Ideas of quantum chemistry

F Compose your own book according to your needs Choose your own path through the TREE (all paths begin at the basis of the TREE) You may also consider the author’s recommendations with two basic paths: • minimum minimorum (a few dozen of pages) with the sign  for those who want to proceed as quickly as possible to get idea what quantum chemistry is all about, • minimum with the signs  and for those who seek basic information about quantum chemistry, as well as other paths, that consist of the minimum path, i.e  and 4, and (following the corresponding flags) special excursions into the subjects of large molecules () molecular mechanics and molecular dynamics (Ä) solid state chemistry/physics () chemical reactions (ʊ) spectroscopy () exact calculations on atoms or small molecules () relativistic and quantum electrodynamics effects () most important computational methods of quantum chemistry (♦) future of quantum chemistry ( ) “magical” aspects of quantum physics () F • • • • • • • • • • IDEAS OF QUANTUM CHEMISTRY Second edition “Things appear, ideas persist” Plato IDEAS OF QUANTUM CHEMISTRY Second edition by LUCJAN PIELA Department of Chemistry, University of Warsaw, Warsaw, Poland AMSTERDAM • BOSTON • HEIDELBERG • LONDON • NEW YORK • OXFORD PARIS • SAN DIEGO • SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Elsevier 225 Wyman Street, Waltham, MA 02451, USA 525 B Street, Suite 1800, San Diego, CA 92101-4495, USA Second edition 2014 © 2014 Elsevier B.V All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: permissions@elsevier.com Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material Notice No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library For information on all Elsevier publications visit our web site at store.elsevier.com Printed and bound in United Kingdom 14 15 16 17 18  10 ISBN: 978-0-444-59436-5 To all on the quest for the Truth Sources of Photographs and Figures ✶ The Figures in this book, except those listed below or acknowledged in situ, are manufactured by the author and reproduced thanks to the courtesy of Wydawnictwo Naukowe PWN, Poland from “ Idee chemii kwantowej”, © 2012 PWN, ✶ the postal stamps of several countries have been used (Austria pp 30, 77, 106, 615, Canada 591, 886, Denmark 7, France 979, e17, e121, 371, Gabon 354, Gambia 4, 927, Germany 302, Great Britain 1003, Greece 795, Guiné-Bissau 111, 874, Guinée 12, 74, 155, 764, 270, 764, Guyana 512, Holland 11, 796, Hungary 250, 524, Ireland 1004, Komi 328, Mali 1, 4, 26, 124, Marshall Islands 446, Micronesia 36, Nevis 340, Sweden 952, Uganda 9, Uruguay 110, USA 107, 260, 594, 612, 723, Vatican 796) ✶ courtesy of The Nobel Foundation (John Rayleigh 5, Niels Bohr 7, Albert Einstein 107, Carl Anderson 126, James Watson 345, Francis Crick 345, Tjalling Koopmans 466, John Pople 501, Walter Kohn 676, John Van Vleck 721, Norman Ramsey 771, Edwards Purcell 771, Yuan Lee 886, Dudley Herschbach 886, Rudolph Marcus 950, Ilya Prigogine 982) ✶ Wikipedia - the web encyclopedia, public domain (7, 27, 62, 64, 110, 111, 172, 286, 347, 363, 505, 507, 516, 585, 771, 975, 991, 745, e10) ✶ photo of Aleksander Jabłoński p.460, courtesy of Physics Department, Nicolaus Copernicus University, Toruń, Poland ✶ courtesy of Professor Roald Hoffmann (Cornell University, USA) 533, 536, 542, 546, 547 ✶ courtesy of Professor Jean-Marie André (Université de Namur, Belgium) 543, 544 ✶ courtesy of Professor Hiroshi Nakatsuji, Japan 658 ✶ courtesy of Professor Sadlej’s family, Poland p.749 ✶ photo of Charles Galton Darwin p.124 - courtesy of Dr.R.C.McGuiness, UK ✶ photo of Christopher Longuet-Higgins, p.261- courtesy of Professor J.D.Roberts, California Institute of Technology, USA ✶ photo of Friedrich Hund p.461- courtesy of Mr Gerhard Hund, Germany ✶ photo of Richard Bader 672 - courtesy of Professor Richard Bader, Canada ✶ portrait of Hans Hellmann p.722 reproduced from a painting by Ms Tatiana Livschitz, courtesy of Professor W.H Eugen Schwartz, Germany ✶ photo, courtesy of Jean-Marie Lehn, France 976 ✶ photo of Gregory Breit - courtesy of Alburtus Yale News Bureau (through Wikipedia) - 146 ✶ Figs 11.10-11.12 reused from S Kais, D.R Herschbach, N.C Handy, C.W Murray, G.J Laming, J Chem Phys., 99 (1993) 417 ✶ Tables 14.1-14.5, courtesy of Professor Sason Shaik, Israel ✶ Fig 8.33 - courtesy of Dr.Witold Mizerski, Poland 493, photographs by the author (PerOlov Löwdin 445, Rudolph Peierls 535, Włodzimierz Kołos 591, Lutosław Wolniewicz 591, Szkocka Café in Lwów 372, Roald Hoffmann 925) Despite reasonable attempts made, we were unable to contact the owners of the copyright of the following images: ✶ photo of Boris Belousov p.995 from “ Geroi i zladiei rossiyskoi nauki”, Kronpress, Moscow, 1997, Figs on p.874 and 875 reproduced from “ Biology Today”, CRM Books, Del Mar, USA, © 1972 Communications Research Machines, MPn method 653 ✶ in the website of St Andrews University, United Kingdom http://www-gap.dcs.st-and.ac.uk/~history (Sommerfeld 8, Bose 26, Bell 48, Weyl 80, Minkowski 119, Klein 123, Hartree 393, Riemann 560, Friedmann 593, Thom 671, Feigenbaum 978, 873 (Tomaglia), Shannon 876, Adleman 1002, Turing 879, Lagrange 997 ✶ in the website of Physics Department, Moscow University http://nuclphys.sinp.msu.ru (Edward Condon 302) ✶ in the website of Duke University (USA) www.phy.duke.edu, photo Lotte Meitner-Graf: Fritz London 611 ✶ in the website of www.volny.cz Gilbert Lewis ✶ in the website met www.epfl.ch: Brillouin 438 ✶ in the website http://osulibrary.orst.edu Slater 397 ✶ in the website http://www.mathsoc.spb.ru: Fock 394 ✶ xxi Sources of Photographs and Figures in the website www.stetson.edu Ulam 372 ✶ in the website http://www.quantum-chemistry-history.com (Hückel 427, Roothaan 432, Hall 432) If you are the copyright owner to any of the images we have used without your explicit permission (because we were unable to reach you during our search), please contact prof.Lucjan Piela, Chemistry Department, Warsaw University, 02093 Warsaw, Poland e-mail: piela@chem.uw.edu.pl, phone (48)-227226692 We will be pleased to place the appropriate information on our website at booksite.elsevier com/978-0-444-59436-5 which supports the present book and represents its integral part xxii Introduction Quantum scimus – gutta est, ignoramus mare What we know is a drop, what we not know is a sea (Latin sentence) We and the Universe: A Potent Interaction Here are a few ways that photons play