The Role of the Lone Pairs in Hydrogen Bonding

Monday, February 5 9:30-10:00
The Role of the Lone Pairs in Hydrogen Bonding
Ivar Olovsson
Materials Chemistry, ˚ Angström Laboratory, Box 538, SE-751 21 Uppsala, Sweden
The paper discusses some aspects of the electron lone-pairs in H-bonded structures: their role in determining
the short-range structure and the effect of the environment on the electron density. In the water
molecule the entire non-bonded region appears to be equally accessible for hydrogen bonding and the
details of the hydrogen-bond arrangement are mainly determined by simple geometrical and topological
requirements. On the other hand, in the case of the OH − ion the electron density is concentrated in
certain directions in the general lone-pair region and accordingly the hydrogen bond donor will preferably
approach the OH − ion in these directions. Many examples may be taken to illustrate that it is
important to take the whole electron and nuclear distribution into account when discussing the relative
arrangement of interacting molecules. The resulting structure of one particular compound is determined
by the net balance of many intermolecular interactions and not only by the hydrogen bonding, even if
the resulting structure is consistent with hydrogen-bond directionality. From structural data it can be
concluded that the immediate acceptor of a hydrogen bond is some negative charge accumulation, such
a in a lone-pair region, but not specifically any individual lone pairs in the traditional, atomic sense.
1

Monday, February 5 10:00-10:30
High-resolution Compton profiles
Pekka Suortti
Department of Physical Sciences, PL 64, FIN-00014 Helsinki University, Finland and European Synchrotron
Radiation Facility, BP 220, F-38043 Grenoble, France, e-mail: Pekka.Suortti@helsinki.fi, suortti@esrf.fr
Compton scattering has played a decisive role in some developments of modern physics, first in interpretation
of photon scattering and conservation laws, then in giving direct evidence that electrons in
solids obey Fermi-Dirac statistics. The history of Compton scattering is that of a dialogue between experiment
and theory at the deepest level, and theory and experiment have taken the lead alternately.
In this work the development of focusing crystal spectrometers for Compton scattering studies from
1930s to present is reviewed. The design principles have stayed the same, but the efficiency has improved
much owing to the availability of large perfect crystal analyzers and efficient detectors. The reflectivity
and energy resolution of the crystal can be tailored to the needs of the experiment by the asymmetric
cut, thickness and bending radius of the crystal, and the response function of the spectrometer can be
calculated precisely. The spectrometers at synchrotron radiation beamlines achieve better than 0.1 a.u.
momentum resolution, and several statistically accurate Compton spectra can be acquired in one day.
The latest developments include spectrometers that operate in the 100 keV range, and count rates are
enhanced by using wide energy bands and dispersion compensation. Experimental momentum density of
crystalline LiH is compared with results of a Hartree-Fock calculation in terms of directional Compton
profiles and reciprocal form factors. The agreement is excellent, and the residual differences are attributed
to electron-electron correlation, which is not included in the H-F calculation. The correlation energy
is calculated from the second moment of the difference between experimental and theoretical Compton
profiles.
2

Monday, February 5 14:30-16:00
Name
Ort
3

Monday, February 5 11:45-13:15
Electron density and density matrix, a key quantity for systems
at and out of equilibrium.
Pierre BECKER, Jean Michel GILLET, Blandine COURCOT
Ecole Centrale Paris, Grande Voie des Vignes, 92295 Chatenay Malabry Cedex, France - SPMS CNRS
Unit, pierre.becker@ecp.fr
The crucial role of one particle reduced density matrices occurs when trying to get complementary
information from different sources of observation for steady state systems. Application to charge, spin
and momentum density analysis has been the main research activity of our group. Taking advantage
of the pioneering work by Vedene Smith and Wolf Weyrich, we were able to develop a ”pseudo-atomic,
pseudo-molecular or clusterëxpansion of the reduced density matrix. This is a generalisation to density
matrix of the celebrated pseudo-atomic expansion of the charge density. Each term takes into account the
interaction with neighboring sites. Transferability is an implied concept to be discussed. Applications
go from solids to molecules in interaction with their surrounding medium. We were able to jointly
analyze Bragg and Compton scattering experiments. A recent generalization to pharmaceuticals and
their interaction with biological medium is considered. Finally first steps for an approach of systems out
of equilibrium and undergoing chemical reactions are discussed.
4

