Topics in organometallic chemistry vol 12 theorectical aspects of transition metal catalysis 2005 springer

2 The Role of the Lower-Lying Electron States of Transition Metal Cations in Oxidative Addition of the s s-Bonds such as H-H, C-H and C-C The study of gas-phase activation of H-H, C-H

Topics in Organometallic Chemistry

Editorial Board:

J.M Brown · P.H Dixneuf · A Fürstner · L.S Hegedus

P Hofmann · P Knochel · S Murai · M Reetz · G van Koten

Palladium in Organic Synthesis

Volume Editor: J Tsuji

in Organic Synthesis and Catalysis

Volume Editor: E.P Kündig Vol 7, 2004

Organometallics in Process Chemistry

Volume Editor: R.D Larsen Vol 6, 2004

Organolithiums in Enantioselective Synthesis

Volume Editor: D.M Hodgson Vol 5, 2003

Organometallic Bonding and Reactivity: Fundamental Studies

Volume Editors: J.M Brown, P Hofmann Vol 4, 1999

Activation of Unreactive Bonds and Organic Synthesis

Volume Editor: S Murai Vol 3, 1999

Lanthanides: Chemistry and Use

in Organic Synthesis

Volume Editor: S Kobayashi Vol 2, 1999

Alkene Metathesis in Organic Synthesis

Volume Editor: A Fürstner Vol 1, 1998

Recently Published and Forthcoming Volumes

of Transition Metal Catalysis

Volume Editor : G Frenking

With contributions by

D V Deubel · G Drudis-Sole · G Frenking · A Lledos · C Loschen

F Maseras · A Michalak · K Morokuma · G Musaev

S Sakaki · V Staemmler · S Tobisch · G Ujaque · T Ziegler

23

lic chemistry, where new developments are having a significant influence on such diverse areas as organic synthesis, pharmaceutical research, biology, polymer research and materials science Thus the scope of coverage includes a broad range of topics of pure and applied organometallic chemistry Coverage is designed for a broad academic and industrial scientific readership starting at the graduate level, who want to be informed about new developments of progress and trends in this increasinly interdisciplinary field Where appropriate, theoretical and mechanistic aspects are included in order to help the reader understand the underlying principles involved.

The individual volumes are thematic and the contributions are invited by the volumes editors.

In references Topics in Organometallic Chemistry is abbreviated

Top Organomet Chem and is cited as a journal

Springer WWW home page: springeronline.com

Visit the Top Organomet Chem contents at springerlink.com

Library of Congress Control Number: 2004116518

ISSN 1436-6002

ISBN-10 3-540-23510-8 Springer Berlin Heidelberg New York

ISBN-13 978-3-540-23510-8

DOI 10.1007/b94252

Bibliographic information published by Die Deutsche Bibliothek

Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliographie; detailed bibliographic data is available in the Internet at <http://dnb.ddb.de>.

This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks Duplication of this publication

or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965,

in its current version, and permission for use must always be obtained from Springer-Verlag Violations are liable to prosecution under the German Copyright Law.

Springer is a part of Springer Science+Business Media

Typesetting: Fotosatz-Service Köhler GmbH, Würzburg

Production editor: Christiane Messerschmidt, Rheinau

Cover: design & production GmbH, Heidelberg

Printed on acid-free paper 02/3141 me – 5 4 3 2 1 0

Professor Dr Gernot Frenking

Prof John M Brown

Dyson Perrins Laboratory

South Parks Road

Oxford OX1 3QY

Prof Gerard van Koten

Department of Metal-Mediated Synthesis

Debye Research Institute

hegedus@lamar colostate.edu

Prof Paul Knochel

Fachbereich Chemie Ludwig-Maximilians-Universität Butenandstr 5–13

Yamadaoka 2-1, Suita-shi Osaka 565, Japan

murai@chem.eng.osaka-u.ac.jp

For all customers who have a standing order to Topics in OrganometallicChemistry, we offer the electronic version via SpringerLink free of charge.Please contact your librarian who can receive a password for free access to thefull articles by registration at:

springerlink.com

If you do not have a subscription, you can still view the tables of contents ofthe volumes and the abstract of each article by going to the SpringerLinkHomepage, clicking on “Browse by Online Libraries”, then “Chemical Sciences”,and finally choose Topics in Organometallic Chemistry

You will find information about the

– Editorial Board

– Aims and Scope

– Instructions for Authors

– Sample Contribution

at springeronline.com using the search function

is also Available Electronically

It has been stated in the past that the search for new catalysts has more the character of an art than a science discipline This is because there was usuallymore speculation than true knowledge about the reaction mechanisms ofcatalytic processes Even the identity of the catalytically active species was frequently not known, which is the reason that systematic testing of all pos-sibly interesting compounds for catalytic reactions was carried out This iscostly and time consuming The situation has changed in the last decadebecause much progress has been made in understanding the mechanisms ofmany catalytic reactions Besides sophisticated experimental tools, quantumchemical calculations of transition states and reaction intermediates played

a prominent role in gaining much better insight into the fundamentals oftransition metal catalysis Estimating solvent effects and the calculation ofspectroscopic data are now routinely included in many theoretical studies.Although the design of new catalytically active species is still largely a trial-and-error process, modern research is guided by theoretical calculations inthe search for new catalysts, which helps researchers to focus on more promis-ing compounds The progress in quantum chemical method development hasled to the present situation where theory and experiment are synergisticallyused in an unprecedented manner In particular, the calculation of transitionmetal compounds is no longer a too-difficult task for quantum chemistrybecause efficient methods are available for dealing with many-electron atomsand with relativistic effects

The seven articles in this volume do not provide a comprehensive view oftheoretical investigations of catalytic reactions, because the field has expandedalready beyond the scope that can be covered in one book The contributionswritten by experts in the field exemplarily demonstrate the strength but alsothe present limitations of quantum chemical methods for giving insights intothe mechanism of transition-metal mediated reactions Because the develop-ment of new theoretical methods is still a very active research area, much progress can be expected in the coming years

G Drudis-Solé · G Ujaque · F Maseras · A Lledós 79

Organometallacycles as Intermediates in Oxygen-Transfer Reactions Reality or Fiction?

D V Deubel · C.Loschen · G Frenking 109

Late Transition Metals as Homo- and Co-Polymerization Catalysts

A Michalak · T Ziegler 145

Co-Oligomerization of 1,3-Butadiene and Ethylene Promoted

by Zerovalent ‘Bare’ Nickel Complexes

Transition Metal Catalyzed s s-Bond Activation

and Formation Reactions

Djamaladdin G Musaev ( ) · Keiji Morokuma

Cherry L Emerson Center for Scientific Computation and Department of Chemistry, Emory University, 1515 Dickey Dr., Atlanta GA 30322, USA

dmusaev@emory.edu, morokuma@emory.edu

1 Introduction 2

2 The Role of the Lower-Lying Electron States of Transition Metal Cations in Oxidative Addition of the s s-Bonds (such as H-H, C-H and C-C) 2

3 Role of Cooperative Effects in the Transition Metal Clusters 6

3.1 Reaction of Pt and Pd Metal Atoms with H2/CH4Molecules 7

3.2 Reaction of Pd2and Pt2Dimers with H2/CH4Molecules 9

4 s-Bond Activation via Nucleophilic Mechanism: the Role of Redox Activity of the Transition Metal Center – Hydrocarbon Hydroxylation by Methanemonooxygenase (MMO) 10

5 Vinyl-Vinyl Coupling on Late Transition Metals Through C-C Reductive Elimination Mechanism 17

5.1 Reductive Elimination from Pt IV Halogen Complexes [Pt(CH=CH2)2X4] 2– (X=Cl, Br, I) 18

5.2 Reductive Elimination from Mixed Pt IV Complexes [Pt{cis-/trans-(CH=CH2)2(PH3)2}Cl2] 19

5.3 Reductive Elimination from Pt II Halogen Complexes [Pt(CH=CH2)2X2] 2– (X=Cl, Br, I) 21

5.4 Reductive Elimination from Pt II Complexes with Amine and Phosphine Ligands [Pt(CH=CH2)2X2] (X=NH3, PH3) 21

5.5 Reductive Elimination from Pd IV Complexes [Pd(CH=CH2)2X4] 2– (X=Cl, Br, I) 23 5.6 Reductive Elimination from Mixed Pd IV Complex [Pd{trans-(CH=CH2)2(PH3)2}Cl2] 23

5.7 Reductive Elimination from Pd II Halogen Complexes [Pd(CH=CH2)2X2] 2– (X=Cl, Br, I) 23

5.8 Reductive Elimination from Pd II Complexes with Nitrogen and Phosphine Ligands [Pd(CH=CH2)2X2] (X=NH3, PH3) 23

5.9 Reductive Elimination from Rh III , Ir III , Ru II and Os II Complexes 24

5.10 General Discussion 24

5.11 Comparison of the Vinyl-Vinyl (Csp2-Csp2) and Alkyl-Alkyl (Csp3-Csp3) Reductive Elimination 26

6 Concluding Remarks 27

References 27

© Springer-Verlag Berlin Heidelberg 2005

Abstract The factors controlling the transition metal catalyzed s-bond (including H-H,

C-H and C-C) activation and formation, the fundamental steps of many chemical mations, were analyzed It was demonstrated that in the mono-nuclear transition metal systems the (1) availability of the lower lying s 1 d n–1 and s 0 d n states of the transition metal atoms, and (2) nature of the ligands facilitating the reduction of the energy gap between the different oxidative states of the transition metal centers are very crucial Meanwhile, in the transition metal clusters the “cooperative” (or “cluster”) effects play important roles in the catalytic activities of these clusters Another important factor affecting the catalytic activity

transfor-of the transition metal systems shown to be their redox activity.

