Chemistry\u27s Essential Tensions: Three Views of a Science

In this generously illustrated lecture several views of chemistry will be presented, stressing its psychological dimension and its tie to the arts: First of all, chemistry is, as it has always been, the art, craft, business of substances and their transformations. It is now also the science of microscopic molecules, both simple and complex. And then there are people’s perceptions of chemistry - alternating between seeing the healing and the hurting aspects of this truly anthropic science. The underlying psychological tensions of this truly anthropic science will be explored

Double-diamond NaAl via Pressure: Understanding Structure Through Jones Zone Activation

Under normal conditions, sodium forms a 1:1 stoichiometric compound with indium, and also with thallium, both in the double-diamond structure. But sodium does not combine with aluminum at all. Could NaAl exist? If so, under what conditions and in which structural types? Instead of beginning with a purely computational and first-principles structure search, we are led to apply the early Brillouin and higher (Jones) zone ideas of the physics determining structural selection. We begin with a brief recapitulation of the higher zone concept as applied to the stability of metals and intermetallic compounds. We then discuss the extension of this concept to problems where density becomes a primary variable, within the second-order band structure approximation. An analysis of the range of applicability of pressure-induced Jones zone activation is presented. The simple NaAl compound serves us as a numerical laboratory for the application of this concept. Higher zone arguments and chemical intuition lead quite naturally to the suggestion that 1:1 compound formation between sodium and aluminum should be favored under pressure and specifically in the double-diamond structure. This is confirmed computationally by density functional theoretic methods within the generalized gradient approximation

The Green’s function for the Hückel (tight binding) model

Applications of the Huckel (tight binding) model are ubiquitous in quantum chemistry and solid state physics. The matrix representation of this model is isomorphic to an unoriented vertex adjacency matrix of a bipartite graph, which is also the Laplacian matrix plus twice the identity. In this paper, we analytically calculate the determinant and, when it exists, the inverse of this matrix in connection with the Green's function, G, of the N × N Huckel matrix. A corollary is a closed form expression for a Harmonic sum (Eq. (12)).We then extend the results to d-dimensional lattices, whose linear size is N. The existence of the inverse becomes a question of number theory. We prove a new theorem in number theory pertaining to vanishing sums of cosines and use it to prove that the inverse exists if and only if N + 1 and d are odd and d is smaller than the smallest divisor of N + 1. We corroborate our results by demonstrating the entry patterns of the Green's function and discuss applications related to transport and conductivity

Varying Electronic Configurations in Compressed Atoms: From the Role of the Spatial Extension of Atomic Orbitals to the Change of Electronic Configuration as an Isobaric Transformation

A quantum chemical model for the study of the electronic structure of compressed atoms lends itself to a perturbation-theoretic analysis. It is shown, both analytically and numerically, that the increase of the electronic energy with increasing compression depends on the electronic configuration, as a result of the variable spatial extent of the atomic orbitals involved. The different destabilization of the electronic states may lead to an isobaric change of the ground-state electronic configuration, and the same first-order model paves the way to a simple thermodynamical interpretation of this process

A Comparative Study of the p(2 × 2)-CO/M(111), M)Pt,Cu,Al Chemisorption Systems

We propose a model for CO chemisorption on late transition metal, noble metal, and main-group surfaces based on the results of energy partitioning studies of surface-CO bonding for the CO/M(111), M)Pt,Cu,Al chemisorption systems. Plane-wave density functional theory was used to calculate the chemisorption geometry for CO on the top, bridge, and hollow sites of the M(111) (M)Pt,Cu,Al) surfaces and to verify the experimentally determined preference for top site CO chemisorption on all three surfaces. To construct a chemically intuitive, molecular orbital based model of surface-CO bonding, an energy partitioning analysis of surface-CO bonding was carried out within a tight binding scheme based on the extended Hückel method. Although within this one-electron formalism we are no longer able to make quantitative assesments of bonding, we are able to readily extract surface-CO bonding trends. By expanding the orbital basis on CO to include energetically low-lying nonfrontier orbitals and explicitly evaluating the role of the surface s and p bands in surface-CO bonding, we note several discrepancies between our model and traditional, frontier orbital based models of surface-CO interaction. Especially important is the role of the CO(4σ) orbital. We note that for CO chemisorption on all three surfaces, the energetic preference for top site chemisorption is the result of a balance between the stabilization associated with the formation of the surface-CO bond and chemisorptionsite-dependent changes in both C-O bonding and M-M (M)Pt,Cu,Al) bonding within the surface layer on chemisorbing CO. Further, by choosing to consider CO chemisorption on the Cu(111) surface as part of a continuous transition from CO chemisorption on late transition metal surfaces to CO chemisorption on spmetal surfaces, we are able to assess the degree to which we may refer to copper as an sp-metal