Monday, February 5 14:30-16:00
Local chemical bonding in metals
Wedig, Ulrich; Nuss, Jürgen; Karpov, Andrey and Jansen, Martin
Max-Planck-Institut für Festkörperforschung, Heisenbergstr. 1, 70569 Stuttgart, Germany
The large variety of structures and properties of solid compounds is caused by a competing interplay
of different bonding types: (1) ionic bonding caused by charge transfer, (2) covalent interactions being
associated with electron localization, (3) metallic bonding requiring itinerant electrons and (4) dispersion
interactions being related to the polarisability of closed electronic shells. As the terms related to chemical
bonding are of conceptual nature and no quantum mechanical observables, it is difficult to identify the
various contributions and their impact on the properties of the solid state compounds. Several quantities
like the electron localization function (ELF), which can be computed from wavefunctions or Kohn-
Sham orbitals, can help to identify covalent and ionic substructures. However, in metals, the analysis
is complicated by the fact, that the subdivision of the entirety of valence electrons into localised and
delocalised parts is not obvious. Therefore it is necessary to validate the application of different bonding
concepts by suitable experiments. In the following, two examples are given. Binary intermetallic phases
of cesium and barium with platinum contain local anionic structures in the Pt sublattice like isolated
anions (Cs2Pt 1 and Ba2Pt 2 ), negatively charged dumbbells (Ba3Pt2 3 ) and chains (BaPt 4 ). Whereas
the charge transfer in the Cs compound is complete, leading to a band gap, all the Ba compounds are
metallic. The topological analyses of the computed electron densities as well as of the ELF gave rise to
the following formal description of the Ba / Pt systems: [(Ba2 +)22e-] ÂPt2-, [(Ba2+)1.5Â1.5e-]ÂPt1.5and
[Ba2+ Âe-]ÂPt-. This charge assignment recently was confirmed by ESCA measurements5 . Even the
arrangement of metal atoms in elemental structures bears open questions. E.g. the crystal structures of
Zn and Cd deviate from hexagonal close packing, as indicated by an exceptional large c/a ratio. The
causes of these deviations are the topic of a combined experimental and theoretical study6 , 7. Electron
correlation including the filled d-shells plays a crucial role in the intraand inter-layer interactions. At
the DFT(GGA, PBE) level, the potential energy surface with respect to the lattice constants is very flat
along the c-axis. This is reflected by an unusual hysteresis in the stress-strain relation8 .
1 Karpov, A.; Nuss, J.; Wedig, U.; Jansen, M.; Angew. Chem. Int. Ed. 2003, 42, 4818-4821. 2 Karpov,
A.; Wedig, U.; Dinnebier, R. E.; Jansen, M.; Angew. Chem. Int. Ed. 2005, 44, 770-773. 3 Karpov, A.;
Wedig, U.; Jansen, M.; Z. Naturforsch. 2004, 59b, 1387-1394. 4 Karpov, A.; Nuss, J.; Wedig, U.; Jansen,
M.; J. Am. Chem. Soc. 2004, 126,14123-14128. 5 Karpov, A.; Konuma, M.; Jansen, M.; Chem. Commun.
2006, 838-840. 6 Jansen, M.; Wedig, U.; Kirfel, A.; Schlenz, H.; Weyrich, W.; project within the DFG
priority program 1178 ExpED. 7 Wedig, U.; Jansen, M.; Paulus, B.; Rosciszewski K.; Sony, P.; to be
submitted. 8 Collaboration with C. Frick, Max-Planck-Institute for Metals research.
5

