Physical inorganic chemistry principles methods and models

PHYSICAL INORGANIC CHEMISTRY PHYSICAL INORGANIC CHEMISTRY Principles, Methods, and Models Edited by Andreja Bakac Copyright Ó 2010 by John Wiley & Sons, Inc All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada 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, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 kver Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose No warranty may be created or extended by sales representatives or written sales materials The advice and strategies contained herein may not be suitable for your situation You should consult with a professional where appropriate Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002 Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic formats For more information about Wiley products, visit our web site at www.wiley.com Library of Congress Cataloging-in-Publication Data: Physical inorganic chemistry : principles, methods, and models / [edited by] Andreja Bakac p cm Includes index ISBN 978-0-470-22419-9 (cloth) Physical inorganic chemistry I Bakac, Andreja QD475.P49 2010 547’.13–dc22 2009051003 Printed in the United States of America 10 To Jojika CONTENTS Preface ix Contributors xi Inorganic and Bioinorganic Spectroscopy Edward I Solomon and Caleb B Bell III 57 Fe M€ ossbauer Spectroscopy in Chemistry and Biology 39 Marlene Martinho and Eckard M€unck Magnetochemical Methods and Models in Inorganic Chemistry 69 Paul K€ogerler Cryoradiolysis as a Method for Mechanistic Studies in Inorganic Biochemistry 109 Ilia G Denisov Absolute Chiral Structures of Inorganic Compounds 143 James P Riehl and Sumio Kaizaki Flash Photolysis and Chemistry of Transients and Excited States 199 Guillermo Ferraudi Application of High Pressure in the Elucidation of Inorganic and Bioinorganic Reaction Mechanisms 269 Colin D Hubbard and Rudi van Eldik Chemical Kinetics as a Mechanistic Tool 367 Andreja Bakac Heavy Atom Isotope Effects as Probes of Small Molecule Activation 425 Justine P Roth 10 Computational Studies of Reactivity in Transition Metal Chemistry 459 Jeremy N Harvey Index 501 vii PREFACE Physical inorganic chemistry is an enormous area of science In the broadest sense, it comprises experimental and theoretical approaches to the thermodynamics, kinetics, and structure of inorganic compounds and their chemical transformations in solid, gas, and liquid phases When I accepted the challenge to edit a book on this broad topic, it was clear that only a small portion of the field could be covered in a project of manageable size The result is a text that focuses on mechanistic aspects of inorganic chemistry in solution, similar to the frequent association of physical organic chemistry with organic mechanisms The choice of this particular aspect came naturally because of the scarcity of books on mechanistic inorganic chemistry, which has experienced an explosive growth in recent years and has permeated other rapidly advancing areas such as bioinorganic, organometallic, catalytic, and environmental chemistry Some of the most complex reactions and processes that are currently at the forefront of scientific endeavor rely heavily on physical inorganic chemistry in search of new directions and solutions to difficult problems Solar energy harvesting and utilization, as well as catalytic activation of small molecules as resources (carbon dioxide), fuels (hydrogen), or reagents (oxygen), are just a few examples It is the goal of this book to present in one place the key features, methods, tools, and techniques of physical inorganic chemistry, to provide examples where this chemistry has produced a major contribution to multidisciplinary efforts, and to point out the possibilities and opportunities for the future Despite the enormous importance and use of the more standard methods and techniques, those are not included here because books and monographs have already been dedicated specifically to instrumental analysis and laboratory techniques The 10 chapters in this book cover inorganic and bioinorganic spectroscopy (Solomon and Bell), Moăssbauer spectroscopy (Muănck and Martinho), magnetochemical methods (Koăgerler), cryoradiolysis (Denisov), absolute chiral structures (Riehl and Kaizaki), flash photolysis and studies of transients (Ferraudi), activation volumes (van Eldik and Hubbard), chemical kinetics (Bakac), heavy atom isotope effects (Roth), and computational studies in mechanistic transition metal chemistry (Harvey) I am extending my gratitude to the authors of individual chapters who have given generously of their time and wisdom to share their expertise with the reader I am grateful to my editor, Anita Lekhwani, for her professionalism, personal touch, and ix x PREFACE expert guidance through the entire publishing process Finally, I thank my family, friends, and coworkers who supported and helped me, and continued to have faith in me throughout this long project ANDREJA BAKAC CONTRIBUTORS ANDREJA BAKAC, The Ames Laboratory and Chemistry Department, Iowa State University, Ames, IA, USA CALEB B BELL III, USA Department of Chemistry, Stanford University, Stanford, CA, ILIA G DENISOV, Department of Biochemistry, University of Illinois at UrbanaChampagne, Urbana, IL, USA GUILLERMO FERRAUDI, Dame, IN, USA Radiation Laboratory, University of Notre Dame, Notre JEREMY N HARVEY, Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol, UK COLIN D HUBBARD, Tolethorpe Close, Oakham, Rutland, UK SUMIO KAIZAKI, Department of Chemistry, Center for Advanced Science and Innovation, Graduate School of Science, Osaka University, Osaka, Japan PAUL KOăGERLER, Germany Institut fuăr Anorganische Chemie, RWTH