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 structure of the bromide, SnSn, has been determined and shown to consist of molecular units in an approximately staggered conformation, with an SnSn distance of 2.841(1) A.
19 citations
TL;DR: In the presence of oxygen, the formation of the corresponding quinone imine N-oxide is observed, leading to new insights into the chemistry of nitric oxide with aminoxyls.
Abstract: 2-Methyl-2-phenyl-3-oxoindolin-1-yloxyl and 2-methyl-2-phenyl-3-aryliminoindolin-1-yloxyl radicals react with nitric oxide in the absence and presence of oxygen to form both substituted and unsubstituted N-nitro and N-nitroso stable compounds as the main products, while mono and dinitro compounds are formed in minor yields In the presence of oxygen, the formation of the corresponding quinone imine N-oxide is observed Mechanisms for the formation of the reaction products are proposed and discussed, leading to new insights into the chemistry of nitric oxide with aminoxyls Crystal structures of 2-methyl-2-phenyl-N-nitrosoindolin-3-one and 2-methyl-2-phenyl-N-nitroindolin-3-one have been determined
19 citations
TL;DR: The crystal and molecular structure of 5−sulphosalicylic acid dideuterate have been studied using three-dimensional single crystal neutron diffraction data as discussed by the authors, and two almost identical D5O2+ cations were found, and both reside on centers of symmetry.
Abstract: The crystal and molecular structure of 5‐sulphosalicylic acid dideuterate has been studied using three‐dimensional single crystal neutron diffraction data. The triclinic unit cell, space group P1, contains two formula units, with dimensions a=7.028(5), b=7.007(5), c=11.678(8) A, α=71.49(4), β=94.07(2), and γ=109.35(2) °. A total of 2883 unique reflections were collected and full matrix least‐squares refinement on F0 2 yielded an R=0.079. Two almost identical D5O2+ cations were found, and both reside on centers of symmetry, suggesting that the cations are best formulated as (D2O⋅D⋅OD2)+ species. The bridging deuterium atoms have their largest vibrational amplitudes along the O–O direction, which is indicative of a broad–flat anharmonic single‐minimum potential energy well. The slight deviations from this direction are correlated with the terminal oxygen atom vibrations. X‐ray versus neutron difference density maps show pronounced polarization of the C–H and O–D bonds.
19 citations
TL;DR: In this paper, complete solution NMR data (119Sn, 13C) are reported for these and other meta- and ortho-substituted aryltins.
19 citations
TL;DR: In this paper, the experimental charge density of a highly substituted fullerene derivative, the Th-symmetrical dodekakis(ethoxycarbonyl)-C60-fullerene cocrystallized with difluorobenzene, C102H60O24·2C6H4F2, was determined, on the basis of a high-resolution synchrotron/CCD data set of more than 350 000 reflections.
Abstract: The experimental charge density of a highly substituted fullerene derivative, the Th-symmetrical dodekakis(ethoxycarbonyl)-C60-fullerene cocrystallized with difluorobenzene, C102H60O24·2C6H4F2, was determined, on the basis of a high-resolution synchrotron/CCD data set of more than 350 000 reflections. A full topological analysis, using Bader's AIM theory, was performed. Experimental bond critical point (BCP) properties, obtained by three multipole models, were compared to each other and to those derived by theoretical methods from HF/6-31G** and from B3LYP/6-31G** calculations. ρ(rBCP) vs bond distance relationships were investigated for the different experimental and theoretical models. Based on linear fits obtained for experimental model densities, ρ(rBCP) values of further C−C bonds can be predicted. Due to substitution, this C60 derivative has six chemically different C−C bonds. A statistical analysis of the BCP properties for these bonds was carried out to explore the reproducibility of different top...
19 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