Monday, February 5 14:30-16:00
The Method of Increments - a Wavefunction-based Ab-initio
Correlation Methods for Solids
Beate Paulus
Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Stra38, 01187 Dresden, Germany
Due to a localization of the orbitals it is possible to apply wavefunction-based correlation methods to
solids. The so-called method of increments is based on a preceding HF treatment explicitly calculates
the many-body wavefunction in contrast to the density-functional theory which relies on the groundstate
density of the system. The correlation energy of the solid is expressed in a incremental expansion
in terms of localised orbitals or of a group of localised orbitals. The method of increments which has
been successfully applied to a great variety of materials with a band gap 1 , is now extended to metals.
There the correlation energy increments are determined in finite, properly embedded fragments of the
metal. In detail the influence of the electronic correlation on the ground-state properties of solid mercury
are discussed. Whereas the DFT treatment yields for mercury not concluding results, the method of
increments achieves a very good agreement with experimental ground state properties 2 − 4. First results
for the structure of the other group IIB metals Zinc and Cadmium are presented, which the hexagonal
close-packed (hcp) structure, but with an anomalous c/a ratio which is far from ideal hcp.
1 B. Paulus, Phys. Rep. 421, 1 (2006). 2 B. Paulus and K. Rosciszewski, Chem. Phys. Lett., 394, 96100
(2004). 3 B. Paulus, K. Rosciszewski, N. Gaston, P. Schwerdtfeger and H. Stoll, Phys. Rev. B 70, 165106
(2004). 4 N. Gaston, B. Paulus, K. Rosciszewski, P. Schwerdtfeger and H. Stoll, Phys. Rev. B 74, 094102
(2006).
6

Monday, February 5 14:30-16:00
WHAT THE SOURCE FUNCTION TELLS US ABOUT CHE-
MICAL BONDING
C. Gatti
CNR-ISTM, Istituto di Scienze e Tecnologie Molecolari, via Golgi 19, 20133 Milano, Italy
Few years ago, 1 Richard Bader and I showed that the electron density ? at any point r within a molecule
may be viewed as consisting of contributions from a local source (LS) operating at all other points r’.
When the LS is integrated over regions ? satisfying the Quantum Theory of Atoms in Molecules (QTAIM)
definition of an atom in a molecule, ?(r) may be equated to a sum of atomic contributions S(r;?), each
of which is termed as the source function (SF) from the atom ? to ?(r). Such a decomposition enables
one to view the properties of the density from a new perspective and establishes the source function
(SF) as an interesting tool to provide chemical insight. 1 , 2, 3 The bond critical points (BCP) have been
generally taken as the least biased choice for points representative of bonding interactions. Analysis of
the LS(BCP, r’) profile, along a bond path, introduces further detail. 4
Although depending on the whole set of interactions within a system, a bond path is topologically
associated only to the two atoms it connects. On the contrary, the SF details how all the other atoms in
a system, in addition to the two linked atoms, contribute to the accumulation of electron density along
a bond path and, in particular, at BCP. 1 , 2, 5 It so discloses non-local information on bonding and on
complex bonding patterns, 3 , 5 analogously to the QTAIM delocalisation index or the synaptic order of
an Electron Localization Function (ELF) valence basin. One advantage of the SF over these two very
powerful interpretive tools is that it is potentially directly amenable to experimental determination, since
to evaluate it only the knowledge of the system’s electron density and Laplacian is required.
The SF can also be used as a very sensitive measure of an atom’s or chemical group’s transferability and of
the consequences derived thereof. 1 , 2Indeed, the”perfect”transferabilityofagrouppropertyfromonemoleculeto
In this talk, I´ll present few paradigmatic applications of the SF concerning chemical transferability and
chemical bonding. In particular Ill show how this function is able to markedly distinguish hydrogen bonds
of different strength or to give a description of the metal-metal (M-M) bonding in d-block organometallic
compounds closely related to that provided by the localization/delocalization indices. This agreement
persists even when the M-M bond is lacking and the internuclear M-M midpoint is taken as a reference
point for evaluating the SF contributions. However, use of the local form of the SF unveils interesting
differences in how the charge density originates at the M-M midpoint when the system is metal-metal
bonded or not. Conversely, most of the topological indices conventionally adopted to describe M-M bonds
fail in reproducing the expected chemical trends for the set of investigated systems. Recent progresses6 in deriving an ambiguity-free full population analysis from the SF will be also mentioned.
1 Bader R.F.W., Gatti C., Chem. Phys. Lett., 1998, 287, 233. 2 Gatti C., Cargnoni F., Bertini L., J.
Comput. Chem., 2003, 24, 422. 3 Gatti C, chapter 7 in Quantum Theory of Atoms in Molecules , C.
Matta and R. Boyd (Eds.), Wiley-VCH 2007, in press, ISBN: 978-3-527-30748-7. 4 Gatti C., Bertini L.,
Acta Cryst. 2004, A60, 438. 5 Gatti C., Lasi D., Faraday Discussion.,2007, 135, 55-78. 6 Gatti C., Lasi
D., 4th European Charge Density Meeting, Branderburg/Havel (Germany), 26-29 January 2006
7

