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Unformatted text preview: CHEM 356, Lecture 26, Fall 2009 1 Atomic Structure and Atomic Spectroscopy. We shall assume that the wavefunctions for a multielectron atom are determined in zeroth order by a centralfield Hamiltonian, : we shall study the effect of adding systematically interelectron repulsion, followed by spinorbit coupling. RussellSaunders Coupling Scheme: The most common coupling scheme for angular momenta is the RussellSaunders scheme, which corresponds to building up the atomic Hamiltonian in three stages, = , = + ee , = + ee + so . Notation: lower case letters are used to designate the angular momenta of the individual electrons in a multielectron atom: , s , j , etc. Procedure: makes extensive use of the fact that mutually commuting operators can have si multaneous eigenfunctions. We shall require at each step that the operators used to label our energy eigenfunctions all commute with . 1. Centralfield Hamiltonian : All , s commute with and with one another: we say that 2 , , 2 , and are SHARP operators, which means that we can obtain simultaneous eigenfunctions of the full set of operators { 2 , , 2 , , } . The form for the Hamiltonian provides a description of the atom at the level of electronic CONFIGURATIONS. 2. Inclusion of Interelectronic repulsions: = + ee The individual vector operators no longer commute with (because they do not commute with ee ); however, two new angular momentum operators L = and S = s do. The corresponding set of sharp operators is then { 2 , 2 , , } . This form for the Hamiltonian provides a description of the atom at the level of electronic TERMS. CHEM 356, Lecture 26, Fall 2009 2 3. Inclusion of SpinOrbit Coupling: = + ee + so . L and S do not commute with so = S L , and hence they do not commute with . The vector operator J , with J = L + S , which represents the total electronic angular momentum of the multielectron atom does commute with , however. The corresponding set of sharp operators is now 2 , and ....
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This note was uploaded on 02/28/2011 for the course CHEM 356 taught by Professor Prof.iaskjd during the Fall '09 term at Waterloo.
 Fall '09
 Prof.Iaskjd
 Electron

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