1

Introduction

Sigma-bond (including H-H, C-H and C-C) activation and formation are fundamental steps of many chemical transformations and have been subject ofnumerous review articles [1] It is well accepted that certain transition metal

complexes significantly facilitate the s-bond activation/formation steps, which

may occur via various mechanisms, including oxidative addition/reductiveelimination, metathesis and nucleophilic attack However, the factors affectingH-H, C-H and C-C activation/formation still need to be clarified in detail Inthis chapter we intend to analyze some factors that control the catalytic activ-ity of transition metal complexes toward H-H, C-H and C-C bond activation/formation Namely, we elucidate the role of (a) lower-lying electronic states oftransition metal cations/atoms, (b) cooperative effects in transition metal clus-ters, (c) redox activity of the transition metal centers, and (d) the role of metaland ligand effects in vinyl-vinyl coupling

2

The Role of the Lower-Lying Electron States of Transition Metal Cations

in Oxidative Addition of the s s-Bonds (such as H-H, C-H and C-C)

The study of gas-phase activation of H-H, C-H and C-C bonds of the gen molecule and saturated hydrocarbons, respectively, by bare transitionmetal atoms and cations is very attractive for getting insight to the mecha-nisms and factors (such as nature of metal atoms and their lower-lying electronic states) controlling catalytic activities of transition metal complexes.Such studies, which are free from the ligand and solvent effects, have been subject of many experimental [2] and theoretical [3] papers in the past 10–15 years Experimental studies indicate that reaction of some transitionmetal cations (such as Fe+, Co+, and Rh+) with methane exclusively leads to the ion-molecule complex M+(CH), while others (such as Sc+ and Ir+) pro-

ceed further via oxidative addition mechanism and leads to methyl and/or MCH2++H2products In order to find some insight to the dif-ference in the reactivity of early and late, as well as first-, second- and third-row transition metal cations (TMCs), we have studied the mechanism ofthe reaction of M+(M=Sc, Fe, Co, Rh and Ir) with CH4at the CASSCF and MR-SDCI levels of theory in conjunction with large basis sets The results ofthese studies have been published elsewhere [4] Here we discuss generaltrends, factors controlling reactivity of the transition metal cations toward

hydrido-metal-s-bonds, and predict the most favorable metal cations that can efficiently

insert into s-bonds.

As expected, the first step of the reaction M++CH4 is the formation ofion-molecule complex M+(CH4) (see Fig 1, which, as an example, includes thepotential energy surface of the reaction Ir++CH4at the several lower-lyingelectronic states of the Ir cation) Our calculations show that these complexesare structurally non-rigid, where M+can nearly freely rotate around the CH4molecule by the pathways (C2v)´(C3v, TS)´(C2v)´… and/or (C3v)´(C2v,

TS)´(C3v)´…, depending on the nature of metal atom and the electronic

state of the complex M+(CH4) These complexes are stable by 21.9 (M=Sc), 15.5(13.7±0.8) (M=Fe), 21.4 (22.9±0.7) (M=Co), 16.8 (M=Rh), and 20.7 (M=Ir)kcal/mol relative to the ground state dissociation limit M++CH4(experimen-tal values are given in parentheses)

From the resultant M+(CH4) complex the reaction proceeds via the C-Hbond activation transition state (TS) to give the hydrido-metal-methyl cationcomplex, HMCH3+ In this step the C-H s-bond is broken and M-H and M-CH3

bonds are formed.Also, the oxidation number of the M-center increases by two

In order to analyze the reactivity of TMCs toward C-H (as well as H-H and C-C) bond, one has to elucidate the factors controlling thermodynamics and kinetics of the reaction M+(CH4)ÆHMCH3+

Our [4] and other [3] studies have shown that thermodynamics of the reaction M+(CH4)ÆHMCH3+is controlled by the two factors The first factor isthe availability of the s1dn–1state of the cation M+, which is expected to be thedominating bonding state in the resultant HMCH3+complex The second factor

is the loss of exchange energy (the loss of high-spin coupling (exchange energy)between valence electrons on the unsaturated transition-metal ion subsequent

to the formation of covalent metal-ligand bonds) upon formation of M-H andM-CH3bonds [5] Upon formation of M-H and M-CH3bonds, which stabilizethe system, the loss of exchange energy occurs and counteracts the stabilization

favor-able one (or easily availfavor-able, i.e the promotion energy from the ground state to

one can easily explain the calculated trends in the exothermicity of the reaction

M+(CH4)ÆHMCH3+, and predict thermodynamically the most favorable tion M+(CH)ÆHMCH+

reac-Our studies show that the reaction M+(CH4)ÆHMCH3+is endothermic by20.3, 32.3, 37.7 and 40.3 kcal/mol for M=Sc, Fe, Co, and Rh, respectively, while

it is exothermic by 8.7 kcal/mol for M=Ir This trend in the energy of the tion M+(CH4)ÆHMCH3+can be qualitatively explained in terms of the energygap between the lower lying s0dn and s1dn–1states of the metal cations and thenecessary exchange energy loss for formation of two covalent bonds to the

reac-s1dn–1state Indeed, the s1dn–1state is a ground state for Ir+, and thus Ir+can

easily form two M-L s-bonds While the ground states of the Sc and Fe cations

are the s1dn–1states, these cations need 3.7 and 41.4 kcal/mol energy (exchangeenergy loss for formation of two covalent bonds to the s1dn–1state) to form twoM-L bonds Meanwhile the ground electronic configurations of Co and Rh arethe s0dnstates, and the calculated exchange energy loss for formation of two covalent bonds to the s1dn–1state plus s0d8Æs1d7promotion energy are 39.2 and77.5 kcal/mol for Co+and Rh+, respectively Thus, the calculated trend in the energy of the reaction M+(CH4)ÆHMCH3+, Ir (–6.6)<Sc (20.3)<Fe (32.3)<Co(37.7)<Rh (40.3), is in a qualitatively agreement with the calculated exchangeenergy loss for formation of two covalent bonds plus the cost of promotion

to the s1dn–1state: Ir<Sc (3.7)<Fe+(41.4)~Co+(39.2)<Rh+(77.5) [5] As the exchange plus promotion costs for formation of two bonds increases via Sc+

(3.7)<Ti+(13.3)<V+(32.9)<Cr+(72.7) and then decreases via Mn+(51.6)>Ni+

(41.6)~Fe+ (41.4)>Co+(39.2) (in kcal/mol) [5],we expect that the namic stability of insertion product to decrease via M=Sc+>Ti+>V+>Cr+andincrease Mn+<Ni+~Fe+~Co+ Furthermore, it is well established that the s1dn–1

thermody-state becomes the most favorable, and the M-L bond strength significantly creases for the third-row transition metal cations Therefore, one may expectthat exothermicity of the reaction M+(CH4)ÆHMCH3+will significantly increaseupon going from the first- and second-row TMCs to the third-row

in-Meanwhile, the kinetic stability (existence of the C-H bond activation TS andthe barrier height) of the HMCH3+complexes is mainly controlled by: (1) theendothermicity of reaction M+(CH4)ÆHMCH3+ The large endothermicity ofreaction reduces the barrier for the reverse reaction HMCH3+ÆM+(CH4), andmakes HMCH3+unstable relative to M+(CH4).As noted above, our studies showthat the reaction M+(CH4)ÆHMCH3+is endothermic by 20.3, 32.3, 37.7 and40.3 kcal/mol for M=Sc, Fe, Co, and Rh respectively, while it is 8.7 kcal/molexothermic for M=Ir (2) The availability of the s0dnelectronic configuration ofthe metal center It is well known that upon oxidative addition of the C-H/H-H

s-bond to transition metal center a charge transfer from the doubly occupied

C-H/H-H s-orbitals to the s (s and d s) orbitals of metal center (called

“dona-tion”) and from metal p-orbitals to the s*antibonding orbital of the C-H/H-Hbond (called “back donation”) takes place (see Scheme 1)

These interactions are efficient when the metal center has empty (or partially

empty) s-type s and d s, orbitals and occupied dporbitals Since Fe+, Co+, Rh+,and Ir+(and all late transition metal atoms) have double occupied dporbitals but

Sc+(and all early transition metal atoms) has none, the “back donation” effect

is expected to be larger for late transition metals compared to the early ones

In contrast, transition metal cations such as Co+and Rh+, have the s0dngroundstate with empty s-orbital as opposed to Sc+, Ir+, and Fe+, and one may expect

the strong s(C-H)Æ(s,d s) (M) donation effects for the former cations Thus,availability of the s0dnstate (with doubly occupied dpand empty s-orbitals) for

Co+and Rh+, as well as Fe+, facilitates both “donation” and “back donation”

effects and makes the s-bond activation significantly easier for these cations

compared to Sc+and Ir+ This statement is consistent with the calculated trends;the reverse reaction HMCH3+ÆM+(CH4) occurs without barrier and is con-trolled by thermodynamic factors for M=Fe+, Co+and Rh+ Meanwhile reaction

M+(CH4)ÆHMCH3+occurs with energetic barrier of 38.5 and 2.1 kcal/mol, forM=Sc and Ir, and is controlled by both thermodynamic and kinetic factors Thereverse reaction HMCH3+ÆM+(CH4) occurs with 18.2 and 10.8 kcal/mol barri-ers for M=Sc and Ir, respectively

On the basis of these discussions, we conclude that: (1) The s 0 d n state of the

and (3) all early first-row (Sc + , Ti + and V + ) transition metals cations, having

stabilize the oxidative addition product complexes.

