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

Сташ, А. И.; Tanaka, Katsufumi; Shiozawa, Kazunari; Makino, Hiroki; Tsirelson, Vladimir G.

doi:10.1107/s0108768105014114

Cited by 27 publications

(21 citation statements)

References 70 publications

(96 reference statements)

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“…As a consequence, the respective bond paths could not be traced either, and ring critical points (RCPs) as well as a cage critical point (CCP) between the sodium atom and the Cp ring could not be found. Such a situation has been similarly reported in the case of slipping indenyl ligands, [19] but the bonding situation could clearly be described as intermediate between h 1 and h 2 . It is well-known that the localization of critical points in the very shallow charge density between metal ions and p ligands is difficult.…”

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confidence: 69%

Strong Intermolecular Interactions Shaping a Small Piano‐Stool Complex

et al. 2013

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Dedicated to Professor Bernt Krebs on the occasion of his 75th birthdaySodium cyclopentadienide is a very important precursor for metallocene synthesis of s and related sandwich-and half sandwich-complexes of d-block elements by transmetallation or salt elimination routes. [1] Parent sodium cyclopentadienide (NaCp), which is easily prepared from dicyclopentadiene and sodium metal in laboratory scale, [2] is virtually insoluble in common organic solvents except tetrahydrofurane (THF), and its solid-state structure of infinite coordination polymer chains of the formula [h 5 -CpNa] 1 was determined [3] only a century after the initial discovery of the substance class. [4] There have been numerous reports of solid-state structures containing CpNa moieties. These smaller aggregates ultimately are nothing else than ligand-terminated fragments derived from the polymeric parent coordination polymer. However, few structural reports contain monomeric sodocene [6] [NaCp 2 ] À , inverse sandwich complexes [7] [L n NaCpNaL n ] + , or heterobimetallic sandwich complexes [8] (with n donating solvent molecules L), and only two different structures of piano stool-like complexes of the type [L n NaCp] have been published. [9] The latter have been restricted to bulky multidentate ligands L with resulting solid-state structures quite contrary to the small archetypical cyclopentadienyl carbonyl d-block metal complexes.The Cp-metal interaction in organo alkali metal species is dominated by the Coulomb attraction between anion and cation when compared to transition-metal complexes, where covalent contributions are more significant. [10] The donor ligand properties, including dipole moments, hapticity, and steric demand, play the most important role for the formation of the molecular assembly. [11] In the course of our work on the synthesis of reactive intermediates with organo alkali metal species, [12] it turned out that ammonia as coordinating solvent facilitates the synthesis of the missing link between the solvent-separated ion pair [L n Na] + [Cp] À and sandwich-or inverse sandwich complexes. The three-legged piano stool contact ion-pair complex [CpNa(NH 3 ) 3 ] (1), reported herein, was only feasible by crystallization from a saturated solution of ammonia in THF at À40 8C.We were able to obtain a high-resolution X-ray diffraction data set of a single crystal of 1 and conducted a XD2006 multipole refinement (Figure 1). A topological analysis according to the framework of Baders quantum theory of atoms in molecules (QTAIM) on the charge density map from an XD2006 multipolar refinement was carried out. [13] As the general structure of 1 is clear and not tainted by secondary (packing) effect of bulky donor bases (see Figure 1), it is a paradigmatic case to study intra-and intermolecular forces in the solid state.Most obviously, the sodium atom is shifted away from the geometric center of the Cp ring by 0.172 . A search in the Cambridge Structural Database (CSD) reveals that the observed shift of the sodium atom in 1 is unusual. ...

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Strong Intermolecular Interactions Shaping a Small Piano‐Stool Complex

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“…scribed elsewhere [27,97]. Bonding analysis in terms of the critical points properties is also given elsewhere [18].…”

Section: Discussionmentioning

confidence: 99%

“…

where gðr; r 0 Þ and Gðr; r 1 Þ are one-electron and two-electron density matrices, respectively, Z a is the charge the nucleus a, e and m are the electronic charge and mass, respectively, and V n is the nuclear repulsion. In particular, it facilitates recognition of the type of atomic interactions from the properties of bond critical points at r b À h e ðr b Þ < 0 and gðr b Þ=rðr b Þ < 1, and ' 2 rðr b Þ < 0, are observed for shared-type atomic interactions whereas h e ðr b Þ q 0, gðr b Þ=rðr b Þ > 1, and ' 2 rðr b Þ > 0 are typical for intermediate and closed-shell interactions [16,18,23,27].Bader has also stressed [26, 28] that the potential energy density represents the field of the virial of the Ehrenfest force [29] acting on an electron at r, the virial field vðrÞ. In particular, it facilitates recognition of the type of atomic interactions from the properties of bond critical points at r b À h e ðr b Þ < 0 and gðr b Þ=rðr b Þ < 1, and ' 2 rðr b Þ < 0, are observed for shared-type atomic interactions whereas h e ðr b Þ q 0, gðr b Þ=rðr b Þ > 1, and ' 2 rðr b Þ > 0 are typical for intermediate and closed-shell interactions [16,18,23,27].

