temperature and liquid-helium temperature by neutron powder diffraction of the fully

deuterated salts. Molecular mechanics and ab initio methods based on these structural results have

then been used to calculate the rotational potentials experienced by the methyl groups. We have also

used inelastic neutron scattering to measure the rotational potential via the rotational tunneling

spectrum of the methyl groups, and this has enabled us to compare different methods for the

calculation of partial charges in these ionic compounds. Good agreement between the observables

and calculations has been obtained for both compounds when ab initio methods are used to

Physics. ͓S0021-9606͑98͒00743-0͔

I. INTRODUCTION

agreement can often be achieved, but accurate structural data

must be available for the crystal at the same temperature as

the tunneling measurements.

Quantum rotational dynamics of methyl groups at low

temperature is well known as a highly sensitive probe of

local potentials in molecular crystals. In the present paper we

are interested in using this sensitivity to investigate the de-

termination of partial charges within the monopole approxi-

mation. Provided that the rotational barrier is not too high

The total rotational potential of a methyl group in a crys-

tal can be regarded as the sum of an intramolecular interac-

tion ͑the rotational potential of an isolated molecule͒, van der

Waals and electrostatic interactions. Although many of the

molecules cited above contain polar or ionic groups, the

electrostatic part only plays a role in the rotational dynamics

of the methyl group when it changes as a function of methyl

orientation. Frequently, Coulomb terms are high but virtually

unchanged by the methyl orientation, and in a few cases

reasonable results have been achieved even when partial

charges have been totally neglected.⁶

͑less than about 50 meV͒, the rotational dynamics are mea-

surable with inelastic neutron scattering ͑INS͒ which pro-

vides a direct observation of the transitions between tunnel-

split librational levels at low temperature. Usually, a single

low-energy transition is observed which arises from the li-

brational ground-state splitting. Where there are several

types of methyl group, one transition is observed for each

crystallographically distinct rotor, each transition being ame-

–8

In the published molecular-mechanics work relating to

methyl tunneling, the electrostatic interactions have been de-

termined within the monopole approximation, that is point

charges centered on the nuclei. The values of these charges

can determined by theoretical or empirical methods, and in

systems where the Coulomb energy is sensitive to methyl

orientation, it can be difﬁcult to obtain agreement between

calculation and experiment. Metal acetates are ideal systems

for studying the use of partial charges since they are ionic,

cover a wide variety of structural classes, and display methyl

tunnelling in a frequency range that is accessible to INS. We

start from the premise that knowing of the low-temperature

crystal structures, we can conﬁdently calculate the internal

and van der Waals contributions to the rotational potential.

Any discrepancy between this calculated potential and that

measured by INS is due to Coulomb terms and we can use

this difference to examine the effects of the partial-charge

distributions by applying a series of models to the cobalt and

nickel salt.

1

nable to the single-particle approach. Cobalt and nickel ac-

etates are isostructural and contain a single type of methyl

group, but nevertheless, both salts show three spectral peaks

in the energy region where methyl tunneling is normally ob-

served. For the purposes of studying partial charges, this ap-

parent complication is unfortunate, but as we will show in

both salts that there is in fact a single type of methyl group

which gives rise to a single tunneling transition.

Several efforts have been made to correlate the poten-

tials extracted from tunneling spectra with structural data, in

order to extract dynamical information. This has been

achieved via ab initio and molecular-mechanics calculations

2

,3

4

with various pair potentials ͑nitromethane, acetophenone,

5

6

7

8

acetamide, p-xylene, diacetyl, halogenomesitylenes, Hof-

mann clathrates, aspirin, acetic acid, a series of organic

9

10

11

1

2

13,14

15

molecules, 2,6 dimethylpyrazine,

lithium acetate ͒.

show clearly that good

The most recent investigations¹

0–15

0021-9606/98/109(20)/9062/13/$15.00

9062

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J. Chem. Phys., Vol. 109, No. 20, 22 November 1998

Nicola ¨ı et al.

9063

We have redetermined the room-temperature crystal

structures of these acetates using neutron powder diffraction

in order to locate the hydrogen ͑deuterium͒ atoms. We have

also determined the crystal structures at 4 K and found that

there is no phase transition on cooling from room tempera-

ture, and that the structures contain a single type of methyl

group.

II. EXPERIMENT

The intense red crystals of Co͑CH COO͒ ,4H O were

3

2

prepared by recrystallization from H O of the commercially

2

available product ͑Prolabo͒. Samples of Co͑CD₃

COO͒ ,4D O were prepared via the reaction of cobalt car-

2

bonate with deuterated acetic acid in D O and puriﬁed by

2

recrystallization from D O. Similarly, the green crystalline

2

samples of nickel acetate were prepared via the reaction of

the nickel carbonate with acetic acid and recrystallized from

water.

For the INS experiments, the hydrogenous polycrystal-

line samples were placed in thin-walled aluminium contain-

ers which were then placed in a standard liquid-helium cry-

ostat with the sample temperature being controlled at 2 K.

The low-energy tunneling spectra were recorded using the

IN16 backscattering spectrometer in its high-intensity con-

ﬁguration ͓unpolished Si͑111͒ analyzers͔ which gave a reso-

lution of 1.2 ␮eV ͓at full width at half maximum ͑FWHM͔͒.

