Chemistry Reference
In-Depth Information
5.1 Preliminary Results for the Second-Row Hydride Series
and Comparisons with Mulliken's Population Analysis
Scheme
The SF population analysis results for the second-row diatomics H-
X
series are
detailed in Table
11
, whereas Fig.
14
concisely illustrates the trends of values
through the series for the elements of the population matrix
M
. A comparison with
values for the corresponding terms in Mulliken's scheme [
17
] is also shown in the
same figure. Indeed, the number of electrons N
e
in the system may be written as
[
17
,
124
]:
N
basis
X
N
basis
X
N
e
¼
P
mn
S
mn
¼
P
mn
S
nm
¼
tr
ð
PS
Þ
(15)
mn
mn
Table 11 Population analysis from the double atomic basin integration of the local source
function in the second-row diatomic hydrides
a
H-
XN
(
O
)
M
(
O
,
O
)
b
M
(
O
,
O
0
)
b
ICP
b
IP(
O
)
c
DEV(
O
)
c
DEVM(
O
)
c
M
(
O
,
O
)/
N
(
O
)
H
1.901
0.23
1.65
0.39
0.12
0.081
0.063
0.063
Li
2.090
1.92
0.16
0.92
0.006
0.009
0.036
H
1.874
0.43
1.42
0.98
0.23
0.035
0.005
0.007
Be
3.125
2.50
0.55
0.80
0.053
0.021
0.033
H
1.787
0.67
1.09
1.48
0.38
0.024
0.000
0.004
B
4.213
3.34
0.81
0.79
0.037
0.027
0.034
H
1.053
0.77
0.27
1.76
0.73
0.016
0.002
0.003
0.002
C
5.947
4.93
0.99
0.83
0.033
0.031
H
0.663
0.62
0.04
1.47
0.94
0.010
0.002
0.002
N
7.337
6.46
0.86
0.88
0.028
0.010
0.030
H
0.386
0.42
0.04
1.04
1.09
0.006
0.001
0.001
O
8.614
7.97
0.62
0.93
0.023
0.001
0.037
H
0.242
0.29
0.05
0.71
1.20
0.004
0.000
0.001
F
9.758
9.30
0.42
0.95
0.017
0.021
0.047
a
HF/6-31G** wavefunction
b
M
(
O
,
O
) represents the contribution of
O
to determining the electron population of its own basin,
while
M
(
O
,
O
0
) is the contribution to this same population from basin
O
0
,with
O
0
being
X
when
O¼
H and vice versa; ICP is the interchanged electron population between
O
and
O
0
, ICP
¼
M
(
O
,
O
0
)
þ
M
(
O
0
,
O
), that is the sum of the contribution to the electron population of
O
from
O
0
and of the
contribution to the electron population of
O
c
All these parameters are related to the numerical accuracy of the population analysis. IP(
O
0
from
)
represents the ignored atomic electron population, that is the atomic sum of the electron population
of those volume elements within
O
that due to their too low average electron density could not be
used in the evaluation of the elements of the matrix
M
(see text). The quantity DEV(
O
) is given by
the atomic integration of the local deviation of the
r
reconstructed through the SF from the exact
r
value; DEVM(
O
O
) is given by this same atomic integration but taking the module of the integrand
(see text)
