The low-barrier hydrogen bond of deuterated benzoylacetone probed by very low temperature neutron and X-ray diffraction studies and theoretical calculations

Article abstract of DOI:10.1002/chem.200601490

Low-temperature neutron diffraction data is used to show that the enol deuteron in deuterated benzoylacetone has a bimodal probability density distribution. In a previous study of normal benzoylacetone we showed that the enol hydrogen atom has a broad unimodal probability density distribution. Deuteration gives hardly any change to the molecular framework other than a small lengthening of the O...O distance. We solve the vibrational Hamiltonian for a series of model hydrogen potentials and show how the proton/deuteron probability density function can become strongly perturbed by small changes to the potential. The potentials are used to show that the deuteron in benzoylacetonc can be interpreted as an atom tunnelling between two possible localised positions, while the proton in benzoylacetone can be viewed as having sufficient energy to shuttle over the low-energy barrier, even at 15 K. We underline the necessity of accounting for the dynamic nature of the hydrogen bond and not relying on a description of the proton/ deuteron by a single atomic coordinate, and compare our results to structure correlation studies.

Full text of DOI:10.1002/chem.200601490

FULL PAPER
DOI: 10.1002/chem.200601490
The Low-Barrier Hydrogen Bond of Deuterated Benzoylacetone Probed by
Very Low Temperature Neutron and X-ray Diffraction Studies and
Theoretical Calculations
Georg K. H. Madsen,*[a] Garry J. McIntyre,[b] Birgit Schiøtt,[a] and Finn K. Larsen[a]
Abstract: Low-temperature neutron
diffraction data is used to show that
the enol deuteron in deuterated ben-
zoylacetone has a bimodal probability
the vibrational Hamiltonian for a series
of model hydrogen potentials and show
how the proton/deuteron probability
density function can become strongly
perturbed by small changes to the po-
tential. The potentials are used to show
that the deuteron in benzoylacetone
can be interpreted as an atom tunnel-
ling between two possible localised po-
sitions, while the proton in benzoylace-
tone can be viewed as having sufficient
energy to shuttle over the low-energy
barrier, even at 15 K. We underline the
necessity of accounting for the dynamic
nature of the hydrogen bond and not
relying on a description of the proton/
deuteron by a single atomic coordinate,
and compare our results to structure
correlation studies.
density distribution. In
a previous
study of normal benzoylacetone we
showed that the enol hydrogen atom
has a broad unimodal probability den-
sity distribution. Deuteration gives
hardly any change to the molecular
framework other than a small length-
ening of the O···O distance. We solve
Keywords: deuterium · enzyme cat-
alysis · hydrogen bonds · low-barri-
er tunneling · neutron diffraction
Introduction
gen bonds (LBHB).[4] In the very strong HBs both hydrogen
and deuterium atoms have sufficient ZPVE to shuttle be-
tween the two hydrogen-bonded acceptors.
Hydrogen bonds (HB) have received much attention due to
their fundamental interest and to their importance in molec-
ular recognition processes.[1–3] They can be classified into
It has been inferred from spectroscopic evidence,[1] crystal
correlation methods[5] and studies of the electron density[6,7]
that short hydrogen bonds have a strong covalent contribu-
tion. This covalent contribution can be expected to be im-
portant for the large HB energies up to 160 kJmolꢀ1 found
for short hydrogen bonds.[2] Because of this large gain in
energy strong hydrogen bonds have been postulated to play
an important role in enzyme catalysis.[8] However, the exis-
tence and importance of strong hydrogen bonds in enzyme
catalysis is a controversial theme.[9–11]
three categories,[2] for example in the case of O H···O HBs:
ꢀ
1) Weak with O···O distances above 3.2 Š, 2) moderately
strong (normal) with distances ranging from approximately
2.5 to 3.2 Š and 3) strong with distances shorter than 2.5 Š.
Based on the nature of the potential well in which the hy-
drogen resides, strong HBs have been further subdivided[1]
into strong HBs and very strong HBs. In the strong HB the
zero-point vibrational energy (ZPVE) of the hydrogen (but
not of deuterium) atom exceeds the proton-transfer barrier.
