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 X-ray structures of N, N,N, N′,N′-Tetramethyloxamide and -monothiooxamide have been determined from Xray data, and refined to R = 0.065 (2) and 0.057 (3) respectively.
Abstract: Die Strukturen der Titelsubstanzen (2 und 3) wurden rontgenographisch bestimmt und bis zu R-Werten von 0.065 (2) bzw. 0.057 (3) verfeinert. 2 kristallisiert in der Raumgruppe C2/c, 3 in der Raumgruppe P21/c. – 2 liegt im Kristall in einer Konfiguration vor, bei der die beiden Molekulhalften um 71.4° gegeneinander verdrillt sind; bei 3 betragt dieser Winkel 87.4°.
Twisted Oxalic Acid Derivatives The Crystal and Molecular Structure of N,N,N′,N′-Tetramethyloxamide and -monothiooxamide
The structures of the title compounds (2 and 3) have been determined from X-ray data, and refined to R = 0.065 (2) and 0.057 (3) respectively. 2 crystallizes in the space group C2/c, 3 in the space group P21/c. – In the crystal 2 exhibits a configuration in which the two halves of the molecule are twisted by 71.4°. This angle amounts to 87.4° in 3.
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TL;DR: In this article, the Keto-Enol Tautomer is found to have a strong temperature dependence of the keto-enol equilibrium, which is a characteristic for the formation of the enol tautomer.
Abstract: Aus Lithium-dihydrogenphosphid · DME (1) [12] und cyclo-Hexoyl- bzw. Adamant-1-oyl-chlorid im Molverhaltnis 3:2 zugangliches Lithium-di-cyclo-hexoylphosphid · DME und -diadamant-1-oylphosphid · 2THF 1) reagieren mit 85proz. Tetrafluoroborsaure · Diethylether-Addukt zu Di-cyclo-hexoyl- 1b) und Diadamant-1-oylphosphan (1 c). Die Lage des Keto-Enol-Gleichgewichts zwischen 203 und 343 K sowie thermodynamische Daten zur Bildung des Enol-Isomers ΔH0= −4,3kJ.Mol−1; ΔS0;=−9,2 J · mol−1 · K−1 () wurden NMR-spektroskopisch an einer 2 M Losung des bei +20°C flussigen Di-cyclo-Hexoyl-Derivates 1b in d8-Toluol ermittelt und mit Werten von 1,3-Diketonen verglichen.
Das farblose, sich aus Benzol in dunnen Plattchen abscheidende Enol-Tautomer des Diadamant-1-oylphosphans (E-1 c) kristallisiert monoklin in der Raumgruppe P21/c {a = 722,2(2) b = 1085,5(4); c = 2434,8(5) pm; s = 96,43(2)° bei - 100 ± 3°C; Z = 4}. Nach den Ergebnissen der Rontgenstrukturanalyse (Rw=0,033) weist das Molekul in beiden des Halften des Enolrings nahezu identische Bindungslangen und -winkel auf PC 179/180; CO 130/129; CC(Adamant-1-yl) 152/153 pm; CPC 99°; PCO 124°/124°; PCC 120°/120°; CCO 116°/116°. Die Geometrie der sehr starken, aber vermutlich asymmetrischen O‥H‥O-Brucke wird diskutiert (OH 120/130; O‥O 245 pm).
Acyl- and Alkylidenephosphines. XXXII. Di-cyclohexoyl- and Diadamant-1-oylphosphine – Keto-Enol Tautomerism and Structure
Lithium dihydrogenphosphide · DME (1) [12] and cyclo-hexoyl or adamant-1-oyl chloride react in a molar ratio of 3:2 to give lithium di-cyclo-hexoylphosphide · DME and the corresponding diadamant-1-oylphosphide.2THF (1) resp. Treatment of these two compounds with 85% tetrafluoroboric acid. diethylether adduct yields di-cyclo-hexoyl- (1b) and diadamant-1-oylphosphine (1c). In nmr spectroscopic studies 1b over a range of 203 to 343 K, a strong temperature dependence of the keto-enol equilibrium is found; thermodynamic data characteristic for the formation of the enol tautomer (ΔH0 = −4.3 kJ. mol−1; ΔS0 = −9.2 J. mol−1. K (−1) are compared of 1,3-diketones.
The enol tautomer of diadamant-1-oylphosphine (E-1c) as obtained from a benzene solution in thin colourless plates, crystallizes in the monoclinic space group P21/c {a = 722.2(2); b = 1085.5(4); c = 2434.8(5) pm; s = 96.43(2)° at –100 ± 3°C; Z = 4}. An X- ray structure analysis (Rw = 0.033) shows bond lengths and angles to be almost identical within the enolic system (PC 179/180; CO 130/129; CC(adamant-1-yl) 152/153 pm; CPC 99°; PCO 124°/124°; PCC 120°/120°; CCO 116°/116°. The geometry of the very strong, but probably asymmetric O‥H‥O bridge is discussed (OH 120/130, O‥O 245 pm).
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TL;DR: From the reaction of nitratotriphenyltin with bis(diphenylphosphinyl)ethane, a dinuclear adduct of formula [{SnPh3(NO3)}2{OPPh2(CH2)2Ph2PO}] has been obtained, in which the organic ligand is present in oxidised form as discussed by the authors.
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TL;DR: In this article, a trigonal bipyramidal [Ni(SnPh 3 )(np 3 )] + cations and BPh 4 -anions with a Ni-Sn bond distance of 2.088 was determined by X-ray diffraction.
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TL;DR: In this article, the double-branched Fischer-type carbene complexes of the Fischer type bearing the carbene carbon atom and the double bond incorporated in the same ring are described.
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References
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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