Electron density of KNiF3: analysis of the atomic interactions

2000 ◽  
Vol 56 (2) ◽  
pp. 197-203 ◽  
Author(s):  
Vladimir Tsirelson ◽  
Yury Ivanov ◽  
Elizabeth Zhurova ◽  
Vladimir Zhurov ◽  
Kiyoaki Tanaka
Keyword(s):  
Electron Density ◽  
Critical Points ◽  
Topological Analysis ◽  
Ionic Radii ◽  
Bond Path ◽  
Coordination Numbers ◽  
Packed Layer ◽  
Atomic Interactions ◽  
Specific Shape ◽  
Close Packed Layer

The topological analysis of the electron density in the perovskite KNiF3, potassium nickel trifluoride, based on the accurate X-ray diffraction data, has been performed. The topological picture of the atomic interactions differs from that resulting from the classic crystal chemistry consideration. The shapes of atoms in KNiF3 defined by zero-flux surfaces in the electron density are, in general, far from spherical. At the same time, their asphericity in the close-packed layer is very small. The topological coordination numbers of K and Ni are the same as the geometrical ones, whereas topological coordination for the F atom (6) differs from the geometrical value. The latter results from a specific shape of the Ni-atom basin preventing the bond-path formation between F atoms in the same atomic close-packed layer, in spite of the fact that the closest F—F distance is the same as K—F. Judging by the electron density value and curvature at the bond critical points, the K—F interaction in KNiF3 can be considered ionic, while the Ni—F bond belongs to the polar covalent type. No correlation of the topological ionic radii with crystal or ionic radii was found in KNiF3. Critical points in the electrostatic potential have also been studied.

Electron density and energy density view on the atomic interactions in SrTiO3

2002 ◽  
Vol 58 (4) ◽  
pp. 567-575 ◽  
Author(s):  
Elizabeth A. Zhurova ◽  
Vladimir G. Tsirelson
Keyword(s):  
Electron Density ◽  
Density Functional ◽  
Topological Analysis ◽  
Theoretical Data ◽  
Bond Path ◽  
Coordination Numbers ◽  
The Density Functional Theory ◽  
Atomic Interactions ◽  
Specific Shape

The results of topological analysis of the electron density in an SrTiO3 crystal based on the experimental (at 145 K) and theoretical data are presented and discussed. The features of the electron density lead to the conclusion that the Ti—O interaction is of the partly polar covalent (or intermediate) type. Complicated atomic shapes defined by the zero-flux surfaces in the electron density are revealed. It is found that, in general, they are far from spherical and have very slight asphericity in the close-packed layers. The topological coordination numbers of Sr and Ti are the same as the geometrical numbers, whereas the topological coordination for the O atom (6) differs from the geometrical value (12). The latter results from the specific shape of the Ti-atom basin, which prevents bond-path formation between the O atoms. The analysis of the kinetic and potential energy densities derived from the electron density using the density functional theory formulae revealed the stabilizing crystal-forming role of the O atoms in SrTiO3. Structural homeomorphism between the experimental electron density and the potential and kinetic energy densities is observed.

A topological analysis of the interion interactions of tetraphenylphosphonium squarate

2006 ◽  
Vol 84 (5) ◽  
pp. 804-811 ◽  
Author(s):  
David Wolstenholme ◽  
Manuel AS Aquino ◽  
T Stanley Cameron ◽  
Joseph D Ferrara ◽  
Katherine N Robertson
Keyword(s):  
Hydrogen Bonding ◽  
Hydrogen Bonds ◽  
Electron Density ◽  
Intermolecular Interactions ◽  
Critical Points ◽  
Topological Analysis ◽  
Van Der Waals ◽  
Van Der Waals Interactions ◽  
Multipole Refinement ◽  
Diverse Interactions

The tetraphenylphosphonium squarate salt crystallizes with a number of diverse interactions, which all have the potential to be classified as hydrogen bonds. The squarate anions are found as dimers linked by O-H···O interactions. The multipole refinement of the tetraphenylphosphonium squarate was performed using the Hansen–Coppens model followed by topological analysis of its intermolecular interactions. A total of 28 interactions were found among the symmetry related molecules, which include a number of C-H···Cπ, C-H···O, and C-H···H-C interactions, along with the O-H···O interaction. With the criteria for hydrogen bonding proposed by Popelier and Koch, it is possible to determine which of these interactions are hydrogen bonds and which are van der Waals interactions. Both linear and exponentially dependent correlations can be seen for the properties of the bond critical points involving the intermolecular interactions that fulfill these criteria. All this leads to a better understanding of the role that hydrogen bonds play in the formation of small organic compounds.Key words: electron density, multiple refinement, hydrogen bonds.