Monday, February 5 16:30-17:30
WHAT COMPTON SCATTERING TELLS ABOUT THE INTRA-
AND INTERMOLECULAR STRUCTURE OF WATER?
M. Hakala
Division of X-Ray Physics, Department of Physical Sciences, P.O.B. 64, FI-00014 University of Helsinki,
Finland Email: mikko.o.hakala@helsinki.fi
Besides being the most familiar and ubiquitous liquid, water is most interesting from the microscopic
point of view. The structure and properties of this molecular liquid are determined by the hydrogen bond
(H bond) network. The H-bond network as well as the intramolecular geometry (e.g. the length of the
covalent O-H bond) depend on the thermodynamic state. The fact that even the structure of the first
coordination shell continues to be debated [1] gives an ample motivation to study water with new and
improved methods. In this talk I will review our recent Compton scattering experiments on water using
synchrotron radiation and the findings we have obtained with model calculations. The experiments we
have carried out include: (i) temperature effect of the liquid [2], (ii) ice-liquid transition [3], (iii) isotope
effect, and (iv) temperature effect of ice. From each set one can extract difference Compton profiles (CPs)
J(q), which can be interpreted by the changes in the intramolecular (O-H length, H-O-H angle) and/or
intermolecular (H-bond length and angle) parameters. I will discuss two computational approaches used
in this work. The first one is a nonselfconsistent model [4], in which additive nearest-neighbor interactions
are assumed between the molecules. The model incorporates the possible changes in the intramolecular
geometry and in the local nearest-neighbor interaction, but excludes the cooperative and anticooperative
properties of the H-bonds. I show that when applied to difference CPs, this model gives a good physical
insight into the changes in the H-bond network, and can be adjusted to reasonably well capture the
main features observed in the experiments. The second approach is an ab initio method, where the CPs
are directly calculated from snapshot structures of a Car-Parrinello molecular dynamics simulation. The
resulting difference CP suffices to qualitatively describe the experimental temperature effect of water.
[1] See, for example, M. Odelius, M. Cavalleri, A. Nilsson, and L. G. M. Pettersson, Phys. Rev. B 73
(2006) 024205; D. Prendergast and G. Galli, Phys. Rev. Lett. 96 (2006) 215502. [2] M. Hakala, K.
Nyg˚ard, S. Manninen, S. Huotari, T. Buslaps, A. Nilsson, L. G. M. Pettersson, and K. Hämäläinen, J.
Chem. Phys 125 (2006) 084504. [3] K. Nyg˚ard, M. Hakala, S. Manninen, A. Andrejczuk, M. Itou, Y.
Sakurai, L. G. M. Pettersson and K. Hämäläinen, Phys. Rev. E 74 (2006) 031503. [4] M. Hakala, K.
Nyg˚ard, S. Manninen, L. G. M. Pettersson and K. Hämäläinen, Phys. Rev. B 73 (2006) 035432.
8

Monday, February 5 10:00-10:30
CHARGE DISTRIBUTION AND CHARGE FLOW: DIPOLE
MOMENTS AND POLARIZATION
Michael Springborg a Bernard Kirtman b Yi Dong a Violina Tevekeliyska a
a Physical and Theoretical Chemistry, University of Saarland, 66123 Saarbrücken, Germany b Department
of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, U.S.A.
For a finite molecule, the dipole moment is closely related to the static charge distribution in position
space. For not too small molecules consisting of essentially identical units, the dipole moment contains
two contributions: one from the charge distribution in the inner part of the system and one from the
terminations. Very often, such systems are treated as being infinite and periodic. However, in that case
the contributions from the terminations are, per construction, removed. Apparently, the polarization,
i.e., dipole moment per repeated unit, differs then from the value found for the finite systems. We shall
show that by assuming that the system is infinite and periodic, it is no longer sufficient to consider the
static charge distribution when calculating the polarization, but an extra term that can be interpreted
as a charge flow has to be included, too. In some cases, this extra term may be the dominating one. In
order to illustrate our approach, results of model calculations on a quasi-onedimensional system shall
be reported. In particular it shall be demonstrated that infinite-chain calculations and ones for finite
chains of sufficient length lead to the same polarization. Subsequently, it shall be demonstrated how such
systems in the presence of an external, electrostatic field can be treated, whereby the correct definition
of polarization becomes crucial. Finally, current limitations and open issues of our approach shall be
discussed.
9

