Physical Chemistry , 1st ed.

c.All of the atoms in chloroform have complete valence shells and all-paired

electrons. This suggests a colorless compound. It is a colorless liquid.

(Although it sometimes has a yellowish tinge, it is generally recognized as

colorless.)

d.Ti in the 4 oxidation state has a noble-gas electron configuration, as do

the O^2 ions. Therefore, this compound is not expected to absorb visible

light. Its electronic transitions are expected to occur in the ultraviolet region

of the spectrum. TiO 2 is very white. It is extensively used in industry as a

white pigment in everything from paints to various food products. (Does it

surprise you that you occasionally eat an ingredient of paint?)

e.With four transition metal atoms, it might be expected that hemoglobin is

colored. It is responsible for the red color of red blood cells.

15.9 Electronic Spectra of Electron Systems:

Hückel Approximations

It is difficult to state generalities about the electronic structure of molecules,

because molecules are so diverse. However, for one group of electrons, there is

a relatively easy framework in which to understand electronic energy levels:

electrons in organic molecules. In particular, we are limiting the following dis-

cussion to molecules that have alternating single and double bonds; that is,

they have conjugatedbonds. In organic molecules,electrons reside in mo-

lecular orbitals formed by the side-on, nonaxial overlap of atomic orbitals of

the carbon atoms, as shown in Figure 15.16. Such orbitals represent a particu-

larly important aspect of carbon-carbon bonding in organic chemistry. The

chemistry of aromatic organic compounds, which are based on benzene, is in

part dictated by the electrons located in conjugated orbitals. Nonaromatic

conjugated electron systems, like 1,3-butadiene, are also relevant molecular

systems. (Recall from organic chemistry that conjugated bonds, alternating

single and double carbon bonds, have a special stability since adjacent double

bonds can overlap with each other, extending the electron system. See Figure

15.16 for an illustration.)

An approximate treatment ofelectron systems was introduced in 1931 by

Erich Hückel and is called the Hückel approximationoforbitals. The first

step in a Hückel approximation is to treat the sigma bonds separately from the

pi bonds. Therefore, in a Hückel approximation of a molecule, only the 

bonds are considered. The usual assumption is that the bonds are under-

stood in terms of regular molecular orbital theory. The bonds form the over-

all structure of the molecule, and the bonds spread out over, or span,the

available carbon atoms. Such bonds are formed from the side-on overlap of

the carbon 2porbitals. If we are assuming that the bonds are independent

of the bonds, then we can assume that the molecular orbitals are linear

combinations of only the 2porbitals of the various carbon atoms. [This is a

natural consequence of our earlier linear combination of atomic orbitals—

molecular orbitals (LCAO-MO) discussion.] Consider the molecule 1,3-butadiene

(Figure 15.17). The orbitals are assumed to be combinations of the 2patomic

orbitals of the four carbon atoms involved in the conjugated double bonds:

(MO) c 1  2 p,C1 c 2  2 p,C2 c 3  2 p,C3 c 4  2 p,C4

where c 1 ,c 2 ,c 3 , and c 4 are the expansion coefficients and C1, C2, C3, and C4

refer to the individual carbon atoms. The combination of four atomic orbitals

15.9 Electronic Spectra of Electron Systems: Hückel Approximations 543

C CCCCC
Figure 15.16 Conjugated bonds are formed
when alternating single and double bonds be-
tween carbon atoms overlap, allowing the elec-
trons to traverse the entire span of the double
bonds, instead of being confined between two
particular carbons.