Atomic interactions in ethylenebis(1-indenyl)zirconium dichloride as derived by experimental electron density analysis

2005 ◽  
Vol 61 (4) ◽  
pp. 418-428 ◽  
Author(s):  
Adam I. Stash ◽  
Kiyoaki Tanaka ◽  
Kazunari Shiozawa ◽  
Hitoshi Makino ◽  
Vladimir G. Tsirelson
Keyword(s):  
Electron Density ◽  
Topological Analysis ◽  
Electronic Energy ◽  
Ligand Interaction ◽  
Atomic Interactions ◽  
Particle Potential ◽  
Density Analysis ◽  
The One ◽  
Electron Density Analysis ◽  
Experimental Electron Density

A topological analysis of the experimental electron density in racemic ethylenebis(1-indenyl)zirconium dichloride, C20H16Cl2Zr, measured at 100 (1) K, has been performed. The atomic charges calculated by the numerical integration of the electron density over the zero-flux atomic basins demonstrate the charge transfer of 2.25 e from the Zr atom to the two indenyl ligands (0.19 e to each) and two Cl atoms (0.93 e to each). All the atomic interactions were quantitatively characterized in terms of the electron density and the electronic energy-density features at the bond critical points. The Zr—C2 bond paths significantly curved towards the C1—C2 bond were found; no other bond paths connecting the Zr atom and indenyl ligand were located. At the same time, the π-electrons of the C1—C2 bond are significantly involved in the metal–ligand interaction. The electron density features indicate that the indenyl coordination can be approximately described as η1 with slippage towards η2. The `ligand-opposed' charge concentrations around the Zr atom were revealed using the Laplacian of the electron density and the one-particle potential; they were linked to the orbital representations. Bonds in the indenyl ligand were characterized using the Cioslowski–Mixon bond-order indices calculated directly from the experimental electron density.

EDMA: a computer program for topological analysis of discrete electron densities

2012 ◽  
Vol 45 (3) ◽  
pp. 575-580 ◽  
Author(s):  
Lukáš Palatinus ◽  
Siriyara Jagannatha Prathapa ◽  
Sander van Smaalen
Keyword(s):  
Computer Program ◽  
Electron Density ◽  
Critical Points ◽  
Topological Analysis ◽  
Three Dimensional ◽  
Real Space ◽  
Principal Curvatures ◽  
Electron Densities ◽  
Structure Solution ◽  
Aperiodic Crystals

EDMAis a computer program for topological analysis of discrete electron densities according to Bader's theory of atoms in molecules. It locates critical points of the electron density and calculates their principal curvatures. Furthermore, it partitions the electron density into atomic basins and integrates the volume and charge of these atomic basins.EDMAcan also assign the type of the chemical element to atomic basins based on their integrated charges. The latter feature can be used for interpretation ofab initioelectron densities obtained in the process of structure solution. A particular feature ofEDMAis that it can handle superspace electron densities of aperiodic crystals in arbitrary dimensions.EDMAfirst generates real-space sections at a selected set of phases of the modulation wave, and subsequently analyzes each section as an ordinary three-dimensional electron density. Applications ofEDMAto model electron densities have shown that the relative accuracy of the positions of the critical points, the electron densities at the critical points and the Laplacian is of the order of 10−4or better.

Experimental observation of charge-shift bond in fluorite CaF2

2017 ◽  
Vol 73 (4) ◽  
pp. 643-653 ◽  
Author(s):  
Marcin Stachowicz ◽  
Maura Malinska ◽  
Jan Parafiniuk ◽  
Krzysztof Woźniak
Keyword(s):  
Quantum Theory ◽  
Density Distribution ◽  
Critical Point ◽  
Electron Density ◽  
Closed Shell ◽  
Atoms In Molecules ◽  
Bond Critical Point ◽  
Ionic Radii ◽  
Bond Path ◽  
Charge Shift