3

Role of Cooperative Effects in the Transition Metal Clusters

In this section we expand the conclusions of the previous section to bare tion metal clusters in order to test them again and to identify another,“coopera-tive”(or “cluster”) effect that affects the reactivity of transition metals In practice,transition metals are important ingredients of heterogeneous and nano-catalysts,therefore clear understanding of their reactivity at electronic level is essential tounravel the secret of their catalytic activities Diverse classes of experimental andtheoretical studies already have provided a wealth of information concerning theelectronic structure, spectroscopic as well as dynamic properties of variety types

transi-of clusters, including Pt [6], Pd [7], Fe+[8], Co+[9], and Nb+[10]

M-(HX) interaction

In particular, in the experimental work of Cox et al [6, 7], the measured rateconstants of CH4and H2activation by unsupported Pt and Pd clusters (n=6~24)show a large variation as functions of the cluster size In the case of Pt clusters,

it was found that dimer through pentamer were the most reactive, while the reactivity dropped significantly starting from Pt6 The single Pt atom was less reactive compared to Pt2–5by an order of magnitude, and the bulk was less reactive by at least several orders of magnitude In the case of Pd clusters, it wasfound that the activation rate constants for both H-H and C-H bonds show sig-nificant oscillation in terms of the cluster size The peak value of the measuredrate constant is around n=8 and 10, and the minimum rate constants have beenobserved for n=3 and n=9 Understanding the size-dependence of reactivity ofclusters has become one of the most fascinating and intriguing issues in clusterchemistry [11]

To unravel the reason behind the observed variation of reactivity as a tion of cluster size [6, 7], we have chosen to study the detailed mechanism of

func-H2and CH4activation on small Ptn and Pdn(n=1–6) clusters Results of thesestudies have already been published [12] Here, we intend to analyze the factorscontrolling the reactivity of these clusters

3.1

Reaction of Pt and Pd Metal Atoms with H 2 /CH 4 Molecules

First of all, we recall briefly the electronic structure and reactivity of Pd and Ptatoms, shown in the previous section, since they are the fundamental buildingblocks of the clusters and their characteristics have a major influence on theproperties of clusters According to a large number of theoretical as well as experimental studies, Pd and Pt atoms have very different electronic structuresand consequently distinct reactivities The ground state of Pd atom has a closed-shell s0d10configuration, where the open-shell s1d9(3D) state is 21.9 kcal/molabove [13] Therefore, based on the conclusions of the previous section, onemay expect that the Pd atom cannot break the H-H or C-H bonds in H2and CH4and rather forms molecular complexes Pd(H2) and Pd(CH4), respectively The calculated Pd-H2bond energy is 16.2 kcal/mol For the Pt atom, the s1d9(3D)state is the ground electronic state, while the s0d10configuration is 11.1 kcal/molhigher in energy [13] Consequently, it has been observed that Pt atom breaksthe H-H and C-H bond, in agreement with the conclusions of the previous sec-tion Since the ground state of Pt atom is a triplet but resultant HPtH or HPtCH3

is a singlet, a curve crossing from the triplet to the singlet state is required, andthe minimum crossing point can be viewed as the transition state for the acti-vation process starting from the ground electronic state atom (Fig 2a) Thebinding energy of H2and CH4to the Pt atoms is 47.4 kcal/mol and 34.3 kcal/mol,respectively Thus, the calculated results for the reactions Pd+H2/CH4 andPt+H2/CH4once again confirm our conclusions from the previous section

Reaction of Pd 2 and Pt 2 Dimers with H 2 /CH 4 Molecules

As seen in the potential energy profile of these reactions, shown in Fig 2b–d,both Pd2and Pt2activate H-H/C-H bonds with very small barrier In reaction

Pt2+H2/CH4, H-H/C-H activation preferentially takes place on a single metalatom.Afterwards, one of the H atoms migrates to the other Pt atom over a neg-ligible isomerization barrier On both the singlet and the triplet state, H-H activation is expected to be barrierless, while C-H activation has a distinct barrier on the triplet state for reaction starting from the ground triplet state Pt2.Nevertheless, since the barrier for C-H activation on the triplet state is smalland lower than the expected minimum of seams of crossing (MSX) betweensinglet and triplet in the Pt-CH4system, it is expected that Pt2activates the C-H bond in CH4with a faster rate than the Pt atom, which is in accord with theexperimental observation of Cox et al [6, 7]

Calculations show that the ground state of the reactants Pd2+H2/CH4is atriplet state, while the product complexes have a singlet ground state Therefore,one may expect that the reaction proceeds either on the excited singlet statesurface or through the minimum of triplet-singlet seams of crossing On thesinglet state potential energy surface of Pd2+H2/CH4(see Fig 2b,c) the reaction

is downhill without activation transition state Meanwhile, the calculatedtriplet-singlet MSX lies lower in energy than the triplet state transition state.Therefore, the H2/CH4activation by Pd2starting from the triplet ground statedimer is expected to proceed via an intersystem crossing mechanism with very

small barrier Interestingly, the activation of s-bonds occurs only upon

per-pendicular approach of H-H/C-H bonds to the Pd-Pd bond

Thus, in contrast to the single atom case where Pd and H2/CH4form only amolecular complex and no H-H/C-H bond cleavage occur, two Pd atoms work

“cooperatively” and readily break H2/CH4 This “cooperative” mechanism for

H2/CH4activation on Pd2is different from the case of Pt2+H2/CH4 In Pt2dimer

H2/CH4activation takes place preferentially on a single atom, while in Pd2dimer

it occurs on the Pd-Pd bond Moreover, in the final activation products, H/CH3groups prefer the bridged sites of Pds, but are localized on metal sites in Pt2.Those results can be rationalized as the following, as illustrated in Scheme 2 Thesinglet state Pd2consists of mainly two s0d10Pd atoms, and the LUMO sghas acorrect symmetry to accept electron density effectively from the H2/CH4s orbital

upon perpendicular approach.As a result, the activation takes place preferentially

in this approach In the case of Pt2+H2/CH4reaction, the metal HOMO and LUMO

are of localized metal d character (as established in a number of studies of metal clusters, the s-s contribution in the metal-metal bonding is dominant, while d-d

interaction is weak) Therefore, the HOMO and LUMO of triplet Pt2are all of

localized d characters, while the s and s* orbitals that contain large s characters

are much lower and higher in energy, respectively, and therefore activation takesplace preferentially on a single atom (rather than on the Pt-Pt bond, where thestrongest HOMO/LUMO interaction between the metal and H is expected

Scheme 2 Orbital diagram of triplet Pd2and Pt2, MO energies (in hartree) are calculated at the full valence (20el./12orb.) CASSCF level

In the final singlet products, Pt2(H)2/Pt2(H)(CH3) and Pd2(H)2/Pd2(H)(CH3),the metal dimers actually are in their triplet configurations In the case of Pt2,

the metal-metal s bonding orbital is low in energy, and the Pt-H/CH3bond has

large d character Therefore, the H/CH3groups in Pt2(H)2/Pt2(H)(CH3) do notlike the bridged sites, but rather localize on each Pt atom In the case of Pd2, in

its triplet electronic state, the metal-metal s bonding orbital is the HOMO.

Therefore, both the CH3/H-Pd-Pd bonding and antibonding orbitals have muchmetal s component As a result, the H/CH3 ligands prefer the bridged sitesrather than the localized metal sites

Thus, our studies of the reactivity of Pd/Pt clusters with H2/CH4moleculesclearly show a “cooperative” effect that could play a significant role in the re-activity of the transition metal clusters Thus, the catalytically inactive metalatoms could form very active clusters !

4

s

s-Bond Activation via Nucleophilic Mechanism: the Role of Redox Activity

of the Transition Metal Center – Hydrocarbon Hydroxylation

by Methanemonooxygenase (MMO)

Another important factor controlling the reactivity of transition metal

cen-ters toward s-bond is their redox activity Indeed, it is well established that

transition metal centers with low redox potential can be active catalysts [14].For example, let us discuss the reactivity in hydrocarbon hydroxylation byMethanemonooxygenase (MMO)

MMO, one of the members of diiron-containing metalloenzyme family, is

an enzyme that catalyzes methane oxidation reaction, i.e conversion of the inert methane molecule to methanol [15] During this reaction two reducingequivalents from HAD(P)H are utilized to split the O-O bond of O2 One O atom

is reduced to water by 2-electron reduction, while the second is incorporatedinto the substrate to yield methanol:

CH4+ O2+ NAD(P)H + H+Æ CH3OH + NAD(P)++ H2O

Experimental studies [16] show that the best-characterized forms of the ble MMO (sMMO) contain three protein components: hydroxylase (MMOH),so-called B component (MMOB) and reductase (MMOR), each of which is re-quired for efficient substrate hydroxylation coupled to NADH oxidation Thehydroxylase, MMOH, which binds O2and substrate and catalyzes the oxidation,

solu-is a hydroxyl-bridged binuclear iron cluster In the resting state of MMOH(MMOHox), the diiron cluster is in the diferric state [FeIII-FeIII], and can acceptone or two electrons to generate the mixed-valence [FeIII-FeII] or diferrous state[FeII-FeII], respectively The diferrous state of hydroxylase (MMOHred) is theonly one capable of reacting with dioxygen and initiating the catalytic cycle

X-ray crystallographic studies of the enzyme from Methylococcus

capsula-tus (Bath) [17] and Methylosinus trichosporium OB3b [18] have unveiled

the coordination environment of the Fe centers of MMOHox and MMOHred.According to these studies, in MMOHox each Fe center has six-coordinate octahedral environment (see Scheme 3) Fe ions are bridged by a hydroxy ion,

a bidentate Glu g-carboxylate and a water molecule (or another carboxylate).