Tunneling spectra at higher energy were recorded using the

time-of-ﬂight spectrometer IN5 with incident wavelengths of

FIG. 1. ͑a͒, ͑b͒ Observed ͑crosses͒, calculated ͑line͒ and difference ͑lower

line͒ diffraction patterns for Co͑CD COO͒ , 4D O at room temperature and

at 4 K. The vertical lines mark the positions of Bragg reﬂections.

3

2

8.81 and 5.00 Å giving resolutions of 19 and 104 ␮eV, re-

spectively. Librational spectra were also obtained using IN5

but with an incident wavelength of 2.0 Å which gave a reso-

lution of 1.63 meV. Vibrational spectra were obtained using

the IN1 beryllium-ﬁlter spectrometer, which has a resolution

Ϫ1

On cooling to liquid-helium temperature, we failed to

of about 7 meV ͑60 cm ͒ in the spectral region of interest,

ﬁnd any structural phase transition, despite previous reports

and the TFXA spectrometer with a resolution equal to 1.5%

of the energy transfer.

from infrared and Raman investigations.¹

9,20

The diffraction

patterns of the cobalt salt at room temperature and liquid-

helium temperature are compared in Figs. 1͑a͒ and 1͑b͒, re-

spectively, with the analogous patterns for the nickel salts in

Figs. 2͑a͒ and 2͑b͒. The low-temperature crystal structure of

the nickel salt is illustrated in Fig. 2͑c͒, the cobalt being

isostructural, and structural data at room and low tempera-

ture are collected in Tables I͑a͒ and I͑b͒ ͑cobalt͒ and II͑a͒

and II͑b͒ ͑nickel͒.

For the diffraction measurements, the deuterated com-

pounds were sealed in thin-walled vanadium containers and

maintained at room temperature and liquid-helium tempera-

ture using a standard cryostat. The neutron powder-

diffraction patterns were obtained using the D1A diffracto-

meter at a ﬁxed neutron wavelength of 1.909 Å. Rietveld

reﬁnement of the patterns was achieved using the GSAS

1

6

program.

III. DESCRIPTION AND DISCUSSION OF THE

STRUCTURE

A. Geometry around the metal atom

Cobalt and nickel acetate tetrahydrate crystalline struc-

tures were originally determined by x-ray diffraction at room

Each metal atom is surrounded octahedrally by four wa-

ter molecules and two oxygen atoms which belong to two

different acetate groups. Because the metal atom occupies a

center of symmetry at ͑0,0,0͒, an octahedron is formed from

three symmetry-related pairs of oxygen atoms. The geometry

and thermal ellipsoids of the octahedral coordination of the

cobalt and the nickel salts are shown in Figs. 3͑a͒ and 3͑b͒,

respectively. There is, however, a slight distortion, the

metal–oxygen bonds being measurably different ͑see Table

III͒.

1

7,18

temperature.

They were found to be isostructural with the

space group P2 /c and Zϭ2. Our work conﬁrmed the es-

1

sential features of the room-temperature structure and lo-

cated the deuterium atoms. The calculated densities of 1.79

3

and 1.80 g/cm for the cobalt salt and the nickel salt, agree

3

well with the measured values: 1.71 and 1.79 g/cm , respec-

tively. There is a single type of acetate group, a single metal

atom, but two crystallographically distinct water molecules.

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9064

J. Chem. Phys., Vol. 109, No. 20, 22 November 1998

Nicola ¨ı et al.

metry at each metal position and a twofold screw axis at

(

1/4)z. The acetates are monodentate with only one oxygen

atom bonding to the metal atom, the remaining oxygen atom

being linked by a hydrogen bond to a water molecule within

the same metal coordination group. The two oxygen atoms

of an acetate group are linked by hydrogen bonds to water

molecules of different groups.

Extensive hydrogen bonding exists. Each acetate is in-

volved in three hydrogen bonds with the surrounding water

molecules, and in addition, the water molecules are hydrogen

bonded to each other. We note that the thermal ellipsoids of

hydrogen atoms in water molecules are almost as large as

those of methyl groups at low temperature, as previously

found in the lithium acetate dihydrate,²

1,15

but again, the wa-

ter dynamics do not appear to effect the tunneling of the

methyl group.

IV. THE ROTATIONAL POTENTIAL

Coherent rotational tunneling is a phenomenon which

occurs in molecular groups whose rotating atoms are indis-

tinguishable such as the hydrogen atoms in a methyl group.

The rotational energy levels of a one-dimensional rotor can

be obtained by solution of the following Schr o¨ dinger equa-

tion in the mean-ﬁeld approach ͑single-particle model͒:

ប²

ͩ

Ϫ

ϩV͑␾͒

ͪ

␺ϭE␺,

͑1͒

2

I

where I is the moment of inertia of the rotor, ␾ the angular

coordinate, and V(␾) the local static crystalline rotational

potential. In this model, the rotor is symmetric and performs

a one-dimensional rigid rotation about its three fold axis. The

rotational potential of CH is periodic and can be expanded

3

in Fourier series as follow:

1

V͑␾͒ϭ

V ͓1Ϫcos͑3n␾ϩ␦₃_n͔͒.

3n

͑2͒

͚

n

2

V₃_nis the amplitude of the 3n-fold contribution and ␦ is a

3n

1

phase. For calculation convenience, the expansion is usually

truncated to the ﬁrst or second order.

Each triply degenerate energy level is split into two tun-

neling states due to the overlap of the wave functions in the

adjacent wells: A states and the doubly degenerate E states.

