Density function theory spin-dependent properties

The above experimental developments represent powerful tools for the exploration of molecular structure and dynamics complementary to other techniques. However, as is often the case for spectroscopic techniques, only interactions with effective and reliable computational models allow interpretation in structural and dynamical terms. The tools needed by EPR spectroscopists are from the world of quantum mechanics (QM), as far as the parameters of the spin Hamiltonian are concerned, and from the world of molecular dynamics (MD) and statistical thermodynamics for the simulation of spectral line shapes. The introduction of methods rooted into the Density Functional Theory (DFT) represents a turning point for the calculations of spin-dependent properties [7],... 

Another model that describes the electronic structure of a system is provided by density functional theory (DFT). In DFT the electron density p of the system in the ground state plays the role of the many-electron wavefunction T in the wavefunction model because it uniquely defines all ground state properties of a system.An advantage of DFT is that T, which is a function of both spatial and spin coordinates of all electrons in the system, is replaced by a function that depends only on a position in Cartesian space p = p(r). The electron density can be obtained by using the variational principle... 

Jonsson et al. review tlie Kohn-Sham density functional theory (DFT) for time-dependent (TD) response functions. They describe the derivation of the working expressions. They also review recent progress in the application of TD-DFT to open shell systems. They reported results on several properties (i) hyperpolarizabilities (e.g. para-nitroaniline, benzene, Cgg fullerene), (ii) excited state polarizabilities (e.g. pyrimidine), (iii) three-photon absorption and (iv) EPR spin Hamiltonian parameters. 

Finally, it is used in the analysis of contributions to a molecular property like a polarizability or NMR spin-spin coupling constant from excitations between individual, typically localized, molecular orbitals (see, e g. Hansen and Bouman (1985), Packer and Pickup (1995), Sauer and Provasi (2008) or Provasi and Sauer (2009)). This is normally done at the level of the random phase approximation or time-dependent density functional theory. 

In a more complex situation than that of two electrons occupying each its orbital one can expect much more sophisticated interconnections between the total spin and two-electron densities than those demonstrated above. The general statement follows from the theorem given in [72] which states that no one-electron density can depend on the permutation symmetry properties and thus on the total spin of the wave function. For that reason the difference between states of different total spin is concentrated in the cumulant. If there is no cumulant there is no chance to describe this difference. This explains to some extent the failure of almost 40 years of attempts to squeeze the TMCs into the semiempirical HFR theory by extending the variety of the two-electron integrals included in the parameterization. 

Many ferromagnets are metals or metallic alloys with delocalized bands and require specialized models that explain the spontaneous magnetization below Tc or the paramagnetic susceptibility for T > Tc. The Stoner-Wohlfarth model,6 for example, explains these observed magnetic parameters of d metals as by a formation of excess spin density as a function of energy reduction due to electron spin correlation and dependent on the density of states at the Fermi level. However, a unified model that combines explanations for both electron spin correlations and electron transport properties as predicted by band theory is still lacking today. 

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