ADVISORY BOARD I Bertini D Darensbourg Universita degli Studi di Firenze Florence, Italy Texas A & M University College Station, Texas, USA L H Gade H B Gray Universität Heidelberg Germany California Institute of Technology Pasadena, California, USA M L H Green P A Lay University of Oxford Oxford, United Kingdom University of Sydney Sydney, Australia A E Merbach J Reedijk Laboratoire de Chimie et Bioanorganique EFPL, Lausanne, Switzerland Leiden University Leiden, The Netherlands P J Sadler Y Sasaki University of Warwick Warwick, England Hokkaido University Sapporo, Japan K Wieghardt Max-Planck-Institut Mülheim, Germany Advances in INORGANIC CHEMISTRY EDITED BY Rudi van Eldik University of Erlangen-Nuărnberg Erlangen Germany Jeremy Harvey University of Bristol Bristol United Kingdom VOLUME 62: Theoretical and Computational Inorganic Chemistry AMSTERDAM • BOSTON • HEIDELBERG • LONDON • NEW YORK • OXFORD PARIS • SAN DIEGO • SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO ACADEMIC PRESS IS AN IMPRINT OF ELSEVIER Academic Press is an imprint of Elsevier 32 Jamestown Road, London NW1 7BY, UK Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA 525 B Street, Suite 1900, San Diego, CA 92101-4495, USA First edition 2010 Copyright Ó 2010 Elsevier Inc 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 ISBN: 978-0-12-380874-5 ISSN: 0898-8838 For information on all Academic Press publications visit our website at elsevierdirect.com Printed and bound in USA 10 11 12 13 14 10 Working together to grow libraries in developing countries www.elsevier.com | www.bookaid.org | www.sabre.org LIST OF CONTRIBUTORS William Ames Dimitrios G Liakos Institut fuăr Physikalische und Theoretische Chemie, Universitaăt Bonn, Bonn, Germany Institut fuăr Physikalische und Theoretische Chemie, Universitaăt Bonn, Bonn, Germany Marc Bruăssel Agust Lledos Wilhelm-Ostwald Institut fuăr Physikalische und Theoretische Chemie, Universitaăt Leipzig, Leipzig, Germany Departament de Qumica, Universitat Auto`noma de Barcelona, Bellaterra, Catalonia, Spain Gemma Christian Aurora Martinez Institut fuăr Physikalische und Theoretische Chemie, Universitaăt Bonn, Bonn, Germany Department of Biomedicine, University of Bergen, Bergen, Norway Russell G Mckinlay Aleix Comas-Vives Department of Chemistry, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, Scotland Departament de Quı´mica, Universitat Auto`noma de Barcelona, Bellaterra, Catalonia, Spain Frank Neese Robert J Deeth Institut fuăr Physikalische und Theoretische Chemie, Universitaăt Bonn, Bonn, Germany Department of Chemistry, Inorganic Computational Chemistry Group, University of Warwick, Coventry, United Kingdom Elaine Olsson E Hey-Hawkins Department of Chemistry, University of Bergen, Bergen, Norway Institut fuăr Anorganische Chemie, Universitaăt Leipzig, Leipzig, Germany Dimitrios A Pantazis Thomas S Hofer Institut fuăr Physikalische und Theoretische Chemie, Universitaăt Bonn, Bonn, Germany Theoretical Chemistry Division, Institute of General, Inorganic and Theoretical Chemistry, University of Innsbruck, Innsbruck, Austria Martin J Paterson Department of Chemistry, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, Scotland Vidar R Jensen Department of Chemistry, University of Bergen, Bergen, Norway Maren Podewitz Laboratorium fuăr Physikalische Chemie, ETH Zurich, Zurich, Switzerland Mario Kampa Institut fuăr Physikalische und Theoretische Chemie, Universitaăt Bonn, Bonn, Germany Andreas B Pribil Theoretical Chemistry Division, Institute of General, Inorganic and Theoretical Chemistry, University of Innsbruck, Innsbruck, Austria Barbara Kirchner Wilhelm-Ostwald Institut fuăr Physikalische und Theoretische Chemie, Universitaăt Leipzig, Leipzig, Germany ix x LIST OF CONTRIBUTORS Bernhard R Randolf Panida Surawatanawong Theoretical Chemistry Division, Institute of General, Inorganic and Theoretical Chemistry, University of Innsbruck, Innsbruck, Austria Institut fuăr Physikalische und Theoretische Chemie, Universitaăt Bonn, Bonn, Germany Knut Teigen Markus Reiher Department of Biomedicine, University of Bergen, Bergen, Norway Laboratorium fuăr Physikalische Chemie, ETH Zurich, Zurich, Switzerland Gregori Ujaque Bernd M Rode Theoretical Chemistry Division, Institute of General, Inorganic and Theoretical Chemistry, University of Innsbruck, Innsbruck, Austria Departament de Quı´mica, Universitat Auto`noma de Barcelona, Bellaterra, Catalonia, Spain Shengfa Ye Michael Roemelt Institut fuăr Physikalische und Theoretische Chemie, Universitaăt Bonn, Bonn, Germany Institut fuăr Physikalische und Theoretische Chemie, Universitaăt Bonn, Bonn, Germany Stefan Zahn James R Rustad Department of Geology, University of California, Davis, CA, USA Michael Seth Department of Chemistry, University of Calgary, Calgary, AB, Canada Tatyana E Shubina Computer-Chemie-Centrum and Interdisciplinary Center for Molecular Materials, Friedrich-Alexander-Universitaăt Erlangen-Nuărnberg, Erlangen, Germany Wilhelm-Ostwald Institut fuăr Physikalische