Conical spin structure

In the conical ferromagnetic structure (fig. 3.64d) the average values of the spin components are... 

For antiferromagnetic materials there exists some other spin arrangement (q 0). Here q is the wave vector of some spin spiral structure (see fig. 14.2) whose wavelength A is equal to 2ir/q. Conical spin arrangements need not be considered here since they are only stabilized by the presence of anisotropy. 

The system provides an opportunity to test our method for finding the conical intersection and the stabilized ground-state structures that are formed by the distortion. Recall that we focus on the distinction between spin-paired structures, rather than true minima. A natural choice for anchors are the two C2v stmctures having A2 and B, symmetry shown in Figures 21 and 22 In principle, each set can serve as the anchors. The reaction converting one type-I structirre to another is phase inverting, since it transforms one allyl structure to another (Fig. 12). 

Structures III and IV that have different spin-pairing schemes are expected to be higher in energy than type-I because of the strain introduced by the cyclopropyl rings. They may be anchors for secondary conical intersections around the most symmetric one. 

Conical intersections are important in molecular photochemistry, according to the current consensus, which is based on the combination of experimental and theoretical data. In this chapter, we tried to show that the location and approximate structure of conical intersections may be deduced by simple considerations of the changes in spin-pairing accompanying a reaction. We have also shown how these ideas may be put to practical computational application. 

Fig. 4 Schematic representation of the benzene radical cation Di/Do crossing. This is a cross-section through the conical intersection along Xi shown in Fig. 1. The quinoid structure (on the right) is a minimum whereas the antiquinoid structure (on the 1 ) is a transition structure in the moat of the conical intersection. Mulliken atomic spin densities are indicated in pink next to each carbon atom. Characteristic bond lengths are indicated in blue. Note that feu the quinoid (u antiquinoid structure, there are actually two resonance structures with the unpaired electron and the positive charge exchanged (this is indicated by +/ )...

The rare earth metals exhibit a variety of ordered states from ferromagnetic to complicated antiferromagnetic structures collinear, spiral, helical, conical and fan structures, which can be altered by temperature, magnetic fields or by the application of pressure (Nikitin et al., 1972). These complicated arrangements of spins result from the balance in energy between magnetocrystalline anisotropy and exchange forces (Elliott, 1965). Much pressure work has been done on pure rare earth metals and alloys in the last decade especially, and measurements... 

Benzene displays a symmetric Cs symmetry) S /So conical intersection between states that correlate with the E2g state 2 in the FC region) and the ground state of the planar equilibrium structure. hS9-92 Scheme 12, we show that the electronic character of the anti-aromatic (i.e. difference of the two Kekule structures indicated with a dashed circle) Si surface B2u) changes along the reaction path due to an avoided crossing between the S2 and Si states. The S2 CE2g) state can be described by a combination of quinoid (Dewar type) and antiquinoid spin couplings. As seen in Fig. 8(a)... 

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