For simplicity, we distinguish two kinds of transition: tun-

neling transitions ͑in the ␮eV range͒ between the tunneling

states A and E of the librational ground state, and librational

transitions ͑in the meV range͒ between the librational ground

state and the ﬁrst librational excited state. The process is

quantum mechanical and at low temperature, ͑less than about

5

0 K͒ the tunneling transitions can be directly measured by

FIG. 2. ͑a͒, ͑b͒ Observed ͑crosses͒, calculated ͑line͒, and difference ͑lower

line͒ diffraction patterns for Ni͑CD COO͒ , 4D O at room temperature and

INS. Because the tunnel splitting has an approximately ex-

ponential dependence on the rotational barrier height, it is

extremely sensitive to the molecular crystal potentials.

3

2

at 4 K. The vertical lines mark the positions of Bragg reﬂections ͑c͒ Illus-

tration of the crystal structure of M͑CD COO͒ , 4D O with MϭCo or Ni at

3

2

4

K.

V. RESULTS

B. The acetate group and hydrogen bonding

Incoherent neutron scattering is largely dominated by

hydrogen dynamics, the cross section of hydrogen being al-

most ten times greater than the cross section of other nuclei.

Consequently, intense peaks in the 1–600 ␮eV region of the

Within experimental errors, the acetate groups C͑7͒–

C͑6͒–O͑2͒–O͑3͒ are found to be planar. Parallel sheets of

acetate groups ͓Fig. 2͑c͔͒ are generated by the center of sym-

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J. Chem. Phys., Vol. 109, No. 20, 22 November 1998

Nicola ¨ı et al.

9065

2

TABLE I. Atomic positions, occupancy ͑occ͒, and thermal parameters ͑in Å ͒ ͑a͒ for cobalt acetate tetrahydrate

at 1.5 K, ͑b͒ for cobalt acetate tetrahydrate at 300 K.

Atoms

x/a

y/b

z/c

occ

Ui/Ue*100

͑a͒ P21/c, aϭ4.7881(1) Å, bϭ11.8664(3) Å, cϭ8.2376(2) Å, ␥ϭ92.659(2)°.

Co͑1͒

O͑2͒

O͑3͒

O͑4͒

O͑5͒

C͑6͒

C͑7͒

D͑8͒

D͑9͒

D͑10͒

D͑11͒

D͑12͒

D͑13͒

D͑14͒

0.0000͑0͒

Ϫ0.2333͑11͒

0.0820͑8͒

0.0000͑0͒

Ϫ0.1485͑4͒

Ϫ0.2587͑4͒

0.0778͑4͒

Ϫ0.0473͑4͒

Ϫ0.2445͑4͒

Ϫ0.3485͑4͒

Ϫ0.4231͑4͒

Ϫ0.3379͑4͒

Ϫ0.3609͑4͒

Ϫ0.0249͑4͒

0.1233͑4͒

0.0000͑0͒

0.0093͑6͒

0.1484͑5͒

0.1519͑6͒

0.2102͑6͒

0.0563͑5͒

Ϫ0.0113͑5͒

0.0567͑5͒

Ϫ0.0065͑5͒

Ϫ0.1335͑6͒

0.2081͑6͒

0.0933͑5͒

0.1991͑5͒

0.2293͑5͒

1

0.03͑33͒

0.59͑11͒

0.34͑11͒

0.20͑11͒

1.31͑12͒

0.10͑10͒

0.47͑11͒

2.02͑12͒

2.38͑12͒

2.50͑12͒

2.09͑13͒

1.40͑12͒

1.59͑13͒

1.24͑12͒

Ϫ0.2838͑9͒

0.2336͑11͒

Ϫ0.1326͑7͒

Ϫ0.2872͑9͒

Ϫ0.2271͑9͒

Ϫ0.5104͑10͒

Ϫ0.2319͑9͒

0.4341͑10͒

Ϫ0.4414͑9͒

0.2219͑8͒

Ϫ0.1302͑4͒

0.1329͑4͒

Ϫ0.2044͑9͒

͑b͒ P21/c, aϭ4.8214(2) Å, bϭ11.9633(4) Å, cϭ8.4525(4) Å, ␥ϭ94.247(3)°.

Co͑1͒

O͑2͒

O͑3͒

O͑4͒

O͑5͒

C͑6͒

C͑7͒

D͑8͒

D͑9͒

D͑10͒

D͑11͒

D͑12͒

D͑13͒

D͑14͒

0.0000

Ϫ0.2260͑20͒

0.0737͑14͒

Ϫ0.2764͑17͒

0.2461͑17͒

Ϫ0.1390͑11͒

Ϫ0.3013͑17͒

Ϫ0.2562͑26͒

Ϫ0.5090͑26͒

Ϫ0.2308͑19͒

0.4434͑18͒

Ϫ0.4341͑15͒

0.2188͑17͒

Ϫ0.1917͑15͒

0.0000

1

0.7͑5͒

Ϫ0.1422͑7͒

Ϫ0.2563͑7͒

0.0848͑6͒

0.0100͑11͒

0.1559͑8͒

0.1533͑10͒

0.2147͑9͒

0.0654͑6͒

0.0023͑9͒

0.0698͑11͒

Ϫ0.0012͑12͒

Ϫ0.1061͑12͒

0.1926͑10͒

0.0893͑9͒

0.1962͑10͒

0.2240͑8͒

4.73͑23͒

3.71͑21͒

4.02͑25͒

3.27͑23͒

1.68͑16͒

3.14͑18͒

9.80͑32͒

11.98͑45͒

9.18͑33͒

6.40͑28͒

5.90͑26͒

6.47͑28͒

3.89͑21͒

Ϫ0.0475͑6͒

Ϫ0.2413͑5͒

Ϫ0.3438͑6͒

Ϫ0.4117͑9͒

Ϫ0.3323͑9͒

Ϫ0.3586͑9͒

Ϫ0.0280͑7͒

0.1234͑7͒

Ϫ0.1288͑7͒

0.1340͑6͒

als are normally attributed to rotational tunneling. However,

in the case of cobalt and nickel acetates tetrahydrate, the

low-temperature crystal structure shows clearly a unique

type of methyl group, which is in conﬂict with the presence

of three peaks due to tunneling. We will now look into the

tunneling spectra in more detail.

