Faraday Symp. Chem. SOC.,1984 19,49-61 Potential-energy Surfaces for Chemical Reactions Dimerization of CH and SiH, the SN2Reaction in Gas-phase Clusters and CH Activation in Transition-metal Complexes BY UIJI ~TSUHISAOHTA,NOBUAKI SHIGERU MOROKUMA,* KOGA OBARA~ AND ERNEST R. DAVIDSON~ Institute for Molecular Science Myodaiji Okazaki 444,Japan Received 3rd September 1984 We present the results of three applications of the molecular-orbital method to problems of potential-energy surfaces that control chemical reactions. In the first application the dimerization of CH and SiH in both their singlet and triplet states is investigated in connection with the path of least motion as against the path of non-least motion. Two ground-state (,B,) methylenes in the path of non-least motion give ground-state ethylene with no barrier.The ground-state (lA,) silylenes give a ground-state disilene with a barrier in the path of least motion and no barrier in the path of non-least motion. In the second problem potential-energy surfaces are calculated for an S,2 reaction (H,O),OH-+CH,Cl -+ HOCH +C1-+nH,O where the reactants are complexed with one or two water molecules. When the hydroxide ion is solvated by two water molecules the reaction takes place through the first step of reactant complex formation followed by inversion of the methyl group. The transition state for methyl inversion has an energy comparable to that of the reactants. The migration of water molecules from the hydroxide side to the chloride side is not involved in the rate-determining process.The last problem is concerned with the activation of an inert CH bond in transition-metal complexes. In six-coordinate Ti do complexes the optimized geometry shows theoretical evidence that the distortion of the ethyl or methyl ligand represented by a short M. -H distance a small M...C-C (or H) angle and a long CH bond is of electronic origin. Electronegative axial ligands are essential for the existence of an agostic interaction which is stabilized by CH a+Ti dzy charge transfer. A similarly distorted ethyl group has been found in the calculation of a three-coordinate Pd complex. The low-energy transition state for p-elimination lies along a smooth extension of the ethyl distortion. 1. INTRODUCTION One of the goals of theoretical chemistry has been a full understanding of the mechanisms rates and dynamics of complicated chemical reactions.Potential-energy surfaces for ground and excited states control reactions and their theoretical studies have been a focal point since the early days of molecular-orbital theories. However in the past such studies have been confined to very qualitative model calculations or to very small (e.g.triatomic) systems. In the last ten years we have seen much progress in this area. The energy-gradient or more generally energy-derivative method is the largest contributor to these activities.l The energy-derivative method has provided quantum chemists with the power to explore efficiently complicated highly multi- 1' Present address Department of Chemistry Faculty of Science Kyoto University Kyoto Japan.$ Present address Department of Chemistry Indiana University Bloomington Indiana 47405 U.S.A. 49 POTENTIAL-ENERGY SURFACES dimensional potential-energy surfaces determine their characteristic features such as equilibrium geometry saddle-point (transition-state) geometry and the point of avoided crossing and characterize such properties of these surfaces as the intrinsic reaction coordinate and seams of crossing. Optimization of the equilibrium structure for molecules having 10 or more atoms is becoming routine and the determination of the transition state for systems of this size is feasible with a reasonable amount of computer time. Since its methodological developments will no doubt be discussed in other papers in this symposium we will restrict ourselves to applications of the method to calculations of potential-energy surfaces.In this paper we present the results of our studies of potential-energy surfaces with regard to three different topics. In the next section we discuss the reactions of both the triplet and singlet states of methylene and silylene i.e. CH +CH -+ CH,CH SiH +SiH -+ SiH,SiH CH +SiH +CH,SiH by comparing the paths of least motion and non-least motion. In the third section we present potential-energy surfaces for an SN2reaction in a hydrated cluster (H,O),OH-+CH,Cl +HOCH +C1-+nH,O (n = 0 1,2). The fourth section deals with the activation of an inert CH bond in transition-metal complexes in particular the equilibrium structure of some Ti complexes and the transition state for @-elimination in a Pd complex.We end with a brief conclusion. 