Aachen, Aachen, MARLE`NE MARTINHO, Department of Chemistry, Carnegie Mellon University, Pittsburgh, PA, USA ECKARD MUăNCK, Department of Chemistry, Carnegie Mellon University, Pittsburgh, PA, USA JAMES P RIEHL, Department of Chemistry, University of Minnesota Duluth, Duluth, MN, USA JUSTINE P ROTH, MD, USA Department of Chemistry, Johns Hopkins University, Baltimore, EDWARD I SOLOMON, USA RUDI Department of Chemistry, Stanford University, Stanford, CA, ă r Anorganische Chemie, Universitaăt ErlangenVAN ELDIK, Institut fu Nuărnberg, Erlangen, Germany xi FIGURE 1.1 As an example, plastocyanin functions in photosynthesis as a soluble electron carrier in the thylakoid lumen transferring electrons from the cytochrome b6/f complex to photosystem I ultimately for ATP synthesis (bottom) Despite its relatively small size, plastocyanin has had a large impact on the field of bioinorganic spectroscopy The protein has a characteristic intense blue color (hence the term blue copper protein) that was later shown to derive from LMCT to the Cu Hans Freeman first reported a crystal structure (light blue ribbon diagram, PDB ID, 1PLC) for plastocyanin in 19788 showing that the Cu site was tetrahedrally coordinated by a methionine, a cysteine, and two histidine resides This was a surprising result given the typical tetragonal structure for small model Cu(II) complexes Since that time, a tour de force of spectroscopy has been applied in blue copper research (projected on the back are selected spectra for methods that are covered in this chapter), many of which were developed and first used on this enzyme, as will be presented The spectroscopic approach combined with electronic structure calculations has allowed elucidation of the geometric and electronic structures of the Cu site (top left blowup) that in turn has been used for structure– function correlations in understanding plastocyanin’s biochemical role in electron transfer (ET) and defining the role of the protein in determining geometric and electronic structure FIGURE 1.4 Tanabe-Sugano diagram for a d5 ion Insets are the d electron configurations for the indicated states ASSESSING AND IMPROVING ACCURACY 495 arises much less frequently in smaller systems This is the existence of multiple conformers For a small system, there may also be several conformers, but typically the number is quite small, and it is relatively straightforward to identify all of them by inspection, and if needed to compute the energy of all of them, and hence identify the global minimum When calculating free energies, enthalpies, entropies, and other statistical mechanical properties, it is usually the case in small systems that the Boltzmann weight of all but the lowest energy conformer is very small and can be neglected For large systems, there may be so many conformers that it is impossible to identify them all This is often the case with large molecular systems of 50–200 atoms and always the case for supermolecular systems of 1000 atoms or more Hence, this problem arises most often when using hybrid methods such as QM/MM, as these are more suited for treatment of very large systems However, it can also happen when carrying out large DFT calculations In these cases, there will be so many conformers that the Boltzmann averages needed in statistical mechanics treatments need to include contributions from many of them, making it difficult to calculate meaningful thermodynamic properties such as activation barriers A simple approach to avoid this problem consists in freezing the position of many of the atoms when carrying out geometry optimization, so as to limit the conformational variability This, however, slightly negates the value of using a large model It is also possible to try and calculate “typical” energy quantities, by comparing the energy of a typical conformer of the reactant species, and the “closest” TS, that is, one corresponding to the same conformer With very large systems of thousands of atoms, as used in QM/MM models, it may be difficult to identify such “closest” TSs, as conformational change may occur quite far from the reacting system, leading to a change in energy of the system that makes the purportedly “typical” energy difference rather untypical Simple visual inspection of structures, which can be relied upon to identify such mishaps for smaller systems, becomes challenging for large systems In summary, calculations on large systems are possible and more and more frequently carried out, especially using hybrid methods Some care is, however, needed for such systems in order to calculate meaningful energies for systems where there may be many more conformers than can be described explicitly For this reason, truncated model systems may actually prove more straightforward (and are often equally informative) Equally, advanced free energy methods as described in Section 10.5 can also be used to avoid such problems, but these are very computationally demanding for large systems 10.8 ASSESSING AND IMPROVING ACCURACY When carrying out any calculation relating to a reaction mechanism, it is important to make some attempt to gauge its accuracy—and, if needed, to improve it The pursuit of accuracy for its own sake can become very time-consuming, as more and more calculations, and increasingly computationally expensive ones, are carried out It can also prove something of a distraction, or even an impediment, to the pursuit of one of 496 COMPUTATIONAL STUDIES OF REACTIVITY IN TRANSITION METAL CHEMISTRY the key aims of computational studies, to provide insight.41 Nevertheless, it is obvious that for a calculation to have some value, it must have at least some accuracy DFT has proved a remarkably