An Alternative Formulation of the Variational Problem

The orbital rotation is given by a unitary matrix U, which can be written as an exponential transformation. 

The X matrix contains the parameters describing the unitary transformation of the Mbasis orbitals, being of the size of Mbasis x Mbaas. The orthogonality is incorporated by requiring that the X matrix is antisymmetric, Xy = -Xp. 

In the general case, the X matrix contains rotational angles for rotating all pairs of orbitals. 

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