Chemistry Reference
In-Depth Information
Fig. 1 (a) Static difference electron density map (
r
C
r
HC-PA
) calculated for the
heptasulfur
imide
molecule in the N-S-S plane. The pseudoatom density was obtained via fitting the para-
meters of the HC-PA model to MP2/cc-pvtz structure factors. (b) Deformation electron density
map (
r
C
r
0
) in the same plane. Contour levels are 0.05 e
˚
3
.
Solid
,
dashed
, and
dotted lines
are
positive, zero, and negative, respectively
difficulties, is provided by a two-step procedure [
49
]; the target molecular ED (
r
C
)
is first fragmented into fuzzy atomic densities (
r
A
),
X
X
n
k
C
k
) r
C
¼
r
C
¼
r
A
(13)
k
A
followed by the projection of each of these units onto RSHs:
Ð
r
A
ð
d
lm
d
Þ
O
A
r
R
lm
ð
r
A
Þ¼
Ð
r
A
ð
(14)
d
lm
d
r
A
r
Þ
The summation in (13) is over the number of occupied MOs (
C
k
), and the
integral in the denominator of (14) gives rise to the multipole populations (
Q
lm
).
The normalized RDFs obtained in such a way correspond to “bonded-atoms”
(derived from molecular rather than atomic wave function) and are uncorrelated
because of the orthogonality of the RSHs at the same center. The integrals are
calculated numerically, on a fine grid of the radial coordinate measured from the
nucleus, to allow for the use of any type of molecular density and partitioning. Each
numerical RDF is fitted with a combination of Slater primitives (10).
Different fuzzy-type decomposition schemes are expected to yield similar RDFs
because the MO density is dominated by the one-center orbital products. The results
discussed here are based on the
stockholder
partitioning method [
50
], which