a part in my life: Crocuses first appear after winter and look breathtaking on the snow, then ultramarine of the violets Later, magnolia flowers seem like proud queens–a bright white with a subtle rosy tint A week later, the lilacs, the ecru of acacia, and finally the rich, extraordinary kingdom of roses all make their debuts The buds of the hydrangea (the beloved flowers of this author) are white, but when they first open, the white reacts with light quanta, and the flowers acquire vibrant, clean colors, ranging from light to dark blue Why does all this happen? Not only colors create a sense of wonder, but unusual shapes, textures, and hues as well What is in our brain that can use photons to translate our interactions with the Universe into an unimaginable variety of complex phenomena, already in our body, that can affect our decisions and actions? Sight represents the most powerful (highly directional and long-range) and, at the same time, the most subtle information channel to our brain Hearing What could compete with the fantasy of the thrush, which sings different masterpieces every spring in my three pine trees? Why does a finch sing completely differently from the thrush, and why does it repeat its melody with amazing regularity? Why all finches sing similar songs? What kind of internal programming compels them to so? The program must be quite robust, being insensitive to thousands of details of the neighborhood, but not to some particular signals of danger Birdsong is still less interesting than human verbal communication, though A person pronounces a particular word, which may have the strength of a tornado for others How is it possible that a local sequence of tiny air pressure amplitudes (sound) can change our world in the global scale? Spring also provides fantastic fragrances: Just after winter, one can smell the heavenly aroma of violets and hyacinths, sometimes the subtle scent of bird cherry is brought by the wind from far xxiii xxiv Introduction away, then a variety of other exciting fragrances follow What is the mechanism of recognizing and remembering smells, admiring some of them and being repelled by others? The taste of fresh bread is unforgettable and is linked to a feeling of happiness, not only for me, but for many people There must be a program imprinted in us with some chemical hardware that lets us appreciate the way things taste What does this hardware look like? Touching, which is based on the Pauli exclusion principle, has changed the history of the world many times ( just think about kissing etc.) Such giant consequences from such a small cause? What Do We Know? Our senses connect us to what we think of as the Universe Using them, we are aware of its presence, while at the same time we become a part of it Sensory operations are the direct result of interactions between molecules, as well as between light and matter All of these phenomena deal first with information processing, but at the same time with chemistry, physics, biology, and even psychology In these complex events, it is impossible to discern precisely where the disciplines of chemistry, physics, biology, and psychology begin and end Any separation of these domains is artificial The only reason for making such separations is to focus our attention on some aspects of one indivisible phenomenon Touch, taste, smell, sight, and hearing–are these our only links and information channels to the Universe? How little we know about it! To realize that, just look up at the sky A myriad of stars around us point to new worlds, which will remain unknown forever On the other hand, imagine how incredibly complicated must be the chemistry of friendship Science cannot answer all legitimate questions that a human being may ask Science is able to discover laws of nature, but is unable to answer a question like “Why does our world conform to any laws at all1 ?” This goes beyond science We try to understand what is around us by constructing in our minds pictures representing a “reality,” which we call models Any model relies on the perception of reality (on the appropriate scale of mass and time) emanating from our experience, and, on the other hand, on our ability to abstract by creating ideal beings Many such models will be described in this book It is fascinating that humans are able to magnify the realm of the senses by using sophisticated tools (e.g., to see quarks sitting in a proton2 ), to discover an amazingly simple equation of motion3 that describes cosmic catastrophes, with intensity beyond our imagination, and the delicate flight of a butterfly equally well A water molecule has exactly the same properties in the Pacific Ocean as it does on Mars, or in another galaxy The conditions in those environments “The most incomprehensible thing about the world is that it is at all comprehensible.” (Albert Einstein) A proton is 1015 times smaller than a human being Acceleration is directly proportional to force Higher derivatives of the trajectory with respect to time not enter this equation, and neither does the nature or cause of the force The equation is also invariant with respect to any possible starting point (position, velocity, and mass) What remarkable simplicity and generality there is (within limits, see Chapter 3) Name Index 1023 Fermi Enrico, 26, 31, 34, 55, 96–97, 101, 320, 340, 397, 506, 579, 608, 665, 702 Feynman Richard Philips, 3, 14, 44, 149, 723, 795 Fiodorow Jewgraf, e36 Fischer Hermann Emil, 874, 971 FitzHugh Richard, 995 Flannery Brian P., 370 Flory John Paul, 350 Fock Vladimir, 106, 124, 126, 142, 145, 389–393, 394, 407–409, 417, 427, 436, 441, 494, 506, 617, 662, 687, 689, 697, 709, 717, 790, 880, 923, e40, e109, e153 Fokkens Roel H., 978 Foresman James B., 687 Fraga Serafin, 420 Franck James, 302, 317 Franken Peter A., 722, 755 Friedmann Alexandr Alexandrovich, 593 Fripiat Joseph G., 103, 155, 441, 565, 749 Frisch Aeleen, 687 Froelich Piotr, 328 Frost Arthur A., 428 Fujimoto Hiroshi, 885 Fukui Kenichi 174, 885, 925–926 Fukutome Hideo 393, 441 Fusaro Massimo 173–174 G Galileo Galilei, 110, 904, Galois Evariste, e17 Ganguli Ashok K., 322 Gelin Bruce, 340 Gellat Charles D., 340 Gentry W Ronald, 886 Germer Lester H., 13 Gershenfeld Neil, 54, 57 Gershinowitz Harold, 885 Gilbert Thomas L., 7, 679, 705 Gillespie Ronald James, 491 Gleick James, 981 Gödel Kurt, e10 Goldstein Herbert, 294 Gombas Pál, 665 Gordan Paul, 344 Gordon Walter, 106 Górecki Jerzy, 995 Gorter Cornelis