4.3 Valence bond theory: multiple
bonding in polyatomic molecules
In the previous section, we emphasized that hybridization of
some or all of the valence atomic orbitals of the central atom
in an XYn species provided a scheme for describing the XY
-bonding. In, for example, the formation of sp, sp2 and sp3
d
hybrid orbitals, some p or d atomic orbitals remain unhybridized
and, if appropriate, may participate in the formation of
-bonds. In this section we use the examples of C2H4, HCN
and BF3 to illustrate how multiple bonds in polyatomic
molecules are treated within VB theory. Before considering
the bonding in any molecule, the ground state electronic con-
figurations of the atoms involved should be noted.
C2H4
C [He]2s
2
2p2
H 1s
1
Ethene, C2H4, is a planar molecule (Figure 4.8a) with
CCH and HCH bond angles of 121.38 and 117.48
respectively. Thus, each C centre is approximately trigonal
planar and the -bonding framework within C2H4 can be
described in terms of an sp2 hybridization scheme (Figure
4.8b). The three -interactions per C atom use three of the
fo
four valence electrons, leaving one electron occupying the
unhybridized 2p atomic orbital. The interaction between
the two 2p atomic orbitals (Figure 4.8c) and the pairing of
the two electrons in these atomic orbitals generates a CC
-interaction. The bond order of the CC bond in C2H4 is
therefore 2, in keeping with Lewis structure 4.1. The -
component of the overall carbon–carbon bond is weaker
than the -component and hence a C¼C double bond,
though stronger than a CC single bond, is not twice as
strong; the CC bond enthalpy terms in C2H4 and C2H6
are 598 and 346 kJ mol1 respectively.
C C
HCN
C [He]2s
2
2p2
N [He]2s
2
2p3
H 1s
1
Figure 4.9a shows the linear HCN molecule, a Lewis structure
(4.2) for which indicates the presence of an HC
single bond, a CN triple bond, and a lone pair of electrons
on N. An sp hybridization scheme is appropriate for both C
and N; it is consistent with the linear arrangement of atoms
around C and with the placement of the lone pair on N as far
away as possible from the bonding electrons. Figure 4.9b
shows the -bonding framework in HCN (each region of
orbital overlap is occupied by a pair of electrons) and the
outward-pointing sp hybrid on N that accommodates the
lone pair. If we arbitrarily define the HCN axis as the z
axis, then after the formation of the -interactions, a 2px
and a 2py atomic orbital remain on each of the C and N
atoms. Each atomic orbital contains one electron. Overlap
between the two 2px and between the two 2py orbitals
leads to two -interactions (Figure 4.9c). The overall CN
bond order is 3, consistent with Lewis structure 4.2.
BF3
B [He]2s
2
2p1
F [He]2s
2
2p5
Boron trifluoride (Figure 4.10a) is trigonal planar (D3h); sp2
hybridization is appropriate for the B atom. Each of the
three BF -interactions arises by overlap of an sp2 hybrid
on the B atom with, for example, an sp2 orbital on the F
atom. After the formation of the -bonding framework,
the B atom is left with an unoccupied 2p atomic orbital
lying perpendicular to the plane containing the BF3
molecule. As Figure 4.10b shows, this is ideally set up for
interaction with a filled 2p atomic orbital on one of the F
atoms to give a localized BF -interaction. Notice that
the two electrons occupying this -bonding orbital both
originate from the F atom. This picture of the bonding in
BF3 is analogous to one of the resonance forms shown in
pink in Figure 4.10c; all three resonance forms (see Section
1.12) are needed to account for the experimental observation
that all three BF bonds are of equal length (131 pm).
Worke