B. Tunneling spectra of nickel acetate tetrahydrate

Previous INS measurements of nickel acetate tetrahy-

drate on IN10 revealed a unique tunneling peak at 1.4 ␮eV,

but there seems to have been no attempt to search for peaks

beyond the range of this spectrometer ͑14 ␮eV͒. Our spectra

of the nickel salt exhibit three peaks: the previously mea-

sured 1.4 ␮eV on IN16, and two additional peaks at 320 and

23

A. Tunneling spectra of cobalt acetate tetrahydrate

7

10 ␮eV on IN5 ͓Figs. 5͑a͒ and 5͑b͒, respectively͔. How-

A neutron-transmission measurement of cobalt acetate

tetrahydrate predicts three distinct tunneling peaks at 1.1, 30,

and 47 ␮eV ͑0.012, 0.35, and 0.55 K͒.²²The INS spectra of

the commercially available product of the cobalt salt, without

further puriﬁcation, show clearly three inelastic peaks: at 30

and 5 ␮eV using IN5, and a third at 1.2 ␮eV using IN16

ever, we found that peaks at 320 and 710 ␮eV are virtually

unchanged by deuteration of the methyl group ͓Fig. 5͑c͔͒, so

we attribute these peaks to magnetic transitions. It transpires

that these transitions correspond remarkably well with those

predicted at 330 and 700 ␮eV by previous magnetic suscep-

tibility measurements on this salt at liquid-helium

temperature.²

͓Figs. 4͑a͒ and 4͑b͒, respectively͔. Although these observa-

4–26

tions are in good agreement with the transmission measure-

ments above, Guckelsberger et al.²²pointed out that their

results depended on sample preparation. A careful examina-

tion of commercial cobalt acetate tetrahydrate reveals a mix-

ture of different types of crystals. After a simple recrystalli-

zation from water, the peaks on the IN5 spectrum vanish,

and only the single peak in the IN16 spectrum at 1.2 ␮eV

remains. This peak corresponds to the expected tunneling of

the crystallographically unique methyl group and the two

extra peaks probably arise from cobalt acetate hydrate with

less than four water molecules. A full characterization of

these hydrates is beyond the scope of the present paper.

C. Librational spectra

Both acetates show a single tunneling transition close to

1.5 ␮eV, with the additional peaks being due to partially

hydrated species in the cobalt salt, and magnetic transitions

in the nickel salt. Correspondingly, we anticipate a single

librational transition which will provide further information

on the rotational potential. Librational spectra were recorded

on IN5 with an incident wavelength of 2 Å and are shown in

Figs. 6͑a͒ and 6͑b͒, respectively. In both cases there is an

intense peak close to 15 meV, with weaker features at about

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9066

J. Chem. Phys., Vol. 109, No. 20, 22 November 1998

Nicola ¨ı et al.

2

TABLE II. Atomic positions, occupancy ͑occ͒, and thermal parameters ͑in Å ͒ ͑a͒ for nickel acetate tetrahy-

drate at 1.5 K, ͑b͒ for nickel acetate tetrahydrate at 300 K.

Atoms

x/a

y/b

z/c

occ

Ui/Ue*100

͑a͒ P21/c, aϭ4.7485 Å, bϭ11.6933 Å, cϭ8.2247 Å, ␥ϭ92.524°.

Ni͑1͒

O͑2͒

O͑3͒

O͑4͒

O͑5͒

C͑6͒

C͑7͒

D͑8͒

D͑9͒

D͑10͒

D͑11͒

D͑12͒

D͑13͒

D͑14͒

0.0000͑0͒

Ϫ0.2386

0.0821

Ϫ0.2866

0.2357

Ϫ0.1346

Ϫ0.2913

Ϫ0.2227

Ϫ0.5177

Ϫ0.2316

0.4271

0.0000͑0͒

Ϫ0.1518

Ϫ0.2598

0.0794

Ϫ0.1497

Ϫ0.2440

Ϫ0.3517

Ϫ0.4278

Ϫ0.3397

Ϫ0.3655

Ϫ0.0255

0.1223

0.0000͑0͒

0.0103

0.1434

0.1499

0.2058

0.0526

Ϫ0.0162

0.0528

Ϫ0.0091

Ϫ0.1395

0.2020

1

0.62

0.58

0.56

0.52

0.33

0.11

0.79

0.94

1.00

0.03

1.00

1.74

2.42

2.47

2.35

1.35

0.75

0.33

Ϫ0.4311

0.2238

Ϫ0.1936

0.0963

0.1967

0.2323

Ϫ0.1315

0.1308

͑b͒ P21/c, aϭ4.7769 Å, bϭ11.7809 Å, cϭ8.4171 Å, ␥ϭ93.826°.