Jacobus, 721 Goudsmit Samuel A., 3, 10 Gour Jeffrey R., 657 Grabowski Ireneusz, 635 Grabowski Zbigniew Ryszard, 962 Gradshtein Israil Solomonowicz, 425 Grangier Philippe, 49 Grant Ian M., 155 Greene Chris H., 896 Gregoryantz Eugene A., 948 Grellmann Karl-Heinz, 962 Gribbin John, 45 Grochala Wojciech, 325, 466 Gross Eberhard K.U., 665, 706, 714–715 Grosshans Frédéric, 47 Grzegorz Łach, 121 Gumi´nski Kazimierz, 427 Gutin Alexander M, 354 Gutowski Maciej, 824 H Haas Arthur, 13 Hagstrom Stanley A., 588 Hall George G., 393, 432 Hameka Hendrik F., 123, 762, 791 Hamilton William Rowan, 1004 Handy Nicholas C., 212, 423, 589, 707, 886, 905 Hartley Ralph Vinton Lyon, 971 Hartree R Douglas, 392, 393, 416, 394, 398, 407–409, 416–420, 431, 433, 437, 484, 501, 548, 580, 620, 657, 664–665, 803, 880, 885, 923, e109, e153 Hartree William, 581 Hasenöhrl Fritz, 78 Havlas Zdenek, 362 Haywood Susan, 328 Head-Gordon Martin, 361–362 Heeger Allan J., 505 Heisenberg Werner Karl, 3, 11–13, 36, 79, 161 Heitler Walter, 13, 581, 610–611 Helgaker Trygve, 502, 653, 660, 787, 790–791 Hellmann Hans Gustav Adolf, 721, 722 Helmholz Hermann, Hemley Russell J., 948 Hennico Géneviéve, 441, 749 Herman R.M., 274 Hermite Charles, 191 Herschbach Dudley R., 161, 212, 589, 707, 886 Hertz Gustav, 302 Herzberg Gerhard 259, 591, 592 Hess Bernd A., 131 Hiberty Philippe C., 705 Hilbert David, 20, 35, 56, 64, 66, 84, 88, 98, 129–130, 210, 232, 241, 392, 616, 661, 831, 902, e10–e11, e20, e110 Hiley Basil, 57 Hill Alan E., 722, 755 Himmler Heinrich, 36 Hinze Juergen, 262, 333 Hirschfelder Joseph O., 254, 806, 836, 881, 885, e94 Hitler Adolf, 6, 11, 77 1024 Name Index Hjorth-Jensen Morten, 657 Hobza Pavel, 362, 881 Hodges Robert S., 868 Hoffmann Roald, 325, 466, 496, 508, 542, 545, 573, 885, 926, 942, 966 Hoffmann-Ostenhoff Maria, 423 Hoffmann-Ostenhoff Thomas, 423 Hogervorst Wim, 150 Hohenberg Pierre, 675 Holthausen Max C., 676, 715, 665, 676 Hooke Robert, 349 Howard Brian J., 899 Hubble Edwin Powell, 594 Huc Ivan, 971, 976 Hückel Erich, 392, 427 Hückel Walter, 427 Hult Erika, 715 Hund Friedrich Hermann, 161, 461 Hurley Andrew Crowther, 610 Huygens Christiaan, 44 Huzinaga Sigeru, 425 Hylleraas Egil Andersen, 232, 246, 581, 587 I Irvin Randall T., 868 Isaacson Alan D., 914 Ishikawa Atsushi, 659 J Jørgensen Poul, 502, 622, 626, 653, 660, 752, 787, 790 Jabło´nski Aleksander, 460, 461 Jacobi Carl Gustav Jacob, 341 Jacques Vincent, 47 Jahn Hans, 536 James Hubert M., 581, 590 Jankowski Karol, 634–635 Jankowski Piotr, 637 Jaszu´nski Michał, 790–791, 846 Jeans James Hopwood, Jennings Donald E., 333 Jeziorski Bogumił, 149, 154, 328, 333, 592, 637, 796, 832, 846, 865 Joliot-Curie Frederick, 722 Joliot-Curie Irene, 722 Jones Steven E., 328 Jordan Pascual, 3, 11–12 Josza Richard, 51 K Kümmel Hermann, 581 Kais Sabre, 161, 212, 589, 707 Kammerlingh Onnes Heike, 322 Karpfen Alfred, 553 Karplus Martin, 340, 354 Karwowski Jacek, 131, 145, 216–217 Kato Tosio, 584, 585 Kauzmann Walter, 796, 867 Kekulé Friedrich August von Stradonitz, 613 Keller Claudia, 46 Kelvin lord (William Thomson), 665 Kemula Wiktor, 428 Kestner Neil R., 881 Ketterle Wolfgang, 35 Kettunen Petteri, 995 Khare Avinash, 218 Kielich Stanisław, 753 Kihara Daisuke, 375 Kim Jongseob, 360 Kim Kwang Soo, 360 Kimball George E., 897, 911, 966, e32 Kirchhoff Gustav, 4, 446 Kirkpatrick Scott, 340, 370 Kitaura Kazuo, 804 Klein Douglas J., 173 Klein Oskar, 123 Klemperer William, Klinowski Jacek, XXXIII Kobus Jacek, 432 Koch Wolfram, 676, 715 Kohn Walter, 50, 665, 676, 677, 679, 680–684, 686, 688, 694, 706, 712–717 Koli´nski Andrzej, 372, 375–376, 385 Kołos Włodzimierz, 591, 796, 832 Komasa Jacek, 154, 274, 275, 333, 592, 597 Konecny Robert, 325 Koopmans Tjalling Charles, 393, 466 Koot Wouter, 301 Koput Jacek, e52 Korchowiec Jacek, 714 Koritsanszky Tibor S., 672 Korobov Vladimir, 150 Korybut-Daszkiewicz Bohdan, 277 Kowalski Karol, 657 Kraka Elfi, 457, 914, 916–920 Krebs Hans Adolf, 995 Krishnan (in fact Raghavachari Krishnan), 622, 637 Kronecker Leopold, 24 Kucharski Stanisław A., XXXIII, 641, 657 Kupperman Aron, 886, 902 Kurokawa Yusaku, 659 Kutzelnigg Werner, 132 Kwast Andrzej, 820 L Łach Grzegorz Euzebiusz, 121, 150, 154, 333, 592 Lagrange Joseph Louis, e121 Laming Gregory J., 212, 589, 707 Langevin Paul, 9, 371 Langreth David C., 715 Laplace Pierre, 191 Larsson Peter, 103 Lattes Cesare G., 152 Name Index 1025 Lauvergnat David L., 705 Lawley Kenneth P., 431 Leach Andrew R., 385 Lederman Leon, 593 Lee Jin Yong, 360 Lee Sik, 360 Lee Tsung Dao, 74 Lee Yuan Tseh, 886 Legendre Adrien, 200 Leherte Laurence, 103, 155 Lehn Jean-Marie, 866, 976 Leibnitz Gottfried Wilhelm, 340 Lenard Philipp Eduard Anton, Lennard-Jones John E., 347, 470, 610 Lenz Wilhelm, 83 Lesyng Bogdan, 369 Levine Raphael David, 161, 887, 966 Levitt Michael, 346 Lévy Bernard, 469, 472, 626 Levy Mel, 665, 667, 715 Lewis Gilbert Newton, 6, 7, Lifson Shneior, 340 Linnaeus Charles, 585 Loeser John G., 886 London Fritz Wolfgang, 13, 581, 611, 612–613, 656, 786, 796, 831, 842, 939 Longuet-Higgins Hugh Christopher, 260, 261, 672, 885, 902 Lopez Xabier, 217 Lorentz Hendrik, 108, 111, 764 Lorenzo Echevarria, 217 Los Joop, 301 Lotka Alfred J., 971, 980 Lotrich Victor, 850 Louis Edwin J., 505 Lưwdin Per-Olov, 444, 445, 472, 581 Luda Eduardo V., 217 Lührmann Karl-Heinz, 581 Lum Ka, 867 Lundqvist Bengt I., 715 Lüthi Hans P., 84 Luty Tadeusz, 860 Lysenko Trofim, 614 M Møller Christian, 581 Małolepsza Edyta, 376 MacDiarmid Allan G., 505 Mach Ernest, 106, 107 Makarov Dmitrij, 715 M¸akosza Mieczysław, 820 Malrieu Jean-Paul, 472, 502 Manz Jưrn, 99 Mao Ho-Kwang, 948 Marcus Rudolph Artur, 951 Marechal Yves, 273 Margenau Henry, 254, 881 Marron Michael T., 423 Martin M.L., 341 Martin P.C., 150 Martin S., 948 Maxwell (Clerk Maxwell) James, 4, e81 McCammon Andy, 340, 369 McCormack Elisabeth F., 592 MacDonald A.H., 714 McMahan Andy K., 948 McWeeny Roy, 581 Meath William J., 806 Meir Yigal, 715 Mendel Johann Gregor, 615 Mendeleev Dmitri Ivanovich, 392, 446 Mermin David, 44 Mertens Franz, 78 Metropolis Nicolas Constantine, 340, 373 Meunier Annie, 469 Meyer Thomas J., 951 Mezey Paul G., 669 Mhin Byung Jin, 360 Michalak Artur, 714 Michalska Danuta, 650 Michelson Albert Abraham, 105, 111 Michl Joseph, 260, 886 Miller John Robert, 954 Miller William H., 886, 905 Millié Philip, 469, 472 Millikan Robert, Minkowski Hermann, 106, 119 Misquitta Alston J., 841 Moissan Henri, 446 Monfils André, 592 Monkhorst Hendrik Jan, 328, 593, 635 Moore Walter, 