Sternheimer equation - TDDFT.org

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Calculation of Born effective charges Standard method: change in polarization for finite atomic displacements. Requires 3N atoms calculations. + Z s E
Example: H 2 O molecule O -0.47 0.00 0.00 0.00 -0.32 0.00 0.00 0.00 -0.65 H 0.23 -0.09 0.00 -0.07 0.32 0.00 0.00 0.00 0.16 Δ = 0.002 DFT/GGA, USPP, 22 Ry, 40 a 0 supercell, displacement/polarization method A Pasquarello and R Resta, Phys Rev B 68, 174302 (2003) O -0.51 0.00 0.00 H 0.25 -0.06 0.00 Δ = 0.07 0.00 -0.34 0.00 -0.07 0.17 0.00 0.00 0.00 -0.64 0.00 0.00 0.32 DFT/GGA, Troullier-Martins PP, 22 Ry, finite system, Octopus O -0.53 0.00 0.00 H 0.26 -0.05 0.00 Δ = 0.01 0.00 -0.36 0.00 -0.07 0.18 0.00 0.00 0.00 -0.66 0.00 0.00 0.33 DFT/GGA, Troullier-Martins PP, 250 Ry, finite system, Octopus Δ is deviation from acoustic sum rule
Page 1 and 2: Non-linear optics, k·p perturbatio
Page 3 and 4: Quantized picture of non-linear opt
Page 5 and 6: Question: How does the liquid envir
Page 7 and 8: Solution measurements of hyperpolar
Page 9 and 10: 1. Effect of electronic confinement
Page 11 and 12: Finite differences Apply static fie
Page 13 and 14: Sternheimer equation: projectors an
Page 15 and 16: Perturbations in Sternheimer equati
Page 17 and 18: Si k.p perturbation
Page 19: Vibrational / rotational contributi
Page 23 and 24: Linear solvers All have failure con
Page 25 and 26: Performance on non-Hermitian system
Page 27: Acknowledgments Steven Louie, Angel

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