Reactivity and Structure Concepts in Organic Chemistry Volume 2 Editors: Klaus Hafner Jean-Marie Lehn Charles W. Rees P. von R. Schleyer Barry M. Trost Rudolf Zahradnik Kenichi Fukui Theory of Orientation and Stereose lection With 72 Figures Springer -Verlag Berlin Heidelberg New York 1975 Kenichi Fukui Kyoto University, Dept. of Hydrocarbon Chemistry, Kyoto, Japan ISBN 978-3-642-61919-9 ISBN 978-3-642-61917-5 (eBook) DOI 10.1007/978-3-642-61917-5 Parts of this book have been published in Topics in Current Chemistry, Vol. 15 (1970) Library of Congress Cataloging in Publication Data Fukui, Kenichi, 1918- Theory of orientation and stereoselection. (Reactivity and structure; v. 2) Bibliography: p. Includes index. 1. Chemical reaction, Conditions and laws of. 2. Stereochemistry. 3. Chemistry, Physical organic. I. Title. II. Series. QD501.F92 547'.1'223 75-25597 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin' Heidelberg 1975. Softcover reprint of the hardcover 1st edition 1975 Typesetting: Hans Meister KG, Kassel, binding: Konrad Triltsch, Wiirzburg Preface Many organic chemists will agree with me that the old "electronic theory" has for a long time been inadequate for the interpretation of various new findings in chemistry, particularly for those of reactivity. Considering the outstanding progress which has been made during the past 20 years in the interpretation of these facts, aided by the molecular orbital theory, the time has finally come for a new book showing what is within and what is beyond the reach of quantum-chemical methods. It was therefore highly suitable that Dr. F. L. Boschke of the Springer Verlag suggested to me to make a contribution to a volume in the series "Topics in Current Chemistry" in February 1969. The article was published as Vol. 15, No 1 in June 1970. This new book is an expanded version of the article written in 1970. In this present volume several of the most up-to-date findings which have been gained in organic chemistry since then have been added. It is highly probable that a certain "theoretical" design in the experimenta lists' mind may have been the reason for these developments, whether they themselves are aware of it or not. Theory produces new experimental ideas and conversely, a host of experimental data add another vista to new theories. Due to the mutual beneficial effect of theory and experiment this book will always retain its value, although the quantum-chemical approach to the theory of reactivity is, of course, still in the develop mental stage. I t is my sincere hope that graduates and young research chemists, in both the theoretical and experimental fields will find this book useful and thereby become acquainted with the quantum-chemical way of thinking in which the concept of the "orbital" of an electron serves as a good explanation within the chemical terminology. I extend my special thanks to Dr. F. L. Boschke and Springer-Verlag for the planning and production of this book. KENICHI FUKUI Kyoto, Japan, May 1975 Contents 1. Molecular Orbitals .................................... 1 2. Chemical Reactivity Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3. Interaction of Two Reacting Species. . . . . . . . . . . . . . . . . . . . . 10 4. Principles Governing the Reaction Pathway ............. 22 5. General Orientation Rule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 6. Reactivity Indices .................................... 34 7. Various Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 7.1. Qualitative Consideration of the HOMO-LUMO Interaction 40 7.2. The Role of SOMO's .................................. 47 7.3. Aromatic Substitutions and Additions. . . . . . . . . . . . . . . . . . . 52 7.4. Reactivity of Hydrogens in Saturated Compounds. . . . . . . . 55 7.5. Stereoselective Reactions .............................. 59 7.6. Subsidiary Effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 7.7. Rehybridization by Neighboring Group Effect. . . . . . . . . . . . 79 8. Singlet-Triplet Selectivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 9. Pseudoexcitation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 10. Three-species Interaction .............................. 88 11. Orbital Catalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 12. Thermolytic Generation of Excited States. . . . . . . . . . . . . . . . 99 13. Reaction Coordinate Formalism. . . . . . . . . . . . . . . . . . . . . . . .. 102 14. Correlation Diagram Approach ......................... 105 15. The Nature of Chemical Reactions. . . . . . . . . . . . . . . . . . . . . . 109 Appendix 1. Principles Governing the Reaction Path - An MO-Theoretical Interpretation. . . . . . . . . . . . . . . 112 Appendix II. Orbital Interaction between Two Molecules. . . . . . . 