174
Chapter 13 “Increased-Valence” Structures for N-Centre Bonding Units
The Se-Se bond lengths
14 of 2.28 Å for
2
4
Se
are shorter than the estimate of
2.34 Å for an Se-Se single bond, and resonance between either the four standard
Lewis structures of type (a) or the two “increased-valence” structures of type (c)
accounts for this observation. However, the “increased-valence” representation
does this in a more economical manner.
The molecular orbitals for the π-electrons are given by Eqn. (13-1), with
μ = λ = 1. For systems such as
2
4
Se
with 4h
D symmetry, the molecular orbitals
2
and
3
are degenerate, as are the excited configurations
2
2
2
2
1
2
4
(MO) ( ) ( ) ( )
and
2
2
2
3
1
3
4
(MO) ( ) ( ) ( )
. These configurations may be linearly combined
15 , with
2
2
2
1
1
2
3
(MO) ( ) ( ) ( )
to generate
the configuration interaction wave-function of Eqn. (2),
1 1
2
2
3
(CI)
(MO)
( (MO)
(MO))
C
C
(2)
with C 2 < 0 when C 1 > 0 in the lowest-energy linear combination (cf. Section
10-3). This C.I. wave-function may be transformed
15 (cf. Section 10-2) and
expressed as
1
2
covalent
covalent
1
2
ionic
ionic
(CI) (
)(
) (
)(
)
C C
C C
(3)
in which
covalent
and covalent
are the wave-functions for “increased-valence”
structures (12) and (13). Because C 1 > 0 when C 2 < 0, these structures must represent the primary valence-bond structures for cyclic 6-electron 4-centre bonding
units with 4h
D symmetry. The same result is true for systems such as
2
(SN) with
2h
C symmetry, for which the “increased-valence” structures are those of (14), and
for the S 4 linkage of the 3 2
S N
dimer
15 . The latter species has 2h
D symmetry for
the S 4 linkage; overlap considerations
15 for it suggest that “increased-valence”
structure (15) has a larger weight than has structure (16). The bond-number for
each of the intermoiety S-S bonds of structure (15) is 0.25 (cf. Section 7-1), and
Chapter 13 “Increased-Valence” Structures for N-Centre Bonding Units
The Se-Se bond lengths
14 of 2.28 Å for
2
4
Se
are shorter than the estimate of
2.34 Å for an Se-Se single bond, and resonance between either the four standard
Lewis structures of type (a) or the two “increased-valence” structures of type (c)
accounts for this observation. However, the “increased-valence” representation
does this in a more economical manner.
The molecular orbitals for the π-electrons are given by Eqn. (13-1), with
μ = λ = 1. For systems such as
2
4
Se
with 4h
D symmetry, the molecular orbitals
2
and
3
are degenerate, as are the excited configurations
2
2
2
2
1
2
4
(MO) ( ) ( ) ( )
and
2
2
2
3
1
3
4
(MO) ( ) ( ) ( )
. These configurations may be linearly combined
15 , with
2
2
2
1
1
2
3
(MO) ( ) ( ) ( )
to generate
the configuration interaction wave-function of Eqn. (2),
1 1
2
2
3
(CI)
(MO)
( (MO)
(MO))
C
C
(2)
with C 2 < 0 when C 1 > 0 in the lowest-energy linear combination (cf. Section
10-3). This C.I. wave-function may be transformed
15 (cf. Section 10-2) and
expressed as
1
2
covalent
covalent
1
2
ionic
ionic
(CI) (
)(
) (
)(
)
C C
C C
(3)
in which
covalent
and covalent
are the wave-functions for “increased-valence”
structures (12) and (13). Because C 1 > 0 when C 2 < 0, these structures must represent the primary valence-bond structures for cyclic 6-electron 4-centre bonding
units with 4h
D symmetry. The same result is true for systems such as
2
(SN) with
2h
C symmetry, for which the “increased-valence” structures are those of (14), and
for the S 4 linkage of the 3 2
S N
dimer
15 . The latter species has 2h
D symmetry for
the S 4 linkage; overlap considerations
15 for it suggest that “increased-valence”
structure (15) has a larger weight than has structure (16). The bond-number for
each of the intermoiety S-S bonds of structure (15) is 0.25 (cf. Section 7-1), and