Symmetry preserving pair creation operators

In addition to the DFT chapters, there are two chapters by John and James Avery the first time a father and son team has published in Advances. In the first, a new and more general type of symmetry-preserving pair creation operator is proposed and extended to cases where orthonormality of orbitals of different configurations cannot be assumed. 

More general symmetry-preserving pair creation operators 197... 

Using Kramers concept of time-reversal, it is possible to construct symmetry preserving pair creation operators of the form [5,7,8]... 

Here, just as in equation (43) we have cut the number of terms in the sum in half, since each orbital appears twice in the sum shown in equation (36). In equation (44) we have included the shell index n explicitly in the label of the symmetry-preserving pair creation operator. In the individual one-electron creation operators of equation (44), this index is implied, as is the subshell index /. 

MORE GENERAL SYMMETRY-PRESERVING PAIR CREATION OPERATORS... 

Commutation relations analogous to (42) can also be derived for the more general symmetry-preserving pair creation operators ... 

The example discussed above was the case of spherical symmetry. We can ask whether general symmetry-preserving pair creation operators analogous to Ikj, can be constructed for other types of symmetry. For example, does the operator... 

In the present paper, we shall discuss a method for generating many-electron states of a given symmetry using Kramers pair creation operators and other symmetry-preserving pair creation and annihilation operators. We will first develop the formalism for the case where orthonormality between the orbitals of different configurations can be assumed. Afterwards we will extend the method to cases where this orthonormality is lost, so that the method also can be used in generalized Sturmian calculations [11-13] and in valence bond calculations. 

As an example of the symmetry-preserving Kramers pair creation operators, we can think of the case of D3 symmetry, where they have the form [8] ... 

Thus, the Kramers pair creation and annihilation operators defined by equations (36) and (37) preserve the symmetry of the states on which they act. 

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