Chemistry Reference
In-Depth Information
Another important step forward in obtaining theoretical solid-state dipole
moments was the introduction of Bader's Quantum Theory of Atoms in Molecules
(QTAIM) [
52
], which provides an atomic partitioning scheme for isolated-
molecular as well as periodic EDD. One characteristic of Bader's partitioning
scheme is that atomic fragments each have a dipole moment. Since the sum of
QTAIM fragments and their properties are additive, they reproduce space
completely, and a molecular dipole moment can be calculated from the sum of
the individual atoms in the gas phase or the bulk. Hence, QTAIM provides an
attractive route to accurate dipole moments and their possible enhancements from
first principles [
53
-
55
]. QTAIM results are not discussed in this study, but are
provided, e.g., in [
53
].
4.1 Dipole-Moment Enhancements from Simple
Theoretical Cluster Calculations
The simplest way to obtain dipole-moment enhancements from theory are
calculations on molecular clusters which we will now discuss. An obvious approxi-
mation made in such an approach is the choice of the distance threshold, for which
surrounding whole molecules are included.
For the seven zwitterionic organic molecules studied, a cluster based on a 3-5
˚
threshold was used. This corresponds to including all surrounding molecules that
are closer than this distance threshold to any atom of the central molecule. Typical
cluster sizes, including the examples of the amino acids studied here, are 14-21
molecules. Input files were generated with the program
BAERLAUCH
[
56
], and require
only atomic positions, a cut-off radius and the space group. To decide which cluster
size was required, we geometry optimized the central molecule in the field of
surrounding molecules using the ONIOM implementation [
57
] of quantum
mechanics/molecular mechanics (QM/MM) in all seven cases (results not shown
here). In case the optimization converged, the cluster size was considered to be
sufficient also in single-point cluster calculations. Computational details of the
ONIOM procedure for molecular crystals are given in [
56
].
Calculations with a field of point charges are not expensive to perform, since the
environment of the cluster is represented by few additional Gaussian functions.
In principle, the method and basis set chosen for the calculations can be as
sophisticated and extended as the computer permits. Computational requirements
are similar to single-point calculations. Cluster calculations with a field of point
charges yield a wavefunction file of an “isolated” molecule. This is in contrast to
ONIOM cluster calculations, where the geometry of the central molecule can
be optimized, but no isolated-molecule wavefunction file is written in
GAUSSIAN
[
44
], since the phase relationship between the different level wavefunctions is
undefined. A projection onto the multipole model is technically only possible
