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Journal ArticleDOI

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
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TL;DR: In this paper, the trans-dioxo cation of ReO2I(PPh3)2 with imidazole (ImH) and its methylated derivatives 1-MeIm, 1,2-Me2Im, 2-meImH, and 4(5)-MeImH yielded pure stable compounds.
Abstract: Reacting ReO2I(PPh3)2 with imidazole (ImH) and its methylated derivatives 1-MeIm, 1,2-Me2Im, 2-MeImH, and 4(5)-MeImH yielded salts of the trans-dioxo cation [ReO2L4]+. Pure stable compounds were isolated for X- = I- and L = ImH, 1,2-Me2Im, and 1-MeIm and X- = B(C6H5)4- and L = 1-MeIm, 2-MeImH and 5-MeImH. The νas(OReO) IR bands were observed between 765 and 794 cm-1, whereas the νs Raman band appeared in the 900−925 cm-1 range. The compounds were also characterized by 1H and 13C NMR and UV−vis spectroscopies. Crystal structures were determined for three compounds: [ReO2(2-MeImH)4][B(C6H5)4]·3CH3OH, triclinic, P1, a = 10.696(3) A, b = 15.128(4) A, c = 15.497(4) A, α = 113.57(2)°, β = 97.25(2)°, γ = 95.94(2)°, Z = 2, R = 0.030; [ReO2(1-MeIm)4][B(C6H5)4]·H2O·0.5CH3OH, monoclinic, P21/n, a = 15.619(2) A, b = 9.486(2) A, c = 27.387(4) A, β = 97.09(1)°, Z = 4, R = 0.057; [ReO2(5-MeImH)4][B(C6H5)4], orthorhombic, P212121, a = 10.199(2) A, b = 13.441(5) A, c = 28.798(10) A, Z = 4, R = 0.043. The complexes adopt...

50 citations

Journal ArticleDOI
TL;DR: The trichlorides of lanthanum, neodymium, samarium, and terbium react with Na(C5Me4H) in THF to yield the homoleptic complexes.
Abstract: Die Trichloride von Lanthan, Neodym, Samarium und Terbium reagieren mit Na(C5Me4H) in THF zu homoleptischen Verbindungen des Typs Ln(C5Me4H)3 [Ln = La (1a), Nd (1b), Sm (1c), Tb (1d)]. Dagegen fuhrt die Reaktion von HoCl3, TmCl3 und LuCl3 mit Na(C5Me4H) nur zu den Dicyclopentadienyl-Komplexen (C5Me4H)2LnCl(THF) [Ln = Ho (2e), Tm (2f), Lu (2h)]. Die Metallocene (C5Me4H)2Ln(THF)2 [Ln = Sm (3c), Yb (3g)] sind durch Umsetzung von LnI2 (Ln = Sm, Yb) mit Na(C5Me4H) erhaltlich. Die neuen Verbindungen wurden durch 1H- und 13C-NMR-Spektren, die Tricyclopentadienylderivate 1 a und 1 c durch Rontgenstrukturanalysen charakterisiert. Organometallic Compounds of the Lanthanides. 93. Tetramethylcyclopentadienyl Complexes of Selected 4f-Elements The trichlorides of lanthanum, neodymium, samarium, and terbium react with Na(C5Me4H) in THF to yield the homoleptic complexes Ln(C5Me4H)3 [Ln = La (1a), Nd (1b), Sm (1c), Tb (1d)]. On the other hand the reactions of HoCl3, TmCl3, and LuCl3 with Na(C5Me4H) result only with formation of the dicyclopentadienyl complexes (C5Me4H)2LnCl(THF) [Ln = Ho (2e), Tm (2f), Lu (2h)]. The metallocenes (C5Me4H)2Ln(THF)2 [Ln = Sm (3c), Yb (3g)] are obtained by the reactions of LnI2 (Ln = Sm, Yb) with Na(C5Me4H). The 1H- and 13C-NMR spectra as well as the X-ray crystal structure of the triscyclopentadienyl complexes 1 a and 1 c are discussed.

50 citations

Journal ArticleDOI
TL;DR: In this article, the reduction of rhCl 3 -3 H 2 O by sodium amalgam in THF solution under an atmosphere of N 2 and in the presence of an excess of a phosphine ligand has resulted in the formation of the hydridodinitrogen complexes RhH(N 2 )-(PPh(t-Bu) 2 ) 2 (I), rhH(P(i-Pr) 3 ) 3 ) 2

50 citations

Journal ArticleDOI
TL;DR: In this article, a nucleophilic substitution-rearrangement was performed upon treatment with various primary amines at elevated temperatures to yield N-1-substituted 4-amino-1H-pyrrolo[3,2-c]pyridines (5-azaindoles).

50 citations

Journal ArticleDOI
TL;DR: In this article, the reduction of cobalt−Schiff base complexes has been explored as a function of the nature of the ligand, and the reduction resulted in the formation of bifunctional Co(I)−Na complexes, while for salophen derivatives the reductive coupling of imino groups was observed.
Abstract: The reduction of cobalt−Schiff base complexes has been explored as a function of the nature of the ligand. In the case of substituted salen complexes, reduction occurred at the metal with the formation of bifunctional Co(I)−Na complexes, while for salophen derivatives the reductive coupling of imino groups was observed. Such C−C bonds function as electron shuttles in chemical reductions. Reduction of [Co(MeOsalen)] (1) with Na metal in THF led to a monomeric [Co(MeOsalen)Na(THF)2] (2A) and a dimeric [{Co(MeOsalen)Na(THF)}2] (2B) compound. Compounds 2A and 2B exemplify a bifunctional acid−base system with both centers in close proximity. The analogous reduction of [Co(salophen)] (3) and [Co(MeOsalophen)] (5) led to dimeric cobalt(II) derivatives containing a bridging C−C bond across two units in [Co2(salophen)2Na2(THF)6] (4) and [Co2(MeOsalophen)2Na2(THF)4] (6), respectively. However, such cobalt(II) centers behave as cobalt(I), since the C−C bond provides a pair of electrons to the metal couple during the...

50 citations

References
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Journal ArticleDOI
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

Journal ArticleDOI
S. C. Wang1
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

Journal ArticleDOI
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