INTRODUCTION TO LIGAND FIELD THEORY BALLHAUSEN PDF

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The following complete article may be found under : C. Ballhausen, Introduction to Ligand Field Theory. McGraw-Hill, New York, , pages History of the Crystal Field Approach C. Ballhausen Taken from C. Ballhausen, Introduction the Ligand Field Theory, pages 2 - 6. Theories of Bonding The all-important question for the coordination compounds of the transition metals is this: How does one describe and characterize the bonding between the central ion and the ligands in terms of some electronic theory?

In modern times three methods have been used to solve the problems of the nature of these bonds and to account for the other properties of the complexes. They are: 1. The molecular-orbital method 2.

The valence-bond theory 3. The crystal or ligand field theory Until recently, most chemists working with the complexes of the transition metal ions have been mainly interested in the application of the valence-bond theory as exemplified by Pauling 2 in his famous book "The Nature of the Chemical Bond. However, more than twenty years have passed since Van Vleck demonstrated the superiority of the crystal field approach in the discussion of the magnetic properties of inorganic complexes.

Now, it must at once be said that for the complexes under discussion both the valence-bond picture and the crystal field picture can be considered as a specialization of the molecular-orbital method.

Thus the best features of both the valence-bond picture and the crystal field theory are incorporated in the ligand field theory, and it is this theory with which we shall be mostly concerned. As we shall not in this book follow the historical line of development, it is perhaps of some value to scan briefly through the most important papers from which the present theory has emerged.

History of the Crystal Field Approach The basic idea of the crystal field theory, namely, that the metal ion in the complexes is subjected to an electric field originating from the ligands, is due to Becquerel 8 The same year saw this proposal formulated into an exact theory by Bethe 6. In a now classic paper, Bethe investigated, by means of symmetry concepts, how the symmetry and strength of a crystalline field affect the electronic levels of the gaseous metal ions.

In doing so, he laid down the foundation for all further work in this field. Nearly simultaneous with the work of Bethe was the work of Kramers 9.

In , the latter succeeded in proving the very important result that the electronic levels in molecules containing an odd number of electrons must remain at least twofold degenerate, provided that no magnetic field is present.

This so-called "Kramers degeneracy" is again closely related to the existence of the "double groups" Bethe. The first application of the new theory to chemistry was made by Van Vleck By realizing that the quenching of the "orbital momentum" would be a consequence of the crystalline field model, he succeeded in explaining why the paramagnetism of the complexes of the first transition series corresponds to a "spin-only" value Furthermore, the crystalline field model was able to predict in which cases there would be small deviations from this empirical rule These predictions were completely justified by the calculations of Schlapp and Penney 12 and of Jordahl 13 , who showed that both the anisotropy and the variation of the magnetic susceptibility with temperature could be exactly predicted and calculated.

Their very important papers directly confirmed the basic idea in the crystal field approach, namely, that the crystal field reduces the degeneracy of the electronic levels of the gaseous metal atom. A note by Gorter 14 , in which it is shown that the crystal field of a regular tetrahedron will produce the same levels as those produced by a regular octahedron but with the level order inverted, concludes the pioneer papers. In the years preceding the war the efforts were mostly concentrated on explaining and calculating the detailed magnetic behavior of the complex ions.

It soon turned out, however, that the theory was hampered because of insufficient experimental data. This period could be called "the period of Van Vleck", because nearly all the important contributions were due to him and his school.

The means by which the absorption bands of inorganic complexes acquire intensity was another problem first treated by Van Vleck He pointed out that it is necessary to couple the electronic wave functions with the odd vibrations of the molecule in order to get band intensities different from zero, if one assumes that the absorption bands are due to transitions between the various split 3dn or 4fn configurations.

Jahn and Teller had shown in that no nonlinear molecule could be stable in a degenerate state apart, of course, from a Kramers degeneracy. If, therefore, a certain configuration is predicted to give rise to an electronic degeneracy, such a configuration must immediately distort, via nuclear displacements in the molecule, in such a way that the degeneracy is removed.

Van Vleck calculated the Jahn-Teller distortions for molecules of the form XY6 and showed how this configurational instability affected the magnetic moment of the molecules. The subsequent paper on the complete energy levels of chrome alum by Finkelstein and Van Vleck 20 laid down the method of calculation employed in nearly all the inquiry that followed.

The development after the war of the spectrophotometer and of the paramagnetic resonance technique brought new life into the theoretical and experimental development of the crystal field theory, and the consequence has been a steadily increasing flood of papers dealing with these subjects.

References to most of this work can be found in seven review papers, Refs. Since we have now reached a point at which the developments cease to be history, we shall leave the subject here. Before we close this chapter, it may perhaps be appropriate to make a few remarks concerning the nomenclature we shall use. By the name "crystal field theory" we shall understand the original theory of Bethe and Van Vleck, i. The ligand field theory incorporates the best features of both the pure crystal field theory and the molecular-orbital theory, and as such is the superior tool for dealing with the complexes.

Nearly all the results of the crystal field theory are also valid in the ligand field theory. However, since the former theory in some ways is the easier to understand, we shall start by treating that case. In the following chapter we shall accordingly proceed to recapitulate some important features of the theory of atomic spectra because that theory is the starting point of the crystal field theory. John C. Bailar, Jr. Van Vleck: J. Van Vleck and A.

Sherman: Revs. Modern Phys. Bethe: Ann Physik, [5], 3: Mulliken: Phys. Becquerel: Z. Physik, Kramers: Proc. Amsterdam, Van Vleck: Phys. Schlapp and W. Penney: Phys. Jordahl: Phys. Gorter: Phys. Van Vleck and W. Penney: Phil. Howard: J. Finkelstein and J. Polder: Physica, 9: Bleaney and K.

Stevens: Repts. Bowers and J. Owen: Repts. Moffitt and C. Ballhausen: Ann. Runciman: Repts. McClure: "Solid State Physics," vol. Dunn: "Modern Coordination Chemistry," p.

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Preface to the title at left, I have tried to give an introduction to that field of chemistry which deals with the spectral and magnetic features of inorganic complexes. It has been my intention not to follow the theory in all its manifestations but merely to describe the basic ideas and applications. This has been done with an eye constantly aimed at the practical and experimental features of the chemistry of the complex ions. The book is thus primarily intended for the inorganic chemist, but it is true that, in order to follow the exposition, a course in basic quantum mechanics is needed. Simple examples are nearly always used to illustrate the arguments, but the quoted experimental evidence must of necessity be limited. Nevertheless, in the last chapter an attempt has been made to cover most of the important work so far performed that lies within the scope of the book.

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