Ni͑1͒

O͑2͒

O͑3͒

O͑4͒

O͑5͒

C͑6͒

C͑7͒

D͑8͒

D͑9͒

D͑10͒

D͑11͒

D͑12͒

D͑13͒

D͑14͒

0.0000͑0͒

Ϫ0.2413

0.0799

Ϫ0.2781

0.2312

Ϫ0.1412

Ϫ0.2922

Ϫ0.2521

Ϫ0.4976

Ϫ0.2338

0.4234

0.0000͑0͒

Ϫ0.1552

Ϫ0.2541

0.0810

0.0000͑0͒

0.0071

0.1589

0.1508

0.2015

0.0674

Ϫ0.0284

0.0561

0.0035

Ϫ0.1207

0.1921

0.0856

0.1973

0.2235

1

0.62

0.58

0.56

0.52

0.95

2.69

2.93

1.28

2.00

1.40

5.93

8.79

8.71

20.01

3.88

5.18

2.87

0.93

Ϫ0.427

Ϫ0.2439

Ϫ0.3487

Ϫ0.4125

Ϫ0.3422

Ϫ0.3598

Ϫ0.0349

0.1204

Ϫ0.4331

0.2149

Ϫ0.1892

Ϫ0.1267

0.1299

10 and 18 meV. We assign the most intense peak to the

The total rotational barrier V_t_o_tcan be expressed as a

librations of the methyl groups, which is in accordance with

the previous assignment of Clough et al. for the nickel salt.²³

We also recorded the librational spectra of the partially

deuterated salts, Co͑CH COO͒ •4D O and Ni͑CH₃

function of the rotational angle of the methyl group

␾:V(␾)ϭV (␾)ϩV_v_d_W(␾)ϩV_C_o_u_l(␾), where V_i_n_tis the

int

internal contribution ͑the barrier of the isolated molecule͒,

V_v_d_Wis the van der Waals ͑vdW͒ contribution, and V_c_o_u_lis

the Coulomb contribution. The internal contribution was cal-

culated by ab initio methods and the external contribution

͑van der Waals and electrostatic͒ by using pair potentials and

a variety of partial-charge methods, as in Ref. 11.

3

2

COO͒ •4D O, and found these to be very similar to those of

2

the protonated compounds. This suggests that despite the

large thermal ellipsoids of the water molecules in the low-

temperature crystal structure, the water motions are indepen-

dent of the methyl groups rotations. A similar observation

was made for lithium acetate dihydrate,¹⁵where there are

also large thermal displacements of hydrogen atoms in water

molecules at 4 K, but deuteration of the water has no mea-

surable effect on the methyl tunneling.

A. Internal barrier

We obtained the internal barrier for the isolated mol-

ecule by ab initio calculations from the program

27

GAMESS-UK using the Hartree–Fock theory and the self-

consistent ﬁeld method. The only split valence basis set

available for ﬁrst-row transition metal in GAMESS-UK is

VI. THE COMPUTATIONAL METHOD

28

3

-21G. We used the experimental geometry ͑bond length,

angles, and torsions͒ as determined by neutron diffraction

see Table III and Figs. 3͑a͒ and 3͑b͔͒, and then performed

single-point calculations over a number of different rota-

tional conformations of the methyl group about the C–C axis

of the acetate group.

According to the single-particle model, the rotating me-

thyl group in the unit cell was modeled as a rigid, equilateral

triangle of hydrogen atoms. The methyl group was symme-

trized as geometric average of crystallographic data ͑CH

lengths, CCH, and HCH angles͒. This single methyl group

was rotated in a stepwise manner, the environment including

all other methyl groups was assumed to be static, the atomic

positions used being those determined by neutron diffraction

at 4 K.

͓

B. External contribution

Molecular mechanics is generally used for the structures

and the conformational energies of organic and biological

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J. Chem. Phys., Vol. 109, No. 20, 22 November 1998

Nicola ¨ı et al.

9067

FIG. 4. ͑a͒ Inelastic neutron spectrum of Co͑CH COO͒ , 4H O measured on

3

2

IN5 at 1.5 K, of the commercial mixture and the fully hydrated form. Inci-

dent wavelength: 13 Å. The intensities are in arbitrary units ͑a.u.͒ ͑b͒ In-

elastic neutron spectrum of Co͑CH COO͒ , 4H O measured on IN10 at

3

2

1.5 K.

6

V_v_d_WϭD ͑i, j͒ͩ ͩ

ͪ

exp

ͫ

␥͑i, j͒

ͩ

1

0

ͭ

␥

͑i, j͒Ϫ6

6

R͑i, j͒

␥͑i, j͒

R͑i, j͒

Ϫ

ͪ

ͬ

Ϫ

ͫ

ͩ

ͪͩ

ͪ

ͬ

ͪ

, ͑3͒

ͮ

R ͑i, j͒

0

␥͑i, j͒Ϫ6 R ͑i, j͒

0

where R(i, j) is the distances between the atoms i and j,

D (i, j) the bond strength, R (i, j) the bond length, and

0

␥

(i, j) a scaling factor ͑typically 12͒.

In some cases, the Coulomb term was also determined

FIG. 3. ͑a͒, ͑b͒ Illustration of the octahedral symmetry around the metal

atom in M͑CD COO͒ , 4D O, with MϭCo and MϭNi, respectively, at 4 K

showing the thermal ellipsoids.

