Abstract
We integrate density functional theory (DFT) into quantitative convergent-beam electron diffraction (QCBED) to create a synergy between experiment and theory called QCBED-DFT. This synergy resides entirely in the electron density which, in real materials, gives rise to the experimental CBED patterns used by QCBED-DFT to refine DFT model parameters. We use it to measure the Hubbard energy U for two strongly correlated electron systems, NiO and CeB_{6} (U=7.4±0.6 eV for d orbitals in NiO and U=3.0±0.6 eV for f orbitals in CeB_{6}), and the boron position parameter x for CeB_{6} (x=0.1992±0.0003). In verifying our measurements, we demonstrate an accuracy test for any modeled electron density.
Highlights
We integrate density functional theory (DFT) into quantitative convergent-beam electron diffraction (QCBED) to create a synergy between experiment and theory called QCBED-DFT
Instead of testing density functionals by comparing system energies and materials properties, QCBED-DFT interrogates ρðrÞ directly because the experimental CBED patterns being matched are a direct consequence of VðrÞ, and ρðrÞ, in the actual material
We report a value of U 1⁄4 7.4 Æ 0.6 eV for d orbitals in NiO from our QCBED-DFT refinements, with a Hund exchange parameter of J 1⁄4 0.95 eV [24,91,98]
Summary
We integrate density functional theory (DFT) into quantitative convergent-beam electron diffraction (QCBED) to create a synergy between experiment and theory called QCBED-DFT. QCBED-DFT, refines DFT model parameters without comparing energies or properties at all, confining the refinements to electron densities alone. Instead of refining small subsets of structure factors, QCBED-DFT refines DFT model parameters, altering the simulated electron density in real space and changing all structure factors used to calculate CBED
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