These strong HBs have also been named low-barrier hydro-
Anharmonic motion and quantum effects such as zero-
point motion and tunnelling are important for the hydrogen
dynamics. This makes a full treatment by ab initio calcula-
tions very difficult. Such effects have been included by using
Feynman path integral techniques, providing very detailed
information about the proton dynamics. One very illustra-
tive example is the study of the high-pressure phase of
ice.[12] The time-averaged proton distribution function was
studied and it was demonstrated that as the water molecules
are forced closer, the hydrogen atom goes from being locat-
ed at one oxygen atom to tunnelling between two oxygen
atoms to finally, at high pressures, being located midway be-
tween two oxygen atoms.[12]
[a] Dr. G. K. H. Madsen, Dr. B. Schiøtt, Dr. F. K. Larsen
Department of Chemistry, University of Aarhus
8000 Šrhus C (Denmark)
Fax : (+45)8619-6199
E-mail: georg@chem.au.dk
[b] Dr. G. J. McIntyre
Institut Laue-Langevin, BP 156
38042 Grenoble Cedex 9 (France)
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5539

Recently a lot of attention has been given to the so-called
[13–15]
ꢀ
migrating proton that can be found in both O H···O
[16–18]
ꢀ
and N H···O systems.
The structural consequences of
deuterating the short hydrogen bond have been studied less,
although considerable consequences for the lower ZPVE of
a deuteron in a strong HB can be envisaged. If the HB has
a low-barrier but the energy difference between the two
minima is sufficiently asymmetric, a hydrogen atom could
exhibit significant motion between the atoms, while a deu-
teron would fall out on one side. To our knowledge such a
situation has only been observed once.[19,20] These neutron
diffraction studies of the short HB bridging the ligands in a
Ni complex, bis(2-amino-2-methyl-3-butanone oximato)nick-
el(II) chloride monohydrate (Ni–AMBO), offer one con-
vincing example of a structural change upon deuteration.
The hydrogen atom was located in a broad, slightly asym-
metric potential well for the normal complex,[19] while in the
deuterated complex the deuterium atom resided in a narrow
and much more asymmetric potential well.[20] The results for
the Ni complex can be interpreted as a proton in a LBHB
with a large enough energy difference between the possible
deuteron positions for it to become localised. However, if
the energy difference between the two positions is sufficient-
ly small, the deuteron may tunnel between the two posi-
tions. To our knowledge a direct observation by neutron
scattering of such a situation has not been reported previ-
ously, but we have now observed this to take place in deu-
terated benzoylacetone (DBA).
Figure 1. ORTEP drawing of the deuterated benzoylacetone molecule
showing the 50% probability ellipsoids obtained by refinement of the
neutron data. For comparison a thermal ellipsoid with the positional and
thermal parameters obtained from HBA[6] has been included in the plot.
Previously we reported a very low temperature combined
neutron and X-ray diffraction study of hydrogenated ben-
zoylacetone (HBA).[6] We demonstrated that the structure is
ordered with the enol hydrogen atom located close to the
midpoint between the two oxygen atoms, but with a very
large mean-square displacement (MSD) along the O···O
vector. The large MSD was interpreted as the hydrogen
atom having a sufficiently large ZPVE to vibrate freely be-
tween the two oxygen atoms.[6] The present paper describes
the change of structure which occurs upon deuteration of
the enol position.
Figure 2. Residual Fourier map from the neutron study with the enol
deuteron omitted from the model. The contour interval is 0.05”
ꢀ3
10ꢀ14 mŠ
.
Results and Discussion
tion (see Figure 1 for labelling of atoms). The MSD of the
enol deuteron refine to much smaller values than were
found for the enol hydrogen atom in HBA. For comparison
the thermal ellipsoid with the positional and thermal param-
eters obtained for the enol hydrogen in HBA[6] has been in-
cluded in Figure 1.
Neutron diffraction: DBA, see Figure 1, is iso-structural
with and very similar to HBA, which was studied previous-
ly.[6] A residual Fourier density map from the neutron dif-
fraction study of HBA with the enol hydrogen omitted from
the model showed
a
broad flat hydrogen distribution
We interpret the difference between the HBA and DBA
residual Fourier density maps as a clear indication of BA
being a case of LBHB with the hydrogen atom vibrating
freely between the two oxygen positions and a deuteron tun-
nelling between two positions, although one could think of
arguments against this interpretation. We will rule them out
consequently.
Firstly, one might contest that a diffraction study provides
direct information that allows us to discriminate dynamic
disorder, such as tunnelling between the two positions, from
(Figure 3 of reference [6]). This can be compared with
Figure 2 of the present paper, which illustrates the same sec-
tion for a residual Fourier density map of DBA. The omit-
ted deuteron shows up as a bimodal probability density dis-
tribution. Refinement of two deuteron positions leads to
ꢀ
two localised positions with bond lengths close to typical O
D distances (Table 1). The deuterium occupancies refined to
0.43(5) for position D(1), 0.44(5) for position D(2), and
0.90(5) for position D(3) indicate a high degree of deutera-
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Benzoylacetone Low-Barrier Hydrogen Bond
FULL PAPER
Table 2. Differences in mean square displacement amplitudes along the
interatomic vector D<u2 >A-B. The numbers correspond to the MSDs ex-
tracted from analysis of the X-ray data. Numbers marked in bold corre-
spond to bonded atoms. Values are in 10ꢀ4 Š2. The grey areas mark the
phenyl and keto–enol groups. The standard deviations are of the order 4–
5”10ꢀ4 Š2.
