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 coordination polyhedron can be described as either a very distorted tetragonal pyramid or a trigonal bi-pyramid and the molecular structure of the Cd{S2CN(n-C4H9)2}2 complex has been determined.
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TL;DR: In this paper, the authors examined the importance of the pyridyl ligandide and NER reactions for coupling reactions, and showed that the coupling product [1,2-bis(tert-butyldimethylsilyl)(2-pyrIDylmethyl) amido]-1-azacyclohexa-3,5dien-1-ide (8) is produced.
Abstract: The zincation of (2-pyridylmethyl)(triisopropylsilyl)amine (1) gives dimeric methylzinc (2-pyridylmethyl)(triisopropylsilyl)amide (2). Further addition of dimethylzinc to a toluene solution of 2 at raised temperatures yields the C−C coupling product [1,2-dipyridyl-1,2-bis(triisopropylsilylamido)ethane]bis(methylzinc) (3). Heating of molten 2, or UV irradiation of 2, results in the formation of 3 and zinc bis[(2-pyridylmethyl)(triisopropylsilyl)amide] (4). The reaction between the zinc dihalide complexes of 1 [5a (X = Cl) and 5b (X = Br)] and methyllithium yields the C−C coupling product 3 and the heteroleptic complex 2, observed by NMR spectroscopy. During this reaction, zinc metal precipitates. The magnesiation of 1 with dibutylmagnesium gives magnesium bis[(2-pyridylmethyl)(triisopropylsilyl)amide] (6) in a quantitative yield. Subsequent addition of dimethylmagnesium results in a dismutation reaction and the formation of heteroleptic methylmagnesium (2-pyridylmethyl)(triisopropylsilyl)amide (7). Treatment of 1 with dimethylmagnesium also gives 7. This complex slowly undergoes an intramolecular metalation during which dark red single crystals of (tetrahydrofuran)magnesium 2-(triisopropylsilylamidomethylidene)-1-azacyclohexa-3,5-dien-1-ide (8) precipitate. In this compound the aromaticity of the pyridyl fragment is abolished. The magnesiation of (tert-butyldimethylsilyl)(2-pyridylmethyl)amine (I) proceeds quantitatively to give methylmagnesium (tert-butyldimethylsilyl)(2-pyridylmethyl)amide (9). This compound also undergoes an intramolecular metalation reaction, which results in the loss of the aromaticity of the pyridyl substituent and the formation of (tetrahydrofuran)magnesium 2-(tertbutyldimethylsilylamidomethylidene)-1-azacyclohexa-3,5dien-1-ide (10). The metalation of 1 with tin(II) bis[bis(trimethylsilyl)amide] yields [bis(trimethylsilyl)amido]tin(II) (2-pyridylmethyl)(triisopropylsilyl)amide (11). The elimination of tin metal occurs even at room temperature, and the C−C coupling product [1,2-dipyridyl-1,2-bis(triisopropylsilylamido)ethane]tin(II) (12) is formed. The metalation of (tert-butyldimethylsilyl)(2-pyridylmethyl)amine with Sn[N(SiMe3)2]2 gives [bis(trimethylsilyl)amido]tin(II) (tert-butyldimethylsilyl)(2-pyridylmethyl)amide (13). Within a few minutes, precipitation of tin metal takes place and the C−C coupled product [1,2-bis(tert-butyldimethylsilylamido)-1,2-dipyridylethane]tin(II) (14) is produced. In order to examine the importance of the pyridyl ligand for the C−C coupling reactions, zinc bis[N-(tert-butyldimethylsilyl)benzylamide] (15) was prepared by means of the metathesis reaction between lithium N-(tert-butyldimethylsilyl)benzylamide and zinc(II) halide. Treatment of 15 with dimethylzinc yields heteroleptic methylzinc N-(tert-butyldimethylsilyl)benzylamide (16). Refluxing of 16 with an excess of dimethylzinc in toluene does not give any C−C coupling reactions.
