A correction for the Hartree-Fock density of states for jellium without screening
Summary (1 min read)
INTRODUCTION
- The uniform electron gas, or jellium model, is an archetypal example in solid-state physics and many-body theory.
- The singleparticle energy ε(k) is the sum of the free-electron energy, k2/2, and the single-particle exchange energy.
- It is well known in the literature that the dispersion relation (1) has a logarithmically divergent derivative at the Fermi energy, shown in Fig.
- Finally, it is well known that in the HF approximation, the density of states (DOS) for jellium vanishes at the Fermi level (Fig. 1), since the DOS is inversely proportional to the derivative of the dispersion.
THE HYPER-HARTREE-FOCK EQUATIONS FOR JELLIUM
- These states are represented by Nelectron Slater determinants, constructed from a common set of spin-orbitals.
- Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions.
- The minimisation leads to the HHF single-particle equations for the three spin-orbitals.
- These variational principles can be derived as special cases from the Helmholtz variational principle in statistical mechanics.
DISCUSSION
- In metals, screening is an important effect that reduces the range of the effective repulsion between electrons, shielding any charge at distances greater than a characteristic screening length.
- This understanding of HF’s failure is further supported by the softening of the divergence in the slope of ε(k), after replacing the bare Coulomb potential in the HF nonlocal exchange term by a screened Coulomb potential.
- Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions.
- The authors find that the wellknown anomalies of the HF description of jellium are still present in the solution of the HHF equations.
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"A correction for the Hartree-Fock d..." refers background or methods in this paper
...01 47 9v 1 [ co nd -m at .s tr -e l] 5 F eb 2 01 5 A correction for the Hartree-Fock Density of States for Jellium without Screening Alexander I. Blair, Aristeidis Kroukis and Nikitas I. Gidopoulos Department of Physics, Durham University, South Road, Durham, DH1 3LE, United Kingdom We revisit the Hartree-Fock (HF) calculation for the uniform electron gas, or jellium model, whose predictions – divergent derivative of the energy dispersion relation and vanishing density of states (DOS) at the Fermi level – are in qualitative disagreement with experimental evidence for simple metals....
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...…for the Hartree-Fock Density of States for Jellium without Screening Alexander I. Blair, Aristeidis Kroukis and Nikitas I. Gidopoulos Department of Physics, Durham University, South Road, Durham, DH1 3LE, United Kingdom We revisit the Hartree-Fock (HF) calculation for the uniform electron…...
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...…HHF equations by Gidopoulos and Theophilou [9, 10], who considered an N -electron system described by a Hamiltonian H and then variationally optimised the average energy ∑ n〈Φn|H |Φn〉 of all configurations (N -electron Slater determinants Φn) constructed from a basis set of R spin-orbitals, R ≥ N ....
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...…(HF) approximation, can be found in classic textbooks [1–6], where, we learn that the HF equations applied to the ground state of the jellium, admit plane wave solutions with energywavevector dispersion relation given by, ε(k) = k2 2 − kF π ( 1 + k2F − k2 2kkF ln ∣ ∣ ∣ ∣ kF + k kF − k ∣ ∣ ∣ ∣ ) ....
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...Other similar artifacts of the HF nonlocal exchange operator, not associated with the lack of electronic correlation, are known in the literature....
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