Broken symmetry generator

The question in the title can be reformulated by asking how much can be dug out of an analogy between broken symmetry in dissipative structures (such as the ripple marks generated by wind, i.e., an external perturbation, in an otherwise flat surface of sand) and broken symmetry defined as phenomena of condensed matter systems of the kind observed near the critical points. The value of Anderson s discussion is to be seen more in the deepening of the question itself than in the answer that cannot yet be final, and for the moment, according to the author, appears to be more on the negative side. 

As we noted above, in fact calculations on stable molecules usually do generate canonical Hartree-Fock orbitals which have the symmetry of the molecular framework. It seems likely that this is a contingent, numerical fact rather than one of principle. If the one-electron terms in the Hartree-Fock Hamiltonian are so large as to dominate the form of the molecular orbitals, these MOs will, presumably, take up a distribution which optimises the energy due to the dominant terms in the Hamiltonian, and the electron-repulsion terms involving the potentially symmetry-breaking effects are too weak to chauige this situation. In molecules, radicals or (particularly) anions which have very weakly bound electrons, one would expect to see the effect of broken symmetry. 

Symmetry breaking is a universal phenomenon, from eosmology to the microscopic world, a perfectly familiar and daily experience whien should not generate the reluctance that it induces in some domains of Physics, and especially in Quantum Chemistry. In elassieal physics, the symmetry breaking of an a-priori symmetrical problem is sometimes refered to as the lack of symmetry of the initial conditions. But it may be a deeper phenomenon, the symmetry-broken solutions being more stable than the symmetrical one. 

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