Spin-flip excitations

Neese, F. 2006. Importance of direct spin-spin coupling and spin-flip excitations to the zero-field splittings of transition metal complexes a case study. Journal of the American Chemical Society 128 10213-10222. 

As explained in the Introduction, this scheme breaks down both for ground and excited states when orbitals from occupied and virtual subspaces become near-degenerate, e.g. at the dissociation limit or in diradicals (see Figure 2). To overcome this problem, the SF model employs a high-spin triplet reference state which is accurately described by a SR wavefunction. The target states, closed and open shell singlets and triplets, are described as spin-flipping excitations ... 

Figure 3. Two electrons in three orbitals system. Configuration (a) is the reference configuration. Single electron excitations with spin-flip produce configurations (bf(g). Two-electron excitations with a single spin-flip produce configurations (h)-(j). Note that non-spin-flipping excitations or excitations that flip the spin of two electrons produce M = l configurations, which do not interact through the Hamiltonian with the final M =0 states, and thus are not...

Electronic transitions in FeOf Tetrahedral Fe04 is characterized by a e ground-state configuration producing A2 (the ground state) and E and Aj(spin-flip) excited states. These states interact with states of the same symmetry stemming... 

Krylov AI (2006) Spin-flip equation-of-motion coupled-cluster electronic structure method for a description of excited states, bond breaking, diradicals, and triradicals. Acc Chem Res 39 83-91... 

Figure 4. Hierarchy of the SF models. Similar to the non-SF SR methods, the SF models converge to the exact n-electron wavefunction when the spin-flipping operator 0 includes up to n-tuple excitations. For example, the SF-CCSD model...

Note that the exchange integral vanishes in this case. The last two terms of Eq. (B2) show a spin flip of the electrons as they are excited from orbital i to orbital a and from orbital j to orbital b. This contribution vanishes, since the Coulomb interaction between the particles does not cause a spin flip. 

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