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 structural properties of 1:1 TiCl4-acetone adducts were characterized using X-ray analysis of the chiral propionyloxazolidone with TiCl 4.
Abstract: Mesityl aldehyde binds TiCl4 leading to the first structurally characterized TiCl4-aldehyde adduct, cis-[(MesCHO)2TiCl4] (Mes = 2,4,6-Me3C6H2) (1), which contains a pseudooctahedral titanium and two aldehyde carbonyl groups in a cis arrangement. However, in the case of 1:1 TiCl4–acetone adduct [(Me2CO)TiCl3)2(μ-Cl)2] (3) the solid-state structure of this acid-base complex is that of a chloro-bridged dimer. Both kinds of structures were suggested for the products [{(PhCOMe)TiCl3}2(μ-Cl)2] (4) and [cis-(PhCOMe)2TiCl4] (5) formed by the reaction of TiCl4 with acetophenone in 1:1 and 1:2 molar ratio. Thioesters behave like acetone in that they give adducts 8 and 9 with TiCl4, where 9, [{(PhSC(Me)O)TiCl3}2(μ-Cl)2], exhibits a solid-state dimeric structure like 3. The bidentate bonding mode of the chiral propionyloxazolidone 12 with TiCl4 was revealed by an X-ray analysis of 13.
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TL;DR: In this paper, a meso-helix structure of a compound with a 2,5,8-trioxanonane-O2,O5,O8)-lithium methylphosphanide is presented.
Abstract: Nach Untersuchungen von Fritz u. a. [10] wird in 1,2-Dimethoxyethan oder Bis(2-methoxyethyl)ether 1 gelostes Methylphosphan bei −60°C durch Lithium-n-butanid in n-Hexan metalliert. Beim Abkuhlen der von Kohlenwasserstoffen weitgehend befreiten Ansatze auf wiederum −60°C kristallisiert (1,2-Dimethoxyethan-O,O′)lithium- (1) bzw. (2,5,8-Trioxanonan-O2,O5) lithium-methylphosphanid (2) in farblosen Quadern aus. Nach einer Rontgenstrukturanalyse (monoklin, P21/n; a = 805,5(1); b = 1 820,6(2); c = 851,5(1)pm; β = 116,76(1)° bei −100 ± 3°C; Z = 4 Formeleinheiten; R = 0,034) liegt Komplex 2 als Polymer in der bislang wenig beachteten achiralen Abfolge einer „meso-Helix” vor. Lithium weist mit Bindungen zu zwei Phosphor- (PLi 252,9 und 253,2 pm; PLiP 131,8°; LiPLi 132,1°) und zu nur zwei Sauerstoffatomen (LiO 203,9 und 206,8; O … O 270,7 pm; OLiO 82,5°) des a priori dreizahnigen 2,5,8-Trioxanonan-Liganden ebenso wie Phosphor die Koordinationszahl 4 auf. Der PC-Abstand ist mit 187,4 pm gegenuber dem Standard (185 pm) geringfugig verlangert. Vor einigen Jahren veroffentlichte Strukturen [26, 27] von (2,5,8-Trioxanonan-O2,O5,O8)- lithium-1-(phenylsulfonyl)alkyl-Verbindungen ermoglichen einen Vergleich charakteristischer Molekulparameter im zwei-oder dreifach koordinierenden Chelatliganden.
