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 crystal structure of N-Nitrosodimethylamine was determined from single crystal low temperature X-ray counter data collected at − 130°C.
Abstract: Die Struktur des festen N-Nitrosodimethylamins bei − 130°C wurde durch Rontgenstruktur-analyse bestimmt. Das Molekul ist im Kristall exakt planar. Die Bindungslangen bei − 130°C sind: N N 1.320(6), N O 1.260(6), C N 1.461(7) und 1.465(7) A. Senkrecht zu den Molekulebenen verlaufende intermolekulare π-Wechselwirkungen stabilisieren einen hoheren Anteil der polaren Struktur
am Bindungszustand gegenuber dem freien Molekul der Gasphase.
Crystal Structure of N-Nitrosodimethylamine
The crystal structure of the title compound has been determined from single crystal low temperature X-ray counter data collected at − 130°C. Bond lengths in the exactly planar molecule were found to be N N 1.320(6), N O 1.260 (6), C N 1.461 (7) and 1.465 (7) A. The bonding in the molecule is significantly closer to the polar structure
compared to the free molecule in the gas phase, this being stabilised by intermolecular π interactions perpendicular to the planes of the molecules.
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TL;DR: In this paper, the absolute configuration of the chiral sulfur of this stereoisomer was determined by X-ray crystallography, and it was obtained in high enantiomeric purity by microbiological sulfoxidation of the corresponding sulfide.
Abstract: (Z)-(R)-(+)-Methyl 2-phenyl-2-(pyrid-4-yl) vinyl sulfoxide was obtained in high enantiomeric purity by microbiological sulfoxidation of the corresponding sulfide by Mortierella isabellina . The (R) absolute configuration of the chiral sulfur of this stereoisomer was determined by X-ray crystallography.
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TL;DR: In this paper, a high-precision neutron diffraction refinement of the structure of potassium hydrogen bis(acetylsalicylate), the acid salt of aspirin, has been carried out.
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TL;DR: In this paper, the authors showed that tris(trimethylsilylmethyl)alane can be used to obtain a centrosymmetric dimer (Me3SiCH2)2Al-P(SiMe3)2] with crystallographic C2 symmetry.
Abstract: Treatment of calcium bis[bis(trimethylsilyl)amide] with two equivalents of tris(trimethylsilylmethyl)alane yields (Me3SiCH2)2Al–N(SiMe3)2 (1) and the dimer [(Me3Si)2N–Ca(μ–CH2SiMe3)2Al(CH2SiMe3)2]2 (2). The five-coordinate bridging carbon atoms show Ca–C bond lengths of 264 and 268 pm. A similar reaction with calcium bis[bis(trimethylsilyl)phosphanide] gives the dimer [(Me3SiCH2)2Al–P(SiMe3)2]2 (3) with crystallographic C2 symmetry. A calcium-containing species is not isolable, however, in the presence of DME – ether cleavage reactions and the formation of the centrosymmetric dimer [(Me3SiCH2)2Al–OCH2CH2OMe]2 (4) are observed. The central moiety is an Al2O2 cycle with fivefold coordinated aluminium centers.
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TL;DR: In this article, the pyrrolyl complexes (C5H5)2Lu(NC4H4) (1) and C5Me5 2Y(NC 4H4)(THF) (2), respectively, were reported and discussed, and the 1H- and 13C-NMR spectra of the new compounds were analyzed.
Abstract: The reactions of Na(NC4H4) with (C5H5)2LuCl(THF) and (C5Me5)2YCl(THF) result in the formation of the pyrrolyl complexes (C5H5)2Lu(NC4H4) (1) and (C5Me5)2Y(NC4H4)(THF) (2), respectively. Na(NC4H2Me2) reacts with (C5H5)2LuCl(THF) to form (C5H5)2Lu(NC4H2Me2(THF) (3). The 1H- and 13C-NMR spectra of the new compounds as well as the X-ray single-crystal structure analysis of 3 are reported and discussed.
27 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