popular theory for inorganic and organometallic chemists, as it seems to hit the sweet spot of being affordable in terms of computer resources, yet accurate enough to yield pertinent results Benchmarks for small compounds42 show average errors in calculating the atomization energy of 4–7 kcal/ mol for modern functionals such as B3LYP This is the energy for breaking all bonds—errors on the energy required to break just one bond, which are more relevant for understanding reactivity, are expected to be smaller—perhaps 2–3 kcal/mol, provided a large enough basis set is used Very often, in practice, one is interested in the relative energy of two TSs that are rather similar in terms of their bonding properties, and for such cases, one can expect even more favorable error cancellation, perhaps of as little as kcal/mol Yet one should be aware that the figures quoted here are average errors for main group compounds Even for the simple species included in the benchmark sets, the maximum error for every functional is over 20 kcal/mol There is increasing evidence that such outliers are quite common with DFT, especially for transition metal compounds.43 The property that is most challenging to compute accurately is usually energy (e.g., bond energies or activation energies), but errors can also occur for predicted geometries and electronic structure This chapter is not the correct place to discuss these difficulties or the progress toward more accurate DFT functionals and more computationally tractable high-level correlated ab initio methods Instead, the following points summarize some of the issues that one should pay attention to when carrying out computational studies Many of these points have been discussed above Which property is one trying to calculate? Some properties, such as molecular structure, are far less sensitive to the level of theory used than others, such as activation energies There is no point in carrying out very time-consuming calculations if a simpler one would have been adequate Is there some related experimental property to which one can meaningfully compare the results of calculations in order to test the accuracy of the latter? For example, an activation barrier may be known for a similar reaction—or the mechanism of a related transformation may be very well known Is there anything known in the literature about the accuracy of the method one wishes to use for the type of problem one wishes to use it for? Carrying out at least some test calculations with a few different methods (e.g., DFT functionals) can be very valuable Is the basis set large enough for results to be converged? Single point energy calculations with large basis sets can be readily carried out using DFT methods For correlated ab initio calculations, very large basis sets may be needed to approach the basis set limit, but these can be very expensive On the other hand, correlated calculations with typical double-z basis sets are often too far from basis set convergence to be meaningful Is the model used able to describe the chemistry one wishes to describe? All important interactions need to be treated When studying reaction mechanisms, a REFERENCES 10.9 497 model may be suitable to describe one mechanism—but not another One important aspect that may need to be treated is solvation effects, for example, using a continuum model When studying a reaction mechanism, has one considered all the reasonable mechanisms in the calculations? If one has studied a single mechanism, this may be reasonable if one’s aims in the project are modest—but it does mean that one may not have proved that the mechanism is correct Have the required statistical mechanical considerations been taken into account? In many cases, converting potential energies to free energies can be done approximately reasonably easily, and it is often free energies that are more relevant to experiment For very large systems with multiple conformers, this aspect can be challenging—and a simpler truncated model may be more informative CONCLUSIONS Computation plays an important role in understanding reaction mechanisms in inorganic chemistry This chapter aims to give insight into the theoretical methods used and illustrate some of the insight that can be derived from their application With the development of powerful computers and general-purpose software, using theoretical methods is possible for all researchers in chemistry, and this is a very exciting development Calculations that may be looked down upon by experienced theoretical chemists as being dull and routine may be of considerable value to researchers trying to understand a particular reaction or property, so it is highly desirable that computation be available to all At the same time, specific problems in inorganic chemistry may pose very interesting challenges for more theoretically oriented chemists, and even lead to development of new theories The future for computational inorganic chemistry is clearly going to be exciting, stimulating, and full of surprises Hopefully, some of the main areas covered in this chapter will continue to be pertinent in the field ACKNOWLEDGMENTS The author thanks the EPSRC for financial support and all his coworkers and collaborators over the years for their work, encouragement, insight, and enthusiasm REFERENCES Many reviews touching on aspects of computational inorganic chemistry have appeared; in fact, too many to list here Several special thematic issues can be highlighted: Chem Rev 2000, 100 (2), 351–818 on computational transition metal chemistry; Coord Chem Rev 2003, 238/239, 1–417 on theoretical and computational chemistry; Struct Bond 2004, 112/113, on principles and applications