Symmetry-breaking orbital instabilities

Perhaps the greatest need for Brueckner-orbital-based methods arises in systems suffering from artifactual symmetry-breaking orbital instabili-ties, " ° where the approximate wavefunction fails to maintain the selected spin and/or spatial symmetry characteristics of the exact wavefunction. Such instabilities arise in SCF-like wavefunctions as a result of a competition between valence-bond-like solutions to the Hartree-Fock equations these solutions typically allow for localization of an unpaired electron onto one of two or more symmetry-equivalent atoms in the molecule. In the ground Ilg state of O2, for example, a pair of symmetry-broken Hartree-Fock wavefunctions may be constructed with the unpaired electron localized onto one oxygen atom or the other. Though symmetry-broken wavefunctions have sometimes been exploited to produce providentially correct results in a few systems, they are often not beneficial or even acceptable, and the question of whether to relax constraints in the presence of an instability was originally described by Lowdin as the symmetry dilemma. ... 

It is known that coupled-cluster (CQ calculations of the FC and SD contributions to the SSCCs for molecules with multiple bonds can exhibit surprisingly large errors. Auer and Gauss calculated the FC and SD contributions to the SSCCs for the CO and N2 molecules at various interatomic distances, and investigated the problem of orbital instabilities and spin-symmetry breaking in CC calculations of SSCCs. That includes calculations at the HF-SCF, CC singles and doubles (CCSD), CC3, CCSD... 

Theoretical study on cation dinitrogen complexes [N2---X---N2] X + = H +, Li +, Na+, Be +, Mg + performed at the MP2/6-311 + + G(d,p) level by Alkorta and Elguero included calculations of Vnn, and Vnn spin-spin couplings. The effect of orbital instabilities for spin-symmetry breaking perturbations, namely the Fermi-contact and spin-dipole contributions to the indirect nuclear spin-spin couplings has been investigated by Auer and Grass. The calculations have been performed for the CO and N2 molecules. 

Cramer considers the appreciation of how DFT performs with diradicals as the major theoretical contribution of the work on benzynes. DFT accommodated much more multireference character in singlet wavefunctions of diradicals than did HF. But restricted DFT breaks down with p-benzyne. People were just beginning to play with UDFT and recognize the interpretation of Professor Dieter Cremer deserves more credit for this than anyone else. My contribution was recognizing that the high symmetry of p-benzyne allows for CC to work properly. But with lower symmetry systems, like pyridynium, CCSD gives wacky results but Bruckner orbitals remove some instabilities and so it works well. ... 

---