Table 1. Selected interatomic distances [Š] and angles [8] for deuterated
benzoylacetone. For comparison the bond distances found for hydrogen-
ated benzoylacetone[6] are also given.
DBA, neutron DBA, X-ray
HBA, neutron
O(1)-O(2)
O(1)-D(1)
O(1)-D(2)
O(2)-D(2)
O(2)-D(1)
O(1)-C(2)
O(2)-C(4)
C(2)-C(3)
C(3)-C(4)
C(1)-C(2)
C(4)-C(5)
2.522(2)
1.002(5)
1.646(4)
0.980(4)
1.611(5)
1.290(2)
1.293(2)
1.403(2)
1.403(2)
1.493(2)
1.482(2)
2.5219(9)
1.0021(6)
1.6459(6)
0.9771(6)
1.6095(6)
1.2884(8)
1.2940(7)
1.4058(6)
1.4045(6)
1.4958(7)
1.4809(5)
2.502(4)
1.329(11)
1.245(11)
1.286(4)
1.293(4)
1.414(4)
1.405(4)
1.499(4)
1.483(4)
O(1)-D(1)-O(2)
O(1)-D(2)-O(2)
C(2)-O(1)-D(1)
C(4)-O(2)-D(2)
O(1)-C(2)-C(1)
O(1)-C(2)-C(3)
C(1)-C(2)-C(3)
148.8(4)
149.0(1)
152.3(6)
152.3(6)
101.2(4)
103.2(4)
117.0(3)
122.1(3)
120.9(2)
119.7(2)
120.9(3)
116.4(3)
122.6(2)
147.9(4)
106.7(3)
108.7(3)
116.8(1)
122.4(1)
120.8(1)
120.3(1)
121.2(1)
116.0(1)
122.8(1)
147.0(1)
106.7(1)
109.3(1)
117.0(1)
122.1(1)
120.9(1)
120.5(1)
121.1(1)
116.3(1)
122.7(1)
C(2)-C(3)-C(4)
O(2)-C(4)-C(3)
O(2)-C(4)-C(5)
C(3)-C(4)-C(5)
torsion angles
O(2)-C(4)-C(5)-C(6)
H(1B)-C(1)-C(2)-O(1)
H(1C)-C(1)-C(2)-O(1)
ꢀ173.7(2)
38.4(5)
ꢀ82.0(7)
ꢀ173.6(1)
38.4(1)
ꢀ81.8(1)
ꢀ173.5(4)
38.0(5)
ꢀ81.0(6)
ened from 2.502(4) Š in HBA[6] to 2.522(2) Š in DBA, con-
forming with previous observations of the Ubbelohde effect
for strong double-well potential HBs,[24] while for very
strong single-well potential HBs deuteration will shorten the
O···O distance, because the lower ZPVE leads to a more lo-
calised deuteron distribution.[25]
static disorder, in which the deuteron is statistically distrib-
uted between two positions in different molecules. However,
analysis of the MSDs has successfully been used to detect
static disorder.[21] This was done by showing that static disor-
der will alter MSDs systematically to deviate from values
calculated for rigid body vibration in molecular parts that
intuitively should be rigid. Table 2 gives the differences in
MSD along interatomic vectors, Dhu2iA-B. Values of Dhu2iA-B
X-ray diffraction: We have also measured 11(1) K X-ray
data on DBA and there is a very good agreement between
the heavy atom positions found in the X-ray and the neu-
tron study (Table 1). This means that the lengthening of the
O···O distance from 2.502(4) Š in HBA[6] to 2.522(2) in
DBA can be used as indirect evidence of a LBHB.
significantly above 10”10ꢀ4 Š imply non-rigidity in the mo-
2
lecular part.[22] Table 2 shows that the methyl group and to
some extent the two oxygen atoms deviate from rigid body
behaviour. Similar enhanced vibration of the oxygen atoms
was also found in a molecular dynamics study of malonalde-
hyde,[23] which showed that when a hydrogen atom vibrates
freely in the potential between two oxygen atoms the main
effect on the framework is an oscillating O···O distance.[23]
Static disorder with concomitant changes in bond lengths
within the keto–enol ring would increase the Dhu2iA-B much
more than observed,[21] so we rule out static disorder.