2

with Cerius . Molecular-mechanics methods commonly use

the monopole approximation, in which point charges are at-

tributed to atomic positions, whereas in organic nonpolar

systems, the electrostatic interactions are small ͑but not neg-

ligible͒, in ionic or polar molecules, the Coulomb contribu-

tions are more important. Unfortunately, it is not possible to

derive site charges directly from observables ͑such as mo-

lecular dipole or multipole moments͒ and it is clear that the

neglect of the charges in molecules which are more polar

than the hydrocarbons will cause unreliable calculation of

equilibrium atomic positions, and potential-energy surfaces.

The Coulomb energy is modeled as follows:

3

2

molecules, there being several speciﬁc force ﬁelds available.

For transition-metal complexes, however, the situation is

very different because of the diversity of geometries, coordi-

nations, and oxidation states which can occur. A recent force

2

9

ﬁeld, UFF, has been developed which successfully repro-

duces the structures of variety of metal-containing

3

0

^Q^Qj

compounds. We used this empirical force ﬁeld and the

i

V_C_o_u_l

ϭ

,

͑4͒

Ewald summation method³to calculate the van der Waals

1

4␲⑀ R͑i, j͒

0

͑

vdW͒ term by molecular mechanics using the commercial

2

32

program Cerius .

where Q and Q represent the partial charges of the atoms i

i j

The expression of the vdW interactions was given by the

exponential-6 potential (exp-6):

and j, respectively.

These point charges can be obtained by two methods:

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9068

J. Chem. Phys., Vol. 109, No. 20, 22 November 1998

Nicola ¨ı et al.

FIG. 6. ͑a͒, ͑b͒ Librational spectra of Ni͑CH COO͒ , 4H O and

3

2

Co͑CH COO͒ , 4H O, respectively, measured on IN5 at 1.5 K. Incident

3

2

wavelength: 2 Å.

Assuming classical mechanics, the position of the atom

found by diffraction corresponds to the equilibrium position

of this atom in the crystal. Accordingly, we choose the me-

thyl conformation found by neutron diffraction at low tem-

perature as the reference ͑␾ϭ0°, ␦ ϭ0͒ for the following

n

calculations, which should clearly correspond to the mini-

mum in the calculated rotational barrier in the crystal.

FIG. 5. ͑a͒ Inelastic neutron spectrum of Ni͑CH COO͒ , 4H O measured on

3

2

IN10 at 1.5 K. ͑b͒ Inelastic neutron spectrum of Ni͑CH COO͒ , 4H O mea-

3

2

sured on IN5 at 1.5 K. Incident wavelength: 5 Å. ͑c͒ Inelastic neutron

spectrum of Ni͑CD COO͒ , 4D O measured on IN5 at 1.5 K. Incident

wavelength: 5 Å.

3

2

A. The internal barrier

The model we have chosen for the ab initio calculations

of the internal barrier is a neutral octahedron comprised of a

metal atom surrounded by two crystallographically equiva-

lent acetates and four water molecules ͓see Table III and

Figs. 3͑a͒ and 3͑b͔͒. This model was selected because the

The ﬁrst method is the empirical Q_e_qcharge equilibra-

tion, which is based on the geometry of the molecule and

experimental atomic properties ͑atomic ionization potentials,

electron afﬁnities, and atomic radii͒.³³

Ϫ

electronic distribution in the acetate ion, CH3COO , is ex-

The second method is potential-derived charges ͑PDC͒

obtained from ab initio method: the electrostatic potential is

determined for the isolated molecule and the charges at

atomic positions are attributed by least-squares ﬁtting to the

potential surface.

pected to be strongly inﬂuenced by the covalent-ionic nature

of the oxygen–metal bonding.

The Fourier coefﬁcients ͓Eq. ͑2͒ were found to be V3

ϭ14.7 meV for nickel acetate tetrahydrate and V3

ϭ9.4 meV for cobalt acetate tetrahydrate, the higher terms

being negligibly small. The ab initio calculations reveal that

the minimum-energy conformation in the isolated molecule

does not correspond to the experimental conformation found

in the crystal, the minimum being at Ϫ18° for the nickel salt

and Ϫ15° for cobalt salt. The ab initio conformation corre-

sponds to one methyl H atom being located in the molecular

plane of the acetate, which strongly implies that the intermo-

lecular interactions in the crystal distort the free-molecule

conformation. A similar result was found for 2,6 dimeth-

ylpyrazine, in which the speciﬁc conformations of two in-

equivalent methyl groups arise exclusively from van der

Waals and Coulomb interactions in the crystal.¹

VII. CALCULATIONS AND DISCUSSION

So far we have discussed the experimental information

concerning the barrier heights and equilibrium methyl con-

formation. We will now consider the calculated equilibrium

orientation, tunneling, and librational frequencies, and com-

pare these with the observed values.

According to the single-particle model ͓see Eqs. ͑1͒ and

͑2͔͒, the energy barrier as a function of the orientation ␾ of

the methyl group can be modeled with the Fourier series of

Eq. ͑2͒ ͑with nϭ3͒.

3,14

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J. Chem. Phys., Vol. 109, No. 20, 22 November 1998

Nicola ¨ı et al.

9069

TABLE III. Geometry of the asymetric unit in M͑CD COO ͒,4D O with MϭCo, Ni at 1.5 K and room

3

2

temperatures, distances are in Å, torsions and angles in degrees.