In addition, each Fe ion is coordinated by one His nitrogen ligand and onemonodentate Glu carboxylate The two Fe centers are different from each other

in that one of them (Fe2) has an additional monodentate glutamate carboxylate,while the other Fe (Fe1) has one additional water molecule Upon reduction, one

of carboxylate ligands undergoes a so-called “1,2-carboxylate shift” from being

a terminal, monodentate ligand bound to Fe2 to a monodentate, bridging ligand between the two irons, with the second oxygen of this carboxylate alsocoordinated to Fe2 In addition, the hydroxyl bridge is lost, and the other hydroxyl/water bridge shifts from serving as a bridge to being terminallybound to Fe1 Also, the terminal water bound to Fe1in the oxidized form ofMMOH seems to move out upon reduction of the cluster Thus, in reduced form

of MMOHredthe ligand environment of Fe ions becomes effectively five dinated, which is reasonable since this is the form of the cluster that activatesdioxygen

coor-It was established that MMOHred reacts very fast with O2 and forms a

metastable, so-called compound O, which spontaneously converts to another compound called P (see Scheme 4) Spectroscopic studies [19] indicate that compound P is a peroxide species, where both oxygens are bound symmetri- cally to the irons Compound P spontaneously converts to compound Q, which

was proposed to contain two antiferromagnetically coupled high-spin Fe(IV)

Scheme 4 Experimentally proposed catalytic cycle of MMO (see [15])

centers EXAFS and spectroscopic studies [20, 21] of compound Q, trapped

from M trichosporium OB3b and M capsulatus, have demonstrated that

com-pound Q has diamond core, (FeIV)2(m-O)2structure with one short (1.77 Å) andone long (2.05 Å) Fe-O bond per Fe atom and a short Fe-Fe distance of 2.46 Å

Compound Q has been proposed to be the key oxidizing species for MMO.

In the literature there have been several computational attempts [22–25] to

elucidate mechanism of methane oxidation by intermediate Q Our results [25]

show that reaction proceeds via the mechanism presented in Fig 3 Later, thismechanism was validated by several times and currently is well accepted

As seen in Fig 3, reaction of compound Q (modeled as structure I) with

methane starts with coordination of CH4 In general, the CH4molecule could

coordinate to I via two distinct pathways: O-side and N-side The O-side

path-way corresponds to the coordination of the methane molecule from the sidewhere the two Glu (carboxylate) located, while the N-side pathway corresponds

to the coordination of CH4from the two His (imidazole) side Our calculationsshow that both pathways proceed via very similar transition states and inter-mediates, and the N-side pathway is thermodynamically and kinetically morefavorable than O-side In spite of this, in this paper we base our discussions only

on the O-side mechanism because it is believe to correspond to the process occurring in the protein The coordination of CH4to complex I leads to the methane-Q complex, structure II The interaction between methane and struc- ture I (compound Q) is extremely weak; the complexation energy is calculated

(relative to the corresponding reactants) to be 0.7 and 0.3 kcal/mol for the

9A and 11A state, respectively Because of unfavorable zero point energy and

entropy factors, it is most likely that the complex II does not exist in reality, and

therefore we will not discuss it

Results in Table 1 show that the 9A state of structure I very qualitatively is the

Fe(IV)-Fe(IV) complex On the other hand, in the 11A state it is the Fe(III) mixed valence species, where Fe2 is in the Fe(III) state with five spins thatare heavily delocalized onto O2 The calculated fact that I_9 (here and below in

Fe(IV)-A_B , A is the structure, while B is the electronic state) is lower in energy than

I_11 suggests that Fe(IV)-Fe(IV) is the preferred state for complex I (and pound Q) This is consistent with the experimental conclusions [21].

com-The activation of the methane C-H bond takes place on the diamond oxygen

O1 At the TS1, structure III, the C-H bond to be broken is elongated from 1.089 Å in II to 1.271 Å and 1.296 Å in transition states III_9 and III_11 Fur-

thermore, the O-H bond is nearly formed, with distance of 1.250 Å and 1.241 Å

at the TSs, compared to 0.983 Å and 0.978 Å in products IV_9 and IV_11, respectively These geometrical changes indicate clearly that III_9 and III_11

are the TSs corresponding to the H abstraction process The H-abstraction barriers are calculated to be 23.2 and 19.0 kcal/mol for the 9A and 11A states,respectively, relative to the corresponding CH4complexes II_9 and II_11, re-

spectively These values of the barrier are in reasonable agreement with

avail-able experimental estimates, 14–18 kcal/mol [23] The spin densities for TS1, III, and product IV are found to be similar to each other within their respective 9Aand 11A states (see Scheme 5 and Table 1) Furthermore, the spin densities arenearly identical between 9A and 11A, except for those on the O2 H CH frag-

the methane activation reaction via O-site pathways: (NH2)(H2O)Fe(m-O)2(h2 -COO)2Fe(H2 (NH2)+CH4Æ(NH2)(H2O)Fe(m-O)(HOCH3)(h2 -HCOO)2Fe(H2O)(NH2)

O)-Scheme 5 The spin recoupling scheme in the intermediates of the reaction

densities (in e) of various intermediates and transition states, for 9 A and 11 A states, for the

reaction of the complex I with molecule of methanea The numbers after slash are relative

a Here, LnFe stands for the (H2O)(NH2)Fe-fragment This table does not include the portion

of spin densities located on the bridging carboxylate ligands, each of which may have about 0.10–0.15e spin.

b H atom located between O 2 and CH3fragments.

c The number for the entire CH fragment.

ment For the CH3 groupitself, the total Mulliken charge (not given in Table 1)

is at most +0.03e for both the 9A and 11A states and the spin densities on thisgroup for 9A and 11A are of same magnitude but of opposite sign One can

interpret all these values in the following way In both TSs, III_9 and III_11, a

radical center begins to develop on the CH3group, with spin densities of –0.46e

and +0.52e, respectively, and in both intermediates, IV_9 and IV_11, the CH3

group is now a real radical with spin densities of –0.98e and 1.00e, respectively.The spin densities on Fe1and Fe2in IV_9 and IV_11, which formally can be

written as L4Fe(m-O)(m-OH)FeL4with the methyl radical only weakly ing via a C HO interaction, can qualitatively be considered to correspond toFe(IV) with four spins and Fe(III) with five spins, respectively In going from

interact-II_9 to III_9, the very qualitative formal oxidation state of Fe2changes from

Fe(IV) to Fe(III), while from II_11 (which is already Fe(III)) to III_11, no such

change is required Since the two Fe centers are coupled ferromagnetically inboth 9A and 11A states, the spin of the CH3radical in both III and IV has to

couple antiferromagnetically (with negative spin) and ferromagnetically (withposition spin) to make the total spin 2S+1 equal to 9 and 11, respectively In the

radical complexes IV_9 and IV_11 the interaction of the CH3radical with thetwo iron atoms is very weak and, therefore, their total energies are nearly iden-tical It is quite interesting that we find that a mixed valence state is responsiblefor the methane oxidation reaction The present spin density analysis clearly

demonstrates that (1) the methane oxidation proceeds via a bound-radical

mechanism, and (2) the first electron transfer from substrate to Fe-centers occurs

through the TS1 and is completed at the resultant bound-radical complex IV.

The second electron transfer from the substrate to Fe-centers starts with therecombination of methyl radical with the bridging hydroxyl ligand at the tran-

sition state, TS2, structure V Indeed, our results show that in the 11A state upon

going from IV_11 to the methanol complex VI_11, Fe1changes its formal dation state from Fe(IV) with four spins to Fe(III) with five spins, while the spindensity on the methyl radical is completely annihilated upon forming a covalentbond between CH3and OH The transition state V_11 has a spin distribution between that of IV_11 and VI_11 On the other hand, in the 9A state upon going

oxi-from IV_9 to the methanol complex VI_9, the spin density on Fe1is reduced byabout 0.5, corresponding to the disappearance of roughly one unpaired electron.Since Fe(V) is not a stable species, it is most likely Fe1changed its formal oxi-dation state from Fe(IV) with four spins to Fe(III) with five formal d electrons.Because of the restriction 2S+1=9, i.e., the total number of unpaired electronsmust be 8 within the Fe(III)-Fe(III) core, Fe1in VI_9 chose to form one d-lone pair with only three spins remaining This complex VI_9 is thus higher in en- ergy than the corresponding complex VI_11 in violation of the Hund rule.