2. LEAST-MOTION versus NON-LEAST-MOTION PATHS FOR THE DIMERIZATION OF CH AND SiH The dimerization of singlet methylenes to form ground-state ethylene had been considered as a textbook example of a reaction path of non-least motion. In the least-motion path (D,,)two o orbitals of CH units (oA,oB) become a ogand a nu orbital in ethylene and ah ok -+ oiniis symmetry-forbidden. In the path of non-least motion proposed by Hoffmann Gleiter and Mallory (hereafter referred to as H.G.M.)2 the reaction path starts with C symmetry mixing o and n orbitals and making the process symmetry-allowed and takes the higher symmetry of D, in a later stage of the reaction.This argument however is based on an extended Hiickel method i.e. a single-determinant wavefunction which is insufficient to describe essential electronic configurations. Moreover the ground state of CH is a triplet ,B1,to which the above argument does not apply. Recent ab initio calculations have shown that two ground-state triplet methylenes can dimerize via the path of least motion without a barrier to give ground-state eth~lene.~ On the other hand two singlet methylenes dimerize via the path of least motion to give a Rydberg excited state of ethylene.* Ohta et aL5 have recently studied the dimerization of singlet methylenes and triplet methylenes via a path of non-least motion. They have also studied the dimerization of triplet and singlet silylene (SiH,) both via the path of least motion and a non-least-motion path.The ground state of silylene is a singlet IAl and the lowest triplet ,B1 is the first excited state the opposite of the case of methylene. The coupling reaction of CH and SiH to give silaethylene CH,=SiH, via the least-motion path and a non-least-motion path has also been investigated. The basis set used is of double-zeta +polarization quality and for ethylene a set of Rydberg-type sp functions has been added. Calculations are mainly K. MOROKUMA K. OHTA N. KOGA S. OBARA AND E. R. DAVIDSON -77.70 -1.5 2.0 2.5 3.0 3.5 4.0 R(C-C)/A Fig. 1. Potential-energy curves for dimerization of CH via the path of non-least motion as functions of the CC distance.carried out with a CAS (complete active space) MCSCF wavefunction including all (20) configurations for 4 active electrons in 4 active orbitals (a,o*,n,n*). Potential curves for the excited states of CH +CH are calculated with multi-reference (MR) CI including all the single and double excitations (6332 spin-adopted configurations) from the four active orbitals to all virtual orbitals. 2. I. NON-LEAST-MOTION DIMERIZATION OF CH +CH We have used the path of non-least motion determined by H.G.M. and augmented it with a few more points at a short CC distance in D,,symmetry. At the far end of this path where the overall symmetry is C, one CH has its C, axis nearly parallel to the line of approach whereas the other CH has its C, axis nearly perpendicular to the line of approach.At a CC separation of 2.45 A the bending angles of the two CH units become equal with overall C, symmetry and a trans conformation. At 2.00 the bending angles become zero and the entire system is planar (D,,). The structure of the CH fragments is fixed at R(CH) = 1.10 A and LHCH = 120" throughout the path. In fig. 1 the potential-energy curves along the path of non-least motion for the ground and some excited states are shown. The ground-state singlet along the curve starts with two triplet (3B1) methylenes and goes without a barrier to the ground state of ethylene. The situation is essentially the same with the least-motion dimerization but differs from the H.G.M. results where two singlet (lA,) methylenes form the ground-state ethylene.The dimerization of two singlet (lA,) methylenes in fig. 1 follows the first excited state which is a valence excited state at long distance passes over a barrier caused by avoided crossing and becomes a Rydberg excited state of ethylene. This situation is again similar to the case of the least-motion path. The third and fourth states represent the dimerization of CH,(lA,) +CH,(lB,). They are nearly degenerate to ca. 2.3 A below which the lower state forms excited ethylene without a barrier. 