Fragments of an Algebraic Quantum Mechanics Program for Theoretical Chemistry

Hans Primas, Harald Atmanspacher A, Anton Amann +1 more

Preface -- Instead of a 'Festschrift' A. Amann, et al. The Primas Effect: On Quanta and Beyond U. Muller-Herold. Hans Primas and Nuclear Magnetic Resonance R.R. Ernst. Fragments of an Algebraic Quantum Mechanics Program for Theoretical Chemistry A. Amann, U. Muller-Herold. Matter. C*- and W*-Algebras of Observables, Their Interpretations, and the Problem of Measurement A. Amann, H. Atmanspacher. Temporal Nonlocality G. Mahler. Macroscopic Purification of States by Interactions H. Narnhofer, W. Thirring. Macroscopic Quantum Phenomena at the SQUID A. Rieckers. The Geometry of Quantum Probabilities K. Gustafson. Probability and Quantum Dynamics E.C.G. Sudarshan. Perspectives on the Molecular Microworld D.H. Rouvray. The Science of Matter: Fascination and Limits C.P. Enz. Mind. Holism A. Shimony. Concepts of Reality: Primas' Nonstandard Realism B. d'Espagnat. Relative Onticity H. Atmanspacher, F. Kronz. Rationalism, Determinism, Freedom V. Hosle. Cuts and Symbols W. Just. Reflections on the Foundations of Quantum Theory C.F. von Weizsacker. Appendices. Publications by Hans Primas (until 1998). List of Contributors. Index.

Seogjoo Jang

Bryce M. Westheimer

The work in this dissertation focuses on the development of novel theoretical models and methods in ab initio fragment-based quantum chemistry. Chapter 2 describes the derivation and application of a mathematically rigorous approach for treating inter-fragment bonds in large covalently bonded systems. Chapter 3 introduces a novel fragment-based quantum chemistry method, referred to as the Expanded Non-Orthogonal Molecular Orbital (ENMO) method, that has been developed by the author. Finally, Chapter 4 describes a fundamental examination on the local nature of the exchange repulsion effect that arises in non-orthogonal formulations of many-particle quantum mechanics as a consequence of the exclusion principle.

So Hirata

Anton Amann, Werner Gans

Abstract Quantum mechanical and classical aspects are of equal importance in chemistry, and theoretical chemistry must be able to deal with this situation. Classical quantities with which a chemist has to deal include, for example, the temperature and the chemical potential of a substance, and chirality, knot‐type and tertiary structures of molecules. Classical concepts of this type are no more consequences of traditional quantum chemistry than is the theory of complex chemical processes (for example adsorption, heterogeneous catalysis) and macroscopic systems. Algebraic quantum mechanics affords a general framework for the discussion of classical quantities and large systems. There are other independent approaches for the theoretical treatment of chemical problems; these can be summarized by using the keywords “fractals”, “chaotic motion”, “quasicrystals” and “knot theory”. The relationships between these four research topics and their connection with algebraic quantum mechanics, as well as their importance for theoretical chemistry, were discussed at a NATO Workshop in 1987 (see Ref. [1]). In an extended theoretical chemistry, the notion of “molecules” will not play a role as central as it does in quantum chemistry. In the theory of large systems in particular, the introduction of complementary approaches appears to be appropriate; the term “molecule” as used by the chemist does not appear either in the description of disordered systems by means of fractals or in the thermodynamic limit of algebraic statistical mechanics.