The barrier heights for the CH3addition to the hydroxyl ligand calculated

relative to the intermediate IV_9 and IV_11 are 9.3 and 7.3 kcal/mol for the 9Aand 11A states, respectively Obviously, this step of the reaction is not rate-de-termining, and can occur rather fast Overcoming the barriers at TS2 leads to

the complexes methanol-complexes VI, LFe(OHCH)(m-O)FeL, and completes

Vinyl-Vinyl Coupling on Late Transition Metals Through C-C Reductive Elimination Mechanism

Another important s-bond activation/formation process discussed in this

article is vinyl-vinyl coupling, shown in Scheme 7 Vinyl-vinyl coupling opens

a convenient route to conjugated 1,3-dienes and is widely employed in manycatalytic coupling reactions The great potential of the field is still under continuous development [26, 27] and, therefore, elucidation of the C-C bondformation mechanism and the factors controlling it are very crucial In litera-ture, numerous mechanistic studies on C-C reductive elimination and reverseprocess, oxidative addition (C-C bond activation), have been reported for di-

the second electron transfer process The overall reaction I + CH4ÆVI is

calculated to be exothermic by 34.3 and 46.8 kcal/mol for the 9Aand 11A states,respectively The final step of elimination of the methanol molecule and regen-eration of the enzyme could be a complex process, and possibilities of differentmechanisms exist but have not yet been studied computationally

Thus, these results clearly show that the Fe-centers are not directly involved

in methane C-H bond cleavage However, they play a crucial role in the methaneoxidation process, by accepting two electrons from the substrate Having lowoxidation potential for Fe-centers is definitely an important factor in thisprocess and significantly facilitates it Thus, during the hydrocarbon hydrox-ylation by MMO, the Fe centers undergo multiple reduction and oxidationsteps; at first, MMOHox [ Fe(III)-Fe(III) state] should be reduced (2-electron reduction) to MMOHred[Fe(II)-Fe(II) state], then it should be oxidized (4-elec-tron oxidation) by O2molecule to [Fe(IV)-Fe(IV) state], after which it again isreduced by substrate to Fe(IV)-Fe(III) state and Fe(III)-Fe(III) states (seeScheme 6) Thus facile oxidation and reduction of Fe-center plays a crucial role

in the hydrocarbon hydroxylation by MMO

alkyl or mixed complexes of Pt [28–34], Pd [31, 35], Rh [33], Ru [32] and Ir [33].Also, several theoretical investigations on C-C bond activation by Pt [36–39],

Pd [36–40], Rh [40–43] and Ir [42, 44] have been performed However, thesestudies were made for Csp3-Csp3and Csp3-Caryl(in most cases methyl-methyl andmethyl-aryl, respectively) bonds, and no theoretical study appears to have beencarried out for reductive elimination of unsaturated vinyl ligands leading to

a conjugated product Therefore, we have published [45] two theoretical (DFTand ONIOM) papers on the mechanism of vinyl-vinyl C-C reductive elimina-tion reaction on the transition metal complexes, major conclusions of which aresummarized here and compared with other C-C coupling processes We also intend to analyze the factors controlling these reactions

5.1

Reductive Elimination from Pt IV Halogen Complexes [Pt(CH=CH 2 ) 2 X 4 ] 2– (X=Cl, Br, I)

As shown in Fig 4, our calculations showed that the reaction involving vinyl

ligands may proceed via two different transition states, 1_TS and 1A_TS, which

possess s-cis and s-trans configuration around the central single bond,

respec-tively Their corresponding energies are given in Table 2 We note here that at

the B3LYP level of theory, the calculated relative energies of s-trans, s-gauche and s-cis conformers are 0.0, 3.5 and 4.0 kcal/mol respectively, in agreement

with earlier findings

Reductive elimination through the s-trans pathway retains C2symmetry andhas to overcome the activation barrier of 29.4 kcal/mol On the other hand, ini-

tial complex (1A_Init) and transition state (1A_TS) for s-cis pathway belong to

Cspoint group and the activation energy is 4.9 kcal/mol higher than for the mer (Table 2) In the latter process, the product buta-1,3-diene will be released

for-in the s-gauche (C2) form Reductive elimination reactions are exothermic by

17.0 and 19.9 kcal/mol for s-cis and s-trans pathways, respectively (Table 2).

Energy difference between the initial bis-s-vinyl complexes 1_Init and

order of the transition states (1_TS and 1A_TS) reflects the stability of

corre-sponding buta-1,3-diene isomers in a free form Thus, s-cis transition states are

expected to lie higher in energy and we will continue the study following the

s-trans pathway only.

Fig 4 S-cis and s-trans reductive elimination pathways from octahedral complexes

Upon examination of the C-C reductive elimination reaction from a series

of halogen complexes (PtIV: X=Cl, Br, I; Table 2), a clear trend is observed; theheavier the ligand, the smaller the activation barrier, and the larger the exother-micity of the process Therefore, the easier reductive elimination reactionshould be expected from iodide complexes of PtIVwith the activation energy

of only 25.0 kcal/mol and reaction energy of –30.3 kcal/mol

5.2

Reductive Elimination from Mixed Pt IVComplexes

[Pt{cis-/trans-(CH=CH 2 ) 2 (PH 3 ) 2 }Cl 2 ]

Introducing phosphine ligand either in cis or trans position to s-vinyl groups

favors C-C bond formation (Table 2) However, in the case trans substitution (4)

the influence is much larger, DE≠=18.5 kcal/mol, compared to DE≠=27.6 kcal/mol

for cis derivative (5) and DE≠=29.4 kcal/mol for the chloride complex (1) It

is found that lower activation barriers are accompanied by higher reaction

exothermicity (cf DEfor 1, 4 and 5 in Table 2).

Reactions of both 4 and 5 lead to the same products, trans-[Pt(PH3)2Cl2] and

buta-1,3-diene Therefore, the difference in reaction energies (DE) reflects the

relative stability of initial bis-s-vinyl derivatives; 5_Init is thermodynamically

more stable by 7.2 kcal/mol than 4_Init.Very likely, destabilization of 4_Init due

to mutual trans orientation of vinyl and phosphine ligands is responsible for

facilitating the reductive elimination process 4_InitÆ Æ 4_TSÆ Æ4_Prod

5.3

Reductive Elimination from Pt II Halogen Complexes [Pt(CH=CH 2 ) 2 X 2 ] 2– (X=Cl, Br, I)

C-C bond formation initiated from the square planar bis-s-vinyl complexes (6,

7 and 8) also proceeds through the three-centered transition state (Fig 5) Upon

metal-carbon s-bond breakage and reductive elimination, the coordination vacancy becomes available at the metal center and a p-complex of buta-1,3-di- ene is formed Double bond coordination (h2-C=C) to the metal atom is preferred in this case, while the structure with central C-C bond coordination

has an imaginary frequency corresponding to h2–C–CÆh2–C=C ment

rearrange-The same trend as noted above for PtIVis observed for the series of PtII

complexes (6 to 8, Table 2); heavier halogen ligands make C-C bond formation

easier by decreasing the activation energy and favoring the process dynamically However, comparing the C-C reductive elimination reaction from

thermo-PtII(6–8, Table 2) complexes with those of PtIV (1–3, Table 2) complexes, one can

deduce a clear preference of the higher oxidation state For the PtIVderivativesthe activation barriers are lower by 11.2–6.2 kcal/mol and the processes aremore exothermic by 16.2–18.0 kcal/mol than the corresponding PtII species

5.4

[Pt(CH=CH 2 ) 2 X 2 ] (X=NH 3 , PH 3 )

The energetics of the C-C bond formation reaction starting from the amine

complex 9 (DE≠=35.2 and DE=–8.5 kcal/mol) are similar to those for the mide derivatives (DE≠=35.4 and DE=–8.3 kcal/mol, Table 2).

bro-However, reductive elimination reaction from phosphine complex 10 is

much easier with the activation energy of only 19.3 kcal/mol and reactionexothermicity of –27.4 kcal/mol (Table 2) This barrier is only slightly higherthan that for the corresponding PtIVphosphine complex (4, Table 2) In addi-

tion, Pt(PH3)2 can be considered as a rather stable product in contrast toPt(NH3)2and PtX22–(X=Cl, Br, I) The finding is consistent with the experi-mental experience that phosphine is often added to reaction mixtures to keep the catalyst from decomposing so that the process can take place underhomogeneous conditions [1a, 28, 29, 46] Obviously, phosphine derivatives arethe best candidates for reductive elimination process among the PtII com-plexes

Reductive Elimination from Pd IV Complexes [Pd(CH=CH 2 ) 2 X 4 ] 2– (X=Cl, Br, I)

In the PdIVcomplexes, the C-C bond formation takes place rather easily with

very low barriers of 12.9 and 11.4 kcal/mol for 11 (X=Br) and 12 (X=I),

respec-tively (Table 2) These are about 14 kcal/mol lower than for the corresponding

PtIVcomplexes, while the exothermicity of the reactions is increased by as much

as 26 kcal/mol The high exothermicity suggests very early transition state tures The results (see Table 2) show that reductive elimination from PdIVcom-plexes would proceed most easily among the MIIand MIVhalogen derivatives(M=Pt, Pd)

struc-5.6

Reductive Elimination from Mixed Pd IVComplex [Pd{trans-(CH=CH2 ) 2 (PH 3 ) 2 }Cl 2 ]

We excluded from consideration the complexes with PH3ligands located cis to

very small effect of PH3on reaction energetics Previous PtIV/PtIIresults (4 and

10, Table 2) suggest that phosphines trans to carbons should significantly

facilitate the reductive elimination process This trend seems to be rather eral and applicable to PdIVcomplexes as well; the corresponding PdIV complex

gen-13with phosphines trans to carbons has a low activation barrier for C-C bond

formation of only 7.3 kcal/mol

5.7

Reductive Elimination from Pd II Halogen Complexes [Pd(CH=CH 2 ) 2 X 2 ] 2– (X=Cl, Br, I)