78 Morgan John D III, 423 Morino Yonezo, 495 Morley Edward Williams, 105, 111 Morokuma Keiji, 369, 804 Morrell G.O., e132 Morse Philip McCord, 161, 192 Mosley David H., 103, 155 Motoike Ikuo N., 996 Mozart Wolfgang Amadeus, 886 Muldero N., 948 Müller Alex K., 322 Mulliken Robert S., 796, 806, 885 Mullis, Kary Bo., 1006 Murphy George M., 254 Murray Christopher W., 212, 589, 707 Murrell John N., 835 Musher Jeremy Israel, 835 Musiał Monika, 641, 657 N Nagata Chikayoshi, 174 Nagumo Jin-Ichi, 995 Nairz Olaf, 46 Nakatsuji Hiroshi, 654, 657, 658, 659, 885 Nakashima Hiroyuki, 659 Nalewajski Roman F., 714 Neddermeyer Seth H., 327 Nemethy George, 796 Neustadter S.P., e101 Newlands John, 446 1026 Name Index Newton Isaac, 4, 84, 103, 106–108, 340, 371, 383, 387 Nguyen-Dang Thanh Tung, 668 Nibbering Nico M.M., 978 Nicolis Gregoire, 971 Noether Emmy Amalie, 63, 64 Nooijen Marcel, 654 Nusair Marwan, 689 Nyholm Ronald S., 491 O Occhialini Giuseppe S.P., 152 Olivucci Massimo, 312, 323 Olsen Jeppe, 502, 653, 660, 752 Oppenheimer Julius Robert, 270 Öpik Uno, 885, 902 Orville-Thomas William J., 100 Ostlund Neil S., 502, 660 P Pachucki Krzysztof, 149, 154, 274, 333 Padé Henri, 795, 843, 971, 979 Paldus Joseph, 441, 637, 648 Papenbrock Thomas, 657 Paramonov Gennadij K., 99 Parr Robert G., 679, 714–715 Parrinello Michele, 377 Pasta John R., 340 Pauli Wolfgang, 3, 10, 12–13, 30, 36, 56, 100, 107, 125–128, 142, 147, 150, 154, 408–410, 545, 608, 697, 708, 837, e187–e188, e190 Pauling Linus Carl, 612 Pauncz Ruben, 444 Pedersen Charles John, 971, 973 Peierls Rudolph, 535 Peres Asher, Pernal Katarzyna, 715 Perrin Jean-Baptiste, 722 Pestka Grzegorz, 145 Peters C Wilbur, 722 Piecuch Piotr, 657, 659, 859 Piela Lucjan, 354, 376, 441, 508, 561, 563, 565, 569, 659, 749, 818, 842, 852, 993, e177 Pisani Lorenzo, 103 Piszczatowski Konrad, 154, 333, 592 Planck Max Karl Ernst Ludwig, 4, 6, 46, 66, 77, 79 Plato, 505 Plesset Milton S., 581, 648, 652, 656, 661 Podolsky Boris, 40, 295–296 Poincaré Jules Henri, 971, 979 Poirier Raymond A., 818, e147 Polášek Marek, 99 Polanyi John Charles, 886, 914 Polanyi Michael, 260, 308, 885–886 Politzer Peter, 420 Polyansky Oleg L., 154 Pople John A., 501, 535, 637, 676, 622 Post Paul H.P., 301 Pound Robert V., 721 Powell Cecil F., 152 Pratt George W., e101 Prigogine Ilya, 972, 982 Pryce Maurice H.L., 885, 902 Przybytek Michał, 154 Pulay Peter, 648 Purcell Edward M., 771, 772 Pyykkö Pekka, 103, 106, 154 Q Quiney Harry M., 155 R Rabi Isidor, 327 Rafelski Johann, 328 Rahman Aneesur, 340 Raman Chandrasekhar Venkata, e58 Ramsey Norman F., 721, 771 Rao Chintamani N.R., 322 Ratajczak Henryk, 881 Ratner Mark A., 951 Rayleigh John William Strutt, Reichlin Robin L., 948 Reimers Jeffrey R., 362 Reines Frederick, 593 Reinhoudt David N., 978 Rejewski Marian, 1003 Ridard Jacqueline, 469 Riemann Georg Friedrich Bernhard, 560 Ripoll Daniel R., 819 Ritz Walther, 232, 239 Robb Michael A., 313, 334 Roch Jean-Franỗois, 47 Rodnikova Margarita, 89, 867 Roger Gérard, 50–51 Rohrmuth R.M.F., 78 Roos Bjưrn O., 623, 628 Roothaan Clemens C.J., 432 Ró˙zycki Jerzy, 1003 Rosen Natan, 3, 40 Rosenbluth Arianna W., 340 Rosenbluth Marshal N., 340, 373 Rotkiewicz Krystyna, 962 Ruedenberg Klaus, 200, 420, 470 Runge Carl, 83, 665 Runge Erich, 706, 714 Ruoff Arthur L., 948 Russell John Scott, Rustam Khaliullin, 361 Rutherford Ernest, 3, 7, 106 Name Index 1027 Rutkowski Andrzej W., 132 Ruud Kenneth, 790–791 Rychlewski Jacek, 597 Rydberg Henrik, 715 S Sack Robert A., 327, 885, 902 Sadlej Andrzej Jerzy, 131, 594, 729, 747, 749 Sakharov Andrei Dimitriy, 328 Salem Lionel, 260, 886 Šali Andrej, 354 Salpeter Edwin E., 147 Sapirstein Jonathan Robert, 149 Satchler George R., 900 Sauvage Jean-Paul, 973 Sawaryn Andrzej, 818, e147 Schütte Christian, 99 Schaad Lawrence J., e132 Schaefer Henry F., 628 Schatz George C., 886, 915 Scheiner Andrew C., 706 Scheiner Steven, 881 Schepens Wijnand, 353 Scheraga Harold A., 11, 42, 63, 77, 78 Schiff Leonard I., 83 Schmalz Thomas G., 173 Schoenflies Artur Moritz, e36 Schrödinger Erwin, xxii, xxvi, 3, 11–13, 21, 40, 42, 62–63, 67, 71, 77, 78–79, 81, 83, 85, 90–91, 95, 98, 101, 103, 105, 115, 120–121, 123, 129, 135, 139, 153, 157, 161, 170, 199, 213, 226, 248, 253, 303, 333, 396, 580, 638, 647, 658, 736, 805, 884, e87 Schuster Peter, 553, 971, 989, 1010 Schwartz Melvin, 593 Schwarz W.H Eugen, 722 Schwinger Julian, 3, 14, 106 Scrinzi Armin, 328–330 Seeger Rolf, 622 Seitz William A., 173 Shaik Sason S., 705, 885, 966 Shakanovich Eugene I., 354 Sham Lu J., 688 Shannon Claude Elwood, 971, 990, 991 Shavitt Isaiah, 885 Shaw Graham, 835 Shingu Haruo, 174 Shirakawa Hideki, 505 Schnoll Simon Eliewicz, 995 Siegbahn Per E.M., 628 Sielewiesiuk Jakub, 995 Silverstone Harris J., 423 Silvi Bernard, 705 Simons Jack, 622 Sims James S., 589 Sinanoˇglu Oktay, 581, 615, 629, 633 Singer Konrad, 594 Skála Lubomir, 227 Skolnick Jeffrey, 372–373, 375 Slater John C., xxx, 204, 270, 379, 389–394, 396, 397, 398, 400, 409, 423, 440, 450–451, 459, 465, 501, 503, 579, 602, 607, 610, 615–616, 624, 653, 665, 924 Smets Johan, 669 Smith Dayle M.A., 669 Smith Vedene, 592 Snelling-Ruël Bianca H.M., 978 Snijders Jaap G., 131 Sokalski Andrzej W., e147 Sommerfeld Arnold, 8, 30, 155 Stafford William, 231 Stalin Josef Vissarionovich (in fact Josif Dzhugashvili), 614 Stanke Monika, 131 Stark Johannes, 36 Staudinger Herman, 505 Stegun Irene A., 559 Steinberger Jack, 593 Steinborn Oliver, 200 Steiner Erich, 254 Stillinger Frank, 796 Stodden Clifford, 328 Stoicheff Boris, 592 Stokes George Gabriel, e88 Stolarczyk Leszek Zbigniew, 75, 217, 563, 569, 659, 869, e177 Stone Anthony J., 818, 881 Stoney George Johnstone, Struzhkin Victor V., 948 Stwalley William C., 592 Sukhatme Uday, 218, 227 Sukumar Candadi V., 161 Sun Cheng E., 885 Swirles Bertha, 581 Syrkin Yakov Kiwowicz, 614 Szabo Attila, 502, 660 Szalewicz Krzysztof, 149–150, 328–330, 593, 841, 846, 850 Szyma´nski Sławomir, 57 T Tanaka Takehiko, 495 Tarczay György, 154 Taylor Brook, 85–86, 88, 141, 312, 352, 445, 726, 840, 843, e3, e70 Taylor John R., 82 Taylor John, 57 Taylor Peter R., 628 Teller Augusta H., 340, 373 Teller Edward, 259, 260, 319, 340, 372–373, 410, 536, 859, 885 1028 Name Index Tennyson Jonathan, 154 Teukolski Saul A., 370 Thom René, 671 Thomas Llewellyn Hilleth, 665 Thomson George, 13 Thomson Joseph John, 6–7 Tildesley Dominic J., Timmerman Peter, 978 Tiomkin Mikhail, 722 Tomonaga Shinichiro, 3, 14, 106 Tonomura Akiro, 45 Topley Brian, 885 Torrey Henry C., 721, 