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, a nonplanar double bond deformation of the olefinic double bond of the title compound has been observed by X-ray techniques to deviate from planarity by 13.2 (0.13,6.3)° (symmetric out-of-plane bending).
Abstract: Non-Planar Double Bond in a Crystalline Derivative of anti-Sesquinorbornene (anti-Tetracyclo[6.2.1.13,6.02,7]dodec-2(7)-ene)
The olefinic double bond of the title compound 2 has been observed by X-ray techniques to deviate from planarity by 13.2 (0.3)° (symmetric out-of-plane bending). Empirical force field calculations for the parent hydrocarbon 1 (anti-sesquinorbornene) give a much larger corresponding deviation of 35.6°. The calculated nonplanar double bond deformations in anti-sesquinorbornene 1 as well as in the syn-isomer 4 and other related olefins are a consequence of substantial widenings of the exocyclic C(sp3)–C(sp2–Csp3) angles when keeping the double bond planar. The considerable computational exaggeration of this novel out-of-plane bending mechanism is attributed to various possible force field deficiencies.
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TL;DR: A trinuclear Cu(II) complex with isonicotinic acid N-oxide, [Cu3(N-inicO)4(OH)2(H2O)5·2H 2O, has been prepared and its crystal structure determined by X-ray analysis as mentioned in this paper.
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TL;DR: The desaurin 3, whose stereochemistry has now been established by an X-ray crystal structure analysis, can be used as a thioketene equivalent (11), and reactions have been carried out with sodium azide/dimethyl sulfate, N,Ndiethyl-aminopropyne, N-methyl benzaldimine, tert-butyl isonitrile and NaN3/CS2 to give the products listed in Schemes I, IV and V as mentioned in this paper.
Abstract: The desaurin 3, whose stereochemistry has now been established by an X-ray crystal structure analysis, can be used as a thioketene equivalent (11). Reactions have been carried out with sodium azide/dimethyl sulfate, N,N-diethyl-aminopropyne, N-methyl benzaldimine, tert-butyl isonitrile and NaN3/CS2 to give the products listed in Schemes I, IV and V. Simple thioketenes (e.g. 16) react analogously with tert-butyl isonitrile, but not with imines where C-C adducts are formed instead of C-S adducts.
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TL;DR: In this article, the molecular structure of gaseous p-bromonitrobenzene has been studied by the electron diffraction method, and the torsion of the nitro group has been treated as a large-amplitude motion and the barrier to internal rotation was found to be 4.2(8) kcal mol −1.
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TL;DR: The crystal and molecular structures of Ni(NO2)2dppe·CH2Cl2 and [Ni(ONO)(NO)dppe]2 have been determined by X-ray crystallography as mentioned in this paper.
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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