Intra- and intermolecular effects in the Compton profile of water
M. Hakala,
1,
* K. Nygård,
1
S. Manninen,
1
L. G. M. Pettersson,
2
and K. Hämäläinen
1
1
Division of X-Ray Physics, Department of Physical Sciences, P.O.B. 64, FI-00014, University of Helsinki, Finland
2
FYSIKUM, Albanova University Center, Stockholm University, S-10691 Stockholm, Sweden
Received 18 August 2005; revised manuscript received 14 November 2005; published 26 January 2006
The electron momentum density of water is measurable in an inelastic x-ray scattering experiment in the
form of the Compton profile. The fine details of the profile, accessible by using high-brilliance synchrotron
radiation, are sensitive to the precise intra- and intermolecular geometries. We present a detailed quantitative
computational study of the sensitivity of Compton scattering to the different terms arising from the intramo-
lecular structure, nearest-neighbor interactions hydrogen bonds, and many-body properties cooperativity and
anticooperativity effects. The Compton profile is found to be predominantly sensitive to the internal O-H bond
length and the hydrogen bond geometry, being less affected by the internal H-O-H angle and the many-body
properties. In addition, an approximative method is introduced to provide a practical scheme for calculating
larger water aggregates.
DOI: 10.1103/PhysRevB.73.035432 PACS numbers: 78.70.Ck, 61.25.Em, 33.15.Dj
I. INTRODUCTION
Under different thermodynamic conditions water exhibits
a variety of intra- and intermolecular geometries whose de-
tection is fundamentally important.
1
In the gas, liquid, and
solid phases the internal H-O-H angle and O-H bond length
of the molecules are slightly different. At the intermolecular
level, the structure of the hydrogen bond H-bond network
depends on the aggregation state and thermodynamic condi-
tions, and determines, e.g., in a subtle way the many anoma-
lies of liquid water. On top of this, the variation of the intra-
and intermolecular geometries takes place simultaneously in
the liquid phase, where the H bonds continuously break and
reform on a picosecond timescale. Given the vital impor-
tance of this molecular liquid, it is important to possess novel
spectroscopies that can probe both the intra- and intermo-
lecular geometries on an equal footing.
The H-bond network in liquid water has recently become
subject of active debate.
2–11
X-ray absorption XAS and
x-ray Raman scattering XRS experiments have opened this
debate concerning the possible local structures and the
amount of broken or weakened H bonds in liquid water.
2
Wernet et al.
2
proposed a significant fraction of twofold co-
ordinated molecules in ambient water. This is in contrast to
the traditional picture from x-ray and neutron diffraction
combined with molecular dynamics simulations, according
to which each water molecule is surrounded by essentially
four other molecules with nearly equal H-bond strengths.
12
The existence of H bonds of widely different strengths may
lead to an important coupling of the intra- and intermolecular
degrees of freedom.
The present work concerns the interpretation of x-ray
Compton scattering CS experiments on water. CS, i.e., in-
elastic x-ray scattering at high momentum and energy
transfer,
13
is a complementary technique to XAS, XRS, x-ray
and neutron diffraction, and nuclear magnetic resonance to
study the local structure and coordination properties in
water.
7,14
We report calculations on the effect of the intra-
and intermolecular geometries in the Compton profile CP
of water, showing that the relevant geometrical terms can be
distinctly observed. Early CS experiments on liquid water
were performed in the 1970s,
15–17
with the conclusion that
the H bonds must be taken into account to explain the ex-
perimental results.
16,18,19
Using modern high-brilliance syn-
chrotron radiation, the statistical and systematic inaccuracy
in a CS experiment can now be as low as 0.02% at the peak
of the CP from liquid water,
7
which allows detailed studies
of the H-bond network. The recent CS studies have concen-
trated on directional anisotropies
20–24
in ice Ih, charge
transfer
25
and local coordination
14
in water clusters, and tem-
perature dependence of H bonds in liquid water.
7
However, a
systematic study of the intra- and intermolecular effects in
the CP has not been available. The lack of quantitative pre-
dictions of these effects fundamentally hampers the interpre-
tation of the fine details in the CS data.
In this work our aim is to fill this gap by performing
model calculations for isotropic CPs to study in detail the
influence of different molecular geometries. In our previous
study we concentrated on showing how CS can be used to
detect the local coordination around water molecules through
the oscillatory features in the CP.
14
Here we extend this
analysis to cover, on a quantitative level, the importance of
all the relevant intra- and intermolecular geometrical param-
eters for water aggregates. We present the spectral finger-
prints Figs. 2–7 and numerical values Table II in the CP
corresponding to the changes in each intra- and intermolecu-
lar geometrical property. These can be directly compared to
the experimentally observed features. We choose as a refer-
ence system the water dimer, relative to which the different
intra- and intermolecular distortions are systematically stud-
ied. We study physically relevant variations in the intramo-
lecular O-H bond lengths and H-O-H angles, as well as in the
H-bond lengths and angles. To study the importance of
many-body cooperativity and anticooperativity properties
in the CP we consider water chains, a ring and tetrahedral
geometries following Ref. 26. Our finding is that the many-
body properties have a relatively small influence on the CP.
This is in line with earlier indications.
14,23
Motivated by this,
an approximative scheme is introduced and proposed to be
PHYSICAL REVIEW B 73, 035432 2006
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