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 paper, 3-oxo esters were shown to react with the dimer of p -methoxyphenyl-thionophosphine sulfide (1) and elemental sulfur in anhydrous toluene at 110° to give the corresponding 3H-1,2-dithiole-3thiones (2 ) in nearly quantitative yields.
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TL;DR: A library has been built of average multipole populations describing the electron density of chemical groups in all 20 amino acids found in proteins, using the Hansen & Coppens multipolar pseudo-atom model to derive molecular electron density and electrostatic potential distributions.
Abstract: With an increasing number of biomacromolecular crystal structures being measured to ultra-high resolution, it has become possible to extend to large systems experimental charge-density methods that are usually applied to small molecules. A library has been built of average multipole populations describing the electron density of chemical groups in all 20 amino acids found in proteins. The library uses the Hansen & Coppens multipolar pseudo-atom model to derive molecular electron density and electrostatic potential distributions. The library values are obtained from several small peptide or amino acid crystal structures refined against ultra-high-resolution X-ray diffraction data. The library transfer is applied automatically in the MoPro software suite to peptide and protein structures measured at atomic resolution. The transferred multipolar parameters are kept fixed while the positional and thermal parameters are refined. This enables a proper deconvolution of thermal motion and valence-electron-density redistributions, even when the diffraction data do not extend to subatomic resolution. The use of the experimental library multipolar atom model (ELMAM) also has a major impact on crystallographic structure modelling in the case of small-molecule crystals at atomic resolution. Compared to a spherical-atom model, the library transfer results in a more accurate crystal structure, notably in terms of thermal displacement parameters and bond distances involving H atoms. Upon transfer, crystallographic statistics of fit are improved, particularly free R factors, and residual electron-density maps are cleaner.
144 citations
TL;DR: In this article, a study of intramolecular hydrogen bonding in benzoylacetone (1-phenyl-1,3-butadione) has been carried out with 8.4(4)K X-ray data and 20(1)K neutron data.
Abstract: A study of intramolecular hydrogen bonding in benzoylacetone (1-phenyl-1,3-butadione) has been carried out with 8.4(4)K X-ray data and 20(1)K neutron data. Analysis of the neutron data shows that the hydrogen, between the two oxygens in the keto−enol part of the molecular structure, is asymmetrically placed in a large flat potential well. The charge density obtained from X-ray and neutron data has been analyzed by using multipolar functions and topological methods, which gave evidence of extensive π-delocalization in the keto−enol group. The multipole populations show that there are large formal charges on the oxygens and the enol hydrogen, which impart polar character to the hydrogen bond. This effect is also evident in the Laplacian and in the electrostatic potential calculated from the X-ray data and it is found that the hydrogen position is stabilized by both electrostatic and covalent bonding contributions at each side of the hydrogen atom. The resonance assisted hydrogen bonding model has been refin...
140 citations
TL;DR: The auracarboranes 1,2-(AuPPh3)2-1,2-C2B10H10 (1) and 1,1'π3'2]-2-[2-(1',2'c2b10h10)-1'pPh3] (2) have been synthesized and characterized by NMR and X-ray crystallography as discussed by the authors.
Abstract: The auracarboranes 1,2-(AuPPh3)2-1,2-C2B10H10 (1) and 1,1‘-(AuPPh3)2-[2-(1‘,2‘-C2B10H10)-1,2-C2B10H10] (2) have been synthesized. Both compounds were characterized by NMR and X-ray crystallography. Compound 2 was found to contain an aurophilic interaction between the gold centers. A variable-temperature NMR investigation indicated that the energy barrier separating the gold−gold bonded state and the nonbonded state is 11 ± 1 kcal/mol. Compound 1 crystallized in the monoclinic space group P21/c with a = 18.3380(9) A, b = 14.1037(6) A, c = 19.4716(8) A, β = 112.003(2)°, V = 4669 A3, and Z = 4. Data were collected using Mo Kα radiation, to a maximum 2θ = 50°, giving 8865 unique reflections, and the structure was solved by heavy atom methods. The final discrepancy index was R = 0.047, Rw = 0.055 for 3423 independent reflections with I > 3σ(I). Compound 2 crystallized in the monoclinic space group P21/c with a = 14.058(6) A, b = 18.365(8) A, c = 20.387(9) A, β = 109.22(1)°, V = 4970 A3, and Z = 4. Data were co...
138 citations
TL;DR: The results indicate that density has migrated from the atomic regions into the bonds and into the nitrogen lone-pair region in the small organic molecule s-triazine.
Abstract: X-ray and neutron-diffraction data were combined for study of deviations from spherical symmetry of the atomic charge distributions in the small organic molecule s-triazine. The results indicate that density has migrated from the atomic regions into the bonds and into the nitrogen lone-pair region. Refinement procedures for x-ray data, which do not take these bonding effects into account, give parameters containing small but measurable errors.
133 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