The following complete article may be found under :
C. J. Ballhausen, Introduction to Ligand Field Theory.
McGraw-Hill, New York, 1962, pages 2-6.
History of the Crystal Field Approach
C. J. Ballhausen
Taken from C.J. Ballhausen,
Introduction the Ligand Field Theory,
pages 2 - 6.
1-b. 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."
Special emphasis was there laid upon the
magnetic properties of the complexes, and a seemingly successful theory was
built upon those features.
However, more than twenty years have passed since
Van Vleck 3-5
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.5,7
Indeed, the most useful approach to these
compounds is now called the ligand field theory, which is really nothing
more than a hybridization of the ideas of Bethe 6 and
Van Vleck 3,4 with those
of Mulliken 5. 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.
1-c. 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 (1929).
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
In 1930, 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 (1932). 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 10 .
Furthermore, the crystalline
field model was able to predict in which cases there would be small deviations
from this empirical rule 11 .
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
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. As some examples we cite Van Vleck and Penney's 15
treatment of the Mn(II) ion, the proof that the crystal field theory and the
theory of Pauling both were special cases of the molecular-orbital theory
the definitions of the "strong" and "weak" crystal field 4 ,
the investigation of
the K3Fe(CN)6 system 16 ,
and the research into the magnetic behavior of the
vanadium, titanium, and chromium alums 17 .
The means by which the absorption bands of inorganic complexes acquire
intensity was another problem first treated by Van Vleck 18 .
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.
To the same period belong
Van Vleck's investigations into the Jahn-Teller theorem as applied to
octahedral molecules 19 . Jahn and Teller had shown in 1937
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. A few other papers, as, for example,
calculation of the magnetic anisotropy of the Cu(II) salts, mark
the close of the second period in the history of crystal field theory.
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.e., the theory which does not consider the role played by the
ligands further than to credit them with producing a steady "crystalline
field." On the other hand, the name "ligand field theory" indicates a
hybridization of the pure crystal field theorywith the molecular-orbital
theory of Mulliken. 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
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.
1. John C. Bailar, Jr.: p. 100 in "Chemistry of the Coordination Compounds,"
Reinhold Publishing Corporation, New York, 1956.
2. L. Pauling: "The Nature of the Chemical Bond,"
Cornell University Press, Ithaca, N.Y., 1940.
3. J. H. Van Vleck: J. Chem. Phys., 3: 803 (1935).
4. J. H. Van Vleck: J. Chem. Phys., 3: 807 (1935).
5. J. H. Van Vleck and A. Sherman:
Revs. Modern Phys.,7: 167 (1935).
6. H. Bethe: Ann Physik, , 3: 133 (1929).
7. H. S. Mulliken: Phys. Rev., 40: 55 (1932).
8. J. Becquerel: Z. Physik, 58: 205 (1929).
9. H. A. Kramers: Proc. Acad. Sci. Amsterdam, 33: 953 (1930).
10. J. H. Van Vleck: "Theory of Magnetic and Electric Susceptibilities,"
Oxford University Press, Oxford and New York, 1932.
11. J. H. Van Vleck: Phys. Rev., 41: 208 (1932).
12. R. Schlapp and W. G. Penney: Phys. Rev., 42: 666 (1932).
13. 0. Jordahl: Phys. Rev., 45: 87 (1934).
14. C. J. Gorter: Phys. Rev., 42: 437 (1932).
15. J. H. Van Vleck and W. G. Penney:
Phil. Mag., , 17(7): 961 (1934).
16. J. B. Howard: J. Chem. Phys., 3: 813 (1935).
17. J. H. Van Vleck: J. Chem. Phys., 7: 61 (1939).
18. J. H. Van Vleck: J. Phys. Chem., 41: 67 (1937).
19. J. H. Van Vleck: J. Chem. Phys., 7: 72 (1939).
20. R. Finkelstein and J. H. Van Vleck:
J. Chem. Phys., 8: 790 (1940).
21. D. Polder: Physica, 9: 709 (1942).
22. B. Bleaney and K. W. H. Stevens:
Repts. Progr. Phys., 16: 108 (1953).
23. K. D. Bowers and J. Owen:
Repts. Progr. Phys., 18: 304 (1955).
24. W. Moffitt and C. J. Ballhausen:
Ann. Rev. Phys. Chem., 7: 107 (1956).
25. W. A. Runciman: Repts. Progr. Phys., 21: 30 (1958).
26. D. S. McClure: "Solid State Physics," vol. 9, p. 399,
Academic Press, Inc., New York, 1959.
27. T. M. Dunn: "Modern Coordination Chemistry," p. 229, Interscience Publishers,
Inc., New York, 1960.
28. Inst. intern. chim.‚ Solvay, Conseil-Chim.;
10e Conseil, Brussels, 1956.
Last updated : May 1, 2002 - 11:15 CET