Within the series of PdIIhalogen complexes 14 (X=Cl), 15 (X=Br) and 16 (X=I),

the expected trends in the energies and geometry changes are again found;the heavier the halogen, the smaller the activation energy and the earlier the

transition state The smallest barrier is calculated for iodide complex DE≠=11.9 kcal/mol and the largest 18.9 kcal/mol for chloride, with bromide in-be-tween, 15.0 kcal/mol Increase in activation energies is accompanied by de-crease in exothermicity (Table 2).As discussed earlier for the corresponding Ptcompounds, reductive elimination reaction from PdIIhalogen complexes alsogives anionic Pd0species [47]

5.8

Reductive Elimination from Pd II Complexes with Nitrogen

and Phosphine Ligands [Pd(CH=CH 2 ) 2 X 2 ] (X=NH 3 , PH 3 )

The activation and reaction energies for the complexes with X=NH3and X=Br

(17 and 15 in Table 2) are similar: DE≠=15.0 and 15.3 kcal/mol and DE=–26.9

and –25.7 kcal/mol for X=Br and X=NH3, respectively Thus, both complexeswould show a similar reactivity in the reductive elimination process However,

the stability of [Pd0Br2]2–and [Pd0(NH3)2] relative to the corresponding

p-com-plex differs significantly, the former being ca 11 kcal/mol less stable than the latter For the PdIIphosphine complex 18 (X=PH3), vinyl-vinyl coupling reaction

is very easy, with the barrier of only 6.8 kcal/mol, the smallest barrier reported

in this article

5.9

Reductive Elimination from Rh III , Ir III , Ru II and Os II Complexes

We extended the study of C-C reductive elimination reactions to other members

of late transition metals in order to find possible alternatives to Pd/Pt complexesfor catalytic coupling reactions The calculations were performed only for thecorresponding phosphine complexes, for which experimental precedents for the

reaction were reported In the case of Rh and Ir derivatives, an extra s-bonded

ligand has to be added to maintain correct oxidation state, because RhIIand

IrIIcompounds are rarely known [48] The chloride has been chosen for this

purpose Thus the model compounds studied are 19 [RhIII(CH=CH2)2(PH3)3Cl],

20[IrIII(CH=CH2)2(PH3)3Cl], 21 [RuII(CH=CH2)2(PH3)3], and 22 [OsII(CH=CH2)2(PH3)3]

-As in the previous cases (Figs 4 and 5), vinyl-vinyl coupling for these pounds also occurs through the three-centered transition states The smallest ac-tivation barrier among these four compounds is found for RhIII19(17.8 kcal/mol),while those for the other complexes are considerably higher (28.1–34.1 kcal/mol)

com-To summarize, the present calculations show that RhIII-based complexes can beconsidered as possible catalysts for vinyl-vinyl reductive elimination, while IrIII,

RuIIand OsIIanalogs are likely to be less active Once again, our calculationsshown that the second raw metals have lower barriers as well as higher exother-micity than the third row metals within each subgroup RhIII>IrIIIand RuII>OsII

5.10

General Discussion

Thus, our calculations, in an agreement with the available experiments, havedemonstrated that the reactivity of the [M(CH=CH2)2Xn] complexes (for M=Pdand Pt) in C-C bond formation depends on the nature of the ligand X, and decreases in the order: X=PH3>I>Br,NH3>Cl for both MIVand MIIoxidationstates In all the cases, phosphine ligands decrease the activation barriers andincrease the exothermicity of the reaction The present results also show thatall the second row metals (Ru, Rh and Pd) show the lower barriers and higherexothermicity than the corresponding third raw metals (Os, Ir and Pt) withineach subgroup (Table 2), i.e the reactivity of the studied complexes decreasesvia PdII>PtII, PdIV>PtIV, RhIII>IrIII, and RuII>OsII The complexes of PtIV aremore reactive than corresponding complexes of PtII Similar results have beenobtained for Pd complexes, while for them this effect is less pronounced Con-sidering the most reactive phosphine complexes, the following overall relative

reactivity order in vinyl-vinyl coupling reaction may be suggested for thesemetals: PdIV, PdII>PtIV, PtII Thus, Pd complexes are suggested to be the most reactive for this reaction.

Furthermore, these results again demonstrate the importance of the

elec-tronic configuration of the metal for s–bond activation/formation reaction.As

pointed out earlier, the change in the degree of oxidation of metal atoms ing the oxidative addition/reductive elimination reactions could be described

dur-in terms of the promotion of electronic configuration of metal atoms In the M0,

MII, and MIVcomplexes, both Pt and Pd atoms possess d10, s1d9and s2d8tronic configurations, respectively.13 In M0no covalent bonds are possible, sinceall five d orbitals are doubly occupied In contrast, MIIand MIVatoms can maketwo and four covalent bonds, respectively, through the hybrid s and d orbitals.The energy differences between the lower-lying electronic configurations of Pdand Pt atoms, and the calculated average reaction energies for C-C reductiveelimination reactions of the Pd/Pt-complexes are given in Table 3

elec-As seen from Tables 3 and 2, the concept of lower lying electronic rations provides reliable qualitative description of the systems studied In particular, (i) MIVÆMIIreductive elimination is always more exothermic than

configu-MIIÆM0, which is consistent with the calculated s2d8Æs1d9and s1d9Æd10motion energies, and (ii) both PdIVÆPdIIand PdIIÆPd0processes are moreexothermic compared to PtIVÆPtIIand PtIIÆPt0, which is again agreed with thecalculated s2d8Æs1d9and s1d9Æd10promotion energies of Pd and Pt atoms Inagreement with the Hammond postulate, (i) the activation energies are lowerwhen the reaction starts from MIVderivatives than from MII, and (ii) C-C bondformation involving palladium complexes requires significantly smaller bar-riers than with platinum

elimina-tion reacelimina-tions from platinum and palladium complexes a,b

Reaction Atomic energy DEaverage

M IIÆM0 –21.9 11.1 –4.8 19.9 –33.8 –17.8 (s 1 d 9Æs0 d 10 ) (14–16) (6–8) [–15.4] [0.9]

a The compounds used for averaging are given in parentheses (see Table 2 for energies).

b For Pt II and Pd II , DE with respect to the final products (MX2+diene), rather than to plexes is used.

p-com-c Experimentally determined.

d Values for X=NH are given in brackets.

Similar considerations are also applicable for the reductive elimination reactions for the other platinum group metals Our calculations on reductiveelimination reactions have shown an energetic preference of RhIII com-pounds to IrIII, RuIIand OsIIcompounds The fact can be rationalized takinginto account that the only exothermic promotion energy of –37.6 kcal/mol13

is expected for s2d7Æs1d8(RhIIIÆRhI) In contrast, s2d7Æs1d8(IrIIIÆIrI) and

s1d7Æd8 (RuIIÆRu0) are endothermic by 25.1 and 9.2 kcal/mol tively [13]

However, the absolute values of activation energies computed for vinyl-vinylcoupling are significantly lower than that for methyl-methyl coupling Particu-

larly, DE≠=49.8 kcal/mol (MP4//MP2 level) [39a], DE≠=60.8 kcal/mol (MP4//HF)

[39b,c], and DH≠=41.1 kcal/mol (GVB) [37a] were reported for ethane reductiveelimination from [PtII(CH3)2(PH3)2] The values are much higher than DE≠=1

9.3 kcal/mol (DH≠=18.2 kcal/mol) calculated in the present work for vinyl-vinylcoupling from [PtII(CH=CH2)2(PH3)2] Ethane elimination from [PdII(CH3)2-(PH3)2] was found to proceed with DH≠=10 kcal/mol (GVB) [37a] and

DE≠=26.3 kcal/mol (MP4//HF) [39c], while our value for [PtII(CH=CH2)2(PH3)2]

is again lower DE≠=6.8 kcal/mol (DH≠=5.9 kcal/mol) Similar relationships arefound for the ethane reductive elimination from [RhIII(CH3)2(PH3)Cp] DE≠=65.6 kcal/mol (MP2//HF) [43] and [PtIV(CH3)2(PH3)2Cl2] DH≠=34.2 kcal/mol(GVB) [37a] as compared to [RhIII(CH=CH2)2(PH3)2Cl] DE≠=17.8 kcal/mol and[PtIV(CH=CH2)2(PH3)2Cl2] DH≠=17.5 kcal/mol given in the present work In addition, vinyl-vinyl coupling is generally much more exothermic than methyl-methyl coupling [37a, 39, 43].The differences may come from the relative stability in the products; D(C-C) in buta-1,3-diene, 115.8 kcal/mol, is consid-erably larger than in ethane, 90.0 kcal/mol [49] Thus, the vinyl-vinyl coupling

is energetically more favored than the methyl-methyl reductive elimination.These theoretical results fairly well agree with experimental findings, whichpoint out that practical implementation of Csp3–Csp3coupling is rather prob-lematic due to slow reductive elimination [50], in contrast to the processes involving vinyl groups

Concluding Remarks

Above we have presented four different factors that control the catalytic

activ-ity of transition metals toward s-bonds In the mono-nuclear transition metal

systems (1) the availability of the lower lying s1dn–1and s0dnstates of the sition metal atoms, and (2) the nature of the ligands facilitating the reduction

tran-of the energy gap between the different oxidative states tran-of the transition metalcenters are very crucial Meanwhile, as was demonstrated, in the transitionmetal clusters the “cooperative” (or “cluster”) effects play important roles in thecatalytic activities of these clusters Another factor, which could be very im-portant for catalytic activity of the transition metal systems is shown to be theirredox activity

However, those four factors are definitely not the only ones that play crucial

roles in the catalytic activity of transition metal systems with s-bonds The transition metal catalyzed s-bond activation and formation are very complex

processes and need more detailed investigations

continu-ous support (presently CHE-0209660) of our homogenecontinu-ous catalysis project.

