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 article, a broad electron beam was used for electron diffraction of Thioacetamide in the gas phase, utilizing a new nozzle construction and using a broad beam beam.
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TL;DR: It is possible, in these alternate modes of binding of hydroxycitrates, for additional binding to side chains in the active site of the enzyme to occur, resulting in extremely potent inhibition.
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TL;DR: In this article, the structure of trans-bis(isothiocyanato), 1,4,8,11-tetraazacyclotetradecane, and 1, 4, 8,12-to-tozinc(II) complexes has been determined by X-ray analyses.
Abstract: Molecular structures of trans-bis(isothiocyanato)(1,4,8,11-tetraazacyclotetradecane and 1,4,8,12-tetraazacyclopentadecane)zinc(II) complexes, [Zn(NCS)2(C10H24N4)] (1) and [Zn(NCS)2(C11H26N4)] (2), have been determined by X-ray analyses. Crystal data are: for 1, orthorhombic, space group P21nb, a=14.502(2), b=18.163(2), c=6.552(1) A, V=1718.0(4) A3, Z=4; for 2, monoclinic, space group P21/a, a=14.453(2), b=14.436(1), c=9.213(1) A, β=104.82(1)°, V=1858.3(4) A3, Z=4. Coordination geometries about Zn(II) in 1 and 2 are of the pseudo-octahedral type with two NCS groups at the trans positions, but the Zn(II) ion in each compound deviates from a plane defined by the four nitrogens of the macrocyclic ligand by 0.179 A on the average in 1 and 0.193 A in 2. Structural features of 1 and 2 suggest, complemented with data reported previously for out-of-plane Zn(II) structures, that potential surface regarding the out-of-plane displacement is very flat. The Zn–NCS distance has been found to decrease as an in-plane Zn–N...
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TL;DR: With loss of the complexating ether solvent this compound forms a dimer 3B of the type R(dme)Ba(&mgr;-R)(3)Ba( dme)(2) in toluene or benzene solution as can be proven by (31)P{(1)H}-NMR spectroscopy.
Abstract: (1,2-Dimethoxyethane-O,O')lithium phosphanide (dme)LiPH(2) reacts with 1,2-bis(chloro-dimethylsilyl)ethane to give 2,2,5,5-tetramethyl-2,5-disilaphospholane, 1, as well as 1,1,4,4-tetramethyl-1,4-bis(2,2,5,5-tetramethyl-2,5-disilaphospholanyl)-1,4-disilabutane, 2 (P(2)Si(6)C(18)H(48), space group Po, a = 943.3(2) pm, b = 1278.3(3) pm, c = 1413.3(2) pm, alpha = 72.45(1) degrees, beta = 78.13(1) degrees, gamma = 70.83(1) degrees, d = 1.081 g cm(-)(3), Z = 2, wR2 = 0.1553 at 6548 F(2) values). The reaction of 2,2,5,5-tetramethyl-2,5-disilaphospholane 1 and barium bis[bis(trimethylsilyl)amide] in 1,2-dimethoxyethane yields nearly quantitatively tris(1,2-dimethoxyethane-O,O')barium bis(2,2,5,5-tetramethyl-2,5-disilaphospholanide), 3A, which crystallizes in the monoclinic space group C2/c (BaP(2)Si(4)O(6)C(24)H(62), a = 2152.3(1) pm, b = 1381.5(1) pm, c = 1459.7(1) pm, beta = 113.73(1) degrees, d(calc) = 1.268 g cm(-)(3), Z = 4, wR2 = 0.0989 at 5220 F(2) values). Due to the high coordination number of eight of the barium center, rather long Ba-P distances of 333 pm are observed. With loss of the complexating ether solvent this compound forms a dimer 3B of the type R(dme)Ba(m-R)(3)Ba(dme)(2) in toluene or benzene solution as can be proven by (31)P{(1)H}-NMR spectroscopy ((2)J(P-P) = 6.7 Hz) and by X-ray structure analysis (Ba(2)P(4)Si(8)O(6)C(48)H(106), space group P2(1)/n, a = 1256.3(2) pm, b = 2000.0(3) pm, c = 2986.9(2) pm, beta = 98.929(9) degrees, d(calc) = 1.257 g cm(-)(3), Z = 4, wR2 = 0.1334 at 11580 F(2) values). The Ba-P bond lengths vary between 318 and 338 pm.
27 citations
TL;DR: In this article, a quantitative description of transition-metal bonding has been obtained through combined analysis of 9(1) K X-ray and 13( 1) K neutron diffraction data.
Abstract: A quantitative description of transition-metal bonding has been
obtained through combined analysis of 9(1) K X-ray and 13(1) K
time-of-flight neutron diffraction data. It is shown that a simple
valence-orbital model is too crude an approximation adequately to
describe the electron-density distribution of
Ni(ND
3
)
4
(NO
2
)
2
. To exhaust
more fully the information present in the very-low-temperature
diffraction data, a more flexible electron-density model was used.
Quantitative measures describing the bonding in the complex have been
achieved through topological analysis of the derived static model
density. To study the effects of co-ordination and intermolecular
interactions, comparisons were made with good-quality wavefunctions
calculated for free nitrite and ammonium ions. Both ligands appear
co-ordinated through predominantly electrostatic interactions. Contrary
to previous studies of
Ni(ND
3
)
4
(NO
2
)
2
, the
topological analysis revealed that the metal–ligand interactions,
besides cylindrical σ contributions, also have non-cylindrical
π contributions to the covalent part of the bonding. Plots of the
Laplacian of the electron density were used to locate regions of charge
concentration and charge depletion in the valence regions of the atoms
in the molecule. For all atoms, maxima in the valence-shell charge
concentration are found in accord with the simple Lewis electron-pair
concept of bonded and non-bonded charge concentrations. The study
demonstrates that X-ray diffraction data measured carefully at very low
temperatures have sufficient precision to allow for a reliable and
detailed topological analysis of transition-metal electron-density
distributions.
27 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
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