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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.
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Journal ArticleDOI
TL;DR: In this article, the total and elastic x-ray scattering intensities from the diatomic molecules CO, N2, and O2 have been calculated within the Waller-Hartree theory.
Abstract: The total and elastic x‐ray scattering intensities from the diatomic molecules CO, N2, and O2 have been calculated within the Waller–Hartree theory. Near Hartree–Fock quality wavefunctions with extensive basis sets at experimental Re values have been employed. The calculated intensities reflect the full accuracy of the published wavefunctions. The electron–nuclear interference terms have also been computed and tabulated so that studies of high energy electron scattering intensities can be made. An independent atom model has been constructed from atomic wavefunctions, which served as a starting basis for calculations of the molecular wavefunctions. It is found in the scattering range for which 4π sinϑ/λ?10 A−1, neither the total nor the elastic x‐ray intensities can be sensibly neglected compared to the electron–nuclear interference terms for the three diatomic molecules studied in this work.

18 citations

Journal ArticleDOI
TL;DR: In this paper, the difference in coordination behavior of one new flexible polytopic ligand H2L (L = C16H14N6O2) has been examined with Cu(II) and Ni(II)-acetate.

18 citations

Journal ArticleDOI
TL;DR: The crystal structure of the title compound has been determined as discussed by the authors, which consists of (HgC12{μ-S(CH2)3NH(CH3)2}] helicoidal chains linked by hydrogen bonding, giving rise to chemically unconnected layers along the (202) planes.

18 citations

Journal ArticleDOI
TL;DR: In this paper, the crystal and molecular structure of the [Co(NS 3 -t-Bu)Br]PF 6 complex has been determined by standard X-ray methods, and refined to R = 0.061.

18 citations

Journal ArticleDOI
20 Oct 2020-Viruses
TL;DR: The AAV-DJ structure has been determined to 1.56 Å resolution through cryo-electron microscopy (cryo-EM), which nearly matches the highest resolutions ever attained through X-ray diffraction of virus crystals.
Abstract: Adeno-associated virus is the leading viral vector for gene therapy. AAV-DJ is a recombinant variant developed for tropism to the liver. The AAV-DJ structure has been determined to 1.56 A resolution through cryo-electron microscopy (cryo-EM). Only apoferritin is reported in preprints at 1.6 A or higher resolution, and AAV-DJ nearly matches the highest resolutions ever attained through X-ray diffraction of virus crystals. However, cryo-EM has the advantage that most of the hydrogens are clear, improving the accuracy of atomic refinement, and removing ambiguity in hydrogen bond identification. Outside of secondary structures where hydrogen bonding was predictable a priori, the networks of hydrogen bonds coming from direct observation of hydrogens and acceptor atoms are quite different from those inferred even at 2.8 A resolution. The implications for understanding viral assembly mean that cryo-EM will likely become the favored approach for high resolution structural virology.

18 citations


Cites background from "Coherent X‐Ray Scattering for the H..."

  • ...Furthermore, it has been noted by others that the orbitals of a σ-bonded hydrogen are not centered on the nucleus, but skewed towards the covalent bond [56,57]....

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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