References

1 (a) Diederich F, Stang PJ (1998) (eds.) Metal-catalyzed cross-coupling reactions VCH, Weinheim; (b) Corlins B, Herrman WA (1996) (eds.) Applied homogeneous catalysis with organometallic compounds VCH, Weinheim; (c) Musaev DG, Morokuma K (1996) In: Prigogine I, Rice SA (eds) Advances in chemical physics, vol XCV Wiley, New York, p 61

2 (a) Ausloos P, Lias SG (1987) (eds) Structure/reactivity and thermochemistry of ions del, Dordrecht, The Netherlands; (b) Russell DH (ed) (1989) Gas phase inorganic chem- istry Plenum, New York; (c) Davies JA, Watson PL, Liebman JF, Greenberg A (eds) (1990) Selective hydrocarbon activation: principles and progress VCH, New York; (d) Eller K, Schwarz H (1991) Chem Rev 91:1121; (e) Fontijn A (ed) (1992) Gas-phase metal reactions Elsevier, Amsterdam; (f) Weisshaar JC (1992) In: Ng C (ed) Advances in chemal physics, vol 81.Wiley-Interscience, New York; (g) Armentrout PB (1991) Science, 251:175; (h) Weiss- haar JC (1993) Acc Chem Res 26:213; (i) Schroder D, Schwarz H (1995) Angew Chem Int

Rei-Ed Engl 34:1973 and references therein

3 (a) Perry JK, Ohanessian G, Goddard WA III (1993) J Phys Chem 97:5238; (b) Perry JK, Ohanessian G, Goddard WA III (1994) Organometallics 13:1870; (c) Blomberg MRA, Siegbahn PEM, Svensson M (1994) J Phys Chem 98:2062; (d) Siegbahn PEM, Blomberg MRA, Svensson M (1993) J Am Chem Soc 115:4191

4 (a) Musaev DG, Koga N, Morokuma K (1993) J Phys Chem 97:4064; (b) Musaev DG, Morokuma K (1993) Isr J Chem 33:307; (c) Musaev DG, Morokuma K, Koga N, Nguyen

KA, Gordon MS, Cundari TR (1993) J Phys Chem 97:11435; (d) Musaev DG, Morokuma

K (1994) J Chem Phys 101:10697; (e) Musaev DG, Morokuma K (1996) J Phys Chem 100:11600

5 Carter EA, Goddard WA III (1988) J Phys Chem 92:5679

6 Trevor DJ, Cox DM, Kaldor A (1990) J Am Chem Soc 112:3742

7 Fayet P, Kaldor A, Cox DM (1990) J Chem Phys 92:254

8 (a) Schnabel P, Irion MP (1992) Ber Bunsengers Phys Chem 96:1101; (b) Irion MP, Schnabel P (1992) Ber Bunsengers Phys Chem 96:1091; (c) Lian L, Su CX,Armentrout PB (1992) J Chem Phys 97:4072

9 Guo BC, Kerns KP, Castleman AW Jr (1992) J Phys Chem 96:6931

10 (a) Jiao CQ, Freiser BS (1995) J Phys Chem 99:10723; (b) Berg C, Schindler T, Lammers

A, Niedner-Schatteburg G, Bondybey VE (1995) J Phys Chem 99:15497

11 See, for example, Ber Bunsengers Phys Chem (1992) 96(6)

12 (a) Cui Q, Musaev DG, Morokuma K (1998) J Chem Phys 108:8418; (b) Cui Q, Musaev

DG, Morokuma K (1998) J Phys Chem A 102:6373; (c) Moc J, Musaev DG, Morokuma K (2000) J Phys Chem A 104:11606; (d) Moc J, Musaev DG, Morokuma K (2003) J Phys Chem A 107:4929

13 Moore CF (1971) Atomic energy levels NSRD-NBS, vol III U.S Government Printing Office, Washington DC

14 Parshall GW, Ittel SD (1992) Homogenous catalysis, 2nd edn Wiley, New York

15 Wallar BJ, Lipscomb JD (1996) Chem Rev 96:2625 and references therein

16 (a) DeRose VJ, Liu KE, Kurtz DM Jr, Hoffman BM, Lippard SJ (1993) J Am Chem Soc 115:6440; (b) Fox BG, Hendrich MP, Surerus KK, Andersson KK, Froland WA, Lipscomb

JD (1993) J Am Chem Soc 115:3688; (c) Thomann H, Bernardo M, McCormick JM, Pulver S, Andersson KK, Lipscomb JD, Solomon EI (1993) J Am Chem Soc 115:8881

17 (a) Rosenzweig AC, Fredrick CA, Lippard SJ, Nordlung P (1930) Nature 366:537; (b) zweig AC, Nordlung P, Takahara PM, Fredrick CA, Lippard SJ (1995) Chem Biol 2:409

Rosen-18 (a) Elango N, Radhakrishman R, Froland WA, Waller BJ, Earhart CA, Lipscomb JD, Ohlendorf DH (1997) Protein Sci 6:556; (b) Nesheim JC, Lipscomb JD (1996) Biochem- istry 35:10240 and references therein

19 (a) Liu KE, Wang D, Huynh BH, Edmondson DE, Salifoglou A, Lippard SJ (1995) J Am Chem Soc 116:7465; (b) Liu KE, Valentine AM, Wang D, Huynh BH, Edmondson DE, Salifoglou A, Lippard SJ (1995) J Am Chem Soc 117:10174; (c) Liu KE,Valentine AM, Qiu

D, Edmondson DE, Appelman EH, Spiro TG, Lippard SJ (1995) J Am Chem Soc 117:4997

20 Wilkinson EC, Dong Y, Zang Y, Fujii H, Fraczkiewicz R, Fraczkiewicz G, Czernuszewicz

RS, Qui L Jr (1998) J Am Chem Soc 120:955

21 Shu LJ, Nesheim JC, Kauffmann K, Munch E, Lipscomb JD, Que L (1997) Science 275:515

22 (a) Dunietz BD, Beachy MD, Cao Y,Whittington DA, Lippard SJ, Friesner RA (2000) J Am Chem Soc 122:2828; (b) Baik MH, Newcomb M, Friesner RA, Lippard SJ (2003) J Chem Rev 103:2385; (c) Gherman BF, Dunietz BD, Whittington DA, Lippard SJ, Friesner RA (2001) 123:3836; (d) Friesner RA, Baik MH, Guallar V, Gherman BF, Wirstam M, Murphy

RB, Lippard SJ (2003) Coord Chem Rev 238/239:267; (e) Baik MH, Gherman BF, Friesner

RA, Lippard SJ (2002) J Am Chem Soc 103:2385

23 (a) Yoshizawa K (2000) J Inorg Biochem 78:23; (b) Yoshizawa K, Suzuki A, Shiota Y, Yamabe T (2000) Bull Chem Soc Jpn 73:815; (c) Yoshizawa K, Ohta T,Yamabe T, Hoffmann

R (1997) J Am Chem Soc 119:12311; Yoshizawa K, Ohta T,Yamabe T (1998) Bull Chem Soc Jpn 71:1899; (d) Yoshizawa K, Shiota Y,Yamabe T (1997) Chem Eur J 3:1160; (e) Yoshizawa

K, Shiota Y,Yamabe T (1998) J Am Chem Soc 120:564; (f) Yoshizawa K (1998) J Biol Inorg Chem 3:318

24 (a) Siegbahn PEM, Crabtree RH (1997) J Am Chem Soc 119:3103; (b) Siegbahn PEM (1999) Inorg Chem 38:2880; (c) Blomberg MRA, Siegbahn PEM (1999) Mol Phys 96:571; (d) Siegbahn PEM, Crabtree RH, Nordlund P (1998) J Biol Inorg Chem 3:314; (e) Siegbahn PEM, Blomberg MRA (2000) Chem Rev 100:421; (f) Siegbahn PEM (2001) J Biol Inorg Chem 6:27; (g) Siegbahn PEM, Wistram M (2001) J Am Chem Soc 11:820

25 (a) Basch H, Mogi K, Musaev DG, Morokuma K (1999) J Am Chem Soc 121:7249; (b) rokuma K, Musaev DG, Vreven T, Basch H, Torrent M, Khoroshun DV (2001) IBM J Res Dev 45:367; (c) Torrent M, Musaev DG, Basch H, Morokuma K (2001) J Phys Chem B 105:4453; (d) Basch H, Musaev DG, Mogi K, Morokuma K (2001) J Phys Chem B 105:8452; (e) Torrent M, Mogi K, Basch H, Musaev DG, Morokuma K (2001) J Phys Chem B, 105:8616; (f) Basch H, Musaev DG, Mogi K, Morokuma K (2001) J Phys Chem A 105:3615; (g) Torrent M, Musaev DG, Morokuma K (2001) J Phys Chem B 105:322; (h) Torrent M, Vreven T, Musaev DG, Morokuma K, Farkas O, Schlegel HB (2002) J Am Chem Soc 124:192; (i) Torrent M, Musaev DG, Basch H, Morokuma K (2002) J Comput Chem 23:59

Mo-26 For some recent examples of vinyl-vinyl coupling see: (a) Gallagher WP, Terstiege I, Maleczka RE (2001) J Am Chem Soc 123:3194; (b) Maleczka RE, Gallagher WP, Terstiege

I (2000) J Am Chem Soc 122:384; (c) Caline C, Pattenden G (2000) Synlett 1661; (d) Kim

