First principles methods for electronic structure calculations of solids
(1997) Abstract
 A straightforward gradient expansion of the exchange energy of a perturbed electron gas is performed. Studied perturbations range from very weak to those that produce, e.g., a siliconlike band structure with a band gap. The expansions involve density gradients up to fourth degree and we include all terms originating in linear and secondorder response theory. The expansion reproduces exactly calculated exchange energies with an accuracy of the order of a few mRy per electron for metallic systems. For systems with a bandgap the accuracy is reduced by an order of magnitude.
We have developed a Tmatrix formalism for performing ab initio calculations on real systems with strong shortrange correlations. The method is... (More)  A straightforward gradient expansion of the exchange energy of a perturbed electron gas is performed. Studied perturbations range from very weak to those that produce, e.g., a siliconlike band structure with a band gap. The expansions involve density gradients up to fourth degree and we include all terms originating in linear and secondorder response theory. The expansion reproduces exactly calculated exchange energies with an accuracy of the order of a few mRy per electron for metallic systems. For systems with a bandgap the accuracy is reduced by an order of magnitude.
We have developed a Tmatrix formalism for performing ab initio calculations on real systems with strong shortrange correlations. The method is applied to Ni and we obtain a satellite structure below the Fermi level as well as a reduced exchange splitting. We also found a new satellite structure above the Fermi level, which can be ascribed to particleparticle scattering.
The onsite screened interaction within the random phase approximation is calculated for Ni. It is found that the value of the statically screened interaction in the 3d orbital is 2.2. eV which is significantly smaller than the values obtained from the constrained LDA method (3.75.4 eV). We analyze the possible origins of the difference and reconcile the discrepancy by taking into account the energy dependence of the screened interaction.
A basisfree method for calculating the bandstructures of periodic systems is developed. The manycenter problem is divided into onecenter problems by employing a projection function. The full solution is then obtained by summing over the onecenter solutions, ensuring the correct Bloch symmetry. Due to the division into onecenter problems, the method is expected to scale as ~N to N^2 where N is the number of atoms in the unit cell. The feasibility of the method is demonstrated by calculating the freeelectron and Cu bandstructures. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/29532
 author
 Springer, Martin ^{LU}
 supervisor
 opponent

 Prof Inglesfield, John
 organization
 publishing date
 1997
 type
 Thesis
 publication status
 published
 subject
 keywords
 screened interaction, Tmatrix, vertex function, GW approximation, Green function, density functional theory, gradient expansion, order N method, Physics, Fysik
 pages
 110 pages
 publisher
 Department of Theoretical Physics, Lund University
 defense location
 Sal F, Teoretisk Fysik
 defense date
 19971017 10:15:00
 external identifiers

 other:ISRN: LUNFD6/(NTFTF1035)/125/(1997)
 ISBN
 9162827065
 language
 English
 LU publication?
 yes
 id
 92ded898e458459593d728a01d39883b (old id 29532)
 date added to LUP
 20160404 12:06:50
 date last changed
 20181121 21:09:05
@phdthesis{92ded898e458459593d728a01d39883b, abstract = {A straightforward gradient expansion of the exchange energy of a perturbed electron gas is performed. Studied perturbations range from very weak to those that produce, e.g., a siliconlike band structure with a band gap. The expansions involve density gradients up to fourth degree and we include all terms originating in linear and secondorder response theory. The expansion reproduces exactly calculated exchange energies with an accuracy of the order of a few mRy per electron for metallic systems. For systems with a bandgap the accuracy is reduced by an order of magnitude.<br/><br> <br/><br> We have developed a Tmatrix formalism for performing ab initio calculations on real systems with strong shortrange correlations. The method is applied to Ni and we obtain a satellite structure below the Fermi level as well as a reduced exchange splitting. We also found a new satellite structure above the Fermi level, which can be ascribed to particleparticle scattering.<br/><br> <br/><br> The onsite screened interaction within the random phase approximation is calculated for Ni. It is found that the value of the statically screened interaction in the 3d orbital is 2.2. eV which is significantly smaller than the values obtained from the constrained LDA method (3.75.4 eV). We analyze the possible origins of the difference and reconcile the discrepancy by taking into account the energy dependence of the screened interaction.<br/><br> <br/><br> A basisfree method for calculating the bandstructures of periodic systems is developed. The manycenter problem is divided into onecenter problems by employing a projection function. The full solution is then obtained by summing over the onecenter solutions, ensuring the correct Bloch symmetry. Due to the division into onecenter problems, the method is expected to scale as ~N to N^2 where N is the number of atoms in the unit cell. The feasibility of the method is demonstrated by calculating the freeelectron and Cu bandstructures.}, author = {Springer, Martin}, isbn = {9162827065}, language = {eng}, publisher = {Department of Theoretical Physics, Lund University}, school = {Lund University}, title = {First principles methods for electronic structure calculations of solids}, year = {1997}, }