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 the supercooled α and β phases of p−dichlorobenzene were determined at 100°K and a detailed comparison was made with the γ phase structure previously reported at that temperature as mentioned in this paper.
Abstract: The structures of the supercooled α and β phases of p‐dichlorobenzene are determined at 100 °K and a detailed comparison made with the γ‐phase structure previously reported at that temperature [Acta Crystallogr B 31, 911 (1975)] The effects of temperature are investigated by a redetermination of the β‐phase structure at room temperature and by measurement of the thermal expansion coefficients for the α‐ and β‐phase crystals The average atomic thermal displacements are found to be in the expected thermodynamic order For chlorine we find Ū (β) =0184 A, Ū (α) =0169 A, and Ū (γ) =0157 A at 100 °K Rigid body analysis of our data gives good agreement between calculated and observed librational lattice frequencies New limits are placed on the density changes associated with the phase transitions [ΔV (α→β) =01±04% and ΔV (γ→α) =05±04%] The effects of crystal field on the molecular geometry are limited to a slight out‐of‐plane displacement (0045 A) of the chlorine atoms in the γ phase The possibility of such distortions in the high temperature α and β phases is masked by slight positional disorder (∼002 A) The chlorine–chlorine interactions are found to be attractive and anisotropic This indicates the necessity of including anisotropic terms in semiempirical atom–atom potential functions All presently available functions, including Coulomb–Coulomb terms, are found to be inadequate for this reason
68 citations
TL;DR: Several optically active electron-rich olefins L2★ have been prepared from readily available chiral starting materials, such as (S)-α-amino-acids or terpene derivatives (e.g., (+)- or (−)-3-pinanecarboxylic acid) as mentioned in this paper.
67 citations
TL;DR: In this paper, the crystal and molecular structure of N-benzyloxycarbonyl-\alpha-aminoisobutyryl-L-prolyl methylamide, the amino terminal dipeptide fragment of alamethicin, has been determined using direct methods.
Abstract: The crystal and molecular structure of N-benzyloxycarbonyl-\alpha-aminoisobutyryl-L-prolyl methylamide, the amino terminal dipeptide fragment of alamethicin, has been determined using direct methods. The compound crystallizes in the orthorhombic system with the space group ${P2}_12_12_1$. Cell dimensions are a = 7.705 A, b = 11.365 A, and c = 21.904 A. The structure has been refined using conventional procedures to a final R factor of 0.054. The molecular structure possesses a 4 \rightarrow 1 intramolecular N-H- - -0 hydrogen bond formed between the CO group of the urethane moiety and the NH group of the methylamide function. The peptide backbone adopts the type III \beta-turn conformation, with ${\phi}_2$ = -51.0 deg, ${\psi}_2$ = -39.7 deg, ${\phi}_3$ = -65.0 deg, ${\psi}_3$ = -25.4 deg. An unusual feature is the occurrence of the proline residue at position 3 of the \beta-turn. The observed structure supports the view that Aib residues initiate the formation of type III \beta-turn conformations. The pyrrolidine ring is puckered in $C^{\gamma}-exo$ fashion.
67 citations
TL;DR: In this paper, the reaction of [N(n-C4H9)4]2[closo-B12H11CH3] with Grignard reagents, RMgX, in the presence of catalytic amounts of trans-Pd(PPh3)2Cl2 and CuI in either tetrahydrofuran or 1,4-dioxane solution produced the corresponding alkylated or arylated polyhedral borane anions in good yield.
Abstract: The reaction of [N(n-C4H9)4]2[closo-B12H11I], [N(n-Bu)4]2[2], with Grignard reagents, RMgX, in the presence of catalytic amounts of trans-Pd(PPh3)2Cl2 and CuI in either tetrahydrofuran or 1,4-dioxane solution produced the corresponding alkylated or arylated polyhedral borane anions, closo-B12H11R2-, in good yield. By this method, we have synthesized [N(n-C4H9)4]2[closo-B12H11CH3], [N(n-Bu)4]2[3]; [N(n-C4H9)4]2[closo-B12H11C6H5], [N(n-Bu)4]2[4]; and Cs2[closo-B12H11(n-C18H37)], Cs2[5]. The structures of Cs2[3] and PPN2[4] have been determined by X-ray diffraction studies. Crystallographic data are as follows: for Cs2[3], orthorhombic, space group Pmcn, a = 954.6(6) pm, b = 1077.0(7) pm, c = 1396.8(9) pm, Z = 4, R = 0.055; for PPN2[4], which cocrystallized with two molecules of DMSO and one molecule of toluene, triclinic, space group P1, a = 1138.4(10) pm, b = 1920.1(17) pm, c = 2143.2(18) pm, α = 93.26(2)°, β = 104.44(2)°, γ = 105.86(2)°, Z = 2, R = 0.076.
67 citations
TL;DR: In this article, the Li4 clusters in the tetramer units of crystalline ethyllithium tend to increase their symmetry at low temperature, and the 4-centre bond peaks CLi3 are observed in difference maps, suggest some covalent bonding inside the tramers.
66 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