On the basis of a multipole refinement of single-crystal X-ray diffraction data collected using an Ag source at 90 K to a resolution of 1.63 Å−1, a quantitative experimental charge density distribution has been obtained for fluorite (CaF2). The atoms-in-molecules integrated experimental charges for Ca2+and F−ions are +1.40 e and −0.70 e, respectively. The derived electron-density distribution, maximum electron-density paths, interaction lines and bond critical points along Ca2+...F−and F−...F−contacts revealed the character of these interactions. The Ca2+...F−interaction is clearly a closed shell and ionic in character. However, the F−...F−interaction has properties associated with the recently recognized type of interaction referred to as `charge-shift' bonding. This conclusion is supported by the topology of the electron localization function and analysis of the quantum theory of atoms in molecules and crystals topological parameters. The Ca2+...F−bonded radii – measured as distances from the centre of the ion to the critical point – are 1.21 Å for the Ca2+cation and 1.15 Å for the F−anion. These values are in a good agreement with the corresponding Shannon ionic radii. The F−...F−bond path and bond critical point is also found in the CaF2crystal structure. According to the quantum theory of atoms in molecules and crystals, this interaction is attractive in character. This is additionally supported by the topology of non-covalent interactions based on the reduced density gradient.

Charge density in crystalline citrinin from X-ray diffraction at 19 K

1996 ◽  
Vol 74 (6) ◽  
pp. 1145-1161 ◽  
Author(s):  
Pietro Roversi ◽  
Felicita Merati ◽  
Riccardo Destro ◽  
Mario Barzaghi
Keyword(s):  
Electron Density ◽  
Chemical Reactivity ◽  
Topological Analysis ◽  
X Ray Diffraction ◽  
X Ray ◽  
Bond Path ◽  
Topological Features ◽  
Path Lengths ◽  
The Stability ◽  
Experimental Electron Density

For the fungal metabolite citrinin, C13H14O5, the total experimental electron distribution ρ(r) and its Laplacian [Formula: see text] have been obtained from an extensive set (36 564 measurements) of single-crystal X-ray diffracted intensities at a temperature of 19 ± 2 K. Relevant steps in data collection and processing are reported. The resulting 7698 independent intensity data have been analysed with a multipole (pseudoatoms) formalism. The topological properties of ρ(r) have been determined according to the quantum theory of atoms in molecules. CC and CO bond path lengths have been obtained by numerical integration; their values are found to be well correlated with those of the electron density at the bond critical points. Topological features have been used to characterize the extension of the conjugated system of the molecule, and to confirm the stability of its rings, particularly the two formed by intramolecular H bonds. Maps of [Formula: see text] are presented, showing details in the valence charge distribution and providing a very sensitive tool for analysing dependence of the density on the model adopted to interpret X-ray data. The known chemical reactivity of the molecule towards nucleophiles at a Csp2 atom is confirmed by the shape of the molecular reactive surface (the zero envelope of [Formula: see text]). Key words: experimental electron density, low-temperature X-ray diffraction, topological analysis, Laplacian of ρ.

scholarly journals Analysis of Oxygen–Pnictogen Bonding with Full Bond Path Topological Analysis of the Electron Density

2021 ◽  
Vol 60 (3) ◽  
pp. 1846-1856
Author(s):  
Brent Lindquist-Kleissler ◽  
John S. Wenger ◽  
Timothy C. Johnstone
Keyword(s):  
Electron Density ◽  
Topological Analysis ◽  
Bond Path

Topological Analysis of Electron Density in Large Biomolecular Systems

2019 ◽  
Vol 16 (4) ◽  
pp. 437-448 ◽  
Author(s):  
Maria A. Grishina ◽  
Vladimir A. Potemkin
Keyword(s):  
Electron Density ◽  
Critical Points ◽  
Topological Analysis ◽  
Time Estimation ◽  
Electron Structure ◽  
Supramolecular Compounds ◽  
Molecular Electron ◽  
Cyp3a4 Substrate ◽  
High Level ◽  
Inorganic Molecules

