Quantum theory, relativistic methods

In Science, every concept, question, conclusion, experimental result, method, theory or relationship is always open to reexamination. Molecules do exist Nevertheless, there are serious questions about precise definition. Some of these questions lie at the foundations of modem physics, and some involve states of aggregation or extreme conditions such as intense radiation fields or the region of the continuum. There are some molecular properties that are definable only within limits, for example, the geometrical stmcture of non-rigid molecules, properties consistent with the uncertainty principle, or those limited by the negleet of quantum-field, relativistic or other effects. And there are properties which depend specifically on a state of aggregation, such as superconductivity, ferroelectric (and anti), ferromagnetic (and anti), superfluidity, excitons. polarons, etc. Thus, any molecular definition may need to be extended in a more complex situation. 

Quantum Systems in Chemistry and Physics is a broad area of science in which scientists of different extractions and aims jointly place special emphasis on quantum theory. Several topics were presented in the sessions of the symposia, namely 1 Density matrices and density functionals 2 Electron correlation effects (many-body methods and configuration interactions) 3 Relativistic formulations 4 Valence theory (chemical bonds and bond breaking) 5 Nuclear motion (vibronic effects and flexible molecules) 6 Response theory (properties and spectra atoms and molecules in strong electric and magnetic fields) 7 Condensed matter (crystals, clusters, surfaces and interfaces) 8 Reactive collisions and chemical reactions, and 9 Computational chemistry and physics. 

As has long been known, every derivation of the bulk properties of matter from its atomic properties by statistical methods encounters essential difficulties of principle. Their effect is that in all but the simplest cases (i.e., equilibrium) the development does not take the form of a deductive science. This contrasts with the usual situation in physics e.g., Newtonian or relativistic mechanics, electromagnetism, quantum theory, etc. The present paper, after focusing on this difficulty, seeks a way out by exploring the properties of a special class of statistical kinetics to be called relaxed motion and to be defined by methods of generalized information theory. 

Advances in relativistic quantum theory and computational methods made it possible to predict properties of the heaviest element compounds by performing accurate calculations of their electronic structures. Relativistic atomic and molecular calculations in combination with various models were useful in helping to design sophisticated and expensive chemical experiments. Experimental results, in turn, were helpful in defining the scope of the theoretical problems and provided an important input. The synergism between the theoretical and experimental research in the last decade led to better understanding the chemistry of these exotic species. 

The Editor would like to thank the authors for their contributions, which give an interesting picture of the current range from studies of the use of the Lie algebra in quantum theory, overestimates of the neutrino mass, to relativistic effects in atoms and molecules and the calculation of lifetimes of metastable states by means of the method of complex scaling. 

The 1998 Nobel prize for chemistry was awarded to two scientists whose principal contribution was to devise methods that brought approximate quantum theory calculations for the medium-sized molecules within the realms of practicality. The suite of programs that the modern chemist has available for calculating molecular structures is extensive and sophisticated. But, in practice, a compromise always has to be made in terms of the computational effort versus the level of approximation, and some issues of approximation cannot be avoided within the framework of the suite. One such example is the assumption of stationary nuclei another is the problem of relativistic velocity effects, which become significant for the electrons of elements heavier than about iron (that is, the heavier two thirds of the elements). The time-independent Schrbdinger equation is based on Newtonian rather than relativistic mechanics. 

This short historical introduction to relativistic electronic structure, and even more so the chapters that follow, illustrates a very alive and active field of research whose vigom is illustrated by the increasing number of publications in this field. Indeed, if in 1986 a single volume published by Pyykkp [2] was sufficient to list all the related publications on relativistic quantum theory (about 3 100) over a period of 70 years, the next 15 years required two more volumes to hold the list of almost 8 000 new articles or reviews devoted to this subject. Although inflation in publishing is a common feature of all fields of research, these figures clearly show the importance to take relativistic and QED contributions into account. The need to include relativistic effects in quantum chemical calculations has stimulated both conceptual and numerical developments to finally fulfil the wish of Dirac for "approximate practical methods"... 

Non-relativistic quantum theory of atoms and molecules is built upon wave-functions constructed from antisymmetrized products of single particle wave-functions. The same scheme has been adopted for relativistic theories, the main difference now being that the single particle functions are 4-component spinors (bispinors). The finite matrix method approximates such 4-spinors by writing... 

