Sternheimer equation - TDDFT.org

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Performance on Hermitian system k·p perturbation for Si 2x2x2 k-sampling (8-atom cubic cell) no complex shift, so Hermitian. 40 Ry cutoff Solver Hamiltonian applications Elapsed time (min:sec) States converged? cg 15k 0:50 most QMR conj. dot product QMR symmetrized 11k 0:58 all 138k 17:49 all QMR general 62k 11:35 all bicgstab 14k 0:52 none
Performance on non-Hermitian system electric perturbation for Si 1x1x1 k-sampling imaginary shift, not Hermitian or symmetric Solver Hamiltonian applications Elapsed time (min:sec) States converged? QMR conj. dot product QMR symmetrized 5k 0:40 all 85k 10:57 all QMR general - - no SCF convergence bicgstab 5k 0:20 most
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 and 20: Vibrational / rotational contributi
Page 21 and 22: Example: H 2 O molecule O -0.47 0.0
Page 23: Linear solvers All have failure con
Page 27: Acknowledgments Steven Louie, Angel

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