Obtaining direct information about the hydrogen distribu-
tion would require differentiating between the difference
charge density of HBA (Figure 9c of reference [16]) and
that of DBA. Figure 3 shows the difference Fourier map cal-
culated from the observed X-ray structure factors (phased
by the model) and the structure factors calculated for an in-
dependent atom model not including the enol deuterons.
This map gives a qualitatively quite similar picture to that of
HBA[26] and no evident indication of a different distribution
of charge in the HBA and DBA molecules.
Secondly, one might point out that the resolution of the
present study is higher than that of the HBA study[6] and
that perhaps the resolution of the earlier study was too low
to resolve two hydrogen positions. We tried including in the
refinement of DBA only data up to the same sinq/l limit as
in the HBA study[6] for calculation of the difference maps,
but were still able to clearly resolve two deuteron positions.
Furthermore, evidence that the HBA and DBA structures
are truly different can be found by comparing the structural
details in Table 1. It is seen that the O···O distance is length-
Ab initio calculations: To gain further insight into the
nature of the potential well of the enol hydrogen atom, we
have calculated the total energy with respect to constrained
hydrogen positions, as described in the computational proce-
dure. The resulting total energies are shown in Figure 4. The
three points marked are: MS, corresponding to the mini-
mum energy structure with the hydrogen located on the
methyl side; PS, corresponding to the minimum energy
structure with the hydrogen located on the phenyl side and
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5541

G. K. H. Madsen et al.
are on BA in the gas phase, which might not be an optimal
model of BA in the crystal. We performed calculations with
the torsion angles between the keto–enol group and the
methyl and phenyl groups fixed at the experimental values
listed in Table 1. This reduced the energy difference be-
tween the two sides from 0.9 to 0.5 mHa. A further source
of uncertainty is that the B3LYP functional is known to un-
derestimate proton-transfer barriers.[27] The influence of the
applied theoretical method could be studied, but, as has just
been shown, the results would again be too dependent on
small details of the structure and crystal environment for
comparisons with experiment to be meaningful at this level
of detail. Furthermore, the hydrogen/deuterium atom of
course does not reside in a one particle potential, and its
motion will be coupled to the rest of the molecule. A full
theoretical comparison would thus involve a treatment of all
atoms and the crystal environment including anharmonic
and quantum effects such as tunnelling[28–30] and lies far
beyond the scope of the present work.
Figure 3. Difference Fourier map calculated from the observed X-ray
structure factors and the structure factors calculated for an independent
atom model not including the enol deuterons. The contour interval is
ꢀ3
0.1 eŠ
.
The important point is that the calculations show that the
potential well is strongly anharmonic and, as will be seen in
the following paragraph, BA is exactly in the range of ener-
gies over which an effect such as the one observed can be
expected. To illustrate the influence of the potential on the
eigenstates we have constructed six potential wells, Figure 5,
and solved the anharmonic eigenvalue problem as described
in the computational section. All six potentials have two
minima and are similar to the calculated potential. They
differ only by small perturbations, but we will show how
these small perturbations can have a large influence on the
calculated distribution functions.
In the first potential (Figure 5a), the minima are 1 au
(0.529 Š) apart and 3.5 mHa deep. This leads to a clear
double maximum in the probability distribution function
(f2) for the lowest deuterium eigenstate and a clear tunnel-
ling splitting. The lower mass of the proton means that the
states lie higher in the potential well, but the lowest state is
still below the barrier and consequently a double maximum
is also seen in the corresponding hydrogen distribution func-
tion. These results are qualitatively comparable to what has
been found theoretically by path integral techniques for ace-
tylacetone. Acetylacetone has a weaker hydrogen bond
(dO···O =2.55 Š) and hence a larger barrier, but both hydro-
gen and a deuteron are found to tunnel between the two
minima.[28] In Figure 5b the minima are only 2 mHa deep,
but still 1 au apart. Here the deuteron probability function
still shows a double maximum, while the lowest hydrogen
state lies at the barrier, and consequently the probability
function shows one broad maximum. In Figure 5c we have
added a very small linear asymmetric term (given as
0.1 mHa/au”x, which raises the right hand side 0.05 mHa
and lowers the left hand side 0.05 mHa) to the potential.
This leads to an asymmetric double peak in the deuteron
probability distribution and an asymmetric broad single
maximum in the proton distribution. This situation is similar
to what we have observed for HBA/DBA in which the po-
tential as seen by the proton was an effective single-well po-
Figure 4. Calculated total energies as a function of the reaction coordi-
nate in bohr radii. The full line corresponds to a fit to a sixth order poly-
nomial. The black points for PS (phenyl side) and MS (methyl side)
mark the fully geometry-optimised structures and TS the transition state
structure.
