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Dynamical matrices, born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory

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Gonze, Xavier [UCL] Lee, C.

Starting from the knowledge of first-order changes of wave functions and density with respect to small atomic displacements or infinitesimal homogeneous electric fields within the density-functional theory, we write the expressions for the diagonal or mixed second-order derivatives of the total energy with respect to these perturbations: dynamical matrices for different wave vectors, Born effective-charge tensors and electronic dielectric permittivity tensors. Interatomic force constants and the phonon-band structure are then obtained by computing the Fourier transform of dynamical matrices on a regular mesh of wave vectors, with an eventual, separate treatment of the long-range dipole-dipole interaction. The same ingredients also allow one to compute the low-frequency response of the crystal to homogeneous electric fields.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 1997
Language Anglais
Journal information "Physical Review. B, Condensed Matter" - Vol. 55, no. 16, p. 10355-10368 (1997)
Peer reviewed yes
Publisher American Physical Soc (College Pk)
issn 0163-1829
Publication status Publié
Affiliation UCL - FSA/MAPR - Département des sciences des matériaux et des procédés
Links
  1. Hohenberg P., Kohn W., Inhomogeneous Electron Gas, 10.1103/physrev.136.b864
  2. Kohn W., Sham L. J., Self-Consistent Equations Including Exchange and Correlation Effects, 10.1103/physrev.140.a1133
  3. Pickett Warren E., Pseudopotential methods in condensed matter applications, 10.1016/0167-7977(89)90002-6
  4. Sugiyama Kazuhiko, Yoda Jun, Production ofYbH+by chemical reaction ofYb+in excited states withH2gas, 10.1103/physreva.55.r10
  5. Ho K. M., Bohnen K. P., First-Principles Calculation of Surface Phonons on the Al(110) Surface, 10.1103/physrevlett.56.934
  6. K. M. Ho, Phys. Rev. Lett., 38, 12 (1988)
  7. Wei Siqing, Chou M. Y., Ab initiocalculation of force constants and full phonon dispersions, 10.1103/physrevlett.69.2799
  8. Chen Y., Tong S. Y., Bohnen K. P., Rodach T., Ho K. M., First-principles phonon and multiple-scattering electron-energy-loss-spectra studies of Cu(111) and Ag(111), 10.1103/physrevlett.70.603
  9. Barmentlo M., ’t Hooft G.W., Eliel E.R., van der Ham E.W.M., Vrehen Q.H.F., van der Meer A.F.G., van Amersfoort P.W., Sum-frequency generation with a free-electron laser: A study of gallium phosphide, 10.1103/physreva.50.r14
  10. Frank W., Elsässer C., Fähnle M., Ab initioForce-Constant Method for Phonon Dispersions in Alkali Metals, 10.1103/physrevlett.74.1791
  11. Miyamoto Yoshiyuki, Cohen Marvin L., Louie Steven G., Ab initiocalculation of phonon spectra for graphite, BN, andBC2N sheets, 10.1103/physrevb.52.14971
  12. Kresse G, Furthmüller J, Hafner J, Ab initioForce Constant Approach to Phonon Dispersion Relations of Diamond and Graphite, 10.1209/0295-5075/32/9/005
  13. Arias T. A., Payne M. C., Joannopoulos J. D., Ab initiomolecular dynamics: Analytically continued energy functionals and insights into iterative solutions, 10.1103/physrevlett.69.1077
  14. Kohanoff Jorge, Andreoni Wanda, Parrinello Michele, Zero-point-motion effects on the structure ofC60, 10.1103/physrevb.46.4371
  15. Kohanoff Jorge, Phonon spectra from short non-thermally equilibrated molecular dynamics simulations, 10.1016/0927-0256(94)90103-1
  16. Onida Giovanni, Andreoni Wanda, Kohanoff Jorge, Parrinello Michele, Ab initio molecular dynamics of C70. Intramolecular vibrations and zero-point motion effects, 10.1016/0009-2614(94)00060-3
  17. Štich I., Kohanoff J., Terakura K., Low-temperature atomic dynamics of the Si(111)-7×7, 10.1103/physrevb.54.2642
  18. King-Smith R. D., Vanderbilt David, Theory of polarization of crystalline solids, 10.1103/physrevb.47.1651
  19. Resta Raffaele, Macroscopic polarization in crystalline dielectrics: the geometric phase approach, 10.1103/revmodphys.66.899
  20. Nunes R. W., Vanderbilt David, Real-Space Approach to Calculation of Electric Polarization and Dielectric Constants, 10.1103/physrevlett.73.712
  21. Ordejón Pablo, Drabold David A., Martin Richard M., Itoh Satoshi, Linear Scaling Method for Phonon Calculations from Electronic Structure, 10.1103/physrevlett.75.1324
