Computational cost of integral generation

It is clear that relativistic molecular structure calculations have the potential to generate a large amount of data. One inherits all of the problems of non-relativistic quantum chemistry amplified by the need to accommodate the spinor structure and the inevitable involvement of components beyond the 

Symmetry relations, derived from the spinor structure of (210) are extremely useful. To describe this, we need to make the dependence on the magnetic quantum numbers explicit, and we shall therefore replace the indices /i by the corresponding m, suppressing the other components of the multi-index. Elementary algebra shows that 

The middle equation is often identified with time reversal symmetry and the last equation expresses the hermitian property of Pauli matrices. These lead to the following integral relations (again suppressing all quantum numbers except the associated ntp)  

It is only necessary to construct half of the Fock matrix explicitly because of its hermiticity. 

---