Spin frustration

Radicals have been known for many years to form organic paramagnetic materials with numerous magnetic properties (ferro- or ferri-magnetism, spin Peierls transition, spin frustration, spin ladder systems) (see [51-60] for verdazyl radicals, [61-68] for thiazyl radicals, [69] for nitronyl nitroxide and [70-78] for Tempo radicals) (Fig. 6). When they are in their cationic form, they are valuable candidates for an association with the M(dmit)2 systems they will then provide the magnetic properties thanks to their free electron(s), whereas the M(dmit)2 moieties will provide the electrical properties. 

New Spin State Originated from Strong Spin Frustrations Quantum Spin Liquid... 

Shimizu Y, Kurosaki Y, Miyagawa K, Kanoda K, Maesato M, Saito G (2005) NMR study of the spin-liquid state and Mott transition in the spin-frustrated organic system, k-(ET)2Cu2(CN)3. Synth Met 152 393-396... 

A different approach simulates the thermodynamic parameters of a finite spin system by using Monte Carlo statistics. Both classical spin and quantum spin systems of very large dimension can be simulated, and Monte Carlo many-body simulations are especially suited to fit a spin ensemble with defined interaction energies to match experimental data. In the case of classical spins, the simulations involve solving the equations of motion governing the orientations of the individual unit vectors, coupled to a heat reservoir, that take the form of coupled deterministic nonlinear differential equations.23 Quantum Monte Carlo involves the direct representation of many-body effects in a wavefunction. Note that quantum Monte Carlo simulations are inherently limited in that spin-frustrated systems can only be described at high temperatures.24... 

Geometric Spin Frustration and Spin-Phase Transitions... 

Express the VB wave functions for the ground state ( B,) and first covalent excited state (2A2) of the pentadienyl radical in terms of Kekule structures. Deduce the qualitative spin distribution change upon excitation. Hints For the excited-state case, you will need to express the Kekule structures in terms of determinants. For the ground state, you may express the wave function as the spin alternant determinant, plus some minor contributions of the two determinants that exhibit a single spin frustration (two identical neighboring spins). You may consult ChemPhysChem. 5, 515 (2004). 

The values of the coefficients A and jjl in Equation 7.26 depend on the geometry of the hexatriene (the length of the various C—C bonds in the molecule). Thus, since the coefficients A and p are not known precisely, the easiest way is to deduce the spin density pictorially from the spin alternant determinant, DqC in part (c) of the figure. It is seen that DQC predicts the mode of spin polarization in the ground state. Addition of the determinants with a single spin frustration, Dr and DL, which have smaller weights due to the Pauli repulsion in the spin frustrated sites, will increase the spin density in the middle carbon and will decrease it on all other carbons. 

Their energies are obtained by counting the number of spin frustrations, giving... 

---