Slater determinants orbital rotations

So far we have based the formalism on an N-electron basis built from Slater determinants. However, as shown above, both the Hamiltonian and the orbital rotations can be described in terms of the orbital excitation operators Ey. All... 

The optimization method outlined in Sections II.C-E shows very fast and stable convergence behaviour when applied to CASSCF wavefunctions, in which all orbital rotations between occupied orbitals are redundant. However, experience has shown that convergence is often much slower when orbital rotations between strongly occupied valence orbitals have to be optimized. It has been shown that this is due to the fact that the energy approximation (T) is not invariant with respect to a unitary transformation between two doubly occupied orbitals . If the 2 x 2 transformation in Eq. (34) is applied to a single Slater determinant with just two doubly occupied orbitals, the second-... 

The Hamiltonian (O Eq. 2.23) maintains full symmetry and is invariant under electronic permutations and under rotation-reflections of the electronic coordinates. Trial functions are usually constructed from atomic orbitals and from their spin-orbitals. Permutational antisymmetry is achieved by forming Slater determinants from the spin-orbitals. Rotational symmetry is usually realized by vector coupling of orbitals that form bases for representations of the rotation group SO(3). Spin-eigenfunctions too are achieved by vector coupling. ... 

These so-called interaction perturbations Hint are what induces transitions among the various electronic/vibrational/rotational states of a molecule. The one-electron additive nature of Hint plays an important role in determining the kind of transitions that Hint can induce. For example, it causes the most intense electronic transitions to involve excitation of a single electron from one orbital to another (recall the Slater-Condon rules). 

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