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: From a comparison of experimental and simulated X-ray powder diffraction patterns, neither 1 nor 2 undergoes a polymorphic transition upon grinding, which indicates that tenoxicam molecules associate by N(+)-H...O and C-H...N hydrogen bonding in both crystal structures.
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TL;DR: Cholesteryl nonanoate is monoclinic, space group P21, with lattice parameters a= 27.24(1), b= 9.183(3), c= 13.96(2)A, β= 91.52°, and Z= 4 [two independent molecules (A and (B) in the unit cell].
Abstract: Cholesteryl nonanoate is monoclinic, space group P21, with lattice parameters a= 27.24(1), b= 9.183(3), c= 13.96(2)A, β= 91.52(2)°, and Z= 4 [two independent molecules (A) and (B) in the unit cell]. The crystal structure was determined by Patterson rotation and translation methods, from the X-ray intensities of 2 496 reflections measured by diffractometer and refined by block-diagonal least-squares to R 0.10. Molecules (A) and (B) have almost fully extended conformations, but differ at the ends of the C(17) chains, in the rotations at the ester bonds, and in the nonanoate chains. The molecules are in antiparallel array forming monolayers with thickness d100 27.2 A, and having molecular long axes tilted at ca. 61° with respect to the layer interface. In the interface region, atoms are almost in the liquid state. The crystal structure is unusual in that the nonanoate chains pack with cholesteryl tetracyclic systems and not with each other. Arrangements of this kind are presumed to exist when cholesterol is incorporated within biological membranes.
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TL;DR: The crystal and molecular structure of two newly prepared chromium(III) complexes [Cr(L-asp)(phen)(H2O)]NO3·2H 2O 1[Lasp =L-aspartate(2)-), phen = 1,10-phenanthroline] and [Cr (terpy)(pydca)][Cr(pydCA)2]·4H2Os 3(pYDCA = pyridine-2,6-dicarboxylate, terpy = 2,2′:6′,
Abstract: The crystal and molecular structure of two newly prepared chromium(III) complexes [Cr(L-asp)(phen)(H2O)]NO3·2H2O 1[L-asp =L-aspartate(2–), phen = 1,10-phenanthroline] and [Cr(terpy)(pydca)][Cr(pydca)2]·4H2O 3(pydca = pyridine-2,6-dicarboxylate, terpy = 2,2′:6′,2′′-terpyridyl) were determined by means of X-ray diffraction. Crystals of 1 are triclinic, space group P, with a= 11.793(5), b= 10.507(5), c= 9.258(5)A, α= 111.43(3), β= 86.44(3) and γ= 111.71(3)°. Crystals of 3 are triclinic, space group P, with a= 19.100(5), b= 12.874(5), c= 7.575(5)A, α= 86.16(3), β= 95.10(3) and γ= 96.62(3)°. The co-ordination around the Cr atom in both 1 and 3 is distorted octahedral, the sixth position of 1 being occupied by a water molecule. Crystals of 3 are built up of two different ionic units. ESR spectra were run on magnetically dilute powders and frozen solutions, and the values of the spin-Hamiltonian parameters obtained by computer simulation. The similarity between these parameters for the chromium(III) species in powders and glasses suggests that the solution species possess the same kind of distortion found for the solid complexes.
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TL;DR: In this article, three empirical potential models (dumbbell, Kihara, and ellipsoidal overlap) are fitted to theoretical calculations of H2-H2 and H2−He repulsion.
Abstract: Three empirical potential models (dumbbell, Kihara, and ellipsoidal overlap) are fitted to theoretical calculations of H2–H2 and H2–He repulsion. The dumbbell model gives a slightly better fit and has better transferability. This model is recommended because of its simplicity and physical meaningfulness.
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TL;DR: The structure of bis(triphenylphosphine) (1,1-dichloro-2,2-dicyanoethylene)platinum(O), Pt[Cl 2 CC(CN) 2 ] [P(C 6 H 5 ) 3 ] 2 has been determined at room temperature from three dimensional X-ray data collected by counter methods as discussed by the authors.
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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
576 citations
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