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: The first octahedral trans-dimethyltitanium(IV) derivative, [Ti(salen)Me2]2, was derived from an aryl migration to the ligand of the imino group of salen as mentioned in this paper.
Abstract: The alkylation of [Ti(salen)Cl2]1[salen =N,N′-ethylenebis(salicylideneiminate)] using LiMe in toluene gave the first octahedral trans-dimethyltitanium(IV) derivative, [Ti(salen)Me2]2. Complex 2 is thermally labile and a thermally induced methyl migration to the ligand salen was observed in solution. The isolation of a compound derived from an aryl migration to the ligand was achieved in the reaction of MgBr(mes)(mes = 2,4,6-Me3C6H2) with 1 leading to [Ti(L)(mes)]3, containing the mesityl group bonded to the metal, and the second one attached to the carbon of the imino group of salen. The alkylation reaction is greatly affected by the solvent. When alkylation or arylation of 1 is carried out in tetrahydrofuran (thf) with MgXR (R = Ph or mes) reductive arylation of 1 occurs with the isolation of the corresponding titanium(III) derivatives [Ti(salen)R(thf)](R = Ph 4 or mes 5). Crystallographic details: complex 2, orthorhombic, space group P212121, a= 22.795(2), b= 14.734(1), c= 6.849(1)A, Z= 4, and R= 0.047 for 882 independent observed reflections; 3, monoclinic, space group P21/n, a= 12.804(1), b= 26.566(3), c= 10.014(1)A, β= 95.27(1)°, Z= 4, and R= 0.057 for 3625 observed reflections; 4, orthorhombic, space group P212121, a= 18.455(2), b= 14.633(2), c= 13.172(2)A, Z= 4, and R= 0.118 for 1524 observed reflections.
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TL;DR: In this paper, a closed-form approximation of Stewart−Slater atoms is proposed, which can be found efficiently from molecular multipole moments and can yield insight into the nature of chemical bonding.
Abstract: Stewart atoms are the unique nuclear-centered spherical functions whose sum best fits a molecular electron density in a least-squares sense. It is difficult, however, to express Stewart atoms in closed form. We therefore introduce new closed-form approximations, Stewart−Slater atoms, and show that these can be found efficiently from molecular multipole moments. Using examples, we argue that the parameters of Stewart−Slater atoms can yield insight into the nature of chemical bonding.
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TL;DR: The reaction of strontium bis[bis trimethylsilyl)amide] with benzonitrile yields strontiam bis[N,N′- bis(trimethylslyl)benzamidinate] · 2THF, which crystallizes in the orthorhombic space group Pbcn (a = 1845.8(3)pm; Z = 4) confirm the isolated appearance of the acetylene molecule without interaction to the metal center in solution and in the solid state, respectively.
Abstract: Bei der Umsetzung des Strontiumbis[bis(trimethylsilyl)amids] mit Benzonitril in THF bildet sich Stronitium-bis[N,N′-bis(trimethylsilyl)benzamidinat] · 2THF, das in der orthorhombischen Raumgruppe Pbcn mit {a = 1 845,4(3); b = 1311,4(2); c = 1838,8(3) pm, Z = 4} kristallisiert. Die entsprechende Reaktion des Barium-bis[bis(trimethylsilyl)amids] mit Benzonitril ergibt das Benzonitril-Addukt Barium bis[N,N′ -bis(trimethylsilyl)benzamidinat] · 2 THF · Benzonitril. Nach der versuchsweisen Umsetzung des Strontium-di(benzamidinats) mit Diphenylacetylen in Diglyme last sich ein Clathrat der Zusammensetzung Strontiumbis[N,N′-bis(trimethylsilyl)benzamidinat] · Diglyme · Diphenylacetylen erhalten, dessen spektroskopische und strukturanalytische Untersuchungen (monoklin, C2/c, a = 1492,2(2); b = 1539,1(2); c = 2337,8(3) pm; β = 100,74(1)°; Z = 4) das Vorliegen eines unkomplexierten Diphenylacetylen-Molekuls sowohl in Losung als auch im Festkorper bestatigen.
Strontium and Barium Bis[N,N′-bis(trimethylsilyl)benzamidinates] from the Addition Reaction of the Alkaline Earth Metal Bis[bis(trimethylsilyl)amides] and Benzonitrile
The reaction of strontium bis[bis trimethylsilyl)amide] with benzonitrile yields strontium bis[N,N′- bis(trimethylsilyl)benzamidinate] · 2THF, which crystallizes in the orthorhombic space group Pbcn (a = 1845.4(3); b = 131 1,3(2); c = 1838,(3) pm; Z = 4). During the similar reaction of barium bis[bis(trimethylsilyl)amide] with benzonitrile the benzonitrile adduct barium bis[N,N′-bis(trimethylsilyl)benzamidinate] · 2 THF · benzonitrile is formed. After the addition of diphenylacetylene to the strontium di(benzamidinate) in diglyme a clathrate of the composition strontium bis[N,N′-bis(trimethylsilyl)benzamidinate] · diglyme · diphenylacetylene could be isolated; the spectroscopic data as well as the X-ray structure (monoclinic, C2/c, a = 1492.2(2); b = 1539.1(2); c = 2337.8(3)pm; Z = 4) confirm the isolated appearance of the acetylene molecule without interaction to the metal center in solution and in the solid state, respectively.
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TL;DR: In this article, the first systematic 57Fe NMR study of ligand effects in cyclopentadienyliron complexes is presented, and four series encompassing a total of 35 compounds have been studied.
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TL;DR: In this paper, the X-ray structure determined using intensity data collected on a CAD4 diffractometer and refined by full-matrix least-squares methods, converged to a conventional R factor value of 0.077 for 1153 observed reflections.
Abstract: N-alkyl-substituted imidazolidine-2-thiones act as monodentate ligands coordinating through sulfur. The gold(I) complex, chloro(N-propyl-1,3-imidazolidine-2-thione)gold(I), [(PrImt)AuCl] crystallizes in the monoclinic space group C2/c with a=10.164(4), b=14.836(2), c=13.590(9)A, β=95.08(5)° and Z=8. The X-ray structure determined using intensity data collected on a CAD4 diffractometer and refined by full-matrix least-squares methods, converged to a conventional R factor value of 0.077 for 1153 observed reflections. Gold(I) has a linear coordination with an S-Au-Cl angle of 173.3° and Au-S and Au-Cl distances of 2.26(1) and 2.27(1)A. The 13C nmr spectra of the complexes indicated a high-field shift of about 8 ppm for the C-S carbon, suggesting identical coordination sites in the solid and solution states. This large shift in 13C resonance can be used as a diagnostic nmr observation for location of coordination sites in solution of these and other C-S bonded complexes.
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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