und Theoretische Chemie, Universitaăt Leipzig, Leipzig, Germany Tom Ziegler Department of Chemistry, University of Calgary, Calgary, AB, Canada Justyna M Z˙urek Department of Chemistry, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, Scotland PREFACE Volume 62 of Advances in Inorganic Chemistry is a thematic issue dedicated to Theoretical and Computational Inorganic and Bioinorganic Chemistry Theory has always played an important role in inorganic chemistry, and with developments in computer power, computation now routinely provides valuable insight to the field in many different ways This volume includes contributions highlighting the role of computation in a broad spectrum of inor­ ganic chemistry, though inevitably many important subfields have been neglected We hope it will prove interesting and inspir­ ing to both computational and experimental researchers in the field Chapter 1, by Robert J Deeth, reviews recent developments in the use of molecular mechanics force fields for transition metal compounds, covering both the theory of including crystal field-like orbital stabilization terms within molecular mechanics and appli­ cations to molecular dynamics simulations of metalloproteins Chapter 2, by Michael Seth and Tom Ziegler, is one of several reviews that focus on methods to calculate spectroscopic observa­ bles for inorganic compounds The particular topic is magnetic circular dichroism prediction with time-dependent density functional theory approaches, with applications ranging from an isolated permanganate ion to enzyme active sites Chapters and describe studies of chemical behavior based on molecular dynamics studies in which the energy surface is computed “on the fly” with density functional theory or ab initio methods Chapter 3, by Marc Brüssel, Stefan Zahn, E Hey-Hawkins, and Barbara Kirchner, describes density functional theory-based studies and applications to nitrogen activation, while Chapter 4, by Bernd M Rode, Thomas S Hofer, Andreas B Pribil, and Bernhard R Randolf, focuses on the Hartree–Fock and other ab initio methods, with applications to the structure and dynamics of hydrated ions Chapter 5, by Maren Podewitz and Markus Reiher, describes the theory involved in understanding electronic spin in molecular systems and especially clusters, going all the way back to the relativistic origin of the spin quantum number Some technical discussion of broken-symmetry approaches to spin states of metal-containing clusters and a dis­ cussion of local spin concepts follows, as well as some applications Chapter 6, by Aleix Comas-Vives, Gregori Ujaque, and Agustí Lledós, is an overview of catalytic hydrogenation mechanisms, largely based on density functional theory studies of potential energy surfaces Mechanisms involving coordination of the xi xii PREFACE substrate to the metal and without such coordination are consid­ ered and compared Chapter 7, by Tatyana E Shubina, concerns the electronic structure and reactivity of metalloporphyrin species with divalent metal ions The binding of small ligands to porphyr­ ins is considered, as is the formation of the metalloporphyrins through metallation Chapter 8, by Frank Neese, William Ames, Gemma Christian, Mario Kampa, Dimitrios G Liakos, Dimitrios A Pantazis, Michael Roemelt, Panida Surawatanawong, and Shengfa Ye, is an overview of a large number of topics related to computa­ tional chemistry of open-shell transition metal compounds The key topics described are reactivity, including the role of electronic structure, and in particular spin state, in iron-containing enzymes with iron- oxo active species; electron paramagnetic resonance, including the theory of how to compute spectroscopic observables; electronic structure and spectroscopy of metal–radical complexes; and magnetic properties of polymetallic clusters Chapter 9, by Russell J Mckinlay, Justyna M Żurek, and Martin J Paterson, is mainly about photochemistry of metal complexes, but includes also a general review of the theory of vibronic coupling in inorganic systems Basic theory, electronic structure of metal carbonyl excited states, and quantum wave packet dynamics studies of dissociation and radiationless transitions are all discussed Chapter 10, by James Rustad, is an example of how computational inorganic chem­ istry now has an impact well outside the traditional heart of the discipline—the title announces “A New Geology” based on computa­ tional insight The review introduces the force-field methods that form the basis for much of the work in the area, and then discusses applications to proton transfer and to interfacial reactions on oxide materials The final contribution, Chapter 11 by Elaine Olsson, Knut Teigen, Aurora Martinez, and Vidar R Jensen, highlights another field in which computational inorganic chemistry now makes major contributions: bioinorganic chemistry Some applica­ tions from this field are touched upon in some of the other chapters, of course, but Chapter 11 focuses purely on the biochemistry and