Theory ligand field

The ligand MOs are of two types a MOs, which are cylindrically symmetrical about the metal-ligand bond, and n MOs which are not. The a type of metal-ligand bonding is usually 

Dah flig -E hig -E e (in square planar ML4) 2a g + fl2u + ig + (in tran -oetahedral ML4L2) 

2fli -E e (in tetrahedral ML3L ) 2fli -E 2e (in all-cM-oetahedral ML3L3) 

2fli -E hi + e (in square pyramidal ML4L ) 3fli -E hi -E e (in oetahedral ML5L ) 

Stronger as, for example, is provided by the lone pair orbital on CO in metal earbonyls. We shall negleet 7i-type bonding and eonsider in detail only oetahedral eases. 

Metal Weak Strong Ligand interaction interaction o orbits 

However, transition metal complexes do absorb in the visible region, giving them a characteristic colour. How can this happen if the transitions are forbidden The answer is that interaction may occur between the motion of the electrons and vibrational motions so that some vibronic transitions are allowed (see Section 7.3.4.2b). 

If an atom has six ligands, then the mutual repulsion of tire six bonding electron pairs results in an octahedral coordination. The positions of the ligands correspond to points on the axes of the coordinate system. If nonbonding electrons are present, these will prefer dy and d because the regions of high charge density of the other two 

Inorganic Structural Chemistry, Second Edition 2006 John Wiley Sons, Ltd. 

Orientation of the regions of high electron density for 3d orhitals. 

True-to-scale drawings of areas with constant value for the wave functions. The dots on the ch cumscribed cubes mark the directions of preferential orientation of the partial clouds  

The Jahn-Teller effect is always to be expected when degenerate orbitals are unevenly occupied with electrons. In fact, it is observed for the following electronic configurations  

ligand-field theory is the name given to crystal-field theory that is freely parameterized. The centrally important point is that ligand-field calculations, whether numerical or merely qualitative, explicitly or implicitly employ a ligand-field Hamiltonian, very much like the crystal-field Hamiltonian, operating upon a basis set of pure d orbitals. Instead of the crystal-field Hamiltonian (Eq. 6.15), 

A simple example of an effective operator with which the reader will be familiar is the use of Zeff e r as the effective nuclear potential experienced by an electron outside of a closed inner shell. Thus, we may compute the energies and wavefunctions for a 2s or 2p electron outside a shell, using the hydrogen-like Hamiltonian, 

Ligand Field Theory plays a somewhat ambiguous role in computational chemistry. On the one hand, undergraduates are invariably introduced to the electronic structure and spectroscopy of TM systems via Russell-Saunders coupling and a Crystal Field/Ligand Field formalism. Thereafter, however, 

LFT seems to fade away to be used in a loose qualitative way to describe certain features of d-d spectra or certain aspects of reaction energies. The latter is invariably couched in terms of Ligand Field Stabilisation Energies (LFSEs). 

Veillard [19] covers a similar range of molecules but from the Hartree-Fock and post-HF view. The discussion is organised more in terms of molecular properties. Thus, he deals with metal carbonyls, carbides, cyanides, C02 complexes, alkyls, carbenes, carbynes, alkenes, alkynes and metallocenes under the headings of electronic states, electronic spectra, optimised geometries, binding energies, Ionisation Potentials and Electron Affinities, nature of M-L bonding and other properties (e.g. vibrational spectra, dipole moments and electron distributions). 

Veillard is not convinced that ab initio Hartree-Fock theory will ever lead to the kind of black box calculations now possible for some organic molecules. Tsipis is rather more positive recognising the possibilities for a complementary interplay between theory and experiment but is nevertheless of the opinion that there exists no general canon for the efficacious selection and application of the most eligible computational method for the study of a certain compound or series of compounds . This view does not appear to be shared by Ziegler or Comba who convey quite positive messages concerning the capabilities of Density Functional Theory and Molecular Mechanics respectively. 

Finally, Duer, Fenton and Gerloch [74] provide an overview of some of the most recent Ligand Field Theory studies as applied to the notion of bent bonding in metal complexes. The data described demonstrate the full capabilities of modem LFT which, for metal complexes of fixed geometry, can now give a unified description of magnetic and excited state properties. 

The terms crystal field theory and ligand field theory are not used in a uniform way. As only interactions between adjacent atoms are being considered, without referring to crystal influences, the term crystal field theory does not seem adequate. Some authors consider certain electronic interactions (like n bonds) as part of ligand field theory, although they originate from MO theory. 

