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 vanadium atom adopts a capped trigonal-prismatic structures with a hexadentate ethylenediammetetraacetato ligand and an aqua ligand.
Abstract: K[V(edta)(H2O)]·2H2O (1a) was prepared by the reaction of VCl3 with K4 edta. The compound was converted to its sodium and ammonium salts by use of a cation exchange resin. Crystal structure analyses of Na[V(edta)(H2O)]·3H2O (1b) and NH4[V(edta)(H2O)]·2.5H2O (1c) revealed that in both compounds the vanadium atom adopts a capped trigonal-prismatic structures with a hexadentate ethylenediammetetraacetato ligand and an aqua ligand. Crystal data are as follows: 1b: Monoclinic, P21⁄a, a=17.831 (3), b=8.408 (1), c=11.595 (2) A, β=109.39 (1)°, Z=4, R=0.045 for 6321 reflections; 1c: Monoclinic, Aa, a=8.552 (1), b=59.948 (6), c=7.226 (A), β=114.95 (1)°, Z=8, R=0.050 for 6087 reflections.
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TL;DR: In this paper, the electron transfer processes of 2-substituted and 1-2-disubstitized indoles are discussed in terms of electron transfer process based on the redox potentials of the reagents, the Marcus theory and the reaction products distribution.
Abstract: 2-Substituted and 1,2-disubstituted indoles react with m-chloroperbenzoic acid and hydrogen peroxide in the presence of acid or calcium chloride affording 2- and 3-(3-oxoindol-2-yl)indoles; whereas 2,3-disubstituted indoles, reacting with the same oxidants, lead to the formation of products typical of pentaatomic ring opening. The reaction mechanisms are discussed in terms of electron transfer processes based on the redox potentials of the reagents, the Marcus theory and the reaction products distribution. The reactions of 1-hydroxy-2-phenylindole, which yield 2-phenylisatogen (2-phenyl-3-oxo-3H-indole 1-oxide), bisnitrone and 3-(3-oxoindol-2-yl)indole are also explained by an electron transfer mechanism depending on the oxidant and on the conditions of the reaction. The structures of 2- and 3-(3-oxoindol-2-yl)indoles have been elucidated by X-ray analysis.
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TL;DR: In this article, the reaction mechanism for the formation of the isolated products are delineated in Schemes 4-7: the primary cycloadduct 3 of the diazo compound and the CS bond of 1 undergoes a base-catalyzed ring opening of the 1,3-thiazole-ring to give 10.
Abstract: Reaction of Ethyl Diazoacetate with 1,3-Thiazole-5(4H)-thiones
Reaction of ethyl diazoacetate (2a) and 1,3-thiazole-5(4H)-thiones 1a,b in Et2O at room temperature leads to a complex mixture of the products 5–9 (Scheme 2). Without solvent, 1a and 2a react to give 10a in addition to 5a–9a. In Et2O in the presence of aniline, reaction of 1a,b with 2a affords the ethyl 1,3,4-thiadiazole-2-carboxylate 10a and 10b, respectively, as major products. The structures of the unexpected products 6a, 7a, and 10a have been established by X-ray crystallography. Ethyl 4H-1,3-thiazine-carboxylate 8b was transformed into ethyl 7H-thieno[2,3-e][1,3]thiazine-carboxylate 11 (Scheme 3) by treatment with aqueous NaOH or during chromatography. The structure of the latter has also been established by X-ray crystallography. In the presence of thiols and alcohols, the reaction of 1a and 2a yields mainly adducts of type 12 (Scheme 4), compounds 5a,7a, and 9a being by-products (Table 1). Reaction mechanisms for the formation of the isolated products are delineated in Schemes 4–7: the primary cycloadduct 3 of the diazo compound and the CS bond of 1 undergoes a base-catalyzed ring opening of the 1,3-thiazole-ring to give 10. In the absence of a base, elimination of N2 yields the thiocarbonyl ylide A′, which is trapped by nucleophiles to give 12. Trapping of A′, by H2O yields 1,3-thiazole-5(4H)-one 9 and ethyl mercaptoacetate, which is also a trapping agent for A′, yielding the diester 7. The formation of products 6 and 8 can be explained again via trapping of thiocarbonyl ylide A′, either by thiirane C (Scheme 6) or by 2a (Scheme 7). The latter adduct F yields 8via a Demjanoff-Tiffeneau-type ring expansion of a 1,3-thiazole to give the 1,3-thiazine.
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TL;DR: In this paper, a stepwise mechanism via delocalized diradical intermediates is postulated to rationalize the observed reaction course, which leads to the oxidation of the C=C bond and the sulfur atom in the six-membered ring.
Abstract: Dihetaryl thioketones possessing thiophen-2-yl and selenophen-2-yl rings react as “superdienophilic” reagents with nonactivated 1,3-dienes such as 2,3-dimethylbuta-1,3-diene, cyclopentadiene, and mixtures of isomeric hexa-2,4-dienes to produce the expected 2H-thiopyrans in moderate to excellent yields. In the latter case, the corresponding cis-2,2-dihetaryl-3,6-dimethyl-3,6-dihydro-2H-thiopyrans are formed as the sole products in a stereoconvergent thia-Diels–Alder reaction. A stepwise mechanism via delocalized diradical intermediates is postulated to rationalize the observed reaction course. Treatment of 4,5-dimethyl-2,2-di(thiophen-2-yl)-3,6-dihydro-2H-thiopyran with excess of m-CPBA at room temperature leads to the oxidation of the C=C bond and the sulfur atom in the six-membered ring.
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TL;DR: In this article, the 1,3-dipolar cycloaddition of carbon disulfide to the coordinated azide in the cyclometal-lated compound [Pd(dmba)(N3)]2 (1), dmba = N,N-dimethylbenzylamine, was investigated.
Abstract: The 1,3-dipolar cycloaddition of carbon disulfide to the coordinated azide in the cyclometal-lated compound [Pd(dmba)(N3)]2 (1), dmba = N,N-dimethylbenzylamine, was investigated. The compound obtained di(μ, N, S-l,2,3,4-thiatriazole-5-thiolate)-bis[(N,N-dimethylbenzylamine-C2, N)palladium(II)] (2), was characterized by IR spectroscopy and X-ray diffraction. Complex (2) is dimeric with the two [Pd(N,N-dimethylbenzylamine)] moieties being connected by the two vicinal bridging N, S-l,2,3,4-thiatriazole-5-thiolate anions in a square-planar coordination for the palladium atoms.
23 citations
References
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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