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 crystal structure of the orthorhombic copper salt Cu2(OH)3NO3 (natural gerhardtite) has been determined from X-ray diffractometer data by means of three-dimensional Patterson and Fourier syntheses, and refined by difference Fourier synthesis and least-squares methods to a finalR index of 0.097 for 532 reflections.
Abstract: The crystal structure of the orthorhombic copper salt Cu2(OH)3NO3 (natural gerhardtite) has been determined from X-ray diffractometer data by means of three-dimensional Patterson and Fourier syntheses, and refined by difference Fourier syntheses and least-squares methods to a finalR index of 0.097 for 532 reflections. Crystals of Cu2(OH)3NO3 are orthorhombic:a=6.087(2),b=13.813(4),c=5.597(2) A,Z=4, space groupP212121. The Cu atoms form deformed hexagonal pseudocells (010). Each Cu(1) ion is surrounded by an approximately square planar arrangement of four OH ions at 1.929, 1.952, 1.993 and 1.998 A and by two O (of NO3 ions) at 2.359 and 2.480 A, completing a deformed coordination octahedron; each Cu(2) ion is similarly coordinated by four OH at 1.989, 1.997, 2.009 and 2.018 A, one OH at 2.309 A, and one O at 2.384 A. The structure involves layers of such deformed octahedra, of theC6-type, linked together by hydrogen bonds through the NO3 ions. Similarities to and differences from the structure of the monoclinic polymorphous form are discussed.
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TL;DR: The first example of bifurcated inter-molecular hydrogen bonds was revealed by an X-ray structure analysis as mentioned in this paper, which was also supported by an observation based on the IR spectrum of the crystals.
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TL;DR: In this article, the crystal and molecular structure of the distorted octahedral complex of MoCl2(NH)O(OPR3) has been determined by x-ray diffraction methods.
Abstract: Reaction of MoOCl3 with Me3SiN3 m THF followed by addition of tertiary phosphine oxides, RPO3(R3=Ph3, Ph2Et, Ph2Me), gives [MoCl2(NH)O(OPR3)2]. The crystal and molecular structure of the compound has been determined by x-ray diffraction methods. The complex crystallises in the monoclinic space group P21 /a with four molecules in a unit cell having dimensions a=15.667(8) A, b=20.135(9) A, c=9.726(7) A and β=95.01(1) A. A total of 3510 reflections were collected by counter techniques using MoKα radiation. The structure was refined on 2597 reflections with I > 2.58 σ (I) by full matrix least squares, using anisotropic temperature factors for all nonhydrogen atoms, to give a final R factor of 0.082. The overall configuration of the distorted octahedral complex istrans-dichloro-cis-bis[ethyl(diphenyl)phosphineoxide]cis-(oxo) imido with the molybdenum formally in the oxidation state (VI). The imido hydrogen has been located, and the Mo-N-H system is nonlinear.
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TL;DR: In this paper, the enantiomeric purity of selected products was determined by means of 1H NMR spectroscopy in the presence of (+)-(R)-(tert-butyl)(phenyl)phosphonothioic acid as a chiral solvating agent.
Abstract: Racemic as well as enantiomerically pure trans-1,1′-(cyclohexane-1,2-diyl)bis(imidazole N-oxides) were prepared from trans-cyclohexane-1,2-bis(methylidenamine) and 1,2-dione monooximes (α-hydroxyiminoketones). The enantiomeric purity of selected products was determined by means of 1H NMR spectroscopy in the presence of (+)-(R)-(tert-butyl)(phenyl)phosphonothioic acid as a chiral solvating agent. Deoxygenation by treatment with Raney-nickel led to the corresponding chiral bis-imidazoles.
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TL;DR: Barium bis(trimethylsilyl) amid is a colorless compound that is a mixture of barium bis[bis[bis] amid with one equivalent of bis[brimethyl silyl]phosphane in 1,2-dimethoxyethane (DME) as discussed by the authors.
