Coherent X‐Ray Scattering for the Hydrogen Atom in the Hydrogen Molecule
01 May 1965-Journal of Chemical Physics (American Institute of PhysicsAIP)-Vol. 42, Iss: 9, pp 3175-3187
TL;DR: In this paper, the x-ray form factors for a bonded hydrogen in the hydrogen molecule have been calculated for a spherical approximation to the bonded atom, and the corresponding complex scattering factors have also been calculated.
Abstract: The x‐ray form factors for a bonded hydrogen in the hydrogen molecule have been calculated for a spherical approximation to the bonded atom. These factors may be better suited for the least‐squares refinement of x‐ray diffraction data from organic molecular crystals than those for the isolated hydrogen atom. It has been shown that within the spherical approximation for the bonded hydrogens in H2, a least‐squares refinement of the atomic positions will result in a bond length (Re value) short of neutron diffraction or spectroscopic values. The spherical atoms are optimally positioned 0.07 A off each proton into the bond. A nonspherical density for the bonded hydrogen atom in the hydrogen molecule has also been defined and the corresponding complex scattering factors have been calculated. The electronic density for the hydrogen molecule in these calculations was based on a modified form of the Kolos—Roothaan wavefunction for H2. Scattering calculations were made tractable by expansion of a plane wave in spheroidal wavefunctions.
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TL;DR: In this article, the tungsten silene complex Cp2W(η2-Me2SiCH2) with germanes HGeR3 (GeR 3 = GeMe3 (2), GeMe2H (3a), GetBu2H(3b), GePh2Cl (3c)).
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TL;DR: The title compound 3 has been synthesized along the hydride route by treatment of the solvent complex (η5-C5Me5)Mn(CO)2(THF) (THF = tetrahydrofuran) with monogermane, GeH4, in the presence of sulfuric acid as mentioned in this paper.
Abstract: The title compound 3 has been synthesized along the hydride route by treatment of the solvent complex (η5-C5Me5)Mn(CO)2(THF) (THF = tetrahydrofuran) with monogermane, GeH4, in the presence of sulfuric acid. A single-crystal X-Ray structural analysis revealed two conformers of 3 being present in the solid state in a 1:1 ratio (C2/c, monoclinic). Pairs of carbonyl groups almost eclipse each other, while the remaining two CO ligands an exhibit an anti-conformation relative to the strictly linear MnGeMn framework. Both enantiomeric conformers are geometrically related by a 180°-rotation of a (C5Me5)Mn(CO)2 fragment around the Mn, Ge, Mn vector. The manganese — germanium bond lenghts average 2.18(2) A and thus correspond to considerable multiple bonding between these atoms.
Mehrfachbindungen zwischen Hauptgruppenelementen und Ubergangsmetallen, III Synthese, Einkristall- und Molekulstruktur von μ-Germanium-bis[dicarbonyl(η5-pentamethylcyclopentadienyl)manganl], μ-Ge-[(η5-C5Me5)Mn(CO)2]2
Die Titelverbindung 3 wurde nach der Hydrid-Methode durch Behandlung des Solvens-Komplexes (η5-C5Me5)Mn(CO)2(THF) (THF = Tetrahydrofuran) mit Monogerman, GeH4, in Gegenwart von Schwefelsaure synthetisiert. Eine Rontgenstrukturanalysse weist das Vorliegen zweier konformationsisomerer Molekule im Kristall nach (C/c, monoklin). Bezuglich des streng linearen MnGeMn-Gerusts stehen zwei Carbonyl-Gruppen annahernd auf Deckung, wahrend die anderen beiden anti-Konformation besitzen. Die aquimolar in der Elementarzelle vorlienanden enantiomeren Konformeren leiten sich geometrisch voneinander durch 180°-Drehung einer (η5-C5Me5)Mn(CO)2-Baugruppe um den Mn, Ge, Mn-Vektor ab. Die Mangan — Germanium-Bindungslangen betragen 2.18(2) A (Mittelwert) und weisen damit erheblichen Mehrfachbindungscharakter auf.
