Atomic complexities information plane

Information Planes and Complexity Measures for Atomic Systems, Ionization Processes and Isoelectronic Series... 

This section is devoted to the analysis and interpretation, from a physical point of view, of the LMC, FS, and CR complexity values and information planes corresponding to all neutral atoms throughout the Periodic Table, within the range of nuclear charges Z = 1-103. Such a study is carried out in position, momentum, and phase/product spaces, which corresponding distributions and their complexities are obtained by means of the accurate wavefunctions provided in Ref. [68]. 

It has also been shown the interest of studying the associated information planes substended by two information functionals, which for the atomic case clearly display the characteristic shell-filling patterns throughout the whole periodic table. It still remains open the question of the existence of additional functionals, planes and complexities providing further information on the atomic structure and the ionization processes, among others. 

Early experimental spectroscopic investigations on Rg- XY complexes resulted in contradictory information regarding the interactions within them and their preferred geometries. Rovibronic absorption and LIF spectra revealed T-shaped excited- and ground-state configurations, wherein the Rg atom is confined to a plane perpendicular to the X—Y bond [10, 19, 28-30]. While these results were supported by the prediction of T-shaped structures based on pairwise additive Lennard-Jones or Morse atom-atom potentials, they seemed to be at odds with results from microwave spectroscopy experiments that were consistent with linear ground-state geometries [31, 32]. Some attempts were made to justify the contradictory results of the microwave and optical spectroscopic studies, and... 

As ontlined below, NRVS stndies have provided information on iron ont-of-plane modes that was previously unavailable. For five-coordinate nitrosyl complexes, classical theory predicts that the three-atom FeNO grouping should have three modes the N-O stretch, the Fe-N stretch, and the FeNO bend, with the latter two expected to be found in the region below 600 cm. In a detailed analysis of [Fe(TPP)(NO)] provided by a series of DFT calculations, the predicted frequency of the stretch was overestimated when the calculation used the BP86 functional and underestimated when the B3LYP functional was employed. The reasons for the difficulties in this prediction appear to arise from the unusual nature of the unpaired electron in the compound that is significantly delocalized over the NO ligand as well as the metal. In this case, the Fe-N stretch was actually observed at 540 cm for [Fe(TPP)(NO)] powder at 80 This... 

In modern powder diffraction the measurement delivers a raw-file of some thousand step-scan data of counted X-ray photons per step. This raw file contains all the needed information to carry out a crystallographic analysis, but in a way that requires follow up. More informative is a list of distinguishable reflections that includes the position (mostly in the form of f-values) and intensity of each reflection. This dif-file (d-values and intensities) contains some tens to hundreds of reflections. The number of reflections depends on the complexity of the structure and the crystal symmetry the more atoms per cell and the lower the symmetry the more reflections can be identified. But the number of detectible reflections also depends on the resolving power of the equipment, best documented by the half-width of the reflections (more accurately half-width at half-maximum, FWHM). Reflections nearer together than this half-width (or even two half-widths) cannot be resolved. In a second step, very often the Miller indices of the originating lattice planes are added to the dif-file. For this the knowledge of the unit cell is necessary (though not of the crystal structure itself). The powder diffraction file PDF of the International Centre for Diffraction Data (ICDD) contains over 100000 such dif-files for the identification and discrimination of solid state samples. 

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