Electrostatic and relaxation effects in ionization of molecular dimers and intermolecular complexes

The shifts in ionization energies which occur when a molecule is incorporated as an asymmetric dimer or in an intermolecular complex are analyzed theoretically. MO ? SCF calculations with 4–31G basis sets were performed on closed- and open-shell states of (HF)₂, H₂O·HF, and their valence–hole ions, as well as on the heterodimers incorporating the higher homologues CH₃F, CH₃OH, and (CH₃)₂O. The analysis concerns the influence of electrostatic, polarization, and charge transfer effects associated with complexation on the initial molecular state of each monomer system, as well as monomer–dimer differences in the electronic relaxation mechanism considered as a final state effect in the ionization process. The calculated ionization energy shifts which agree well with the experimental data available for (CH₃)₂O·HF, show that the shifts are dominated by electrostatic effects, but some effects arising from differences in molecular size and electric polarizability of the monomers can be discerned.     

Uncovering the Hidden Landscape of Tris(4-pyridyl) Ligands: Topological Complexity Derived from the Bridgehead

Supramolecular main group chemistry is a developing field which parallels the conventional domain of metallo-organic chemistry. Little explored building blocks in this area are main group metal-based ligands which have the appropriate donor symmetry to build desired molecular or extended arrangements. Tris(pyridyl) main group ligands (E(py)₃, E=main group metal) are potentially highly versatile building blocks since shifting the N-donor arms from the 2- to the 3-positions and 4-positions provides a very simple way of changing the ligand character from mononuclear/chelating to multidentate/metal-bridging. Here, the coordination behaviour of the first main group metal tris(4-pyridyl) ligands, E(4-py)₃ (E=Sb, Bi, Ph−Sn) is explored, as well as their ability to build metal-organic frameworks (MOFs). The complicated topology of these MOFs shows a marked influence on the counter anion and on the ability of the E(4-py)₃ ligands to switch coordination mode, depending on the steric and donor character of the bridgehead. This structure-directing influence of the bridgehead provides a potential building strategy for future molecular and MOF design in this area.     

The photoelectron spectrum and molecular geometry of bicyclo[2.1.1]hexane

The He(I) photoelectron spectrum of bicyclo[2.1.1]hexane shows excellent correlation with a theoretical spectrum based on the eigenvalues obtained in an ab initio calculation at the theoretical molecular geometry. By contrast, a calculation performed at the experimental geometry exhibits an effect of enhanced ring strain in showing a first ionization energy which is considerably lower than the experimental value. This observation offers experimental support for the recent claim that the published structure for bicyclo [2.1.1]hexane based on electron-diffraction measurements is incorrect. It also accounts for inconsistencies observed in the calculated values of some spin—spin coupling constants for substituted bicyclo[2.1.1]hexanes.     

Electronic structure of the valence bands of SnCl2 and SnBr2 studied by ultraviolet photoelectron spectroscopy

A photoelectron study of the outermost bands of solid-phase SnCl₂ and SnBr₂ using 40.81 eV photons is reported. The main features of the spectra are successfully interpreted in terms of molecular orbital theory for the appropriate isolated molecules.     

Resonance-enhanced multiphoton ionisation photoelectron spectroscopy of the ClO radical: the C 2 sigma- state

A (2 + 1) one-colour resonance-enhanced multiphoton ionisation study is carried out on the C 2 sigma- state of the ClO radical in the one-photon energy range 29,500-31,250 cm-1. The ClO radical is produced by one-photon photolysis of ClO2 employing 359.2 nm photons derived from a separate laser. In this way a significant concentration of vibrationally excited ClO in its spin-orbit split X 2 pi omega (omega = 3/2 or 1/2) electronic ground state is produced. In addition to mass-resolved excitation spectra, kinetic-energy resolved photoelectron spectra for the X 3 sigma-(v+)<--C 2 sigma-(v' = 3-5) transitions are measured. These transitions are not completely Frank-Condon diagonal, and indicate a decrease in bond length on removal of the Rydberg electron from the C 2 sigma- state. In addition to an unambiguous assignment of the C 2 sigma- state, valuable information is obtained on the degree of vibrational excitation with which the nascent ClO radical is formed in the photolysis of ClO2. Analysis of the photoelectron spectra is supported by Franck-Condon calculations based on potential energy curves either from experimental spectroscopic parameters, or obtained by theoretical ab initio methods.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.