 2. Linear Combination of Atomic Orbitals The Linear
Combination of Atomic Orbitals (LCAO) approximation is fundamental to
many of our current models of chemistry. Both the vast
majority of the calculational programs that we use, be
they ab initio, density functional,
semiempirical molecular orbital, or even some
sophisticated force-fields, and our qualitative
understanding of chemistry are based on the concept that
the orbitals of a given molecule can be built from the
orbitals of the constituent atoms. We feel comfortable
with the p-HOMO (highest occupied
molecular orbital) of ethylene depicted as a combination of two
carbon p-orbitals, as shown in Figure 2.1,
although this is not a very accurate description of the
electron density of this molecular orbital
(MO). The use of the p-atomic
orbitals (AOs),
however, makes it easier to understand both the
characteristics of the MO itself and the transformations
that it can undergo during reactions.
In principle,
we could build up MOs from many sorts of function that
can describe an electron density probablility
distribution, but we have learnt to understand
combinations of AOs and to use them in our models of
chemical bonding and reactivity. Indeed, if confronted
with an MO that was calculated, for instance, using plane
waves, most chemists would immediately translate it into
a combination of AOs. In the following, we will describe
the LCAO approximation and demonstrate some of the
effects that are important when AOs interact with each
other to form MOs. Next: |