117 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 120 Author Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 1. Molecular Orbitals Many chemical problems can be discussed by way of a knowledge of the electronic state of molecules. The electronic state of a molecular system becomes known if we solve the electronic Schrodinger equation, which can be separated from the time-independent, nonrelativistic Schrodinger equation for the whole molecule by the use of the Born-Oppenheimer approximation In this approximation, the electrons are considered to 1). move in the field of momentarily fixed nuclei. The nuclear configuration provides the parameters in the Schrodinger equation. The nonrelativistic, electronic Schrodinger Hamiltonian operator, designated as H, is represented by H = ..!!;: (_ ~ L1t _ L~.... zae2 ) + L...!.!.;.: ~ + L~.... ZaZbe2 (1.1) ~ 8n2m ria ri} rab 1-1 a 1,}-1 a,b (I<}) (a<b) in which N is the number of electrons, L1t is the Laplacian operator for electron i, Zae is the positive charge of nucleus, a, and rtf, ria, and r ab are the distances between electrons i and j, nucleus a and electron i, and nuclei a and b, respectively: e and m are the charge and the mass of an electron: h is the Planck constant. The eigenstate of the operator H may be described in terms of 4 N electron coordinates, Xt, yt, Zt, and ~t (i = 1, 2, -----N), where the first three are the Cartesian coordinates and the last one is the spin coordinate. The wave junction, 'l', of an eigenstate of H is therefore 1 Molecular Orbitals represented by P(I2 -----N) in which i(i = 1,2, -----N) stands for the set of coordinates (X(, y(, z(, ;(). From the well-known statistical requirement for an assembly of Fermi particles, P(I2 -----N) is subject to a limitation in its form of anti symmetric character with respect to electron exchange. In addition to this, we have to note that an eigenstate of H can be specified also by the eigenvalues of 82 and 5z, where 8 is the total electronic spin angular momen tum vector. In this way, we are able to obtain information about the general form which should be satisfied by the simultaneous eigenfunction of H, 82, and 5z. Let such a function be denoted by PSMs in which 5 and Ms specify the eigenvalues of 82 and 5z, respectively. In this way, the form which must be taken by an antisymmetric spin-eigenstate N -electron wave function can be derived. For instance, as is well known, the general form of wave functions with N =2,5=0, Ms=O is + {1p (12) 1p (2I)} {oc (1) P( 2) - P( 1) oc (2)} (1.2) P where 1p (12) is an arbitrary two-electron spatial function, and oc and are the usual spin functions. If an "exact" eigenfunction of H for a two electron system were obtained, it would naturally be of this form. Such a "general" form of wave function is easily written explicitly for each set of values of N, 5, and Ms. Any appropriate form of approx imate wave functions, like determinantal functions composed of one electron functions ("molecular spin orbitals"), the "bond eigenfunctions" used in the valence bond approach, and so on, is shown to fulfil this requirement. Some of these approximate forms of wave function possess a character of particular theoretical interest. One such is the "uni-configurational" wave function. This implies an appropriate linear combination of anti symmetrized products of molecular spin orbitals in which all antisym metrized products belong to the same "electron configuration". The electron configuration of an antisymmetrized product is defined as the set of N spatial parts appearing in the product of spin orbitals. For instance, a uni-configurational wave function with N = 2, 5 = 0, M s = 0 is expressed as (iJ)-(ij) (1.3) where (i])= ji(l)OC(l)j(I)P(l)j etc., P i (2) oc (2) j (2) (2) 2 Molecular Orbitals and the set [ij] stands for the electron configuration. The spatial part of a spin orbital is often called simply an "orbital". The orbital which appears only once in an electron configuration is said to be "singly occupied", and that appearing twice "doubly occupied". The general form of such uni-configurational wave functions can be obtained for any set of N, 5, and Ms. It is easy to see that such a form of wave functions duly satisfies the general requirement mentioned above, as in Eq. (1.2). Some uni-configurational wave functions consist of only one deter minant. This is called a single-determinant wave function. A single-deter minant can be a spin-eigenstate wave function only if the eigenfunctions possess the values of 5= JMsJ =l(N -2 v) where v is the number of doubly occupied orbitals in the determinant. Thus [case A] open-shell wave functions with maximum multiplicity (v=O, 5= JMsJ =N/2) , [case B] closed-shell wave functions (v=N/2, 5= JMsl =0), and [case C] wave functions with a closed-shell structure of v doubly occupied orbitals with additional open-shell structure of 5=IMsl=l(N -2 v) belong to this category. Any other uni-configurational wave functions consist of more than one determinant. We can discuss the "best" uni-configurational wave function by the usual variational method of the Hartree-Fock -type. This means making a search for the function P which minimizes the quantity f p* H PdT / f p* PdT. (1.4) If an excited state is concerned, this is done under the restriction that the function should be orthogonal to all of the lower-energy states. We may specify these as the "uni-configurational Hartree-Fock wave functions". The "best" orbitals constructing the determinants in