TS, the transition state structure. The MS is 3.5 mHa and
the PS is 2.6 mHa lower in energy than TS (Table 3). The
energies are shown as a function of a reaction coordinate
given as: (d(O H)ꢀd(O H)/2. Thereby the two energy minima
1ꢀ
2ꢀ
A
ACHTREUNG
are approximately 0.5 Š apart, as found experimentally (Fig-
ures 1 and 2) and theoretically (Table 3).
Table 3. Theoretically calculated atomic distances and energies (E) rela-
tive to the TS structure.
ꢀ
ꢀ
E [mHa]
O(1) H(Š)
O(2) H(Š)
O(1)···O(2)(Š)
TS
MS
PS
0.00
ꢀ3.5
ꢀ2.6
1.20
1.01
1.56
1.21
1.58
1.01
2.36
2.51
2.50
The optimised structures agree well with experiment. The
energy differences find the MS to be slightly more stable
than the PS, in slight disagreement with the experimental
probability density distribution. However, the calculations
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Benzoylacetone Low-Barrier Hydrogen Bond
FULL PAPER
of approximately 1 mHa (Figure 5d) means that the second
level, which has a mirror plane and a maximum at the right
hand side, will be significantly populated at room tempera-
ture. The Ni–AMBO complex would thus be an interesting
candidate for a multi-temperature neutron diffraction study.
This approach demonstrated its usefulness in explaining the
migrating proton by the fact that the two lowest eigenstates
of the asymmetric single-well vibrational Hamiltonian are
located in opposite sides of the potential well.[15] As the tem-
perature is lowered the second level will be depopulated,
the average position of the proton will shift and the proton
migrates as a function of temperature.[15]
Finally we have constructed two potentials in which the
minima are just 0.8 Bohr apart and 2 mHa deep (Figure 5e
and 5f). In Figure 5f we have furthermore added the same
small asymmetric term as in Figure 5c. In both cases the
lowest energy levels lie at the barrier and the potentials are
effectively single-well potentials. We believe the symmetric
case has recently been observed by neutron diffraction for
the very short hydrogen bond in the molecule 4-cyano-
2,2,6,6-tetramethyl-3,5-heptanedione (CTMH).[31] The com-
pound CTMH is claimed to have the shortest symmetrical
ꢀ
O H···O hydrogen bond yet reported with dO···O
=
2.388(5) Š.[31] Neutron crystallography (20 K data) revealed
ꢀ
the hydrogen-bonded proton to be nearly centred (O H=
1.216(9) Š and O···H=1.220(8) Š) between the two oxygen
atoms. In the slightly asymmetric case (Figure 5f) the proba-
bility distribution is shifted markedly and it is clear that
even a small perturbation can result in a relatively large
change in the mean hydrogen/proton position. Such a situa-
tion we recently observed in nitromalonamide (NMA),[32]
ꢀ
which offers another example of an equally very short O
H···O hydrogen bond at an O···O distance of 2.391(3) Š.[32]
Neutron crystallography (15 K data) showed that the enol
hydrogen atom had an asymmetric position, due to intermo-
Figure 5. Double-well potentials and their resulting zero point probability
distribution functions. The full lines represent hydrogen and the dashed
lines deuteron vibrational levels and probability distribution functions.
See text for the details of a)–f). The thin dotted lines added to c), d) and
f) represent the asymmetric terms added to the potentials.
ꢀ
lecular hydrogen bonding, O H=1.140(10) Š and H···O=
1.308(11) Š, between the two oxygen atoms in the otherwise
quite symmetrical molecule.
tential,[6] while for the deuteron we observed a double peak.
If a larger asymmetric term (0.3 mHa/au”x) is added (Fig-
ure 5d), the proton distribution maintains its broad asym-
metric single maximum character, while the deuteron distri-
bution is peaked at one side of the potential. This situation
can be compared to what was observed for the Ni–AMBO.
In the normal protonated complex the non-hydrogen atoms
of the Ni-AMBO conform closely to C2v symmetry, but even
so the enol proton was found to be located at a slightly
Discussion: Steiner and Saenger have compiled much infor-
ꢀ
mation on the geometry of O H···O hydrogen bonds from a
survey of low-temperature neutron diffraction studies.[33]
Based on results from 81 low-temperature neutron diffrac-
tion structures, they showed that there is a smooth correla-
ꢀ
ꢀ
tion between O H and H···O distances in O H···O interac-
tions. An interpolated curve through these data points is
ꢀ
shown in Figure 6. The O H bond continuously elongates
ꢀ
asymmetric position with O H bond lengths of 1.187(5) and
with concomitant shortening of the H···O distance until a
1.242(5) Š and an O···O distance of 2.420(3) Š.[19] The ther-
mal displacement of the enol hydrogen atom along the
O···O direction is substantially bigger than in other direc-
tions, which leads to the conclusion that the hydrogen atom
moves in a broad single-minimum potential. The deuterated
symmetric O H···O geometry is reached at an O···O separa-
ꢀ
tion of about 2.39 Š.
