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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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Journal ArticleDOI
TL;DR: In this article, the synthesis and conformational analysis of two Aib-containing cyclic hexapeptides, cyclo(Gly-Aib-Leu-AIB-Phe-Gly Aib -Phe Phe Aib) 1 and cyclo (Leu Aib, Phe GlyAib, Aib)-Aib 2, is described.

29 citations

Journal ArticleDOI
TL;DR: In this article, the structure of the principal constituent, coraxeniolide-A (1) was determined by X-ray diffraction studies, and Spectral analysis and chemical correlations elucidated the structures of CORAXENiolides B(3), C(7), C'(10), and corabohcin (13).

29 citations

Journal ArticleDOI
TL;DR: In this article, the meso-octaethylporphyrinogen tetraanion (Et8N4) was shown to be able to be further oxidized by an excess of Cp2FeBPh4 with O 2 or O 2 to [Et 8N4(Δ)2Mn−Cl]+[Cu 9Cl11Cl11]0.5, 7.5.
Abstract: This report deals with the different transition metal- and alkali cation-assisted oxidation pathways of the meso-octaethylporphyrinogen tetraanion [Et8N4]4-. The two-electron oxidation of [Et8N4Mn{Na(thf)2}2], 4, with Cp2FeBPh4 led to the corresponding monocyclopropane derivative [Et8N4(Δ)Mn], 6, [Δ ≡ cyclopropane], while the one-electron oxidation with CuCl2 or O2 led to the Mn(III)−porphyrinogen [Et8N4Mn][Li(thf)4], 5, which can be further oxidized by an excess of CuCl2 to [Et8N4(Δ)2Mn−Cl]+[Cu9Cl11]0.5, 7. The formation of 7 does not follow the expected sequence Mn(II) → Mn(III) → Mn(II)−monocyclopropane → Mn(II)−biscyclopropane−porphyrinogen. In the case of iron(II)−porphyrinogen, [Et8N4Fe{Li(thf)2}2], 9, the oxidation led in a preliminary stage to the iron(III) derivative [Et8N4Fe][Li(thf)4], 10, then to the metalated form of the biscyclopropane−porphyrinogen [Et8N4(Δ)2Fe−Cl]{μ-Cu4Cl5}], 11. The supposed stabilization of the biscyclopropane by the copper(I) cluster was ruled out by carrying the oxidat...

29 citations

Journal ArticleDOI
TL;DR: Zusammenfassung et al. as mentioned in this paper showed that with an equimolar amount of Na 2 (DAD) [DAD = (Ph)N=C(Ph)C(P)Ph)=N(Ph)] in the presence of DAD or with two equivalents of Na(DAD] results in the formation of the ionic complex, which has been characterized by IR and NMR spectroscopy.

29 citations

Journal ArticleDOI
TL;DR: In this paper, the one-electron density function for a molecule of first row atoms is partitioned into core and valence density pieces, and the residual density, after removal of the core density, constitutes the valence densities, which are assumed to be chemically interpretable.
Abstract: The one‐electron density function for a molecule of first‐row atoms is partitioned into core‐electron and valence‐electron density pieces. The SCF 1s AO's are used to define the core‐electron density pieces. The residual density, after removal of the core density, constitutes the valence density, which is assumed to be chemically interpretable. The partitioning is explored in reciprocal space to provide insight into x‐ray diffraction experiments. The contribution from valence scattering within the CuKᾱ sphere is 10%–30% of the total scattering. Valence‐electron density maps have been Fourier synthesized from x‐ray diffraction data of uracil. The density maps reveal trigonal bonding for the nitrogen atoms and bridge densities in the middle of the C(5)–C(6) and C(4)–C(5) bonds. The densities near the time‐average nuclear positions are unreliable.

29 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