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: Barium bis[bis(trimethylsily)amide] metalates bis(isopropyldimethyl silyl)phosphane (1) to yield nearly quantitatively the corresponding barium bis [bis[isopropylsilyl]phosphanide] (3), which shows a temperature-dependent monomer-dimer equilibrium in toluene solution as discussed by the authors.
Abstract: Barium bis[bis(trimethylsily)amide] metalates bis(isopropyldimethylsilyl)phosphane (1) to yield nearly quantitatively the corresponding barium bis[bis(isopropyldimethylsilyl)phosphanide] (3). This compound shows a temperature-dependent monomer-dimer equilibrium in toluene solution. Both the isomers were characterized by X-ray crystal structure analyses. The monomeric derivatives precipitate as a tetrakis(tetrahydrofuran) complex with a P–Ba–P bond angle of 139.9°. The barium atoms of the monocyclic, centrosymmetric dimer are pentacoordinated by two tetrahydrofuran molecules, one terminal and two bridging phosphanide ligands. The endo- and exocyclic Ba–P distances with values of 332 and 316 pm, respectively, lie within the characteristic range.
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TL;DR: The tripeptide, L-prolyl-glycyl-glycine, crystallizes in the trigonal space group P3(2), and adopts a left-handed helical conformation similar to that of polyglycines II and polyproline II.
Abstract: The tripeptide, L-valyl-glycyl-glycine (C9H17N3O4, molecular weight = 231), crystallizes in the monoclinic space group C2, with a = 24.058(3)A, b = 4.801(1), c = 10.623(2), β = 110.02(1)° and Z = 4. The structure was determined by direct methods and refined to a final R-index of 0.043 for 830 reflections (sinθ/Λ ≤ 0.53 A-1) with I> 1.0s. The molecule exists as a zwitterion. The peptide units are trans and one of them shows significant deviations from planarity (Δω2 = 9.3°). The peptide chain repeat distance, 1Cα-3Cα, is 7.23A and the molecule displays a highly extended conformation with backbone torsion angles of ψ1 = 123.1°, ω1 = - 179.4°, o2 = - 155.1°, ψ;2 = 154.7°, ω2 = 170.7°, o3 = - 146.6° and ψ3 = 180.0°. For the valyl side chain, χ11 = - 52.5°, χ12 = 174.2°. The packing involves hydrogen-bonded interactions between successive molecules related by the β-translation of the lattice, giving rise to the familiar parallel β-sheet structure which appears to be the most extended one observed to date.
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TL;DR: In this article, an H-shift in the intermediate thiocarbonyl aminides was shown to yield cycloadducts of type 22, and two possible mechanisms of its formation were proposed in Schemes 8 and 9.
Abstract: First Example of an H-Shift in ‘Thiocarbonyl Aminides’ (N-(Alkylidenesulfonio)aminides)
Reaction of benzyl azide (15a) with the sterically hindered CS group of 4,4-dimethyl-1,3-thiazole-5(4H)-thiones 14 (Scheme 3) and 1,1,3,3-tetramethylindane-2-thione (17, Scheme 4) at 80° leads to the corresponding imines in high yield, without formation of any by-product. In contrast, 15a and 2,2,4,4-tetramethyl-3-thioxocyclobutanone (7) under the same conditions yielded, in addition to imine 19, products 20a and 21 (Scheme 5). For the formation of 20a, a reaction mechanism via [1,4]-H shift in the intermediate ‘thiocarbonyl aminides’ 23 is proposed (Scheme 6). Product 21 as well as the dithiazole derivative 22, which is formed only in the reaction with 4-nitrobenzyl azide (15c), are formal adducts of the dipole 23. Whereas precedents are known for the formation of cycloadducts of type 22, the pathway to 21 is not known. Two possible mechanisms of its formation are proposed in Schemes 8 and 9.
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TL;DR: In this article, the reaction of phenyldiazomethane with 1,3-thiazole-5(4H)-thiones in toluene at room temperature yields the thiiranes trans- and cis-1,4-dithia-6-azaspiro[2.4]
Abstract: Reaction of Phenyldiazomethane with 1,3-Thiazole-5(4H)-thiones: Base-Catalyzed Ring Opening of the Primary Adduct
Reaction of 1,3-thiazole-5(4H)-thiones 1 and phenyldiazomethane (2a) in toluene at room temperature yields the thiiranes trans- and cis-1,4-dithia-6-azaspiro[2.4]hept-5-enes (trans- and cis-4; Scheme 2). With Ph3P in THF at 70°, these thiiranes are transformed stereospecifically into (E)- and (Z)-5-benzylidene-4,5-dihydro-1,3-thiazoles 5, respectively. In the presence of DBU, 1 and 2a react to give 1,3,4-thiadiazole derivatives 6 or 7via base-catalyzed ring opening of the primary cycloadduct (Scheme 3). In the case of 2-(alkylthio)-substituted 1,3-thiazole-5(4H)-thiones 1c and 1d, this ring opening proceeds by elimination of the corresponding alkylthiolate, yielding isothiocyanate 7. The structures of (Z)-5c and 6b have been established by X-ray crystallography.
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TL;DR: In this paper, the molecular structure of 1,1,2,2-tetrabromodisilane has been investigated using gas-phase electron diffraction data obtained at 110°C.
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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