Avoiding symmetry breaking problem

Another category of approaches that avoids the symmetry breaking problem of the orbitals for the target state is based on using a related, well-behaved HF reference instead. Examples of such techniques include quasi-restricted Hartree-Fock coupled-cluster (QRHF CC) (11,19), symmetry adapted cluster configuration interaction (SAC-CI) (22,23), coupled-cluster linear response theory (CCLRT) (24-26) or equivalently equation-of-motion coupled-cluster (EOM-CC) (27-32), Fock space multi-reference coupled-cluster (FSMRCC) (33-37), and similarity transformed equation-of-motion coupled-cluster (STEOM-CC) (38-40). In the case of NO3 and N03, the restricted Hartree-Fock (RHF) orbitals of the closed-shell N03 anion system can be used as the reference. The anion orbitals are stable with respect to symmetry perturbations, and the system does not suffer from the artifactual symmetry breaking of the neutral and cation. 

If one attempts to avoid the Scylla of spin contamination, which plagues calculations based on UHF wavefunctions, one encounters the Charybdis of symmetry breaking in ROHF wavefunctions. Symmetry breaking often makes ROHF geometry optimizations and energies even less reliable than their UHF counterparts, and RMP2 calculations will not solve the problems caused by symmetry-broken ROHF wavefunctions. 

The fundamental difference between CN and Nj is simply that one molecule is centrosymmetric while the other is not. The lowest-energy UHF wave function in both cases suffers from unphysical spin localization, and it is illusory to believe that, 2 is the easier of the two molecules to calculate. The low spin-contamination solution to the UHF equations exists simply because of the molecular symmetry, while in CN the lower symmetry of the molecule allows the equations to converge to the lowest energy solution. This is a somewhat unappreciated difficulty in calculations on open-shell molecules. If one has appropriate elements of symmetry, then unphysical solutions can be avoided by enforcing the constraints on the wave function. Even if the constraints are not enforced, problems with the reference function are easily identifiable nonzero dipole moments along directions where the exact value must vanish by symmetry, unsymmetric spin densities, and so on. However, the issue is more diabolical in lower-symmetry species where localization does not break the framework molecular symmetry. In these cases, UHF and ROHF... 

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