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
More filters
TL;DR: In this article, the reaction of strontium bis[bis(trimethylsilyl)amide] with bis[trimethyisilyl)-phosphine in toluene with subsequent addition of a few drops of THF yields a compound with three bridging and one terminal phosphide ligand.
42 citations
TL;DR: In this article, a single-crystal analysis reveals (2S, 3S) absolute configuration of (+)-1 on the basis of tentative comparison of CD data with those for the 1,4-benzodiazepine derivative (+)-8 of known absolute configuration.
Abstract: Resolution of racemic cis-3-(2-aminophenylthio)-2-hydroxy-3-(4-methoxyphenyl) propionic acid (2) via the cinchonidine salt 3, and brucine salt 4, isolation of the calcium salts (+)- and (−)-5, as well as their cyclization to enantiomeric 1,5-benzothiazepines (+)- and (−)-1, are described. X-Ray single-crystal analysis reveals (2S, 3S) absolute configuration of (+)-1 on the basis of tentative comparison of CD data with those for the 1,4-benzodiazepine derivative (+)-8 of known absolute configuration.
42 citations
TL;DR: The peptide N‐ Boc‐L‐Gly‐dehydro‐Phe‐NHCH3 was synthesized by the combination of N‐Boc‐ L‐Glys‐deHydro‐phe azlactone and methylamine by direct methods using SHELXS 86 and the structure was refined by full‐matrix least squares procedure to an R value of 0.049.
Abstract: The peptide N-Boc-L-Gly-dehydro-Phe-NHCH 3 was synthesized by the combination of N-Boc-L-Gly-dehydro-Phe azlactone and methylamine. The peptide crystallizes in orthorhombic space group P2 1 2 1 2 1 with a = 5.679(2) A, b = 16.423(9) A, c = 19.198(10) A, V = 1791(2) A 3 , Z = 4, dm = 1.212(5) Mg m −3 , dc = 1.237(1) Mg m −3 . The structure was determined by direct methods using SHELXS 86. The structure was refined by full-matrix least squares procedure to an R value of 0.049 for 1509 observed reflections. The molecular dimensions are, in general, in good agreement with the standard values. The bond angle C α -C β -C γ ; in the dehydro-Phe residue is 133.6(5)°. The peptide backbone torsion angles are θ 1 = −171.4(4)°, ω 0 = 178.2(4)°, Φ 1 = −57.2(6)°, ψ 1 = 141.2(4)°, ω 1 = −174.4(4)°, Φ 2 = 71.5(6)°, ψ 2 = 7.2(6)°, and ω 2 = −179.8(5)°. These values show that the backbone adopts the β-bend type II conformation. The Boc group has a trans-trans conformation. The side-chain torsion angles in dehydro-Phe are χ 2 = 1.6(9)°, χ 2,1 2 = 0.5(9)°, and χ 2,2 2 = 179.8(6)°. The plane of C α 2 -C β 2 -C γ 2 is rotated with respect to the plane of the phenyl ring at 0.5(6)° , which indicates that the atoms of the side chain of the dehydro-Phe residue are essentially coplanar. As a result of the β-bend in the structure, an intramolecular hydrogen bond is formed between the oxygen of the ith residue and the NH of the (i + 3)th residue at a distance of 2.940(5) A. The crystal structure is stabilized by a network of hydrogen bonds and van der Waals interactions.
42 citations
TL;DR: In this article, it was shown that the two octahedral tin sites in the structure of SnMe2Cl2·2[Ni(3MeO-salphen)·H2O appear to result from two isomeric forms of the adduct coexisting in a lattice as a result of hydrogen-bonding interactions.
Abstract: 1:1 Addition complexes of [NiIIL]·H2O [H2L =N,N′-bis(3-methoxysalicylidene)ethylenediamine (3MeO-H2salen), N,N′-bis(3-methoxysalicylidene)propane-1,2-diamine (3MeO-H2salpn) or N,N′-bis(3-methoxysalicylidene)-o-phenylenediamine (3O-H2salphen)] with SnR2Cl2(R = Me or Ph), SnBunCl3, or SnCl4 have been found to be generally monoaqua adducts of the tin Lewis acids with the water engaged in hydrogen bonding with the methoxy and phenolic oxygen atoms of the Schiffbase ligand. Both water and methoxy oxygen atoms are involved in donor-bond formation to tin in the polymeric structures 2SnMe2Cl2·[Ni(3MeO-salen)]·H2O and SnMe2Cl2·[Ni(3MeO-salphen)]·H2O, each of which has two very different tin environments. The two octahedral tin sites in the structure of SnMe2Cl2·2[Ni(3MeO-salphen)·H2O] appear to result from two isomeric forms of the adduct co-existing in a lattice as a result of hydrogen-bonding interactions. Crystal-structure determinations revealed that the monoaqua adducts of dimethyltin dichloride which exist in the structures SnMe2Cl2·[Ni(3MeO-salen)]·H2O and SnMe2Cl2·[Ni(3MeO-salon)]·H2O differ in that, in the former tin is in a trigonal-bipyramidal environment, whereas in the latter it is in an octahedral environment as a result of an intermolecular Sn ⋯ Cl contact of 3.615 A.
41 citations
TL;DR: In this paper, the first trischelates of the dichalcogenolene ligands 1,3-dithiole-2-thione-4,5dithiolate (dmit) and 1,2-dimethyl-diselenolate (dmt) with the central ions In(III), Tl(III) and V(IV) are reported.
41 citations
References
More filters
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