2.2. SiH +SiH +SiH,SiH Fig. 2 shows four potential-energy curves for overall singlet states for the dimerization of SiH,. Curves (a)-(c) are for the least-motion paths and curve (d)is POTENTIAL-ENERGY SURFACES -580.00-0 c 2 -580.05 -2 1 ril -580.0-I I I I 2.0 3.0 4.0 5.0 R(Si-Si)/A Fig. 2. Potential-energy curves for dimerization of SiH as functions of the SiSi distance. for a path of non-least motion. In (a)the SiH distance and the HSiH angle are fixed at the calculated values for the lA ground state of SiH, i.e. 1.497A and 93.9'. This represents the dimerization of singlet silylenes in the path of least motion. Fig. 2 and an analysis of the wavefunction indicate that in the first half of the dimerization reaction the potential curve is repulsive as the SiSi distance decreases and the total wavefunction (singlet) consists mainly as expected of a product of a2 singlet wavefunctions of the reactants. At ca. 3.1 A the triplet (an)x triplet (an) configuration takes over which leads to the ground-state disilene.The barrier is caused by avoided crossing between two major configurations and is a typical example of symmetry-forbidden reactions. Curves (6) and (c) both assume the SiH distance and HSiH angle fixed at the calculated values for 381 SiH, i.e. 1.460 A and 118.0'. In our calculation the singlet is lower in energy than the triplet even at this geometry. Therefore the lower curve (b) as in (a) consists mainly of a singlet x singlet configuration and becomes triplet x triplet inside the barrier owing to avoided crossing at ca. 4.0 A. The barrier is earlier in (b)than in (a),because the assumed fragment geometries in (b)are more favourable to the triplet x triplet configuration than the singlet x singlet configuration.The upper curve (c) although determined only as the second root of the CI equation in the MCSCF procedure represents the least-motion path for dimerization of 3B silylenes. The triplet x triplet wavefunction at a long distance goes through an avoided crossing with (b)and is adiabatically correlated to an excited state of disilene. The path of non-least motion for dimerization of singlet SiH was determined by the Hartree-Fock-Roothaan (H.F.R.) optimization of geometrical parameters as functions of the SiSi distance. At an early stage the SiH units have a singlet-like structure; one has its C,,axis nearly parallel to the line of approach while the others are perpendicular. In the final stage there are two SiH units with triplet-like structure trans bending angle becoming small.The MCSCF potential-energy curve along this path is shown in fig. 2(d). There is no barrier along this path starting from singlet silylenes. In conclusion the ground-state singlet SiH dimerizes to form the ground state of K. MOROKUMA K. OHTA N. KOGA S. OBARA AND E. R. DAVIDSON -328.9 t I -328.95 I--329.051 / I I I I 2.0 3.0 4.0 R(C-Si)/A Fig. 3. Potential-energy curves for CH +SiH -+ CH,SiH as functions of the SIC distance. disilene without a barrier on the path of non-least motion and with a substantial barrier on the least-motion path. Therefore the H.G.M. conclusion is applicable to the dimerization of SiH,. The excited-state triplet SiH is led adiabatically to an excited state of disilene but actually is likely to form ground-state disilene with no barrier through a non-adiabatic transition in the least-motion path.If the triplet silylene is lower in energy than the singlet silylene at the optimum geometry of the triplet a non-adiabatic transition will be unnecessary and the path of least motion will give the ground-state product without a barrier. 2.3. CH +SiH -+ CH,SiH At infinite separation for this mixed system our calculations give the total energy of the singlet pairs as slightly lower in energy than the triplet pairs. Therefore as shown in fig. 3 the lowest least-motion path is curve (a) where the fragment geometries are fixed at the optimum values for CH,(lA,) and SiH,(lA,). Curve (a) is repulsive as all the least-motion singlet x singlet curves are and goes over a large barrier at ca.3.2 A to reach the ground-state product. In curves (b)and (c) the fragment geometries are frozen at the values in the equilibrium geometry of silaethylene CH,SiH, which are not far from those in the triplet fragments. The lowest curve (b) essentially describes the least-motion reaction for triplet pairs which reaches the ground-state silaethylene with no barriers. Curve (d)represents the potential-energy curve on the path of non-least motion which was