We have superimposed on the curve results from the pres-
ent study of deuterated benzoylacetone as well as for the
previously studied normal benzoylacetone,[6] and also results
from the Ni–AMBO studies.[19,20] It is worth noting that for
both the Ni–AMBO and BA, the deuterated samples show
distances in good accordance with the Steiner and Saenger
curve. In contrast to this, the normal protonated BA and
complex showed an even more pronounced asymmetry with
[20]
ꢀ
O D bond lengths of 1.058(9) and 1.391(10) Š. However,
it is difficult to say anything conclusive as the experiments
were performed at room temperature. The tunnel splitting
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5543

G. K. H. Madsen et al.
The large RMSD of the enol hydrogen raises the question
of how the structure of a short strong hydrogen bond should
be described. At the heart of a correlation such as the Stein-
er–Saenger curve presented in Figure 6 lies a view of a
structure as a set of coordinates/interatomic distances. How-
ever, the fact that the enol hydrogen atom has an RMSD
larger than the difference in hydrogen-bonded distances
shows that summarizing the structure of a short hydrogen-
bonded system just by a hydrogen coordinate is too simplis-
tic a model. We did put forward a similar view in the study
of NMA.[32] Here the mean position (coordinate) of the hy-
drogen was found significantly closer to one oxygen atom
than the other. However, the calculated probability density
function for the enol hydrogen atom showed that there is
also a large probability of finding the enol hydrogen atom
close to the other oxygen atom.[32]
Figure 6. Interpolated curve using the data of Steiner and Saenger.[33] The
structures of nitromalonamide[32] (NMA), benzoylacetone[6] (BA), the
cyano-tetramethyl-heptanedione (CMTH) and Ni-AMBO[19,20] have been
superimposed. The horizontal lines indicate the size of the root mean
square displacement of the enol hydrogen along the O···O vector. The
filled points correspond to the hydrogenated samples and the open
points to the deuterated samples.
Gilli et al. recently presented an attempt of a general de-
ꢀ
scription of the nature of the strong O H···O hydrogen
bond in b-diketone enol RAHB systems.[37] They illustrated
the possible shapes of hydrogen-transfer potentials, ranging
from symmetric single wells with barriers of different
heights, to weakly asymmetric single wells, to asymmetric
double wells with different barrier heights. Gilli et al. pro-
ceeded to present a few 100 K X-ray structures of com-
pounds with hydrogen bonds of the internal RAHB keto–
enol type and used them to illustrate the variety in nature of
ꢀ
Ni–AMBO structures show O H distances that are inter-
mediate between values at the two branches of the Steiner–
Saenger curve (see Figure 6). However, this can be recon-
ciled by viewing the proton as shuttling freely between two
positions in a broad shallow potential well. In a standard
crystallographic refinement the width of the potential well is
measured by the root-mean-square displacement (RMSD).
In a standard harmonic model the RMSD is the half-width
of the Gaussian probability density distribution.[34]
ꢀ
the strong O H···O hydrogen bond. They also referred to
our work on HBA,[6] and suggested that the intramolecular
hydrogen bond has a weakly asymmetric double-well low-
barrier potential. We arrive at the same conclusion for the
qualitative shape of the potential well. However, there is a
big difference in the interpretation of the resulting hydrogen
bond. Gilli et al. suggested that the hydrogen bond in BA is
disordered, a static distribution of tautomeric forms.[37] We
have ruled out static disorder on the basis of the Hirshfeld
rigid-bond test and instead, by detailed analysis of ab initio
calculations, shown that the very low temperature neutron
diffraction data can be explained by a deuterium atom tun-
nelling between two possible localised positions and an enol
proton that, even at the low temperature of 15 K, has suffi-
cient energy to shuttle over the low-energy barrier.
ꢀ
The RMSD component of the O H···O hydrogen atom
along the O···O direction is also marked in Figure 6. For the
Ni–AMBO the RMSD of hydrogen in the O···O direction is
0.37 Š at room temperature and for HBA the RMSD of hy-
drogen along the O···O direction is 0.28 Š at 20 K. In the
study of protonated BA this leads to the conclusion that the
hydrogen atom moves in a broad single-minimum potential.
With the added information from the present study of the
deuterated compound one may conclude in greater detail
that the potential should be described as a weakly asymmet-
ric (almost symmetric) low-barrier potential, similar to Fig-
ure 5c. The deuterium atom tunnels between two possible
localised positions and the enol proton even at the low tem-
perature of 15 K has sufficient energy to shuttle over the
low-energy barrier.
