Crystal field theory introduced

The foregoing discussion of valence is. of course, a simplified one. From ihe development of the quantum theory and its application to the structure of the atom, there has ensued a quantum theory of valence and of the structure of the molecule, discussed in this hook under Molecule. Topics thal are basically important to modem views of molecular structure include, in addition to those already indicated the Schroedinger wave equation the molecular orbital method (introduced in the article on Molecule) as well as directed valence bonds bond energies, hybrid orbitals, the effect of Van der Waals forces and electron-dcticiem molecules. Some of these subjects are clearly beyond the space available in this book and its scope of treatment. Even more so is their use in interpretation of molecular structure. [However, sec Crystal Field Theory and Ligand.)... 

Crystal field theory was introduced in the late 1920s by Bethe and Van Vleck and, although initially formulated and applied by physicists, incorporates the inorganic paradigm of primary concern with the consequences at the metal. The crystal field theory... 

The crystal field theory. The basics of the CFT were introduced in the classical work by Bethe [150] devoted to the description of splitting atomic terms in crystal environments of various symmetry. The splitting pattern itself is established by considering the reduction in the symmetry of atomic wave functions while the spatial symmetry of the system goes down from the spherical (in the case of a free atom) to that of a point group of the crystal environment. It is widely described in inorganic chemistry textbooks (seee.g. [152]). 

An Ionic Bonding Model - Introducing Crystal Field Theory... 

The organic chemists also considered quantum chemistry and from an early time we recall in this context the well-accepted and popular volume by Streitwieser [29]. In the inorganic chemistry area we cannot avoid recalling the crystal field theory advances, and refer for example to C. BalUiausen [30]. For additional references on this period we refer also to the volumes published in memory of Per-Olov Lowdin [31 ]. I take this occasion to stress the exceptional educational effort by Per-Olov in forming today s computational chemists his Florida meetings and his summer school in Sweden had a truly catalytic effect and introduced chemistry to the necessary level of mathematics rigor. As stressed above, there should be many and many more references, omitted only because I must cover the period 1960-2000, which all in all mainly harvested what was seeded from 1930 to 1960. 

The basic difficulty with the CFT treatment is that it takes no account of the partly covalent nature of the metal-ligand bonds, and therefore whatever effects and phenomena stem directly from covalence are entirely inexplicable in simple CFT. On the other hand, CFT provides a very simple and easy way of treating numerically many aspects of the electronic structures of complexes. MO theory, in contrast, does not provide numerical results in such an easy way. Therefore, a kind of modified CFT has been devised in which certain parameters are empirically adjusted to allow for the effects of covalence without explicitly introducing covalence into the CFT formalism. This modified CFT is often called ligand field theory, LFT. However, LFT is sometimes also used as a general name for the whole gradation of theories from the electrostatic CFT to the MO formulation. We shall use LFT in the latter sense in this Chapter, and we introduce the name adjusted crystal field theory, ACFT, to specify the form of CFT in which some parameters are empirically altered to allow for covalence without explicitly introducing it. 

In Figure 10.5 we again see Ag, a symbol introduced in crystal field theory Aq is also used in ligand field theory as a measure of the magnitude of metal-ligand interactions. 

CFT may be divided into weak field theory (WF-CFT) and strong field theory (SF-CFT). WF-CFT is a state interaction model of the type just mentioned. For example, the Ni " ion with eight 3d electrons has a F ground state, consistent with Hund s rule. The crystal field is introduced as a perturbation and the F is split into three states. 

I should also like very much to thank my good friend Carl J. Ballhausen for introducing me to crystal field theory (unpublished lectures, Department of Chemistry, Harvard University, Fall 1955), and for our years of happy collaborative effort together, which collaboration resulted in the rigorous ligand field solution of the inorganic intensity problem. 

Experimentally, this relationship has been found to hold remarkably well, a fact which is perhaps not too surprising in crystal field theory because the I factor arises from the geometric relationship of a tetrahedral complex to an octahedral—it is the squared ratio of the number of ligands (f). It becomes more surprising when, as in the previous chapter, the n bonding in octahedral and tetrahedral complexes is introduced and compared. 

In this paper a method [11], which allows for an a priori BSSE removal at the SCF level, is for the first time applied to interaction densities studies. This computational protocol which has been called SCF-MI (Self-Consistent Field for Molecular Interactions) to highlight its relationship to the standard Roothaan equations and its special usefulness in the evaluation of molecular interactions, has recently been successfully used [11-13] for evaluating Eint in a number of intermolecular complexes. Comparison of standard SCF interaction densities with those obtained from the SCF-MI approach should shed light on the effects of BSSE removal. Such effects may then be compared with those deriving from the introduction of Coulomb correlation corrections. To this aim, we adopt a variational perturbative valence bond (VB) approach that uses orbitals derived from the SCF-MI step and thus maintains a BSSE-free picture. Finally, no bias should be introduced in our study by the particular approach chosen to analyze the observed charge density rearrangements. Therefore, not a model but a theory which is firmly rooted in Quantum Mechanics, applied directly to the electron density p and giving quantitative answers, is to be adopted. Bader s Quantum Theory of Atoms in Molecules (QTAM) [14, 15] meets nicely all these requirements. Such a theory has also been recently applied to molecular crystals as a valid tool to rationalize and quantitatively detect crystal field effects on the molecular densities [16-18]. 

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,... 

Liquid crystalline polymers can be regarded as a long chain with rods connected in sequence, each rod being, in some sense, equivalent to a small molecular mass liquid crystal. This is the so-called freely-jointed-rod chain, the simplest model of polymers. It is understood that the constituent units — small molecular mass liquid crystals play an essential role in liquid crystalline polymers. Here, we introduce an important theory for small molecular mass liquid crystal — the Maier-Saupe mean field theory (Maier Saupe, 1959, 1960). 

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