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 structure of 1,3-selenazolidines and perhydro-1, 3-thiazines were established by X-ray crystallography.
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TL;DR: In this article, a planar AlN2C skeleton was obtained from NMR, IR and Raman data and the structure was refined to an R-value of 0.041.
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TL;DR: In this paper, the reaction of aldimines with α-(hydroxyimino) ketones of type 10 (1,2-diketone monooximes) was used to prepare 2-unsubstituted imidazole 3-oxides bearing an alkanol chain at N(1) (Scheme 2, Table 1).
Abstract: The reaction of aldimines with α-(hydroxyimino) ketones of type 10 (1,2-diketone monooximes) was used to prepare 2-unsubstituted imidazole 3-oxides 11 bearing an alkanol chain at N(1) (Scheme 2, Table 1). These products were transformed into the corresponding 2H-imidazol-2-ones 13 and 2H-imidazole-2-thiones 14 by treatment with Ac2O and 2,2,4,4-tetramethylcyclobutane-1,3-dithione, respectively (Scheme 3). The three-component reaction of 10, formaldehyde, and an alkane-1,ω-diamine 15 gave the bis[1H-imidazole 3-oxides] 16 (Scheme 4, Table 2). With Ac2O, 2,2,4,4-tetramethylcyclobutane-1,3-dithione or Raney-Ni, the latter reacted to give the corresponding bis[2H-imidazol-2-ones] 19 and 20, bis[2H-imidazol-2-thione] 21, and bis[imidazole] 22, respectively (Schemes 5 and 6). The structures of 11a and 16b were established by X-ray crystallography.
43 citations
01 Jun 1977
TL;DR: In this article, the exact position of coronene molecules in an n-heptane single crystal exhibiting Shpol'skii effect was determined using X-ray diffraction and ESR analysis.
Abstract: In order to determine the exact position of coronene molecules in an n-heptane single crystal exhibiting Shpol'skii effect, two crucial experimentas were performed: X-ray diffraction study of host n-heptane and ESR investigation of guest coronene. The X-ray experiments were carried out at 100 K; from calculations with an R value of 8% it is found that n-heptane crystallizes in a centered triclinic P 1 system. The resonance fields of the Δm = ± 1 transitions of triplet coronene were measured at 77 K as a function of the orientation of the single crystal in the cavity. Those two experiments demonstrate that the coronene molecules occupy mainly substitutional sites in the n-heptane lattice by replacing three alkane chains in the plane including the c axis.
43 citations
TL;DR: In this article, a tautomeric equilibrium between keto and enol forms was shown in β-diketones, and the packing of molecules was studied in detail.
Abstract: Tris(trimethylsilyl)phosphin reagiert mit Pivalinsaurechlorid unter Spaltung von zwei SiP-Bindungen zum Dipivaloyltrimethylsilylphosphin. Reaktion mit Methanol fuhrt zum Dipivaloylphosphin. Nach NMR-Untersuchungen liegt wie in β-Diketonen ein Tautomerengleichgewicht zwischen Keto- und Enolform vor. Die Enolform kristallisiert in der orthorhombischen Raumgruppe Pmmn mit Molekulen in zwei kristallographisch verschiedenen Punktlagen [Zellkonstanten bei −75°C ± 5°C: a = 14,04(1), b = 13,82(1), c = 6,28(2) A]. Eine Rontgenstrukturanalyse (R = 5,0%) liefert folgende Beweise fur das Vorliegen der Enolform im Festkorper: Molekulsymmetrie mm2 (C2v); verkurzte PC- und verlangerte CO-Abstande; symmetrische Wasserstoffbrucke mit sehr kurzem Sauerstoff–Sauerstoff-Abstand (2.41 A). Bindungsabstande und -winkel werden mit denen anderer β-Diketone verglichen. Die Packung der Molekule wird naher untersucht.
Syntheses and Properties of Acylphosphines. III. Molecular and Crystal Structure of Dipivaloylphosphine
In the reaction of tris(trimethylsilyl)phosphine with pivaloyl chloride two SiP bonds are cleaved and dipivaloyltrimethylsilylphosphine is formed. Reaction with methanol yields dipivaloylphosphine. N.m.r. investigations show a tautomeric equilibrium between keto and enol form as in β-diketones. The substance crystallizes in the orthorhombic space group Pmmn with molecules in two crystallographically different sites [cell parameters: a = 14.04(1), b = 13.82(1), c = 6.28(2) A]. An X-ray structure determination (R = 5.0%) proves the existence of the enol form in the solid, in that (1.) the molecular symmetry is mm 2(C2v), (2.) PC bonds are shortened and CO bonds are elongated, and (3.) we find a symmetric hydrogen bridge with a very short OO distance. Bond lengths and angles are compared with those of other β-diketones. The packing of molecules is studied in detail.
43 citations
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