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Unformatted text preview: Chem 120A Term Symbols for Atoms and Diatomic Molecules 04.24.06 Spring 2006 Lecture 36 Reading: Engel Ch 10.7-10.8 and Ch 15.2, McQuarrie and Simons Physical Chemistry: 8.8-8.10 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 inter-electronic 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). 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 Clebsch-Gordon 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 non-negative. 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 analogous to labeling the l states as s , p , d , etc. L = S L = 1 P L = 2 D L = 3 F L = 4 G A closed shell has 0 orbital angular momentum because all the individual orbital angular momenta sum to zero. Therefore when working out term symbols, we need consider only the electrons of the unfilled shell.zero....
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