Tuesday, February 6 08:45-10:15
Maximum Probability Domains From Quantum Monte Carlo
Calculations
Anthony Scemama 1 , Michel Caffarel 1 , Andreas Savin 1
1 Laboratoire de Chimie et Physique Quantique, IRSAMC CNRS and Université Paul Sabatier, 118 route
de Narbonne, 31062 Toulouse Cedex, France 2 Laboratoire de Chimie Théorique, CNRS and Université
Paris Pierre et Marie Curie, Case 137, 4 place Jussieu, 75252 Paris Cedex 05, France
Although it would be tempting to associate the Lewis structures to the maxima of the squared wave
func- tion Èy È2 , we use domains of the three-dimensional space, which maximize the probability
of containing opposite-spin electron pairs. We find for simple systems (CH4, H Â2O, Ne, N2,
C2H2)domainsqualitativleycomparabletothoseobtainedwiththeelectronlocalizationfunction(ELF )orbylocaliz
and of the symmetric hydro- gen bond in FHF- . Furthermore, the presence of multiple solutions has an
analogy with resonant structures, as shown in the trans-bent structure of Si2H2.
Correlated wave functions were used (MCSCF or Slater-Jastrow) in the Variational Quantum Monte
Carlo framework.
10

Tuesday, February 6 08:45-10:15
On the nature and consequences of ligand-induced charge concentrations
in transition metal oxides and alkyls
Wolfgang Scherer
Institut für Physik, Universität Augsburg, Universitätsstr. 1, D-86159 Augsburg, Germany, Tel: 49-821-
598-3351, Fax: 49-821-598-3227, wolfgang.scherer@physik.uni-augsburg.de
Since the theoretical prediction [ 1] and experimental verification [ 2] of so-called ligand-induced charge
concentrations (LICCs) in the valence shell of transition metals in electron-deficient complexes several
attempts have been undertaken to understand their origin and chemical relevance. In pioneering studies
we could demonstrate that these LICCs not only influence the geometry of coordination compounds
in non-VSEPR complexes such as Me2T iCl2, Me3NbCl2 or Me2NbCl3 [ 3] but also serve as controlling
parameters for important chemical reactions like C-H bond activation in transition metal alkyls. [ 4] Furthermore,
in covalent oxides such as polymeric methyltrioxorhenium pronounced LICCs appear to induce
electron localization phenomena as revealed by metal-to-insulator transitions at low temperatures. [ 5] The
complex interplay of ligand-induced charge concentrations with the physical and chemical properties of
molecules and solids is therefore the central topic of this contribution. We will also demonstrate that
LICCs are an integral part of the chemical bond between a transition metal atom and its ligands.
Key References:
[1] I. Byetheway, R. J. Gillespie, T. H. Tang, R. F. W. Bader, Inorg. Chem. 1995, 34, 2407.
[2] W. Scherer, P. Sirsch, D. Shorokhov, M. Tafipolsky, G. S. McGrady, E. Gullo, Chem. Eur. J. 2003,
9, 6057.
[3] G. S. McGrady, A. Haaland, H. P. Verne, H. V. Volden, A. J. Downs, D. Shorokhov, G. Eickerling,
W. Scherer, Chem. Eur. J. 2005, 11, 4921.
[4] (a) W. Scherer, G.S. McGrady, Angew. Chem. Int. Ed. 2004, 43, 1782. (b) W. Scherer, G. Eickerling,
M. Tafipolsky, G. S. McGrady, P. Sirsch, N. P. Chatterton, Chem. Commun. 2006, 2986.
[5] R. Miller, E.-W. Scheidt, G. Eickerling, Ch. Helbig, F. Mayr, R. Herrmann, W. Scherer, H.-A. Krug
von Nidda, V. Eyert, P. Schwab, Phys. Rev. 2006, 373, 165113.
11

