7-2 The Long Weak N-N Bond of N2O4: Molecular Orbital Theory
91
differ in valence-bond structures (3)-(7) for N 2 O 4 are therefore those that are
displayed in Figure 7-2, namely two nitrogen hybrid and four oxygen 2p -
orbitals, which have been designated as “mobile σ-electron” orbitals
6, 7, 10-13 . The
“mobile σ-electron” wavefunctions for the electron-pair bonds of structures (3)-(7)
are assumed to be constructed using the Heitler-London procedure (Section 3-3).
For example, the wave-function for the N-N bond of the standard Lewis structure
(3) is h 2 (1)h 3 (2) + h 3 (1)h 2 (2) in which 2
h and 3
h are the hybrid orbitals displayed
in Figure 7-2. But it is also possible to construct a molecular orbital wave-function
for this bond, namely σ(1)σ(2) for which
2
3
h h
is the N-N bonding
molecular orbital. We shall now use this latter formulation of the N-N bond wavefunction to provide a molecular orbital explanation
11, 12 for the existence of a long,
weak N-N bond for N 2 O 4 .
7-2 The Long Weak N-N Bond of N 2 O 4 : Molecular Orbital
Theory
11,12
For the molecular orbital description of the N-N bond of structure (3), two electrons with opposite spins occupy the N-N σ-bonding molecular orbital
2
3
h h
.
In this structure, the oxygen 2p orbitals, which overlap with the nitrogen h 2 and
h 3 orbitals, are doubly-occupied. However, the appreciable electronegativity of N
+
relative to O
– in structures of type (3) induces substantial delocalization of the
oxygen 2p electrons into the antibonding N-N
*
-orbital,
*
2
3
h h
, which
is vacant in these structures. The N-N σ-bond order
i is then reduced below the
value of unity that pertains to structure (3), thereby generating a long, weak N-N
bond. An estimate of 0.525 for this bond-order has been obtained from molecular
orbital studies of the photoelectron spectrum
7c .
To obtain the “long-bond” Lewis structures (4)-(6) from the standard Lewis
structure (3), either one or two electrons have been delocalized from the oxygen
1
and 4
orbitals of Figure 7-2 into the singly occupied nitrogen hybrid orbitals
h 2 and h 3 . We shall now use these orbitals to construct the 4-centre delocalized
molecular orbitals for the mobile σ-electrons. (A fuller treatment that includes the
5
and 6
orbitals is described in Refs. 7b, c, 11 and 12.)
Initially we shall form the bonding and antibonding linear combinations of each
pair of nitrogen and oxygen atomic orbitals. The resulting symmetry orbitals are
given in Eqs. (1) and (2),
1
2
1
2
3
s (h
h ) / 2
,
1
2
2
2
3
s
(h
h ) / 2
,
(1)
i These delocalizations are calculated to occur at the N-N single-bond length of 1.45 Å as well as
at the experimental length of 1.78 Å.
91
differ in valence-bond structures (3)-(7) for N 2 O 4 are therefore those that are
displayed in Figure 7-2, namely two nitrogen hybrid and four oxygen 2p -
orbitals, which have been designated as “mobile σ-electron” orbitals
6, 7, 10-13 . The
“mobile σ-electron” wavefunctions for the electron-pair bonds of structures (3)-(7)
are assumed to be constructed using the Heitler-London procedure (Section 3-3).
For example, the wave-function for the N-N bond of the standard Lewis structure
(3) is h 2 (1)h 3 (2) + h 3 (1)h 2 (2) in which 2
h and 3
h are the hybrid orbitals displayed
in Figure 7-2. But it is also possible to construct a molecular orbital wave-function
for this bond, namely σ(1)σ(2) for which
2
3
h h
is the N-N bonding
molecular orbital. We shall now use this latter formulation of the N-N bond wavefunction to provide a molecular orbital explanation
11, 12 for the existence of a long,
weak N-N bond for N 2 O 4 .
7-2 The Long Weak N-N Bond of N 2 O 4 : Molecular Orbital
Theory
11,12
For the molecular orbital description of the N-N bond of structure (3), two electrons with opposite spins occupy the N-N σ-bonding molecular orbital
2
3
h h
.
In this structure, the oxygen 2p orbitals, which overlap with the nitrogen h 2 and
h 3 orbitals, are doubly-occupied. However, the appreciable electronegativity of N
+
relative to O
– in structures of type (3) induces substantial delocalization of the
oxygen 2p electrons into the antibonding N-N
*
-orbital,
*
2
3
h h
, which
is vacant in these structures. The N-N σ-bond order
i is then reduced below the
value of unity that pertains to structure (3), thereby generating a long, weak N-N
bond. An estimate of 0.525 for this bond-order has been obtained from molecular
orbital studies of the photoelectron spectrum
7c .
To obtain the “long-bond” Lewis structures (4)-(6) from the standard Lewis
structure (3), either one or two electrons have been delocalized from the oxygen
1
and 4
orbitals of Figure 7-2 into the singly occupied nitrogen hybrid orbitals
h 2 and h 3 . We shall now use these orbitals to construct the 4-centre delocalized
molecular orbitals for the mobile σ-electrons. (A fuller treatment that includes the
5
and 6
orbitals is described in Refs. 7b, c, 11 and 12.)
Initially we shall form the bonding and antibonding linear combinations of each
pair of nitrogen and oxygen atomic orbitals. The resulting symmetry orbitals are
given in Eqs. (1) and (2),
1
2
1
2
3
s (h
h ) / 2
,
1
2
2
2
3
s
(h
h ) / 2
,
(1)
i These delocalizations are calculated to occur at the N-N single-bond length of 1.45 Å as well as
at the experimental length of 1.78 Å.