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, the structures of dimethyldichalkogenanes (H3C)2E2 liquid at room temperature have been determined by single-crystal x-ray diffraction.
Abstract: Element-Element Bonds. XI Chain Formation in Crystalline Dimethyldichalkogenanes
The structures of dimethyldichalkogenanes (H3C)2E2 liquid at room temperature have been determined by single-crystal x-ray diffraction {E = S, α-form 1a, P21/c; Z = 4; a = 860.9(5); b = 648.0(4); c = 845.9(4) pm; β = 94.23(4)°; −141 ± 2 °C; β-form 1b, P21/c; Z = 4; a = 518.3(3); b = 1445.6(10); c = 670.9(3) pm; β = 107.30(5)°; −141 ± 2 °C; E = Se, 2, Fdd2; Z = 16; a = 2236.6(5); b = 1759.0(9); c = 520.9(2) pm; −120 ± 2 °C; E = Te, 3, C2/c; Z = 4; a = 1260.8(4); b = 849.1(4); c = 561.0(3) pm; β = 107.04(6)°; −130 ± 2 °C}. As a remarkable result intermolecular E··E interactions indicated by the ratio Q = (E··E)/(E−E) increase gradually in strength when dimethyldisulfane with ordinary van der Waals contacts (1a, Q = 1.86; 1b, Q = 1.84) is compared with the selenium (2, Q = 1.54) and the tellurium derivatives (3, Q = 1.38). Taking these E··E contacts into account, an association of the binuclear molecules to pairs can be detected for polymorph 1b, whereas zigzag chains are encountered in the remaining crystal structures (1a, E−E··E = 95° and 174°; 2, 156° and 161°; 3, 151°). Additionally, by a careful inspection several crystal structures already published by other authors turn out to exhibit similar phenomena. Furthermore, the molecular packing modes of α-dimethyldisulfane (1a) and elementary chlorine resemble each other, whereas the β-polymorph 1b and the isotypic crystal structures of β-dibromo- and dichlorodiselane as described by Kniep, Korte und Mootz constitute a pair of polytypoid stacking variants. A similar relationship could be established between the structures of dimethyldiselane (2) and the homologous ditellane 3. In comparison with numerous literature data the intermolecular interactions observed with these dimethyldichalkogenanes have to be classified as only weak.
35 citations
TL;DR: The photo-induced reaction of Cp′ 2 M(CO) 2 complexes with trimethylphosphine provides the substitution products Cp 2 TiCl(PMe 3 ) (CO) in high yields as mentioned in this paper.
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TL;DR: In this paper, a series of new optically active 1H-imidazole 3-oxides with a substituted acetate group at N(1) as the chiral unit were prepared by the reaction of a-(hydroxyimino) ketones, a-amino acid methyl esters, and formaldehyde.
Abstract: A series of new optically active 1H-imidazole 3-oxides 5 with a substituted acetate group at N(1) as the chiral unit were prepared by the reaction of a-(hydroxyimino) ketones, a-amino acid methyl esters, and formaldehyde. In an analogous reaction, ethyl 2-(hydroxyimino)-3-oxobutyrate and 1,3,5- trialkylhexahydro-1,3,5-triazines gave 3-oxido-1H-imidazole-4-carboxylates 14, which easily rearranged into the 2-oxo derivatives 15. Selected examples of N-oxides 5 could be transformed into the corresponding 2,3-dihydro-1H-imidazole-2-thione derivatives 10 via a 'sulfur-transfer reaction', and the reduction of the histidine derivative 5i with Raney-Ni yielded the optically active 2,3-bis(imidazolyl)propanoate 12.
Furthermore, reaction of the (1H-imidazol-1-yl)acetates with primary amines yielded the corresponding acetamides.
35 citations
TL;DR: The chiral bicyclic guanidinium compound (2b) binds oxoanionic guests by a unique ion pairing pattern, which is confirmed by the X-ray crystal structure of the nitrate salt (2S, 8S)-2,8-bis(t-butyldiphenylsilyloxymethyl)-3,4,6,7,8,9-hexahydro-2H-pyrimido[1,2a]pyrimidine hydronitrate, and allows enantiodifferentiation of racemic
Abstract: The chiral bicyclic guanidinium compound (2b) binds oxoanionic guests by a unique ion pairing pattern, which is confirmed by the X-ray crystal structure of the nitrate salt (2S, 8S)-2,8-bis(t-butyldiphenylsilyloxymethyl)-3,4,6,7,8,9-hexahydro-2H-pyrimido[1,2a]pyrimidine hydronitrate, and allows enantiodifferentiation of racemic carboxylic acids by NMR.
35 citations
TL;DR: In this article, a linear dependence on Tolman's electronic parameter χ with metal shielding increasing as the acceptor character of the P(OR)3 ligand increases was found for the series of Os(p-cymene)X2PMe3.
35 citations
References
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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