Understanding the Uniqueness of 2p Elements in Periodic Tables

The Periodic Table, and the unique chemical behavior of the first element in a column (group), were discovered simultaneously one and a half centuries ago. Half a century ago, this unique chemistry of the light homologs was correlated to the then available atomic orbital (AO) radii. The radially nodeless 1s, 2p, 3d, 4f valence AOs are particularly compact. The similarity of r(2s)≈r(2p) leads to pronounced sp-hybrid bonding of the light p-block elements, whereas the heavier p elements with n≥3 exhibit r(ns) ≪ r(np) of approximately -20 to -30 %. Herein, a comprehensive physical explanation is presented in terms of kinetic radial and angular, as well as potential nuclear-attraction and electron-screening effects. For hydrogen-like atoms and all inner shells of the heavy atoms, r(2s) ≫ r(2p) by +20 to +30 %, whereas r(3s)≳r(3p)≳r(3d), since in Coulomb potentials radial motion is more radial orbital expanding than angular motion. However, the screening of nuclear attraction by inner core shells is more efficient for s than for p valence shells. The uniqueness of the 2p AO is explained by this differential shielding. Thereby, the present work paves the way for future physical explanations of the 3d, 4f, and 5g cases.

Orbitals and the Interpretation of Photoelectron Spectroscopy and (e,2e) Ionization Experiments

Electron momentum spectroscopy, scanning tunneling microscopy, and photoelectron spectroscopy provide unique information about electronic structure, but their interpretation has been controversial. This essay discusses a framework for interpretation. Although this interpretation is not new, we believe it is important to present this framework in light of recent publications. The key point is that these experiments provide information about how the electron distribution changes upon ionization, not how electrons behave in the pre-ionized state. Therefore, these experiments do not lead to a "selection of the correct orbitals" in chemistry and do not overturn the well-known conclusion that both delocalized molecular orbitals and localized molecular orbitals are useful for interpreting chemical structure and dynamics. The two types of orbitals can produce identical total molecular electron densities and therefore molecular properties. Different types of orbitals are useful for different purposes.

Theoretical methods for ultrafast spectroscopy

Time-resolved spectroscopy in the femtosecond and attosecond time domain is a tool to unravel the dynamics of nuclear and electronic motion in molecular systems. Theoretical insight into the underlying physical processes is ideally gained by solving the time-dependent Schrödinger equation. In this work, methods currently used to solve this equation are reviewed in a compact presentation. These methods involve numerical representations of wavefunctions and operators, the calculation of time evolution operators, the setting up of the Hamiltonian operators and the types of coordinates to be used hereto. The advantages and disadvantages of some methods are discussed.

Understanding the Woodward–Hoffmann Rules by Using Changes in Electron Density

The Woodward-Hoffmann rules for pericyclic reactions are explained entirely in terms of directly observable physical properties of molecules (specifically changes in electron density) without any recourse to model-dependent concepts, such as orbitals and aromaticity. This results in a fundamental explanation of how the physics of molecular interactions gives rise to the chemistry of pericyclic reactions. This construction removes one of the key outstanding problems in the qualitative density-functional theory of chemical reactivity (the so-called conceptual DFT). One innovation in this paper is that the link between molecular-orbital theory and conceptual DFT is treated very explicitly, revealing how molecular-orbital theory can be used to provide "back-of-the-envelope" approximations to the reactivity indicators of conceptual DFT.