Abstract: Bei der Reaktion von Barium-bis[bis(trimethylsilyl)amid] mit einem Aquivalent Bis(trimethylsilyl)phosphan in 1,2-Dimethoxyethan (DME) wird heteroleptisches, dimeres (1,2-Dimethoxyethan-O,O′)barium-bis(trimethylsilyl)-amid-bis(trimethylsilyl)phosphanid isoliert. Diese farblose Verbindung kristallisiert in der monoklinen Raumgruppe P21/n mit a = 1 259,1(3), b = 1 822,7(4), c = 1 516,1(3) pm, β = 110,54(3)° und Z = 4. Das zentrale Strukturelement des zentrosymmetrischen Molekuls ist der planare Ba2P2-Cyclus mit BaP-Bindungslangen von 329 und 334 pm. In Gegenwart des Bis[bis(trimethylsilyl)amino]stannylens erhalt man heterobimetallische Bis(trimethylsilyl phosphanide von Zinn(II) und Barium. Wird die Umsetzung von Ba[N(SiMe32]2 and Sn[N(SiMe3)2]2 im molaren Verhaltnis 1:2 mit sechs Aquivalenten HP(SiMe3)2 durchgefuhrt, kann Barium-bis{zinn(II)-tris-[bis(trimethylsilyl)phosphanid]} isoliert werden. Diese Verbindung kristallisiert in der orthorhombischen Raumgruppe P212121 mit a = 1 265,1(1), b = 2 290,1(3), c = 2 731,9(3) pm und Z = 4. Die Anionen {Sn[P(SiMe3)2])3}− binden als zweizahnige Liganden an das Bariumatom, das dadurch die ungewohnlich niedrige Koordinationszahl vier aufweist. Die Zugabe von THF zu der oben beschriebenen Reaktionslosung fuhrt zur Eliminierung von Tris(trimethylsilyl)phosphan und der Bildung von Barium-bis{zinn(II)-bis(trimethylsilyl)phosphanid-trimethylsilylphosphandiid). Das Derivat kristallisiert aus Toluol in der monoklinen Raumgruppe P21/c mit a = 1 301,9(2), b = 2 316,3(3), c = 3 968,7(5) pm, β = 99,29(1)° und Z = 8.
Synthesis and Characterization of Hetero-bimetallic Bis(trimethylsilyl)phosphanides of Barium and Tin
The reaction of barium bis[bis(trimethylsilyl)amide] with one equivalent of bis(trimethylsilyl)phosphane in 1,2-dimethoxyethane (dme) yields the heteroleptic dimeric (dme)barium bis(trimethylsilyl)amide bis(trimethylsilyl)phosphanide. This colorless compound crystallizes in the monoclinic space group P21/n with a = 1 259.1(3), b = 1 822.7(4), c = 1 516.1(3) pm, β = 110.54(3)° and Z = 4. The central moiety of the centrosymmetric molecule is the planar Ba2P2-cycle with BaP-bond lengths of 329 and 334 pm. In the presence of bis[bis(trimethylsilyl)amino]stannylene hetero-bimetallic bis(trimethylsilyl)phosphanides of tin(II) and barium are isolated. If the reaction of Ba[N(SiMe3)2]2 and Sn[N(SiMe3)2]2 in the molar ratio of 1:2 with six equivalents of HP(SiMe3)2 is performed in toluene, barium bis{tin(II)-tris[bis(trimethylsilyl)phosphanide]} can be isolated. This compound crystallizes in the orthorhombic space group P212121 with a = 1 265.1(1), b = 2 290.1(3), c = 2 731.9(3) pm and Z = 4. The anions {Sn[P(SiMe3)2]3}− bind as two-dentate ligands to the barium atom which shows the extraordinary low coordination number of four. The addition of tetrahydrofuran (thf) to the above mentioned reaction solution leads to the elimination of tris(trimethylsilyl)phosphane and the formation of thf complexes of barium bis{tin(II)-bis(trimethylsilyl)phosphanide-trimethylsilylphosphandiide}. The derivative crystallizes from toluene in the monoclinic space group P21/c with a = 1 301.9(2), b = 2 316.3(3), c = 3 968.7(5) pm, β = 99.29(1)° and Z = 8.
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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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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