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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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Journal ArticleDOI
TL;DR: In this paper, six binuclear copper(II) complexes with 2-[2-(dialkylamino)ethylthio]ethanol, Cu2{R2N(CH 2)2S(CH2)2O}2X2 (abbreviated as Cu(R-nso)X, where R=CH3, C2H5, n-C3H7, n -C4H9; X=Cl, Br), were characterized by magnetic susceptibility.
Abstract: Six binuclear copper(II) complexes with 2-[2-(dialkylamino)ethylthio]ethanol, Cu2{R2N(CH2)2S(CH2)2O}2X2 (abbreviated as Cu(R-nso)X, where R=CH3, C2H5, n-C3H7, n-C4H9; X=Cl, Br), were characterized by magnetic susceptibility (80–300 K). The temperature dependence of the magnetic susceptibilities of Cu(C2H5-nso)Cl and Cu(n-C4H9-nso)Cl can be interpreted by the Bleaney-Bowers equation based on a binuclear structure, while the magnetic data of the other complexes do not obey the Bleaney-Bowers equation. X-Ray structure analyses have revealed that the structures of all the complexes consist of discrete alkoxo-bridged binuclear units, and the coordination geometry of each copper atom is a distorted square pyramid with two oxygen, one sulfur and one chlorine or bromine atoms in the basal plane and a nitrogen atom in the apical position. The major structural difference corresponding to the different magnetic behaviors was attributed to the conformations of the chelate ring (Remark: Graphics omitted.).

36 citations

Journal ArticleDOI
TL;DR: In this paper, an intermediate thiocaronyl ylide of type E (Scheme 4), generated by the 1.3-dipolar cycloaddition of diazomethane with the exocyclic CS bond of 1 and elimination of N2, has been established by X-ray crystallography.
Abstract: Reaction of 1,3-Thaiazole-5(4H)-thiones and Diazometane Reaction of 4,4-dimethyl-1,3-thiazol-5(4H)-thiones 1 with diazomethane in Et2O at −78° or 0° leads to a mixture of the corresponding 1,4-dithiane 10,1,3-dithiole 11, thiirane 12, 4,5-dihydro-5methylidene-1,3-thiazole 13, and 1,3-thiazol-5(4H)-one 14 (Scheme 3). The structures of 10a, 11a, and 11bhave been established by X-ray crystallography. The formation of the products can be explained via an intermediate thiocaronyl ylide of type E (Scheme 4), generated by the 1.3-dipolar cycloaddition of diazomethane with the exocyclic CS bond of 1 and elimination of N2. Head-to-head dimerization of E yields 10, 1, 3-dipolar cycloaddition of E and 1 gives the ‘Schonberg product’ 11, and cyclization of E leads to 12, which undergoes a desulfurization to give 13. The thiazolone 141 is formed by hydolysis of E. The similarity of the ratio of the products at −78° and at 0° shows that, in contrast to the reaction of 1 and 2-diazopropane, the elimination of N2 in the primary cycloadduct already occurs at −78°.

35 citations

Journal ArticleDOI
TL;DR: In this article, the metathesis reaction of magnesium bis[bis(trimethylsilyl)phosphanide] and bis[ bis(trimsilyl)-amino]stannylene yields the dimeric bis[brimethyl silyl]phosphanyl]stanylene, and bis [brimylsily larsynyl)arsynide, and the red arsenic derivative crystallizes as a cis isomer in the orthorhombic space group P212121 with a

35 citations

Journal ArticleDOI
TL;DR: In this article, the transmetallierungsreaktion zur Synthese of Calcium-bis(disilylamiden) via transmetalization was studied.
Abstract: Stannylene und Stannane mit substituierten Disilylamino-Substituenten eignen sich als Edukte fur die Transmetallierungsreaktion zur Synthese von Calcium-bis(disilylamiden). Anwendung fanden Bis[2,2,5,5-tetramethyl-2,5-disilaaza-cyclo-pentyl]stannylen 1 und Bis[trimethylsilyl-tris(trimethylsilyl)silylamino]stannylen 2 (monoklin, P21/c, a = 1492,6(2), b = 1705,2(2), c = 1865,3(3) pm, β = 109,03(2)o, Z = 4). Bei der Verwendung von 2 greift das destillierte Calcium allerdings nicht nur die Sn—N-, sondern auch die NSi-Bindung an. Ahnlich wie bei dem Quecksilber-bis[trimethylsilyl-tris(trimethylsilyl)silylamid] 3 beobachtet man bereits bei Tageslicht die homolytische Spaltung der SnN- bzw. HgN-Bindung und die Bildung des Trimethylsilyl-tris(trimethylsilyl)silylamino-Radikals 5 (g = 2,00485; a(N) = 16,2G). Der heterogen gefuhrte Zinn-Calcium-Austausch bei Verbindung 1 in THF fuhrt in guten Ausbeuten zum Tris(tetrahydrofuran-O)calcium-bis[2,2,5,5-tetramethyl-2,5-disilaaza-cyclo-pentanid] 4 (monoklin, P21/n, a = 1060,9(2), b = 1919,3(5), c = 1686,0(3) pm, β = 90,30(2)o, Z = 4). Auch die Stannane Men–4Sn[N(SiMe3)2]n mit n = 1 oder 2 eignen sich als Synthone zur Synthese von Bis(tetrahydrofuran-O)calcium-bis[bis(trimethylsilyl)amid]. Synthesis of Substituted Calcium-bis(disilylamides) by Transmetalation of Tin(II) and Tin(IV) Amides Stannylenes as well as stannanes with substituted disilylamino groups are valuable synthons for the synthesis of alkaline earth metal bis(disilylamides) via the transmetallation reaction. Whereas bis[2,2,5,5-tetramethyl-2,5-disilaaza-cyclo-pentyl]stannylene 1 is a suitable reagent for this type of reaction, bis[trimethylsilyl-tris(trimethylsilyl)silylamino]stannylene 2 (monoclinic, P21/c, a = 1492.6(2), b = 1705.2(2), c = 1865.3(3) pm, β = 109.03(2)o, Z = 4) is not only attacked at the SnN-bond but also the NSi-bond is cleaved by calcium metal. Similar light sensitivity as for 2 is observed for the mercury bis[trimethylsilyl-tris(trimethylsilyl)silylamide] 3, the homolytic MN-bond cleavage leads to the formation of the trimethylsilyl-tris(trimethylsilyl)silylamino radical (g = 2.00485; a(N) = 16.2 G). The calcium tin exchange reaction of 1 in THF yields tris(tetrahydrofuran-O)calcium-bis[2,2,5,5-tetramethyl-2,5-disilaaza-cyclo-pentanide] 4 (monoclinic, P21/n, a = 1060.9(2), b = 1919.3(5), c = 1686.0(3) pm, β = 90.30(2)o, Z = 4). The stannanes Men-4Sn[N(SiMe3)2]n with n = 1 or 2 are also valuable materials for the synthesis of bis(tetrahydrofuran-O)calcium-bis[bis(trimethylsilyl)amide].

35 citations

Journal ArticleDOI
TL;DR: The crystal structures of the title compounds, [Ln(H2O)9](CF3SO3)3 with Ln = Nd3+ and Ho3+, were determined by three-dimensional X-ray diffraction methods and refined anisotropic to final R values of 0.026 and 0.030 from 636 and 676 reflections with I > 3σ(I), respectively as discussed by the authors.

35 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