Miroslav Kohout

Insight into the informational-structure behavior of the Diels-Alder reaction of cyclopentadiene and maleic anhydride

The course of the Diels-Alder reactions of cyclopentadiene and maleic anhydride were studied. Two reaction paths were modelled: endo- and exo-selective paths. All structures within the transient region were characterized and analyzed by means of geometrical descriptors, physicochemical parameters and information-theoretical measures in order to observe the linkage between chemical behavior and the carriage of information. We have shown that the information-theoretical characterization of the chemical course of the reaction is in complete agreement with its phenomenological behavior in passing from reactants to products. In addition, we were able to detect the main differences between the two reaction mechanisms. This type of informational analysis serves to provide tools to help understand the chemical reactivity of the two simplest Diels-Alder reactions, which permits the establishment of a connection between the quantum changes that molecular systems exert along reaction coordinates and standard physicochemical phenomenology. In the present study, we have shown that every reaction stage has a family of subsequent structures that are characterized not solely by their phenomenological behavior but also by informational properties of their electronic density distribution (localizability, order, uniformity). Moreover, we were able to describe the main differences between endo-adduct and exo-adduct pathways. With the advent of new experimental techniques, it is in principle possible to observe the structural changes in the transient regions of chemical reactions. Indeed, through this work we have provided the theoretical concepts needed to unveil the concurrent processes associated with chemical reactions.

Bonding indicators from electron pair density functionals.

The bonding analysis of a chemical system is usually based on some descriptors. Distinct approaches are used to generate the bonding descriptors, whereby the usefulness of a particular approach is emphasized by the desire to yield a description consistent with the examined effects. Thus, whereas the bond path from the electron density gradient field yields the connectivity of the atomic fragments, the orbital picture can easily rationalize the rotational rigidity of a double bond. On the other hand none of the former is able to describe the volume demand of the bonds, which can be accessed by descriptors originating from approaches using space partitioning. As a conceivable way to describe the bonding situation a class of functionals based on the electron pair density integrals in both, direct and momentum space, is proposed. The localizability indicators defined by those functionals are examined on several molecules.

Contribution to the electron distribution analysis. I, Shell structure of atoms

Relativistic spherically averaged numerical all‐electron densities ρ were computed for the atoms Be–Ba, B–Tl, C–Pb, Cu–Au, and Zn–Hg. The Laplacian of these densities is not able to resolve the valence shell from the inner shells in case of heavy atoms, starting with the fourth row. The distribution of the local kinetic energy Ekin shows a valence maximum even for these heavy atoms, unfortunately, in a region of negative kinetic energy; i.e., nonclassically allowed. The quantity −‖∇ρ‖/ρ was also investigated. For all computed atoms, the −‖∇ρ‖/ρ diagrams are capable of describing the complete shell structure. −‖∇ρ‖/ρ is sensitive to basis set quality: poor Gaussian basis sets exhibit spurious oscillations and a premature onset of the linear decay. For the atoms B–Tl, Ba, Au, Hg, and Pb, nonrelativistic numerical calculations were performed to examine the effect of the relativity on the aforementioned quantities. Tests with pseudopotential densities reveal that for pseudopotential calculations, it is advisa...

Direct space decomposition of ELI-D: interplay of charge density and pair-volume function for different bonding situations.

The topological features, i.e., gradients and curvatures of the same-spin electron pair restricted electron localizability indicator (ELI-D) in position space are analyzed in terms of those of the electron density and the pair-volume function. The analysis of the topology of these constituent functions and their interplay on ELI-D attractor formation for a number of molecules representing chemically different bonding situations allows distinguishing between different chemical bonding scenarios on a quantum mechanical basis without the recourse to orbitals. The occurrence of the Laplacian of the electron density in the expression for the Laplacian of ELI-D allows us to establish a physical link between electron localizability and electron pairing as displayed by ELI-D and the role of Laplacian of the density in this context.

Electron localization and delocalization indices for solids

The electron localization and delocalization indices obtained by the integration of exchange‐correlation part of pair density over chemically meaningful regions of space, e.g., QTAIM atoms are valuable tools for the bonding analysis in molecular systems. However, among periodic systems only few simplest models were analyzed with this approach until now. This contribution reports implementation and evaluation of the localization and delocalization indices on the basis of solid state DFT calculations. A comparison with the results of simple analytical model of Ponec was made. In addition, a small set of compounds with ionic (NaCl), covalent (diamond, graphite), and metallic (Na, Cu) bonding interactions was characterized using this method. Typical features of different types of bonding were discussed using the delocalization indices.

