scispace - formally typeset
Search or ask a question
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
More filters
Journal ArticleDOI
TL;DR: A binuclear copper (II) complex, isothiocyanato{2-[dimethylamino)ethylthio]ethanolato}copper(II), (Cu(CH3-nso)NCS), was prepared and characterized by elemental analysis, infrared and electronic spectra, magnetic susceptibility (90-300 K), and single-crystal X-ray diffraction as discussed by the authors.
Abstract: A binuclear copper(II) complex, isothiocyanato{2-[2-(dimethylamino)ethylthio]ethanolato}copper(II), (Cu(CH3-nso)NCS), was prepared and characterized by elemental analysis, infrared and electronic spectra, magnetic susceptibility (90–300 K), and single-crystal X-ray diffraction. The complex exhibits a band at 25×103 cm−1 characteristic of alkoxo-bridged structure. The temperature dependence of the magnetic susceptibility is unusual and shows a dramatic change in the temperature range 240–180 K. The magnetic data were fitted to the Bleaney-Browers equation separately in the two temperature ranges (−2J=535 cm−1 for 300≥T≥240 K; −2J=595 cm−1 for 170≥T≥90 K).

19 citations

Journal ArticleDOI
TL;DR: In this article, the structure of (1,3,8-trimethylxanthinium)2[Pd2Br6] belongs to the monoclinic P21/c space group.

19 citations

Journal ArticleDOI
TL;DR: In this article, the molecular structure of methyl borate has been investigated by electron diffraction from the vapour and the data were found to be consistent with a B(OC)3 skeleton of C3h symmetry.

19 citations

Journal ArticleDOI
TL;DR: In this paper, the crystal structure of Cu(C2H5-sno)Cl2·2H2O was determined form three-dimensional X-ray diffractometer data, and the structure was solved by the heavy atom method and refined by block-diagonal least-squares method to R = 0.022 for 1908 independent reflections.

19 citations

Journal ArticleDOI
TL;DR: The crystal structures of two sulfathiazole complexes, one involving theophylline and the other sulfanilamide, were determined by X-ray diffraction methods by determining the hydrogen-bonding schemes in the two complexes.

19 citations

References
More filters
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