Not even the slightest Jahn-Teller distortion and therefore no deviation from the ideal octahedral symmetry are to be expected when the t2g and eg orbitals are occupied evenly. This applies to the following electronic configurations  

Crystal field theory and molecular orbital theory were combined into ligand field theory by Griffith and Orgel. Many of the details presented here come from their work. 

Like atomic orbitals (AOs), molecular orbitals (MOs) are conveniently described by quantum mechanics theory. Nevertheless, the approach is more complex, because the interaction involves not simply one proton and one electron, as in the case of AOs, but several protons and electrons. For instance, in the simple case of two hydrogen atoms combined in a diatomic molecule, the bulk coulombic energy generated by the various interactions is given by four attractive effects (proton-electron) and two repulsive effects (proton-proton and electron-electron cf figure 1.20)  

To obtain the wave function appropriate to the case examined in figure 1.20, we must introduce in the general equation (eq. 1.10). However, the complexity of the problem does not allow an analytical solution, and the wave function is thus derived by application 

The term in parentheses in equation 1.130 is defined as the quantum-mechanic hamilto-nian (i cf appendix 2)  

Multiplying both terms in equation 1.131 by i//, extracting E, and integrating over the Cartesian coordinates, we obtain the energy of molecular orbitals (MOs)  

Equation 1.132 has the property of never giving an energy that is lower than the true energy resonance principle cf Pauling, 1960). This property allows us to assign to the MO wave functions that are obtained by linear combination of the AO functions of the separate atoms (Linear Combination of Atomic Orbitals, or LCAO, method), by progressive adjustment of the combinatory parameters, up to achievement of the lowest energy. 

One final point just as we found that the number of unpaired electrons in an octahedral complex can vary with the crystal field, so, too, in other geometries. However the effects tend to be more subtle and difficult to disentangle. Thus, for five-coordinate complexes they are interwoven with the trigonal bipyramidal and square pyramidal structural possibilities.  

We conclude by reconsidering what we must now call the ligand field splitting parameter of an octahedral transition metal complex. A, since the factors affecting its magnitude are evidently more complicated than we at first supposed. We have encountered three such factors  

This does not exhaust the list of factors influencing the magnitude of A, but there are believed to be no others of comparable importance. A recitation of most of the evidence that supports the ligand field model in preference to the crystal field model is deferred until Section 12.1. 

In practice it is not possible to separate the further reading relevant to this chapter from that appropriate to Chapter 6. The contents of the two chapters go together. In addition to the references given at the end of Chapter 6, two others which follow the pattern of the present chapter but with a more mathematical approach are Chapter 13 of Valence Theory by J. N. Murrell, S. F. A. Kettle and J. Tedder, Wiley, London, 

1970 and, more simply, in Chapter 12 of The Chemical Bond by the same authors, J. Wiley, Chichester, 1985. 

Although we shall not be concerned with the mathematics of ligand field theory, it is important to comment upon it briefly since we shall be using ligand field stabilization energies (LFSEs) later in this chapter. 

Ligand field theory is an extension of crystal field theory which is freely parameterized rather than taking a localized field arising from point charge ligands. 

In crystal field theory, we have considered repulsions between -electrons and ligand electrons, but have ignored interactions between fi -electrons on the metal centre. This is actually an aspect of a more general question about how we describe the interactions between electrons in multielectron systems. We will now show why simple electron configurations such as or do not uniquely 

In the answer to worked example 1.7, we ignored a complication. In assigning quantum numbers to the four 2p electrons, how do we indicate whether the last electron is in an orbital with w/ = -t 1, 0 or -1 This, and related questions, can be answered only by considering the interaction of electrons, primarily by means of the coupling of magnetic fields generated by their spin or orbital motion hence the importance of spin and orbital angular momentum (see Section 1.6). 

For any system containing more than one electron, the energy of an electron with principal quantiun number n depends on the value of /, and this also determines the orbital angular momentum which is given by equation 21.8 (see Box 1.5). 

Ligand field, like crystal field, theory is confined to the role of d orbitals, but unlike the crystal field model, the ligand field approach is not a purely electrostatic model. It is a freely parameterized model, and uses and Racah parameters (to which we return later) which are obtained from electronic spectroscopic (i.e. experimental) data. Most importantly, although (as we showed in the last section) it is possible to approach the bonding in rf-block metal complexes by using molecular orbital theory, it is incorrect to state that ligand field theory is simply the application of MO theory.  

