Specification of an orbital hilbert space using a minimal number of parameters

The concept of the invariance of a subspace of a finite-dimensional orbital Hilbert space to a unitary transformation among the basis orbitals of the subspace leads to a specification of the subspace in terms of fewer parameters than would otherwise be possible. The general form of one such parameterization is presented, and its application to the optimization of the orbital space of a “full configuration interaction” wavefunction is discussed. Other variational forms for which this parameterization is of value are also enumerated and discussed, and mention is made of a possible application of the parameterization to analytical studies of subspaces of finite-dimensional Hilbert spaces.