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 structures of dinuclear complexes with 3-diphenylphosphino)benzoic acid moieties were determined by X-ray diffraction analyses.
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TL;DR: The crystal structure of 1′,1'''-dipropylbiferrocenium (PrFcFcPr)+I3− was determined by X-ray diffraction.
Abstract: The crystal structure of 1′,1'″-dipropylbiferrocenium (PrFcFcPr)+I3−, which shows averaged-valence irons at 298 K and trapped-valence irons at 110 K, was determined by X-ray diffraction. The crystal at 298 K is triclinic, space group P\bar1, a=8.5148(8), b=8.5482(5), and c=10.9032(13) A, α=89.546(9), β=115.582(9), and γ=108.488(7)°, U=671.10(9) A3, and Z=1. The crystal at 110 K is triclinic, space group P1, a=8.431(2), b=8.478(2), and c=10.816(3) A, α=88.58(3), β=117.39(2), and γ=108.65(2)°, U=643.4(3) A3, and Z=1. Structures were refined to R=0.042 at 298 K and R=0.050 at 110 K. At 298 K cation (PrFcFcPr)+ sits on the symmetry center and the two Fc units are crystallographically equivalent, whereas at 110 K the symmetry center is lost and ferrocene-like and ferrocenium-like Fc units are distinguished. A three-dimensional hydrogen-bond network is clearly found between the cation and iodine atoms at 110 K, in contrast to the result at 298 K. Infrared spectra of 1′,1'″-diethyl- and 1′,1'″-dipropylbiferrocen...
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TL;DR: The crystal structure of the organic charge transfer salt DBTTF-TCNQF4 was determined by single-crystal x-ray diffraction techniques and has been shown to consist of segregated stacks of donor and acceptor molecules.
Abstract: The crystal structure of the organic charge‐transfer salt DBTTF–TCNQF4 is reported. The structure has been determined by single‐crystal x‐ray diffraction techniques and has been shown to consist of segregated stacks of donor and acceptor molecules. Within both the donor and acceptor stacks, significant dimerization is observed at room temperature. From the geometries of the DBTTF and TCNQF4 molecules, it is concluded that the charge transfer is complete. The electrostatic contribution to the crystal cohesion for DBTTF–TCNQF4 has been calculated and compares well to those for similar salts of unit charge transfer. It is suggested that the room‐temperature structure may well be representative of the low‐temperature phase of a system affected by a Peierls instability. Based on diffraction data, a phase transition near 390 K is reported. The driving force for the transition is likely a spin–phonon instability. Crystal data for DBTTF–TCNQF4 are triclinic, space group P1; a = 13.159(3) A, b = 13.703(4) A, c = ...
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TL;DR: The tetrahydrofuran complexes of the alkaline earth metal bis[bis(trimethylsilyl)phosphanides] react with 2 equiv of benzonitrile to the bis[1,3-bis-2-phenyl-1-aza-3-phosphapropenides] of magnesium (1), calcium (2), strontium (3), and barium (4).
Abstract: The tetrahydrofuran complexes of the alkaline earth metal bis[bis(trimethylsilyl)phosphanides] react with 2 equiv of benzonitrile to the bis[1,3-bis(trimethylsilyl)-2-phenyl-1-aza-3-phosphapropenides] of magnesium (1), calcium (2), strontium (3), and barium (4). Whereas 1 and 2 crystallize as bis(tetrahydrofuran) adducts, the heavier homologous derivatives 3 and 4 precipitate as tris(tetrahydrofuran) complexes. The bidentate trans/trans-isomeric 1,3-bis(trimethylsilyl)-2-phenyl-1-aza-3-phosphapropenide ligands of all these compounds display very similar spectroscopic data; however, the influence of the alkaline earth metal is observed in the silicon NMR. The nitrogen atoms of these anions have trigonal planar geometry, whereas the phosphorus atoms are coordinated trigonal pyramidal. Crystallographic data: 1, monoclinic, P21/c, a = 1505.3(3) pm, b = 1259.0(2) pm, c = 2278.4(5) pm, β = 91.91(2)°, Z = 4, wR2 = 0.1279; 2, monoclinic, P21/c, a = 1522.8(7) pm, b = 1279.2(5) pm, c = 2314.0(10) pm, β = 92.53(2)°...
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TL;DR: The synthesis, thermal behaviour and crystal structure of lithium glutaratehydrogenglutaratedioxouranate (VI) tetrahydrate was described in this article, where the carboxylic groups were chelated on the uranium and monodentate on the lithium.
39 citations
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
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576 citations
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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
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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
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133 citations