37 citations
TL;DR: In this paper, a method for the synthesis of isoselenocyanates, malonitrile or 2-cyanoacetate, and 1,2-dibromoethane or α-halogenated carboxylic acid derivatives is presented.
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TL;DR: This paper presents the first crystallographically characterized, contiguous series of 4-coordinate transition metal compounds having a common organometallic ligand set and differing only in the identity and oxidation state of the metal.
Abstract: This paper presents the first crystallographically characterized, contiguous series of 4-coordinate transition metal compounds having a common organometallic ligand set and differing only in the identity and oxidation state of the metal. This series spans from d7 to d9 with overlapping examples for d8. M = Co(II), Ni(II), Cu(III), and Cu(II).
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TL;DR: In this article, it is suggested that the latter is first formed by loss of Me 3 SiF from (MeSi) 3 CSiPh 2 F, and then internal cyclizations involving addition of aryl CH bonds across SiC bonds then occur to give the observed products.
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TL;DR: In this article, the quantum mechanical wave functions of molecules are discussed and an attempt is made to effect a simultaneous regional and physical partitioning of the molecular density, the molecular pair density, and the molecular energy, in such a way that meaningful concepts can be associated with the density and energy fragments thus formed.
Abstract: The quantum mechanical wave functions of molecules are discussed. An attempt is made to effect a simultaneous regional and physical partitioning of the molecular density, the molecular pair density, and the molecular energy, in such a way that meaningful concepts can be associated with the density and energy fragments thus formed. The origin of chemical binding is interpreted in terms of the concepts formulated in the partitioning process. (T.F.H.)
768 citations
576 citations
TL;DR: The solution of Schroedinger's equation for the normal hydrogen molecule is approximated by the function $C[{e}^{\ensuremath{-}\frac{z({r}_{1}+{p}_{2})}{a}}+{e^{\ensem{-]-{m{e})+{m}−m{n}−n}]$ where m is the distance of one of the electrons to the two nuclei, and r is the distances of one electron to the other electron.
Abstract: The solution of Schroedinger's equation for the normal hydrogen molecule is approximated by the function $C[{e}^{\ensuremath{-}\frac{z({r}_{1}+{p}_{2})}{a}}+{e}^{\ensuremath{-}\frac{z({r}_{2}+{p}_{1})}{a}}]$ where $a=\frac{{h}^{2}}{4{\ensuremath{\pi}}^{2}m{e}^{2}}$, ${r}_{1}$ and ${p}_{1}$ are the distances of one of the electrons to the two nuclei, and ${r}_{2}$ and ${p}_{2}$ those for the other electron. The value of $Z$ is so determined as to give a minimum value to the variational integral which generates Schroedinger's wave equation. This minimum value of the integral gives the approximate energy $E$. For every nuclear separation $D$, there is a $Z$ which gives the best approximation and a corresponding $E$. We thus obtain an approximate energy curve as a function of the separation. The minimum of this curve gives the following data for the configuration corresponding to the normal hydrogen molecule: the heat of dissociation = 3.76 volts, the moment of inertia ${J}_{0}=4.59\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}41}$ gr. ${\mathrm{cm}}^{2}$, the nuclear vibrational frequency ${\ensuremath{
u}}_{0}=4900$ ${\mathrm{cm}}^{\ensuremath{-}1}$.
292 citations
TL;DR: In this paper, a simple wave function for the normal state of the hydrogen molecule, in which both the atomic and ionic configurations are taken into account, was set up and treated by a variational method.
Abstract: A simple wave function for the normal state of the hydrogen molecule, in which both the atomic and ionic configurations are taken into account, was set up and treated by a variational method. The dissociation energy was found to be 4.00 v.e. as compared to the experimental value of 4.68 v.e. and Rosen's value of 4.02 v.e. obtained by use of a function involving complicated integrals. It was found that the atomic function occurs with a coefficient 3.9 times that of the ionic function. A similar function with different screening constants for the atomic and ionic parts was also tried. It was found that the best results are obtained when these screening constants are equal. The addition of Rosen's term to the atomic‐ionic function resulted in a value of 4.10 v.e. for the dissociation energy.
253 citations
133 citations