Bader has also stressed [26, 28] that the potential energy density represents the field of the virial of the Ehrenfest force [29] acting on an electron at r, the virial field vðrÞ.

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confidence: 99%

Interpretation of Experimental Electron Densities by Combination of the QTAMC and DFT

Tsirelson

2007

The Quantum Theory of Atoms in Molecules

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where gðr; r 0 Þ and Gðr; r 1 Þ are one-electron and two-electron density matrices, respectively, Z a is the charge the nucleus a, e and m are the electronic charge and mass, respectively, and V n is the nuclear repulsion. These functions are related by the local form of the virial theorem [20]:Finally, the density of the total electronic energy is defined as:Exploration of energy distributions in molecules by use of wavefunction-based calculations [21][22][23][24][25][26] has revealed that analysis of the local electronic energy is a direct approach to characterization of bonding in molecules and crystals. In particular, it facilitates recognition of the type of atomic interactions from the properties of bond critical points at r b À h e ðr b Þ < 0 and gðr b Þ=rðr b Þ < 1, and ' 2 rðr b Þ < 0, are observed for shared-type atomic interactions whereas h e ðr b Þ q 0, gðr b Þ=rðr b Þ > 1, and ' 2 rðr b Þ > 0 are typical for intermediate and closed-shell interactions [16,18,23,27].Bader has also stressed [26, 28] that the potential energy density represents the field of the virial of the Ehrenfest force [29] acting on an electron at r, the virial field vðrÞ. Irrespective of the type of atomic interaction, each bond path in the electron density at equilibrium geometry is homeomorphically mirrored by a virial path, a line of maximum negative potential energy density linking the same nuclei [24]. The presence of the bond paths and virial path provides, according to Ref. [26], an indicator of bonding atomic interaction. A network of the virial and bond paths defines a molecular graph, which is independent of the nuclear vibrations in a stable system.It was, of course, a challenge to perform real-space energy analysis of bonding on the basis of the experimental electron density (ED). There is, fortunately, a theory which establishes the interconnection between the electron density and energy densities of different kinds. This is the density-functional theory (DFT) [30][31][32][33][34][35][36][37][38][39][40] which exploits r as a main variable and determines all the properties of atoms, molecules, and crystals in the ground electronic state [41]. Thus, DFT is a basis for quantitative characterization of bonding in terms of energy densities and other functions related to electron density. It is, therefore, attractive to combine the formalism of the DFT with experimental electron density to analyze the nature of atomic and molecular interactions in molecules and solids in terms of the local energies. This might, in principle, be done in two different ways. The exact functionals connecting r and the energy densities of electrons -the kinetic, potential, exchange and correlation densities -are, in general, unknown [41]. DFT methods therefore use either the Kohn and Sham orbital scheme [42] or approximate functionals with explicit (but nonunique) dependence of these functions on r and its derivatives [31]. The former approach might be achieved by use of an idempotent one-electron density matrix iteratively reconstructed from ...

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“…A Pilatus 100 k area detector is mounted on the diffractometer arm. 11 The primary sample motions (2S) are comprised of η and χ . In this arrangement, η = 0 • is defined when the reference vector, or sample surface normal is vertical.…”

Section: A Diffraction Geometrymentioning

confidence: 99%

Modular instrument mounting system for variable environment in operando X-ray experiments

Folkman

Highland

Perret

et al. 2013

Review of Scientific Instruments

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In the growing field of in operando and in situ X-ray experiments, there exists a large disparity in the types of environments and equipment to control them. This situation makes it challenging to conduct multiple experiments with a single mechanical interface to the diffractometer. Here, we describe the design and implementation of a modular instrument mounting system that can be installed on a standard six-circle diffractometer (e.g., 5021 Huber GmbH). This new system allows for the rapid changeover of different chambers and sample heaters and permits accurate sample positioning (x, y, z, and azimuthal rotation) without rigid coupling to the chamber body. Isolation of the sample motion from the chamber enclosure is accomplished through a combination of custom rotary seals and bellows. Control of the pressure and temperature has been demonstrated in the ranges of 10(-6)-10(3) Torr and 25°C-900°C, respectively. We have utilized the system with several different modular instruments. As an example, we provide in situ sputtering results, where the growth dynamics of epitaxial LaGaO3 thin films on (001) SrTiO3 substrates were investigated.

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

Cited by 27 publications

References 70 publications

Strong Intermolecular Interactions Shaping a Small Piano‐Stool Complex

Strong Intermolecular Interactions Shaping a Small Piano‐Stool Complex

Interpretation of Experimental Electron Densities by Combination of the QTAMC and DFT

Modular instrument mounting system for variable environment in operando X-ray experiments

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