Background: A great step toward describing the structure of the molecular electron was made in the era of quantum chemical methods. Methods play a very important role in the prediction of molecular properties and in the description of the reactivity of compounds, which cannot be overestimated. There are many works, books, and articles on quantum methods, their applications, and comparisons. At the same time, quantum methods of a high level of theory, which give the most accurate results, are time-consuming, which makes them almost impossible to describe large complex molecular systems, such as macromolecules, enzymes, supramolecular compounds, crystal fragments, and so on. Objective: To propose an approach that allows real-time estimation of electron density in large systems, such as macromolecules, nanosystems, proteins. Methods: AlteQ approach was applied to the tolopogical analysis of electron density for “substrate - cytochrome” complexes. The approach is based on the use of Slater’s type atomic contributions. Parameters of the atomic contributions were found using high resolution X-ray diffraction data for organic and inorganic molecules. Relationships of the parameters with atomic number, ionization potentials and electronegativities were determined. The sufficient quality of the molecular electron structure representation was shown under comparison of AlteQ predicted and observed electron densities. AlteQ algorithm was applied for evaluation of electron structure of “CYP3A4 – substrate” complexes modeled using BiS/MC restricted docking procedure. Topological analysis (similar to Atoms In Molecules (AIM) theory suggested by Richard F.W. Bader) of the AlteQ molecular electron density was carried out for each complex. The determination of (3,-1) bond, (3,+1) ring, (3,+3) cage critical points of electron density in the intermolecular “CYP3A4 – substrate” space was performed. Results: Different characteristics such as electron density, Laplacian eigen values, etc. at the critical points were computed. Relationship of pKM (KM is Michaelis constant) with the maximal value of the second Laplacian eigen value of electron density at the critical points and energy of complex formation computed using MM3 force field was determined. Conclusion: It was shown that significant number of (3,-1) bond critical points are located in the intermolecular space between the enzyme site and groups of substrate atoms eliminating during metabolism processes.

Experimental and theoretical charge-density study of a tetranuclear cobalt carbonyl complex

2009 ◽  
Vol 65 (6) ◽  
pp. 715-723 ◽  
Author(s):  
Jacob Overgaard ◽  
Jamie A. Platts ◽  
Bo B. Iversen
Keyword(s):  
Charge Density ◽  
Electron Density ◽  
Critical Points ◽  
Random Noise ◽  
Topological Analysis ◽  
Carbonyl Complex ◽  
Structure Factors ◽  
Common Motif ◽  
Close Proximity ◽  
Experimental Electron Density

Details of the complex bonding environment present in the molecular centre of an alkyne-bridged dicobalt complex have been examined using a combination of experimental and theoretical charge-density modelling for two compounds which share a central Co2C2 tetrahedral moiety as their common motif. Topological analysis of the experimental electron density illustrates the problem of separating the Co—C bond-critical points (b.c.p.s) from the intervening ring-critical point (r.c.p.), due largely to the flat nature of the electron density in the CoC2 triangles. Such a separation of critical points is immediately obtained from a topological analysis of the theoretical electron density as well as from the multipole-projected theoretical density; however, the addition of random noise to the theoretical structure factors prior to multipole modelling leads to a failure in consistently distinguishing two b.c.p.s and one r.c.p. in such close proximity within the particular environment of this Co2C2 centre.

Electron density and electrostatic potential of KMnF3: a phase-transition study

2004 ◽  
Vol 60 (4) ◽  
pp. 359-368 ◽  
Author(s):  
Yury Ivanov ◽  
Tatsuya Nimura ◽  
Kiyoaki Tanaka
Keyword(s):  
Phase Transition ◽  
Electron Density ◽  
Critical Points ◽  
Room Temperature ◽  
Topological Analysis ◽  
Closed Shell ◽  
Atomic Displacements ◽  
Transition Mechanism ◽  
Fourth Level ◽  
Transition Study

Three accurate X-ray diffraction experiments (Mo Kα, T = 190, 240 and 298 K) were carried out to track the temperature dependence of the electron density in the cubic perovskite potassium manganese trifluoride, KMnF3, from room temperature to just above that of the phase transition to the tetragonal structure (186 K), and to correlate the parameters of the critical points with the phase-transition mechanism. The data obtained were approximated by the Hansen–Coppens multipole model expanded up to hexadecupoles; the anharmonicity of the atomic displacements up to the fourth level was considered. Topological analysis shows only two types of chemical bond at room temperature, Mn—F and K—F. However, at low temperature the K—F bonds blocking the rotation of the MnF6 octahedra are weakened and new Mn—K bonds are formed to keep the crystal structure from disintegrating. The Mn—K bonds become stronger as the temperature approaches 186 K. This rearrangement of chemical bonds can be regarded as a precursor effect, which starts 50–60° above the phase-transition temperature. The effective one-particle potential of the F atom has a single minimum at 298 K and four well separated minima (with a shift of 0.2 Å from the equilibrium position towards the structural holes) at 190 K. Parameters of the critical points of the electron density indicate closed-shell type interactions between K—F and Mn—K pairs, whereas the Mn—F bond can be considered as an intermediate type. The topology of the electrostatic potentials is discussed as well.

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