CALTECH CH 213A - Advanced Ligand Field Theory (33 pages)

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Advanced Ligand Field Theory



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Advanced Ligand Field Theory

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33
School:
California Institute of Technology
Course:
Ch 213a - Advanced Ligand Field Theory

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Chemistry 213a Advanced Ligand Field Theory Problem Sets A Weak Crystal Fields B Strong Crystal Fields C Intermediate Crystal Fields Tanabe Sugano Diagrams D Introduction to Electronic Spectra Texts Ballhausen C J Introduction to Ligand Field Theory McGraw Hill 1962 Figgis B N Introduction to Ligand Fields Wiley 1966 Figgis B N and Hitchman M A Ligand Field Theory and Its Applications Wiley 2000 Griffith J S The Theory of Transition Metal Ions Cambridge University Press 1961 Additional references have been placed on permanent reserve in the Millikan Library on the eighth floor 1 Introduction The four accompanying problem sets will illustrate the development of crystal field theory for the d3 electronic configuration in an octahedral ligand environment In principle once the calculations are understood for this case they can be applied readily to other configurations The theory of atomic spectroscopy provides the starting point for the crystal field formalism For a many electron ion or atom the Hamiltonian has the form Ze 2 e2 h2 2i i ri li si H 2m i rij i i j rij i Here the potential function takes into account interelectron repulsion and spin orbit coupling in the last two terms respectively For simplicity the spin orbit contribution will be ignored initially and considered later in the second half of this course Ch 213b The total energy of a dn term is given by the sum of its own electrostatic energy and its energy in the field of the core electrons For our purposes the core energy can be neglected since to a first approximation the core energy should be the same for all d3 configurations and will vanish when energy differences between terms are considered Upon complex formation the Hamiltonian for the free ion will change to include the interactions between the electrons and the ligand field Vi present in the complex The strength of the ligand field relative to other electronic forces present will vary from one complex to another allowing three principle cases to



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