Download Ground State and Bonding State Electronic Configurations

CH221 CLASS 2
CHAPTER 1: STRUCTURE AND BONDING, CONTINUED
Synopsis. This class takes a more detailed look at the covalent bonding of
organic molecules (and some important inorganic molecules), especially from the
viewpoint of atomic orbital hybridization. Finally, the molecular orbital model is
used to describe  and  bonds, the two most important kinds of covalent bonds
found in organic molecules.
Ground State and Bonding State Electronic Configurations
A glance at carbon, whose ground state electronic configuration is 1s2s22p2,
would suggest initially that this element might be bivalent. However, carbon is
well known to be tetravalent in the vast majority of its organic compounds, hence
it must use the 2s orbital, as well as the three 2p orbitals in its bonding electronic
configuration. This means that some sort of energy promotion is required from
the ground state:
The stability gained by forming 4 bonds, instead of 2, more than compensates for
the promotional energy.
Hybridization: sp3 Orbitals and Methane
From the above picture, it is expected that methane (CH 4) has two kinds of C-H
bonds – one type from the carbon 2s orbital and the other kind from the 2p
orbitals – but this is not the case. Linus Pauling, in 1931, showed how an s orbital
and three p orbitals can combine or hybridize to form four equivalent sp3 hybrid
atomic orbitals, that are arranged tetrahedrally about the carbon nucleus. This
is illustrated in the diagram overleaf.
2s + 3 x 2p atomic orbitals
4 x sp3 hybrid orbitals
A set of 4 sp3 hybrid orbitals
Linus Pauling
Each sp3 hybrid has asymmetric directionality, and like p orbitals there is one
angular node:
When the four identical orbitals of an sp3 hybridized carbon atom overlap with the
1s orbitals of four hydrogen atoms, four identical C-H bonds are produced and
methane results:
Each angle HCH is 109.5o, the so-called tetrahedral angle. Whenever carbon
forms four single bonds (“saturated carbon”), the hybridization mode is always
sp3, as shown for the saturated hydrocarbon ethane (C2H6), below
Ethane is the simplest molecule containing a carbon-carbon bond: it can be
represented by several formula types, the most important of which are shown
below.
H H
H H
.. ..
H:C:C:H
CH3CH3
H C C H
.. ..
H H
H H
Purely 2-dimensional formulas
HH
H
H C
H
H
C
H
H
H
HH
H
Formulas depicting 3 dimensions
(for the eclipsed conformer)
The same kind of hybridization is used by carbon in millions of other compounds,
including more complex alkanes, the family of hydrocarbons to which methane
and ethane belong. More complex alkanes or other organic compounds can be
written conveniently as line formulas. These formulas omit the symbols for
carbon and hydrogen and show only the carbon-carbon bonds and bonds to
heteroatoms (O, N, S, Cl, etc) or to functional groups (OH, NH2, COOCH3, etc).
Carbon is assumed to be at line intersections or at the end of lines. Some
examples are shown overleaf.
Line formula
CH3
CH3
CH3CHCH2CHCH3
2,4-Dimethylpentane
CH3CH2OCH2CH3
Diethyl ether
O
O
O
C
CH CH
CH.CH
2,4-Cyclopentadienone
Hybridization: sp2 Orbitals and the Structure of Ethylene (Ethene)
Although sp3 hybridization is the most common electronic bonding state of
carbon (saturated carbon), there are many other situations (unsaturated carbon)
where carbon uses a different kind of hybridization in its bonding. Such an
example is ethylene (ethene), the simplest member of the alkene family of
hydrocarbons. Here, the two carbon atoms are linked by a double bond, the
molecule is planar and the bond angles are approximately 120 o, giving a trigonal
planar structure. In this molecule, each carbon atom forms three equivalent sp 2
hybrids from the 2s orbital and two of the 2p orbitals, leaving a p orbital
unperturbed. This is illustrated overleaf.
2s + 2 x 2p atomic orbitals
3 x sp 2 hybrid orbitals
A set of 3 sp2 hybrid orbitals
A set of 3 sp2 hybrids and a p orbital for each carbon
atom of ethylene. The orbital lobes are elongated for clarity.
The three sp2 hybrids form the  skeleton of ethene, by head-on overlap with
another sp2 hybrid (carbon) or 1s orbitals (hydrogen), whilst the p orbitals overlap
sideways to form a  bond, as shown on the next page. Again, the orbital lobes
are deliberately elongated, for clarity.
The double bond of ethylene is both shorter and stronger than the C-C single
bond of ethane, because it is formed by sharing four electrons, instead of just two.
See the table at the end of class1 and Table 1.3 on p. 17 of the textbook.
The structure of ethylene is summarized below.
Hybridization: sp Orbitals and the Structure of Acetylene (Ethyne)
Using similar arguments as for ethane and ethylene, the bonding in the molecule
acetylene is illustrated on the next page. Note the presence of a triple bond,
formed by the sideways overlap of four p orbitals (two on each carbon atom). The
sp skeleton is shown in A, whereas the two  bonds are emphasized in B.
2s + 2p atomic orbitals
2 x sp hybrid orbitals
A set of 2 sp hybrid orbitals
Acetylene is thus a linear molecule with an even shorter and stronger carboncarbon bond than ethylene (see table at the end of class 1 and Table 1.3 on p. 17
of the textbook).
Its structure is summarized below.
Hybridization and Other Atoms
Nitrogen, oxygen and other elements commonly found in organic molecules, also
use sp3, sp2 and sp hybrid atomic orbitals to form covalent bonds. Electron pairs
in hybrid orbitals that are not used in bonding are called lone pairs or non-bonded
pairs, as illustrated for ammonia (NH3) and water (H2O), overleaf. Note that
hybridization leads to weaker lone pair-bond pair repulsions, which endows
additional stability.
The organic derivatives of ammonia (e.g. amines) and of water (e.g. alcohols and
ethers) have similar bonding arrangements. Oxygen and nitrogen that are doubly
or triply bonded in organic molecules use, like carbon, sp 2 and sp hybrid orbitals,
respectively.
Class Question
What is the hybridization of carbon and, where appropriate, nitrogen and oxygen
in the following molecules?
Molecular Orbital Theory of Bonding
Like valence-bond (VB) theory, molecular orbital (MO) theory recognizes that
electrons cannot be localized on a single atom when that atom is part of a
molecule. One major difference between the two methods is that MO theory
calculates the molecular orbitals that may be produced from the available atomic
orbitals. Only after this determination are electrons allocated to molecular energy
levels, according to the Aufbau principle and the Pauli exclusion principle. The
VB method concentrates on electron pairs from the beginning and determines
the energy of various canonical (or resonance) structures, which collectively have
all the electrons in the molecule paired in all possible ways.
MO theory in essence describes covalent bond formation as arising from a
mathematical combination of the wave functions of the atomic orbitals. If the
atomic orbital wave functions are in phase, the combination is constructive and
results in a bonding molecular orbital (m.o.). On the other hand, if the a.o.
wave functions are out of phase, the combination is destructive and leads to an
antibonding (*) m.o. Both molecular orbitals are derived by combination of the
atomic orbitals, as illustrated for one of the simplest cases, H2, below.
For more complex (polyatomic) molecules the picture is much more involved, as
shown for methane, overleaf.
Thus, any MO description in this course will be largely confined to individual
bonds. For example, the  bonding and * antibonding m.o. of ethylene, resulting
from combination of p atomic orbitals can be represented simply as follows.