of density functional theory in inorganic chemistry; J Comput Chem 2006, 27 (12), 1221–1475 on theoretical bioinorganic chemistry, and no doubt many others 498 COMPUTATIONAL STUDIES OF REACTIVITY IN TRANSITION METAL CHEMISTRY See, for example, Jensen, F Introduction to Computational Chemistry, 2nd edition; Wiley: Chichester, UK, 2007; Cramer, C J Essentials of Computational Chemistry: Theories and Models, 2nd edition; Wiley: Chichester, UK, 2004 Rosa, A.; Ricciardi, G.; Gritsenko, O.; Baerends, E J Struct Bond 2004, 112, 49–115 See, for example, Pyykko, P Chem Rev 1988, 88, 563–594 Weinhold, F.; Landis, C R Valency and Bonding: A Natural Bond Orbital Donor–Acceptor Perspective; Cambridge University Press: Cambridge, UK, 2003 Bader, R F W Acc Chem Res 1985, 18, 9–15; Popelier, P L A Coord Chem Rev 2000, 197, 169–189 Kitaura, K.; Morokuma, K Int J Quant Chem 1976, 10, 325–340 Ziegler, T.; Rauk, A Theor Chim Acta 1977, 46, 1–10 Frenking, G.; Wichmann, K.; Fr€ohlich, N.; Loschen, C.; Lein, M.; Frunzke, J.; Rayo´n, V M Coord Chem Rev 2003, 238/239, 55–82 10 Elian, M.; Hoffmann, R Inorg Chem 1975, 14, 1058–1076 11 Dickens, B.; Lipscomb, W N J Chem Phys 1962, 37, 2084–2093 12 Bennett, M J.; Cotton, F A.; Takats, J J Am Chem Soc 1968, 90, 903–909 13 Lough, A J.; Park, S.; Ramachandran, R.; Morris, R H J Am Chem Soc 1994, 116, 8356–8357 14 Lee, J C., Jr.; Peris, E.; Rheingold, A L.; Crabtree, R H J Am Chem Soc 1994, 116, 11014–11019 15 Peris, E.; Lee, J C., Jr.; Rambo, J R.; Eisenstein, O.; Crabtree, R H J Am Chem Soc 1995, 117, 3485–3491 16 Pantazis, D A.; McGrady, J E.; Besora, M.; Maseras, F.; Etienne, M Organometallics 2008, 27, 1128–1134 17 For reviews, see Kaupp, M.; B€uhl, M.; Malkin, V G., Eds Calculation of EPR and NMR Parameters: Theory and Applications; Wiley-VCH: Weinheim, 2004 18 Sinnecker, S.; Slep, L D.; Bill, E.; Neese, F Inorg Chem 2005, 44, 2245–2254 19 Kitaura, K.; Obara, S.; Morokuma, K J Am Chem Soc 1981, 103, 2891–2892 20 Noyori, R.; Ohkuma, T Angew Chem., Int Ed 2001, 40, 40–73 21 Abdur-Rashid, K.; Clapham, S.; Hadzovic, A.; Harvey, J N.; Lough, A J.; Morris, R H J Am Chem Soc 2002, 124, 15104–15118 22 Leyssens, T.; Peeters, D.; Harvey, J N Organometallics 2008, 27, 1514–1523 23 Sandoval, C A.; Ohkuma, T.; Mun˜iz, K.; Noyori, R J Am Chem Soc 2003, 125, 13490–13503 24 Laidler, K J Chemical Kinetics; 3rd edition, Prentice-Hill: 1987 25 Truhlar, D G.; Garrett, B C.; Klippenstein, S J J Phys Chem 1996, 100, 12771–12800 26 For some exceptions, see Yang, S -Y.; Ziegler, T Organometallics 2006, 25, 887–900; Michel, C.; Laio, A.; Mohamed, F.; Krack, M.; Parrinello, M.; Milet, A Organometallics 2007, 26, 1241–1249 27 Again, there are some exceptions; for a review, see van Speybroeck, V.; Meier, R J Chem Soc Rev 2003, 32, 151–157 28 For a leading reference, see Meyer, H -D.; Worth, G A Theor Chem Acc 2003, 109, 251–267 REFERENCES 499 29 Kuhlmann, R.; Clot, E.; Leforestier, C.; Streib, W E.; Eisenstein, O.; Caulton, K G J Am Chem Soc 1997, 119, 10153–10169 30 Daniel, C Coord Chem Rev 2003, 238/239, 143–166 31 Poli, R.; Harvey, J N Chem Soc Rev 2003, 32, 1–8 32 Harvey, J N Phys Chem Chem Phys 2007, 9, 331–343 ´ ; Harvey, J N Adv Inorg Chem 2009, 61, 33 Besora, M.; Carreo´n-Macedo, J -L.; Cimas, A 573–623 34 Harvey, J N Struct Bond 2004, 112, 151–183 35 See, for example, Siegbahn, P E M.; Borowski, T Acc Chem Res 2006, 39, 729–738 36 For a study of the mechanism of this enzyme based on potential energy surfaces calculated for a model similar to that of Figure 10.13, see Olsson, M H M.; Siegbahn, P E M.; Warshel, A J Biol Inorg Chem 2004, 9, 96–99; Olsson, M H M.; Siegbahn, P E M.; Warshel, A J Am Chem Soc 2004, 126, 2820–2828 37 Svensson, M.; Humbel, S.; Froese, R D J.; Matsubara, T.; Sieber, S.; Morokuma, K J Phys Chem 1996, 100, 19357–19363; see also Maseras, F.; Morokuma, K J Comput Chem., 1995, 16, 1170–1179 38 Senn, H M.; Thiel, W Top Curr Chem., 2007, 268, 173–290 39 Warshel, A.; Levitt, M J Mol Biol., 1976, 103, 227–249 40 Claeyssens, F.; Harvey, J N.; Manby, F R.; Mata, R A.; Mulholland, A J.; Ranaghan, K E.; Sch€utz, M.; Thiel, S.; Thiel, W.; Werner, H -J Angew Chem., Int Ed., 2006, 45, 6856–6859 41 For eloquent discussions of this negative aspect of the pursuit of accuracy, see Hoffmann, R J Mol Struct (Theochem) 1998, 424, 1–6; Shaik, S New J Chem 2007, 31, 2015–2028 42 Staroverov, V N.; Scuseria, G E.; Tao, J.; Perdew, J P J Chem Phys 2003, 119, 12129–12137 43 Furche, F.; Perdew, J P J Chem Phys 2006, 124, 044103; Harvey, J N Ann Rep Prog Chem., Sect C.: Phys Chem 2006, 102, 203–226; Rinaldo, D.; Tian, L.; Harvey, J N.; Friesner, R A J Chem Phys, 2008, 129, 164108 INDEX ab initio methods 459, 464 absolute configuration 144, 158 absorption dissymmetry ratio 165 absorption spectroscopy, optical absorption spectroscopy 112–116, 120, 124, 126–134 p-acceptor 18, 31 accuracy in calculations 484, 485, 490, 495–497 acetaldehyde 371 acetic acid 373 acid-base equilibrium 390, 391, 392, 394, 395 actinide ions 289 activation 367, 372, 375; energy 396, 402; parameters 385, 396–401, 413–416 activity 60, 61, 62 adiabatic cooling 97 adiabatic pathway 312 adiabaticity 241, 246 aggregation of molecules 58, 63 agostic interactions 476 alkali metal catalysis 343, 344 alkoxyl radical 381, 382 alkyl exchange 399 aminopolycarboxylate ligands 294, 296, 297 anion effect 394–395 anion-anion reactions 311, 347 anisotropic medium 203 anisotropy 62 anisotropy barrier 95 annealing 113, 115–120, 122–130, 133–134 antibonding (acceptor) molecular orbital 20 antiferromagnetic order 63 antiferromagnetically coupled 46, 56, 59 antiferromagnetism 75 antitumor activity 304, 319 antitumor complexes 307, 308 aqueous cluster 300 