Chemistry Reference
In-Depth Information
3 On the Ability of the Multipole Model to Reproduce Theoretical Dipole Moments . . . . . . 32
4 Dipole-Moment Enhancements from Theory . . . ............................................. 34
4.1 Dipole-Moment Enhancements from Simple Theoretical Cluster Calculations . . . . . 35
4.2 Theoretical Estimate of Dipole-Moment Enhancements with Cluster
Charges and Dipoles . .................................................................. 37
5 Dipole-Moment Enhancements by Combining Theory and Experiment ................... 37
5.1 Molecular Dipole Moments and Their Enhancement in the Solid State from
Experimental Multipole Refinement and Invariom Refinement . ..................... 38
5.2 Molecular Dipole Moments and Their Enhancement from Hirshfeld-Atom
Refinement and Wavefunction Fitting ................................................. 40
6 Discussion: Agreement Between Experimental and Theoretical Results .................. 41
7 Conclusion . . . ................................................................................. 42
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
1
Introduction
Intermolecular forces are of great interest in chemistry and physics. The classical
electrostatic interaction energy between two species can be expanded in a multipole
series. Its most important term (for neutral species) is the dipole moment [
1
]. The
dipole of a system is of fundamental and continuing interest.
When non-spherical scattering models were introduced in the late-1960s [
2
-
4
]
and optimized throughout the 1970s [
5
-
7
] it became possible to obtain dipole and
higher multipole moments from accurate single-crystal X-ray diffraction data. The
basic characteristic common to these different non-spherical scattering models is
that they provide an analytical description of the electron density distribution
r
(r)
(EDD) in terms of products of atom-centred radial and spherical harmonic angular
functions. Only the populations of the latter angular functions (and possibly a radial
scaling parameter
k
) are adjusted (via a least-squares procedure) to reproduce the
intensities of the diffraction experiment. The Hansen/Coppens approach [
7
] has
proven to be successful throughout the last decades in that it has enabled experi-
mental characterization of solid state electronic structure and bonding.
Lately, the multipole model [
5
,
7
] has undergone significant development and
a change in philosophy. Instead of the multipole parameters being refined from the
X-ray data, they can alternatively be predicted by fitting to theoretical data obtained
from quantum mechanical calculations [
8
]. Not only the multipole parameters but
also H-atom vibration parameters (the atomic displacement parameters or ADPs)
can additionally be derived from theoretical calculations or other external sources
of information like neutron diffraction [
9
-
11
]. Programs and schemes have been
developed to transfer electron-density parameters from atoms in smaller molecules
into larger molecules where the chemical environment is similar. Thus, the tradi-
tional role of the experimental measurements determining bonding density has been
depreciated in favour of an emphasis on accurate geometric parameters, especially
for larger molecules. The significance of these developments on dipole-moment
determination from X-ray diffraction data requires substantial characterization.
