Exchange interaction, model

AEI Atomic exchange interaction (model) LMTO Linear muffin-tin orbital (method)... 

Our treatment so far has dealt with non-interacting electrons, yet we know for sure that electrons do interact with each other. Dirac (1930b) studied the effects of exchange interactions on the Thomas-Fermi model, and he soon discovered that this effect could be modelled by adding an extra term... 

The Lines approximation is expected to be quite accurate for the description of the exchange interaction between a strongly axial doublet and an arbitrary isotropic spin. For all other cases, the Lines model [84] is a reasonable approximation. Efficient implementation of the Lines model was done in the program POLY ANISO. 

Anisotropic exchange interaction within the Lines model described above. Dipole-dipole magnetic interaction between centres is calculated fully ah initio and is added to the exchange matrix. 

Ferromagnetic ordering of two-dimensional systems with dipole-dipole and exchange interactions in the approximation of a spherical model was examined in Ref. 73. The main simplifying assumption of the spherical model is the replacement of the condition er = 1 on the orientation vectors with the weaker condition... 

Let us now consider interpretation ii). Its pertinence was essentially discussed on the basis of a relation between the value of the rate k j and that of an exchange parameter J. This parameter characterizes the exchange interactions that take place between the P and H radicals when electron transfer is blocked beyond H. J was estimated to be about 10 cm from different experiments performed in R. sphaeroides [177, 178]. In Sect. 2.2.1, we have described a simplified model leading to relation (16) between the exchange parameter J and the electronic factor Tab, but we shall see that this relation cannot be applied to the primary electron transfer, due to the existence of numerous low-energy charge-transfer states. 

The Xa multiple scattering method generates approximate singledeterminant wavefunctions, in which the non-local exchange interaction of the Hartree-Fock method has been replaced by a local term, as in the Thomas-Fermi-Dirac model. The orbitals are solutions of the one-electron differential equation (in atomic units)... 

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