Chemistry Reference
In-Depth Information
Richard Bader has repeatedly shown how transferability of form and properties
is particularly evident for atomic groupings corresponding to the building block of
biological macromolecules [
25
,
27
] or of some series of molecules, like the hydro-
carbons [
6
]. In particular, the terminal methyl group in
n
-alkanes, past ethane, is
characterized by very transferable atomic properties, regardless of the length of the
chain, and including its energy, electron population, volume, and spectroscopic
behavior [
6
]. Transferability does not only show up in the integrated properties, but
it is so good that, for instance, a constant value of 0.2827 au for
r
b
at the unique
C-H bond of the terminal methyl group is also detected (RHF/6-311G** level).
Analysis of SF contributions to this density value in the ethane, propane, butane,
and pentane series leads [
1
], Table
1
, to two important results: (a) the “internal”
contributions from the atoms in the methyl group are actually constant at 0.270 au
throughout the series, with the two equivalent methyl group hydrogen atoms
contributing 0.0210 au in all four molecules, and (b) the “external” contribution
remains also almost constant, regardless of the length of the chain. The two SF
conditions of a
perfect transferability
are thus both fulfilled for the methyl group, at
least at its C-H bcp. The constancy of the external contribution implies that the
ethyl group in propane has to contribute the same as the propyl group in butane
or the butyl group in pentane. It is this constraint that leads the H and C atoms of
the methyl group to exhibit characteristic properties in hydrocarbons. The trend
Table 1 Source function (SF) and atomic group transferability. Source contributions to the
H-CH
2
bcp density in CH
3
(CH
2
)
n
CH
3
(
n
¼
0-3) and to the Li-
X
bcp density in the Li-
X
F, O, N, Cl, H) Series
a
n-hydrocarbons
,CH
3
(CH
2
)
n
CH
3
N
(
X
¼
r
b
(H-CH
2
) (r
b
; ext)
b
)
b
S(r
b
,
O
0
0.2830
0.0126
H-CH
2
CH
2
H
0.2704
0.0100
0.0026
1
0.2827
0.0126
H-CH
2
CH
2
CH
3
0.2701
0.0091
0.0035
2
0.2827
0.0127
H-CH
2
CH
2
CH
2
CH
3
0.2701
0.0091
0.0020
0.0016
3
0.2827
0.0127
H-CH
2
CH
2
CH
2
CH
2
CH
3
0.2702
0.0090
0.0019
0.0008
0.0009
Li-X series
Li-
X
[R
e
(R
Li
)]
c
S%(r
b
, Li) N(Li)
d
E(Li)
d
r
b
S(r
b
, Li)
Li-F
2.935 (1.128) 0.078
0.033
42.9
2.059
7.3419
Li-O (
2
P
) 3.158 (1.175) 0.067
0.028
41.6
2.066
7.3467
Li-N (
3
S
) 3.477 (1.242) 0.054
0.022
39.9
2.075
7.3565
Li-Cl
3.846 (1.294) 0.045
0.018
39.8
2.065
7.3274
Li-H
3.039 (1.347) 0.040
0.016
40.0
2.086
7.3655
a
Data from [
1
,
3
,
9
], all quantities in au
b
S(r
b
; ext) is the sum of “external” source contributions to
r
b
(H-CH
2
), i.e., those other than from
the methyl group. It is thus given by the sum of the atomic group source contributions listed, for
each molecule, in the last column minus S(r
b
,
H-CH
2
)
c
R
e
and (R
Li
) are the equilibrium distance and the distance from the Li nucleus to the bcp
d
N(Li) and E(Li) are the electron population and the atomic energy of Li
O ¼