Metal Derivatives of Molecular Compounds. VIII. catena-Poly[(2,5,8-trioxanonane-O2,O5) lithium-methylphosphanide] — a Compound with a meso-Helix Structure
Studies of Fritz et al. [10] showed methylphosphane to be lithiated at −60°C in 1,2-dimethoxyethane or bis(2-methoxyethyl) ether 1 solution by stoichiometric amounts of lithium n-butanide in n-hexane. After removing the hydrocarbons almost completely by distillation and cooling the solutions to −60°C again, colourless square crystals of (1,2-dimethoxyethane-O,O′)lithium (1) and (2,5,8-trioxanonane-O2,O5)lithium methylphosphanide (2) precipitate. As shown by an X-ray structure determination (monoclinic, P21/n; a = 805.5(1); b = 1820.6(2); c = 851.5(1) pm; β = 116.76(1)° at −100 ± 3°C; Z = 4 formula units; R = 0.034) complex 2 forms a polymer which has the shape of an up to now scarcely noted meso-helix. Four-coordinated lithium is bound to two phosphorus (PLi 252.9 and 253.2 pm; PLiP 131.8°; LiPLi 132.1°) and to two oxygen atoms (LiO 203.9 and 206.8; O … O 270.7 pm; OLiO 82.5°) of the inherently tridentate 2,5,8-trioxanonane ligand. As compared to the standard value (185 pm) the PC distance (187.4 pm) is slightly lengthened. Structure determinations of (2,5,8-trioxanonane-O2,O5,O8) lithium 1-(phenylsulfonyl)alkyl compounds published some years ago [26, 27], allow a comparison of molecular parameters characteristic for the twofold or threefold coordinating chelate ligand.
31 citations
TL;DR: Density functional theoretical QM/MM computations are able to play the role of an alternative benchmark to neutron diffraction and solve the last remaining problem to obtain accurate X−H bond lengths to hydrogen atoms more frequently.
Abstract: Amino acid structures are an ideal test set for method-development studies in crystallography. High-resolution X-ray diffraction data for eight previously studied genetically encoding amino acids are provided, complemented by a non-standard amino acid. Structures were re-investigated to study a widely applicable treatment that permits accurate X-H bond lengths to hydrogen atoms to be obtained: this treatment combines refinement of positional hydrogen-atom parameters with aspherical scattering factors with constrained "TLS+INV" estimated hydrogen anisotropic displacement parameters (H-ADPs). Tabulated invariom scattering factors allow rapid modeling without further computations, and unconstrained Hirshfeld atom refinement provides a computationally demanding alternative when database entries are missing. Both should incorporate estimated H-ADPs, as free refinement frequently leads to over-parameterization and non-positive definite H-ADPs irrespective of the aspherical scattering model used. Using estimated H-ADPs, both methods yield accurate and precise X-H distances in best quantitative agreement with neutron diffraction data (available for five of the test-set molecules). This work thus solves the last remaining problem to obtain such results more frequently. Density functional theoretical QM/MM computations are able to play the role of an alternative benchmark to neutron diffraction.
31 citations
TL;DR: In this article, the crystal structure of bis(N-benzoylglycinato)-triaquozinc(II) dihydrate was determined from three-dimensional X-ray data collected by counter methods.
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Journal Article•
TL;DR: The crystal and molecular structures of two isomeric inhibitors of carcinogenesis by certain polycyclic aromatic hydrocarbons are described and it is predicted that a nonplanar conformation is most probable for these flavone derivatives, as a result of the presence of a biphenyl-like system.
Abstract: The crystal and molecular structures of two isomeric inhibitors of carcinogenesis by certain polycyclic aromatic hydrocarbons are described The two compounds are 7,8-benzoflavone and 5,6-benzoflavone, which are shown by X-ray crystallographic studies to differ appreciably in their three-dimensional structures Polycyclic aromatic hydrocarbons are metabolically activated by an enzyme system that is responsibe for the detoxification of many chemicals that enter the body The two benzoflavones described here differ in their effect towards specific enzymes in the metabolizing system Potential energy calculations predict that a nonplanar conformation is most probable for these flavone derivatives, as a result of the presence of a biphenyl-like system Such a conformation is found for 7,8-benzoflavone with a torsion angle of 23 degrees between the phenyl group and the rest of the molecule The isomeric 5,6-benzoflavone is, in contrast, found to be a predominantly flat molecule There is an interaction between O(4) and a neighboring -C-H group which may explain the planarity of 5,6-benzoflavone A comparison is made with structures of some common carcinogenic polycyclic aromatic hydrocarbons, the activities of which these two benzoflavones inhibit
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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