determined by H.F.R. geometry optimization as a function of the CSi distance. The singlet pairs form the ground-state product without a barrier. Therefore the overall qualitative situation for this mixed system is similar to the case of SiH +SiH, although the detailed features of the potential curves are different.Note that in the early stage of the path of non-least motion the preferred geometry POTENTIAL-ENERGY SURFACES has the SiH plane nearly perpendicular to the line of approach and the CH plane nearly parallel to it as though SiH were acting as an electron acceptor and CH as an electron donor. An analysis reveals that in the early stage of the reaction electrostatic interactions are dominant and it is most favourable to have the large CH dipole aligned parallel to the line of approach. 3. POTENTIAL-ENERGY SURFACES FOR THE SN2 REACTION IN GAS-PHASE CLUSTERS Chemical reactions in gas-phase clusters are attracting considerable attention. Not only are cluster reactions interesting in themselves but their mechanisms rates and dynamics should provide information on solvent effects and may fill the gap between reactions in the gas phase and in so1ution.6y7 The S,2 reaction in solvated clusters is one of the few reactions in which rate constants in the cluster have been determined for various numbers of solvent molecules as well as in the gas phase and in solution.For instance the rate constant for the reaction (H,O),OH-+ CH,Cl+ HOCH + C1-+nH,O is fastest in the gas phase; it is slower in clusters for n = 1 2 and 3 by ca. .6 500 and 5000 times respectively while in solution it is lo1 times s10wer.~ Previously we have carried out calculations of potential-energy surfaces for the following symmetric S,2 reactions:* (H,O),Cl-+ CH,Cl + ClCH + Cl-(H,O), (n = 0 1,2).Our findings can be summarized as follows. (i) The most favourable reaction path for n = 1 is reactants -+ reactant complex + transition state for CH inversion -+ transfer of H,O from the left (the newly formed CH,Cl side) to the right (the newly formed C1- side) -+ product complex -+ products. Since the system is symmetric the process by which H,O transfer takes place before CH inversion is equally favourable. The path of simultaneous CH inversion and H,O transfer is both energetically and entropically unfavourable. (ii) For n = 2 the most favourable path is reactants -+ re-actant complex + transfer of one H,O molecule from the left (Cl-) to the right (CH,Cl) -+CH inversion -+transfer of the other H,O molecule from left (newly formed CH,Cl) to the right (newly formed C1-).Having one water molecule on each chlorine is the best way to stabilize the intrinsically symmetric transition state for CH inversion of reaction (2). (iii) The transfer of H,O from one side to the other takes place with little or no barrier via an intermediate having a bent Cl.-*C.*-Cl configuration. However the situation wth the experimentally studied reaction (1) could be substantially different. While reaction (2) is thermoneutral reaction (1) is highly exothermic (AEPexptl = -47.5 kcal mol-l). Because of high exothermicity the path following the transition state for CH inversion is expected to be downhill and the system loaded with much released energy is expected to shake off solvent molecules.The transition state for reaction (2) is symmetric and just at the midpoint between the reactants and products whereas that for reaction (1) is expected to be ‘early’. Because both the electronic structure and geometry of the transition states are expected to be different the number of solvent molecules on each site (OH or Cl) could be different between the two near their respectively favourable transition states. K. MOROKUMA K. OHTA N. KOGA S. OBARA AND E. R. DAVIDSON 0 -10 OH -+ C H3 CI OH-+CH3CI-W -20 I -0 E -30 W-OH'+CH-JCI I 6 0 .r 4 W-OH-+CH3CI-W -40 '-reaction coordinate Fig. 4. Potential-energy profiles for W,OH-+CH,ClW + [W,OH.**CH;**ClW,]- W = H,O. Ohta and Morokumag have recently studied potential-energy surfaces for the following five SN2reactions (W denotes H20) OH-+ CH,C1 -+ [OH.**CH,..*Cl]--+ products (3) OH- +CH,ClW -+ [OH*.-CH;-CIW]-+ products (4) WOH-+ CH,Cl + [WOH-..CH;.*Cl]-+ products (5) WOH-+ CH,ClW -+ [WOH...CH,.**ClW]-+ products (6) W20H-+ CH,Cl -+ [W,OH***CH;**Cl]-+products.