Electronic Structure with the Elk Code

July 18, 2011 to July 23, 2011
Location : CECAM-HQ-EPFL, Lausanne, Switzerland
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  • John Kay Dewhurst (Max Planck Institute of Microstructure Physics, Halle, Germany)
  • Sangeeta Sharma (Max Planck Institute of Microstructure Physics, Germany)
  • Eberhard K.U. Gross (Max Planck Institute of Microstructure Physics, Halle/Saale, Germany)




The last two decades have seen a dramatic rise in both the quality and quantity of calculations for condensed matter systems thanks to vastly increased computer power as well as the availability of new techniques. The most popular of these is density functional theory (DFT), which is also the method of choice for determining the state around which sophisticated perturbation theory methods, such as the GW approximation, are applied.

The simplest basis set for periodic solids is the set of plane waves, but because of the highly oscillatory nature of orbitals near the nucleus, an unfeasibly large number of them is required to accurately expand the Kohn-Sham wavefunctions. This can be avoided by replacing the true nuclear Coulomb potential and core states, with an effective pseudopotential, smooth enough to allow an expansion in plane waves. A far more accurate way, however, is to employ an {em all-electron} basis set, such as the {em augmented plane waves} (APW). Codes which use the APW basis are the most accurate in use today, and although more complicated for development, users can be assured of highly reliable results free from anomalies arising from the use of pseudopotentials.

Elk is an all-electron full-potential linearized augmented-plane wave (FP-LAPW) code with many advanced features, and which has been in development for eight years. It is released under the GNU General Public License (GPL), so as to encourage scrutiny of the code itself, free development of new techniques as well as a lively community of users. Its major features include

- Flexible all-electron APW for highest accuracy calculations
- General treatment of spins: magnetisation is a free vector field allowing for non-collinear magnetic systems including spin-spiral states
- Interface to the ETSF exchange-correlation library libxc making available almost every local density approximation (LDA) and generalised gradient approximation (GGA) functional invented
- Calculation of phonon dispersions and electron-phonon coupling parameters
- The only solid state code capable of calculating ground state properties using one-body reduced density matrix functional theory (RDMFT)
- Linear and non-linear optical response functions
- Most importantly in addition to being  user friendly, it is highly developer friendly -- new ideas within the field of DFT can easily be implemented within Elk

What is unique to Elk is that it is specifically programmed so that most features can be used in combination with one another. For example, it is the only code that can produce a phonon spectrum for a non-collinear magnetic system in conjunction with LDA+U. This gives Elk the ability to study properties of materials which are inaccessible to other codes.
These features have made Elk used by over four hundred people around the world. 


DFT, functionals
R. M. Dreizler, E. K. U. Gross, Density Functional Theory, Springer, Berlin (1990)
J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys: Rev. Lett. 77 , 3865 (1996)

LAPW, Magnetism, LDA+U
D. J. Singh and L. Nordstrom, Planewaves Pseudopotentials and the LAPW Method, Springer, New York (2006)
L. Nordstrom and D. J. Singh, Non-collinear intra-atomic magnetism, Phys. Rev. Lett. 76, 4420 (1996)
F. Cricchio, F.Bultmark, O. Granas, and L. Nordstrom, Itinerant Magnetic Multipole Moments of Rank Five as the Hidden Order in URu2Si2, Phys. Rev. Lett. 103, 107202 (2009)

S. Sharma and C. Ambrosch-Draxl, Linear and second-order optical response from first principles, Physica Scripta T109, 128 (2004)

Forces, Phonons
S. Baroni, S. de Gironcoli, A. Dal Corso and P. Giannozzi, Phonons and related crystal properties from density-functional perturbation theory, Rev. Mod. Phys. 73, 515 (2001)
J. M. Soler and A. R. Williams, Simple formula for the atomic forces in the augmented-plane-wave method, Phys. Rev. B 40, 1560–1564 (1989)

L. N. Oliveira, E. K. U. Gross, W. Kohn, Density-Functional Theory for Superconductors, Phys. Rev. Lett. 60, 2430 (1988)
J. P. Carbotte, Properties of boson-exchange superconductors, Rev. Mod. Phys. 62, 1027 (1990)

T. L. Gilbert, Hohenberg-Kohn theorem for nonlocal external potentials, Phys. Rev. B 12, 2111–2120 (1975)
S. Sharma, J. K. Dewhurst, N. N. Lathiotakis and E. K. U. Gross, Reduced Density Matrix Functional for Many-Electron Systems, Phys. Rev. B 78, 201103 Rapid Comm. (2008)

E. Runge and E. K. U.Gross, Density-Functional Theory for Time-Dependent Systems, Phys. Rev. Lett. 52, 997 (1984)