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: Aryl isoselenocyanates as discussed by the authors react with different phenacyl halides in the presence of hydrazine hydrate in a one-pot reaction to give selenadiazines 3a−3f in good-to-excellent yields.
Abstract: Aryl isoselenocyanates 1 react with different phenacyl halides 2 in the presence of hydrazine hydrate in a one-pot reaction to give selenadiazines 3a–3f in good-to-excellent yields.
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01 Jan 2012
TL;DR: A review of the efforts to determine a strategy for the modeling of hydrogen atoms, as well as a number of recent studies where the modeling has had a major impact on the chemical conclusions drawn from analysis of the experimental charge densities can be found in this paper.
Abstract: Hydrogen atoms are elusive seen from the point of view of the X-ray crystallographer. But they are also extremely important, being involved in a wealth of intermolecular interactions and thereby defining the way molecules interact. Most experimental charge density studies are performed on compounds containing hydrogen, yet a commonly accepted strategy to deal with these elusive but so important atoms is only just about to surface. We review the efforts to determine a strategy for the modeling of hydrogen atoms, as well as a number of recent studies where the modeling of hydrogen atoms has had a major impact on the chemical conclusions drawn from analysis of the experimental charge densities.
20 citations
Cites background or methods from "Coherent X‐Ray Scattering for the H..."
...As mentioned previously, the standard SDS scattering factor [5] improved the description of the hydrogen atoms tremendously as compared to the scattering factor of an isolated H atom, however it leads to bond lengths that are about 20% too short, as compared to the values obtained from neutron diffraction data....
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...The so-called SDS scattering factor based on the ab initio electron density of the hydrogen molecule [5] lead to a considerable improvement, and this scattering factor is today the standard in popular structure refinement programs....
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...In this study the hydrogen atoms were restrained to the standard neutron distances as listed in the International Tables for Crystallography [39], and a preliminary multipole refinement was conducted using isotropic displacement parameters and an SDS scattering factor [5] for the hydrogen atoms....
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TL;DR: The crystal structure of dibrom-1-(2-pyridyl-2,5-diaza-5-methyl-hexa-1-enezinc(II), C10H15N3ZnBr2 has been determined from three-dimensional X-ray diffraction data collected on a Picker automatic single crystal diffractometer with MoKα radiation.
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TL;DR: In this article, the structures of the sugar units in the glycosylamine complexes from all natural aldohexoses can be classified into either the above two types, the only difference being the relative absolute configuration at C2 and C5.
Abstract: Some natural aldohexoses reacted with [Ni(tn)3]2+(tn = trimethylenediamine) to yield octahedral nickel(II) complexes containing glycosylamine ligands. The complexes were characterized by elemental analyses, magnetic moments, electronic and CD spectra. The molecular structure of [Ni(L-Rha-tn)2]Br2·2H2O·MeOH [L-Rha-tn = 1-(3-aminopropylamino)-1,6-dideoxy-L-mannose]1 has been determined by single-crystal X-ray techniques: orthorhombic, space group P212121, a= 12.373(1), b= 21.614(2), c= 11.272(1)A, least-squares refinement led to a final R factor of 0.044 using 2657 reflections having Fo > 3σ(Fo). From X-ray crystallographic studies of glycosylamine complexes, two typical co-ordination structures of the aldose unit have been found in 1 and [Ni(D-GlcN-en)2]2+[D-GlcN-en = 2-amino-1-(2-aminoethylamino)-1,2-dideoxy-D-glucose], which can be discriminated by the two geometrical isomeric forms arising from the two substituents on C1 and C2 of the pyranoside ring, namely cis and trans. The sugar unit of 1 has cis geometry containing equatorial and axial substituents on C1 and C2 of the pyranoside ring. In contrast, the sugar unit of the D-GlcN-en complex has trans geometry at these positions, which are both equatorial. Assuming the 4C1(chair) conformers to be the most stable and based on some stereochemical considerations of both the sugars and the chelate rings, the structures of the sugar units in the glycosylamine complexes from all natural aldohexoses can be classified into either of the above two types, the only difference being the relative absolute configuration at C2 and C5. This classification is well correlated with the CD spectral patterns obtained in methanolic solutions.
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TL;DR: The structure of C7H4NO8U (C7H11N2) has been determined by Patterson and Fourier methods from single crystal X-ray diffraction data collected on a four-circle diffractometer as mentioned in this paper.
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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