HO, Ogbu CO, Nelson S, Kahn M (1998) Synlett 1059; (e) Ma Y, Huang X (1997) J Chem Soc Perkin Trans 2953; (f) Panek JS, Hu T (1997) J Org Chem 62:4912; (g) Alcaraz L, Taylor RJK (1997) Synlett 791; (h) Jang SB (1997) Tetrahedron Lett 38:1793; (i) Yang DY, Huang X (1997) J Organomet Chem 543:165; (j) Allred GD, Liebeskind LS (1996) J Am Chem Soc 118:2748

27 C-C cross coupling catalyzed by palladium complexes with nitrogen ligands: (a) van Asselt R, Elsevier CJ (1994) Organometallics 13:1972; (b) van Asselt R, Elsevier CJ (1994) Tetrahedron 50:323

28 Collman JP, Hegedus LS, Norton JR, Finke RG (1987) Principles and application of otransition metal chemistry University Science Books, Mill Valley, CA

organ-29 Parshall GW, Ittel SD (1992) Homogeneous catalysis: the applications and chemistry of catalysis by soluble transition metal complexes, 2nd edn Wiley-Interscience, New York

30 (a) Williams BS, Goldberg KI (2001) J Am Chem Soc 123:2576; (b) Crumpton DM, berg KI (2000) J Am Chem Soc 122:962; (c) Hill GS, Yap GPA, Puddephatt RJ (1999) Organometallics 18:1408; (d) Albrecht M, Gossage RA, Spek AL, van Koten G (1999) J Am Chem Soc 121:11898; (e) Hill GS, Puddephatt RJ (1997) Organometallics 16:4522; (f) Goldberg KI,Yan JY, Breitung EM (1995) J Am Chem Soc 117:6889; (g) Goldberg KI,Yan JY,Winter EL (1994) J Am Chem Soc 116:1573; (h) Brown MP, Puddephatt RJ, Upton CEE (1974) J Chem Soc Dalton Trans 2457; (i) Appleton TG, Clark HC, Manzer LE (1974) J Organomet Chem 65:275; (j) Ruddick JD, Shaw BL (1969) J Chem Soc A 2969; (k) Chatt

Gold-J, Shaw BL (1959) J Chem Soc 705

31 Baylar A, Canty AJ, Edwards PG, Slelton BW, White AH (2000) J Chem Soc Dalton Trans 3325

32 Van der Boom ME, Kraatz HB, Hassner L, Ben-David Y, Milstein D (1999) Organometallics 18:3873

33 Rybtchinski B, Milstein D (1999) Angew Chem Int Ed 38:870 and references therein

34 Rendina LM, Puddephatt RJ (1997) Chem Rev 97:1735

35 (a) Reid SM, Mague JT, Fink MJ (2001) J Am Chem Soc 123:4081; (b) Moravskiy A, Stille

JK (1981) J Am Chem Soc 103:4182; (c) Loar MK, Stille JK (1981) J Am Chem Soc 103:4174; (d) Ozawa F, Ito T, Nakamura Y,Yamamoto A (1981) Bull Chem Soc Jpn 54:1868; (e) Gillie

A, Stille JK (1980) J Am Chem Soc 102:4933

36 Tatsumi K, Hoffmann R, Yamamoto A, Stille JK (1981) Bull Chem Soc Jpn 54:1857

37 (a) Low JL, Goddard WA (1986) J Am Chem Soc 108:6115; (b) Low JL, Goddard WA (1986) Organometallics 5:609

38 Hill GS, Puddephatt RJ (1998) Organometallics 17:1478

39 (a) Sakaki S, Mizoe N, Musashi Y, Biswas B, Sugimoto M (1998) J Phys Chem A 102:8027; (b) Sakaki S, Ogawa M, Musashi Y, Arai T (1994) Inorg Chem 33:1660; (c) Sakaki S, Ieki

M (1993) J Am Chem Soc 115:2373

40 (a) Siegbahn PEM, Blomberg MRA (1995) In: van Leeuwen PWNM, van Lenthe JH, Morokuma K (eds.) Theoretical aspects of homogeneous catalysis, applications of ab ini- tio molecular orbital theory Kluwer Academic Publishers; (b) Siegbahn PEM, Blomberg MRA (1992) J Am Chem Soc 114:10548; (c) Blomberg MRA, Siegbahn PEM, Nagashina

U, Wennerberg J (1991) J Am Chem Soc 113:424

41 (a) Sundermann A, Uzan O, Martin JML (2001) Organometallics 20:1783; (b) mann A, Uzan O, Milstein D, Martin JML (2000) J Am Chem Soc 122:7095

Sunder-42 Cao Z, Hall MB (2000) Organometallics 19:3338

43 Koga N, Morokuma K (1991) Organometallics 10:946

44 Krogh-Jespersen K, Goldman AS (1999) In: Truhlar DG, Morokuma K (eds) Transition state modeling for catalysis ACS symposium series, ACS, Washington DC, p 151

45 (a) Ananikov VP, Musaev DG, Morokuma K (2001) Organometallics 20:1652; (b) Ananikov

VP, Musaev DG, Morokuma K (2002) J Am Chem Soc 124:2839

46 Brandsma L,Vasilevsky SF,Verkruijsse HD (1998) Application of transition metal catalysts

in organic synthesis Springer, Berlin Heidelberg New York

47 (a) Amatore C, Azzabi M, Jutand A (1991) J Am Chem Soc 113:8375; (b) Negishi E, Takahashi T, Akiyoshi, K (1986) J Chem Soc Chem Commun 1338

48 Cotton SA (1997) Chemistry of precious metals Blackie Academic and Professional (Chapman & Hall), London

49 Lide DR (ed.), (1999) CRC handbook of chemistry and physics 1999–2000, 80th edn CRC Press, Boca Raton

50 Knochel P (1998) In: Diederich F, Stang PJ (eds) Metal-catalyzed cross-coupling tions VCH, Weinheim, p 387

reac-Theoretical Studies of C-H s s-Bond Activation

and Related Reactions by Transition-Metal Complexes

2.1 Important Orbital Interaction 33 2.2 Electron Correlation Effects in Oxidative Addition 35 2.3 Transition State Structure 38 2.4 Activation of sp 3 and sp 2C-H s-Bonds 42

2.5 s-Bond Activation of Various Substrates 51

2.6 Reductive Elimination from the p-Allyl Complex

and Oxidative Addition Leading to the p-Allyl Complex 55

3.1 Reliability of Computational Methods for Metathesis 57

3.2 Metathesis via Heterolytic s-Bond Scission 58

3.3 Metathesis via Homolytic s-Bond Scission 64

addition and metathesis, except for several examples Important orbital interactions and tronic process in the oxidative addition are discussed first.Also, the characteristic features of the transition state are reviewed in several typical oxidative addition reactions of H2, CH4, SiH4, C2H6, and SiH3CH3 The significant differences in reactivity among C-H, Si-H, C-C, and

elec-C-B s-bonds are discussed in terms of the orbital interaction in the transition state and the bond energy Also, theoretical studies of the s-bond activation via metathesis are reviewed,

in which the heterolytic C-H s-bond activation of benzene and methane by palladium(II) formate complex and the homolytic Si-H s-bond activation of silane by Cp2Zr(C2H4) and

Cp2Zr(R1)(R2) (R1, R2=H, alkyl, or silyl) are mainly discussed to clarify the electronic process and the driving force At the end of this chapter, several theoretical studies of transition-

metal-catalyzed reactions via s-bond activation are presented as typical examples.

Metathesis · Heterolytic s-bond activation

© Springer-Verlag Berlin Heidelberg 2005

List of Abbreviations

CASPT2; CAS-SCF calculation followed by the second order perturbation theory CAS-SCF Complete active space SCF method

CCSD(T) Coupled cluster expansion with single and double excitations,

where contribution of triple excitations is non-iteratively incorporated with perturbation

MP4(SDQ) Möller-Plesset 4-th order perturbation theory incorporating single,

double, and quadruple excitations

MPn Möller-Plesset n-th order perturbation theory

1

Introduction

C-H s-bond activation of hydrocarbons by transition metal complexes is of

considerable importance in modern organometallic chemistry and catalyticchemistry by transition-metal complexes [1], because a functional group can

be introduced into alkanes and aromatic compounds through C-H s-bond

activation For instance, Fujiwara and Moritani previously reported synthesis

of styrene derivatives from benzene and alkene via C-H s-bond activation of

benzene by palladium(II) acetate [2] Recently, Periana and his collaborators

succeeded to activate the C-H s-bond of methane by the platinum(II) complex

in sulfuric acid to synthesize methanol [3] Both are good examples of the

re-action including the C-H s-bond activation.

In my understanding, the s-bond activation is classified into two main

categories, oxidative addition (Eq 1) and metathesis (Eq 2), except for severalexamples In the product of the oxidative addition, both A and B groups arebound with the metal center Because the A and B groups are considered anionwhen they coordinate with the metal center, the oxidation state of the

M(R2C=CR¢2)Ln+ A-B Æ M(B)(CR2-CAR¢2)Ln (2b)transition-metal center increases by +2 in a formal sense through the oxidativeaddition reaction In the metathesis, on the other hand, the oxidation state ofthe metal center does not always increase For instance, the A group is boundwith an X ligand and the B group is bound with the metal center in the prod-ucts of Eq (2a) In this case, the oxidation state of the metal center does not change If the X ligand is anion, the A group becomes positively charged inA-X, while the B group becomes negatively charged because it is bound with the

transition-metal center in the product It is likely to say that the s-bond

break-ing of A-B occurs in a heterolytic manner In Eq (2b), however, the metal