Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science
Markus Reiher
Language: English
Pages: 750
ISBN: 3527334157
Format: PDF / Kindle (mobi) / ePub
Einstein proposed his theory of special relativity in 1905. For a long time it was believed that this theory has no significant impact on chemistry. This view changed in the 1970s when it was realized that (nonrelativistic) Schrödinger quantum mechanics yields results on molecular properties that depart significantly from experimental results. Especially when heavy elements are involved, these quantitative deviations can be so large that qualitative chemical reasoning and understanding is affected. For this to grasp the appropriate many-electron theory has rapidly evolved. Nowadays relativistic approaches are routinely implemented and applied in standard quantum chemical software packages. As it is essential for chemists and physicists to understand relativistic effects in molecules, the first edition of "Relativistic Quantum Chemistry - The fundamental Theory of Molecular Science" had set out to provide a concise, comprehensive, and complete presentation of this theory.
This second edition expands on some of the latest developments in this fascinating field. The text retains its clear and consistent style, allowing for a readily accessible overview of the complex topic. It is also self-contained, building on the fundamental equations and providing the mathematical background necessary. While some parts of the text have been restructured for the sake of clarity a significant amount of new content has also been added. This includes, for example, an in-depth discussion of the Brown-Ravenhall disease, of spin in current-density functional theory, and of exact two-component methods and its local variants.
A strength of the first edition of this textbook was its list of almost 1000 references to the original research literature, which has made it a valuable reference also for experts in the field. In the second edition, more than 100 additional key references have been added - most of them considering the recent developments in the field.
Thus, the book is a must-have for everyone entering the field, as well as for experienced researchers searching for a consistent review.
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volumes V the electromagnetic fields are completely embedded in this volume V and no fields are leaving this volume. Hence the right-hand side of Eq. (2.111) vanishes and Emat + Eem ≡ Etot = const (2.112) holds. In the absence of external forces the total energy of a system consisting of matter and electromagnetic fields is therefore conserved. 2.4.2.2 Momentum and Maxwell’s Stress Tensor The investigation of the momentum transfer occurring in the system requires a similar reasoning. According
Elementary Electrodynamics gauge fields are independent dynamical variables, which will give rise to only two transverse photons in the quantized theory (cf. chapter 7). 2.4.4.3 Retarded Potentials From the previous section and, specifically, from inspection of the Poisson integral in Eq. (2.141) it is clear that the scalar potential is transmitted instantaneously; retardation effects do not show up in Coulomb gauge for the scalar potential (however, this is not true for the vector potential).
rotation of the coordinate axes. Now all three Lorentz boost matrices occurring in Eq. (3.95) are of the most general form given by Eq. (3.81) with a yet undetermined resulting velocity V . We thus have to evaluate Eq. (3.95) directly. In order to achieve this task, it is convenient to introduce the abbreviations γ1 = γ(v1 ) , γ2 = γ(v2 ) , (3.101) γ = γ (V ) where the Lorentz factors γ(v) are defined according to Eq. (3.78). We can now calculate the 00-element of Λ(V ), = [Λ(V )]0 0 = Λ(v2
( t0 ) where Ψ(t0 )=Ψ(t=0) is time-independent. The ansatz for Ψ(t) obviously fulfills the equation of motion given in Eq. (4.16), which may easily be verified by insertion. According to what has been said in the preceding section about unitary transformations, we have two sets of operators, Oˆ (H) = U † (t) Oˆ (S) U (t) (4.35) where the superscript ‘(H)’ denotes the Heisenberg picture, respectively. That is, the unitary transformation U (t) allows us to switch from an operator in the
Stiebritz, L. Yu) for their dedicated work. AW is deeply indebted to Barbara Pfeiffer for her continuous support and patience in the course of preparing this manuscript. Last but not least, it is a pleasure to thank Dr. Elke Maase and Dr. Rainer Münz of WileyVCH for help with all publishing issues of this book. Markus Reiher and Alexander Wolf Zürich, June 2008 XXV 1 1 Introduction This first chapter provides a short reader’s guide, which may help to make the material presented in this