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: The crystal structure of H2SO4·2H2O has been determined from three-dimensional single-crystal x-ray data recorded at −190°C as discussed by the authors.
Abstract: The crystal structure of H2SO4·2H2O has been determined from three‐dimensional single‐crystal x‐ray data recorded at −190°C. The crystals are monoclinic, space group C2 / c, with 12 formula units in a cell with the dimensions: a = 13.008, b = 7.979, c = 14.881, and β = 101.60°. The structure consists of H3O+ and SO42− ions. Each of the three independent H3O+ ions is hydrogen bonded to three different SO42− ions (0···0 distances, 2.520–2.590 A) is such a way that a three‐dimensional hydrogen‐bond pattern is formed. The average S–O distance in the sulfate ion is 1.474 A.
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TL;DR: The successful synthesis of 4 suggests that the reaction of Na2[Os(CO)4] with Os3[CO)12 generates [Os4[CO]2-, thus providing a relatively easy route for the preparation of this dianion as mentioned in this paper.
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TL;DR: The first reported organotin and triphenyllead metal carbonyl derivatives which contain a transition metal in a formal negativ oxidation state was reported in this paper, where the crystal structure of [Et 4 N] [(Ph 3 Sn) 2 V(CO) 5 ], which is synthesized in low yields (ca. 15%) from the photolysis of [N] [V (CO) 6 ] in the presence of Ph 6 Sn 2, has been determined by single crystal X-ray diffraction techniques.
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TL;DR: The peptide N-Boc-L-Pro-dehydro-Leu-NHCH 3 was synthesized to examine the nature of β-bend as a result of dehydro-leu in the sequence.
Abstract: The peptide N-Boc-L-Pro-dehydro-Leu-NHCH 3 was synthesized to examine the nature of β-bend as a result of dehydro-Leu in the sequence. The peptide crystallizes from methanol-water mixture at 4° in orthorhombic space group P22 1 2 1 with a = 5.726(1)A, b = 14.989(4) A, c = 24.131(9) A, V = 2071(1) A 3 , Z = 4, dm = 1.064(5)gcm −3 and dc = 1.0886(5)gcm −3 . The structure was solved by direct methods using SHELXS 86 and it was refined by full-matrix least-squares procedure to an R value of 0.059 for 957 observed reflections. The peptide is found to adopt a β-bend type II conformation with φ 1 =− 51(1)°, ψ 1 = 133(1)°, φ 2 = 74(2)° and ψ 2 = 8(2)°. The β-bend is stabilized by an intra-chain hydrogen bond between the carbonyl oxygen of ith residue and the NH of (i + 3)th residue. The five-membered pyrrolidine ring of Pro-residue adopts an ideal C γ -exo conformation with torsion angles of χ 1 1 = −25(1)°, χ 1 2 = 38(1)°, χ 2 = −34(1)°, χ 4 1 = 20(1)° and χ 0 1 = 2(1)°. The side chain conformation angles of dehydro-Leu residue are χ 2 = 12(2)°, χ 2 2.1 = −112(2)° and χ 2 2.2 = 136(2)°. The crystal structure is stabilized by a network of hydrogen bonds and van der Waals interactions.
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TL;DR: The X-ray structure of the dimeric Lithium Trimethylsilyl-[tris(trimethylSilyl)Silylamine and the lithiated and silylated Derivatives is described in this article.
Abstract: Die Ammonolyse von Chlor−, Brom- oder Trifluormethansulfonyl-tris(trimethylsilyl)silan ergibt das bei 51°C/0,02 Torr zu destillierende, farblose Tris(trimethylsilyl)silylamin Durch Lithiierung erhalt man das in Benzol dimer vorliegende Lithium-tris(trimethylsilyl)silylamid; die anschliesende Umsetzung mit Chlortrimethylsilan und abermalige Lithiierung fuhren zu dem in Benzol ebenfalls dimer auftretenden Lithiumtrimethylsilyl-[tris(trimethylsilyl)silyl]amid, das in der monoklinen Raumgruppe P21/n mit a = 1 386,7(2); b = 2 040,2(3); c = 1 609,6(2) pm; β = 96,95(1)° und Z = 4 Dimeren kristallisiert Das zentrale Strukturelement bildet der Li2N2-Cyclus mit LiN-Abstanden um 202 pm und einem kurzen Li … Li-Kontakt von 229 pm Das dimere Molekul weist nahezu C2-Symmetrie auf, so das das eine Lithiumatom agostische Bindungen zu den zwei Trimethylsilyl-Gruppen, das andere hingegen zu den Tris(trimethylsilyl)silyl-Substituenten aufweist, allerdings last sich in benzolischer Losung 7Li{1H}-NMR-spektroskopisch nur ein Hochfeld-verschobenes Singulett bei — 1,71 ppm beobachten Im 29Si{1H}-NMR-Spektrum last sich durch die Lithiierung des Trimethylsilyl-[tris(trimethylsilyl)silyl]amins eine Hochfeldverschiebung um 12 ppm fur den Me3SiN-Rest registrieren, wahrend die NMR-Parameter des Tris(trimethylsilyl)silyl-Liganden eine nur geringe Verschiebung erfahren
Tris(trimethylsilyl)silylamine and the lithiated and silylated Derivatives — X-Ray Structure of the dimeric Lithium Trimethylsilyl-[tris(trimethylsilyl)silyl]amide
The ammonolysis of the chlor, brom or trifluormethanesulfonyl tris(trimethylsilyl)silane yields the colorless tris(trimethylsilyl)silylamine, destillable at 51°C and 002 Torr The subsequent lithiation, reaction with chlor trimethylsilane and repeated lithiation lead to the formation of lithium tris(trimethylsilyl)silylamide, trimethylsilyl-[tris(trimethylsilyl)silyl]amine and finally lithium trimethylsilyl-[tris(trimethylsilyl)silyl]amide, which crystallizes in the monoclinic space group P21/n with a = 1 3867(2); b = 2 0402(3); c = 1 6096(2) pm; β = 9695(1)° and Z = 4 dimeric molecules The cyclic Li2N2 moiety with LiN bond distances displays a short transannular Li … Li contact of 229 pm The dimeric molecule shows nearly C2-symmetry, so that one lithium atom forms agostic bonds to both the trimethylsilyl groups, the other one to the tris(trimethylsilyl)silyl substituents However, the 7Li{1H}-NMR spectrum displays a high field shifted singlet at —171 ppm The lithiation of trimethylsilyl-[tris(trimethylsilyl)silyl]amine leads to a high field shift of the 29Si{1H} resonance of about 12 ppm for the Me3SiN group, whereas the parameters of the tris(trimethylsilyl)silyl ligand remain nearly unaffected
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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