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: The crystal structures of two mononuclear peroxotitanium(IV) chelates, the triclinic, deep red, pleochroitic diaquoperoxitanium dipicolinate [TiO2(C7H3O4N) (H2O)2]2H 2O as discussed by the authors, have been determined from X-ray diffractometer data, and refined to R = 2.7% and R = 5.1% (2324 reflections) respectively.
Abstract: The crystal structures of two mononuclear peroxotitanium(IV) chelates, the triclinic, deep red, pleochroitic diaquoperoxotitanium dipicolinate [TiO2(C7H3O4N) (H2O)2]2H2O, and the monoclinic, orange difluoroperoxotitanium dipicolinate K2[TiO2(C7H3O4N)F2]2H2O, have been determined from X-ray diffractometer data, and refined to R = 2.7% (3488 reflections) and R = 5.1% (2324 reflections) respectively. Analogous to a yellow-orange dinuclear peroxotitanium dipicolinate described earlier, the utanium atoms are coordinated approximately pentagonal bipyramidally, with the peroxo group and the chelate ligand occupying the equatorial sites and with H2O or F- forming the apices. The OO bond length in the peroxo group is the same in all structures, but there is a very slight variation of the Ti-peroxide distances apparently connected with the colours of the compounds. The more basic the apical ligands are (H2O F− μ-oxygen), the higher is the frequency of the absorption band, the longer are the Ti-peroxide distances, and the shorter are the apical bond lengths. Difference Fourier maps based on the final structures agree with this. The red diaquo complex shows highest residual peaks between titanium and the peroxo group, whereas the orange difluoro complex shows them near the apical TiF bonds. The packing of the complexes and hydrogen bonding are discussed. HO distances seem to indicate that the very acidic diaquo complex is near a transitional state towards a hydroxonium salt.
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TL;DR: In this article, the organometallic chemistry of niobium based on a macrocyclic ligand has been investigated, and it has been shown that the Niobium V complex has the properties similar to those of the (meso-octaalkylporphyrinogen)niobium(V) complex.
27 citations
27 citations
TL;DR: In this paper, a hexadentate ligand derived from triethylenetetetramine and salicylaldehyde has been synthesized in two crystalline forms, monoclinic and twin crystals.
Abstract: Iron(III) complexes of [FeL]BPh4·acetone containing the hexadentate ligand derived from triethylenetetramine and salicylaldehyde have been synthesized. These complexes were grown in two crystalline forms, monoclinic and the twin crystals. The crystal structure of the monoclinic form was determined at 290 K, at which temperature the complex is in a transition spin-state between high- and low-spin states; the spin-state interconversion rate of the monoclinic form is as fast as the inverse of the Mossbauer lifetime (1×10−7s) above 200 K. The monoclinic crystal of [FeL]BPh4·acetone is of space group P21⁄a, with a=27.418(4), b=10.097(2), c=14.726(3) A, β=98.00(1)°C, and Z=4. The average bond distances of Fe–O (1.875 A), Fe–Nimine (1.988 A), and Fe–Namine (2.069 A) are in good agreement with the expected values for the transition spin-state between high- and low-spin states. Twin crystals are in a high-spin state over the temperature range 78–320 K.
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TL;DR: In this article, the existence of a half-unit 7-amino-4-methyl-5-aza3-heptene-2-one (AEH) ligand was confirmed by a single-crystal X-ray structural analysis of di-μ-bromo-bis.
Abstract: Under suitable conditions, the single condensation of acetylacetone with ethylenediamine may occur to yield a “half-unit”, 7-amino-4-methyl-5-aza3-heptene-2-one (AEH), which has been characterized by 1H and 13C NMR. The existence of this ligand is definitively supported by a single-crystal X-ray structural analysis of di-μ-bromo-bis(7-amino-4-methyl-5-aza-3-heptene-2-onato)(1-)dicopper(II). EPR spectra give proof of spin-spin interactions between pairs of copper ions within dimers in the solid state and in solution. Low temperature spectra suggest that the interaction is antiferromagnetic.
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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