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 authors synthesize four-coordinated organoaluminium, gallium, and indium compounds from O -[dialkylamino]methyl]phenyllithium, [O -(dimethylamino)phenyl]methithium.
Abstract: Intramolecularly stabilized four-coordinated organoaluminium, -gallium, and-indium compounds R2MC6H4CH2NR'2-(2) (1–7), Me2MCH2C6H4NMe2-(2) (8, 9), Me2MCH2C6H4CH2-NMe2-(2) (10, 11), and Me2GaC6H4NMe2 (12) have been synthesized from O -[(dialkylamino)methyl]phenyllithium, [O -(dimethylamino)phenyl]methyllithium, {O -[(dimethylamino)methyl]phenyl}methyllithium and O -(dimethylamino)phenyllithium, respectively. The 1H-, 13CNMR, and mass spectra of the new compounds and the X-ray crystal structures of 2 and 7 are reported and discussed.
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TL;DR: In this article, the structure of 2,2-dimethylpropionyl chloride with bis(trimethylsilyl)-phosphano]methane is studied.
Abstract: Bis[bis(trimethylsilyl) phosphano]methan reagiert mit 2,2-Dimethyl-pro-pionylchlorid zum Bis[(−2,2-dimethyl-1-trimethylsiloxypropyliden)phosphano]methan. Die Verbindung (Schmp. 39°) wurde bei −95 ± 5°C rontgenstrukturanalytisch untersucht. Sie kristallisiert in der nichtzentrosymmetrischen Raumgruppe Pca21 mit a = 15,61(1);b = 12,84(1); c = 11,84(2) A. Z = 4; R = 0,039.
NMR- und IR-spektroskopische Untersuchungen zeigen, das die Trimethylsilylgruppen an die Sauerstoffatome gebunden sind und die dritte Valenz der zweifach koordinierten Phosphoratome uber Doppelbindungen zu den benachbarten Kohlenstoffatomen abgesattigt wird. Dies wird durch die Rontgenstrukturanalyse bestatigt. Die von der P C-Gruppe ausgehenden Bindungen liegen in einer Ebene; beide Ebenen des Molekuls sind um 85,1° gegeneinander verdreht. Die Anordnung der Substituenten entspricht einem Z/Z-Isomeren. In beiden Molekulhalften weichen mit Ausnahme der Winkel an den Sauerstoffatomen (141°,135°) Bindungsabstande und -winkel nur geringfugig voneinander ab. Charakteristische Werte sind : PC (1,69), PC (1,85), CO (1,35) und SiO (1,67 A) sowie CPC (103°). Der P = C-Abstand und der Winkel am Phosphoratom werden mit Werten aus ahnlichen Verbindungen verglichen. Die Konformation des Molekuls und die Packung im Kristall werden naher untersucht.
Syntheses and Properties of Acylphosphanes. VII. Synthesis, Molecular and Crystal Structure of Bis [(−2,2-dimethyl-1-trimethylsiloxypropyliden) phosphano]methane
In the reaction of 2,2-dimethylpropionyl chloride with bis[bis(trimethylsilyl)-phosphano]methane bis[(−2,2-dimethyl-1-trimethylsiloxypropyliden)phosphano]methane is formed. The structure of the compound (m.p.39°C) was determined at −95 ±5°C by X-ray diffraction. It crystallizes in the non-centrosymmetric space group Pca21 with a = 15.61(1); b = 12.84(1); z = 11.84(2) A. Z = 4; R = 0.039.
N.m.r. and i.r. spectroscopic investigations show the trimethylsilyl groups to be bound to the oxygen atoms and the third valence of the twofold coordinated phosphorus atoms engaged in double bonds to the neighbouring carbon atoms. This is confirmed by the X-ray structure determination. All bonds leading to the PC group lie in a plane; both planes of the molecules are mutually inclined by 85.1°. The arrangement of substituents corresponds to a Z/Z-isomer. In both parts of the molecule bond distances and angles differ only slightly, the angles at the oxygen atoms (141°,135°) excepted. Characteristic values are: PC distance and the angle at the phosphorus atom are compared with values are: PC (1,69), PC (1,85), CO (1,35) und SiO (1,67 A) as well as CPC (103°). The P = C distance and at the phosphorus atom are compared with values of of similar compounds. The molecular conformation and the packing of molecules are studied in detail.
