Compound orbital occupation

Hubbard (13) elucidated a mathematical description of the change from one situation to another for the simplest case of a half-filled s band of a solid. His result is shown in Figure 11. For ratios of W/U greater than the critical value of 2/ /3 then a Fermi surface should be found and the system can be a metal. This critical point is associated with the Mott transition from metal to insulator. At smaller values than this parameter, then, a correlation, or Hubbard, gap exists and the system is an antiferromagnetic insulator. Both the undoped 2-1 -4 compound and the nickel analog of the one dimensional platinum chain are systems of this type. At the far left-hand side of Figure 11 we show pictorially the orbital occupancy of the upper and lower Hubbard bands. 

Transition metal (TM) chemistry stands in contrast to this. Many compounds involve metal centres with partially filled d shells, and/or with one or several unpaired electrons. Therefore, it is not always straightforward to predict the orbital occupation pattern of a given stable compound. For intermediates on a reactive pathway, this is an even greater problem. This is also true for organometallic chemistry, despite the fact that many compounds obey the 18-electron rule and have closed-shell singlet ground states. Thus, there are many 16- or even 14-electron intermediates, odd-electron species [1], and polymetallic clusters and complexes for which the spin state is not readily predicted. 

We now use the relationship between d vacancies and L edge resonance area shown in Fig. 2 to obtain quantitative information on the d orbital occupancy in the Ir catalysts. We have found using SCF-)fci atomic wave functions that the oscillator strength for the 2p 5d transition in the Ir atom is very close to that of the corresponding transition in the Pt atom, so the relationship in Fig. 2 should be applicable to Ir compounds also. The resonance lines for the supported catalysts were... 

For the Cr and Co compounds, the natural orbital occupation numbers in Table XVI reveal some clear trends, which can be related to the nature of the metal-ligand interaction. First we notice that for the tt donors F , H2O, and NH3, correlation effects within the representa-... 

Alkene activation by Compound I of P450 takes place on close-lying doublet and quartet spin state surfaces with a rate-determining electrophilic addition of the oxo group to the terminal carbon atom of the double bond with transition state TSe- The intermediates are radicalar with orbital occupation... 

Kugel and Khomskii proposed a model in which there is a one-to-one correspondence between orbital occupancy and spin alignment (i.e., a particular pattern of magnetic configuration is most favored because of OO). For example, in the parent compound of manganites, LaMnOj, the occupancies of the Mn d state are t2gt... 

Table 4 Comparison of calculated bond orders for a series of dinuclear molybdenum compounds with those predicted by two alternative electron-counting methods. In each case, the bond order predicted by the [p.-LX] half-arrow method corresponds exactly to that derived by consideration of the orbital occupations, whereas the half-electron method fails for compounds with bridging hydride and methyl ligands. Data ttiken from reference 6...

I 7.4. Acetylene complexes are fairly common however, Nielson et al. [73] reported the structure of a tungsten complex, see below. Construct the important valence orbitals for this compound and indicate the orbital occupation. 

The standard basis set has to be modified for certain purposes, such as hydrogen bonding, hypervalent compounds, and the treatment of anions or ionic crystals. In the case of hydrogen bonding an additional set of diffuse 2p functions is added on hydrogen atoms. For hypervalent compounds with second-row elements there is an option to include 3d orbitals on these atoms. The orbital exponents of atoms in anions are modified depending on their actual orbital occupations. In this formalism we use a set of orbital exponents which are adjusted to reproduce experimental energies of atomic anions. 

The co-ordination number in ionic compounds is determined by the radius ratio - a measure of the necessity to minimize cationic contacts. More subtle effects are the Jahn-Teller effect (distortions due to incomplete occupancy of degenerate orbitals) and metal-metal bonding. 

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