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Chem 120A
Supplement  Term Symbols for Atoms
04/16/07
Spring 2007
Lecture 33
Reading: Ratner and Schatz Ch. 9
1
What are Term Symbols?
A given electron conﬁguration can result in several different atomic (molecular) states with different energies
as a result of the interelectronic interactions. States with the same energy are constitute a ’term’. Term
symbols are thus labels for groups of states with the same energy for multiple electron systems (both atoms
and molecules). The attached schematic shows the order in which the labels are evaluated, namely going
from the largest interactions at the top to the smallest interactions at the bottom.
Term symbols are written in the following way:
2
S
+
1
L
J
(1)
where
L
is the total orbital angular momentum.
L
tells us the magnitude of the angular momentum through
¯
h
[
L
(
L
+
1
)]
1
/
2
. It has 2
L
+
1 distinguished by the quantum number
M
L
. Similar remarks apply to
S
, the
total spin angular momentum (where 2
S
+
1 is known as the multiplicity) as well as
J
, the total angular
momentum
J
=
L
+
S
. The value of L is obtained by using what is known as the ClebschGordon series, for
a two electron system, this would be:
L
=
l
1
+
l
2
,
l
1
+
l
2

1
,...

l
1

l
2

(2)
where the modulus sign is attached to
l
1

l
2
as the value of
L
must be nonnegative. The maximum value
of
L
is obtained when the two orbital angular momenta are in the same direction. The lowest value,

l
1

l
2

is obtained when they are in opposite directions. The value of
L
is normally designated as a capital letter
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 Spring '07
 Whaley
 Physical chemistry, Electron, Mole, pH

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