ebook img

Relativistic Quantum Theory of Atoms and Molecules (Springer Series on Atomic, Optical, and Plasma Physics) PDF

813 Pages·2006·7.37 MB·English
Save to my drive
Quick download
Download
Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.

Preview Relativistic Quantum Theory of Atoms and Molecules (Springer Series on Atomic, Optical, and Plasma Physics)

Springer Series on ATOMIC, OPTICAL, AND PLASMA PHYSICS 40 Springer Series on ATOMIC, OPTICAL, AND PLASMA PHYSICS The Springer Series on Atomic, Optical, and Plasma Physics covers in a comprehensive manner theory and experiment in the entire field of atoms and molecules and their interaction with electromagnetic radiation. Books in the series provide a rich source of new ideas and techniques with wide applications in fields such as chemistry, materials science, astrophysics, surface science, plasma technology, advanced optics, aeronomy, and engineering. Laser physics is a particular connecting theme that has provided much of the continuing impetus for new developments in the field. The purpose of the series is to cover the gap between standard undergraduate textbooks and the research literature with emphasis on the fundamental ideas, methods, techniques, and results in the field. 27 Quantum Squeezing By P.D. Drumond and Z. Ficek 28 Atom, Molecule, and Cluster Beams I Basic Theory, Production and Detection of Thermal Energy Beams By H. Pauly 29 Polarization, Alignment and Orientation in Atomic Collisions By N. Andersen and K. Bartschat 30 Physics of Solid-State Laser Physics By R.C. Powell (Published in the former Series on Atomic, Molecular, and Optical Physics) 31 Plasma Kinetics in Atmospheric Gases By M. Capitelli, C.M. Ferreira, B.F. Gordiets, A.I. Osipov 32 Atom, Molecule, and Cluster Beams II Cluster Beams, Fast and Slow Beams, Accessory Equipment and Applications By H. Pauly 33 Atom Optics By P. Meystre 34 Laser Physics at Relativistic Intensities By A.V. Borovsky, A.L. Galkin, O.B. Shiryaev, T. Auguste 35 Many-Particle Quantum Dynamics in Atomic and Molecular Fragmentation Editors: J. Ullrich and V.P. Shevelko 36 Atom Tunneling Phenomena in Physics, Chemistry and Biology Editor: T. Miyazaki 37 Charged Particle Traps Physics and Techniques of Charged Particle Field Confinement By V.N. Gheorghe, F.G. Major, G. Werth 38 Plasma Physics and Controlled Nuclear Fusion By K. Miyamoto 39 Plasma-Material Interaction in Controlled Fusion By D. Naujoks 40 Relativistic Quantum Theory of Atoms and Molecules By I.P. Grant Vols. 1–26 of the former Springer Series on Atoms and Plasmas are listed at the end of the book I.P. Grant Relativistic Quantum Theory of Atoms and Molecules Theory and Computation I.P.Grant Mathematical Institute Oxford University Oxford,UK [email protected] Library ofCongress Control Number:2006926733 ISBN-10:0-387-34671-6 Printed on acid-free paper. ISBN-13:978-0387-34671-7 © 2007 Springer Science+Business Media,LLC All rights reserved.This work may not be translated or copied in whole or in part without the written permission ofthe publisher (Springer Science+Business Media,LLC,233 Spring Street, New York,NY 10013,USA),except for brief excepts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation,computer software,or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication oftrade names,trademarks,service marks,and similar terms,even if they are not identified as such,is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States ofAmerica. (MVY) 9 8 7 6 5 4 3 2 1 springer.com For my wife, Beryl, my sons, Paul and David, and my grandchildren Jacob, Georgia, Joshua, and Imogen Preface Relativistic atomic structure theory has been widely used for many years for predicting atomic energy levels, transition rates, collision cross sections and many other properties. The results have been important for fundamental physics experiments as well as providing data for space science, controlled fusion, and industrial applications. The development of a relativistic theory of the electronic structure and properties of molecules and condensed matter is more recent because it is technically more complex and needs more elabo- rate mathematical machinery than nonrelativistic theory. The first attempts in the early 1980s at relativistic molecular electronic structure calculations based on Dirac’s Hamiltonian were unsuccessful and were mostly abandoned in favour of semi-relativistic approximations for the bulk of applications to quantum chemistry. Now that the dust has settled, there is a need for a book on rigorous foundations that sets out workable and economical methods of fully relativistic calculations for atoms, molecules and clusters that can be used by both physicists and chemists. Part I of the book, which is nonspecialist, aims to equip the reader to rec- ognizethequalitativesignatureofrelativisticeffectsintheelectronicstructure of atoms and molecules. Part II deals with the theoretical foundations of the field.Theformofrelativisticwaveequationsisdeterminedbythegeometryof Minkowski space-time and the structure of the Lorentz and Poincar´e groups. Quantumelectrodynamicsdescribesthephysicsoftheinteractionofelectrona andelectromagneticfields;theequationsaretoocomplicatedtosolveexactly, but we can write down systematic approximation schemes that have proved very effective for modelling electronic structure. This provides the foundation for practical applications to atomic and molecular physics in Part III of the book. The electrostatic potential near each atomic nucleus is almost spherical, so that the nonrelativistic electron wavefunctionhasacharacteristiccentralfield characterinthatregion,permit- tingfactorizationintoradialandangularparts.Relativisticeffectsonelectron dynamics are most marked in the strong electric field near the nucleus; the consequentialcouplingofthefourcomponentsofDiraccentralfieldspinorsin VIII Preface thatregionthereforecharacterizesrelativisticatomicwavefunctions.Thelong- range electron-electron interaction propagates relativistic effects right across the atom or molecule, so that it is essential to treat the whole many-electron system relativistically in order to get reliable results. The coupled radial components of Dirac atomic spinors can be approxi- mated numerically with finite differences, finite elements, or by expansion in analytic functions. Only the last approach