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TL;DR: The multistep synthesis of the novel diphosphine reference ligand L(2), 6, Ph (2)P(o-C(6)H(4)CH(2)C( 6)H (4)-o)PPh (2), has been streamlined and can be prepared on a ca.
Abstract: The multistep synthesis of the novel diphosphine reference ligand L2, 6, Ph2P(o-C6H4CH2C6H4-o)PPh2, has been streamlined and can be prepared on a ca. 20 g scale. It forms metallacycles with a variety of metal fragments. The resulting, and very rigid, boat−boat conformation forces a proton (Hendo) of the bridging methylene in close proximity to the metal, which in turn renders these protons (Hendo, Hexo) diastereotopic. The NMR spectra of [L2MCl2] [M = Pd, 9; M = Pt, 10] and of the organometallic derived compounds [L2Pd(PPh3)], 11, and [L2Pd(Cl)(η2-CH2Ph)], 12, consist of a pair of doublets, with the Hendo coupled to the P of the metallacycle. The CH2−metal close proximity drives the electrophilic metalation of the bridging methylene by RhCl3 to form [L*2Rh(Cl)2(MeCN)], 13, [L*2 = Ph2P(o-C6H4CHC6H4-o)PPh2]. A significant example, which shows how the coordination number of the metal can affect the Hexo−Hendo resonance separation, is provided by the couple [L2Ni(C2H4)], 14, and [L2Ni(CO)2], 15. In order to s...
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TL;DR: The reaction of aryl (selenophen-2-yl) thioketones with CH2N2 occurs with spontaneous elimination of N2, even at low temperature (−65°), to give regioselectively sterically crowded 4,4,5,5-tetrasubstituted 1,3-dithiolanes and/or a novel type of twelve-membered dithia-diselena heterocycles as dimers of the transient thiocarbonyl S-methanides as discussed by the authors
Abstract: The reactions of aryl (selenophen-2-yl) thioketones with CH2N2 occur with spontaneous elimination of N2, even at low temperature (−65°), to give regioselectively sterically crowded 4,4,5,5-tetrasubstituted 1,3-dithiolanes and/or a novel type of twelve-membered dithia-diselena heterocycles as dimers of the transient thiocarbonyl S-methanides. The ratio of these products depends on the type of substituent located at C(4) of the phenyl ring. Whereas the formation of the 1,3-dithiolanes corresponds to a [3+2] cycloaddition of an intermediate thiocarbonyl ylide with the starting thioketone, the twelve-memberd ring has to be formed via dimerization of the ‘thiocarbonyl ylide’ with an extended biradical structure.
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TL;DR: In this paper, aus dem zuerst genannten Ansatz kristallin isolierten Bis(1,2-dimethoxyethan-O,O)bis(tetrahydro-furan)-O)(μ-1, 2,4-triphospholo]-1,3,5,7-tetraonato(2−)-O1,O7:O3,O5)dilithium (2a) and
Abstract: Bis(1,2-dimethoxyethan-O,O′)lithoxy-methylidinphosphan PCOLi(dme)2(1,2) (1a) [2] setzt sich bei −50°C mit Schwefeldioxid oder Iod in 1,2-Dimethoxyethan annahernd quantitativ zu dem mit 40proz. Ausbeute aus dem zuerst genannten Ansatz kristallin isolierten Bis(1,2-dimethoxyethan-O,O′)bis(tetrahydrofuran-O)(μ-1,2,4-triphospholo[1,2-a]-1,2,4-triphosphol-1,3,5,7-tetraonato(2−)-O1,O7:O3,O5)dilithium (2a) und Lithiumdithionit bzw. -iodid um. Die Bildung des aus vier PCO-Einheiten aufgebauten anionischen Heterozyklus last sich uber eine Redoxreaktion, den nachfolgenden nukleophilen Angriff weiterer [PCO]−-Anionen und sich anschliesende, gekoppelte „intramolekulare” Cycloadditionen verstehen. Das 31P{1H}-NMR-Spektrum weist zwei Tripletts mit δ-Werten von 81,4 und 36,9 ppm sowie einer 2J(PP)-Kopplungskonstanten von 31,7 Hz fur je zwei Phosphoratome der Koordinationszahlen zwei und drei auf; die 13C{1H}-Resonanzen des [(PCO)4]2−-Anions gehoren zu einem ABMM′X-Spektrum, dessen X-Teil analysiert wird.