767 Toth Agota, 995 Treussart Franỗois, 47 Tripet Brian, 868 Truhlar Donald G., 886, 914 Tsuzuki Seiji, 841 Turing Alan M, 1003 U Ubachs Wim, 150, 155 Ugalde Jesus M., 217 Uhlenbeck George E., 3, 10 Ulam Stanisław Marcin, 260, 340, 371, 372, 381 Unsöld Albrecht, 587 V van der Avoird Ad, 836 van der Waals Johannes Diderik, 342, 346, 349, 796, 894, 962, 971 van der Zande Wim J., 301 van der Zouw Gerbrand, 46 Van Dyck Robot S Jr, 757 Van Vleck John Hasbrouck, 721 Vassen Wim, 150 Vecchi Mario P., 340, 370 Velenik Alka, 328 Vercauteren Daniel, 103, 155 Vetterling William T., 370 Vila Jorge A., 819 Vinh Josiane, 469 Vohra Yogesh K., 948 Volterra Vito, 971, 980 von Kármán Theodore, 524 von Neumann John (Janos) 8, 259, 260, 261, 374, 381, 524, 885, 966, e10 Vosko Sy H., 689, 714 Voss-Andreae Julian, 48 Vracko Marjan, 103, 155 W Walker P Duane, 669 Walmsley Stuart H., 535 Walsh Stephen P., 915 Walter John, 676, 897, 911, 966, e32 Wang Yan Alexander, 688, 700 Watson James Dewey, 345 Watts Robert O., 362 Weeks John D., 867 Wegener Alfred Lothar, 269 Weidmann Jean-Luc, 978 Weinberg Steven, 571 Weinfurter Harald, 3, 15 Weinhold Frank, 150 Weinreich Gabriel, 722, 755 Werner Hans-Joachim, 659 Weyl Hermann, 77, 80 Wheeler John Archibald, 8, 46, 723 Wieman Carl E., 35 Wigner Eugene Paul, 146, 259, 260, 516, 647, 656, e44 Wilk Leslie, 689 Wilson Steven, 431 Wimmer Erich, 706, 716 Wirtinger Wilhelm, 78 Witkowski Andrzej, 273 Witmer Enos E., 592 Włoch Marta, 657 Wo´zniak Krzysztof, 648 Wo´znicki Wiesław, 588 Wojciechowski Walter, 650 Woli´nski Krzysztof, 648 Wolniewicz Lutosław, 98, 259, 262, 333, 581, 591 Wong Wah Y., 868 Woodward Robert Burns, 885, 926, 942, 966 Wootters William K., 3, 51 Wormer Paul E.S., 10 Wu Chien Shung, 74 Wu E., 47 Wu Y.-S Mark, 902 Wyatt Robert E., 886 Y Yang Czen Ning, 74 Yang Weitao, 679, 715 Yang Zhang, 375 Yelkhovsky Aleksander, 150 Yonezawa Teijiro, 174 Yoshikawa Kenichi, 996 Yoshizawa Shuji, 995 Yu Li, 868 Yutsis Adolfas A.P., 588 Z Zahradnik Rudolf, 881 Zaleski-Ejgierd Patryk, 103 Zare Richard N., 295 Zavoiski Evgeniy, 721 Zeegers-Huyskens Thérese, 650 Zeeman Pieter, 764 Zeilinger Anton, 3, 15, 46, 51, 56–57 Zewail Ahmed, 886, 889 Zhabotinsky Anatol M., 3, 15, 46, 56–57, 995 Zhao Xun, 328 Zhukovitskiy A.A., 722 Zierkiewicz Wiktor, 650 Ziesche Paul, 715 Zimmerman Howard E., 259 Zimmerman Neil M., 948 Zygalski Henryk, 1003 Subject Index A acceptor-donor (AD) reaction theory, 920 active space, 628 adiabatic and non-adiabatic theory, 302 adiabatic approximation, 268 adiabatic approximation, vibrationally, 907, 914 adiabatic curve, 306, 309, 950 adiabatic potential, vibrationally, 908 affinity separation, 1007 Aharonov-Bohm effect, e88 algebraic approximation, 427 algorithm, Car-Parrinello, 377 algorithm, Metropolis, 374 amphiphilicity, 867 amplitudes, Coupled cluster, 637 angular momenta addition, 343 annealing, simulated, 370 antibonding orbital, 439, e142 anticommutation relation, 127 antisymmetric function, 34, 604, 836 apparent forces, 106 approximants, Padé, 843 approximation, adiabatic, 268 approximation, Born-Oppenheimer, 269, 270 associated Laguerre polynomials, 202 associated Legendre polynomials, 200 asymptotic convergence, 250 atom, hydrogen-like, 238, e91 atomic basis set, 529 atomic orbital, 420 atomic orbital dimension, 471 attractor, 670, 978 autocatalysis, 375, 983 autocorrelation, 366 automata, cellular, 372, 381 avoided crossing, 306, 940 Axilrod-Teller dispersion energy, 879 B Bader analysis, 667 balance, kinetic, 132 band, conduction, 533–534 band gap, 537 band structure, 523, 527 band, valence, 537, 610 bandwidth, 532 barrier as shell opening, 948 barrier of dissociation, 801 barriers of reaction, 948 basis, biorthogonal, 513 basis set, atomic, 428, 431, e137 basis set superposition error (BSSE), 803 1029 baryon number, 71 Bell inequality, 47, 49 Berry phase, 314, 901 bifurcation, 980 binding energy, 198, 800 biorthogonal basis, 513 bipolaron, 535 bispinors, 128 Bloch function, 517, 528 Bloch theorem, 511 bobsleigh effect, 896 Bohr magneton, 757 bond, chemical, 7, 198, 346, 451 bonding orbital, 443, 475, 739, e142 Boolean variables, 382 Born-Oppenheimer approximation, 269, 270, 390, 665 bound state, 69, 82, 299 box with ends, 162 Breit equation, 146 Brillouin theorem, 617 Brillouin-Wigner perturbation theory, 647 Brillouin zone, 516 Brueckner function, 581 brusselator, 982 C Car-Parrinello algorithm, 377 Cartesian multipole moments, 729 catalyzed muon fusion, 327, 328 catastrophe set, 672 1030 Subject Index catenans, 801 cell, unit, 565 cellular automata, 372, 381 cell, Wigner-Seitz, 516 channels of reaction, 890 chaos, 980 characteristic frequency, 359 charge conjugation, 76, 820 chemical bond, 7, 346, 451 chemical reaction, acceptor-donor (AD) theory, 920 chemical shift, 773, 778 CI method, full, 587, 615 clamped nuclei Hamiltonian, 264, 303 classes, Fukutome, 440, 442 closed shell, 408, 411, 463 cluster operator, 630, 631 collapse, polarization, 835, 838 collective coordinate, 957 combinatorial chemistry, 976 commutator expansion, 626 complete set of functions, 20, 246, 614 complex, encounter, 298 complex, endohedral, 801 complex systems, 936, 972, 976 conditional extremum, 408, e121 conduction band, 533, 537 configuration, 615 configuration, electronic, 451, 463, 926 configuration interaction, 579 configuration mixing, 615 conical intersection, 261, 310 constant, lattice, 508, 517, 527 contact term, 148, 765 contraction of length, 156 contraction of orbitals, 140 convergence, asymptotic, 250 cooling protocol, 370 cooperativity, 974 coordinate, collective, 957 coordinates, democratic, 898 coordinates, mass-weighted, 903, 905 coordinates, natural, 906 coordinate system, Jacobi, 341, 896 coordinate system, skew, 893 Coriolis coupling, 906, 913 corrections to energy, 244, 253 corrections to wave function, 289, 603 correlation energy, 578, 618, 650 correlation, explicit, 584 correlation factors, 213 correlation hole, 595, 695–697 correlation, spatial, 366 correlation, time, 366 Coulomb hole, 595, 597 Coulombic operator, 403, 413 coupled cluster amplitudes, 629, 633, 638 coupling constant, 272, 781, 783 coupling, Coriolis, 906, 913 coupling, curvature, 906, 913 covalent structure, 303, 611, 940 creation particle-antiparticle, 148, 150 critical (stationary) points, 669, 712 crossing, avoided, 305, 309, 940, 960 cross section of reaction, 901 crystal orbitals, 528 current, 534, 538 curvature coupling, 906, 913 cusp condition, 584 cyclic