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between the N2 andN3 atoms and then releasingN
2
to form an azo cation species (PC2
and PC3).
With the aid of a hydroxide ion (this could be formed from the protonation of
making the nitrenium ion), the azo cation could easily release H
þ
to form a neutral
azo species. In the
cis
pathway, a transition state (TS4) was found and inspection of
Figure 7.17 and Table 7.1 suggests that when a hydroxide ion is near, the bond
lengths of N2
N4, N4
H6, and H6
O7 all decrease while the reaction proceeds
from the azo cation (PC3b) through TS4 to form the
cis
4,4-azobisbiphenyl species
and this seems to correlate to a pathway in which the azo cation releases H
þ
to form a
water molecule from the reaction with a hydroxide ion, and the N
N single bond
becomes a N
C6 varies
distinctly as the reaction takes place, from 49
(PC3b) to 40
(TS4) to 11
(
cis
4,4
0
-
azobisbiphenyl), and this clear variation of the C1
N double bond. The dihedral angle of C1
N2
N4
C6 dihedral angle
indicates the dihedral angle twist also serves as a driving force for the H
þ
to be
released from the azo cation. The geometry of the azo cation changes when a
hydroxide ion is near, and this can be seen in Figure 7.17 and Table 7.1 where the
bonds of C1
N2
N4
C6 are all becoming longer because of the
presence of the hydroxide ion and the dihedral angles of C1
N2, N2
N4, and N4
C6 are
different without and with a hydroxide ion being nearby and they are 15.4 and 49.1
,
respectively. This type of differences in the geometries of the azo cation is reasonable
to occur because of the stabilization caused by the hydroxide ion being nearby.
In the
trans
pathway, the dihedral angles of C1
N2
N4
C6 are about 0
in
both PC2 and
trans
4,4
0
-azobisbiphenyl suggesting there is little driving force due to
a dihedral angle twist. The TR
3
experiments were done in an aqueous solution where
hydroxide ions and water molecules interact with the reactant molecules and with
each other and this is very hard to actually model with the simple computations
considered here and no reasonable transition states were seen to connect PC2 and
trans
4,4
0
-azobisbiphenyl from the DFT computations even though this reaction
probably happens under experimental conditions.
The reaction of the 4-biphenyl nitrenium ion with 4-biphenyl azide takes place
in an aqueous solution and the solvent effect on the reaction was investigated and
Table 7.2 presents the computation results for the activation barrier and reaction
energies in the gas and aqueous phases. Compared with the results found in the gas
N2
N4
TABLE 7.2. The Barrier and Reaction Energies Computed at the B3LYP/6-31G
Level
with ZPE Corrections (Unit: kcal/mol) for the Reactions of Interest
Gas Phase (kcal/mol)
Aqueous Phase (kcal/mol)
Barrier
Reaction Energies
Barrier
Reaction Energies
cis
Pathway (TS1) 13.87 13.02 6.83
5.53
cis
Pathway (TS3) 3.06
80.34
1.96
65.06
cis
Pathway (TS4) 0.19
45.90 4.16
42.38
trans
Pathway (TS2) 12.70
76.30 7.30
80.50
Source
: Reprinted With Permission from Ref. 47. Copyright (2008) American Chemical Society