The conclusion of Gilli et al. that the hydrogen bond in
BA is disordered,
a static distribution of tautomeric
forms,[37] was based on the result of their so-called l-test
which relies on a correlation between the p-delocalisation
and a proton-transfer reaction coordinate. Several structures
do not fit these correlations and were claimed to give “in-
correct” positions in the correlation diagrams because of in-
ternal structural disorder due to double-well hydrogen
bonds being misinterpreted as single-well hydrogen
bonds.[37] Among the so-called “mispositioned points” was
our low-temperature neutron and X-ray diffraction study of
HBA.[6] In our opinion the methodologies, and hence con-
clusions by Gilli, are problematic for a number of reasons.
First of all, we find a procedure in which a correlation is
postulated, and many results that do not agree with the ex-
pected behaviour are simply claimed to be “mispositioned”
We have also superimposed on the Steiner–Saenger curve
data from the very short hydrogen bonds in CTMH[27] and
NMA.[28] The bond lengths show good agreement with the
curve. It is interesting to note that in both systems the ther-
mal motion of the enol hydrogen atom is much elongated
along the direction between the two oxygen atoms.[35] In
NMA the RMSD of the enol hydrogen atom along the
O···O vector is 0.18 Š at 15 K.[22] The RMSD is also shown
in Figure 6 and the enol hydrogen atom makes substantial
excursions in a broad potential around the midpoint[36] be-
tween the two oxygen atoms and the hydrogen vibrates
freely in what can be considered an effective single-well po-
tential.
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Chem. Eur. J. 2007, 13, 5539 – 5547

Benzoylacetone Low-Barrier Hydrogen Bond
FULL PAPER
without further justification, to be problematic. Secondly, if
a correlation between the hydrogen position and the sym-
metry of the ring is to be claimed it should be based on only
high quality data. The correlations given and the analysis of
the hydrogen-transfer pathways in the work by Gilli et al. is
largely based on 38 selected putative accurate crystal struc-
tures mostly determined from X-ray data collected at room
temperature. This was done in spite of the well-known prob-
lem of carrying out an accurate deconvolution of positional
and thermal parameters solely from analysis of X-ray data,
in particular for the hydrogen atoms. The severe asphericity
problem in the charge density accumulating in the covalent
tributions of the hydrogen positions in short O···O hydrogen
bonds corresponding to selected double-well potentials have
been calculated (Figure 5), and show the diversity and rich
detail in the nature of the strong O···O hydrogen bonds.
Structure correlation studies such as the ones reported in
references [3,5,14,33,37] are definitely useful in getting an
overview of hydrogen-bonded systems, but also risk over-
simplifying a problem that is, in its nature, complex. Fig-
ures 5 and 6 underline the inherent dynamic nature of the
hydrogen bond and that the hydrogen position can not be
described fully by a single coordinate. Neutron diffraction
studies of individual cases will continue to be very desirable
in efforts to obtain more general understanding of chemical
ꢀ
ꢀ
O H bond creates an artificial shortening of the O H bond,
which is not properly addressed. As discussed above there is
very little difference between the difference charge density
of HBA (Figure 9c by Herbstein et al. in reference [26]) and
that of DBA, Figure 3. They look very much the same al-
though the hydrogen-transfer pathways in the two cases are
very different. We agree that Gilli et al. earlier demonstrat-
ed a certain correlation between the O···O distance and the
symmetry of the enol ring.[5] However, the correlation be-
tween the ring symmetry and the hydrogen position is much
more controversial in our opinion. Firstly there are the
above-mentioned reservations, whether one can meaningful-
ly speak of a hydrogen coordinate in a short hydrogen bond.
Secondly, the flat potential well means that the hydrogen
can be shifted significantly in the hydrogen bond with little
change of the energy of the system. As an example the hy-
drogen-bond energy in NMA was more than 110 kJmolꢀ1,
while the difference in energy between centred and off-cen-
tred hydrogen was only 0.3 kJmolꢀ1 (0.1 mHa).[32] Conse-
quently the enol hydrogen position can easily be perturbed.
This is seen both experimentally, in which intermolecular
hydrogen bonding leads to an asymmetric hydrogen posi-
tion,[32] and theoretically, in which the addition of a small
asymmetry term to the model potential leads to a large shift
in mean position (Figure 5f). Experimentally it was also
found that an asymmetric hydrogen position resulted in only
a small deviation from symmetry in the enol ring. NMA was
not included in the correlations by Gilli.[37]
ꢀ
bond aspects of the O H···O hydrogen bond.