box, 167 cycloaddition reaction, 944 D Darwin solution, 135 decoherence, 40, 45 deexcitations, 94, 636 democratic coordinates, 898 density matrix, 665, 715 density matrix, one-particle, 391, 408, 698 determinant, secular, 532, e65 determinant, Slater, 396, e109, e116, e191 diabatic curve, 303, 309 diabatic and adiabatic states, 949 diagonal correction for the motion of the nuclei, 268 diagram of Jabło´nski, 460, 461 diamagnetic effect, 780 diamagnetic spin-orbit contribution, 782, 784 digonal hybridization, e151 dilation of time, 118, 152 dimension of atomic orbital, 420 dimension of electronic pair, 467, 477, 491 dipole moment, e146, e149, e151 dipole, magnetic, 778, 784, 788 Dirac notation, 20, 399 Dirac electronic sea, 125, 131 Dirac equation, 13, 128, 133, 136 Subject Index 1031 Dirac vacuum, 26, 125, e153, direct method, 622 direct spin-spin interaction, 781 dispersion energy, 808 dispersion energy, Axilrod-Teller, 660, 879 dissipative structures, 982, 987 dissociation barrier, 801 dissociation energy, 198, 592, 801 DNA computing, 1003 DNA hybridization 1006 donating mode, 914, 919 “drain-pipe” of reaction, 884, 893 dynamics, Langevin, 9, 371 dynamics, molecular, 364, 369 dynamics, Monte Carlo, 371, 372 E effect, Aharonov-Bohm, e88 effect, bobsleigh, 895, 896 effect, diamagnetic, 780 effect, funnel, 317, 259 effect, harpooning, 307, 308, 321 effect, hydrophobic, 867, 868 effect, Jahn-Teller, 535, 536 effect, paramagnetic, 780 effect, split nucleus, 330 eigenfunction, 22, 189, 748 eigenvalue problem, 80, 265, 404, e108 Einstein equation, 121, 152 electron gas, 706 electronic configuration, 307, 449, 463 electronic density distribution, 681, 688, 746 electronic pair dimension, 475 electron pair distribution, 690 electronic shells, 448, 533, 948 electron paramagnetic resonance, 51 electronic-vibrationalrotational spectroscopy, 278 electrophilic attack, 921, 938 electrostatic energy, 807, 814, 827 electrostatic potential, 413, 921 enantiomers, 73, 74 encounter complex, 298 endohedral complexes, 801 energy, penetration, 454, 814 energy continuum, 125 energy corrections, 555, 851–852 energy, correlation 578, 650, 710 energy, exchangecorrelation, 690, 697, 709 energy, free, 353, 910 energy functional, 400, 402, 677 energy of reorganization 952, 953, 962 energy, self-interaction, 415, 708 entangled states, 14, 51 entrance and exit channels, 894, 909 entropy, 957, 992, 993, e108 Equation-of-Motion Coupled Cluster method (EOM-CC), 638, 639 EPR effect, 42, 51 Equation, Hylleraas, 247 equation, secular, 239, 548, 617 evolution in time, 85, 88 exchange-correlation energy, 683, 688, 694 exchange-correlation hole, 695–697 exchange-correlation potential, 689, 712 exchange-deformation interaction, 843 exchange hole, 597–598, 601–602 exchange operator, 403, 415–416 exo- and endothermic reactions, 909 experiment of Aspect, 50, 270 explicit correlation, 656 exponentially correlated function, 594, 655 extremum, conditional, 402, 408, e121 F feed-back, 978, 980–983 FEMO, 165–166, 169–170 femtosecond spectroscopy, 886, 889 Fermi contact contribution, 784, 789 Fermi golden rule, 95–98, 961 Fermi level, 533, 535–537 field compensation method, 568–570 finite field method, 746–747, 788 First Brillouin Zone, 516, 571 fixed point, 978, 981 Fock-Klein-Gordon equation, 123–124, 126–127 focus (stable and unstable), 986 force field, 345–350 forces, apparent, 108, 110–111 Franck-Condon rule, 302, 316–317 1032 Subject Index forcing of symmetry, 835 Franck-Condon factors, 962 free energy, 353 free particle, 161, 175, 224 frequency, characteristic, 95–97, 163 frozen orbitals, 624 Fukutome classes, 440, 442–443 full CI method, 654 function, antisymmetric f wave f., symmetric f., 84, 95, 398, 604 function, Brueckner, 581, 615 function, Heitler-London, 611–614 function, James-Coolidge, 590, 592 function, Kołos-Wolniewicz, 590, 592 function, molecular, 989, 1002, 1009 function, variational, 235–236, 247 function with adapted symmetry, 852, 878 functional, energy, 162, 167, 211 functional, Hohenberg-Kohn, 675, 677, 680 functional, Hylleraas, 247, 256 funnel effect, 256, 317 fusion, muon catalyzed, 327–328 fusion, nuclear, 327–328 G Galilean transformation, 110–113, 120 gap of band, 523, 527 Gauge Invariant Atomic Orbitals (GIAO), 785–786 gauge symmetry, 71, 571 Gaussian-type orbital (GTO), 421, 423–428 Gedankenexperiment, 37, 40 geminal, 589, 594 General Hartree-Fock method (GHF), 407–408, 411–412 ghosts, 837 global minimum, 237, 353–354 global optimization, 354, 384 golden rule of Fermi, 26–27, 95–97 gradient approximation, NLDA (GEA), 688, 700 gyromagnetic factor, 757–758, 788 H Hamilton graph, 1004 Hamiltonian, clamped nuclei, 77, 264, 287 Hamiltonian of reaction path, 905, 914, 915 “hand-glove” interaction, 871–872 harmonic generation, second/third, 754 harmonic helium atom, 589, 708 harmonic oscillator, 80, 124, 186 harmonics, spherical, 200 harpooning effect, 307–308, 321 Hartree-Fock method, general, 407–408 (GHF) Hartree-Fock method, restricted (RHF), 408–409, 411 Hartree-Fock method, Unrestricted (UHF), 441–445 Hartree-Fock-Roothaan method, 548, 552 Heisenberg uncertainty principle, 12, 35–36 Heitler-London function, 611–614 helium harmonic atom, 589, 661 Hermite polynomials, 191 Hohenberg-Kohn functional, 665, 680 hole, correlation, 695–697 hole, Coulomb, 595, 597 hole, exchange, 597–598, 600 hole, exchange-correlation, 695–697 HOMO, 861, 927 Hund’s rule, 461 hybrid approximations, NLDA, 688 Hybridization, tetrahedral, trigonal, digonal, e151 hybrids, 480–484 hydrogen bond, 768, 778, 863 hydrogen-like atom, e91, e97 hydrophobic effect, 373, 377, 867 Hylleraas equation, 247 Hylleraas function, 247 Hylleraas functional, 247 Hylleraas variational principle, 246–247 hypercycles, 988 hyperpolarizability, multipole, 732–735 I induction energy, 820–821 inertial system, 108 instability, 441 insulators, 534, 553 interaction energy, 556, 730 interaction energy, van der Waals, 347, 349 interaction non-additivity, 847, 1008 invariance of theory, 98 invariance with respect to a unitary transformation, 406 interference of particles, 44, 45 Subject Index 1033 intermediate spin-spin coupling, 768 intersection, conical, 261, 310 intrinsic reaction coordinate (IRC), 902, 904 intrinsic semi-conductor, 537–538 inverse lattice, 513–516 inverse Marcus region, 954 inversion, 72–74 ionic structure, 611–614 isotope effect, 285–286, e62 J Jabło´nski diagram, 460–461 Jacobi coordinate system, 897–898 Jahn-Teller