Broken-symmetry states

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]. 

Here we have allowed the delocalization parameter in the broken symmetry state, B, to differ from that in the high spin state the Xa results reported below show that this indeed happens. Eigenvalues for the broken symmetry case are E 2 -(25/4)J 5B and E3 = -(15/4)J. 

Figure 2. As in Figure 1, but for the broken symmetry state. Iron "a" is the unique iron, and "b" labels the equivalent pair. The three orbitals marked with an asterisk show the g and u spindown orbitals on the "b" irons (whose energy difference determines B), and the spin-up orbital mostly localized on iron "a". The plot corresponds to the state with the final electron in the lower a orbital marked with an asterisk. 

Figure 3. As in Figure 1, for the lowest energy broken symmetry state of the doubly-reduced ZnFeg cluster. Valence orbitals are numbered within each symmetry and have been placed in three columns depicting the location of their primary charge distribution. Vertical bars indicate occupied orbitals. 

Condensed matter phases and structures are commonly reached via symmetry breaking transitions. In such systems, when the continuous symmetry is broken, temporary domain-t5q)e patterns are formed. The domain structures eventually coarsen, and disappear in the long-time limit, leaving a uniform broken-symmetry state. This state possesses so-called long-range order (LRO), in which the spatially dependent order parameter correlation function does not decay to zero in the limit of large distances. 

An alternative mapping between the electronic and spin Hamiltonians can be carried out by employing broken-symmetry (BS) states [14-16]. The triplet states I ft) and I U ) of the dimer are referred to as the high spin states IHS), and the Neel states I fi ) and I if ) as the broken-symmetry states IBS)... 

Figure 6.13 Relevant broken-symmetry states of the FeMoco without central ligand (see text).

We shall not recount the rrrany attempts to explain the broken symmetry states of URu2Si2 but rather concerrtrate on two typical examples that seem to be compatible with the recent importarrt resrrlts of the pressttre investigations just described. 

The variational parameter is now the volume fraction of water The main difference of interpretation is that any broken-symmetry state (t/> 1/2) must be interpreted, not as a single phase, but a coexisting symmetric pair of states related by the interchange of oil and water. Thus the region of coexistence between the symmetric sponge phase and a dilute phase (small vesicles or micelles) becomes a... 

Mapping Analysis Based on Broken-Symmetry States... 

With DFT calculations, the energy-mapping between the energy spectra of Heiec and Hspin is carried out by using high-spin and broken-symmetry states ( HS) and BS), respectively) [1,34-37]. For example, let us reconsider the spin dimer shown in 24.10, for which the pure-spin HS) and 6S) states are given by... 

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