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Journal ArticleDOI

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.
Citations
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TL;DR: The crystal structure of [Fe6(µ3-S)8(PEt3)6][PF6]2 has been determined by measuring the temperature variation of the magnetic susceptibility between 300 and 4.2 K, the field dependence of the magnetisation at three different temperatures in the range 2-10 K and the polycrystalline powder Mossbauer spectra at variable temperature.
Abstract: The crystal structure of [Fe6(µ3-S)8(PEt3)6][PF6]2 has been determined. It is isostructural with the parent tetraphenylborate complex. The electronic structures of [Fe6(µ3-S)8(PEt3)6][PF6] and of [Fe6(µ3-S)8(PEt3)6][PF6]2 have been investigated experimentally by measuring the temperature variation of the magnetic susceptibility between 300 and 4.2 K, the field dependence of the magnetisation at three different temperatures in the range 2–10 K and the polycrystalline powder Mossbauer spectra at variable temperature. The complex [Fe6(µ3-S)8(PEt3)6][PF6] possesses a S= 7/2 spin state well isolated from the excited states, while [Fe6(µ3-S)8(PEt3)6][PF6]2 shows a marked temperature dependence of the magnetic susceptibility. The magnetic structures of the complexes have been characterised empirically with the Heisenberg–Dirac–van Vleck exchange spin Hamiltonian. The nature of the magnetic states is rationalised in the framework of Xα-SW theory.

23 citations

Journal ArticleDOI
TL;DR: In this article, the structure of the platinum alkyl compound PtI(Me)(PEt 3 ) 2, and p -chlorophenyl isocyanide was determined and refined by full-matrix isotropic-anisotropic least squares on 1791 independent counter data, to a final unweighted R factor of 3.8%.

22 citations

Journal ArticleDOI
TL;DR: In this article, the crystal structure of Cp2TiC6H5CN-2,6-(CH3)2C 6H3 is reported, and the iminoacyl ligand is η2-coordinated at the metal (TiC 2.096(4), TiN 2.149(4) A).

22 citations

Journal ArticleDOI
TL;DR: The structure of glabratephrin, a flavone isolated from Tephrosia semiglabra Sond, is known as (4'-acetoxy-5',5'-dimethyltetrahydrofuran-2'-one)-3'-spiro-9-(8,9-dihydro-2-phenyl-4H-furo[2,3] as mentioned in this paper.

22 citations

Journal ArticleDOI
TL;DR: The ligand 2,2,2′,2″-nitrilotriphenol reacts with P(III) and P(V) compounds to form corresponding phosphorus complexes.
Abstract: The ligand 2,2′,2″-nitrilotriphenol reacts with P(III) and P(V) compounds to form corresponding phosphorus complexes. Syntheses and NMR data of 2,2′,2″-nitrilotriphenyl phosphite (II), 2,2′,2″-nitrilotriphenyl phosphate (III) and of a hydrolysis product of II, 2,2′-[N-(2-hydroxyphenyl)imino]diphenly phosphonate (IV), are reported, as well as crystal structures of II and IV. Phosphite II shows a bicycloundecane framework; no NċPinteraction is present. The phosphonate IV shows two coordinated and one dangling phenol group; the N-atom does not interact with the P-atom. Strong acids protonate II as well as III to form cations: in these, NMR evidence indicates coordination of the N-atom to the P-atom.

22 citations

References
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Journal ArticleDOI
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

Journal ArticleDOI
S. C. Wang1
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

Journal ArticleDOI
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