Ab_init stress perturbation theory - Department of Physics and ...

More documents

Recommendations

Info

$GRTEX â To Make Multiple Exam Versions from LATEX 1 ...$

Abinit reduced coordinate (~) formulation • Strain derivatives act only on the metric tensors, Ω ∂Ξ ∂ϒ Ξ ≡ = R R + R R , ϒ ≡ =−G G −G G ( αβ ) ij P P P P ( αβ ) ij P P P P ij αi β j βi α j ij αi β j βi α j ∂ηαβ ∂ηαβ ∂ Ξ Ξ ≡ = ( + ) + ( + ) 2 ( αβγδ ) ij P P P P P P P P ij δαγ Rβ iRδ j Rδ iRβ j δβγ Rα iRδ j Rδ iRα j ∂ηγδ ∂ηαβ P P P P P P P P αδ ( Rβ iRγ j Rγ iRβ j) + δβδ ( Rα iRγ j Rγ iRα j), + δ + + • has uniquely simple derivatives for Cartesian Strains 2 ∂Ω ∂ Ω = δ Ω, = δ δ ∂η ∂η ∂η αβ αβ γδ αβ αβ γδ • Key decision: strain will be Cartesian throughout the code – Existing perturbations will remain in reduced-coordinates Ω
Stress and strain notation Cartesian xx yy zz yz xz xy Cartesian 1 1 2 2 3 3 2 3 1 3 1 2 Voigt 1 2 3 4 5 6 ipert, idir natom+3, 1 natom+3, 2 natom+3, 3 natom+4, 1 natom+4, 2 natom+4, 3 • All forms used at various places internally and in output
Page 1 and 2: Implementation of the Strain Pertur
Page 3 and 4: Strain tensor h ab as a perturbatio
Page 5: Abinit reduced coordinate (~) formu
Page 9 and 10: DFPT for elastic and piezoelectric
Page 11 and 12: Design of development process • F
Page 13 and 14: Design of development process (cont
Page 15 and 16: Subroutines for strain perturbation
Page 17 and 18: Nonlocal pseudopotential strain der
Page 19 and 20: XC non-linear core correction • O
Page 21 and 22: Strain perturbation for metals •
Page 23 and 24: 2DTE terms in output file • Mix o
Page 25 and 26: Input file for anaddb run dieflag 3
Page 27 and 28: Global comparison with numerical de
Page 29 and 30: Future development, continued • P
Page 31 and 32: Mathematica for nonlocal psp, , con

Ab_init stress perturbation theory - Department of Physics and ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?