Open-shell singlet

Since the singly excited determinants effectively relax the orbitals in a CCSD calculation, non-canonical HF orbitals can also be used in coupled cluster methods. This allows for example the use of open-shell singlet states (which require two Slater determinants) as reference for a coupled cluster calculation. 

Grafenstein, J., Kraka, E., Cremer, D., 1998, Density Functional Theory for Open-Shell Singlet Biradicals , Chem. Phys. Lett., 288, 593. 

Note 0 The CISD energies, which include Davidson correction for unlinked quadruple excitations, where obtained ot the MCSCF/6-31 G(d)optimized geometries and used a TC-SCF reference for closed-shell singlet states and a single configuration reference for triplet and open-shell singlet states. The SCF/6-31G(d) geometry was employed for the A state. See Ref. 55. 

Both l3A"-4b and 23A"-4b are predicted to be minima on the potential surface at the CASSCF level.61 This is in contrast with the situation for 4a, where one triplet state is calculated to be a transition state for pseudorotation of the other.55-57 A derivative of triplet 4b has been implicated in solution trapping experiments,49 but there have been no reports of the direct observation of 4b. Facile intersystem crossing from the triplet ground state (13A") to the open-shell singlet state ( A"), followed by vibrational relaxation to one of the enantiomers of 3b (Fig. 12), would be expected to rapidly depopulate the 13A" state of 4b. Thus, direct detection of triplet 4b may prove to be much more difficult than detection of 4a was.lla... 

The corresponding hyperconjugative interactions in an open-shell singlet description of radical dissociation would similarly promote homolytic bond cleavage. 

It is found that triplet (S = l) is the ground state for a linear Fe-O-O conformation, with the same electronic configuration as found for the open-shell singlet ... 

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 ... 

Number of a and -ir electrons contributed by each diradical center. For example, a /a-ir means that one center has a closed-shell singlet local configuration and the other has cttt occupancy. The latter may correspond to triplet or to open-shell singlet local configuration. 

The states can be approximated as the combination of a triplet carbene with a nitrene in which its ct- and -rr-electrons have opposite spins (Fig. 14). If the latter configuration is taken to correspond to an open-shell singlet nitrene (as... 

Like their para isomers, 43,47, and 53 have open-shell singlet (M ) ground states (Table 4). The triplet ( A ) and quintet ( A ) states are predicted to be about 2 and 20-25 kcal/mol higher in energy, respectively. Thus, the S-Q splittings are approximately 5 kcal/mol smaller than the corresponding ones of the para isomers (13, 16 and 8, respectively), but qualitatively very similar, as expected due to the similar electronic properties of the o- and p-phenylene linkers. 

Because of the high symmetry of the NH molecule, the singlet state of imidogen cannot be classihed as either open or closed shell. The closed-shell and open-shell singlets have exactly the same energy and form the two components of a doubly degenerate state. °... 

Here, we should mention that there exists an extensive discussion in the literature on the capabilities of spin-DFT regarding, for instance, the question whether the Kohn-Sham spin density has to be equal to the spin density of the fully interacting system of electrons (and in the case of open-shell singlet broken-symmetry (BS) determinants (see below) for binuclear transition-metal clusters this is certainly not the case see Ref. (33) for a more detailed discussion). But the situation is much more subtle and one may basically set up the variational procedure in a Kohn-Sham framework such that the spin density of the Kohn-Sham system of noninteracting fermions represents the true spin density. However, the frame of this review is not sufficient to present all details on this matter (34,35). 

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