Mixed-symmetry states

In the last two decades, important discoveries in the field of superconductivity [1] have reopened the question of what is the symmetry of the superconducting state. In this contribution, after a brief historical introduction, the classification of superconducting states will be reviewed. Some consequences of the symmetry of the state will be then discussed, especially in view of the recent interest in the symmetry of high-7) superconductors. Finally, a novel approach particularly useful for mixed symmetry states will be introduced. 

The effect of neutron-proton symmetry breaking on the distribution of M1 strength in the SU(3) limit of the Interacting Boson Model (IBA-2) is studied. A possible alternative choice for the Majorana force is investigated, with a structure that resembles more closely that which is calculated in microscopic theories. It is found that the specific choice for the Majorana interaction has important consequences for the magnetic strength distribution function. In addition it allows for an alternative interpretation of the second excited K7T=0+ band in rare earth nuclei, as a mixed-symmetry state. 

If the rare-earth ion is immersed in a crystal field, the perfect symmetry of the free ion is destroyed, leaving parity in some cases not quite a good quantum number. Under this circumstance, electric-dipole transitions become quite possible. It was Van Vleck (25), in his classic 1937 paper The Puzzle of Rare Earth Spectra, who first pointed out that the weak electric dipole emission was due to this mixing of states of opposite parity by the crystal field. 

Even though the system is stable in symmetric form, a vibronic part acts in the inner resorts of the electronic structure. Anticipating, the aromaticity can be presented as the situation when the distortion tendency does not overcome the non-vibronic positive harmonic constant maintaining the high symmetry. The lAg ground state have the aspect of in-phase combination of the Kekule resonance structures, whereas the first excited lB2u state results from their out-of-phase mixing. These states are mixed via the b2u distortion coordinate of bond alternation. Additionally... 

It is obvious that the superoperator II acts as a projection operator in the Liouville space, cutting out those components of the 10 x 10 transition density matrices which mix 7h state with the 7l state, which is only possible if the symmetries of the perturbations of both the symmetry of deformation rdef and the symmetry of substitution Ts satisfy the selection rule ... 

The fact that states with definite parities are almost never observed experimentally cannot be explained alone by the persistence of mixed-parity states. Obviously, symmetry-breaking phenomena are in operation whether or not external perturbations are present. For species in condensed media, symmetry breaking is brought about by intermolecular interactions. In the extreme case of solids, these interactions are so strong that it is proper... 

Intermolecular interactions are capable of stabilizing broken-symmetry states in other ways. For example, contrary to intuitive expectations, random molecular collisions tend to preserve mixed-parity states [23]. 

The crystal structure has tetragonal symmetry with the space group /4i/a. The planar DMe-DCNQI anions are stacked in ID columns along the tetragonal c axis. The LUMO consists of orbitals and forms a wide ID conduction band which is partly filled with electrons donated by the cations. The Cu ions are in a mixed valence state, namely [Cu ] [Cu" "] = 1 2... 

A new compound of mixed oxidation state is the product from reduction of a mixture of BiCl3 and HfCl4 with metallic bismuth.783 Full identification was achieved only by an X-ray structure determination, which showed the composition to be Bi+Bi +(HfCI )3.140 The hafnium anions are distorted octahedral while the Big+ ion has C3h symmetry. Co-ordination of the Bi+ ion is unusual as it is co-ordinated to three chlorines from the anions. 

It is worth pointing out that the idea of searching directly for a state-specific solution for the wavefunctions of multiply excited states (MES) implies projections on distinct function spaces with separate optimization of some type, thereby avoiding serious problems having to do with the undue mixing of states and channels of the same symmetry. This idea has since been a central element of our analyses and state-specific computations. In fact, in recent years, such concerns have led to appropriate modifications of conventional methods of quantum chemistry, such as perturbation or coupled-cluster. 

---