effect, 441, 535–536 James-Coolidge function, 796 Jeziorski-Kołos perturbation theory, 796 K “key-lock” interaction, 971, 973 kinetic balance, 132, 144 kinetic minimum, 353–354 Kohn-Sham system, 591, 680–682 Kołos-Wolniewicz function, 590 Koopmans theorem, 465 L Lagrange multipliers, 406, 686, e121 Laguerre polynomials, 202 Laguerre polynomials, associated, 201 Langevin dynamics, 371, 383 lattice constant, 508, 517 lattice, inverse, 513 Lattice, primitive, 513, 571 Legendre polynomials, 200 Legendre polynomials, associated, 201 length contraction, 113 Lennard-Jones potential, 347–348 lepton number, 71 level, Fermi, 533, 535–537 limit cycle, 979–982 linear response, 732–733, 738 local density approximation, LDA, 687–688 local magnetic field, 761 localization of orbitals, 573 logical gate, 54, 995 logistic equation, 980–981 London orbitals, 786–787 Lorentz transformation, 113, 115–117 LUMO, 410–412 M magnetic dipole, 755, 760 magnetic moment, 761–765 magneton, Bohr, 757 magneton, nuclear, 757, 789 many-body expansion, 848–849 many body perturbation theory (MBPT), 641, 643 mass-weighted coordinates, 903–905 mathematical solution, 84 Maxwell equations, e81–e83 MC SCF unitary method, 624–629 mean field, 414–416 mean force potential, 957 mean value of an operator, 25 measurement, 301 measurement, wave function, 282, 301 mechanics, molecular, 349–352 Mendeleev Periodic Table, 446–448 metals, 533–534 metastable states, non-bound, 298 method, direct, 621 method, Equation-ofMotion Coupled Cluster (EOM-CC), 638–640 method, General Hartree-Fock (GHF), 407–408 method, finite field, 746–747 method, Hartree-FockRoothaan, 431, 433 method, MC SCF unitary, 624–629 method, SCF multiconfigurational, 626 method, Restricted Hartree-Fock (RHF), 408–409 method, perturbational, 641 method, Ritz, 238, 344 method, sum over states, 743, 788 method, Unrestricted Hartree-Fock (UHF), 408 method, Valence Bond (VB), 484, 490 Metropolis algorithm, 374 Michelson-Morley experiment, 111–112 minimal model of a molecule, 489–490 minimum, global, 237, 338, 353 minimum, kinetic, 354 minimum, thermodynamic, 353–354 Minkowski space-time, 104, 117 MO and AD pictures, 923 model, minimal of a molecule, 489 mode, donating, 914 modes, normal, e58, e105 1034 Subject Index molecular dynamics, 364–365 molecular electrostatic potential, 922 molecular evolution, 1010 molecular function, 1009 molecular libraries, 976 molecular mechanics, 349 molecular orbital, 475, 480 molecular spinorbital, 615, 625 moment, dipole, 740–743 Monte Carlo dynamics, 371 Morse oscillator, 192 motif, 509 Møller–Plesset perturbation theory, 648 multiconfigurational SCF methods, 624 multipliers, Lagrange, 658 multipole expansion, 810–815 multipole hyperpolarizability, 738 multipole moments, Cartesian, 729–730 multipoles, permanent, 815, 826 multipole polarizability, 738 multireference methods, 623 muon catalyzed fusion, 327–328 Murrell-Shaw and Musher-Amos (MS-MA) perturbation theory, 833–835 N nanostructures, 867 natural coordinates, 906 natural division, 798 natural orbitals, 621–622 NMR, 768 NMR shielding constants, e163 nodes (stable and unstable), 987 non-additivity, interaction, 1008 non-adiabatic theory, 265 non-bound metastable states, 297 non-bound states, 280 non-crossing rule, 305 non-linear response, 732–733 non-nuclear attractor, 670–671, 712 non-radiative transitions, 316–317 normal modes, 217, 321, 338 NP-hard problem, 1009 nuclear fusion, 258, 327–328 Nuclear Magnetic Resonance, 339, 456, 512 nuclear magneton, 757 nucleophilic attack, 884, 921, 936 O occupied orbital, 409, e115, e145 octupole moments, 728 one-particle density matrix, 698, 715 operator, cluster, 655, 661 operator, Coulombic, 202, 264 operator, exchange, 403, 412, 415 operator of a quantity, 18 operator, wave, 416, 418 optimization, global, 354 orbital, antibonding, 439, e145 orbital, atomic, 451, 482 orbital, bonding, 612, 739 orbital centering, 422, 426 orbitals, crystal, 511, 528 orbital, frozen, 624 orbital, Gaussian-type, 423–424 (GTO) orbital, hybrid, 479–480 orbital localization, 490, 500 orbital, London, 723, 786, 789 orbital, molecular, 865, 923 orbital, natural, 621–622 orbital, occupied, 410, 928, e115 orbitals σ, π, δ, 474–475, 482 orbital, Slater, 501, 603, 613 orbital, Slater-type, 390, 423, 481 orbital, virtual, 410, 499, 501 oscillator, harmonic, 5, 748, 1067 oscillator, Morse, 160, 162, 192 P Padé approximants, 795, 843, 847 pair distribution, 664, 673, 690, 713 paramagnetic effect, 780 paramagnetic resonance, 721 paramagnetic spin-orbit effect, 782, 784 parameters, variational, 131, 747, e159 particle-antiparticle creation, 148 particle in a box, 165, 180, e194 Pauli blockade, 842, 858, 948 Pauli matrices, 29, 142, e133 Peierls transition, 534–535, 573 penetration energy, 454, 794, 814 periodic perturbation, 62, 97, 101 Periodic Table, Mendeleev, 446, 448, 538 Subject Index 1035 permanent multipoles, 815, 826–827 perturbation, 585, 641–642, 647 perturbational method 231, 240, 253–256 perturbation theory, Brillouin-Wigner, 580, 647, 656 perturbation theory, first-order, 692, 713, 836 perturbation theory, Jeziorski-Kołos, 796, 836 perturbation theory, Møller–Plesset, 648, 653 perturbation theory, Murrell-Shaw and Musher-Amos (MS-MA), 833 perturbation theory, polarization, 833, 835, 841 perturbation theory, RayleighSchrödinger, 232, 240, 580 perturbation, time-independent, 91, 95, 580 perturbation, periodic, 97 perturbed system, 240, 248–249, 253 phase, Berry, 314, 884, 901 photochemical reaction, 316, 317, 332, 945 photons, virtual, 148 physical solutions, 62, 83–84 polarizability, multipole, 706, 734 polarization amplifier, 829, 831 polarization approximation, symmetrized, 831, 838 polarization catastrophe, 858 polarization collapse, 835 polarization of spin, 878 polarization of vacuum, 151 polarization perturbation theory, 814, 833 polymer chain reaction (PCR), 1006, 1007 polynomials, Hermite, 191, 226, e39 polynomials, Laguerre, 201, 202 polynomials, associated Laguerre, 201, 202 polynomials, Legendre, 200, e171 polynomials, associated Legendre, 200, e171 positron, 126, 128, 208 potential, electrostatic, 884, 878, 921 potential energy curve, 581, 950, 956 potential, exchangecorrelation, 664, 694–697 potential energy (hyper)surface, 153, 276 potential, Lennard-Jones, 347, 348, 610 potential of mean force, 957 potential, torsional, 349 primitive lattice, 506, 509 protocol, cooling, 370, 383 Q quadrupole moments, 787 qubit, 52, 54–55 R