Tuesday, February 6 08:45-10:15
Size Effects in Clusters
Jan-Ole Joswig
Physikalische Chemie und Elektrochemie, TU Dresden, 01062 Dresden
Clusters are intermediates between atoms and the solid state. Usually, they have diameters of a few
˚Angström up to several nanometers and contain, therefore, up to several thousand atoms. In this size
range, the properties of the system of interest are affected by quantum-size effects. Thus, clusters have
different properties compared to those observed in the macroscopic world. These vary, moreover, with
the cluster size. In order to gain insight in this size-dependence, the structural, electronic and optical
properties of various metal and semiconductor clusters with up to several hundred atoms have been
studied using different computational methods and methodological approaches.
12

Tuesday, February 6 10:45-11:45
Electron and Magnetization Density in the Transition Metal
Oxide Co3V2O8
H. Fuess, N. Qureshi, H. Ehrenberg
Technische Universität Darmstadt, Fachbereich Material- und Geowissenschaften, Fachgebiet Strukturforschung,
Petersenstraße 23, 64287 Darmstadt, Germany E-mail: hfuess@tu-darmstadt.de
Cobaltorthooxovanadate is a spin-3/2 system on a Kagomé staircase which exhibits a sequence of five
magnetic phase transitions 1 due to the relief of frustration by the decreased symmetry of the magnetic
lattice (space group Cmca, Co1 on 4a and Co2 on 8e sites) 2 compared to the ideal Kagomé net. It shows a
ferromagnetic ground state below 6K and an intermediate antiferromagnetic region between 6K and 11K
with various commensurate and incommensurate magnetic structures. Our neutron powder diffraction
experiments 3 revealed that within the ferromagnetic phase the magnetic moments align along the a-axis
with a slight canting along c with different values for the two different Co sites. The antiferromagnetic
phase can be described by a propagation vector k=(0,ky,0) with a temperature dependent ky which
changes throughout the phase. The complexity of the magnetic structures and phase transitions is be attributed
to the balancing of the multiple Co-O-Co superexchange interaction pathways. This complexity
can be disturbed by partially substituting Co with Ni resulting in antiferromagnetic (CoxNi1 − x)3V2O8
compounds exhibiting only one magnetic phase transition, which has been verified for powder samples
with x=0.27, 0,52 and 0.76 4 . In order to examine the superexchange pathways in Co3V2O8, preliminary
electron and magnetization density measurements have been carried out which should provide a base
for theoretical interpretation of the complicated magnetic behaviour by refining the obtained data sets
using the multipole formalism. Hence, the anisotropy of the Co 2 + form factor, i.e. the deviation from
the spherical model, should be revealed resulting in important information about the highly interesting
superexchange coupling mechanisms.
[1] Y. Chen, J.W. Lynn, Q. Huang, F.M. Woodward, T. Yildirim, G. Lawes, A.P. Ramirez, N. Rogado,
R.J. Cava, A. Aharony, O. Entin-Wohlman, A.B. Harris Phys. Rev. B 2006, 74, 014430 [2] H. Fuess, E.F.
Bertaut, R. Pauthenet, A. Durif Acta Cryst. 1970, B26, 2036. [3] N. Qureshi, H. Fuess, H. Ehrenberg,
T.C. Hansen, D. Schwabe Sol. State Comm., submitted [4] N. Qureshi, H. Fuess, H. Ehrenberg, T.C.
Hansen, C. Ritter, K. Prokes, A. Podlesnyak, D. Schwabe Phys. Rev. B 2006, 74, 212407
Acknowledgment: This research was supported by the Deutsche Forschungsgemeinschaft through the
DFG 125/45 program and the Deutscher Akademischer Austausch-Dienst (DAAD).
13

