How Structure Factor and the Electron Density Are Related by a Fourier Transform?
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The relationship between Structure Factor and Electron Density is elucidated through Fourier Transform. Fourier synthesis techniques, such as the presented ME type approach, reconstruct Electron Density (ED) and its Laplacian distributions from structure-factor sets with varying resolutions. Initially applied in crystal structure determination in the 1920s, Fourier series, aided by phase information from the Patterson function, led to the visualization of electron density corresponding to atomic positions. Furthermore, in the context of dynamical X-ray diffraction, analytical formulae like Pendellosung are derived to expand electronic density via Fourier transformations, showcasing the intricate relationship between Structure Factor and Electron Density. The Fourier Transform serves as a crucial mathematical operation that interconverts these fundamental quantities, enabling the visualization and interpretation of molecular structures in crystals.
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| The structure factor and electron density are related by a Fourier transform, providing analytical formulas for Pendellosung and electronic density in small deformed crystals. | |
| Structure factors and electron density are related by a Fourier transform, where the phases of structure factors are crucial for meaningful synthesis of electron density in crystal structure determination. | |
| Structure factors and electron density are related by a Fourier transform, where the electron density is the transform of the structure factors, showcasing the mathematical relationship between them in crystallography. | |
| The Fourier-synthesis approach in the study links static structure factors of CaB6 to electron-density distributions, enabling reconstruction of bonding features through mathematical weighting functions. | |
| The Fourier-synthesis approach reconstructs electron-density from theoretical structure factors, showing a convergent relationship between quantum-chemically calculated structure factors and electron-density distributions. |
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