Nach den Ergebnissen einer Rontgenstrukturanalyse {Cmcm; a = 1 277,14(11); b = 1 487,7(2); c = 1 556,94(11) pm bei −100 ± 3°C; Z = 4 Molekule; R1 = 0,061; wR2 = 0,150} an blasgelben Kristallen liegt Verbindung 2a als Neutralkomplex mit der Symmetrie mm2 vor. Der anionische Molekulteil baut sich aus zwei an der PP-Gruppe anellierten 1,2-Dihydro-5-oxo-1,2,4-triphosphol-3-olat-Ringen (P1P1′ 215,3; P1C1 189,1; C1
P2 178,4; C1
O1 123,9 pm; C1–P1–P1′ 98,4; C1P1C1″ 91,2; C1
P2
C1′ 98,7°) auf. Er kann sowohl den PP-Heterozyklen mit Schmetterlingsstruktur [71–75] als auch den Diacylphosphaniden mit einer allerdings ungewohnlichen E,E-Konfiguration beider OCPCO−-Einheiten zugeordnet werden. Freie Valenzen an den beiden quadratisch pyramidal koordinierten Lithium-Kationen (LiO 193,5 bis 209,1 pm) werden durch je einen 1,2-Dimethoxyethan-und Tetrahydrofuran-Liganden abgesattigt.
Alkylidynephosphanes and -arsanes. II. Oxydation of Lithoxy-methylidynephosphane PCOLi with Sulphur Dioxide and Iodine
At −50°C bis(1,2-dimethoxyethane-O,O′)lithoxymethylidynephosphane PCOLi(dme)21,2) (1a) [2] reacts almost quantitatively with sulphur dioxide or iodine in 1,2-dimethoxyethane solution to give bis(1,2-dimethoxyethane-O,O′)bis(tetrahydrofuran-O)(μ-1,2,4-triphospholo[1,2-a]-1,2,4-triphosphol-1,3,5,7-tetraonato(2−)-O1,O7:O3,O5)dilithium (2 a) and lithium dithionite or iodide respectively. From the reaction with sulphur dioxide the crystalline, pale yellow compound is obtained in 40% yield. The formation of the unusual anionic heterocycle, built up of four PCO units, may be explained by an oxydation of two [PCO]− species first, followed by a nucleophilic attack of two other [PCO]− anions and coupled „intramolecular” cycloaddition reactions. In the 31P{1H} nmr spectrum two phosphorus atoms each of coordination number two and three give rise to two triplets with chemical shift values of 81.4 and 36.9 ppm and a 2J(PP) coupling constant of 31.7 Hz; the 13C{1H} resonances of the [(PCO)4]2− anion come from an ABMM′X spin system, the X part being discussed in detail.
An X-ray structure determination {Cmcm; a = 1 277.14(11); b = 1 487.7(2); c = 1 556.94(11) pm at −100 ± 3°C; Z = 4 molecules; R1 = 0.061; wR2 = 0.150} shows compound 2a to crystallize as a neutral complex of symmetry mm2. The anionic part of the molecule consists of two anellated 1,2-dihydro-5-oxo-1,2,4-triphosphol-3-olate rings which share the central PP unit (P1P1′ 215.3; P1–C1 189.1; C1
P2 178.4; C1
O1 123.9pm; C1P1P1′ 98.4; ClP1C1″ 91.2; C1
P2
C1′ 98.7°). Thus compound 2a may be assigned to the group of PP heterocycles with a butterfly structure [71–75] as well as to the well-known diacylphosphanides taking into account, however, the unusual E,E configuration of both OCPCO− units. The lithium cations are square pyramidally coordinate (LiO 193.5 to 209.1 pm), each additionally binding an 1,2-dimethoxyethane and a tetrahydrofuran molecule.
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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.)
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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