Highly-ionized atoms DHF calculations on isoelectronic sequences of few-electron ions serve as the starting point of fundamental studies of physical phenomena, though many-body corrections are now applied routinely using relativistic many-body theory. Relativistic self-consistent field studies are used as the basis of investigations of systematic trends in ionization energies [137-144], radiative transition probabilities [145-148], and quantum electrodynamic corrections [149-151] in few-electron systems. Increased experimental precision in these areas has driven the development of many-body methods to model the electron correlation effects, and the inclusion of Breit interaction in the evaluation of both one-body and many-body corrections. 

DFT-Based Pseudopotentials. - The model potentials and shape-consistent pseudopotentials as introduced in the previous two sections can be characterized by a Hartree-Fock/Dirac-Hartree-Fock modelling of core-valence interactions and relativistic effects. Now, Hartree-Fock has never been popular in solid-state theory - the method of choice always was density-functional theory (DFT). With the advent of gradient-corrected exchange-correlation functionals, DFT has found a wide application also in molecular physics and quantum chemistry. The question seems natural, therefore Why not base pseudopotentials on DFT rather than HF theory ... 

Recent advances in relativistic quantum theory and computational methods have raised the research in the theoretical chemistry of the heaviest elements to a qualitatively new level. It became possible to predict properties of the heaviest elements, their gaseous compounds and complexes in solutions with a sufficiently high accuracy. On the basis of those calculations, the behaviour of the heaviest element species in specific chemical experiments was reliably predicted and confirmed by specially designed experiments. 

Eqs. (l)-(3), (13), and (19) define the spin-free CGWB-AIMP relativistic Hamiltonian of a molecule. It can be utilised in any standard wavefunction based or Density Functional Theory based method of nonrelativistic Quantum Chemistry. It would work with all-electron basis sets, but it is expected to be used with valence-only basis sets, which are the last ingredient of practical CGWB-AIMP calculations. The valence basis sets are obtained in atomic CGWB-AIMP calculations, via variational principle, by minimisation of the total valence energy, usually in open-shell restricted Hartree-Fock calculations. In this way, optimisation of valence basis sets is the same problem as optimisation of all-electron basis sets, it faces the same difficulties and all the experience already gathered in the latter is applicable to the former. 

Quantum chemistry with the Douglas-Kroll-Hess approach to relativistic density functional theory Efficient methods for molecules and materials... 

An interesting approach to the quantum mechanical description of many-electron systems such as atoms, molecules, and solids is based on the idea that it should be possible to find a quantum theory that refers solely to observable quantities. Instead of relying on a wave function, such a theory should be based on the electron density. In this section, we introduce the basic concepts of this density functional theory (DFT) from fundamental relativistic principles. The equations that need to be solved within DFT are similar in structure to the SCF one-electron equations. For this reason, the focus here is on selected conceptual issues of relativistic DFT. From a practical and algorithmic point of view, most contemporary DFT variants can be considered as an improved model compared to the Hartree-Fock method, which is the reason why this section is very brief on solution and implementation aspects for the underlying one-electron equations. For elaborate accounts on nonrelativistic DFT that also address the many formal difficulties arising in the context of DFT, we therefore refer the reader to excellent monographs devoted to the subject [383-385]. 

Our ambition is to provide a modern introduction to the field of relativistic quantum chemistry, aimed at the advanced student and the practicing nonspecialist researcher. The material has been divided into five parts. Parts I and II provide the necessary background from classical physics, relativistic quantum mechanics, and group theory. Part III covers the application of these principles to fully relativistic methods for quantum chemistry within a four-component framework. Part IV deals with the main... 

Autschbach has outlined some basic concepts of relativistic quantum chemistry and recent developments of relativistic methods for the calculation of the molecular properties, including important for NMR spectroscopy, nuclear magnetic resonance shielding, indirect nuclear spin-spin coupling and electric field gradients (nuclear quadrupole coupling). The author analysed the performance of density functional theory (DFT) and its applications for heavy-element systems. Finally, the author has reviewed selected applications of DFT in relativistic calculation of magnetic resonance parameters. 

---