Wave functions ligand

When the combination of the two wave functions of the ligands and the pz orbital of the metal is made, the signs of the lobes on the pz orbitals require the negative lobes on the "bottom" ligand wave function be directed upward as shown in Figure 21.17. The combination of the dyz orbital can be... 

Fig. 11.17 Overlap of ligand orbitals in the rv plane with metal (a) and ilty (b) orbitals. Note that an appropriate choice of sign for the ligand orbitals provides positive overlap with the dxi.ys orbital, however, no single sign choice for the ligand wave function produces positive overlap with the d orbital...

The rather good agreement with experimental data for ECM was obtained by taking into account the effect of overlap of central ion and ligand wave function, whereas the results obtained in PCM reveal the well-known weakness of this model. 

The basic ideas of the exchange-charge model of the crystal field as outlined in Ref. [40] are as follows The CFPs of any impurity ion, i.e., q(nT), are represented as a sum of two different contributions that arise from the point charges of aU crystal lattice ions and introduced fictitious exchange charges (placed in the space between an impurity ion and ligands) due to the spatial overlap of the impurity-ion and ligand wave functions ... 

The HF wave funetion eontains equal amounts of ionie and eovalent eontributions (Section 4.3), For covalently bonded systems, like H2O, the HF wave funetion is too ionie, and the effect of electron correlation is to increase the covalent contribution. Since the ionic dissociation limit is higher in energy than the covalent, the effect is that the equiUbrium bond length increases when correlation methods are used. For dative bonds, such as metal-ligand compounds, the situation is reversed. In this case the HF wave function dissociates correctly, and bond lengths are normally too long. Inclusion of... 

The Wyboume crystal field parameters B (f, f), B (d, d), and Bjj(f, d), which describe the interaction due to the presence of the ligands onto the electrons of the lanthanide center. They are deduced from the ligand field energies and wave functions obtained from Kohn—Sham orbitals of restricted DFT calculations within the average of configuration (AOC) reference by placing evenly n — 1 electrons in the 4f orbitals and one electron in the 5d.33... 

In a similar way, we obtain the wave functions for combinations of ligand group orbitals with the py and pz orbitals from the metal ion. They can be written as... 

The interaction of the metal s and dzi orbitals with those of the cyclopentadienyl anion can be illustrated as follows. We begin by placing the metal orbital between the two ligands that have the orbitals oriented to match the sign of the wave function of the metal orbital. Therefore, for the s and dzi orbitals, the combinations are shown in Figure 21.16. 

The AOM has been used to parameterise the ligand field in detailed analyses of magnetic properties in non-cubic complexes. It may also be used to obtain the ground state wave function in systems of low symmetry where d-orbital mixing is important the mixing coefficients can be obtained from the off-diagonal elements of the AOM matrix in terms of parameters, whose magnitudes can be found from the d-d spectrum. 

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