Chemistry Reference
In-Depth Information
Since high-resolution data were not available in the case of
L
-cysteine, we use
recently introduced methodology [
43
] to obtain an experimental dipole moment
despite limitations in data resolution by including ADPs from a previous invariom
refinement [
33
] in a block-matrix refinement of
L
-cysteine. This procedure and the
low data-collection temperature of 30 K allowed to reach the same accuracy as
achieved for the other examples.
Requirements for data resolution are more modest for invariom refinements and
when using other databases. Nevertheless, despite the success of the suggested
block-matrix refinement procedure for
L
-cysteine, high-resolution data are certainly
preferred or even required for the multipole refinements used in our comparative
studies.
3 On the Ability of the Multipole Model to Reproduce
Theoretical Dipole Moments
The initial question raised is simple: How well does the multipole model allow to
reproduce theoretical dipole moments from a DFT calculation with the B3LYP
functional and the comparably extended basis-set D95++(3df,3pd)? In order to
answer this question twenty-two molecules exhibiting a dipole moment were
chosen (see Table
2
for details). They can be considered representative of organic
chemistry with some relevance to biological systems. The test set is neither
complete nor exhaustive; e.g. zwitterionic compounds are not part of it. For the
amino acids, which are zwitterionic in the solid state, multipole projections of the
isolated-molecular dipole moments are given in Sect.
5.1
.
Geometries of the test-set molecules were optimized with tight convergence
criteria in the program
GAUSSIAN
[
44
] followed by a frequency calculation to make
sure the global minimum was reached. From the resulting wavefunction, real
structure factors for a unit cell with dimensions of 30
˚
in space group
P
1
were
calculated with the program
TONTO
[
45
], following a procedure introduced earlier
[
46
]. This way a “projection” of the isolated-molecular density onto the multipole
model was achieved. Multipole parameters were then refined using these static
theoretical structure factors, “simulating” experimental data. Typical R-Factors
from such a refinement are around 0.5% (better when heavier nuclei are present),
with residual electron density features less than 0.05 e/
˚
3
. Better figures of merit
cannot be achieved with the standard Hansen/Coppens multipole model, since the
core density remains unadjustedunlikeinarecentstudy[
47
], and since the order
l
of the multipole expansion is limited to four for the valence region.
In all refinements a consistent refinement strategy was applied. Chemical
constraints and local-atomic site symmetry were used where possible. However,
it was assured that such choices did not affect the resulting dipole moments when
compared to a full refinement of all possible multipoles: differences were found to
be negligible. On the other hand, more substantial changes were caused by refining
