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: In this article, diphenyl phosphorazidate (DPPA) was used as the azide source in a one-pot synthesis of 2,2-disubstituted 3-amino-2H-azirines.
Abstract: Diphenyl phosphorazidate (DPPA) was used as the azide source in a one-pot synthesis of 2,2-disubstituted 3-amino-2H-azirines 1 (Scheme 1). The reaction with lithium enolates of amides of type 2, bearing two substituents at C(2), proceeded smoothly in THF at 0°; keteniminium azides C and azidoenamines D are likely intermediates. Under analogous reaction conditions, DPPA and amides of type 3 with only one substituent at C(2) gave 2-diazoamides 5 in fair-to-good yield (Scheme 2). The corresponding 2-diazo derivatives 6–8 were formed in low yield by treatment of the lithium enolates of N,N-dimethyl-2-phenylacetamide, methyl 2-phenylacetate, and benzyl phenyl ketone, respectively, with DPPA. Thermolysis of 2-diazo-N-methyl-N-phenylcarboxamides 5a and 5b yielded 3-substituted 1,3-dihydro-N-methyl-2H-indol-2-ones 9a and 9b, respectively (Scheme 3). The diazo compounds 5–8 reacted with 1,3-thiazole-5 (4H)-thiones 10 and thiobenzophenone (13) to give 6-oxa-1,9-dithia-3-azaspiro[4.4]nona-2,7-dienes 11 (Scheme 4) and thiirane-2-carboxylic acid derivatives 14 (Scheme 5), respectively. In analogy to previously described reactions, a mechanism via 1,3-dipolar cycloaddition, leading to 2,5-dihydro-1,3,4-thiadiazoles, and elimination of N2 to give the ‘thiocarbonyl ylides’ of type H or K is proposed. These dipolar intermediates with a conjugated CO group then undergo either a 1,5-dipolar electrocyclization to give spirohetrocycles 11 or a 1,3-dipolar electrocyclization to thiiranes 14.
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TL;DR: The MnCl2 (H2 DIP) · 5H2O complex [H2DIP = 2,6-diacetyl-pyridinebis(picolinoylhydrazone)] has been synthesized and examined by i.r.-spectroscopy and x-ray diffractometry as discussed by the authors.
Abstract: The MnCl2 (H2 DIP) · 5H2O complex [H2DIP = 2,6-diacetyl-pyridinebis(picolinoylhydrazone)] has been synthesized and examined by i.r.-spectroscopy and x-ray diffractometry. Crystals are triclinic (P\((P \bar 1)\)) with unit-cell dimensions:α = 15.00(1),b= 13.65(1),c = 7.565(6) A,α = 92.4(1),β = 97.5(1),γ = 117.5(1)°; Z = 2. The structure was solved from 1788 independent diffractometer data by direct methods and refined anisotropically by block-diagonal leastsquares calculations toR = 5.4%. The manganese ion has a distorted pentagonal-bipyramidal geometry, in which the organic molecule acts as a pentadentate ligand. A disordered distribution involving chlorine ions and water molecules is present.
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TL;DR: In this paper, stepwise reaction mechanisms via zwitterionic intermediates are proposed to stabilize [3+2] cycloadducts stabilize via extrusion of COX or ring opening.
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TL;DR: In this article, the reaction of calcium with bis[bis(trimethylsilyl)methyl]tin(II) in a solvent mixture of toluene and 1,2-dimethoxyethane yields calcium-bis{tris[bis[bis-trimelilyl]methyl]stannanide}·2DME, tris[bi(trimsilyl)-methyl]-stannane and benzyl-tris [bis-bi-sily lm]methyl], stannane; only the first two
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TL;DR: The crystal and molecular structure of the adduct (HAlN-i-Pr)6AlH3 has been determined from single-crystal and three dimensional X-ray diffraction data collected by counter methods as discussed by the authors.
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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