(7) According to previous calculations8? lo the absolute value of the barrier height in S,2 reactions is very sensitive to the basis set used in particular to polarization and diffuse functions but depends little on electron correlation. Therefore we used the 6-3 lG* basis set augmented with C1 and 0 anionicp functions for CH,Cl and OH- and the 6-31G basis set for solvent water molecules. The geometries of the reactants reactant complex and transition state for CH inversion/transfer were optimized and their energies were calculated with the H.F.R.energy gradient under the restriction of C symmetry. The profiles of the potential-energy surfaces are shown in fig. 4. Since the interaction energy with H20 is much larger for OH- than for CH3C1 the profiles for reactions (4) and (6) are similar to those of reactions (3) and (5),respectively. At the transition state for CH inversion some net charge develops on the chloride. Therefore the water molecule on the chloride stabilizes the system and lowers the barrier from the reactant complex substantially for reactions (4) (calculated barrier height 1.O kcal mol-1 and (6) (2.3 kcal mol-l) as compared with reactions (3) (2.8 kcal mol-l) and (5) (4.7 kcal mol-l) respectively.In the dihydrated systems (6) and (7) the transition state for CH inversion for reaction (7) has a substantially lower energy than that for POTENTIAL-ENERGY SURFACES H2.95 H995 108.9 0 108.6 0 10.99 Il.01 6 172.3H 5 172.1~ / / H 1.68:’ H 4,95 Hq.95 108.8 0 109.1 0 10.99 8 172.6H 7 172.1 H/loo U 1.68; ,109.5 H ,’1-61 103 7 H CI h Fig. 5. Geometriesof reactant complexes and transition states. Compound numbers correspond to those in fig. 4. reaction (6). Therefore the reaction of W20H-should proceed first through the transition state for CH inversion without transferring water molecules. Migration of water molecules from the newly formed CH,OH to C1-will take place after this transition state during an exothermic energy release so that H20migration will not be involved in the rate-determining step.This situation is in contrast to the case of CI-+CH,Cl where H,O migration is an important part of the rate process. The barrier height for reaction (7) is large (9.5 kcal mol-l) and the energy of the transition state is as high as that of the reactants. This is consistent with the experimental finding that the rate of reaction decreases abruptly at n = 2 suggesting that the overall barrier relative to the isolated reactants must have become positive. The geometries of reactant complexes and transition states are shown in fig. 5. The location of the transition state relative to the reactant complex and the product complex can be related to the change in exothermicity upon hydration.Because of space limitation further discussion is omitted here. K. MOROKUMA K. OHTA N. KOGA S. OBARA AND E. R. DAVIDSON / 12.571) D' H Fig. 6. Optimized geometries of Ti(C,H,)(PH,),(Cl),(H) and Ti(CH,)(PH,),(Cl),. 4. CH ACTIVATION IN TRANSITION-METAL COMPLEXES Activation of inert CH bonds by transition-metal complexes is a topic of current interest in organometallic chemistry and homogeneous catalysis. X-ray and neutron diffraction studies have identified several complexes in which the hydrogen atom in a CH bond is located unusually close to the metal centre,ll indicating a direct interaction between the metal and a CH bond. The transition metals involved are of a wide variety including Ti Mn Fe Cu Mo Ru Rh Pd and Ta.In all cases an electron count shows that the central metal is electron deficient and the inclination to satisfy the 18-electron rule has been considered to be a necessary condition for interaction. This kind of hydrogen atom called an agostic hydrogen has been taken as evidence for the incipient activation of an inert CH bond by a transition metal. However experimental evidence is limited to the structures of stable complexes and there is little direct evidence of agostic hydrogen having a high reactivity in intramolecular hydrogen-migration reactions. 