D orbital populations

TABLE 10.14 Iron d-Orbital Populations (Electrons) and Percentages of the Total Population of bis(Pyridine)(meso-tetra-phenylporphinato)iron(II) Without and With Anharmonic Treatment of the Fe Atom. Axes as Defined in Table 10.7... 

In the planar-octahedral equilibria of nickel(II) the d orbital population changes by transfer of one electron from the d2 orbital to the dx2-y2 a antibonding orbital. This results in a substantial increase in the nickel-nitrogen distances in the plane. Accompanying this is the formation of new metal-ligand bonds in the axial positions. 

Once the multipole analysis of the X-ray data is done, it provides an analytical description of the electron density that can be used to calculate electrostatic properties (static model density, topology of the density, dipole moments, electrostatic potential, net charges, d orbital populations, etc.). It also allows the calculation of accurate structure factors phases which enables the calculation of experimental dynamic deformation density maps [16] ... 

Table 4. Experimental Iron Atom d-Orbital Populations of TPPFe(THF)2 Compared to the Iron II High-Spin State [34]...

The X-ray method is able to provide information on the detailed electronic ground state of transition metal complexes. As the agreement with EH results for the d-orbital populations of the bipyridyl complex indicates, a quick calculation may often provide answers which can only be obtained with much effort from the experiment. However, as illustrated for the four-coordinated Fe porphyrins and phthalocyanins, situations occur in which the independent X-ray evidence is invaluable. The combination with polarized neutron data is powerful, but requires the availability of large, good quality crystals. With further improvements in neutron source intensities this limitation should become less important. 

Table 1 shows the relativistic effects in the orbital populations of Mg clusters. As mentioned above, the charge reconstruction due to the relativistic effects can be seen. When we compare them in the same group, it is found that the decrease of the d orbital population and the increases of the s and p orbital populations become remarkable for the elements with large atomic number. Then the relativistic effects bring about very large changes in the orbital populations for the 5d elements. For the elements where the d band is almost filled, namely Cu, Ag and Au, the relativistic effects appear in a little different manner. For Au, the d band is rather clearly split into two bands by the spin-orbit... 

The photoelectron spectrum and ab initio SCF calculations of sulphur dichloride have been presented, and an assignment of observed states of the SCF radical cation was attempted.71 For the SC12 ground state the calculated dissociation energy, dipole moment, total atomic population, and total d -orbital population were given. The photolysis of sulphur monochloride with a series of saturated aliphatic hydrocarbons has been shown to yield alkyl chlorides, di- and poly-sulphides, hydrogen chloride, and elemental sulphur.72... 

Charge density analyses can provide experimental information on the concentration of electron density around atoms and in intra- and intermolecular bonds, including the location of lone pairs. Transition metal d-orbital populations can be estimated from the asphericity of the charge distribution around such metal centers. A number of physical properties that depend upon the electron density distribution can also be calculated. These include atomic charges, dipole and higher moments, electric field gradients, electrostatic potentials and interaction... 

For example, the d-orbital populations on sulphur in F2S02, SF4 and S02 (in the 6-31G basis) are 0.751,0.416 and 0.444 electrons, respectively. This indicates that the S=0 bond contributes significantly to the central sulphur d-orbital occupancy. Since the sulphur d-orbital populations in F2SH2 and (HO)2SH2 (same basis set) are 0.266 and 0.273 electrons, respectively, a good part of the d-orbital occupancy on the sulphur atom in the S02 fragment must come from the S—O n bond. 

Table X. Experimental d-orbital populations from accurate x-ray diffraction experiments...

The r-3 dependence should produce a significant reduction in QS if d orbitals expand significantly with increase of covalency, but a reduction in QS from one compound to another may equally well be caused by the effect of covalency on the d orbital populations. No general correlation between IS and QS need be expected as was pointed out by Sawatzky and van der Woude... 

D-Orbital Population in Cobalt Complexes, Qystal Field Theory Chromium Complexes... 

Table 9.6. Local properties of chemical bonding in titanium oxide crystals in the restricted and unrestricted HF methods titanium d-orbital populations Pd, atomic charges Qa, covalencies Ca, atomic valences Va, and bond-orders Wab for nearesteneighbor atoms ...

Am. Chem. Soc., 110, 7024 (1988). Cobalt-59 NMR of Cobalt(III) Porphyrin Complexes. 2. Electric Field Gradients, d-Orbital Populations, and Hydrogen Bonding. 

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