ETD

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Tesi etd-11142018-232409


Tipo di tesi
Tesi di laurea magistrale
Autore
NAIM, CARMELO
Indirizzo email
carmelonaim94@gmail.com
URN
etd-11142018-232409
Titolo
Analysis of nondynamic electron correlation in DFT
Dipartimento
FISICA
Corso di studi
FISICA
Relatori
relatore Prof. Amovilli, Claudio
correlatore Dott. Matito, Eduard
Parole chiave
  • Quantum Monte Carlo
  • Quantum Chemistry
  • Konh Sham
  • GVB
  • Fermi distribution
  • Unrestricted DFT
Data inizio appello
10/12/2018
Consultabilità
Completa
Riassunto
A comprehensive description of nondynamic correlation is still an open controversy in the Kohn-Sham Density Functional Theory (KS-DFT). The separation of electron correlation effects is strictly related to the shape of the wavefunction, however, because the KS wavefunction does not describe the realistic system, is not possible to analyze the relevance of electron correlation and its predominant type. Nondynamic correlation is significant for systems with a multiconfigurational character. These systems are treated inadequately by the Density Functional Approximations(DFAs). An estimation of nondynamic effects in KS-DFT is therefore of paramount importance. In this work, an analysis of nondynamic correlation in the context of KS-DFT has been performed. Starting from a KS electronic density, we have extracted information to recover the correlated first order reduce density matrix (1-RDM). The 1-RDM has been obtained in a diagonal form by an expansion over a basis of natural orbitals. Appropriate fractional occupation numbers have been computed by two different approaches. All the calculations have been performed on three diradical molecules, namely para-benzyne, meta-benzyne and ortho-benzyne. These systems have been chosen because they show different percentages of nondynamic correlation. In the first implementation, we have fitted a correlated electronic density computed at Variational Monte Carlo (VMC) level by means of a scheme based on the use of a N-representable Generalized Valence Bond (GVB)form. The GVB wavefunction was expanded from KS-DFT localized bonding and antibonding orbitals. This wavefunction, due to its shape, is able to provide a correlated 1-RDM. The corresponding kinetic energy gives closer results to the VMC one than the starting Ts, namely the KS single particle kinetic energy. The second analysis was done through an unrestricted DFT method, which allows the extraction of fractional occupancies. Several DFAs have been considered in order to analyze how nondynamic correlation is treated in different rungs of the Jacob's ladder. The information on nondynamic correlation from these two sets of occupation numbers has been further tested by computing the correlation indicators developed by Ramos-Cordoba and Matito. The occupation numbers calculated with both approaches are then connected to KS restricted single particle orbital energies through the Fermi distribution. For each fit we obtain a fictitious temperature Tf and a chemical potential μ. The results obtained for the global nondynamic indicators appear to be in some cases contradictory, whereas for the local ones there is an interesting agreement among the data. The fitted occupation numbers that best reproduced the reference ones were the GGA. Therefore, by computing the local indicators for this type of functionals is possible to extract information about nondynamic correlation even in restricted DFT calculations. The results of this thesis could be useful for a development of new kind of functionals that use multiconfigurational densities constructed from KS occupied and virtual orbitals.
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