Atoms

MϭCo, 1.5 K

MϭNi, 1.5 K

MϭCo, 300 K

MϭNi, 300 K

M͑1͒

C͑6͒

O͑3͒

C͑7͒

D͑8͒

D͑9͒

D͑10͒

O͑4͒

D͑12͒

D͑14͒

O͑5͒

D͑11͒

D͑13͒

O͑2͒

C͑6͒

C͑7͒

M͑1͒

O͑4͒

M͑1͒

O͑5͒

2.090

1.289

1.260

1.531

1.079

1.063

2.103

1.030

0.978

2.094

0.972

0.989

2.109

1.230

1.258

1.556

1.097

1.088

1.078

2.094

0.943

0.994

2.071

0.954

0.960

2.025

1.331

1.246

1.529

1.007

1.009

1.016

2.177

1.002

0.913

2.169

1.01

2.066

1.344

1.271

1.618

1.043

1.037

0.853

2.124

1.005

0.923

2.025

0.931

0.994

0.992

Angles

Atoms

MϭCo, 1.5 K

MϭNi, 1.5 K

MϭCo, 300 K

MϭNi, 300 K

M͑1͒

O͑3͒

C͑7͒

D͑8͒

D͑9͒

D͑10͒

O͑4͒

D͑12͒

D͑14͒

O͑5͒

O͑2͒

C͑6͒

C͑7͒

M͑1͒

O͑4͒

M͑1͒

O͑5͒

C͑6͒

O͑2͒

C͑6͒

O͑2͒

M͑1͒

O͑2͒

M͑1͒

124.26

125.60

115.80

111.08

110.85

108.58

89.26

115.53

116.05

90.55

122.65

127.17

115.29

109.99

109.52

108.77

89.17

115.98

112.85

90.17

127.32

124.60

116.85

111.45

112.46

104.92

90.67

110.99

115.21

90.44

122.82

124.86

109.68

98.90

102.27

114.14

88.99

110.38

113.43

92.55

112.94

100.37

D͑11͒

D͑13͒

114.23

99.46

111.79

100.83

104.42

93.84

Torsions

Atoms

Atoms Atoms Atoms MϭCo, 1.5 K MϭNi, 1.5 K MϭCo, 300 K MϭNi, 300 K

M͑1͒

C͑7͒

D͑8͒

D͑9͒

D͑10͒

O͑4͒

D͑12͒

D͑14͒

O͑5͒

D͑11͒

D͑13͒

O͑2͒

C͑6͒

C͑7͒

M͑1͒

O͑4͒

M͑1͒

O͑5͒

C͑6͒

O͑2͒

C͑6͒

O͑2͒

M͑1͒

O͑2͒

M͑1͒

O͑3͒

O͑2͒

D͑8͒

C͑6͒

O͑2͒

D͑12͒

O͑4͒

O͑2͒

D͑11͒

23.7

Ϫ178.3

Ϫ164.8

120.7

Ϫ118.4

Ϫ123.8

Ϫ95.3

Ϫ119.5

87.7

25.6

Ϫ179.7

Ϫ164.2

121.5

Ϫ116.0

Ϫ125.9

Ϫ95.8

Ϫ123.8

89.1

19.1

Ϫ175.1

Ϫ164.9

120.6

Ϫ115.8

Ϫ119.3

Ϫ91.4

Ϫ125.3

86.9

17.8

Ϫ165.2

Ϫ159.8

92.6

Ϫ125.0

Ϫ118.0

Ϫ90.7

Ϫ125.8

86.5

140.6

Ϫ111.8

145.4

Ϫ117.1

137.7

Ϫ109.9

132.5

Ϫ105.4

B. The external contributions

. van der Waals contributions

The vdW contribution can be estimated by summing the

der Waals contribution to rotational potential, which is simi-

lar to results reported for lithium acetate dihydrate.¹⁵

1

pairwise interactions between each of the methyl H atoms

and the other atoms in the model. This contribution was

2. Coulomb contributions

found to be V ͑vdW͒ϭ17.9 meV, the minimum of the en-

3

ergy being at Ϫ33° for the nickel salt and

The sum of the van der Waals and internal contributions

V ͑vdW͒ϭ22.4 meV with the minimum at Ϫ37° for the co-

to the rotational barrier is too small to account for the ob-

served tunneling and librational frequencies. Further, the

minimum in this rotational potential does not correspond

well to the crystallographically determined methyl orienta-

tion, and it is clear that Coulomb interactions must play an

important role in this crystal. We have tested four models of

the charge distributions which are essentially based on two

methods of estimating the partial charges of a molecule: em-

3

balt salt. The different contributions to the vdW potential can

be analysed on an atom-by-atom basis, and this reveals that

the contributions of the surrounding metal atoms and the

carbon are negligibly small ͓see Figs. 7͑a͒ and 7͑b͒ for the

nickel salt and the cobalt salt, respectively͔. It is essential

that the contributions from the hydrogen and the oxygen at-

oms of the surroundings water molecules dominate the van

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9070

J. Chem. Phys., Vol. 109, No. 20, 22 November 1998

Nicola ¨ı et al.

TABLE IV. Partial charges of the 29 atoms of the octahedron calculated by

Q_e_qmethod or ab initio method ͑PDC: potential-derived charges͒ and used

in the calculations of the rotational potential.

