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Table 4 Source function description of C-C bonds in cyclic conjugated and aromatic hydrocarbons a
System
R e , ˚
C j ) b,c
H j ) b,c
C jnn ) b,c
Bond
C i -C j
r b
S%(C i þ
S%(H i þ
S%(C inn þ
S% (
S other C )
S%(
S other H )
Benzene
C 1 -C 2
1.411
0.300
84.7 ( 0.254 )
5.7 ( 0.017 )
5.3 ( 0.016)
1.4
2.8
(84.4, 0.3) e
1.6) e
(3.4, 1.9) e
(7.3,
(0.5z) d
0.245
82.5 ( 0.202 )
6.6 ( 0.016 )
6.1 ( 0.015 )
1.6
3.4
(73.8, 8.7) e
1.9) e
(3.8, 2.3) e
(8.5,
(1.0z) d
0.141
72.6 ( 0.101 )
10.2 ( 0.014 )
8.9 ( 0.013 )
2.6
5.6
(45.2, 27.4) e
3.3) e
(4.9,4.0) e
(13.4,
(1.5z) d
0.065
50.6 ( 0.033 )
18.5 ( 0.012 )
14.8 ( 0.010 )
4.4
11.6
(3.1, 47.5) e
6.8) e
(6.5, 8.3) e
(25.3,
(2.0z) d
0.027
4.0 ( 0.001 )
35.4 ( 0.010 )
24.3 ( 0.006 )
9.4
27.1
63.0, 67.0) e
15.3) e
(5.8, 18.5) e
(
(50.7,
Cyclohexadiene
C 1 -C 2
1.358
0.328
87.2 ( 0.286 )
5.3 ( 0.017 )
3.2 ( 0.010 )
0.8
3.7
C 1 -C 6
1.474
0.267
81.9 ( 0.219 )
6.2 ( 0.017 )
7.2 ( 0.019 )
0.4
4.1
C 2 -C 3
1.518
0.247
79.6 ( 0.196 )
10.3 ( 0.025 )
4.9 ( 0.012 )
1.2
4.1
C 3 -C 4
1.566
0.225
75.9 ( 0.171 )
14.5 ( 0.033 )
4.1 ( 0.009 )
1.9
3.5
Cyclohexene
C 1 -C 6
1.350
0.331
87.4 ( 0.289 )
5.3 ( 0.018 )
2.5 ( 0.008 )
0.1
4.4
79.6 ( 0.200 )
10.2 ( 0.025 )
5.0 ( 0.013 )
C 1 -C 2
1.508
0.251
0.1
5.0
76.4 ( 0.174 )
14.6 ( 0.033 )
3.4 ( 0.008 )
C 2 -C 3
1.558
0.228
0.9
4.8
C 3 -C 4
1.568
0.224
76.1 ( 0.170 )
15.1 ( 0.033 )
2.4 ( 0.005 )
1.0
5.2
a Atomic numbering in Scheme 2 . If not otherwise stated, all quantities in au; DFT/BP86 [ 34 - 36 ] D95V Dunning-Hay basis set [ 37 ]
b SF value in parenthesis and in italic
c C inn and C jnn are the nearest neighbor C atoms of C i and C j , respectively. H i and H j are the H atoms linked to C i and C j , respectively
d Points along an axis perpendicular to the xy molecular plane and passing through the C-C bcp are taken as rps. The symbol denotes the z distance (au) of the rp
from the molecular plane
e
s and p percentage contributions, in this order, with s % þ p % ¼ S%( X i + X j ), X ¼ CorH
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