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686 Periodic Table (Chemistry)

resonance hybrid of VB descriptors. Depending upon the
arrow combinations specified within each VB descriptor,
each bond may be either of the T or the I variety. Hence,
the overall resonance hybrid has a fixed number of bonds
which have resonant T and I character. Bond character,
T versus I, depends, to a first order, on atom electroneg-
ativity. I-bonding engenders CT and is favored by low
electronegativity in homonuclear systems and by combi-
nations of atoms differing greatly in electronegativity in
heteronuclear systems. This leads to the rule that non-
metal atoms like H, C, N, O, and F (i.e., the atoms of
“organic chemistry”) support T-bonding, while semimetal
and metal atoms increasingly support I-bonding. We have
now broken ties with conceptual molecular orbital (MO)
theory as presently practiced. Because of the conceptual
intractability of this method, emphasis is placed on or-
bital symmetry and electron-count considerations. What
we say here is that two molecules may have identical sym-
metry constraints and identical electron counts and yet
can be fundamentally different on account of differing
electronegativities which implies differing binding mech-
anisms, T versus I. FIGURE 8 Sequential development of the electronic structure of
a double bond. (a) The reference configuration. (b) Arrows are af-
B. What Is a Multiple Bond? fixed on the electrons of the reference configuration in accordance
with the association rule to create the arrow formula. (c) The most
Consider the double bond of ethylene produced by favorable ways of pairing the arrows to make a bond correspond
3
combining two methylenes, each containing one sp - to two (resonant) VB descriptors of the C C bond. Arrows of the
same type (solid or dashed) are paired.
hybridized carbon. Our first task is to allocate electrons
to the constituent fragments in a way that minimizes en-
ergy consistent with potential bonding. This produces the quartet represents a pair of T-bonds or a pair of I-bonds.
reference configuration shown in Fig. 8a. Next, we affix The three quartets represent the following bond combi-
the arrows according to the association rule in order to nations: (ab/cd): [T + T]; (ad/bc): [I(ROX) + I(ROX)];
produce the arrow formula shown in Fig. 8b. Note how (ac/bd): [I(OX) + I(RED)]. The term ROX denotes that
each dot gets one outbound and one inbound arrow as CT causes simultaneous reduction and oxidation of one
dictated by the association rule. There are a total of four center, OX implies two-electron oxidation, and RED sig-
arrows and, hence, a total of two (4 divided by 2) bonds. nifies two-electron reduction. The emerging viewpoint is
The nature of each bond (T or I) depends on how we com- that bonds have resonant T and I characters and that our
bine two arrows to make one pair. Each arrow is labeled C C bond can be represented as a resonance hybrid of
by a letter, and we use this lettering designation to define two VB descriptors as shown in Fig. 8c.
the possible combinations. One possible set of pairwise Additional VB descriptors can contribute to our reso-
combinations is ab and cd. Each of these combinations nance hybrid, but these are disregarded because the VB
represents a T-bond. This is one possible VB descriptor configurations which they span are high in energy. An
designated (ab/cd). A second possible set of combinations example is the one involving the pairwise arrow combina-
is ad and bc, each now representing an I-bond. This is a tions ac and bd. Such a contributor becomes important in
second possible VB descriptor denoted by (ad/bc). Note the case of a highly heteropolar double bond. What is the
onecharacteristic difference: the two arrows spanthe same principal character of the double bond of ethylene? Let
overlap region in the case of the T-bond, while they op- us answer this question after we explicitly examine the
erate in two different overlap regions in the case of the consequences of the delocalization implied by the arrows.
I-bond. As shown below in Fig. 9, the ab (exchange 2 − e hop)
In summary, the arrow formula of a double bond in- conserves charge by permitting each electron to occupy a
volves four arrows. There exist (4 − 1)! pairwise (ij) com- different AO. By contrast, the bc (CT 2 − e hop) confines
binations of arrows and (3 − 1) quartet (ij/kl) selections. two electrons in one AO at the price of severe interelec-
Each arrow pair represents one T- or I-bond. Each arrow tronic repulsion, measured by the index J 11 = IP − EA,