  22. Baroni Stefano, Giannozzi Paolo, Testa Andrea, Green’s-function approach to linear response in solids, 10.1103/physrevlett.58.1861
  23. Dalgarno A., Stewart A. L., A Perturbation Calculation of Properties of the Helium Iso-Electronic Sequence, 10.1098/rspa.1958.0182
  24. J. O. Hirschfelder, Advances in Quantum Chemistry (1964)
  25. Kleinman Leonard, Bylander D. M., Efficacious Form for Model Pseudopotentials, 10.1103/physrevlett.48.1425
  26. Louie Steven G., Froyen Sverre, Cohen Marvin L., Nonlinear ionic pseudopotentials in spin-density-functional calculations, 10.1103/physrevb.26.1738
  27. Dal Corso Andrea, Baroni Stefano, Resta Raffaele, de Gironcoli Stefano, Ab initiocalculation of phonon dispersions in II-VI semiconductors, 10.1103/physrevb.47.3588
  28. Gonze X., Charlier J.-C., Allan D.C., Teter M.P., Interatomic force constants from first principles: The case of α-quartz, 10.1103/physrevb.50.13035
  29. Lee Changyol, Gonze Xavier, Lattice dynamics and dielectric properties ofSiO2stishovite, 10.1103/physrevlett.72.1686
  30. Lee Changyol, Gonze Xavier, Ab initiocalculation of the thermodynamic properties and atomic temperature factors ofSiO2α-quartz and stishovite, 10.1103/physrevb.51.8610
  31. Lee Changyol, Gonze Xavier, The pressure-induced ferroelastic phase transition of SiO2stishovite, 10.1088/0953-8984/7/19/003
  32. Ghosez Ph, Gonze X, Michenaud J.-P, Coulomb interaction and ferroelectric instability of BaTiO3, 10.1209/epl/i1996-00404-8
  33. X. Gonze, Phys. Rev. B, 49, 13 (1989)
  34. Gonze Xavier, Adiabatic density-functional perturbation theory, 10.1103/physreva.52.1096
  35. Giannozzi Paolo, de Gironcoli Stefano, Pavone Pasquale, Baroni Stefano, Ab initiocalculation of phonon dispersions in semiconductors, 10.1103/physrevb.43.7231
  36. Yu Rici, Krakauer H., Linear-response calculations within the linearized augmented plane-wave method, 10.1103/physrevb.49.4467
  37. Savrasov S. Y., Linear-response theory and lattice dynamics: A muffin-tin-orbital approach, 10.1103/physrevb.54.16470
  38. Gonze Xavier, Allan Douglas C., Teter Michael P., Dielectric tensor, effective charges, and phonons in α-quartz by variational density-functional perturbation theory, 10.1103/physrevlett.68.3603
  39. Savrasov S. Yu., Linear response calculations of lattice dynamics using muffin-tin basis sets, 10.1103/physrevlett.69.2819
  40. M. Born, Dynamical Theory of Crystal Lattices (1954)
  41. Car R., Tosatti E., Baroni S., Leelaprute S., Dielectric band structure of crystals: General properties and calculations for silicon, 10.1103/physrevb.24.985
  42. Hybertsen Mark S., Louie Steven G., Ab initiostatic dielectric matrices from the density-functional approach. I. Formulation and application to semiconductors and insulators, 10.1103/physrevb.35.5585
  43. Because of different conventions, Phys. Rev. B, 50, 13 (1994)
  44. Pick Robert M., Cohen Morrel H., Martin Richard M., Microscopic Theory of Force Constants in the Adiabatic Approximation, 10.1103/physrevb.1.910
  45. Levine Zachary H., Allan Douglas C., Linear optical response in silicon and germanium including self-energy effects, 10.1103/physrevlett.63.1719
  46. Zhong W., King-Smith R. D., Vanderbilt David, Giant LO-TO splittings in perovskite ferroelectrics, 10.1103/physrevlett.72.3618
  47. L. Landau, Electrodynamics of Continuous Media (1960)
  48. Cochran W., Cowley R.A., Dielectric constants and lattice vibrations, 10.1016/0022-3697(62)90084-7
  49. Monkhorst Hendrik J., Pack James D., Special points for Brillouin-zone integrations, 10.1103/physrevb.13.5188
  50. Gonze X., Ghosez Ph., Godby R. W., Density-Polarization Functional Theory of the Response of a Periodic Insulating Solid to an Electric Field, 10.1103/physrevlett.74.4035
  51. Adler Stephen L., Quantum Theory of the Dielectric Constant in Real Solids, 10.1103/physrev.126.413
  52. Wiser Nathan, Dielectric Constant with Local Field Effects Included, 10.1103/physrev.129.62
  53. Ehrenreich H., Cohen M. H., Self-Consistent Field Approach to the Many-Electron Problem, 10.1103/physrev.115.786
  54. Robertson I. J., Farid Behnam, Does the Harris energy functional possess a local maximum at the ground-state density?, 10.1103/physrevlett.66.3265
Bibliographic reference Gonze, Xavier ; Lee, C.. Dynamical matrices, born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory. In: Physical Review. B, Condensed Matter, Vol. 55, no. 16, p. 10355-10368 (1997)
Permanent URL http://hdl.handle.net/2078.1/46303