Split occupation

Displacement disorder and fractional site occupation arise from steric constraints. High amounts of these types of disorder occur for example in ff-Al Mgz from incompatibilities in the packing of Friauf polyhedra. Split occupation is also caused by geometrical hindrances. In this case, two lattice sites are too close to be occupied simultaneously. Locally, only one site can be occupied, while the other remains empty, which in the average structure corresponds to an occupation factor of 0.5 for both sites. 

Eor transition metals the splitting of the d orbitals in a ligand field is most readily done using EHT. In all other semi-empirical methods, the orbital energies depend on the electron occupation. HyperChem s molecular orbital calculations give orbital energy spacings that differ from simple crystal field theory predictions. The total molecular wavefunction is an antisymmetrized product of the occupied molecular orbitals. The virtual set of orbitals are the residue of SCE calculations, in that they are deemed least suitable to describe the molecular wavefunction. 

Normally, you would expects all 2p orbitals in a given first row atom to be identical, regardless of their occupancy. This is only true when you perform calculations using Extended Hiickel. The orbitals derived from SCE calculations depend sensitively on their occupation. Eor example, the 2px, 2py, and 2pz orbitals are not degenerate for a CNDO calculation of atomic oxygen. This is especially important when you look at d orbital splittings in transition metals. To see a clear delineation between t2u and eg levels you must use EHT, rather than other semiempirical methods. 

The heat input from human occupants depends on their number (or an estimate of the probable number) and intensity of activity. This must be split into sensible and latent loads. The standard work of reference is CIBSE Table A7.1, an excerpt from which is shown in Table 23.2. 

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 ). 

That corresponds to the structure of chalcopyrite, CuFeS2. Another tetragonal subgroup of F43m with doubled c axis is /42m. It has the position 4c of zinc blende split into three positions, 2a, 2b and 4d. Their occupation by atoms of three elements corresponds to the structure of stannite, FeSnCu2S4. 

We first examine the relationships between electron structure and the emission and absorption spectroscopy of metal complexes. Transition metal complexes are characterized by partially filled d orbitals. To a large measure the ordering and occupancy of these orbitals determines emissive properties. Figure 4.2 shows an orbital and state diagram for a representative octahedral MX6 d6 metal complex where M is the metal and X is a ligand that coordinates or binds at one site. The octahedral crystal field of the ligands splits the initially degenerate five atomic d-orbitals by an amount... 

Since the results of the previous sections indicate that the site preference and tendency toward migration of Mn or Co is strongly affected by the electron occupancy of the d levels split by ligand-field effects, it is possible that this may be the case for all of the 3d TM ions. 

In order to test the various approximations of the Coulomb matrix, all electron basis set and numerical scalar scaled ZORA calculations have been performed on the xenon and radon atom. The numerical results have been taken from a previous publication [7], where it should be noted that the scalar orbital energies presented here are calculated by averaging, over occupation numbers, of the two component (i.e. spin orbit split) results. Tables (1) and (2) give the orbital energies for the numerical (s.o. averaged) and basis set calculations for the various Coulomb matrix approximations. The results from table... 

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