Crystal field theory calculations

In crystal field theory calculations the direction of the axial distortion is along the z-axis. Therefore, the dz2 orbitals in iron atoms in Fig. 15 are along the line adjoining the two iron atoms. Remembering that the dz2 orbital lies lowest in this symmetry, the effect of reducing the complex is to add electron density to the dz% orbitals of the iron atoms. Since the dz2 iron-orbitals in Fig. 15 overlap, this structure results in an electron repulsion term between the iron atoms which increases as the iron atoms in these proteins are reduced. Thus, the negative reduction potentials (Table 1) of the plant-type ferredoxins can be accounted for by this model. 

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, ... 

Crystal field splitting parameter, 2, 309 Crystal field theory, 1, 215-221 angular overlap model, 1, 228 calculations, 1, 220 generality, 1,219 low symmetry, 1,220 /-orbital, 1, 231 Crystal hydrates, 2, 305,306 bond distances, 2, 307 Crystals... 

So, 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),... 

In the case of covalent compounds, crystal-field theory is a poor model for estimating electric field gradients because of the extensive participation of ligand atomic orbitals in the chemical bonds. MO calculations are a much better choice, since the corresponding interactions are considered, and realistic (noninteger) population numbers are obtained for the central metal as well as the ligand atomic orbitals. 

In those calculations, the contributions from electronic orbital motion (induced by spin-orbit mixing) were estimated from crystal field theory (for the copper atom) or were neglected (for the nitrogen and hydrogen atoms). Here I discuss for the first time direct calculations of these contributions to the copper and nitrogen hyperfine tensors, as well as to the molecular -tensor. 

Crystal field theory enables us to define certain parameters in order to characterize and distinguish the different europium site configurations. Crystal field parameter calculation involves several steps ... 

Symmetry considerations derived from group theory predict three main absorption-bands for Cr + in an octahedral environment and a number of low-intensity quartet-doublet-transitions in addition. The energies of the corresponding levels are calculated by means of crystal-field theory to be those of table 2 for the special choices AjB = 20 and 30 respectively ). 

Historically, crystal field theory was the first theoretical model (11, 86, 101, 123) used to explain d-d transition energies in metal complexes. Its usefulness is restricted to those complexes whose bonding is largely ionic, and its mqjor deficiency arises from its inability to account for charge transfer transitions. The iterative extended Hiickel and the ab initio, limited basis set, Hartree-Fock calculations are capable of de-... 

Pd(I) ion has a 4d9 electronic configuration. Consequently, this ion behaves in a tetragonal field in the same manner as Cu(II) ion. The g values calculated from the crystal field theory (12) are ... 

For example, [MoC+,]3 has a total of thirty-nine valence electrons from the molybdenum 4d5 5s and six chlorine 3p5 configurations, and the —3 charge on the ion. Its electron configuration is therefore cr12 n24 (2/2 )3. Thus the MO theory of these ML6 complex ions confirms that the electrons of prime importance are those occupying the t2g and eg levels on the metal, as predicted by crystal-field theory. However, the MO theory points the way to the more accurate calculation of electronic structure and properties. 

All the off-diagonal matrix elements of the spin-orbit coupling in the >, Tl> [ basis are thus reduced by the factor y, and we use the experimentally observed quenching to calculate Ej j and the corresponding geometrical distortion (14). In the Cs2NaYClg host lattice the total spread of the four spin-orbit components of T2 is 32 cm whereas crystal field theory without considering a Jahn-Teller effect predicts a total spread of approximately 107 cm-. ... 

The theoretical energy values for 3H4, JG4, JD2 are shown in tables 10-12 together with the observed values and the values obtained by semiempirical calculations based on crystal field theory (Faucher and Moune, 1997). T s are the irreducible representations in S4 symmetry. The possible irreducible representations are l i. r2, r3, r4 for a two-electron system where r3 and F4 are degenerate. The theory overestimates Stark splittings of the 3H4 level, compared to the experimental values. One reason for this is the neglect of lattice relaxation... 

Xu Zitu, Zheng Chusheng Peng Mingsheng (1982) Calculation of crystal field theory of Mn3+ in piemontite. Kexue Tongbao, 27,1199-203. 

Co(ni) acetylacetonates show frequencies closer to the low spin high spin. Co(tfac)3 has an even lower v(Co—O) band than calculated for low spin, i.e. 445 vi. 451 cm , respectively . Therefore, metal-ligand vibrations for a series of octahedral metal complexes are in order Co(II) < Ni(II) and Zn(II) < Ni(II) within the same ligand system. Fe(III) < Mn(III) < Cr(III) is observed, as expected from crystal field theory . 

---