Partial occupancy

Update of Fermi-energy and partial occupancies, charge density mixing. 

This involves partial occupation of the 7r -orbital and hence a lengthening of the C—C bond moreover, as the bonding at carbon changes, acquiring some sp3 character, so the bond angle at carbon will decrease below 120°. 

Fig. 8.4 Crystal structures of a-Ca3(BN2)2 (a) and a-Sr3(BN2)2 (b) high-temperature phases. Striped atoms indicate partial occupations on special positions 8f (occupied by 7/8) and 2a (occupied by 1 /2).

Cul) is not due to point defects but to partial occupation of crystallographic sites. The defective structure is sometimes called structural disorder to distinguish it from point defects. There are a large number of vacant sites for the cations to move into. Thus, ionic conductivity is enabled without use of aliovalent dopants. A common feature of both compounds is that they are composed of extremely polarizable ions. This means that the electron cloud surrounding the ions is easily distorted. This makes the passage of a cation past an anion easier. Due to their high ionic conductivity, silver and copper ion conductors can be used as solid electrolytes in solid-state batteries. 

On the other hand, this MO description matches a crystal field description of a Cu(II) ion insofar as the five highest occupied MO s are concerned four of these are doubly occupied and have a predominant copper 3 d character (65 % at least), whereas the fifth orbital contains the unpaired electron and still has 50% copper 3 d character. The very small MuUiken charge on the copper atom, which does not fit in the description of a Cu(II) ion, is caused by the partial occupation of the 4 p orbitals, which effect is neglected in the crystal field theory. 

Plastic crystals and crystals with orientational disorder still fulfill the three-dimensional translational symmetry, provided a mean partial occupation is assumed for the atomic positions of the molecules whose orientations differ from unit cell to unit cell ( split positions ). 

Quantitative analysis of ESP is important for several reasons. The precise knowledge of the ESP is necessary to allow comparison of atomic potentials in different structures, analysis of composition (partial occupancy) and chemical bonding (crystal formation, structure property relations). 

The generic chemical problem involving both dynamic and nondynamic correlation is illustrated in Fig. 1. The orbitals are divided into two sets the active orbitals, usually the valence orbitals, which display partial occupancies (assuming spin orbitals) very different from 0 or 1 for the state of interest, and the external orbitals, which are divided into the core (largely occupied in the target state) or virtual (largely unoccupied in the target state) orbitals. The asymmetry between... 

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