Parametrization of molecular orbital transformations

It is proved that any orthogonal matrix U can be represented in the form U=e^XŪ where X is real, antisymmetric, and block off-diagonal, and Ū is orthogonal and block diagonal with arbitrary block structure. The unique elements of X constitute the orbital rotation subset of a larger set (p, q, X) of independent perturbational and variational parameters. These provide a convenient separation of variables for orbital optimization and for analytic computation of derivative properties of variational wave functions.