Comparing theories

Williams, D.

doi:10.1088/0031-9112/32/7/001

Cited by 15 publications

(17 citation statements)

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“…To minimize E SIC by the steepest descent method [50], we imagine having in the mth iteration the set of orbitals ψ (m) α , which satisfy Eq. (9) but do not yet minimize E SIC , the orbitals of the (m + 1)th iteration are defined by stepping along the gradient of E SIC :…”

Section: Minimization Of Sic-lsd Energy Functionalmentioning

confidence: 99%

Self-interaction-corrected local-spin-density calculations for rare earth materials

Svane

Temmerman

Szotek

et al. 2000

Int. J. Quant. Chem.

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ABSTRACT:The ab initio self-interaction-corrected (SIC) local-spin-density (LSD) approximation is discussed with emphasis on the ability to describe localized f -electron states in rare earth solids. Two methods for minimizing the SIC-LSD total energy functional are discussed, one using a unified Hamiltonian for all electron states, thus having the advantages of Bloch's theorem, the other one employing an iterative scheme in real space. Results for cerium and cerium compounds as well as other rare earths are presented. For the cerium compounds the onset of f -electron delocalization can be accurately described, including the intricate isostructural phase transitions in elemental cerium and CeP. In Pr and Sm the equilibrium lattice constant and zero temperature equation of state is greatly improved in comparison with the LSD results.

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Section: Minimization Of Sic-lsd Energy Functionalmentioning

confidence: 99%

Self-interaction-corrected local-spin-density calculations for rare earth materials

Svane

Temmerman

Szotek

et al. 2000

Int. J. Quant. Chem.

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“…In the plane-wave basis set we use in the examples, this amounts to including the kinetic part of the Hamiltonian and the average value of the effective potential. The algorithm introduced by Williams and Soler 15 can be generalized to solve Eq. ͑16͒ iteratively.…”

Section: ͑16͒mentioning

confidence: 99%

Errors in Hellmann-Feynman forces due to occupation-number broadening and how they can be corrected

1998

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In ab initio calculations of electronic structures, total energies, and forces, it is convenient and often even necessary to employ a broadening of the occupation numbers. If done carefully, this improves the accuracy of the calculated electron densities and total energies and stabilizes the convergence of the iterative approach towards self-consistency. However, such a broadening may lead to an error in the calculation of the forces. Accurate forces are needed for an efficient geometry optimization of polyatomic systems and for ab initio molecular dynamics ͑MD͒ calculations. The relevance of this error and possible ways to correct it will be discussed in this paper. The first approach is computationally very simple and in fact exact for small MD time steps. This is demonstrated for the example of the vibration of a carbon dimer and for the relaxation of the top layer of the ͑111͒ surfaces of aluminum and platinum. The second, more general, scheme employs linearresponse theory and is applied to the calculation of the surface relaxation of Al͑111͒. We will show that the quadratic dependence of the forces on the broadening width enables an efficient extrapolation to the correct result. Finally the results of these correction methods will be compared to the forces obtained by using the smearing scheme, which has been proposed by Methfessel and Paxton. ͓S0163-1829͑97͒04647-X͔In ab initio electronic structure and total-energy calculations the integrals over the Brillouin zone are commonly replaced by the sum over a mesh of k points.1,2 This approach is very efficient for insulators, but for metallic systems convergence with respect to the number of k points becomes slow. Here the introduction of fractional occupation numbers is a convenient way to improve the k-space integration and in addition to stabilize the convergence in the iterative approach to self-consistency. In these broadening schemes the eigenstates are occupied according to a smooth function, e.g., a Gaussian 3 or the Fermi function 4,5,7,8 at a finite temperature.When a broadening scheme is employed in a density functional theory calculation, the computed electron density of the ground state n 0 (r) does not minimize the functional of the total energy E but the functional of the free energy A: A͓T el ;n͔ϭE͓T el ;n͔ϪT el S͓T el ;n͔, ͑1͒where S denotes the entropy associated with the occupation numbers of the Kohn-Sham orbitals and T el is the broadening parameter. In the case of Fermi broadening 6 we getSince the temperatures commonly used for the broadening are much higher than the physical ones ͑it is convenient to use k B T el ϳ0.1 eV), neither the total energies nor the free energies ͓Eq. ͑1͔͒ are directly meaningful.One way to obtain the ground-state energy at zero temperature is based on the well-known fact 6 that for the freeelectron gas, the quantities A and E depend quadratically on T el . Therefore one can write:

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“…The optimal decomposition is one which is neither purely spatial nor purely orbital, but a combination of the two. [32] which, while very similar to CP, is not identical.…”

Section: F Parallel Algorithm For Rhoofrmentioning

confidence: 85%