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, a new concept for molecular switches, based on thermal or photochemical double-bond shifts (DBS) in [4n]annulenes such as heptalenes or cyclooctatetraenes, is introduced.
Abstract: A new concept for molecular switches, based on thermal or photochemical double-bond shifts (DBS) in [4n]annulenes such as heptalenes or cyclooctatetraenes, is introduced (cf. Scheme 2). Several heptalene-1,2- and -4,5-dicarboxylates (cf. Scheme 4) with (E)-styryl and Ph groups at C(5) and C(1), or C(4) and C(2), respectively, have been investigated. Several X-ray crystal-structure analyses (cf. Figs. 1–5) showed that the (E)-styryl group occupies in the crystals an almost perfect s-trans-conformation with respect to the CC bond of the (E)-styryl moiety and the adjacent CC bond of the heptalene core. Supplementary 1H-NOE measurements showed that the s-trans-conformations are also adopted in solution (cf. Schemes 6 and 9). Therefore, the DBS process in heptalenes (cf. Schemes 5 and 8) is always accompanied by a 180° torsion of the (E)-styryl group with respect to its adjacent CC bond of the heptalene core. The UV/VIS spectra of the heptalene-1,2- and -4,5-dicarboxylates illustrated that it can indeed be differentiated between an ‘off-state’, which possesses no ‘through-conjugation’ of the π-donor substituent and the corresponding MeOCO group and an ‘on-state’ where this ‘through-conjugation’ is realized. The ‘through-conjugation’, i.e., conjugative interaction via the involved s-cis-butadiene substructure of the heptalene skeleton, is indicated by a strong enhancement of the intensities of the heptalene absorption bands I and II (cf. Tables 3–6). The most impressive examples are the heptalene-dicarboxylates 11a, representing the off-state, and 11b which stands for the on-state (cf. Fig.8).
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TL;DR: In this paper, the reaction of bis[bis(trimethylsilyl)methyl]zinc with 2,2′-bipyridine yields 2, 2′-Bipyridyl-bis[bis (trimethyltransmilyl), methyl]Zinc which crystallizes from cyclo-pentane in the monoclinic space group P21/c with a 888.4(3), b 1612.9(5), c 2175.7(6) pm, β 101.07(1)
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TL;DR: Exhaustive methylation of 15 with methyl triflate furnishes closo-B-decamethoxy-1,12-bis(methyl sulfonate)-p-carborane (20), the characterization of closomer 20 also includes its crystal structure determination.
Abstract: The reaction of closo-1,12-bis(lithio)-1,12-dicarbadodecaborane(12) (1,12-bis(lithio)-p-carborane) with SO(2) formed closo-1,12-bis(lithiosulfinato)-p-carborane (10) in nearly quantitative yield. The latter was converted to closo-1,12-bis(sulfinic acid)-p-carborane (13) via H(+)-exchange. The corresponding 1,12-bis(sulfonic acid) derivative of p-carborane (12) was obtained in high yield by treating 10 with SO(2)Cl(2) and subsequent AlCl(3) mediated hydrolysis of the closo-1,12-bis(chlorosulfonyl)-p-carborane intermediate. The exhaustive oxidation of 12 in hot aqueous H(2)O(2) (30%) afforded B-decahydroxy-1,12-bis(sulfonic acid)-p-carborane (15) in 40% yield. As a byproduct, closo-B-decahydroxy-1-sulfonic acid-p-carborane (14) was formed. Both 14 and 15 were also obtained from the hydroxylation of 10 and 13. Compound 14 was obtained directly in 88% yield by heating 1-sulfinic acid-p-carborane (17) in H(2)O(2) (30%). Compound 17 was synthesized from diphenylmethylsilyl-protected p-carborane by using the method employed in the synthesis of 13. The X-ray structures of 15, its disodium salt, and its dipotassium salt are presented and discussed. Exhaustive methylation of 15 with methyl triflate furnishes closo-B-decamethoxy-1,12-bis(methyl sulfonate)-p-carborane (20). The characterization of closomer 20 also includes its crystal structure determination.
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TL;DR: In this article, the crystal structure of OAs(o-tolyl)3H2O is reported and the lowest energy two-ring flip exchange mechanism is analyzed.
Abstract: Variable temperature NMR studies have established equilibrium constants and/or activation parameters for the exo2↔exo3 equilibrium in the series M(o-tolyl)3(M = P, As), XM (o-tolyl)3(M = P, X = O, S, Se; M = As, X = O, S) and [MeM(o-tolyl)3]n+(n= 0, M = Si; n= 1, M = P, As). The crystal structure of OAs(o-tolyl)3H2O is reported. Molecular mechanics studies of P(o-tolyl)3 reproduce correctly the ground state exo3 conformation and provide an analysis of the lowest energy two-ring flip exchange mechanism.
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TL;DR: In this article, the structure of a ten-membered ring-enlargement product was established by X-ray crystallography (Fig. 1 ). But no ring enlargement was observed with the sterically crowded 1e, which bears an isopropyl group at C(2).
Abstract: The reaction of 3-(dimethylamino)-2,2-dimethyl-2H-azirine (1a) with 4,S-dihydro-7,8-dimethoxy-l,2-benzothiazepin-3-one 1,1-dioxide (4) in dioxane at room temperature gave the correspondingly substituted 4H-1,2,5- benzothiadiazecin-6-one 1,1-dioxide 5a in 64% yield (Scheme 2). The structure of this novel ten-membered ring-enlargement product was established by X-ray crystallography (Fig.). Under more vigorous conditions (refluxing dichloroethane), 5a was formed together with the isomeric 6a, both in low yield. The 3-(dimethylamino)-2H-azirines 1b and 1c reacted sluggishly to give the two isomeric ring-enlargement products of type 5 and 6 in yields of 24-29 % and 2-4 % , respectively (Table 1 ). Even less reactive is 2,2-dimethyl-3-(N-methyl-N-phenylamino)-2H-azirine (1d), which reacted with 4 in MeCN only at 65°. Under these conditions, besides numerous decomposition products, only traces of 5d and 6d were formed. No ring enlargement was observed with the sterically crowded 1e, which bears an isopropyl group at C(2).
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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
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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