Chemistry Reference
In-Depth Information
Table 3 Source function description of C-C bonds in CH
n
-CH
n
(
n
¼
1-3) hydrocarbons
a,b
System N(C)
R
e
,
˚
r
b
S(r
b
,C) S(r
b
,H) S%(r
b
,C+C
0
)
Ethane 6.013 1.542 0.233 0.091 0.008 78.6
Ethene 6.075 1.349 0.331 0.148 0.009 89.4
Ethyne 6.159 1.225 0.380
c
0.182
c
0.007 96.0
c
a
Some of the data from [
14
]; if not otherwise stated, all quantities in au; rp is the C-C bcp
b
DFT/BP86 [
34
-
36
] D95V Dunning-Hay basis set [
37
]
c
There is a nonnuclear attractor [
23
] at the C-C midpoint; the reported source from each C atom
includes half the contribution from the central nonnuclear basin
ethyne series), or with not enough electrons for a Lewis structure to be written (the
3c-2e bridging bonds in diborane) or instead forming a dative bond in a typical
Lewis acid-base adduct (BH
3
-PH
3
). Atoms in Fig.
2
are displayed as spheres with
volume proportional to their percentage source function contribution, S%(r
p
,
O
), at
the selected bcp.
As expected for a well-known covalent bond, most of the SF contributions to the
C-C bcp density come from the two neighboring C atoms, with percentage con-
tributions increasing with increased formal bond order from one to three (78.6%,
89.4%, and 95.8%), increased bcp density and C atom population (Fig.
2
; Table
3
)
[
9
,
14
]. The collective percentage contribution from the H atoms accordingly
decreases along the series and so also does the percentage contribution from a
single H atom, being 3.6% in ethane, 2.6% in ethene, and only 2.1% in ethyne,
although the H source remains almost constant and small in value through the series
(Table
3
). Since both the percentage contributions from C and the density at bcp
increase, the source function contributions from C significantly boost along the
series, being doubled in ethyne, S(C)
¼
0.091 au (Table
3
). Both C and H SF contribution and percentage trends agree with
the increased strength,
s
character, and localization of C-C bonds along the series.
Comparing the bridging and terminal B-H bonds in diborane, one immediately
notices [
14
] important differences in the source contributions from the two linked
atoms. They exceed 80% for the terminal B-H bond, analogously to the B-H bond
in BH
3
(Fig.
2
), while they are as low as 54.3% for the bridging bond, with the
residual contribution, except for a fourth of it, being shared almost equally among
the other H
bridge
atom and each of the two terminal H atoms closest to the reference
bcp. Note that for both bonds and contrary to the case of C-C bond in hydrocarbons,
the contributions from the two bonded atoms is largely asymmetric, the more
electronegative atom - the hydridic H - contributing in both cases over 60% of
the bcp density
determined
by these two atoms.
Despite being involved in the so-called 3c-2e bond, the contribution to the
density at the B-H
bridge
bcp from the other B
0
atom is less than 3%. A similar
description arises, however, when the delocalization indices
d
(
¼
0.182 au, with respect to ethane, S(C)
O
0
)[
38
] are
analyzed, although delocalization indices and source function contributions are
not physically related in a direct way [
14
]. Delocalization indices are obtained
through double integration of the pair density
O
,
(r, r
0
) over the basins of atom
and
O
0
, with the electrons being kept in separate basins and provide a quantitative
p
O
