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Journal ArticleDOI

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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Journal ArticleDOI
TL;DR: The protected poly-Aib oligopeptides Z-(Aib)n-N(Me)Ph with n=2-6 were prepared according to the "azirine/oxazolone method" as mentioned in this paper.
Abstract: The protected poly-Aib oligopeptides Z-(Aib)n-N(Me)Ph with n=2–6 were prepared according to the ‘azirine/oxazolone method’, i.e., by coupling amino or peptide acids with 2,2,N-trimethyl-N-phenyl-2H-azirin-3-amine (1a) as an Aib synthon (Scheme 2). Following the same concept, the segments Z-(Aib)3-OH (9) and H-L-Pro-(Aib)3-N(Me)Ph (20) were synthesized, and their subsequent coupling with N,N′-dicyclohexylcarbodiimide (DCC)/ZnCl2 led to the protected heptapeptide Z-(Aib)3-L-Pro-(Aib)3-N(Me)Ph (21; Scheme 3). The crystal structures of the poly-Aib oligopeptide amides were established by X-ray crystallography confirming the 310-helical conformation of Aib peptides.

20 citations

Journal ArticleDOI
TL;DR: In this article, the X-ray crystal structure was determined of one of the products, in which N -(2-aminoethyl)- d -fructopyranosylamine and ethylenediamine are coordinated to a nickel ion.

20 citations

Journal ArticleDOI
TL;DR: A molecular adduct of nitratotriphenyltin with pyridine N -oxide, [Sn(C 6 H 5 ) 3 (NO 3 )(C 5 H 5 NO)], has been synthesized and characterized by infrared spectroscopy and X-ray structural analysis as discussed by the authors.

20 citations

Journal ArticleDOI
TL;DR: The crystal structure of quinolinic acid (2,3-pyridinedicarboxylic acid) has been determined by the method of X-ray diffraction as discussed by the authors.
Abstract: The crystal structure of quinolinic acid (2,3-pyridinedicarboxylic acid) has been determined by the method of X-ray diffraction. The crystal is monoclinic, with a space group of P21/c and with cell dimensions of a=7.421, b=12.729, c=7.850 A, and β=116.96°. The crystal structure was solved by the inspection of a Patterson map. The final R value was 6.78% for 1224 observed reflections. The quinolinic acid molecule takes the form of a zwitter ion in the crystal. The pyridine ring in the molecules shows a significant deformation from the C2V symmetry of idealized geometry. The lengths of the two C–C bonds joining the carboxyl groups to the ring are longer than the normal value. There is an intramolecular hydrogen bond between the adjacent carboxyl groups. The bond lengths in the two C–O groups which participate in this intramolecular hydrogen bond are longer than those of the other two C–O groups. One of the two carbonyl oxygen atoms participates in a hydrogen bond, while the other is free from it. The molecu...

20 citations

Journal ArticleDOI
TL;DR: The PTZ:PMDA 1:1 donor-acceptor complex has been shown to have a modest fold about the N...S axis (dihedral angle 176.4°), however, the deviation from planarity is small in comparison with that in PTZ crystals as discussed by the authors.
Abstract: Single crystals of the black phenothiazine : pyromellitic dianhydride (PTZ:PMDA) 1:1 donor–acceptor complex, have been grown by sublimation from the zone‐refined components. The PTZ:PMDA complex crystalizes with P1 symmetry (Z=2), a=7.197(1), b=19.072(5), c=6.886(1) A, α=84.79(1) °, β=72.98(1) °, γ=85.72(2) ° at T=23 °C. The crystal structure model was refined with 5214 data { (sin ϑ/λ)max=0.8071 A−1} to give R=0.049 and Rw=0.089. The crystal packing consists of two polar endless ...DADA... stacks related to one another by 1. The packing is compared with that in the analogous anthracene : PMDA complex. The PTZ molecule displays a modest fold about the N...S axis (dihedral angle 176.4°), however, the deviation from planarity is small in comparison with that in PTZ crystals. The stack axis is nearly perpendicular to the molecular planes, consequently the CT‐dichroism lies essentially in the principal axis system of the indicatrix. The absorption edge is not very sharp, even at 4.2 K; it is located at 900±...

19 citations

References
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Journal ArticleDOI
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

Journal ArticleDOI
S. C. Wang1
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

Journal ArticleDOI
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