Experimental Section
Sample preparation: Benzoylacetone was deuterated by repeated recrys-
tallisation in CH3OD. This readily exchanges H with D for the enol hy-
drogen atom between O(1) and O(2) and the H at C(3). As the signal
from the keto–enol hydrogen is difficult to detect by NMR spectroscopy,
the degree of deuteration was monitored by the peak corresponding to
the hydrogen bound to C(3). Large single crystals were grown by slow
evaporation of CH3OD containing a seed crystal.
Neutron diffraction: Single-crystal neutron diffraction data were collect-
ed at 15ꢁ0.5 K by using monochromatic thermal neutrons with a wave-
length of 0.955 Š on D19, a four-circle neutron diffractometer, on the
H11 thermal beam at the Institut Laue-Langevin, Grenoble. A structural
model including anisotropic thermal parameters on all atoms was fitted
to the experimental data. The relevant experimental and refinement de-
tails are summarised in Table 4.
Table 4. Experimental details for deuterated benzoylacetone.
X-ray study
Neutron study
formula
space group
a [Š]
b [Š]
c [Š]
C10O2H8D2
P21/c
C10O2H8D2
P21/c
8.016(1)
5.486(1)
19.445(3)
110.37(1)
801.6(2)
0.5616
8.015(1)
5.485(1)
19.462(1)
110.34(1)
802.2(1)
0.840
b [8]
V [Š3]
l [Š]
T [K]
11(1)
15(1)
Conclusion
data collection
diffractometer
scan method
type 512 HUBER
w-2q
D19 at the ILL
normal beam
Weissenberg
4536
3388
5.10%
We have shown how an enol deuteron in benzoylacetone
has a bimodal probability density function, while an enol hy-
drogen atom was earlier shown to have a broad unimodal
probability density function. This is the very definition of a
low-barrier hydrogen bond. By analysis of very low temper-
ature neutron diffraction data supported by extensive theo-
retical calculations, we have shown how the data can be in-
terpreted as the deuterium atom tunnelling between two
possible localised positions and the enol proton having suffi-
cient energy to shuttle over the low-energy barrier, even at
15 K.
measured reflns
unique reflns
RI
21063
6613
2.90%
ꢀ7ꢂhꢂ15
ꢀ10ꢂkꢂ10
ꢀ38ꢂlꢂ24
index range
ꢀ12ꢂhꢂ12
0ꢂkꢂ9
0ꢂlꢂ30
refinement
R(F)/R(F2) [%]
wR(F)/wR(F2) [%]
GoF
2.85/3.94
2.78/5.46
0.978
7.60/9.83
8.04/14.23
2.340
observed reflns [I>2s(I)]
parameters
weighting scheme
4644
2921
393
209
We have thereby underlined the dynamic and quantum
nature of the hydrogen bond. The zero-point probability dis-
1/s2(F2)
1/s2(F2)
Chem. Eur. J. 2007, 13, 5539 – 5547
ꢀ 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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5545

G. K. H. Madsen et al.
X-ray diffraction: Single-crystal X-ray diffraction data were collected at
11ꢁ0.5 K using AgKa radiation on a four-circle diffractometer with a dis-
plex mounted. A full multipole model[38] including a functional expansion
up to the octapole level for the carbon and oxygen atoms and up to the
quadrupole level for the hydrogen atoms was used. The hydrogen atoms
were fixed at the positions found in the neutron study. MSDs for the hy-
drogen atoms were derived by scaling the values obtained in the neutron
study. The relevant experimental and refinement details are summarised
in Table 4.
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2ꢀ
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ꢀ
were found for compression of the two O H covalent bonds.
For solving the anharmonic vibrational Hamiltonian we used a method
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earlier study[15] as it is not perturbative, and consequently potentials with
several minima and resulting tunnelling can be treated, as long as the
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Acknowledgements
[35] This is seen from the plot of the thermal ellipsoids in CTMH. Un-
fortunately the MSD of the hydrogen are not included in the at-
tached structure in reference [31] Therefore we can not study it
quantitatively.
[36] It should also be pointed out that the RMSD is actually a small
number compared to the distances covered by the enol hydrogen.
To just cover 50% of the probability density distribution a distance
of 1.54 times the RMSD is needed.
The help of Allesandra Silvani in deuterating benzoylacetone is gratefully
acknowledged. Computation time was allocated by the Danish Center
for Scientific Computing. B.S. thanks the Natural Danish Science Re-
search Council for a Skou grant. G.K.H.M. thanks the Carlsberg Founda-
tion for financial support.
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Chem. Eur. J. 2007, 13, 5539 – 5547

Benzoylacetone Low-Barrier Hydrogen Bond
FULL PAPER
Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari,
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Published online: March 15, 2007
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5547