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 p-n-propoxy-and pn-pentoxy-benzoic acids (3OBAC and 5OBAC) have been determined at room temperature by single-crystal x-ray analysis.
Abstract: The crystal structures of p-n-propoxy- and p-n-pentoxy-benzoic acids (3OBAC and 5OBAC) have been determined at room temperature by single-crystal x-ray analysis. Both crystals have sheet structures. Within each sheet the molecules are arranged as hydrogen-bonded dimers in head-to-tail fashion in parallel staggered rows. The long axes of the aromatic nuclei are almost normal to crystal b. The alkyl chains are in planar extended form, but the ether oxygen and C(γ) are in a gauche relation about the C(α)-C(β) bond of the chain. The stacking of sheets is slightly different in 3OBAC which undergoes a solid-solid transition before yielding a nematic phase, than in 5OBAC which transforms directly to the nematic state. The tight face-to-face overlap of phenyl rings characteristic of the crystal structures of the two lowest homologs in the series, which are non-mesogenic at atmospheric pressure, is absent in these crystal structures where the ring planes in adjacent sheets are inclined to one another by a...
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TL;DR: The ‘azirine/oxazolone method’ has been used as a superior method for the introduction of the Aib as well as the Iva units into the peptide chain and the problem of the instability of the amide function of the Gln side chain under the conditions of the acid‐catalyzed hydrolysis of Z‐Gln‐(Aib)n‐N(Me)Ph was solved.
Abstract: The synthesis of a mixture of epimeric derivatives of the peptaibol trichotoxin A-50 (G) is described. The 'azirine/oxazolone method' has been used as a superior method for the introduction of the Aib as well as the Iva units into the peptide chain. In this protocol, 2,2-disubstituted 2H-azirin-3-amines are the synthons for 2,2-disubstituted glycines, which undergo coupling with N-protected amino or peptide acids in high yield, and without any need of coupling reagents. The problem of the instability of the amide function of the Gln side chain under the conditions of the acid-catalyzed hydrolysis of Z-Gln-(Aib)(n)-N(Me)Ph was solved by using an appropriate protecting group for the amide function of the Gln side chain, e.g., the triphenylmethyl (trityl; Tr) group. The structures of two intermediate peptides, i.e., the segments comprising residues 1-5 and 10-13, resp., were established by X-ray crystallography.
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TL;DR: In this paper, PdX 2(phmPz)2] (X = Cl−, N− 3) and PdN3(N3)2(pz) 2 (pdCl 2(pkPz),pz=1-phenyl-3-methylpyrazole) were obtained by metathesis from PdCl2(CH3CN) or by substitution of the chloride in by the azide ion.
Abstract: Mononuclear pyrazolyl Pd(II) complexes of the type [PdX 2(phmPz)2] (X = Cl−, N− 3) have been prepared. The 1-phenyl-3-methylpyrazole displaces acetonitrile from [PdCl2(CH3CN)2] to form [PdCl2(phmPz)2] (phmPz=1-phenyl-3-methylpyrazole) (1). [Pd(N3)2(phmPz)2] (2) could be obtained by metathesis from [PdCl2(CH3CN)2] or by substitution of the chloride in (1) by the azide ion. Both complexes were characterized by elemental analysis, infrared spectroscopy, 1H and 13C NMR and by single crystal X-ray diffraction. The coordination geometry around Pd(II) in these complexes is nearly square-planar, with the ligands in a trans configuration.
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TL;DR: In this article, the crystal and molecular structure of bis(creatinine)silver(II) perchlorate dihydrate, [Ag(C4H7N3O)2] ClO4·2H2O, was determined from single crystal three-dimensional X-ray data collected by counter methods.
23 citations
10 Apr 1984
TL;DR: L-Lysine d-pantothenate, a 1:1 amino acid-vitamin complex, has been solved by direct methods and refined to an R value of 0.053 for 1868 observed reflections.
Abstract: L-Lysine d-pantothenate, a 1:1 amino acid-vitamin complex, crystallizes in the monoclinic space group P21 with
Image Full-size image (1K) .The structure has been solved by direct methods and refined to an R value of 0.053 for 1868 observed reflections. The zwitterionic positively charged lysine molecules in the structure assume the sterically most favourable conformation with an all-trans side chain trans to the α-carboxylate group. The pantothenate anion has a somewhat folded conformation stabilised by an intramolecular bifurcated hydrogen bond. The unlike molecules aggregate into separate alternating layers. The molecules in the lysine layers form a head-to-tail sequence parallel to the a-axis. The interactions which hold the adjacent layers together include those between the side chain amino group of lysine and the carboxylate group in the pantothenate anion. The geometry of these interactions is such that each carboxylate group is sandwiched between two amino groups in a periodic arrangement of alternating carboxylate and amino groups.
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References
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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