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 triclinic, space group P1, a= 11.432, b= 13.395, c= 15.28, β= 87.75, γ= 73.87, and Z= 2.
Abstract: The complex [Cu6(dmpymt)6]·H2O was synthesised by electrochemical oxidation of copper in an acetonitrile solution of the neutral ligand 4,6-dimethylpyrimidine-2-thione (Hdmpymt). The reaction of [Cu6(dmpymt)6] with 1,2-bis(diphenylphosphino)methane (dppm) and 1,2-bis(diphenylphosphino)ethane (dppe) yielded compounds of general formulae [Cu(dmpymt)(dppm)] and [Cu2(dmpymt)2(dppe)3]. The molecular structure of [Cu6(dmpymt)6] was determined: the crystals are triclinic, space group P1, a= 11.432(3), b= 13.395(2), c= 15.694(4)A, α= 80.28(2), β= 87.75(2), γ= 73.87(2)° and Z= 2. The six copper atoms are arranged with distorted-octahedral geometry, each copper atom being trigonally co-ordinated to one nitrogen and two sulfur atoms of three different ligands. Infrared, 1H, 13C and 31P NMR spectral data are presented for all the compounds.
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TL;DR: In this article, photolysis of methylmolybdenum and tungsten complexes, Cp*M(CO)3Me (M = Mo, W), in the presence of BH3·PMe3 (1) afforded nonsubstituted boryl complexes with concomitant evolution of methane.
Abstract: Photolysis of methylmolybdenum and tungsten complexes, Cp*M(CO)3Me (M = Mo, W), in the presence of BH3·PMe3 (1) afforded nonsubstituted boryl complexes Cp*M(CO)3(BH2·PMe3) (2a: M = Mo, 3a: M = W) with concomitant evolution of methane. The structures of 2a and 3a were determined by single-crystal X-ray crystallography. The boryl group in these complexes adopts a tetra-coordinate geometry with coordination of trimethylphosphine to the boron atom. The tungsten−boron bond distance in 3a is significantly longer than those of boryltungsten complexes with a tri-coordinate boryl group. The CO stretching bands in the IR spectra of 2a and 3a were observed at lower wavenumbers than those of the corresponding methyl complexes, indicating the pronounced polarization of the M−B bond, M(−)−B(+). Reactivity of the boryl complexes also featured the polar M−B bond. Boryl complexes having a nonsubstituted cyclopentadienyl ligand, CpM(CO)3(BH2·PMe3) (2b: M = Mo, 3b: M = W) were generated by the similar photoreaction altho...
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TL;DR: Ferrocenyl Schiff-base derivatives of the form [Fe(η-C5H5), η-c5H4CHNR] have been prepared from ferrocenecarbaldehyde.
Abstract: Ferrocenyl Schiff-base derivatives of the form [Fe(η-C5H5)(η-C5H4CHNR)][R = NCH(C6H4NO2-p)1, C6H4CN-p2, C6H4NO2-p3, C6H4F-p4, C6H4Cl-p5, C6H4Br-p6, C6H4NO2-m7, NH(C6H4NO2-o)8, NH(C6H4NO2-p)9 or NH(C6F5)10], have been prepared from ferrocenecarbaldehyde. Proton, 13C NMR, UV/VIS and 57Fe Mossbauer spectroscopic data are presented. A number of these derivatives contain the donor–π-acceptor-(D–π-A) structural motif desired for non-linear optical materials. The behaviour of the ferrocenyl moiety as a donor is compared to that of the 4-dimethylaminophenyl group. The UV/VIS spectra of compound 1 showed considerable solvatochromism. As a result of this and its extended donor–π-acceptor nature, 1 was tested for non-linear optical properties, specifically, second harmonic generation. The results, however, were negative. A single-crystal X-ray study revealed 1 to crystallize in a centrosymmetric space group P21/n, with a= 5.885(1), b= 30.745(3), c= 8.662(1)A, β= 96.40(2)° and Z= 4. The most striking feature of the molecular structure is the coplanarity of the substituent group with the η-C5H4 ring of the ferrocenyl moiety. The crystal structure reveals stacks of ferrocenyl, phenyl, phenyl, ferrocenyl moieties with inter-ring distances of 3.529 A between the C5–C6 rings and 3.478 A between the C6–C6 ring planes. The observation of a DAAD in contrast to a DADA stack is discussed.
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TL;DR: In this paper, a new molecular surface, the promolecule electron density isosurface arising from the superposition of spherical atomic electron density functions, is compared and contrasted with the Hartree-Fock ab initio electron density surface, and the fused-sphere van der Waals (CPK) surface.
Abstract: A new molecular surface, the promolecule electron density isosurface arising from the superposition of spherical atomic electron density functions, is compared and contrasted with the Hartree–Fock ab initio electron density isosurface, the fused-sphere van der Waals (CPK) surface, and the smooth Connolly surface. From application to a number of small to medium-sized molecules, including several amino acids, the promolecule surface is shown to be very similar to the Hartree–Fock electron density isosurface but, in contrast, is trivial to calculate. The promolecule electron density surface constructed with a contracted hydrogen atom provides remarkably reliable, and consistent, estimates of ab initio surface areas (typically within 0.5%) and volumes (routinely overestimated by less than 4%). Differences between ab initio and promolecule surfaces are explored visually by mapping the deformation density on the promolecule surface. To highlight the usefulness of the promolecule surface, a promolecule 0.002 au isosurface of the small protein crambin is shown. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 933–942, 2000
57 citations
TL;DR: The crystal and molecular structure of the nematogen 4′-n-Pentyloxy-4-Biphenyl carbonitrile has been determined by direct methods as mentioned in this paper.
Abstract: The crystal and molecular structure of nematogen 4′-n-Pentyloxy-4-Biphenylcarbonitrile has been determined by direct methods. The crystals belong to the monoclinic system with space group P21/n. a = 21.378(5), b = 5.695(3), c = 12.789(2) A, β = 106.074(17)° with four molecules per unit cell. Least-squares refinement leads to R = 0.050 (Rw = 0.038) for 1773 observed reflections. The molecules are in their most extended conformation, the rigid part lies parallel to a-axis while the chain part is inclined to it. Rigid part is also highly planar and is almost parallel to ab-plane. The molecules are stacked along c-axis. The molecules associate in pairs about the centre of inversion. In the unit cell the adjacent molecules are antiparallel to each other. The structure is of a common type for nematogens and could transform to the nematic state by means of a simple displacive transition.
57 citations
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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