p-arene-bpy compounds of Ru(II) 299 p-arene ligand 299 Arrhenius 396, 403, 406 asymmetry parameter of efg, h 41, 45 A-term 10–13 atoms in molecules (AIM) 473, 477 axial ZFS parameter, D 40, 41, 44, 47, 48, 49, 53 B-term 11–13 B3LYP 467, 482, 496 backbonding 472, 476 p-backbonding 1, 18, 30, 31 basis sets 468, 469 [Be(Cl)(12-crown-4]2 þ , [Be(H2O)(12-crown-4)]2 þ , [Be(NH3)(12-crown-4)]2 þ 349 [Be(Cl)(crown ether)]2 þ 291 Beer’s law 204, 207, 211 Bein, K 144, 145 beta-scission 382 bidentate diamine ligands 167 Bigeleisen/Goeppert-Mayer Formalism 429 Bijvoet method 190 bimolecular 372, 375, 377, 398, 399, 412 bimolecular reactions 486 biotransformation 307 biphotonic event 206 Bleaney-Bowers equation 78, 80 Physical Inorganic Chemistry: Principles, Methods, and Models Edited by Andreja Bakac Copyright Ó 2010 by John Wiley & Sons, Inc 501 502 INDEX Bloch wall 76 blocking temperature, tb 63 blue copper 2, 26, 27, 29–32 Bohr magneton 72 Boltzmann distribution 72, 82, 102 Boltzmann factor 45 bonding (donor) molecular orbital 20 bonding analysis 472, 473 Bonner Fisher model 91 boranes, chiral structures 164 Born cycle 241 Born-Druid-Nernst theory 343 boron compounds 236, 237 Brillouin function 14, 73, 101 bromide 373, 375 g-butyrolactone 350, 351 C/A Nomenclature 147, 148 Cahn-Ingold-Prelog (CIP) rules 146, 147, 149, 154 carbon radical 371, 415 carbonate complexes of Co(III) 255 carbonyl 372 carboplatin 305, 306 Car-Parrinello shell 291 CASPT2 467, 468 catalase 113, 114, 116, 119 catalysis 384 CCSD(T) 466, 467 CD component rule 168, 181, 184, ceruloplasmin 116 charge separation 232 transfer (CT) 1, 3, 4, 18–22, 237, 238, 262 transfer excited states 18–22 transfer transitions 167 chiral actinide complexes 164 chiral ligands 145 chloroperoxidase 116, 128, 133 circular dichroism (CD) 1, 8–10, 152, 163, 165–177, helicates 156 polarization 165, 175 circularly polarized luminescence (CPL) 177 cis-dihydride rhodium(III) 341 cis-platin 304, 305 cis-trans isomerization 234 Co 112, 116, 124, 130 Co-C bond 255 Co(NH3)5X2 ỵ (X ẳ Cl, Br, NO2, N3) 253 255 Co(bpy)33 ỵ 225 Co(CN)63 231 Co(CO)3NO 260 Co(NH3)63 þ 231, 257, 258 CO3H radical 255 cobalamin 116, 303, 304 aqua 303, 340 cyano 303 5-deoxy-adenosyl 303 cobalt 116, 125, 127 coercitive field 76 competition kinetics 381 competitive fractionation 428 complete active space self-consistent field (CASSCF) 466, 468 complex refractive index 203 composite parameters 396 Compound 114, 127–128, 132–133; See also peroxo-ferric Compound I 119, 122,123, 127–129, 132 Compound II 119, 128–130, 132 Compound III 128, 132; See also oxo-ferrous, superoxo-ferric Compound Q 59 compressibility coefficient of activation 274 computational resources 468, 490 concerted 396–397 configuration interaction (CI) 5, 20 configurational CD 172 configurational symmetry 148 conformers and sampling 495 consecutive reactions 382–384 cooperative phenomena 76 copper 59, 60, 61, 62, 63 copper proteins 116, 117, 134 core excited states 22–34 corpuscular nature of light 200 corrin ring 303 coupled-cluster theory 466 covalency 1, 6, 21, 25, 29, 30, 32, 33, 34 covalent delocalization 26 trans-[Cr([14]aneN4)(CNRu(NH3)5)2]5 ỵ 261 60 INDEX Cr(bpy)33 ỵ 217221 Cr(phen)33 ỵ 241 CrIII(NH3)5Xz ỵ (X ¼ H2O, Cl, Br, I, SCN) 239 cryoradiolytic reduction 112–116, 119, 120, 124, 130, 134 cryosolvents 110, 112, 115, 117, 127, 128, 133 137 Cs 118 C-term 10–14 CTTS 234 Cu K-edge 25 Cu(I) 24, 25 Cu(II) 2, 3, 5–7, 9, 13, 14, 18–20, 22, 25, 29, 32 CuCl4 19, 22, 25–27, 29 Curie law 53, 72, 92 Curie temperature 76 Curie-Weiss law 75, 92, 99 cyclic voltammetry 285, 344, 345 cyclization 381, 398 CYP101 120–124, 129, 130, 132–134 CYP119 124 cytochrome b5 116, 130 cytochrome c 113–116, 119, 130, 134, 312, 313, 314, 315 cytochrome c oxidase 114, 116 cytochrome c peroxidase 130 cytochrome c552 120 cytochrome P450 114–115, 120–122, 124, 129, 130, 133, 138, 140, 142, 327, 332, 337, 339, 341, 3454 D2 symmetry 152 D3 symmetry 148, 153, 176 dead-end intermediate 412 Debye temperature 84 Debye-H€uckel 312, 343 Debye-Waller factor 43 Delepine’s active racemate method 181 densitometer 287 density functional theory (DFT) 3, 50, 51, 57, 58, 432–437, 292, 293, 307, 341, 346, 348, 459, 464, 467, 468, 469, 473, 475, 477, 496 detector response 220 deuterium 371, 401, 403, 413 Dexter treatment of energy transfer 232 diamagnetism 70 503 diastereomer solubility criterion 180 differential orbital covalency (DOC) 30 diffusion-controlled 302, 325, 327, 335, 338 dihydrogen bonding 475 diiron center 117,118 diiron(III) 46, 51, 53, 59, 60, 61, 62 diiron(IV) 44, 51, 53, 54, 59 dilatometer 287 dioxygen 114, 118, 120, 121, 125, 126, 128, 133; O-O bond 120, 121, 124, 125, 128, 133 dioxygen reduction 425, 426, 444–448 disproportionation 389, 392, 409, 410 dissociation 369, 372, 375, 376, 385, 394 distorted square planar structures 154 dithionite 375 dodecyl b-d-maltoside 63 s-donor 18, 31 p-donor 1, 18, 30, 31 Doppler shift 42 dose dependent yield 115, 116–117, 122, 124, 131–133 double-pump flash photolysis 225 10Dq 5–7, 27 dynodes 217 effective core potential (ECP) 469 effective nuclear charge (Zeff) 19, 25 Eigen-Tamm-Wilkins mechanism 281, 302 electric dipole transition 4, 8, 9, 13, 18, 20, 25, 26–29, 32 electric field gradient, efg 41, 44, 45 electric quadruple transition 25 electromagnetic waves 200 electron correlation 464, 466, 467, 469 electron ionization mass spectroscopy 58 electron microscopy 109, 112, 131 electron paramagnetic resonance (EPR) 9, 10, 16–18, 26, 32, 85 electron transfer 241, 259, 397, 398, 438 electron–electron repulsion 5, 6, 21, 27, 30, 32 electronic absorption spectroscopy 3, electronic g tensor 42 electronic Hamiltonian, he 40, 41, 48 electronic