Time-Reversal and Point-Group Symmetry

Matrix blocking will already be effected by the point-group symmetry of the molecule. We do not expect time reversal to reduce the symmetry because the time-reversal operator K commutes with all operations of the point group. If time reversal introduces new symmetries, we will gain further blocking. We must therefore establish the relation between time-reversal symmetry and point-group symmetry. 

One possibility would be to extend the point group G = gi i =, h) in the same manner as already done for the double groups in chapter 6. There we constructed a new 

We can illustrate this problem by considerin the associative conditions that the group has to fulfil (Tinkham 1964). The action of /C on a product of two group elements yields 

If the time-reversal operator is considered an element of the group, then the associative law must hold, such that 

We have made use of the fact that K commutes with all elements of the group. Thus, the representation matrices of the time-reversed spinor [r are the complex conjugates of those for 

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