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 reaction of (AsPh4)2[TcN(CN)4(OH2)]·5H2O (1) with KCN and added AsPh4Cl in CH3CN/H 2O yields crystals of (asPh4)-2[tcN (CN) 4(OH 2]·5 H2O(1).
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TL;DR: The crystal structure of 3,4 pyridinedicarboxylic acid (3,4-pyridine) has been determined by the method of X-ray diffraction.
Abstract: The crystal structure of cinchomeronic acid (3,4-pyridinedicarboxylic acid) has been determined by the method of X-ray diffraction. The crystals are orthorhombic, with a space group of P212121, and with cell dimensions of a=11.211, b=11.206, and c=5.285 A. The structure was determined by the method of symbolic addition. The final R value was 5.90% for 828 observed reflections. The molecule takes the form of a zwitter ion in the crystal. The pyridine ring has, approximately, the C2v symmetry. One carboxyl group consists of C=O and C–O (H) groups, while the other consists of two O(Remark: Graphics omitted.)O groups. These carboxyl groups twist out of the plane of a pyridine ring by 39.6° and 73.0° respectively. The hydrogen bonds are in the forms of two spirals around the two-fold screw axes parallel to the c axis, thus linking the molecules three-dimensionally. There are four molecules per turn of the spiral along the c axis. The carbonyl oxygen atom O(2) is free from the hydrogen bond, while the nitrogen ...
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TL;DR: The crystal structure of triglycine sulphate after X-irradiation/field treatment is reported in this paper, where a hydrogen atom is found bonded to a sulphate oxygen, thus forming a bisulphate ion.
Abstract: The crystal structure of triglycine sulphate after X-irradiation/field treatment is reported The crystals are monoclinic with unit cell dimensions a = 9421 (1), b = 12656(1), c = 5732(1) A, β = 11035 (1)° space group P21, Z = 2 Least-squares refinement using 1267 independent X-ray reflections hasreached R = 0049The structure is basically similar to that determined at low X-ray dosage but there is one crucial difference The non-planar glycine, glycine I, is found to be a neutral molecule rather than a glycinium ion Instead a hydrogen atom is found bonded to a sulphate oxygen, thus forming a bisulphate ion The structure could therefore be designated diglycine glycinium bisulphate The inhibition of ferroelectric polarity reversal in irradiation/field treated triglycine sulphate is discussed in the light of these results
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TL;DR: The title compound (molecular formula C 25 H 30 Fe) forms prismatic crystals from hexane which belong to the monoclinic space group P 2 1 / n with lattice constants a 9.486, b 12.134, c 16.024, β 93.12, and Z = 4.12.
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TL;DR: In this article, a computer simulated mechanical model for molecular packing analysis of benzene C6H6 at 293 K has been proposed to account for short interatomic distances, especially under pressure.
Abstract: With a computer simulated mechanical model for molecular packing analysis, the reconstitution and identification of the intermediate pressure‐induced phase II of solid benzene C6H6 at 293 K, has been undertaken. The atom‐atom intermolecular potential of the Buckingham type was generalized to account for short interatomic distances, especially under pressure. The model includes thermal motion and molecular deformation effects. Various crystal structures calculated in the pressure range of phase II and checked by their reticular distances and structure factors, are compared with the structure IIo proposed for this phase. Among them two possible monoclinic structures IIc and IIc′ have been evidenced by the calculation. Structure IIc has energy and enthalpy levels lower than that of phases Ic and IIIc, in the pressure range 0.5
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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