paramagnetic resonance, see EPR 504 INDEX electronic structure 1–34 electronic structure methods 463 electronic Zeeman interaction 40, 41 electrons, radiolytic 109–112, 116, 125, 131, 133, 134 electrostatic effects 5, 34 electrostriction 297, 319, 320, 323 elementary reaction 369 elimination 372, 410, 415; beta 371, 381; reductive 373, 406, 407 emission-detected CD 176 energy decomposition analysis 473 enthalpy 396, 411 entropy 367, 411 enzyme active sites 491 enzyme kinetics 367 epr spectroscopy 40, 41, 53, 55, 59, 62, 63, 113–131, 135 equilibrium isotope effect 431–437 equilibrium kinetics 385, 386 EXAFS 58, 114, 131, 134, 293, 300 exchange correlation functional 467 exchange coupling 40, 42, 77 exchange energy 75 exchange mechanism of energy transfer 233 excimer 231 exciplex 231 excited state annihilation reaction 232 excited states 468, 478 excited states of representative elements (np*, ns*, pp*) 234 excited-state radiative decay 226 exciton CD 158, 173–175 expectation value of electronic spin, hsi 41, 42, 43, 44, 45, 46, 47, 48, 49, 53, 54, 57 exponential 377 extended x-ray absorption fine structure (EXAFS) 1, 23–25 extinction coefficient Eyring equation 396, 403, 463 57 Fe 39 Fe M€ossbauer spectroscopy 39, 40, 55, 60, 61, 62 Fe(II) 16, 17, 21 Fe(III) 3, 5, 6, 14, 15, 18, 21, 22, 27, 28, 30–33 FeII 43, 44, 46, 47, 63 FeIII 41, 56 FeIV 41, 43, 46, 47, 48, 49, 50, 51, 54, 56, 57, 58, 59 FeIV¼O 47, 50, 51, 53, 55 FeV 51, 53, 55, 56, 57, 58 FeV¼O 55 FeIV-FeIII dimer 53 Fe(H2O)62 þ 241 Fe(H2O)63 þ 241 femtosecond - nanosecond time domain flash photolysis 223 Fenton 47, 50, 413–415 Fermi’s golden rule 228, 232 ferredoxin 119 ferric phosphate 63 ferrimagnetism 77, 95 ferromagnetically coupled 51, 54 ferromagnetism 75 ferrozine 298, 315, 317 Fe-S clusters 46, 59, 60, 61, 62, 63 final states 21, 27, 28, 30, 32, 33 first law of photochemistry 199 first-order kinetics 369–372 Flack parameter 190 flash photolysis 214–225, 281, 324, 332, 339 flow (continuous) 280 flow methods 280 F€oster treatment of energy transfer 233 Frank-Condon reorganization energy 242 free energy 367, 372, 396 linear relationship 403, 420 front-face irradiation 215 frozen solution 39, 42, 45 gadolinium(III) 290 GdIII 295 geminate recombination 250 geometric structure 1, 3, 24 glass transition 112, 113 glass-forming solvent 58 ground state 3, 16, 17, 38, 206 gyromagnetic factor 71 57 half-order kinetics 375–376 Hamiltonian operator 464 Hamiltonian, 39, 40, 54 Hammett 420 Hartree-Fock level 348 INDEX 505 in X-ray crystallography 131–134 mixed valent 117 intermolecular coupling 70 internal magnetic field, bint 41, 42, 43, 44, 45, 46, 49, 54, 57, 60 intersystem crossing 489 intramolecular 372, 373, 38 intramolecular coupling 70 ion-pairing 390 IPCT 257 iron 40, 41, 44, 59, 61 iron–sulfur 32–34 iron-sulfur cluster 46, 59, 60, 61, 62, 63, 119, 132, 134 irradiation, 110–111, 115, 122 irradiation dose 112, 122, 128, 131, 132 g-irradiation 113, 116–119, 124, 126–127 Ising model 89, 90 isoelectronic 300 isomer shift, d 40, 62 isotopic labelling 289, 291 isotopic substitution 269, 343 IUPAC nomenclature rules 146, 148 Hartree-Fock method 464, 465, 467, 469, 475 Heisenberg Hamiltonian 78, 80, 92, 99, 104 helical chirality 149 heme 30, 31 heme iron 113, 123, 128, 130 heme oxygenase 119–122, 126–129 heme protein 111–115, 119–121, 122–133 hemoglobin 115, 119–122, 125–126, 130 heterolytic cleavage 369, 371 high pressure electrochemical cell 345 high spin-low spin transitions 94 high-spin 41, 44, 47, 324, 327, 331, 332, 335, 338, 339 high-spin FeII 44 high-spin FeIII 41, 43, 45, 46, 47, 48, 49, 50, 59, 63 high-temperature series expansion 75, 91 Hilbert space 93 homolytic cleavage 369, 398, 399, 415 Hund’s rule 81 Hush 310, 311, 313, 315, 319 hydrogen abstraction 234 atom 372, 394, 404, 413, 417 bond 401, 408 peroxide 450–452 hydrogenase 59 hydrogenation 481–485 hydroperoxo 368, 371, 372, 374, 375, 384, 394, 405 hydroperoxo-ferric intermediate, see Peroxoferric, Compound hydroxo-bridged complexes 117, 118 hyperconjugation 401 hyperfine coupling 26, 30, 32 hyperfine interaction 41, 86, 89 Ka 385, 393, 394, 409, 410 Kagome lattice 98 Keplerate structures 98 kinetic isotope effect 401–411, 437–445 kinetic probe 380–381 King, V L 143 Kohn-Sham orbitals 467 Kotani theory 74 Kramers ion 15–16 Kramers systems 43, 44, 48 Kuhn anisotropy factor Kuhn, W., 144 145 impurities 82, 88 initial rate 388 inner filter in photolysis 210 inner-sphere 397, 398 integer spin 44, 50, 53 p-interaction 1, 7, 17–20, 22, 31 intermediates reactive 110, 127, 129–132, 134 catalytically active 119, 122, 123, 127–129 labeling 401, 406 lanthanide ions 270, 285, 289, 299 lanthanide shift reagents 299 lanthanides 299 Laporte forbidden transition 4, Larmor precession 44 laser 385, 386, 412 laser flash photolysis 321, 327, 335, 337 LAXS 293 least squares 370, 391 Jahn–Teller distortion 7, 19, 21 506 INDEX Lenz rule 71 LIESST 95 ligand centered (LC) 238, 262 ligand donor strength 21 ligand field (LF) 238–240 excited states 3–18 splitting 5–7, 17, 27, 30, 32 theory (LFT) 3–10 ligand K-edge 31–34 ligand K-pre-edge 31–33 ligand to metal charge transfer (LMCT), 18–21, 237, 238, 244, 245, 247–250, 253, 255–257 ligand valance ionization energy 19 ligand–metal bond 1, 19, 32 light intensity 199, 203 – 211 light waves 200 limiting reagent 376 linewidth, G 40 linkage isomerization 234 long-wave approximation 4, 25 low-spin 326, 335, 338 luminescence dissymmetry ratio 177 M(pc)X ( M¼ Rh(III), Al(III) ; X ¼ Cl, Br) 225, 226 magnetic anisotropy 63 circular dichroism (MCD) 1, 10–18, 113, 114 dipole 4, 9–10 dipole interaction 41, 42, 43 entropy 85 excitation spectrum 70, 82 field strength 71 flux density 