Tuesday, February 6 10:45-11:45
Density-Matrix Study of the Hydrogen-Antihydrogen Molecule
Alejandro Saenz
AG Moderne Optik, Institut für Physik, Humboldt-Universität zu Berlin Hausvogteiplatz 5-7, D-10 117
Berlin, Germany
There is a long history of the interest in antimatter and its properties. Starting from the theoretical
prediction of its existence by Dirac and its first experimental detection antimatter stimulated scientists,
but even science fiction authors. The scientific interest is closely linked to its role with respect to fundamental
symmetries of nature. According to the standard model of physics, equal amounts of matter and
antimatter were formed in the Big Bang creating our universe. However, we are evidently (and in view
of annihilation processes fortunately!) practically only surrounded by matter. There is no evidence for
large matterantimatter annihilation taking place in our (visible) part of the universe. This leads directly
to a fundamental open question: where is the antimatter gone? A good candidate for antimatter research
are antihydrogen atoms that consist of an antiproton and a positron. They are polarisable and can thus
be trapped. On the other hand, they are electrically neutral which avoids that they are sensitive to stray
fields. In addition, the matter analogy (atomic hydrogen) has a long history of being the workhorse for
validating quantum mechanics as well as quantum electrodynamics, because it is accessible to very precise
theoretical and experimental studies. This motivated on-going experiments at CERN and planned
future ones at GSI (Darmstadt). One interesting question in the context of antihydrogen research is
its interaction with ordinary atoms. The simplest example is evidently atomic hydrogen. As our studies
have shown, the hydrogen-antihydrogen system is an interesting object by itself. Although it is related to
molecular hydrogen, the change of the sign of the charges and the absence of exchange interaction leads
to a number of effects that are specific to antimatter-matter systems, but absent for ordinary molecules.
Nevertheless, hydrogen-antihydrogen can form an in the chemical sense bound molecular system. On
the first glance, the bonding should be of electrostatic nature and thus ionic. Based on a study of the
leptonic densities and density matrices the character of the bond is, however, investigated in more detail
in this work. Such investigations are non-trivial, since the leptons (electron and positron) are highly
correlated. The theoretical description of the hydrogen-antihydrogen molecule requires therefore very
accurate quantum-chemical approaches.
14

Tuesday, February 6 12:00-13:00
Quantum mechanical simulation of the vibrational properties
of crystalline solids with the CRYSTAL06 computer code. The
case of garnets and related minerals.
R. Dovesi
Dipartimento de Chimica IFM, Via P. Giuria 5, I-10125 Torino, Italia E-mail: roberto.dovesi@unito.it
One of the new features of the CRYSTAL06 [1] computer code, in distribution since September 2006,
is the FREQUENCY option, that permits the investigation of the vibrational properties of crystalline
solids at the à point of the Brillouin zone. CRYSTAL is a periodic ab initio program, that uses a
local variational basis set (Ätomic Orbitals”) to build the crystalline orbitals. An all-electron basis and
the B3LYP hamiltonian have been used. The vibrational properties of pyrope, grossular, andradite and
other members of the garnet family (80 atoms/cell) have been generated and compared with IR and
RAMAN experimental data, that for the present compounds are very accurate [2], [3]. The symmetry
of the modes is authomatically determined by the code. The eigenvectors of the dynamical matrix have
been analyzed with different tools, including direct inspection, isotopic substitution, graphical animation;
some of the classificationinterpretation questions raised by previous studies are discussed. The agreement
with experiment is, in most of the cases, excellent (6-8 cm−1 the mean absolute difference). The present
work permits, however, to fill the gaps in the experimental sets, and to solve a few assignement problems
present in the experimental studies (mainly due to low intensities) and in previous simulations (based
on force fiend models).
[1] Dovesi, R.; Saunders V.R.; Roetti, C.; Orlando, R.; Zicovich-Wilson, C.; Pascale, F; Civalleri, B;
Harison, N.; Doll, K.; Bush, I.; D?Arco, Ph.; Llunell, M. (2003) CRYSTAL2006 user?s manual. University
of Torino, Torino. [2] Kolesov, B.; Geiger, C. Phys. Chem. Min, 2000, 27, 645. [3] Hofmeister, A.;
Chopelas, A. Phys. Chem. Min, 1991, 17, 503.
15

