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 X-ray structure analysis of indium tribromide with 3-(dimethylamino)propyllithium and bis[3]-propyl]indium chloride with NaO2C-CF3, LiOC6F5, C2H5MgBr, and t-C4H9Li, respectively.
Abstract: Synthesis and X-ray Structural Analysis of Airstable Bis[3-(dimethylamino)propyl]indium Derivatives
Pentacoordinate, intramolecularly base-stabilized organoindium compounds [Me2N(CH2)3]2InBr (1), [Me2N(CH2)3]2InO2-CCF3 (2) and [Me2N(CH2)3]2InOC6F5 (3) as well as [Me2N-(CH2)3]2InC2H5 (4), [Me2N(CH2)3]2In(i-C3H7) (5), and [Me2N-(CH2)3]2In(t-C4H9) (6) have been prepared by the reaction of indium tribromide with 3-(dimethylamino)propyllithium and of bis[3-(dimethylamino)propyl]indium chloride with NaO2C-CF3, LiOC6F5, C2H5MgBr, i-C3H7MgBr, and t-C4H9Li, respectively. The 1H-, 13C-, 19F-NMR and mass spectra of the new compounds as well as the single-crystal X-ray structure analysis of 1 are described and discussed.
24 citations
01 Jan 2013
TL;DR: In this paper, the quantum mechanical background of electron probability distribution functions (the electron density and the pair functions), of the electron localization function, of the source function, and of some other related local descriptors of electron distribution and its properties are presented in the first part of this chapter.
Abstract: Accurate electron densities and related functions are sources of chemical information enabling the understanding of the structure and chemical properties of molecules and solids. The quantum mechanical backgrounds of the electron probability distribution functions (the electron density and the pair functions), of the electron localization function (ELF), of the source function, and of some other related local descriptors of the electron distribution and of its properties are presented in the first part of this chapter. The rough data provided by these functions do not always reveal all of the expected chemical information, such as the characterization of bonding properties, and, therefore, methodological bridges are necessary to recover the phenomenological chemical concepts. The chapter is focused on the topological approaches that provide a description in the position space consistent with the Lewis structures and with the valence shell electron pair repulsion model. The theory of dynamical systems, applied to the gradient field of the electron density and of the ELF, is the most used mathematical tool enabling a rigorous partition of the space into basins of attractors that are chemically significant and also to propose criteria for a qualitative characterization of the bonding interactions and of their evolution during a chemical reaction. A deep quantitative insight is further achieved by integrating the one particle and pair densities as well as other density of property functions over the basin volumes. The statistical analysis of the variance and covariance of the basin populations provide a measure of the electron delocalization. The use of these techniques of analysis of the electron density properties is illustrated by a series of examples belonging to the field of inorganic chemistry.
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TL;DR: In this paper, the electron density distribution in crystals of (meso-tetraphenylporphinato)iron(II) has been analyzed using accurate x-ray diffraction data collected at 120 K.
Abstract: The electron density distribution in crystals of (meso‐tetraphenylporphinato)iron(II) has been analyzed using accurate x‐ray diffraction data collected at 120 K. The structural results are in agreement with those of the room temperature study. Theoretical calculations predict several different ground states for the complex and in particular support the 3 A 2g and the 3 E g A states. The experimental electron density distribution shows large peaks above and below the iron atom which would not be present for a 3 E g Aground state. Comparison with Mossbauer quadrupole splittings and the result of the aspherical atom refinement indicate that the axial peaks may be systematically too high in this acentric crystal structure. Nevertheless, it is concluded that their presence indicates a relatively small contribution of the 3 E g A state to the ground state of the complex. This implies that the ground state of FeTPP is different from that of iron(II)phthalocyanine in the crystal. A significant population of electrons is found in the d x 2−y 2 orbital which is mainly attributed to σ donation of electrons from the porphyrin ligand.
24 citations
TL;DR: In this article, new syntheses of condensed cyclopentanes are described, based on insertion into a sufficiently stable PdC bond of molecules able to provide an easy reductive elimination step.
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TL;DR: In this article, the preparation of a pentadentate binucleating ligand 2,6-bis[(N-methyl piperazin-1-yl) methyl]-4-bromo phenol (HL) is described together with the corresponding acetato bridged Cu(II) complex [Cu2L(CH3COO)2]ClO4·H2O
24 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