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Approximating the electron correlation energy of quasi-one-dimensional systems using STLS theory

Authors: Pascal Sattler

Ref.: Bachelor thesis, Martin-Luther University of Halle-Wittenberg (2021)

Abstract: STLS theory has proven itself to be an accurate way of obtaining correlation energy values in numerous publications. The self-consistent calculation of the dielectric function and the structure factor is an elegant and high-quality approach to the study of electronic systems. By including a local field correction depending on this structure factor in the dielectric function it accounts for the short-range correlations between the electrons. In this way one can obtain smaller and more accurate values of the correlation energy over the whole range of metallic densities, improving on the RPA which only is applicable at high densities.

In this thesis we successfully replicated the original work of Singwi, Tosi, Lund and Sjölander and adapted this theoretical framework to quasi-one-dimensional systems governed by the soft- Coulomb potential. We have shown that major parts of the theory in three dimensions can be simply converted to a one-dimensional theory yielding equations that are almost identical in structure. The only substantial difference arises in the calculation of the local field correction and derivation of the correlation and Hartree-Fock energy, following from the use of the soft- Coulomb potential. Interestingly we discovered that the end result for the correlation energy is also proportional to 1/rs2 regardless of the used interaction potential. The same is true for the kinetic and exchange parts of the Hartree-Fock energy which coincides with the result of Schlesier, Benavides-Riveros and Marques where they showed that both parts have universal rs-dependence regardless of the dimension