Chemical Hardness Guest-Editor: K.D. Sen With contributions by J. A. Alonso, B.G. Baekelandt, L.C. Balbas P.K. Chattaraj, J.L. Gazqu6z, M.E. Grice L. Komorowski, N.H. March, W.J. Mortier J. S. Murray, R.F. Nalewajski, R.G. Parr R. G. Pearson, P. Politzer, IL A. Schoonheydt K. D. Sen With 53 Figures and 52 Tables galreV-regnirpS Berlin Heidelberg New kroY London Paris Tokyo Hong Kong Barcelona Budapest :rotidE-tseuG Professor K. D. Sen School of Chemistry, University of Hyderabad, Hyderabad 500 134, India ISBN 3-540-56091-2 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-56091-2 Springer-Verlag New York Berlin Heidelberg This work is subject to copyrighL All rights are reserved, whether the whole or part of the material is concerned, specifically rite rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on ndcrofilms or in other ways, and storage in data banks. Dublieation of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee mustalways be paid. (cid:14)9 Springer-Verlag Berlin Heidelberg 1993 s in Germany The use of general descriptive names, trade marks, etc. in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anonyme. Typ~etting: Maenfillan India Ltd., Bangalore-25, India printing: Colordruck, Berlin; Bookbindh~g: Lfideritz & Bauer, Berlin 51/3020 - 5 4 3 2 1 0 - Printed on acld-free paper Editorial Board Professor MichaelJ. Clarke, Boston College, Department of Chemistry, Chestnut Hill, Massachusetts 02167, U.S.A. Professor John B. Goodenough, Center of Materials Science and Engineering, University of Texas at Austin, Austin, Texas 78712, U.S.A. Professor James A. lbers, Department of Chemistry, Northwestern University, Evanston, Illinois 60201, U.S.A. Professor Christian K. Jorgensen, D6pt. de Chimie Min6rale de l'Universit6 30 quai Ernest Ansermet, CH-1211 Gen6ve 4 Professor David Michael P. Mingos, Imperial College of Science, Technology and Medicine, Dept. of Chemistry, South Kensington, London SW7 2AY, Great Britain Professor Joe B. Neilands, Biochemistry Department, University of California, Berkeley, California 94720, U.S.A. Professor Graham A. Palmer, Rice University, Department of Biochemistry, Wiess School of Natural Sciences, P.O. Box 1892, Houston Texas 77251, U.S.A. Professor Dirk Reinen, Fachbereich Chemic der Philipps-Universit~t Marburg, Hans-Meerwein-StraBe, D-3550 Marburg Professor Peter J. Sadler, Birkbeck College, Department of Chemistry, University of London, London WCIE 7HX, Great Britain Professor Raymond Weiss, Institut Le Bcl, Laboratoire de Cristallochimie et de Chimie Structurale, 4, rue Blaise Pascal, F-67070 Strasbourg Cedex Professor Robert Joseph P. Williams, Wadham College, Inorganic Chemistry Laboratory, Oxford OXI 3QIL Great Britain Table of Contents Chemical Hardness - An Historical Introduction R. G. Pearson ...................................... Density Functional Theory of Chemical Hardness P. K. Chatteraj, R. G. Parr ......................... 11 Hardness and Softness in Density Functional Theory J. L. G~quez ................................... 27 Hardness Indices for Free and Bonded Atoms L. Komorowski ................................. 45 The Ground-State Energy of Atomic and Molecular Ions and its Variation with the Number of Electrons N. H. March ................................... 71 Isoelectronie Changes in Energy, Electronegativity and Hardness in Atoms via the Calculations of K. D. Sen ..................................... 87 Charge Capacities and Shell Structures of Atoms P. Politzer, J. S. Murray, M. E. Grice ................. 101 The Hardness Based Molecular Charge Sensitivities and Their Use in the Theory of Chemical Reactivity R. F. Nalewajski ................................ 115 The EEM Approach to Chemical Hardness in Molecules and Solids: Fundamentals and Applications B. G. Baekelandt, W. J. Mortier, R. A. Schoonheydt ..... 187 Hardness of Metallic Clusters J. A. Alonso, L. C. BalbSs ......................... 229 Author Index Volumes 1- 80 ......................... 259 Chemical Hardness- A Historical Introduction Ralph G. Pearson Chemistry Department, University of California, Santa Barbara, Ca 93106, USA A brief account is given of the origin and early development of the idea of hardness, introduced to chemistry as hard and soft Lewis acids and bases. There is also a discussion of the merging of this early view of hardness with the modern definition, based on density functional theory. I Early Work ........................................................... 2 2 Hard and Soft Acids and Bases ............................................ 3 3 The Definition of Hardness ............................................... 7 4 References ............................................................ 10 erutcurtS dna ,gnidnoB .loV 08 ~,.