Crystals crystal field theory

For Iran sition metals th c splittin g of th c d orbitals in a ligand field is most readily done using HHT. In all other sem i-ctn pirical meth -ods, the orbital energies depend on the electron occupation. HyperCh em s m oiccii lar orbital calcii latiori s give orbital cri ergy spacings that differ from simple crystal field theory prediction s. The total molecular wavcfunction is an antisymmetrized product of the occupied molecular orbitals. The virtual set of orbitals arc the residue of SCT calculations, in that they are deemed least suitable to describe the molecular wavefunction, ... 

For transition metal complexes, techniques derived from a crystal-field theory or ligand-field theory description of the molecules have been created. These tend to be more often qualitative than quantitative. 

Transition metals readily form complexes, such as [Fe(CN)6], the ferrocyanide ion, Ni(CO)4, nickel tetracarbonyl, and [CuC ], the copper tetrachloride ion. MO theory applied to such species has tended to be developed independently. It is for this reason that the terms crystal field theory and ligand field theory have arisen which tend to disguise the fact that they are both aspects of MO theory. 

Color from Transition-Metal Compounds and Impurities. The energy levels of the excited states of the unpaked electrons of transition-metal ions in crystals are controlled by the field of the surrounding cations or cationic groups. Erom a purely ionic point of view, this is explained by the electrostatic interactions of crystal field theory ligand field theory is a more advanced approach also incorporating molecular orbital concepts. 

E. Basolo and R. G. Pearson, Mechanisms of Inorganic Reactions, 2nd ed., John Wiley Sons, Inc., New York, 1967. An excellent volume that stresses the reactions of complexes ia solution a background and a detailed theory section is iacluded that is largely crystal field theory, but some advantages and disadvantages of molecular orbital theory are iacluded. 

Herzfeld, C. M., and Meijer, P. H. E., Group Theory and Crystal Field Theory, in F. Seitz and D. Turnbull, eds., Solid State Physics, Yol. 12, Academic Press, Mew York, 1961. 

There are two major theories of bonding in d-metal complexes. Crystal field theory was first devised to explain the colors of solids, particularly ruby, which owes its color to Cr3+ ions, and then adapted to individual complexes. Crystal field theory is simple to apply and enables us to make useful predictions with very little labor. However, it does not account for all the properties of complexes. A more sophisticated approach, ligand field theory (Section 16.12), is based on molecular orbital theory. 

FIGURE 16.24 In the crystal field theory of complexes, the lone pairs of electrons that serve as the Lewis base sites on the ligands (a) are treated as equivalent to point negative charges (b). 

The effects of the bonding electrons upon the d electrons is addressed within the subjects we call crystal-field theory (CFT) or ligand-field theory (LFT). They are concerned with the J-electron properties that we observe in spectral and magnetic measurements. This subject will keep us busy for some while. We shall return to the effects of the d electrons on bonding much later, in Chapter 7. 

Crystal-field theory (CFT) was constructed as the first theoretical model to account for these spectral differences. Its central idea is simple in the extreme. In free atoms and ions, all electrons, but for our interests particularly the outer or non-core electrons, are subject to three main energetic constraints a) they possess kinetic energy, b) they are attracted to the nucleus and c) they repel one another. (We shall put that a little more exactly, and symbolically, later). Within the environment of other ions, as for example within the lattice of a crystal, those electrons are expected to be subject also to one further constraint. Namely, they will be affected by the non-spherical electric field established by the surrounding ions. That electric field was called the crystalline field , but we now simply call it the crystal field . Since we are almost exclusively concerned with the spectral and other properties of positively charged transition-metal ions surrounded by anions of the lattice, the effect of the crystal field is to repel the electrons. 

Except to note that the occurrence of the coefficients 15 and 10 in 155 and lOD obviate the need for fractions here or elsewhere in crystal-field theory thus, they are there for reasons of convenience and definition only. 

Much useful understanding of the processes of crystal-field theory, however, can be had from a study of just the free-ion ground terms. Application of the simple process in Section 3.7 identifies the ground terms for d free ions as D, D,... 

The spectrochemical series was established from experimental measurements. The ranking of ligands cannot be fully rationalized using crystal field theory, and more advanced bonding theories are beyond the scope of general chemistry. 

Color is a spectacular property of coordination complexes. For example, the hexaaqua cations of 3 transition metals display colors ranging from orange through violet (see photo at right). The origin of these colors lies in the d orbital energy differences and can be understood using crystal field theory. 

In the final section of this chapter, we shall attempt to give a brief rationalization of the regularities and peculiarities of the reactions of non-labile complexes which have been discussed in the previous sections. The theoretical framework in which the discussion will be conducted is that of molecular orbital theory (mot). The MOT is to be preferred to alternative approaches for it allows consideration of all of the semi-quantitative results of crystal field theory without sacrifice of interest in the bonding system in the complex. In this enterprise we note the apt remark d Kinetics is like medicine or linguistics, it is interesting, it js useful, but it is too early to expect to understand much of it . The electronic theory of reactivity remains in a fairly primitive state. However, theoretical considerations may not safely be ignored. They have proved a valuable stimulus to incisive experiment. 

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