Chemistry Reference
In-Depth Information
approaching to zero. However, all three
O_R
42
[E]
functions (
E
¼
C
O
2
,
C
O
OH
,
) exhibit a well-defined second maximum at
r
~ 1.2
˚
.
and
C
¼O
For
the C-atoms (Fig.
6d
),
the differences include second minima in
O]
and
C_R
10
[COO
]
. The quadrupole functions split into two groups:
one with a maximum close to 0.25
˚
, and another with a maximum at around
0.5
˚
. As in the case of N-atoms, the octupolar SPA-RDFs show maxima at
r
~ 0.5-0.6
˚
, but unlike for the O-atom, no nodes are observed. The hexadecapolar
functions are closer in shape to those found for the N than for the O-atoms.
C_R
11
[C
¼
9 Stockholder Pseudoatom Databank
The fairly good chemical transferability of the SPA-RDFs suggests that it is
possible to design radial density basis sets for different type of atoms in a high
variety of bonding situations. Such a library appears to be of foremost importance
for experimental charge density research if data quality continues to improve at the
current rate. Similar efforts using the conventional model have shown that applica-
tion of HC-PA databanks can be beneficial for routine small- and macro-molecular
crystallography [
67
,
68
] and even for molecular modeling [
69
]. Our approach to
SPA database building has many new elements. The density (
r
X
)ofan
X
-type
SPA in a given bonding environment (
E
) is approximated by a combination of
a transferable part (
½
E
r
X
) and a correction to it (
d
X
½
E
):
X
X
1
N
E
r
X
¼r
X
þ d
X
r
E
þ
Q
lm
R
l
d
lm
½
E
½
E
¼
(19)
E
lm
The transferable term is the average SPA taken over a set of equivalents
ð r
E
N
E
Þ
derived from a large number of reference molecules each containing
the
X
-type embedded in slightly different bonding environments. The RDFs of the
nontransferable (
d
X
) part are derived via minimizing the RMS composed of
residual EDs not accounted for by the average term:
½
E
ð
X
d
X
2
e
X
r
E
r
X
¼
½
E
dr
(20)
E
The
m
-independent RDFs of the correction terms (
d
X
) are expanded over an
auxiliary Slater basis, which is derived by the principal component analysis of the
½
E
set of equivalent SPAs
r
E
N
E
.
The database building is a five-step procedure:
1. Selection of reference molecules containing the atoms to be included in the
library. The current version was built from about 1,800 molecules composed of
second period (B-F) and some heavier elements, such as P, S, and Cl. Accurate
structures were taken from the CSD, as described above.
