Sternheimer equation - TDDFT.org

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Solution measurements of hyperpolarizability Measurements are usually in solution for molecules. Solvent effects can be strong and complicate comparison between experiment and theory. (In theory, handle via polarizable continuum models or explicit solvent in small clusters or periodic system.) (Time-averaged) inversion symmetry of solution makes ordinary measurement give zero. Electric-field-induced second-harmonic generation (EFISH) is coherent third-order process, based on field lining up molecules. What is measured directly and often reported: Hyper-Rayleigh scattering (HRS) is incoherent second-order process, based on orientational fluctuations.
Solution measurements of hyperpolarizability Consider projection along dipole moment. Vertical-vertical and horizontal-vertical polarizations for experiment.
Page 1 and 2: Non-linear optics, k·p perturbatio
Page 3 and 4: Quantized picture of non-linear opt
Page 5: Question: How does the liquid envir
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 and 24: Linear solvers All have failure con
Page 25 and 26: Performance on non-Hermitian system
Page 27: Acknowledgments Steven Louie, Angel

Sternheimer equation - TDDFT.org

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