(( teV-regnirpS ag nilreB grcblediell 3991 2 Ralph G. Pearson 1 Early Work The earliest observations leading to the concept of chemical- or absolute- hardness, go back to the days of Berzelius. It was noted that some metals occurred in nature as their sulfide ores, and others as their oxide or carbonate ores. Table 1 puts this in more quantitative terms. Listed are the cohesive energies, AH ~ for a number of binary metal oxides and sulfides, MX. MX~ I = M~} + X~AH ~ (1) It can be seen that the cohesive energies of the oxides are always greater than those of the sulfides. But the amount, A, by which it is greater for a given metal can vary greatly. Thus A is as large as 54 kcal mol- 1 for Mg, and as small as 1 kcal mol- 1 for Hg. If we look at an exchange reaction such as CaS + CdO = CdS + CaO AHex = - 16 kcal mol -I (2) we see that the products are more stable than the reactants. Since CaO would be converted to CaCO 3 by air, we expect that CdS and CaCO3 are more likely to be found in nature than CaS and CdCO3, even if CaS were not so readily hydrolyzed. The entries in Table 1 enable us to write an order of decreasing A for the several metals, or rather metal ions. Mg 2+ > Fe z+ > Ca 2+ > Zn 2+ > pb 2+ > Cu 2+ > Cd 2+ > Hg 2+ This ordering would later bc called an order of decreasing hardness, or increas- ing softness. To facilitate matters later, the modern symbol 1"1 will be used for hardness, and 0 for softness. The relationship between them is simply r I = 1/0. The above ordering presumably is one of decreasing values of rl. The foundations for the concept of chemical hardness lie in the works of Schwarzenbach I-1 and Chatt .12,1 Independently, they showed that metal ions could be divided into two classes, (a) and (b), depending on the relative affinities for ligands with various donor atoms. Tabk .1 Cohesive energies of some metal oxides and sulfides at 298K, kcalmol -t Mg Fe Ca Zn Pb Cu Cd Hg ~H~,MO 932 422 452 471 851 871 841 69 AH~ 581 091 222 341 731 061 231 59 A 45 43 23 72 12 81 61 1 Chemical Hardness - A Historical Introduction 3 class (a) N>> P > As > Sb O>>S> Se>Te F>CI>Br>I class (b) N<

As > Sb O<AH (6) 6 Ralph G. Pearson where h is read as the harder of the two acids (bases) and s as the softer of the two bases (acids) .1"6 Thus the reaction is exothermic if the acid-base complexes are matched up hh and ss. This rule is not inviolate because of the complication due to acid-base strength. Strength here is used as a catch-all phrase to mean all the other things that determine bond energies. These include charges and sizes, electronegativity, matching of orbital overlaps and steric repulsions. For Eq. )6( to be valid, one must compare acids, or bases, of the same charge, and roughly of the same strength. Table 2 lists some acids such as Si 4+ and Th 4§ which have no real existence, and where the charges refer to oxidation states. The true acids are species such as (RO)3Si § or SiH~. The hardness of a given center depends strongly on the attached groups. The general rule is that hard ligands (bases) make the central atom hard, and soft ligands make the central atom soft. This observation was first made by Klixbull Jorgensen 6, who named the phenomenon the "symbiotic effect." Si(OR)~" is harder than SiH~, accordingly 7. In Table 2, we see that BF3 is hard and BH 3 is soft. The explanation for the symbiotic effect is readily seen. In BF3, the bonding is very ionic and boron has an actual charge close to its oxidation state of 3 +. In BH3, the bonding is covalent and boron has an actual charge of close to zero. Increased positive charge on the acceptor atom always increases the hardness. Theoretical explanations of the HSAB Principle were also quickly put forward 5, 8. The most important feature was that hard-hard combinations were held together by ionic bonds, primarily, and soft-soft combinations used covalent bonding. In addition, various stabilizing effects of combining two polarizable species could be postulated. Solvation energies also played a role, but an indirect one. For example, in the gas phase F- is always a stronger base than I-, because of size. In aqueous solution F- has a greater heat of hydration than I- by 53 kcal/mol. This difference is what enables I- to complete with F- for various Lewis acids in water. For soft acids, I- wins out. For hard acids F- is still the stronger base. In spite of these various complications, the HSAB concept proved to be useful in many applications to chemistry, as well as to chemically related fields, such as medicine and geology 9. Two of the articles on HSAB 5, 10 have been identified by Current Contents as among the most widely quoted publica- tions in the chemical literature. For many chemists the vague terms "hard" and "soft" seemed to fill a need in their chemical vocabularies. The very fact that they were ill-defined terms probably made them more useful. An analogy might be made to the term "solvent polarity", which is hard to define, but quite indespensable to chemists running reactions in solution. For other chemists the words "hard" and "soft" were anathema. Quantities which could not be measured, and to which numbers could not be assigned, were held to have no place in exact science. I also think there was a prejudice

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