Construction of orbital angular momentum eigenfunctions for many-particle systems by harmonic projection

Formulas are derived which allow the direct construction of total orbital angular momentum eigenfunctions for many-particle systems without the use of Clebsch–Gordan coefficients. One of the equations is closely analogous to Dirac' identity for the total spin operator. This equation describes the action of L² on a function of the particle coordinates in terms of a class operator of the symmetric group and a "contraction operator." A general projection operator for constructing symmetric eigenfunctions of L² is presented.     

Longest cycles in generalized Buckminsterfullerene graphs

It is shown that every regular 3-valent polyhedral graph whose faces are all 5-gons and 6-gons contains a cycle through at least 4/5 of its vertices.     

On the configuration interaction method for singlet states

The direct CI method, which avoids explicit calculation of the Hamiltonian matrix, is presented in a new form. The method is linked with Davidson's algorithm for iterative evaluation of the ground state eigenvector. The viability of the method is indicated by the test calculations on water which are described.     

Molecular orbital calculations of iron(II) complexes of diimine ligands

Summary Molecular orbital calculations using-, the INDO method have been carried out fm the [FeL(CN)₄]² and [FeLH(CN)₄] complexes, as well as for the tree ligands, with L 2 × pyridine, 1,10-phenanthroline.2,2-bipyridyl. 2,2-rimidine, 2, 3,3-bipyridazine and 4.4-bipyrimidine. Calculations of residual charge at carbon atoms in the ligand rings. correlating with relative nucleophilicity of the compounds, corresponds with observed differences of rate of reaction of the complex [FeI;]² With nucleophiles.     

Polyvalent iodine in organic chemistry

Tricoordinate, I(III), and pentacoordinate, I(V), polyvalent iodine compounds have been known for over a century. In the last twenty years, new polyvalent iodine reagents have been introduced along with synthetic methodologies, based on these and derived reagents, that play an ever increasing role in contemporary organic chemistry. In this Perspective, an overview of these developments is provided with emphasis on the chemistry and uses of aryl-, alkenyl-, and alkynyliodonium salts in preparative and synthetic organic chemistry. It is hoped that this brief overview, along with recent more comprehensive reviews of the field, will stimulate further developments and applications of this useful class of compounds across a broad spectrum of organic chemistry.     

A new look at rotational and vibrational excitation in the scattering of Li+ from N2 and CO at energies between 4 and 17 eV

New experimental time-of-flight distributions are reported for Li⁺-N₂ and Li²-CO at two center-of-mass energies of about 8 and 16 eV and large scattering angles θ_lab ? 120°. The Li⁺-N₂ spectra show two widely spaced maxima, whereas the Li⁺-CO spectra show two and sometimes three maxima. The results are consistent with the model of rotational rainbows, and have also been analyzed in terms of an impulsive model involving collisions with the individual atoms of the molecules with energy-dependent masses. Classical trajectories for a simple model potential reveal only small contributions from vibrational excitation.     

Stereochemistry of Polynuclear Cadmium(II)thioglycolates: Crystal Structure of [ICd8(SCH2CH2OH)12]3+ · 3I− · H2O

Crystals of the title compound are triclinic, a = 27.87 Å, b = 10.77 Å, c = 12.94 Å, α 73.1°, β 116.1°, γ 120.0°, space group P1 . The structure consists of octanuclear ions: Eight Cd(II) ions are found at the corners of a distorted cube, the center of the cube is occupied by an iodide, the twelve thioglycolate sulfur atoms bridge the twelve edges of the cube thereby forming a distorted icosahedron. Cadmium ions are either five or seven coordinate. The phase problem for this structure was solved using a combination of very high and very low E-values.     

New pyrimidino-crown ether ligands

Eight new macrocyclic ligands containing the pyrimidine subcyclic unit ( 3-10 , Figure 1) have been prepared. Two of these new crown ethers are chiral. Pyrimidino-crowns 3-8 were prepared by treating the di-tosylate derivative of the appropriate oligoethylene glycol with 4-methoxy-5-raethyl-2,6-pyrimidinedimeth-anol in basic conditions. The yields were in the 30-50% range giving the crowns as viscous oils. Chiral dimethyl-substituted pyrimidino-crown 9 was prepared from 4-methoxy-5-methyl-2,6-pyrimidinedimethyl di-tosylate and chiral dimethyl-substituted tetraethylene glycol. Treatment of dimethyl 4-methoxy-5-methyl-2,6-pyrimidinedicarboxylate with the diamine derivative of chiral dibenzyl-substituted tetraethylene glycol gave the chiral dibenzyl-substituted pyrimidino-crown diamide 10. Starting 4-methoxy-5-methyl-2,6-pyrimidinedi-methanol was prepared by a six step process from acetamidine hydrochloride and diethyl oxalpropionate.     

Rydberg fingerprint spectroscopy: a new spectroscopic tool with local and global structural sensitivity

Rydberg spectra are shown to provide a spectral fingerprint that is sensitive to molecular structure in unique ways. The concepts are demonstrated using a set of isomeric fluorophenols and a sequence of aliphatic diamines. In the fluorophenols, the sensitivity extends to the placement of a single hydrogen atom and can be traced to the molecular charge distributions associated with the locations of atoms and functional groups with respect to the charge center. Experiments on tetramethyl diamines demonstrate that the structural sensitivity encompasses the extended molecular structure, including parts of the molecule that are remote from the ionization center. This global structure sensitivity makes Rydberg fingerprint spectroscopy uniquely suited to characterize structures of large-scale molecular systems.