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 structure of puromycin, a broad spectrum antibiotic and a structural analogue of the terminal 3′-aminoacyladenosine moiety of charged transfer tRNA's has been accurately determined using a total of 1968 reflections measured on a diffractometer as mentioned in this paper.
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TL;DR: Herbstein et al. as mentioned in this paper showed that the structure of tetra(«-butyl)ammonium triiodide has been determined in outline using graphite-monochromated MoATa, and the number of reflections used in the final refinement cycle were: 15370, II5295, III 2971.
Abstract: The structures of the ordered crystals of tetra(«-butyl)ammonium triiodide [I: a = 15.791(8), b = 15.993(8), c = 9.578(5) Α, α = 74.48(8)°, 0 = 101.52(9), y = 96.63(9)°, P I , Ζ = 4)] and (benzamide)2 · ΗΙ3; [II: a = 20.824(10), b == 9.874(5), c = 9.620(5) A, α = 95.58(9), β = 102.10(10), y = 94.72(9)°, PU Ζ = 4] have been fully refined, while that of caffeine · H 2 0 · HI3 [III: a = 14.043(5), b = 12.202(5), c = 9.701(5) Α, β = 106.5(1), P2Ja, Ζ = 4] has been determined in outline because of unresolved problems of disorder. Intensity measurements were made on a four-circle diffractometer using graphite-monochromated MoATa. The numbers of reflections used in the final refinement cycle were: 15370, II5295, III 2971.1 has cations of D2¿ symmetry (i.e. in the form of flattened crosses) which interleave to form channels of rectangular cross-section with axes along [001]; these channels contain single, almost-linear chains of triiodide ions, with weak 13 — 13 interactions within the chains. II is a pseudo-Type A basic salt, with pairs of benzamide molecules, (joined by a short, presumably symmetrical, proton bond between carbonyl groups) forming the cations; these cations are arranged so as to leave channels (axes along [001]) of rectangular cross-section which contain double, almost-linear chains of triiodide ions. In III the caffeine molecules are presumably protonated at N(9) and are hydrogen bonded via water molecules to form corrugated sheets, the molecular plane being in the sheets. These sheets are so disposed as to leave channels of rectangular cross-section which contain double chains of polyiodide ions. One of the three iodines is disordered along the chain direction and it was not possible to identify the nature of the chains ( — IJ * Pa r t i l i of Crystal Structures of Polyiodide Salts and Molecular Complexes; for Pa r t i i see Herbstein and Kapon, 1979 12 F. H. Herbstein et al.: Structures of three triiodides Table 1. Crystal data (n -C 4 H 9 ) ,NI 3 (Benzamide)2 • HI 3 Caffeine · Η 2 0 · Η Ι 3 f W t 615.12 624.00 593.92 F(000) 116
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TL;DR: In this paper, the chemistry of V−C functionalities anchored to a quasi-planar O4 matrix represented here by the [p-But-calix[4]-(OMe)2(O)2]2- macrocycle was dealt with.
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TL;DR: In this paper, a 1,5-dipolar electrocyclization of an acyl-substituted "thiocarbonyl-ylide" was proposed, which opens a convenient access to this type of five-membered heterocycles.
Abstract: The reaction of alpha-diazoketones 15a,b with 4,4-disubstituted 1,3-thiazole-5(4H)-thiones 6 (Scheme 3), adamantanethione (17), 2,2,4,4-tetramethyl-3-thioxocyclobutanone (19; Scheme 4), and thiobenzophenone (22; Scheme 5), respectively, at 50-90° gave the corresponding 1,3-oxathiole derivatives as the sole products in high yields. This reaction opens a convenient access to this type of five-membered heterocycles.The structures of three of the products, namely 16c, 16f, and 20b, were established by X-ray crystallography. The key-step of the proposed reaction mechanism is a 1,5-dipolar electrocyclization of an acyl-substituted ‘thiocarbonyl-ylide’ (cf. Scheme 6). The analogous reaction of 15a,b with 9H-xanthen-9-thione (24a) and 9H-thioxanthen-9-thione (24b) yielded alpha,beta-unsaturated ketones of type 25 (Scheme 5). The structures of 25a and 25c were also established by X-ray crystallography. The formation of 25 proceeds via a 1,3-dipolar electrocyclization to a thiirane intermediate (Scheme 6 ) and desulfurization. From the reaction of 15a with 24b in THF at 50°, the intermediate 26 (Scheme 5) was isolated. In the crude mixtures of the reactions of 15a with 17 and 19, a minor product containing a CHO group was observed by IR and NMR spectroscopy. In the case of 19, this side product could be isolated and was characterized by X-ray crystallography to be 21 (Scheme 4). It was shown that 21 is formed - in relatively low yield - from 20a. Formally, the transformation is an oxidative cleavage of the C=C bond, but the reaction mechanism is still not known.
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TL;DR: The crystal structure of phenoxatellurine, C12H8OTe, was determined by X-ray diffracto-meter methods as mentioned in this paper, where the positions of all atoms, including hydrogen, were found.
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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