Advances in Theory

This section describes theoretical work of a fundamental nature that does not clearly belong in one of the sections above. Work focused on a particular chemical system - for example, DFT calculations of hyperfine chemical shifts in porphyrins are described in the Porphyrins section. 

1 NMR relaxation of S l/2 Paramagnetic Ions. - Paramagnetic ions with S l/2 experience a complex physical situation, since the electron spin hamil-tonian is a sum of non-commuting terms due respectively to the Zeeman and zfs interactions. In solution phases, the zfs portion of the spin hamiltonian is an explicit function of time due to Brownian reorientation and colhsional distortion 

To describe the relaxation phenomenon theoretically, Kowalewski and his coworkers have developed a formalism based on the Stochastic Liouville Equation (SLE). In recent work, Kowalewski et aP have compared theoretical simulations of Ri field dispersion profiles computed using the SLE formalism with the results of more restricted theory developed in Florence that neglects reorientational motion of the zfs tensor. Kruk and KowalewskP describe a theoretical model that incorporates fast reorientational motion of the zfs tensor. These workers also present theoretical calculations describing the situation where collisional distortions of the zfs tensor are much larger than the time-averaged zfs tensor. 

Miller et aF have employed Spin Dynamics techniques to calculate NMR relaxation enhancements produced by Cr(III)(acac)3, an S = 3/2 spin system for which sufficient physical information is available that an accurate first principles calculation should be possible (i.e., a calculation without variation of undetermined physical paramaters). 

---

The present book, with contributions from a group of very knowledgable scientists in the field, is an attempt to provide a basis for addressing Bridgman s concerns. The response requires multidisciplinary contributions from solid mechanics, solid-state physics, materials science, and solid-state chemistry. Certainly, advances in theory, experimentation, and numerical simulation are impressive, and many aspects of shock-compressed solids have been studied in detail. At the fundamental level, however, it is certainly appropriate to question how well shock-compression processes are understood. 

Advances in theory and developments in methodology arose mostly from fundamental research. This aspect was decisive for the research output in Europe and shoutd remain so. 

The increase in computing power and recent advances in theory have enabled the study of the dynamics of reactive intermediates, which cannot be properly described by classical force fields due to their unconventional bonding properties. To achieve quantitative accuracy in the study of energetics of... 

This volume in Advances in Chemical Physics provides a broad yet detailed survey of the recent advances and applications of reduced-density-matrix mechanics in chemistry and physics. With advances in theory and optimization, Coulson s challenge for the direct calculation of the 2-RDM has been answered. While significant progress has been made, as evident from the many contributions to this book, there remain many open questions and exciting opportunities for further development of 2-RDM methods and applications. It is the hope of the editor and the contributors that this book will serve as a guide for many further advenmres and advancements in RDM mechanics. 

To this point, it would be fair to say that the dominant question was the comparison of experiment with theory by attempts to designate the ground state and if possible to determine the energy separation between it and the next higher state. To a considerable extent, this line of development was driven by the advances in theory itself, whose predictions were made with ever-increasing confidence, sophistication, and refinement. However, one should not conclude that this is the extent and sole purpose of research in the non-Kekule domain. These molecules really... 

Low-dimensional Solids. - 2.10.1 Introduction. The magnetic properties of one and two-dimensional arrays of localized spins coupled by Heisenberg exchange interactions have been studied as a rather specialized branch of theoretical physics since the earliest days of quantum mechanics. However, recent advances in theory, and the preparation of real materials that are a good approximation to the theoretical models, have made low-dimensional systems much more central to condensed-matter science. There is enormous scope for synthetic chemistry in this area and, as will be seen later in this section, many new materials have been discovered recently. 

---