71 hyperfine interaction 40, 44, 46, 47, 57, 58, 62, 63 hyperfine splitting 42, 62 hyperfine tensor, a 42, 44, 47, 40, 50, 53, 54 induction 71 level crossing 78, 101 moment 41, 42, 71 resonance imaging (MRI) 290, 299 susceptibility 41, 71, 102 magnetically ordered compound 63 magnetization 71 curves 44, 45, 49 hysteresis 76, 97 manganese 119, 131, 134 many-electron states 21 Marcus theory 310, 311, 313, 315, 319 Marcus-Hush 246 Mars mission, NASA 39 matrix isolation 110, 111, 113, 134, 135 (ref 11) Maxwell thermodynamic equality 288 metal carbonyls 474 centered (MC) 238 K-edge 24–28 K-pre-edge 27 L-edges 28–31 valence ionization energy 19 metal-to-ligand-charge-transfer (MLCT) 1, 18, 222, 226, 238, 244 – 246, 258–260 metallocenes 149 metalloenzymes 445–451 metalloproteins 459 metamagnet 77 methane 59 methane monooxygenase, MMO 46, 59, 60, 62, 117, 118 methanol 59 methemerythrin 117 methemoglobin 323 methyl radical 382 methylaquocobaloxime 255 methylviologen (MV2 ỵ ) 222 metmyoglobin 321, 335 microscopic reversibility 368, 417 MII(bpy)32 ỵ (M ẳ Ru, Os) 259 mitochondria 62 mixed-valent dimer 53 MM’CT 261 Mo72Fe30 cluster 300, 301 (see also aqueous cluster 300) model construction 491 molecular dynamics (MD) 462, 487 molecular field model 76 molecular magnetism 69 molecular mechanics 459, 460, 464, 494 INDEX molecular orbital 19–21, 29, 32, 465, 472, 475, 476, 477 molecular orbital theory 21 molecular properties 459, 472, 473, 478 molecular structure 472, 474, 483 Møller-Plesset perturbation theory 466 Monte Carlo simulation 93, 99 M€ ossbauer spectroscopy 88, 95, 114–116, 118–120, 126 multiconfiguration self-consistent field (MCSCF) 466 multiple scattering theory 23 multipole expansion 4, 25 multireference configuration interaction (MRCI) 467, 468 multireference methods 466 multistep volume profile 308, 310 myoglobin 59, 113, 115, 120–122, 125–130, 132, 133 nanoparticles 62, 63 naphthalene dioxygenase 134 NASA mission 39 natural bonding orbital (NBO) analysis 473 near-edge region 23 Neel temperature 63, 76 nephelauxetic effect neutron scattering 85, 101, 103 nickel 117 nitrite 392, 412 nitrite reductase 134 nitrogen donor-based complexes 50, 51 nitrogenase 43, 119 nitrone 415, 418, 419 nitroxyl 415, 417 L,D nomenclature 149 NO2 radical 256 non-Kramers ion 16–18 non-Kramers systems 44 nuclear Hamiltonian, hn 41 magnetic moment, mn 42, 43 precession frequency 44 octahedral structures (OC-6) 147, 150–153 ONIOM method 493 O-O Raman mode 124, 127 507 optical electronegativity 245 rotation 143, 144, 164 dense condition 210 dilute condition 210 orbital angular momentum operator 9, 10 orbital moment 71 organometallic chemistry 269, 276 organometallic species 286, 298 oscillator strength outer-sphere complex 302 mechanism - 310, 311, 317 p-overlap 18, 20, 21 s-overlap 20, 21 oxaliplatin 305, 306 oxidation state 39, 41, 57, 60 oxidative addition 478 oxo group 51, 56, 57 oxo-bridged 51, 55, 59, 118 oxo-ferryl intermediate 122, 126, 130, 132; See also Compound I, Compound II oxo-ferrous, superoxo-ferric 114, 116, 120, 122–124, 126, 128, 129, 132, 133 oxygen 372, 382, 384, 411, 414 32 P 111, 124 P450cam, see CYP101 parallel path 380, 395; reactions 377–382 paramagnetic 13, 18 complexes 40, 45 paramagnetism 70 parity forbidden transition 4, partial molar volume 274 partial spin pairing 81 partition functions 429, 430, 436 Pascal’s constants 71 peroxidase 114, 116, 119–121, 128–130, 133, 134 peroxo 51, 53, 59 peroxo-cobaltic 127 peroxo-ferric 114, 119–129, 132–133 peroxyl radical 380, 419 perturbation theory 172 Pfeiffer-effect 175, 176 pH effect 390–394 phenothiazines 317 photocathode 216 508 INDEX photochemical reactor 210 photodiode 216 photodiode array 216 photodissociation 234 photoelectron spectroscopy (PES) 24 photoisomerization 234 photolysis 412, 416 photomultiplier 216–222 photon’s kinetic momentum 205 photoreduction 132–134 Photosystem II 131, 134 phthalocyanine (pc) 225, 226 pill box 279, 280, 288 piston cylinder (high pressure) apparatus 278, 280 planar chirality 149 plastocyanin 2, 26, 27, 29, 31, 32 pMMO 59, 60, 61, 62, 63 polarizable continuum methods (PCM) 470, 471 polarization functions 469 polarized absorption 22 polarized light 202, 225 polyaminocarboxylate complexes 183–188 polyatomic anions photochemistry 236 polynuclear system 42 porphyrin 321, 324, 329, 331, 337, 340, 341 potential energy 367 potential energy surfaces 460, 463, 464, 481, 487 powder average 42, 43 pre-edge 1, 22, 24–29, 31–34 pressure-jump method 281, primary photochemical processes 199 product ratio 378 protein 59 pseudo A-term 12, 13 pseudo nth order 376–377 pseudo-first order 373–377 Pt0(PPh3)2C2H4 260 pulse radiolysis 283, 380 pump and probe 215 putidaredoxin 131 pyridine-2-azo-p-diethylaniline 303 QM/MM methods 493 quadrupole doublet 41, 44, 45, 51, 57, 60, 62, 63 interaction 40, 41 splitting, Deq 41, 42, 45, 46, 47, 50, 53, 57, 59, 60, 61, 62, 63 quantum mechanics of nuclei 488 Monte Carlo simulation 93 tunneling 95 yield 199, 239 R/S nomenclature 146 Racah parameter racemic mixtures 146, 161 racemic structures 151 racemization 146 radiation chemistry 109, 114, 131, 134, 135, 136 damage 109, 131, 132 dose 112, 115, 116–118, 122, 126, 128, 130–133 radiationless relaxation rate constant 228 – 231 radiative decay rate constant 226 radical 56, 109–111, 116–118, 122, 131, 133, 135 clock 381 self-reaction 373, 375, 412 anion 373, 375 radical-ion pair 250 – 253 radioactive isotopes 111, 124 radiolysis 109–116, 118, 120–122, 124–132, 134 radiolytic reduction 110–112, 114–117, 119–122, 124, 126, 128, 130–134 Raman spectroscopy 115, 120, 124, 126, 127, 133 randomly oriented molecules 42, 45 rapid freeze quenching 47, 49, 50, 58 rate constants 