reactivity of aromatic amino acid hydroxylase enzymes We trust the readers in the inorganic and bioinorganic chem­ istry communities will find this volume informative and useful Rudi van Eldik University of Erlangen-Nürnberg Germany Jeremy Harvey University of Bristol United Kingdom June 2010 MOLECULAR MECHANICS FOR TRANSITION METAL CENTERS: FROM COORDINATION COMPLEXES TO METALLOPROTEINS ROBERT J DEETH Inorganic Computational Chemistry Group, Department of Chemistry, University of Warwick, Coventry CV4 7AL, United Kingdom I II III IV V VI VII VIII IX X XI XII XIII XIV Introduction Conventional Molecular Mechanics Shortcomings of MM for TM Systems: Angular Potentials Effects from d Electrons Ligand Field Molecular Mechanics LFMM Parameterization Simple Metal, Simple Ligand: Ga(III) Hydroxamates Simple Metal, Complex Ligand: Mn(II) Carboxylates Difficult Metals: Jahn–Teller Effects in Cu(II) and the trans Influence in Pt(II) Spin States Metalloproteins and Molecular Dynamics: Copper Proteins Bond Energies and Reaction Mechanisms: Water Exchange Effects of M-L π Bonding Conclusions Summary References I 10 11 13 16 20 22 28 33 36 37 37 Introduction Transition metal (TM) systems present a fundamental dilemma for computational chemists On the one hand, TM centers are often associated with relatively complicated electronic structures which appear to demand some form of quantum mechanical (QM) approach (1) On the other hand, all forms of QM are relatively compute intensive and are impractical for conformational search­ ing, virtual high-throughput screening, or dynamics simulations THEORETICAL AND COMPUTATIONAL INORGANIC CHEMISTRY VOLUME 62 ISSN 0898-8838 / DOI: 10.1016/S0898-8838(10)62001-6 Ó 2010 Elsevier Inc All rights reserved ROBERT J DEETH since all these approaches may require many hundreds of thou­ sands of individual calculations Consequently, TM computa­ tional chemists tend to restrict themselves to smaller “model” systems with limited conformational freedom This is particularly marked in bioinorganic chemistry where the calculation focuses on the “important” active site region but the bulk of the protein is not treated explicitly (2,3) In contrast, those interested in purely “organic” systems have long enjoyed the advantages of “cheap,” classical molecular mechanics (MM) and molecular dynamics (MD) to study the entire molecular system including the surrounding solvent How­ ever, conventional MM is not well suited to TM systems since it does not provide a general way of accounting for the important effects arising from the d electrons (4,5) In response, hybrid QM/ MM methods have appeared (6) The metal center and its immediate environment is handled by a “high level” QM method, typically based on Density Functional Theory (DFT), with the rest of the system treated by MM As the many technical difficulties of QM/MM have progressively been solved—most importantly how to couple the quantum region to the classical region—QM/MM has grown in popularity However, the inclusion of any QM, even on a relatively small piece of the whole system, soon exacts a huge cost in execution time Just a few minutes per calculation soon equates to years of CPU time The only options are either to use thousands of computers or to develop a method which is as accurate as QM, but many orders of magnitude more efficient We have taken the second path by augmenting MM with additional terms designed to provide a physically meaningful description of metal–ligand bonding and thus be able to emulate the behavior of more sophisticated, but expensive, QM methods However, in order to put our model into perspective, we must first appreciate the nature of “conventional” MM and its shortcomings when applied to TM systems II Conventional Molecular Mechanics Molecular mechanics in its simplest form expresses the total potential energy, Etot, as a sum of terms describing bond stretch­ ing, Estr, angle bending, Ebend, torsional twisting, Etor, and nonbonding interactions, Enb (1) The latter can include both van der Waals (vdW) interactions and, by assigning to each atom a partial atomic charge, electrostatics Etot ¼ X X Estr ỵ Ebend ỵ X X Etor ỵ Enb 1ị MOLECULAR MECHANICS FOR TRANSITION METAL CENTERS Each term in (1) is represented by a simple mathematical expression as exemplified in (2), where the k are appropriate force constants,  are bond angles, τ are torsion angles, n is the torsional periodicity parameter,  is the torsion offset,  are partial atomic charge, ε is the dielectric constant, A and B are Lennard-Jones vdW parameters, and the summations run over bonded atom pairs (ij), angle triples (ijk) and torsional quadru­ ples (ijkl) The nonbonded terms are summed over the distances, dij, between unique atom pairs excluding bonded pairs and the atoms at either end of an angle triple For the atoms at the ends of a torsion quadruple, the nonbonded term may be omitted or scaled Etot ¼ X kij rij r0 ; ij ị ỵ i;j X kijk ijk 0 ; ijk ị i;j;k X ỵ kijkl ẵ1 ỵ cos nijkl fijkl ị i;j;k;l " ỵ X i