We now begin to understand how the 7t-interaction can explain the observed spectro-chemical series. The anomalous strong field ligands, such as carbon monoxide, pyridine, 2,2 -bipyridine and CN, all possess vacant orbitals of 7t-symmetry of similar energy to the metal valence shell orbitals (Fig. 1-15). 

The orbitals of importance are the empty antibonding 7t -levels of the ligands. The magnitude of A increases as a consequence of the interaction of the t2g orbitals of the metal with the 7i -levels of the ligand and their resultant lowering in energy as shown in Fig. 1-16. 

The energy difference between the actual distribution of electrons and that for all electrons in the uniform field levels is called the crystal field stabilization energy (CFSE). It is equal in magnitude to the ligand field stabilization energy (LFSE) described later in this chapter. 

The chief drawbacks to the crystal field approach are in its concept of the repulsion of orbitals by the ligands and its lack of any explanation for bonding in coordination complexes. As we have seen in all our discussions of molecular orbitals, any interaction between orbitals leads to both higher and lower energy molecular orbitals. The purely electrostatic approach does not allow for the lower (bonding) molecular orbitals, and thus fails to provide a complete picture of the electronic structure. 

CF splitting diagram. With no unpaired electrons, [lrCIJ will be diamagnetic. 

There is currently a lot of evidence in the chemical literature for covalency in coordination compounds. Nuclear magnetic resonance (NMR) studies have shown that 

Basis set for the generation of the symmetries of the six SALCs in an octahedral ligand fieid where the iigands are acting soleiy as tj-donors. [Biatt Communications.] 

MO diagram for the formation of [MLg] , where the metal-ligand bonding involves only (T-interactions. 

FIGURE 16.22 Two canonical forms for metal-carbonyl bonding, showing the pi character in the resonance hybrid. 

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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. 

One way that molecular mechanics methods have been adapted to transition metal applications is by including one orbital-based term in the force field to describe the metal center. These terms are typically based on semiempirical methods or even some variation of ligand field theory. 

Fenske Hall is essentially a quantification of ligand field theory. The interactions are primarily electrostatic in nature. It does a reasonable job of re-... 

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. 

When the ligands interact more strongly the MOs of the ligands must be taken into account. This type of MO theory is referred to as ligand field 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. 

Color from Charge Transfer. This mechanism is best approached from MO theory, although ligand field theory can also be used. There are several types of color-producing charge-transfer (CT) processes. 

Color from Color Centers. This mechanism is best approached from band theory, although ligand field theory can also be used. Consider a vacancy, for example a missing CF ion in a KCl crystal produced by irradiation, designated an F-center. An electron can become trapped at the vacancy and this forms a trapped energy level system inside the band gap just as in Figure 18. The electron can produce color by being excited into an absorption band such as the E transition, which is 2.2 eV in KCl and leads to a violet color. In the alkaU haUdes E, = 0.257/where E is in and dis the... 

Frontier Molecular Orbital theory is closely related to various schemes of qualitative orbital theory where interactions between fragment MOs are considered. Ligand field theory, as commonly used in systems involving coordination to metal atoms, can be considered as a special case where only the d-orbitals on the metal and selected orbitals of the ligands are considered. 

Jorgensen, C. K. [1971] Modern Aspects of Ligand Field Theory, North-Holland, Amsterdam. 

Recent progress in ligand field theory. C. K. Jorgensen, Struct. Bonding (Berlin), 1966,1, 3-31 (49). 

Development of Coordination Chemistry Since 1930 Coordination Numbers and Geometries Nomenclature of Coordination Compounds Cages and Clusters Isomerism in Coordination Chemistry Ligand Field Theory Reaction Mechanisms... 

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 16.36 I1ie tear-shaped objects are representations of the six ligand atomic orbitals that are used to build the molecular orbitals of an octahedral complex in ligand field theory. They might represent s- or p-orbitals on the ligands or hybrids of the two. 

Using concepts of ligand field theory, explain why water is a weaker field ligand than ammonia. 

Is there a correlation between the ligand field strength of the halide ions F, Cl, Br, and 1 and the electronegativity of the halogen If so, can this correlation be explained by ligand field theory Justify your answer. 

Libby, W., 713 ligand, 671, 672 ligand field splitting, 682 ligand-field theory, 688 ligand-to-metal transition, 686 light, 4, 6... 

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. 

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