1. 1 2. 2 3. ! (branch) cf. [Ypez, Calles and Castro: A simple algorithm for the group theoretical classification of quantum states, Applied Mathematics and Computation 133, 119-130 (2002)] ! ! ! : [Oleg V. Yazyev, Konstantin N. Kudin, and Gustavo E. Scuseria: Efficient algorithm for band connectivity resolution, Phys. Rev. B 65, 205117 (2002)] 3 4. ! ! (self-consistent) q ! q: 4x4x4 inter- atomic force constant (IFC) Z* [X. Gonze and C. Lee: Dynamical matrices, Born effective charges, dielectric permittivity tensors and interatomic force constants, Phys. Rev. B 55, 10355 (1997)] 4 5. Inter-atomic interaction , = x, y, z 5 6. 6 7. X. Gonze and C. Lee, Phys. Rev. B 55, 10355 (1997). ABINIT 8. 8 I, J 3x3 submatrices in 3Nx3N matrix dyadic product 9. 9 10. 10 11. ! Fortran 90maxloc(ary,mask) || 11 12. 12 13. q 13 14. q 14 15. ! (fcc)! a = 4.026 ! a = 4.076 15 16. q 16 17. q 17 18. PzPz Ed=-4PzPz .18 19. 19 20. Only LO has this element 20 21. 21 22. ! space group: P42/mnm (No.136) ! tetragonal a = b = 4.59373 c = 2.95812 Ti O 22 23. discontinuous at the point 24. ! GNUPLOT 24 25. ! ! ! Fortran 90maxloc() ! ABINIT http://www.ABINIT.org/ Quantum Espresso http://www.quantum-espresso.org/ ! ! LO-TO splitting ! GNUPLOT 25