is viable for polyatomic systems. Justasnonrelativisticmolecularwavefunctionsareoftenapproximatedaslin- earcombinationsofGaussianfunctions(GTF),sorelativisticmolecularwave- functionscanbeconstructedfromG-spinors–four-componentgeneralizations of GTF having relativistic central field character. These incorporate all the internal relations between the components to satisfy the boundary conditions at the nuclei. Nonrelativistic GTF and G-spinors both represent the electron distribution between atoms and the resultant molecular bonding in much the sameway.Thefailuresofthe1980swereduetotheincorrectassumptionthat the four components of a Dirac spinor can be considered independent and that variational calculations made with this assumption would reproduce the internal structure of orbital spinors with sufficient accuracy. Successful four component calculations need a spinor basis set. Thebodyofthebookpresentsthetechnologyneededforpracticalcalcula- tions;theappendicescontainsupplementarymaterial.Chapters6to8setout the mathematical machinery of relativistic electronic structure calculations on atoms and ions, illustrated with output from a version of the GRASP computer package. Chapter 9, centred on the DARC relativistic R-matrix package,discussesmainlyelectron-atom/ionscattering,photo-excitation,and photo-ionization. The construction and application of the relativistic molecu- lar structure code BERTHA are described in Chapters 10 and 11. Appendix A lists frequently used mathematical formulae, whilst Appendix B presents mathematical background material on linear operators in Hilbert space, Lie groups and Lie algebras, angular momentum theory (including diagram tech- niques), and various aspects of numerical approximation including the theory ofvariationalmethodsforDiracoperatorsanditerativesolutionof(MC)DHF equations. The book is primarily intended as a resource for research physicists and chemists, experimental or theoretical, who recognize that using the available relativistic electronic structure packages as “black boxes” is not always wise. These readers need to understand the physical and theoretical background in order to appreciate what can be done with existing codes and. what is just as important, what cannot be done. I have tried to include enough detail so that this book can be used by graduate students starting work in the field as well as by experts. Some material, especially Chapter 1, should be accessible to undergraduates. More difficult sections marked with an asterisk (∗), can be skipped on a first reading. When the late Charles Coulson first suggested that I write a book on rel- ativistic atomic structure theory more than 30 years ago, I had no inkling Preface IX how much the subject would develop nor how long the writing would take. I regret I have not been able to find more space for some important topics such as relativistic many-body theory and the calculation of radiative cor- rections. The relativistic atomic structure package GRASP owes its present form to many collaborators: in particular Nicholas Pyper, Steven Rose, Neil Beatham, Bruce McKenzie, Jiro Hata, Ken Dyall, Patrick Norrington, and Farid Parpia. Charlotte Froese Fischer who, with Farid Parpia and others, has developed GRASP92 for modern multi-processor computers in order to study complex electronic structures in heavy atoms, continues to introduce further innovations, and her influence can be seen on both Chapters 7 and 8. I am also grateful to Stephan Fritzsche, whose RATIP procedures take rela- tivistic atomic calculations in a new direction, and to illuminating correspon- dence with Steven Manson on photoionization theory and RRPA methods. The DARC code for relativistic R-matrix calculations, Chapter 9, much of which is based on GRASP, was mainly developed by Patrick Norrington and Wasantha Wijesundera. The BERTHA relativistic molecular structure code, Chapters 10 and 11, involved a close collaboration with Harry Quiney and Haakon Skaane. Harry Quiney’s Oxford D. Phil. thesis laid the foundations of the relativistic basis set method in 1987 which were implemented in the DHF atomic code that preceded BERTHA. This book reflects the innumer- ablediscussionsonallaspectsofrelativisticatomicandmoleculartheorythat we have had over the past 20 years. I am most grateful for his careful reading of much of the draft, which has resulted in many improvements. All errors and omissions are, of course, my responsibility alone. Oxford, Ian Grant August 2006 Contents Part I Relativity in atomic and molecular physics 1 Relativity in atomic and molecular physics ................ 3 1.1 Elementary ideas ........................................ 3 1.2 The one-electron atom ................................... 7 1.2.1 Classical Kepler orbits ............................. 7 1.2.2 The Bohr atom ................................... 8 1.2.3 X-ray spectra and Moseley’s Law.................... 9 1.2.4 Transition to quantum mechanics.................... 9 1.2.5 Sommerfeld’s relativistic orbits and Dirac’s wave equation ......................................... 10 1.2.6 Dirac and Schro¨dinger charge distributions ........... 13 1.2.7 The Dirac hydrogenic spectrum at high Z ............ 17 1.3 Many-electron atoms..................................... 19 1.3.1 Central field models of the atom .................... 20 1.3.2 Closed and open shells ............................. 21 1.3.3 Mean field potentials .............................. 23 1.3.4 Comparison of Hartree-Fock and Dirac-Hartree-Fock models for ground states ........................... 24 1.3.5 The mechanism of shell filling....................... 35 1.3.6 Other approaches ................................. 38 1.4 Applications to atomic physics ............................ 40 1.4.1 X-ray spectra ..................................... 41 1.4.2 Applications to astrophysics and plasma physics....... 43 1.4.3 Modelling atomic processes in plasmas ............... 44 1.5 Relativistic molecular structure ........................... 45 1.5.1 Relativistic interpretations of chemical anomalies...... 46 1.5.2 Relativistic effective core potentials and other approximations ................................... 48 1.5.3 Dirac four-component methods for molecules.......... 51

See more

The list of books you might like

Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.