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: Magnesium bis[bis(trimethylsilyl)phosphide as discussed by the authors has been shown to have a trigonal pyramidal coordination, and it is distorted tetrahedrally surrounded by two oxygen and two phosphorus atoms with MgP-and MgO-bond lengths of 248.7 (2) and 204.7(5) pm, respectively.
Abstract: Magnesium-bis[bis(trimethylsilyl)phosphanid] · DME kristallisiert in der tetragonalen Raumgruppe I4c2 mit a = 1652,9(2); c = 2282,6(5) pm und Z = 8. Das Magnesiumatom ist von zwei Sauerstoff- und zwei Phosphoratomen mit MgP- und MgO-Bindungslangen von 248,7(2) bzw. 204,7(5) pm verzerrt tetraedrisch umgeben. Das Phosphoratom ist trigonal pyramidal koordiniert.
Molecular and Crystal Structure of Magnesium Bis[bis(trimethylsilyl)phosphide] · DME
Magnesium bis[bis(trimethylsilyl)phosphide] crystallizes in the tetragonal space group I4c2 with a = 1652.9(2); c = 2282.6(5) pm and Z = 8. The magnesium atom is distorted tetrahedrally surrounded by two oxygen and two phosphorus atoms with MgP- and MgO-bond lengths of 248.7(2) and 204.7(5) pm, respectively. The phosphorus atom displays a trigonal pyramidal coordination.
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TL;DR: In this article, the authors report the first quantitative theoretical analysis of the energetics of intramolecular H···S bonds in the recently synthesized triazacyclononane complex.
Abstract: Extended Huckel, DFT, and ab initio MP2 calculations have been carried out to rationalize the unprecedented structural characteristics of the recently synthesized complex (μ−η1-S2)3 (Fe-TACN)2 (TACN = triazacyclononane). The orbital interaction diagram between the metal−macrocycle dimer and the three disulfide ligands accounts for some of the observed properties of the complex: diamagnetism, existence of an Fe−Fe single bond, nucleophilicity of the terminal sulfur atoms. The unprecedented occurrence of a M2S6 core, as the very unusual μ−η1 coordination of the S2 ligands, however, requires further analysis. It was assumed that the key to the structural singularities of this complex should be sought in the network of intramolecular H···S bonds revealed by the crystallographic analysis and involving all six NH groups and all three terminal S atoms. We therefore report the first quantitative theoretical investigation of the energetics of intramolecular H···S bonds. Geometry optimizations have been carried ou...
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TL;DR: In this paper, an x-ray single crystal diffraction was used to crystallize an air-sensitive red chystals in space group C2/c with four molecules in a unit cell of dimensions a = 14.45(2), b= 14.12(2) A, c=14.70(3) A and β = 100° 50(15)′.
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TL;DR: Copper(I) is five coordinate in (1,10-phenanthroline)tetrahydroborato(triphenylphosphine)copper( I).
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TL;DR: In this paper, a very unusual new copper(II) complex with isonicotinate N-oxide (N-inicO), Cu4(N-oxide)4SO4(OH)2(H2O)4 has been prepared and its crystal and molecular structure determined from three dimensional X-ray diffraction data.
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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
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