Atoms

MϭCo, Q_e_q

MϭNi, Q_e_q

MϭNi, PDC

M͑1͒

O͑2͒

O͑3͒

O͑4͒

O͑5͒

C͑6͒

0.5892

Ϫ0.4589

Ϫ0.6555

Ϫ0.7297

Ϫ0.7417

0.6115

0.4845

Ϫ0.4579

Ϫ0.6662

Ϫ0.7514

Ϫ0.7556

0.6373

1.1650

Ϫ0.8304

Ϫ0.8470

Ϫ0.8659

Ϫ0.9670

1.1139

C͑7͒

H͑8͒

Ϫ0.3077

0.1757

Ϫ0.3122

0.1711

Ϫ0.6407

0.1589

H͑9͒

0.1399

0.1520

0.1643

H͑10͒

0.1620

0.1714

0.1501

H͑11͒

0.3702

0.3851

0.4672

H͑12͒

0.3651

0.3846

0.4749

H͑13͒

0.3930

0.4048

0.4812

H͑14͒

0.3917

0.3948

0.5563

O͑2͒ bis

O͑3͒ bis

O͑4͒ bis

O͑5͒ bis

C͑6͒ bis

C͑7͒ bis

H͑8͒ bis

H͑9͒ bis

H͑10͒ bis

H͑11͒ bis

H͑12͒ bis

H͑13͒ bis

H͑14͒ bis

Ϫ0.4589

Ϫ0.6555

Ϫ0.7297

Ϫ0.7417

0.6115

Ϫ0.3077

0.1757

0.1399

0.1620

0.3702

0.3651

0.3930

Ϫ0.4579

Ϫ0.6662

Ϫ0.7514

Ϫ0.7556

0.6373

Ϫ0.3122

0.1711

0.1520

0.1714

0.3851

0.3846

0.4048

Ϫ0.8189

Ϫ0.8423

Ϫ0.8610

Ϫ0.9594

1.0959

Ϫ0.6407

0.1517

0.1591

0.1463

0.4640

0.4725

0.4820

FIG. 7. Contributions of the carbon, metal, oxygen, and hydrogen atoms to

the van der Waals component of the rotational potential. Carbon: solid line

and an open circle, metal: solid line and a cross, oxygen: solid line and a

solid triangle, hydrogen: dotted line with a solid circle. ͑a͒ In nickel acetate

tetrahydrate, ͑b͒ in cobalt acetate tetrahydrate.

0.3917

0.3948

0.5476

^pⁱ^rⁱ^c^a^l^c^a^l^c^u^l^a^tⁱ^oⁿ^s^wⁱ^t^h^t^h^e^Qeq method in the crystal and

the potential-derived charges calculated via ab initio meth-

ods.

b. Discussion. The partial charges used for the calcula-

tions are presented in Table IV and Fig. 8 and the results of

the four methods outlined above are shown in Figs. 9͑a͒–

a. The four methods. ͑1͒ In this method, the charges are

evaluated with Q_e_qfor the experimental conformation of the

methyl groups, with the point charges being evaluated for the

octahedron in the crystal. The charges of the environment

and the three H atoms of the probe methyl are constrained to

these calculated values during rotation of the methyl group.

9

͑d͒ for the nickel salt. It can be seen from Table IV that the

͑

2͒ Potential-derived charges are evaluated for all the

atoms of the octahedron by ab initio method. They are trans-

ferred in the crystal to obtain to total Coulomb contribution

to the potential. As in method 1, the charges of the methyl

group and the environment are kept ﬁxed during the rigid

rotation of the methyl group, the charges of the three H at-

oms being averaged.

͑

3͒ According to Q , the partial charges depend upon

eq

the geometry and consequently upon the conformation of the

molecules, the partial charges of the methyl group can vary

during the rotation. Consequently, in the third method, we

performed a new Q_e_qcalculation at every step of the rigid

rotation of the methyl groups in the crystal.

FIG. 8. Partial charges of the hydrogen H͑8͒ of the rotating methyl group

^c^a^l^c^u^l^a^t^e^d^b^y^Qeq method in the cobalt and the nickel salts as a function of

the methyl-group orientation angle. Comparison with the partial charges

calculated by ab initio method. Charges in the cobalt salt calculated with

Q_e_q: solid line with solid circle. Charges in the nickel salt calculated with

Q_e_q: dotted line with open triangle. Charges calculated by ab initio method:

solid line. The minima and maxima are similar in the three cases but the

form of curves is different between Q_e_qand ab initio method. Moreover, in

Q_e_q, the charges of the H atoms of the methyl group are varied. In ab initio,

the charge of the carbon atom varies with the charges of the H atoms. The

charges of all other atoms are invariant during rotation.

͑

4͒ Because the potential-derived charges are determined

from a wave function which depends on the atomic posi-

tions, they should be calculated for the isolated octahedron at

each step of the rotation and then introduced into the crystal.

This method is much more computationally expensive than

the preceding three methods.

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J. Chem. Phys., Vol. 109, No. 20, 22 November 1998

Nicola ¨ı et al.

9071

FIG. 9. Calculation of the rotational potential in nickel acetate tetrahydrate.

Total potential: solid curve with solid circle, van der Waals: dotted curve

with open circle, Coulomb: dashed curve with open square, Internal: dotted

curve with a cross. ͑a͒ Partial charges are calculated with the Q_e_qmethod

and are ﬁxed during the rotation of the methyl group. ͑b͒ Partial charges are

calculated with ab initio method and are ﬁxed during the rotation of the

methyl group. ͑c͒ Partial charges are calculated with the Q_e_qmethod and

vary during the rotation of the methyl group. ͑d͒ Partial charges are calcu-

lated with ab initio method and vary during the rotation of the methyl group.

FIG. 10. Calculation of the rotational potential in cobalt acetate tetrahydrate.