Symmetry breaking open-shell molecules

Symmetry-breaking arising from the presence of nuclear spin interactions, even in closed shell molecules, was discussed by Herzberg [267] and observed for the I2 molecule by Pique, Hartmann, Churassy and Bacis [268], As Bunker and Moss [265] point out, it will be most important for homonuclear open shell molecules with large... 

E. R. Davidson and W. T. Borden, /. Phys. Chem., 87, 4783 (1983). Symmetry Breaking in Polyatomic Molecules Real and Artifactual. See also T. Bally and W. T. Borden, in Reviews in Computational Chemistry, K. B. Lipkowitz and D. B. Boyd, Eds., Wiley-VCH, New York, Vol. 13, pp. 1-97. Calculations on Open-Shell Molecules A Beginner s Guide. 

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... 

Finally, we should mention that the localization of spin (and charge in the case of radical ions), which occurs as a consequence of symmetry breaking, does not require the presence of molecular symmetry. The two valence structures that arise by localization of spin in different parts of a molecule need not necessarily be identical, as they are in allyl radical. Since ROHF has a general tendency to localize unpaired electrons in open-shell molecules, where higher level calculations show this localization to be artifactual, one should, in general, avoid using ROHF to optimize geometries. 

Another way to computationally treat unpaired electrons is to employ restricted open-shell HF (ROHF) theory. Here, we encounter another pit-fall. It is an artifact called symmetry breaking (97). Whereas ROHF wave functions are pure spin states, the ROHF wave function may not retain the symmetry of the molecule. Suppose a molecule has C2V symmetry. The wave function should have the same symmetry, e.g., the orbital lobes on either side of the symmetry plane should be identical. However, with symmetry breaking, the two sides are not equal. The unsymmetrical ROHF wave function may even give lower energy than a physically correct (symmetrical)... 

The allyl radical is of particular theoretical interest as a small molecule which exhibits the phenomenon of doublet instability, or symmetry breaking. As a consequence, the restricted open-shell HF (ROHF) method fails to reproduce the C2v equilibrium structure predicted by experimental smdies [74]. One must, therefore, resort to unrestricted (UHF or UKS) or multiconfigurational (MCSCF) methods. The results obtained using different functionals are reported in table 4. As for the methyl radical, a good agreement is found between the... 

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