........ published in NEWSLETTER # 59
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........ published in NEWSLETTER # 59
NEW METHODS IN QUANTUM THEORY
by Professor C.A. Tsipis, Aristotle University, Thessaloniki (Greece), Professor V.S. Popov, Inst.of Theoretical and Experimental Physics, Moscow (Russia), Professor D.R. Herschbach, Harvard University, Cambridge (U.S.A.), and Professor J.S. Avery, H.C.Oersted Institute, University, Copenhagen (Denmark)
An accurate and consistent treatment of electron correlation is one of the great challenges currently confronting electronic structure calculations in theoretical chemistry, atomic and molecular physics, and condensed matter theory. Such a treatment is critical for many aspects of the ab initio determination of atomic and molecular structure.
In the last few years, there has been an upsurge in the evolution of novel many-body correlation methods with hitherto unsurpassed degrees of sophistication. A number of post-Hartree-Fock methods, either configurational or perturbational, have been developed adding many-body correlation at various levels of approximation. But all these conventional correlation methods scaling in the N6 regime become arduous or intractable even with the mighty computing power now available or in prospect. Other important formalisms that treat exactly the correlation energy are density functional theory, electron propagator and quantum Monte Carlo methods. The former approach is gaining momentum and is useful in a variety of applications. Besides, there has been a fresh approach towards solving directly the many-particle Schroedinger equation in a hyperspace, without making use of the usual approximations such as the Born-Oppenheimer or the Hartree-Fock approximations. In the emerged new technique, known as dimensional scaling, the dimensionality of space, D, is treated as a variable parameter, and perturbation expansions in 1/D are employed to calculate the wavefunctions and energetics of a system at the physical 3-dimensional world. The new procedure provides a convenient and intuitively meaningful way of treating electron correlation.
A related method of solving directly the many-particle Schroedinger equation, also involving hyperspaces, makes use of hyperspherical coordinates and hyperspherical harmonics. The hyperspherical method yields very accurate solutions both to bound-state problems in many-body quantum theory and to problems involving reactive scattering. Last, but not least, breakthroughs have been made in the development of ab initio relativistic electronic structure theory. The Dirac's relativistic theory provides a very natural and convenient way of treating magnetic effects in quantum chemistry and solid state theory. Since both the relativistic and electron correlation effects are expected to be very pronounced, it is mandatory to treat both these effects accurately for systems of heavy elements. Therefore, there is an urgent need for a concerted effort by leading scientists working in both areas, to delineate and difuse the state-of-the-art theoretical and computational strategies so as to enable scientists to mount a joint attack on these gargantuan problems.
This book (NATO ASI SERIES 3-8) contains all of the invited lectures presented at the NATO Advanced Research Workshop on "New Methods in Quantum Theory" held in Halkidiki, Greece in May 1995. This survey of new perspectives, techniques, and results in quantum theory contains 26 chapters by leading quantum chemists and physicists. The book covers a wide range of topics, though the emphasis throughout is on new approaches and their interrelationships. Topics covered include: dimensional scaling; the hyperspherical method applied both to reactive scattering theory and to bound state problems; chaotic behaviour; large-order perturbation theory; complex eigenvalues and quasistationary states; semiclassical methods; cusps in hyperaccurate wave functions; density functional theory; relativistic quantum theory; and quantum Monte Carlo methods.
Reference books: 3-8, B120, B144, B161, B224, B295, B310, B328, B347