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Journal ArticleDOI

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.
Citations
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Journal ArticleDOI
TL;DR: In this article, wide-angle x-ray scattering (WAXS) of glassy PET and two samples annealed at 190°C for 15 and 30 min were analyzed by differential radial distribution function (DRDF) methods.
Abstract: Wide-angle x-ray scattering (WAXS) of glassy PET and two samples annealed at 190°C for 15 and 30 min were analyzed by differential radial distribution function (DRDF) methods. The corrected intensity profile of the glassy sample show three peaks at 4.19, 2.13, and 1.19 A. The sample annealed for 15 min shows splitting of the 4.19 A peak into three peaks at 3.50 (d100), 3.96 (d110), and 5.21 (mainly d010 and unresolved d011-and d-111) A. Longer annealing for 30 min produces two more peaks at 4.11 (d-111) and 5.40 (d011) A. Annealing does not affect the peaks at 1.19 and 2.13 A (which are caused by first and second nearest atoms in the chain). The DRDFs of all three samples are similar in some respects as all show intrachain peaks at ∼ 1.45, 2.45, and 4.05 A. From theoretical calculations of the intrachain distances and their contributions to the DRDF, the peak at the 4.90 A in the glassy sample was found to be mainly due to intermolecular distances. Since the peaks above 4.9 A are relatively weak,...

26 citations

Journal ArticleDOI
TL;DR: The Pd atom in these structures lies on the crystallographic inversion center; in a square-planar coordination geometry made by two sulfur and two nitrogen atoms of the ligands, both in trans positions as mentioned in this paper.
Abstract: Mononuclear palladium(II) complexes containing both pyrazole-type ligands and thiocyanate, of general formula [Pd(SCN)2(L)2] {L = pyrazole (HPz) and 1-phenyl-3-methylpyrazole (phmPz)} have been prepared and characterized by elemental analysis, i.r. and n.m.r. spectroscopy and by single crystal X-ray diffraction methods. The Pd atom in these structures lies on the crystallographic inversion center; in a square-planar coordination geometry made by two sulfur and two nitrogen atoms of the ligands, both in trans positions.

26 citations

Journal ArticleDOI
TL;DR: In this paper, the 1H and 13C-NMR spectra of the new compounds as well as the single-crystal X-ray structural analyses of the polymeric metallocenes 5 and 6 are described and discussed.
Abstract: [(Dimethylphenylsilyl)tetramethylcyclopentadienyl]thallium(I) and [(Benzyldimethylsilyl)tetramethylcyclopentadienyl]-thallium(1) - Polymeric Organometallic Compounds with Chain Structure (Dimethylphenylsilyl)tetramethylcyclopentadiene (2) and (benzyldimethylsilyl)tetramethylcyclopentadiene (3) were prepared from (tetramethylcyclopentadienyl)lithium (1) and chlorodimethylphenylsilane or benzylchlorodimethylsilane, respectively. 2 and 3 react with TIOC2H5 (4) to form [C5Me4(SiMe2Ph))TI (5) and [C5Me4(SiMe2CH2Ph)]TI (6), respectively. The 1H- and 13C-NMR spectra of the new compounds as well as the single-crystal X-ray structural analyses of the polymeric metallocenes 5 and 6 are described and discussed.

25 citations

Journal ArticleDOI
TL;DR: In this paper, a diastereoselective synthesis of some branched functionalized homoallylic amine derivatives is described, starting with a 3,6-dihydrothiazine-1-oxide, which is readily obtained in a totally stereospecific manner by the hetero-Diels-Alder cycloaddition of an N-sulfinyl dienophile and a 1,3-diene.

25 citations

References
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Journal ArticleDOI
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

Journal ArticleDOI
S. C. Wang1
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

Journal ArticleDOI
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