Parameter double exchange

Figure 8. Energy level diagram for exchange coupled Fe2+(SA = 2)-Fe3+(Ss = 5/2) dimer plotted versus the delocalization (double exchange) parameter B. The diagram is symmetric around B = 0.

Scheme 7.1 Isodesmic equation for the conversion of methane and propane into ethane (the abbreviation for the theoretical method, B3LYP/6-31 G(d), indicates the use of Becke s three-parameter hybrid exchange functional with the Lee-Yang-Parr correlation functional and a double-f Pople-type split valence basis set with one set of d-type polarization functions).

Here, S is the total spin of the cluster, J is the parameter of the HDVV exchange interaction, t is the parameter of double exchange, Sa and 5 are the spins of the cluster ions, and is the minimal of these spins. For the sake of definiteness the orbitals are assumed to be spherical, and the symmetry labels of D4h point group are employed. The presence of these levels in the electronic spectrum of MV dimers and their mixing by the out-of-phase mode q (q = (Qa - Qb)lV2 Qa and Qb are the full symmetric vibrational modes of the cluster fragments (Fig. 29a))... 

Here, S is the total spin quantum number. The first term is the Heisenberg coupling energy, and the other two terms represent the resonant delocalization (double-exchange) energy of the Fe Fe pairs, with parameter B. 

In the spin Hamiltonian description, the presence of double exchange can be described by the introduction of a new parameter ... 

B3PW91 Becke s three-parameter hybrid exchange functional with Perdew and Wang s 1991 gradient corrected correlation functional BD Bruckner doubles coupled cluster expansion including single and... 

---