Symmetry restrictions in the spin-orbital basis

Having seen the need for restricted spin-orbital rotations, let us first see how the antisymmetric k operator (3.2.6) 

Since k in (3.3.4) must be anti-Hermitian, the number of independent spin-orbital excitation parameters KpQ in a basis of M spin orbitals becomes 

For the optimization of M real spin orbitals, it is sufficient to consider the real part of k and ignore the phase factors. The resulting spin-orbital operator 

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