C467 Term Symbols and other notations

C467 Term Symbols and other notations - Mulliken Symbols...

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C467 Term Symbols and other notations.doc 7 Mulliken Symbols For splitting in a tetrahedral crystal field the components are similar, except that the symmetry label g (gerade) is absent. The ground term for first-row transition metal ions is either D, F or S which in high spin octahedral fields gives rise to A, E or T states. This means that the states are either non- degenerate, doubly degenerate or triply degenerate. Copyright © 2006 by Robert John Lancashire, all rights reserved. Created and maintained by Prof. Robert J. Lancashire (with grateful assistance from Prof. W.J. Jones and Tiffany Timberlake), The Department of Chemistry, University of the West Indies, Mona Campus, Kingston 7, Jamaica. Created June 2000. Links checked and/or last modified 18th Septemberr 2006. URL http://wwwchem.uwimona.edu.jm/courses/RScoupling.html
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C467 Term Symbols and other notations.doc 6 The Crystal Field Splitting of Russell-Saunders terms The effect of a crystal field on the different orbitals (s, p, d, etc.) will result in splitting into subsets of different energies, depending on whether they are in an octahedral or tetrahedral environment. The magnitude of the d orbital splitting is generally represented as a fraction of Δ oct or 10Dq. The ground term energies for free ions are also affected by the influence of a crystal field and an analogy is made between orbitals and ground terms that are related due to the angular parts of their electron distribution. The effect of a crystal field on different orbitals in an octahedral field environment will cause the d orbitals to split to give t 2g and e g subsets and the D ground term states into T 2g and E g , (where upper case is used to denote states and lower case orbitals). f orbitals are split to give subsets known as t 1g , t 2g and a 2g . By analogy, the F ground term when split by a crystal field will give states known as T 1g , T 2g , and A 2g . Note that it is important to recognise that the F ground term here refers to states arising from d orbitals and not f orbitals and depending on whether it is in an octahedral or tetrahedral environment the lowest term can be either A 2g or T 1g . The Crystal Field Splitting of Russell-Saunders terms in high spin octahedral crystal fields. Russell-Saunders Terms Crystal Field Components Note that, for simplicity, spin multiplicities are not included in the table since they remain the same for each term. The table above shows that the Mulliken symmetry labels, developed for atomic and molecular orbitals, have been applied to these states but for this purpose they are written in CAPITAL LETTERS.
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C467 Term Symbols and other notations.doc 5 A simple graphical method for determining just the ground term alone for the free-ions uses a "fill in the boxes" arrangement.
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C467 Term Symbols and other notations - Mulliken Symbols...

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