Spin-polarized DFT

Then, it is clear that the functional of the energy could be written in terms of any of the two sets of variables E[p, ps] or E p, p J. Consequently, the nonrelativistic spin-polarized DFT can be developed in both sets of variables p, ps or pT, pL [. In the next section, the set of variables p, ps will be used in the discussion of the reactivity parameters. 

The purpose of spin-polarized DFT is again to describe the system (molecule, cluster,...) with an auxiliary noninteracting system of one-particle spinors xJ/j,. ..,v]/N. The ground state density matrix of this noninteracting system... 

Electronic structure and intramolecular exchange constants have been calculated (spin-polarized DFT calculations) for three cyanide-bridged molecular magnets, Fem(Tp )(CN)3Mn(DMF)412-(OTf)2-2DMF (Mn=Mn, Co, Ni).264... 

In any chemical reaction, the approaching molecular systems experiences both electron transfer (in some cases, spin polarization) and external potentials changes while the interacting system evolves towards the final state. Behind the perturbative approximation we are here concerned, and within the context of the [A( , Np, v (r), v (r)] representation of spin polarized DFT, the nonlocal descriptors are defined as first (and higher) order derivatives of the electron density of a given spin p (r) with respect to the spin external potentials Vo-(r). In particular, the symmetric linear response (or polarizability) kernels, defining the spin density... 

This appealing model implies however the search of different interpolation schemes at each side of the E vi. N curve. An exploration of some approximate models to both electrophilic and nucleophilic reactivities has been explored in the context of a comparison with experimental scales. Within the spin polarized version of DFT the minimization procedure searching for the analog of electrophilicity can be performed both for charge transfer as well as for spin polarization. " As it has been emphasized, the mathematical expressions in any of the representations of spin-polarized DFT have exactly the same form as the spin-free definition of electrophilicity. We therefore obtain, ... 

As noted above, Cohen s NFF descriptor was introduced in the spin free or conventional conceptual DFT formalism in order to measure (indirectly) the effect of changes in the external potential. The NFF becomes then defined in terms of the derivative of the force on the nucleus k, F, with respect to the number of electrons N, or equivalently, as the change of chemical potential upon variations in the spatial coordinates of nucleus k. Within the representation of spin polarized DFT, two nuclear... 

It is clear that two NFFs can be also defined within the linearly related [7V ,A ] representation of the spin polarized DFT. In this case the set of nuclear descriptors are explicitly expressed in terms of the spin components of the density,... 

In work of Nava and coworkers (2003), Pd clusters were studied using the spin-polarized DFT method in the range N = 2-309. The N = 13 cluster was foimd to have an icosahedral structure with a high spin state. It is seen to undergo a very slight Jahn-Teller distortion, which increases the cohesive energy only by 0.01 eV. The truncated decahedron and the cuboctahedron are found to be less stable. 

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