Tuesday, February 6 12:00-13:00
ON THE DIFFICULTIES OF JOINT REFINEMENT OF 1-
MATRICES FROM DIFFERENT EXPERIMENTAL DATA
JEAN-MICHEL GILLET
Ecole Centrale Paris ” Laboratoire SPMS, UMR CNRS 8580 ” 92295 Chatenay-Malabry Cedex, France,
jean-michel.gillet@ecp.fr
High resolution x-ray diffraction, convergent beam electron diffraction, deep in- elastic x-ray scattering
(Compton scattering), e-2e and ◦ -e- ◦ spectroscopies have in common to be directly related to the Oneelectron
Reduced Density Matrix (1- RDM)[13]. On the other hand, it is well known [7][3] that the
1-RDM contains all the information about the electronic structure available at the one-electron level.
Unfortunately, and to our best knowledge, few attempts for refining 1-RDM models have been carried out
[2][8][5][12][6] [1]. With the exceptions of Schmider [9][10] for atomic systems, and Schulke and co-workers
[11] only x-ray diffraction data were employed as experimental references. The purpose of this talk is
to discuss to what extent the successfull decomposi- tion of the electron density into aspherical pseudoatomic
contributions [4] can be adapted to the 1-RDM case. Furthermore, we intend to show that, with
such a model, the complementarity between very different experiments can be better ex- ploited through
a joint refinement. Emphasis will be made on the diffculties which are specific to a joint refinement of
1- matrices from different experimental data as opposed to usual ”mono-experimental”refinements.
References
1. Y. Aleksandrov, V Tsirelson, I. Reznik, and R. Ozerov, Phys. Status Solidi B 155 (1989), 201-207.
2. W.L. Clinton and L.J. Massa, Phys. Rev. Lett. 29 (1972), no. 20, 1363. 3. C.A. Coulson, Present
state of molecular structure calculations, Review of Modern Physics 32 (1960), no. 2, 170-177. 4. N.K.
Hansen and P. Coppens, Testing aspherical atom refinements on small-molecule data sets, Acta Cryst.
A 34 (1978), 909-913. 5. S.T. Howard, J.P. Hulke, P.R. Mallinson, and C.S. Frampton, Density matrix
refinement for molecular crystals, Phys. Rev. B 49 (1994), no. 11, 7124-7136. 6. D. Jayatilaka and D.J.
Grimwood, Acta Cryst. A 57 (2001), 76-86. 7. P.-O. Löwdin, Quantum theory of many-particle systems
i, Physical Review 97 (1955), no. 6, 1474. 8. L. Massa, M. Goldberg, C. Frishberg, R.F. Boehme,
and S.J. La Placa, Wavefunctions derived by quantum modeling of the electron density from coherent
x-ray diffraction: Beryllium metal., Phys. Rev. Lett. 55 (85), no. 6, 622-625. 9. H. Schmider, K.E.
Edgecombe, V. H. Smith, and W. Weyrich, One-particle density matrix along the molecular bonds in
linear molecules, J. Chem. Phys. 96 (1992), no. 11, 8411-8419. 10. H. Schmider, V. H. Smith, and W.
Weyrich, Z. Naturforsch. A 48 (1993), 211-220. 11. W. Schulke, U. Bonse, and S. Mourikis, Phys. Rev.
Lett. 47 (1981), no. 17, 12091212. 12. J.A. Snyder and E.D. Stevens, A wavefunction and energy of
the azyde ion in potassium azide obtained by a quantum-mechanically constrained fit to x-ray diffraction
data., Chem. Phys. Lett. 313 (1999), 293-298. 13. W. Weyrich, One-electron density matrices and related
observables, Quantum Mechanical Ab- initio Calculation of the Properties of Crystalline Matrials (C.
Pisani, ed.), Springer-Verlag, 1996, pp. 245-272.
I wish to express my warm gratitude to N. Ghermani and Y. Sakurai for essential exchanges on experimental
issues. P.J. Becker, B. Courcot and P. Cortona are greatly thanked for stimulated discussions as
well as the SSpin, Charge and Momentum DensitiesSSagamore community for inspiring this work.
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