radius, van der Waals, 347, 796, 860 Ramsey theory, 720, 778, 781 rate of reaction, 240, 647, 805 Rayleigh-Schrödinger perturbation theory, 833, 836, 847 reaction, photochemical, 316–317, 332 reaction center, 877, 948, 1009 reaction channels, 890, 958 reaction coordinate, 884, 902, 913 reaction cross section 210, 213, 901 reaction, cycloaddition, 884, 944 reaction “drain-pipe”, 884, 893 reaction, exo- and endothermic, 909 reaction path Hamiltonian, 884, 914 reaction rate, 889, 914, 953 reaction spectator, 917, 920 reaction stages, 884, 927, 933 reactive and non-reactive trajectories, 892 reduced resolvent, 580, 644, 795 relativistic mass, 105, 120 relativistic mass effect, 105 relativity principle, 152 renormalization, 117 reorganization energy 962, 963–964 repellers, 1009 resonance state, 146, 181, 299–300 resonance theory, 579, 610, 612 Restricted Hartree-Fock method (RHF), 408–409, 499 retarded potential, 145–146 RHF, Restricted Hartree-Fock method, 416, 427 rigid rotator, 160, 259, 341 Ritz method, 238, 344 rotational symmetry, 73, 98 rotator, rigid, 277, 341, 721 rotaxans, 801 1036 Subject Index rovibrational spectrum, 340 rule, Franck-Condon, 302, 316–317, 960 rule, Hund’s, 461–464, 499 rules, WoodwardHoffmann, 884, 926, 942 S saddle point, 889–890, 904 saddle point of reaction, 1009 Sadlej relation, 748–750, 788 SCF multiconfigurational methods, 432, 417 Schrödinger equation, 633, 658, 676 second/third harmonic generation, 754 secular determinant, 139, 240 secular equation, 239, 249, 1120 self-interaction energy, 415, 708 self-organization, 970, 989, 1003 semi-conductor, intrinsic, n–type, p–type, 537, 538, 572 shells, electronic shielding constants σ, π, δ-molecular orbitals, 475, 485 simulated annealing, 370, 384 single-exchange (SE) mechanism, 853–855 size consistency, 579, 582, 637 skew coordinate system, 893 Slater determinant, 924–927, e5 Slater orbital, 397, 501, 613 Slater-type orbital (STO), 390, 423, 481 soliton, 535, 574 space-time of Minkowski, 119, 104 spatial correlation, 366 spectator of reaction, 917, 920 spectroscopic state, 99 spectroscopy , electronicvibrationalrotational, 258, 278, 871 spectroscopy, femtosecond, 795, 886 spectrum, rovibrational, 303, 340 spherical harmonics, 209, 339 spin, 26–31 spin angular momentum, 26–27, 464 spin coordinate, 55, 394–397 spin-dipole contribution, 782, 784 spin magnetic moment, 100, 153, 768 spin-orbit coupling,147, 463 spin-orbit effect, paramagnetic, 782, 784 spinorbital, molecular, 782 spinors, 128, 129–131 spin polarization, 687 spin-spin coupling, 772, 777 split nucleus effect, 329, 330 state, non-bound, 280, 297 state, underground, 84, 995 stationary (critical) points, 670, 987 stationary state, 74, 164 steepest descent trajectory (SDP), 891, 964 stellar nodes (stable and unstable), 1009 steric effect, 921 structure, band, 536, 542 structure, covalent, 303, 611 structure, ionic, 612, 705 sum of states, 339, 957 sum over states method, 720, 791 supermolecular method, 796, 804 supramolecular architecture, 989 supramolecular chemistry, 976, 1003 surface, potential energy, 889, 910 symmetric function, 84, 207 symmetrized polarization approximation, 836, 842 Symmetry Adapted Perturbation Theory (SAPT), 878, e184 symmetry C, 99 symmetry forcing, 794, 796, 835 symmetry of division into subsystems 570 symmetry of Hamiltonian, 99 symmetry orbital, 513, 517 symmetry P, 99 symmetry, rotational, 73, 99 symmetry, translational, 98, 571 symmetry of wave function, 63, 508 synthon, 870, 873, 1005 system, unperturbed, 248, 641 system, perturbed, 240, 641 T teleportation, 51–53, 59 tetrahedral hybridization, 501 theorem of Brillouin, 516, 579, 617 theorem of Koopmans, 390, 465, 466 theory of resonance, 612, 614 Subject Index 1037 thermalization, 367–368, 383 thermodynamic minimum, 353–354 three-body polarization amplifier, 857, 859 time correlation, 366 time dilation, 118, 152 time evolution equation, 21, 55, 84 time-evolution operator, 99 time-independent perturbation, 96, 99, 101 torsional potential, 349 trajectories, reactive and non-reactive, 892, 911 “trajectory-in-molasses”, 904 trajectory, steepest descent (SDP), 891, 964 transformation, Galilean, 110–111 transformation, Lorentz, 104, 106, 111 transition, non-radiative, 317, 968 transition, Peierls, 535–536 translational symmetry, 68, 98, 173 transmission coefficient, 176, 180, 182 travelling salesman problem 1004, 1006 trial function, 237, 252 trigonal hybridization, 483, 501 triple-exchange (TE) mechanism, 854 tunnelling effect, 161, 278, 909 Turing machine, 1003, 1009 two-state model, 101, 608, e65 U uncertainty principle, 36, 58 underground states, 84, 236 unitary MC SCF method, 579, 626 unitary transformation, invariance, 406, 408, 667 unit cell, 507, 509, 516 unperturbed system, 240, 248, 253, 641 Unrestricted Hartree-Fock method (UHF), 408, 687 V vacuum polarization, 148, 150 valence band, 533–534 Valence Bond (VB) method, 610 valence repulsion, 838, 840–841, 862 Valence Shell Electron Pair Repulsion (VSEPR), 491 van der Waals interaction energy, 347, 796 van der Waals radius, 849 variable, Boolean, 382 variational function, 399 variational method, 838, 940 variational parameters, 236 variational principle, 232 variational principle for excited states, 235 variational principle, Hylleraas, 246 variation of a spinorbital 440 velocity addition law, 116 vibrationally adiabatic approximation, 273 vibrationally adiabatic potential, 273 virtual orbital, 410, 466 virtual photons, 148 v-representability, 677 VSEPR, Valence Shell Electron Pair Repulsion, 491 W wave function, 615, 641, 645 wave function evolution, 85 wave function “matching”, 85, 615, 645 wave function “measurement”, 85, 615, 645 wave operator, 631, 634 wave vector, 510, 520, 526 width of band, 542 Wigner-Seitz cell, 516, 571 Woodward-Hoffmann rules, 945, 947 Z Zero Differential Overlap (ZDO), 743 Zone, Brillouin, 516 ... • • • • • IDEAS OF QUANTUM CHEMISTRY Second edition “Things appear, ideas persist” Plato IDEAS OF QUANTUM CHEMISTRY Second edition by LUCJAN PIELA Department of Chemistry, University of Warsaw,... () relativistic and quantum electrodynamics effects () most important computational methods of quantum chemistry (♦) future of quantum chemistry ( ) “magical” aspects of quantum physics ()... favor of exposing the interrelationships of problems In this respect, any division between physics and chemistry, organic chemistry and quantum chemistry, quantum chemistry for chemists and quantum