Hyperspherical Harmonics And Generalized Sturmians

HYPERSPHERICAL HARMONICS AND GENERALIZED STURMIANS Progress in Theoretical Chemistry and Physics VOLUME 4 Editor-in- Chief: J. Maruani (Laboratoire de Chimie Physique, Paris, France) S. Wilson (Rutherford Appleton Laboratory Oxfordshire, United Kingdom) Editorial Board: D. Avnir (Hewbrew University of Jerusalem, Israel) J. Cioslowski (Florida State University, Tallahassee, FL, U.S.A.) R. Daudel (European Academy of Sciences, Paris, France) E.K.U. Gross (Universität Würburg Am Hubland, Würzburg, Germany) W.F. Van Gunsteren (ETH-Zentrum, Zurich, Switzerland) K. Hirao (University of Tokyo, Japan) I. Hubac (Komensky University, Bratislava, Slovakia) M.P. Levy (Tulane University, New Orleans, LA, U.S.A.) W.N. Lipscomb (Harvard University, Cambridge, MA, U.S.A.) G.L. Malli (Simon Fraser University, Burnaby, BC, Canada) J. Manz (Universität Würzburg, Germany) R. McWeeny (Università di Pisa, Italy) P.G. Mezey (University of Saskatchewan, Saskatoon, SK, Canada) I. Prigogine (Université Libre de Bruxelles, Belgium) P. Pyykkö (University of Helsinki, Finland) J. Rychlewski (Polish Academy of Sciences, Poznan, Poland) D.R. Salahub (Université de Montreal, Quebec, Canada) S.D. Schwartz (Yeshiva University, Bronx, NY, U.S.A.) Y.G. Smeyers (Institute de Estructura de la Materia, Madrid, Spain) S. Suhai (Cancer Research Center, Heidellberg, Germany) O. Tapia (Uppsala University, Sweden) P.R. Taylor (University of California, La Jolla, CA, U.S.A.) R.G. Woolley (Nottingham Trent University United Kingdom) Hyperspherical Harmonics and Generalized Sturmians by John Avery H.C. ø rsted Institute, University of Copenhagen. Copenhagen, Denmark KLUWER ACADEMIC PUBLISHERS NEW YORK / BOSTON / DORDRECHT / LONDON / MOSCOW eBook ISBN: Print ISBN: 0-306-46944-8 0-792-36087-7 ©2002 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: and Kluwer's eBookstore at: http://www.kluweronline.com http://www.ebooks.kluweronline.com Dedicated to Professors Dudley R. Herschbach Carl E. Wulfman and Vincenzo Aquilanti with admiration for their pioneering research. This page intentionally left blank. Contents Introduction 1 Acknowledgements 6 1 MANY-PARTICLE STURMIANS 7 2 MOMENTUM-SPACE WAVE FUNCTIONS 23 3 HYPERSPHERICAL HARMONICS 33 4 THE MOMENTUM-SPACE WAVE EQUATION 59 5 MANY-CENTER POTENTIALS 75 6 ITERATION OF THE WAVE EQUATION 95 7 MOLECULAR STURMIANS 109 8 RELATIVISTIC EFFECTS 119 A Generalized Slater-Condon Rules 133 B Coulomb and exchange integrals for atoms 136 Solutions to the exercises 141 Bibliography 163 Index 193 This page intentionally left blank. 1 Introduction This book explores the connections between the theory of hyperspherical harmonics, momentum-space quantum theory, and generalized Sturmian basis functions; and it introduces methods which may be used to solve many-electron problems directly, without the use of the selfconsistent-fie