New methods for the computation of the linear response within the density functional theory in spin polarized system (Metodi innovativi per il calcolo della risposta lineare in density functional theory per sistemi spin polarizzati)

Davide Sangalli

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arXiv · 1208.3152

New methods for the computation of the linear response within the density functional theory in spin polarized system (Metodi innovativi per il calcolo della risposta lineare in density functional theory per sistemi spin polarizzati)

Davide Sangalli

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Abstract

In the present thesis we study absorption spectra of spin polarized isolated systems. Thus we introduce the density functional theory (DFT) formalism and its time dependent extension (TDDFT) together with the approximation used. In particula the Casida formulation of TDDFT is described. The equations for the description of open shell systems have been implemented in the abinit code. Then we used the BeH molecule as a test case. Studying the results for this molecule we underline the limits of the commonly used approximations. In particular we discuss why the the spin symmetry of excited states is broken and we propose a rule to find which excitation energies are affected by this problem. Finally, in the last part, we discuss how a better approximation could be obtained starting from the many body perturbation theory. ----- Il lavoro della presente tesi \`e focalizzato sullo studio dello spettro di eccitazione di sistemi isolati spin polarizzati. Quindi vengono esposte la Density Functional Theory (DFT), la sua estensione al caso dipendente dal tempo (TDDFT) e le approssimazioni utilizzate. In particolare vien esposta la formulazione di Casida della TDDFT. Le equazioni per lo studio di sistemi spin-polarizzati sono state implementate all'interno del software ABINIT. \`E stata poi scelta la molecola di BeH per testare l'implementazione fatta. I calcoli eseguiti ci hanno permesso di mettere in luce i limiti delle approssimazioni comunemente utilizzate. In particolare abbiamo discusso l'impossibilit\`a di mantenere la corretta simmetria di spin in sistemi spin polarizzati. Viene quindi proposta una regola per individuare quali siano, negli spettri calcolati, le energie di eccitazione affette da questo problema. Nell'ultimo capitolo della tesi viene inoltre esposta una possibile soluzione per superare l'approssimazione adiabatica.

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Davide Sangalli. 2012-08-15. New methods for the computation of the linear response within the density functional theory in spin polarized system (Metodi innovativi per il calcolo della risposta lineare in density functional theory per sistemi spin polarizzati). https://arxiv.org/abs/1208.3152

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