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 paper, the reaction of tetrakis(tetrahydrofuran-O)barium bis[bis(trimethylsilyl)phosphanide] with diphenylbutadiyne yields dimeric 2,5-diphenyl-3-(1,4-dipsylbutene-3-yne-2-ide-...
Abstract: The reaction of tetrakis(tetrahydrofuran-O)barium bis[bis(trimethylsilyl)phosphanide] with diphenylbutadiyne yields dimeric (tetrahydrofuran-O)barium 2,5-diphenyl-3-(1,4-diphenylbutene-3-yne-2-ide-...
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TL;DR: It is demonstrated that X-ray charge density analysis is able to reveal subtle new features of significant physical and chemical importance on complex molecular systems.
Abstract: The electron density distributions (EDD) of the redox active mixed valence trinuclear oxo-centered iron carboxylate, [Fe3O(CH2ClCOO)6(H2O)3]·3H2O, 1, and the oxidized form of 1, [Fe3O(CH2ClCOO)6(H2O)2(CH2ClCOO)]·1H2O, 2, as well as of [Fe3O(C(CH3)3COO)6 (NC5H5)3], 3, have been determined from accurate single-crystal X-ray diffraction data measured at 100 K (1, 2) and from extensive synchrotron radiation X-ray diffraction data measured at 28 K (3). Analysis of the EDDs shows that the central oxygen atom has a very different EDD in the mixed valence complexes (1 and 3) compared with the oxidized complex (2). Furthermore, in 1 and 3 the chemical bonds between formally identical trivalent Fe atoms and the central oxygen are fundamentally different. This is in direct contrast to the FeIII-(μ3-O) bonds in the oxidized complex, which are practically identical. Analysis of the d-orbital populations on the metal sites in the three complexes shows that the extra electron density on the FeII site primarily is distri...
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TL;DR: In this article, the crystal and molecular structures of the tetramer (HAlN-i-Pr)4 (I) and its methylated derivative (MeAlN i-Pr4 (II) have been determined from single-crystal, three-dimensional X-ray diffraction data obtained on a diffractometer.
59 citations
TL;DR: The tripeptide was synthesized as a model peptide to produce a specific β‐turn with the help of dehydro‐Phe and the structure is solved by direct methods using MULTAN 80 and refined by the block‐diagonal least‐squares method.
Abstract: The tripeptide, N-Boc-L-Phe-dehydro-Phe-L-Val-methyl ester (C 29 H 37 N 3 O 6 ) was synthesized as a model peptide to produce a specific β-turn with the help of dehydro-Phe. This peptide crystallizes in the triclinic space group Pl with a = 6.085(2) A, b = 9.515(4) A, c = 13.243(5) A, α= 105.16(3)°, β = 92.69(3)°, γ= 104.9(3)°, and Z = 1. The structure was solved by direct methods using MULTAN 80. The structure was refined by the block-diagonal least-squares method to an R value of 0.075 for 2438 observed reflections. The bond lengths and angles, in general, are in good agreement with the standard values. The peptide backbone adopts the β-conformation as a result of deprotonation at the C α ; and C β atoms in the dehydro-Phe residue. The backbone conformations around the C α atoms are cis, and the corresponding moieties are nonplanar. The backbone segments between the Cα atoms have extended trans conformations with highly planar configurations. The chain conformation angles-Φ 1 , ψ 1 , ω 1 , Φ 2 , ψ 2 , ω 2 , φ 3 , and ψ-are -45.4(11)°, -45.6(6)°, - 179.3(4)°, -46.5(5)°, -38.0(6)°, 165.3(9)°, 51.7(5)°, and 43.0(6)°, respectively. The phenyl rings of Phe and dehydro-Phe are essentially planar and their planes are inclined with respect to each other at 69.7(5)°. The C β -C γ bonds in Phe and dehydro-Phe are trans with respect to the N-C α bonds, with a X 1 torsion angle (about C α -C β ) of −176.3(1)° and −179.4(5)°, respectively. The C'-Cα bonds are cis and trans with respect to the C β -C γ bonds, with torsion angles of −56.8(7)° and −170.0(16)° in Phe and dehydro-Phe, respectively. The β-turn conformation is stabilized by an intramolecular hydrogen bond, N 3 -H 3 ... O 2 , of a distance of 3.116(6) A. The molecules are held in the crystal structure by a network of hydrogen bonds and the van der Waals forces.
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TL;DR: By treating Cp2MCl2 (M = Ti, Zr) with magnesium in the presence of the diazadienes R1N = CR2CR2 NR1 (R1 R2 Ph:1a; R1 Ph, R2 Me: 1b) metallocene complexes have been obtained in good yields as mentioned in this paper.
Abstract: Titanocene- and Zirconocene(diazadiene) Complexes: Preparation, Characterization, and Structure
By treating Cp2MCl2 (M = Ti, Zr) with magnesium in the presence of the diazadienes R1N = CR2CR2 NR1 (R1 R2 Ph:1a; R1 Ph, R2 Me: 1b) metallocene complexes of formula Cp2) (M Ti: 2a, b; M Zr: 3a, b) have been obtained in good yields. 2a–3b exhibit dynamic NMR spectra indicating a rapid intramolecular migration of the bent metallocene unit Cp2M from one “face” of the reduced diazadiene to the other. From the 1H-NMR Cp-coalescence ΔG‡ values for the activation barrier of this automerization process have been obtained. Complex 3a was characterized by X-ray diffraction. The five-membered metallacyclic ZrNCCN ring system adopts an “envelope”-conformation.
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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