Features of the electron density in magnesium diboride: reconstruction from X-ray diffraction data and comparison with TB-LMTO and FPLO calculations

Features of the electron density in MgB(2) reconstructed from room-temperature single-crystal X-ray diffraction intensities using a multipole model are considered. Topological analysis of the total electron density has been applied to characterize the atomic interactions in magnesium diboride. The shared-type B-B interaction in the B-atom layer reveals that both sigma and pi components of the bonding are strong. A closed-shell-type weak B-B pi interaction along the c axis of the unit cell has also been found. The Mg-B closed-shell interaction exhibits a bond path that is significantly curved towards the vertical Mg-atom chain ([110] direction). The latter two facts reflect two sorts of bonding interactions along the [001] direction. Integration of the electron density over the zero-flux atomic basins reveals a charge transfer of approximately 1.4 (1) electrons from the Mg atoms to the B-atom network. The calculated electric-field gradients at nuclear positions are in good agreement with experimental NMR values. The anharmonic displacement of the B atoms is also discussed. Calculations of the electron density by tight-binding linear muffin-tin orbital (TB-LMTO) and full-potential non-orthogonal local orbital (FPLO) methods confirm the results of the reconstruction from X-ray diffraction; for example, a charge transfer of 1.5 and 1.6 electrons, respectively, was found.

How does the ambiguity of the electronic stress tensor influence its ability to reveal the atomic shell structure

The electronic stress tensor is not uniquely defined. Therefore, shell indicators stemming from the quantum stress tensor may inherit this ambiguity. Based on a general formula of the stress tensor this ambiguity can be described by an external parameter λ. Two functions derived from the quantum stress tensor have been evaluated according to their ability to serve as shell indicators. The influence of λ is analyzed and the consequences for the representation of the atomic shell structure are discussed in detail. It is found that the trace of the stress tensor does not fully reveal the atomic shell structure. In contrast, the scaled trace (whereby the scaling function is proportional to the Thomas-Fermi kinetic energy density) produces fairly good representation of the atomic shell structure over a wide range of λ values.

Domain-averaged Fermi-hole analysis for solids

The domain-averaged Fermi hole (DAFH) orbitals provide highly visual representation of bonding in terms of orbital-like functions with attributed occupation numbers. It was successfully applied on many molecular systems including those with non-trivial bonding patterns. This article reports for the first time the extension of the DAFH analysis to the realm of extended periodic systems. Simple analytical model of DAFH orbital for single-band solids is introduced which allows to rationalize typical features that DAFH orbitals for extended systems may possess. In particular, a connection between Wannier and DAFH orbitals has been analyzed. The analysis of DAFH orbitals on the basis of DFT calculations is applied to hydrogen lattices of different dimensions as well as to the solids diamond, graphite, Na, Cu and NaCl. In case of hydrogen lattices, remarkable similarity is found between the DAFH orbitals evaluated with both the analytical approach and DFT. In case of the selected ionic and covalent solids the DAFH orbitals deliver bonding descriptions, which are compatible with classical orbital interpretation. For metals the DAFH analysis shows essential multicenter nature of bonding.

EuTM2Ga8 (TM = Co, Rh, Ir) - A Contribution to the Chemistry of the CeFe2Al8-type Compounds

The isostructural compounds EuTM(2)Ga(8) (TM = Co, Rh, Ir) were prepared by direct reaction of the elements by high-frequency thermal treatment. All three phases are isotypic with CeFe(2)Al(8) (space group Pbam, Pearson symbol oP44, Z = 4). The crystal structure was established from single-crystal X-ray diffraction data: a = 12.4322(7) A, b = 14.3814(9) A, and c = 4.0378(2) A for EuCo(2)Ga(8); a = 12.6001(6) A, b = 14.6757(7) A, and c = 4.1172(2) A for EuRh(2)Ga(8); and a = 12.6237(7) A, b = 14.6978(8) A, and c = 4.1486(2) A for EuIr(2)Ga(8), respectively. Analysis of the chemical bonding in EuRh(2)Ga(8) with the electron localizability tools reveals formation of the 3D [Rh(2)Ga(8)] polyanion build by polar covalent bonds. Europium interacts in two ways with the polyanion: mainly as a cation by charge transfer and additionally covalently by means of the electrons of the inner shells. Magnetic susceptibility measurements show Curie-Weiss paramagnetic behavior above 40 K with effective magnetic moments of 7.81, 8.05, and 8.27 micro(B)/f.u. for EuTM(2)Ga(8) (TM = Co, Rh, Ir). Antiferromagnetic ordering of Eu moments is observed in all three compounds below 20 K. Independently on the chemical composition of the coordination sphere, magnetic behavior and, especially, X-ray absorption spectra indicate predominantly the 4f(7) electronic configuration of europium with small admixture of the 4f(6) state.

New insights from domain-averaged Fermi holes and bond order analysis into the bonding conundrum in C2

ABSTRACT The bonding in the ground state of C2 is examined using a combined approach based on the analysis of domain-averaged Fermi holes and of the contributions to covalent bond orders that can be associated with individual localised natural orbitals. The σ system in this molecule turns out to be particularly sensitive, evolving from a description that includes a fairly traditional shared electron pair σ bond, for a range of intermediate nuclear separations, to a somewhat different situation near equilibrium geometry, where non-classical repulsive interactions are particularly important. The various results provide further support for the view that the electronic structure of this molecule sufficiently exceeds the scope of traditional bonding paradigms that attempts to classify the bonding in terms of a classical bond multiplicity are highly questionable.