Representation fully reducible

Fig. 7. Schematic representation of the redox and spin states attained by center 1 and center 2 of D. desulfuricans Fuscoredoxin as indicated by EPR and Mossbauer spectroscopies. The fully reduced state indicated in the figure remains to be completely understood. In particular, the numbers of electrons accepted are still under debate. Filled circles represent Fe(II).

When such a complete reduction has been achieved, the component representations rF),r(2 are called the irreducible representations of the group G and the representation T is said to be fully reduced. An irreducible representation may occur more than once in the reduction of a reducible representation T. Symbolically... 

Others (e.g., Fukashi Sasaki s upper bound on eigenvalues of 2-RDM [2]). Claude Garrod and Jerome Percus [3] formally wrote the necessary and sufficient A -representability conditions. Hans Kummer [4] provided a generalization to infinite spaces and a nice review. Independently, there were some clever practical attempts to reduce the three-body and four-body problems to a reduced two-body problem without realizing that they were actually touching the variational 2-RDM method Fritz Bopp [5] was very successful for three-electron atoms and Richard Hall and H. Post [6] for three-nucleon nuclei (if assuming a fully attractive nucleon-nucleon potential). 

The main conclusion of this section is that the matrix elements of all terms in the collision Hamiltonian in the fully uncoupled space-fixed representation can be reduced to simple products of integrals of the type (8.46). Such matrix elements are very easy to evaluate numerically. The fiilly uncoupled representation is therefore very convenient for the development of the coupled channel codes for collision problems involving open-shell molecules with many angular momenta that need to be accounted for. The price for simplicity is a very large number of basis states that need to be included in the expansion of the eigenstates of the full Hamiltonian to achieve full basis set convergence (see Section 8.3.4). 

The electronic matrix element Hfj can be analyzed in terms of the group theory it adopts a nonzero value only when the direct product of the corresponding IRs (which is a reducible representation) contains the fully symmet-... 

Fig. 18. Redox-coupled conformational change in a loop between helices I and II of subunit I. A stereoview (A, see color insert) and a schematic representation of the hydrogen bond network connecting Asp-51 with the matrix space (B). (A) The molecular surface on the intermembrane side is shown by small dots. Maroon and green sticks represent the structures in the fully oxidized and reduced states. (B) Dotted lines show hydrogen bonds. The rectangle represents a cavity near heme a. The two dotted lines connecting the matrix surface and the cavity represent the water path. The dark balls show the positions of the fixed water molecules.

If a representation (which in general is reducible), being the direct product of the irreducible representations. .., does not contain the fully symmetric representation... 

---