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In this talk, we introduce two simple, yet computationally efficient and numerically accurate matrix-algebraic approaches to correct both scalar-relativistic and spin-orbit two-electron picture-change effects arising within an exact two-component (X2C) Hamiltonian framework. The popular one-electron X2C (1eX2C), while accurate for valence orbitals, is shown to give sizeable errors for core orbital energies, and this is corrected by these new X2C Hamiltonians. In addition, the approach has been extended to time-dependent density functional theory, demonstrating that these new Hamiltonians provide four-component quality results for standard as well modern pump-probe X-ray absorption experiments at two-component cost.
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