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 peptide N‐Ac‐dehydro‐Phe‐L‐Val‐L-Val‐OCH3 (C22H31N3O5) was synthesized by the usual workup procedure and finally by coupling the N‐ Ac‐deHydro‐phe‐l‐Val-OH to valine methyl ester toValine methylEster to crystallize from its solution in acetonitrile‐water mixture at 4°C.
Abstract: The peptide N-Ac-dehydro-Phe-L-Val-L-Val-OCH3 (C22H31N3O5) was synthesized by the usual workup procedure and finally by coupling the N-Ac-dehydro-Phe-L-Val-OH to valine methyl ester. It was crystallized from its solution in acetonitrile-water mixture at 4°C. The crystals belong to the space group P1 with a = 8.900(3) A, b = 11.135(2) A, c = 12.918(2) A, α = 90.36(1)°, β = 110.14(3)°, γ = 90.10(3)°, V = 1207.7(6) A,3Z = 2, dm = 1.156(5) Mgm−3, dc = 1.148(5) Mgm−3. The structure was determined by direct methods using SHELXS86. The structure was refined by full-matrix least-squares procedure to an R value of 0.077 for 3916 observed reflections. The molecular dimensions and conformations of the two crystallographically independent molecules are in good agreement. In the dehydro residues, the average Cα–Cβ distance is 1.31(2) A whereas the bond angle Cα–Cβ–Cγ is 132(1)°. The average backbone torsion angles are ω0 = 169(1)°, ϕ1 = −40(1)°, ψ1 = −50(1)°, ω1 = −177(1)°, ϕ2 = 54(1)°, ψ2 = 46(1)°, ω2 = −174(l)°, ϕ3 = 103(1)°, ψ = −139(1)°, and θ = −176(1)°. The acetyl group is in the trans conformation, while the backbone adopts a right-handed and left-handed helical conformation alternatingly. The two crystallographically independent molecules are held together by three hydrogen bonds: N21–H21–O′12 = 2.911(12) A, N22–H22–O′11 = 2.941(12) A and N23–H23–O11 = 3.005 (9) A. The crystal structure is stabilized by van der Waals forces and three additional hydrogen bonds: N11–H11–O2, = 2.896(15) A, N12–H12–O′21 = 2.947(14) A and N13–H13–O21 = 2.987(15) A.
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TL;DR: A preliminary survey of the present knowledge of the solid-mesophase relationships has been given by Bryan as discussed by the authors, who pointed out that although this is true of at least the majority of the small number of cases so far known, it is a generalisation which must at this stage be treated with caution.
Abstract: It is now well established that for a proper understanding and interpretation of several physical properties of liquid crystalline phases, a knowledge of the molecular arrangement in the crystalline state is very useful. A preliminary survey of the present knowledge of the solid-mesophase relationships has been given by Bryan1. The classical view is that in typical nematogen crystals the long narrow molecules lie more or less parallel and are interleaved giving what was described by Bernal and Crowfoot2 as an imbricated packing and that the transformation from the solid to the nematic phase is characterised by the breakdown of the positional order of the molecules but not of the orientational order. Leadbetter3 has however pointed out that although this is true of at least the majority of the small number of cases so far known, it is a generalisation which must at this stage be treated with caution. Hence the determination of the crystal and molecular structure of the title nematogenic compound w...
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TL;DR: A combined experimental and theoretical charge density study of the coordination polymer Zn(HCOO)(2)(H(2)O)(2), which serves as a nonmagnetic reference for the isostructural magnetic compounds containing 3d transition metals, shows that the Zn atom densities are highly spherical but show small accumulations of charge toward the negative ligands.
Abstract: We present a combined experimental and theoretical charge density study of the coordination polymer Zn(HCOO)2(H2O)2, which serves as a nonmagnetic reference for the isostructural magnetic compounds containing 3d transition metals. The charge density has been modeled using the multipole formalism against a high-resolution single-crystal X-ray diffraction data set collected at 100 K. The theoretical model is based on periodic density functional theory calculations in the experimental geometry. To gauge the degree of systematic bias from the multipole model, the structure factors of the theoretical model were also projected into a multipole model and the two theoretical models are compared with the experimental results. All models, both experiment and theory, show that the Zn atom densities are highly spherical but show small accumulations of charge toward the negative ligands. The metal–ligand interactions are found to be primarily ionic, but there are subtle topological indications of covalent contribution...
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TL;DR: These results confirm the existence of two separate chelate sites, N(1)-O(2) and O(4)-N(5), in the flavoquinoid system and offer further evidence that both these chelate Sites will nearly always be occupied by positive ions or dipoles.
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TL;DR: In this paper, X-ray structure analyses of 1,2,3,4-Tetraphenyl-cyclo-5-carba were performed on triclinic trichlinic crystals and the results showed that the P4C-ring has twist conformation, the carbon atom lies almost in the mean plane of the ring.
Abstract: Rontgenstrukturanalysen von 1,2,3,4-Tetraphenyl-cyclo-5-carba-1,2,3,4-tetraphosphan 1 und 1,4-Dithio-1,2,3,4-tetraphenyl-cyclo-5-carba-1,2,3,4-tetraphosphan 2 ergaben:
kristallisiert in der monoklinen Raumgruppe Cc mit a = 22,272, b = 13,726, c = 7,492 A, β = 96,82° und Z = 4. Der P4C-Ring liegt in der „envelope”-Konformation vor. Die Phenylgruppen sind alternierend auf beiden Seiten des Ringes angeordnet.
bildet trikline Kristalle, Raumgruppe P1, a = 10,900, b = 10,663, c = 12,233 A, α = 106,26, β = 100,04, γ = 70,65°, Z = 2. Der P4C-Ring liegt in der Twist-Konformation vor; das C-Atom befindet sich nahezu auf der mittleren Ringebene. Die Schwefelatome sind exostandig an den dem C-Atom benachbarten Phosphoratomen gebunden und in trans-Postion zueinander angeordnet.
Contributions to the Chemistry of Phosphorus. 66. Crystal and Molecular Structure of 1,2,3,4-Tetraphenyl-cyclo-5-carba-1,2,3,4-tetraphosphane, (PC6H5)4CH2, and 1,4-Dithio-1,2,3,4-tetraphenyl-cyclo-5-carba-1,2,3,4-tetraphosphane, (PC6H5)4CH2S2
The following results were achieved by X-ray structure analyses of 1,2,3,4-Tetraphenyl-cyclo-5-carba-1,2,3,4-tetraphosphane 1 and 1,4-Dithio-1,2,3,4-tetraphenyl-cyclo-5-carba-1,2,3,4-tetraphosphane 2:
crystallises in the monoclinic space group Cc with a = 22.272, b = 13.726, c = 7.492 A, β = 96.82° and Z = 4. The P4C-ring has an envelope conformation. The phenyl groups are arranged alternately on both sides of the ring.
forms triclinic crystals, space group P1, with a = 10.900, b = 10.663, c = 12.233 A, α = 106.26, β = 100.04, γ = 70.65°, Z = 2. The P4C-ring has twist conformation, the carbon atom lies almost in the mean plane of the ring. The sulfur atoms are bonded in exo position to the phosphorus atoms neighbouring the carbon atom and in trans position to each other.
23 citations
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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