51 citations
TL;DR: In this article, the tris(trimethylsilyl) silyl-rubidium-toluol (2/1) (2 a) and tris (trimmethylsilylsilyl sily l-cesium cesium, toluene (2 /3) (3 a) suitable for X-ray structure analysis are iso- lated.
Abstract: Die Umsetzung der Bis[tris(trimethylsilyl)silyl]-Derivate der Zink-Gruppe mit Kalium, Rubidium und Caesium in n-Pentan liefert Tris(trimethylsilyl)silyl-kalium (1), -rubidium (2) und -caesium (3) als farblose, pyrophore Pulver. Nach Zugabe von Benzol order Toluol zu den solvensfreien Verbindungen bilden sich losliche, farbige Aromaten-Solvate. An den Addukten Tris(trimethylsilyl)silyl-rubidium—Toluol (2/1) (2 a) und Tris(trimethylsilyl)silyl-caesium—Toluol (2/3) (3 a) wurden Kristallstrukturanalysen durchgefuhrt [2a: orthorhombisch; P212121; a = 1 382,1(3); b = 1 491,7(5); c = 2 106,3(6) pm; Z = 4 (Dimere); 3a: orthorhombisch; P212121; a = 2 131,0(6); b = 2 833,1(2); c = 925,2(2) pm; Z = 4 (Dimere)]. Demzufolge liegen sie im Festkorper als dimere Molekule mit viergliedrigen, gefalteten Rb2Si2-bzw. Cs2Si2-Ringen vor. Die mit 100 bis 104° relativ kleinen SiSiSi-Winkel deuten ebenso wie die im 29Si-NMR-Spektrum beobachtete extreme Tieffeldverschiebung der Resonanzen des zentralen Siliciumatoms auf eine weitgehende Ladungsubertragung von den Alkalimetallatomen auf das Tris(trimethylsilyl)silyl-Fragment, d. h. vorwiegend ionische Wechselwirkungen in den Ringen aus Alkalimetall- und Siliciumatomen hin.
About the Synthesis of Tris(trimethylsilyl)silyl Potassium, Rubidium and Cesium and the Molecular Structures of two Toluene Solvates.
Solventfree tris(trimethylsilyl)silyl potassium (1), rubidium (2) and cesium (3) are obtained by the reaction of the zink group bis[tris(trimethylsilyl)silyl] derivatives with the appropriate alkali metal in n-pentane. Addition of benzene or toluene to the colourless powders yields deeply coloured solutions. From these solutions single crystals of tris(trimethylsilyl)silyl rubidium—toluene (2/1) (2 a) and tris(trimethylsilyl)silyl cesium—toluene (2/3) (3 a) suitable for X-ray structure analysis are iso- lated [2a: orthorhombic; P212121; a = 1 382.1(3); b = 1 491.7(5); c = 2 106.3(6) pm; Z = 4 (dimers); 3a: orthorhombic; P212121; a = 2 131.0(6); b = 2 833.1(2); c = 925.2(2) pm; Z = 4 (dimers)]. The central structure moieties are folded four-membered Rb2Si2 and Cs2Si2 rings, respectively. Small SiSiSi angles (100 to 104°) on the one hand and extreme highfield 29Si-NMR shifts of the central silicon atoms on the other hand indicate a strong charge transfer from the alkali metal atoms to the tris(trimethylsilyl)silyl fragments, i.e. mainly ionic interactions between alkalimetal and silicon atoms.
51 citations
TL;DR: A series of monocyclopentadienyltitanium complexes containing the 1-(2-phenylethyl)-2,3,4,5-tetramethylcyclopentadiyl ligand (C5Me4CH2CH2Ph) have been synthesized and characterized as mentioned in this paper.
51 citations
TL;DR: The crystal and molecularn structure of (π-cyclopentadienyl)(π-cyclobutadiene)- cobalt (C 5 H 5 )(C 4 H 4 ) has been determined by single crystal X-ray diffraction techniques using three-dimensional data gathered at ca.-35 C by counter methods as discussed by the authors.
51 citations
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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
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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