these wave functions are in general not orthogonal to each other. In [case A] and [case B] mentioned above, the "best" wave function thus obtained is of particular practical importance. The set of N orbitals appearing in these functions is in general definitely determined, except for an arbitrary numerical factor of which the absolute value is unity, as being mutually orthogonal and having a definite "orbital energy" [d. 3 Molecular Orbitals Eq. (3.15)]. The concept of "electron occupation" of orbitals is thus unequivocal in these cases. The best orbitals in these cases are called "Hartree-Fock orbitals" 2,3). The wave function of [case A] is in general written in the form (,h(l) <P2(1) ------ <pN(I) 1 <Pi (2) <P2 (2) ------ <PN (2) V N! ------------------- (1(8) (1, 2, -----N) (1.5) <pl(N) 1>2(N) ---- <PN(N) where <Pt (k) is the ith orbital occupied by the kth electron and (1(8) (1,2,-----N) is the totally symmetric N-electron spin function. The wave function of [case B] with N = 2 can be written as 1 V2 <Pl(l) <Pi (2) {cx(l) {J(2) - {J(I) cx(2)} (1.6) The closed-shell wave functions with N > 2 can no longer be separated into spatial and spin parts, but are expressed in the following form: 1>1(1) cx(l) <Pl(l) {J(I) <P2(1) cx(l) <P2(1) {J(I) ---<p,,(I) cx(l) <p,,(I) {J(I) <Pl(2) cx(2) ----------------------------- <p,,(2) {J(2) I V 1 (1.7) (2,,)! ------------------------------------------- I 1>l(N) cx(N) ---------------------------<p,,(N) {J(N) Such a determinantal form of wave function is often called the Slater determinant. Thus, we have the N-electron wave function with separated spatial and spin parts only in the cases of two-electron singlet states and N + electron (N 1)-plet states. The Hartree-Fock orbitals are defined as those functions 1>, which make the wave functions (1.5), (1.6), and (1.7) best. The usual variation technique leads to the N(case A) or 1I(case B) simultaneous differential equations which have to be satisfied by <Pt (i = 1,2,---N in case A, and i = 1, 2,---11 in case B). These equations are called the Hartree-Fock equations. The Hartree-Fock orbitals are obtained by solving these differential equations simultaneously. Besides the occupied orbitals, these equations possess solutions corresponding to actually unoccupied, virtual orbitals. Some of them happen to possess negative energies (corresponding to "bound one-elec- 4 Molecular Orbitals tron states"), whereas the others have nonnegative energies. The Har tree-Fock unoccupied orbital, rather than its realistic physical meaning, is important in the sense that it is used in constructing excited-state wave functions and plays a significant role in the theory of chemical inter actions (Chap. 3). It is to be remarked that the mathematical means suitable for describing the unoccupied orbitals are not always the same as those representing the occupied orbitals with tolerable approx imation. The Hartree-Fock equations for the hydrogen molecule have been solved by Kolos and Roothaan 4), by obtaining the binding energy value of 3.63 e V for the ground state, which is ca. 1.1 e V smaller than the exact theoretical value 4,5). This difference corresponds to the corre lation error. The Hartree-Fock orbital energies of other homonuclear diatomic molecules, C2, N 2, O2 and F 2, have been obtained by Buenker et al. 6). A review has been given by Wahl et al. 7) with illustrative orbital maps for the F2, NaF, and N2 molecules. Also calculations have been made with respect to simple hydrocarbons such as CH4, C2H6, C2H4, and C2H2 6,8,9). The Hartree-Fock orbitals are expanded in an infinite series of known basis functions. For instance, in diatomic molecules, certain two-center functions of elliptic coordinates are employed. In practice, a limited number of appropriate atomic orbitals (AO) is adopted as the basis. Such an approach has been developed by Roothaan 10). In this case the Hartree-Fock differential equations are replaced by a set of nonlinear simultaneous equations in which the limited number of AO coefficients in the linear combinations are unknown variables. The orbital energies and the AO coefficients are obtained by solving the Fock-Roothaan secular equations by an iterative method. This is the procedure of the Roothaan LCAO (linear-combination-of-atomic-orbitals) SCF (self consistent-field) method. The basis AO adopted may be Slater-type orbital (STO) 11), Gaussian type orbital (GTO) 12), and Hartree-Fock AO 13), Lowdin's orthogonaliz ed AO 14), and so on. In many cases the Slater AO's for the valence-shell electrons are taken. Clementi has extended the basis beyond the valence shells 15). Frequently, the exponents of Slater AO's are optimized. Clementi has also adopted two different variable exponents for "one" Slater AO 15). Even an exact Hartree-Fock calculation cannot be exempt from the correlation error. A practical method of evaluation has been proposed by Hollister and Sinanoglu 16). An LCAO SCF method has been applied to the calculation of the heat of various simple reactions by Snyder and Basch 17). They have evaluated the correlation error by the method of Hollister and Sinanoglu 16). 5