2-5 “Long-Bond” Lewis Structures and a Need for an “Increased-Valence” Theory
29
If we use the result that a 1-electron bond between a pair of atoms A and Β
summarizes resonance between valence-bond structures (A B)
and (A B) (i.e.
A · Β (A B)
(A B)
), it is easy to demonstrate that each of the structures
(I)-(IV) summarizes resonance between one standard and three of the “long-bond”
Lewis structures of Figure 2-9. Thus,
(I) (1) ↔ (5) ↔ (6) ↔ (9),
(II) (2) ↔ (5) ↔ (7) ↔ (9),
(III) (3) ↔ (6) ↔ (8) ↔ (9) and
(IV) (4) ↔ (7) ↔ (8) ↔ (9),
as is shown in Figure 2-11. Therefore by invoking resonance between structures
(I)-(IV), we are able to summarize resonance between all of the Lewis octet structures of Figure 2-9. It may be noted also that each of (I)-(IV) seems to have two
more bonding electrons than has any of the octet structures (1)-(9). Therefore (for
reasons that will be developed further in Section 11-1), structures (I)-(IV) are
examples of a class of valence-bond structures, which have been designated as
“increased-valence” structures
13, 20 .
For illustrative purposes only, the formal charges for “increased-valence” structures are usually to be assigned on the assumption
ii that bonding electrons are
shared equally by pairs of adjacent atoms. If we invoke the electroneutrality
principle, then the absence of formal charges for structure (I) would suggest that
this structure is more important than are any of the structures (II), (III) and (IV).
By assuming this to be the case, we may conclude that the electronic structure of
2
N O more-closely resembles that of (I) than that for any of the other increasedvalence structures. Indeed, if we select structure (I) alone to represent (approximately) the electronic structures of 2
N O , we may deduce that the N-O bondlength should be similar to that of a double bond, and that the N-N bond-length
should be longer than that of a triple bond, but still resemble a triple bond. Both of
these deductions are in accord with the observations reported in Section 2-4 (a).
The N-O double-bond character for structure (I) is implied by the presence of four
bonding electrons located in the N-O bond region. Relative to the N-N triple bond
of N 2 , the reduction of the N-N bond-number for structure (I) arises because this
ii This is the normal procedure that is used to assign formal charges to the atoms of valencebond structures. The actual atomic formal charges for a molecule are then determined (primarily) by the weights of the different valence-bond structures that participate in resonance.
However, because an “increased-valence” structure summarizes resonance between a number
of Lewis structures, some of which will have different weights, the “best” set of formal
charges for an “increased-valence” structure will in general not be integer or 1
2 -integer in
magnitude. In the absence of knowledge as to what they are, we shall use the same procedure
that Linnett
3 had used to assign atomic formal charges for his non-paired spatial orbital
structures, namely to assume that bonding electrons are shared equally by adjacent atoms of
the “increased-valence” structures. In generalized valence-bond structures, such as (A B)
,
(A B) , (A • B), Y─A B: and Y⌐⌐A • B•, atomic formal charges will usually be omitted.
29
If we use the result that a 1-electron bond between a pair of atoms A and Β
summarizes resonance between valence-bond structures (A B)
and (A B) (i.e.
A · Β (A B)
(A B)
), it is easy to demonstrate that each of the structures
(I)-(IV) summarizes resonance between one standard and three of the “long-bond”
Lewis structures of Figure 2-9. Thus,
(I) (1) ↔ (5) ↔ (6) ↔ (9),
(II) (2) ↔ (5) ↔ (7) ↔ (9),
(III) (3) ↔ (6) ↔ (8) ↔ (9) and
(IV) (4) ↔ (7) ↔ (8) ↔ (9),
as is shown in Figure 2-11. Therefore by invoking resonance between structures
(I)-(IV), we are able to summarize resonance between all of the Lewis octet structures of Figure 2-9. It may be noted also that each of (I)-(IV) seems to have two
more bonding electrons than has any of the octet structures (1)-(9). Therefore (for
reasons that will be developed further in Section 11-1), structures (I)-(IV) are
examples of a class of valence-bond structures, which have been designated as
“increased-valence” structures
13, 20 .
For illustrative purposes only, the formal charges for “increased-valence” structures are usually to be assigned on the assumption
ii that bonding electrons are
shared equally by pairs of adjacent atoms. If we invoke the electroneutrality
principle, then the absence of formal charges for structure (I) would suggest that
this structure is more important than are any of the structures (II), (III) and (IV).
By assuming this to be the case, we may conclude that the electronic structure of
2
N O more-closely resembles that of (I) than that for any of the other increasedvalence structures. Indeed, if we select structure (I) alone to represent (approximately) the electronic structures of 2
N O , we may deduce that the N-O bondlength should be similar to that of a double bond, and that the N-N bond-length
should be longer than that of a triple bond, but still resemble a triple bond. Both of
these deductions are in accord with the observations reported in Section 2-4 (a).
The N-O double-bond character for structure (I) is implied by the presence of four
bonding electrons located in the N-O bond region. Relative to the N-N triple bond
of N 2 , the reduction of the N-N bond-number for structure (I) arises because this
ii This is the normal procedure that is used to assign formal charges to the atoms of valencebond structures. The actual atomic formal charges for a molecule are then determined (primarily) by the weights of the different valence-bond structures that participate in resonance.
However, because an “increased-valence” structure summarizes resonance between a number
of Lewis structures, some of which will have different weights, the “best” set of formal
charges for an “increased-valence” structure will in general not be integer or 1
2 -integer in
magnitude. In the absence of knowledge as to what they are, we shall use the same procedure
that Linnett
3 had used to assign atomic formal charges for his non-paired spatial orbital
structures, namely to assume that bonding electrons are shared equally by adjacent atoms of
the “increased-valence” structures. In generalized valence-bond structures, such as (A B)
,
(A B) , (A • B), Y─A B: and Y⌐⌐A • B•, atomic formal charges will usually be omitted.