Vector algebra and molecular symmetry: a tribute to Professor Josiah Willard Gibbs

Vector algebra, as developed by Josiah Willard Gibbs, is much simpler than matrix or tensor algebra, therefore, it is more suitable to introduce the students of chemistry into the wonderful world of molecular symmetry. A program based on elementary vector algebra has been written to determine all symmetry elements and symmetry operations of rigid molecular structures. The program also contains data for 57 point groups common in chemistry. Therefore, it automatically supplies the particular point group to which the structure belongs. Since the locations of the nuclei related to the symmetry elements are also revealed by the program, even the detailed notation of the framework group of the molecular structure can be deduced. The program can be a great help in determining the symmetries of the normal modes of vibration, too.     

Guest Editorial: A path through quantum crystallography: a short tribute to Professor Lou Massa

Professor Lou Massa’s contributions since the late 1960s to the founding of the field now known as “Quantum Crystallography” (QCr) are briefly described. The term itself has been coined in 1995 by L. Huang, L. Massa, and J. Karle (1985 Nobel Laureate in Chemistry). Originally, QCr referred to the Clinton-Massa’s iterative approach that, for the first time, delivered N-representable electron densities that are consistent with the observed structure factors. These densities satisfy, at once, experimental observation and the necessarily underlying quantum mechanical requirement of being derived from an antisymmetric wavefunction. The single-determinantal quantum mechanical structure Huang, Massa, and Karle (HMK) imposed in their original work can be extended to any method that uses MOs including CI or DFT, as they demonstrate in their papers. HMK use the Clinton-Massa method to reconstruct approximations to the first order reduced density matrix of large molecules in a piecemeal manner from computationally-tractable fragments. The idea was also adapted by J. Hernández Trujillo and R. F. W. Bader in the context of the Quantum Theory of Atoms in Molecules (QTAIM). Massa et al. simplified and generalized this fragmentation method into what came to be known as the “Kernel Energy Method” (KEM) which delivers the properties of large molecules accurately, at a fraction of the computational time, and within any model chemistry as applications to DNA, tRNA, the proto-ribosome, insulin, and graphene, amply demonstrate. Lou Massa has also pushed the envelope in other directions as well. In 1992, he and W. Lipscomb (1976 Nobel Laureate in Chemistry) published several papers predicting the structure and stability of Boron nanotubes and boron fullurene 12 years before they were eventually synthesized in laboratories at Yale and at Brookhaven. More recently, in 2006 L. Massa, J. Karle, and A. Yonath (2009 Nobel Laureate in Chemistry) (MKY) proposed a startling alternative to the then widely-accepted mechanism of the peptide bond formation in the active site of the ribosome. In sharp contrast with the accepted “shuttle mechanism”, MKY’s “direct” mechanism is simpler and, importantly, reproduces the measured thermodynamic and kinetic parameters. Massa has also contributed to other domains, for example interstellar chemistry, and to the policy, history, and philosophy of science. His TV program and Oxford University Press book (both titled “Science and the Written Word”) represent an invaluable and candid documentation of some of the key discoveries in the words of a dozen Nobel Laureates and a constellation of scholars representing the Who’s Who of current science. It is with both admiration and affection that this paper (and this issue) is dedicated to Lou Massa, the person and the scientist.     

A tribute to Professor Revaz R. Dogonadze: The man and his works

In materials with high optical absorption, such as in metals, the interaction of light and medium is sufficiently strong for the observation of light scattering (LS) from various surface excitations. Here the surface enhanced Raman scattering has definitely in the past attracted the most attention. In the case of the magnetic surface excitations it is only the Damon Eshbach (DE) type of surface mode which has up to now been detected by this method. Earlier investigations of this mode were performed by means of microwave experiments. In this article the present state of the LS investigations is described. The physical background of various theoretical and experimental aspects will be discussed. The benefits of the new method are essentially threefold. Firstly it can be used for the determination of magnetic parameters from the observation of LS from the standing spinwave modes in thin films. Secondly, it allows a direct observation of thermal amplitudes. Of particular interest here are very thin films, where the DE mode amplitudes display a tremendous increase. Thirdly, LS is also particularly well suited to investigate the magnetic modes of multilayer systems. Recent theoretical investigations show that for such systems the coupling of the DE modes of the single layers is of great importance.     

Professor Oldham’s contributions to applied mathematics: a tribute on the occasion of his 80th birthday

Based on our 40-year collaboration and friendship, this essay attempts to identify a few of the main themes of Professor Keith B. Oldham’s numerous contributions to the field of applied mathematics. Dedicated to the 80th birthday of Keith B. Oldham.