460, 481 rate law 367–389 rate-limiting 372, 375, 387, 410, 417, 483 reaction coordinate 367, 368, 402, 407 reaction mechanisms 460, 479–481 reactive intermediates 459, 460 recoilless fraction, f 43 Redlich-Teller product rule 430 reduction potential 387 reductive coupling 410, 411 reductive elimination 372, 406, 407 INDEX ReI(CO)3(1,10-phen)Cl 259, 260 ReI(CO)3(2,20 -bpy)X (X¼ Cl, Br) 222, 259 ReI(CO)3(4-phenylpyridine)2Cl 226 relativistic effects 469 relaxation, after annealing 111–113, 115, 117, 119, 120, 123 relaxivity 300, 348 remnant magnetization 76 resolution 40 resonance Raman (rR) 22 Rh(NH3)63 ỵ 231, 239 Rh(phen)33 þ 241 rhombicity, E 40, 44, 47, 48, 49, 53 ribonucleotide reductase 46, 117, 118 Richardson, F S 143 ring conformation 149 ring-pairing method 149 rotational strength 8–9, 168 rotatory strength 165 [Ru(edta)(H2O)]À 327, 331, 332 rubredoxin 116 S ¼ 41, 42, 45, 46, 54, 60, 63 S ¼ 1/2 41, 44, 45, 53, 56, 58 S ¼ 50, 54 S ¼ 43, 44, 45, 48, 50, 53, 54 S ¼ 3/2 53 S ¼ 5/2 43, 44, 48, 49 S K-edge 32, 33 Saito, Y 143 sample and hold circuitry 219, 220 saturation magnetization 14–18, 73, 78, 82 scavenger 116, 133, 388, 399, 417 Schottky anomaly 85 Schr€odinger equation 464, 465, 468 second law of photochemistry 199 secondary photolysis 211 second-order kinetics 372–375 sector rules 168 see-saw structures (SS-4) 147 selectivity 483 s-electron density 41 selenium, chiral structures 163 semiempirical methods 464, 467, 474 side-on 372 side-on irradiation 215 single-molecule magnets 95 skew-line convention 145, 148, 161 509 SMCT 257 sMMO 59, 60, 62, 63 sodium nitroprusside 42 solvated electron 234 solvent cage 250 effects 470, 480, 481 isotope substitution 271 molecules: explicit treatment 471 (solvento)Ru(II) species 298 Soret (region) 321, 322, 326 specific heat capacity 84 spin chain 90 change 322, 327 crossover 489 density 325 dipolar interaction 58 expectation value 16, 17 frustration 97 Hamiltonian 1, 15, 17, 19, 39, 40, 50 moment 71 multiplicity 228, 335 Peierls transition 92 quantum number 70, 77, 100 relaxation 43, 44, 45, 47, 49, 50, 53 reorganization 327 state 312, 324, 332 trap 419 spin-admixed 324, 325, 331 spin-allowed transition 4, 7, spin-coupled system 46 spin-forbidden reactions 489 spin-only magnetism 73 spin–orbit coupling (SOC) 12, 13, 29, 30, 70, 74, 86, 95, 228, 230 spin–orbit parameters 13 spin-pairing energy spin-phase transitions 97 spin-spin interaction 75 spin-state change 325, 338 square antiprism structures 161 square-prismatic structures (SPY-5 and SPY-4) 147, 154, 155 SQUID 83, 84 statistical mechanics 463, 471, 495 steady-state 386–388, 416 Stokes shift 229 Stoner-Wohlfarth model 76 510 INDEX stopped-flow 47, 280, 281, 302, 327, 332, 335, 337, 340, 343, 384 strong coupling limit 229 substituent effects 460, 478, 481 sulfur, chiral structures 163 sum rule 13 superoxide 448–449 superoxide dismutase 116, 344 superoxo-ferrous complex 125 superparamagnetic relaxation 63 superparamagnetism 76 supramolecular complexes 155 Swift and Connick 346 synchrotron 22–23 TAML activator 55, 56, 57 TAML activator B* 55, 56, 57, 58, 59 TAML activator DMOB 56, 57 TAML activator MAC* 57 Tanabe–Sugano diagram 5, tellurium, chiral structures 163 temperature 385, 396, 398, 403, 406, 411, 416 temperature-independent paramagnetism 74, 75 temperature-jump (method) 281, 302, 303 tetrahedral (T-4) structures 146, 147, 153–154 tetranuclear complexes 156 time-dependent DFT (TDDFT) 168, 169, 174, 468, 478 total energy 465 TPA ligand 51, 52, 53, 54, 55 trans effect 305 transfer of electronic energy 232, 233 transition moment 3, 4, 13, 18, 20, 21 transition state 367–389, 460, 462, 476, 478, 482 transition state theory 460, 463, 481, 485 trans-labilization 299 trans-Pt-N bond 308 trapping reaction 327, 331, 332 trigonal tricapped prism 159 trigonal-bipyramidal (TBY-5) 147, 154 trigonal-pyramidal (TPY-3) 147 triple helicate structures 157 12-tungstoaluminate (5À/6À) couple 343 tunneling 403, 406, 487, 489 two-window high pressure cell 279 ultrasound method 281 unimolecular reactions 369, 381, 396, 398, 486 UV/Vis spectroscopy 47 Van Vleck equation 72, 74, 78 variable-temperature variable-field MCD (VTVH MCD) 14–18 vibrating sample magnetometer 84 vibrational CD (VCD) 177 vibrational frequencies 463, 478 viscosity 276, 285 vitamin B12 340, 341 volume of activation 274–276 water oxidation 426 wavefunction 464, 466, 468 weak coupling limit 230 Weiss district 76 Weiss temperature 75, 76, 104 Werner, A 143, 153, 164, 180 whole cells 61, 62, 63 WMOSS software 40 X (X ¼ Cl, Br, I, SCN, O) 234–236 X2 À (X ¼ Cl, Br, I, SCN) 234, 235 XANES 115, 134 XAS 134 x-ray absorption spectroscopy (XAS) 1, 22–34 X-ray crystallography 109, 112, 131, 132, 133 X-ray diffraction 145, 163, 190, X-ray irradiation 119, 125, 128, 131–133 X-ray spectroscopy 109, 114 - See also EXAFS, XANES, XAS XY model 90 yield of radiolytic electrons 110–112, 133 Zeeman effect 10, 11, 14, 15, 17, 71, 85, 95 zero-field splitting (zfs) 12, 14, 15–17, 40, 41, 42, 43, 44, 45, 53, 70, 81, 86, 87, 95 zero-order 392, 400 zero-point energy 401–403, 411, 488 zinc 60, 62 ... Data: Physical inorganic chemistry : principles, methods, and models / [edited by] Andreja Bakac p cm Includes index ISBN 978-0-470-22419-9 (cloth) Physical inorganic chemistry I Bakac, Andreja... dichroism (CD), magnetic Physical Inorganic Chemistry: Principles, Methods, and Models Edited by Andreja Bakac Copyright Ó 2010 by John Wiley & Sons, Inc INORGANIC AND BIOINORGANIC SPECTROSCOPY... xi Inorganic and Bioinorganic Spectroscopy Edward I Solomon and Caleb B Bell III 57 Fe M€ ossbauer Spectroscopy in Chemistry and Biology 39 Marlene Martinho and Eckard M€unck Magnetochemical Methods