4.1. DISTORTED ETHYL AND METHYL GROUPS IN SIX-COORDINATE Ti do COMPLEXES Recently Koga et aZ.13 found the first theoretical evidence of an agostic hydrogen in an ab initio calculation.The optimized structure of the six-coordinate Ti do complex Ti(C,H,)(PH,),(Cl),(H) 1 shown in fig. 6 was obtained using the H.F.R. method with a double-zeta-quality basis set for the valence electrons of Ti and C,H and a minimal set for the core electrons and other ligands. Note that the distance between Ti and one p hydrogen of the ethyl group is very small 2.23 A indicating a direct interaction between them. The TiCC angle is 89" substantially less than the standard tetrahedral angle expected in an sp3-hybridized carbp atom and the CHB bond distance involved in the interaction 1.11 A is 0.03 A longer than the other CH bonds. These structural features are in agreement with the X-ray diffraction results for Ti(C,H,)(drnpe)(Cl), 2 [dmpe = dimethylphosphinoethane P(CH,),CH,CH,P-(CH,),] which are shown in fig.6 in parentheses.12 The present calculation indicates that these unusual structural features are of electronic origin not caused by crystal-packing forces. An analysis of the wavefunction reveals that the complex has low-lying vacant molecular orbitals consisting of Ti dxy,to which electron delocalization takes place from the CHP bonding orbital. Additional calculations indicate that the distortion of the ethyl group is sensitive to POTENTIAL-ENERGY SURFACES Table 1. Dependence of geometrical parameters of Ti(CH,)(PH,),(X),Y on ligands X and Y and PTiP angles X Y LPTiP/" LTiCH1/' P/" R(TiC)/A R(TiH1)/A H H H H 91.60pa 75.0as 108.3 107.1 110.6 110.5 2.135 2.122 2.685 2.657 H C1 89.40~ 106.2 110.6 2.135 2.653 C1c1c1 Hc1c1 87.90~ 88.60~ 75.0as 102.6 100.2 99.6 109.8 109.2 108.9 2.094 2.102 2.085 2.566 2.533 2.510 a op optimized; as assumed.\ /p Fig. 7. Contour map of the LUMO of 2. Solid and dotted lines denote positive and negative values respectively. the choice of ligand. In both Ti(C,H,)(PH,),(H),(Cl) and Ti(C,H,)(PH,),(H),(H) the ethyl group is found to be undistorted with a large M*.-Hdistance of 3.01 A a normal CCTi angle of 114" and normal CH distances. The axial chlorides are essential to the distortion. A similar distortion has been found by Obara et al.14for the corresponding methyl compound. The optimized structure for Ti(CH,)(PH,),(Cl),(Cl) 3 is also shown in fig.6 in which the PTiP angle was fixed at 75" to simulate the situation for the experimentally studied Ti(CH,)(dmpe)(Cl), 4. The TiCHl angle is 99.6" substantially smaller than the standard tetrahedral angle or the other TiCH angle (1 13.1"); i.e. the CH group is distorted. The angle D between the pseudo-three-fold axis of CH and each CH bond is 109* indicating that the tetrahedral methyl group as a whole is twisted away from the standard three-fold axis. An earlier structure for 4 determined by X-ray diffraction giving a TiCHl angle of 70" turned out to be unreliable.' The latest neutron diffraction results,12 shown in parentheses in fig. 6 give LTiCHl = 93.7" and R(Ti**-H)= 2.45 A in reasonable agreement with our theoretical prediction. K.MOROKUMA K. OHTA N. KOGA S. OBARA AND E. R. DAVIDSON 1626 H H H Fig. 8. Geometries of reactant 5 (R) product 6 (P) and the transition state (T) for the p-elimination reaction. The extent of distortion is sensitive to both axial and cis ligands X and Y as well as the PTiP angle as shown in table 1. Starting with a nearly undistorted CH for X =Y = H the TiCHl angle is decreased by the replacement of X or Y by C1 and a decrease in the PTiP angle. The most effective is the axial ligand C1 as in the case of the above-mentioned ethyl analogue 1. The donative interaction from the CH bond to an unoccupied Ti dzyorbital appears to be responsible for this distortion as in the case of the ethyl distortion. Fig. 7 shows the LUMO of 3 at the optimized geometry of fig.6. This mainly consists of a Ti dxy orbital with some mixing of s and p orbitals and extends to the direction x =y to take in the out-of-phase CH bonding orbital. This implies that in the occupied molecular-orbital space the CH bonding orbital will have a small portion of this Ti vacant orbital mixed in-phase contributing to direct M*-.H bonding. 4.2. AGOSTIC HYDROGEN AND FACILE /I-ELIMINATION IN THREE-COORDINATE Pd COMPLEXES Agostic hydrogens in the above-mentioned Ti complexes are not reactive since the complexes already have six ligands and the agostic hydrogens therefore cannot be transferred to metal centres. Reactive intermediates without sufficient ligands would not be stable enough to make themselves available to experimental structural analysis.Theoretical calculations capable of predicting the geometries of stable complexes should be able to give structural and energetic information as to the existence and behaviour of agostic hydrogens in unstable reactive intermediates. Koga et al.15 have recently found in an ab initio calculation a three-coordinate intermediate Pd(C,H,)(PH,)(H) 5 to have an agostic hydrogen. The path of /I-elimination to give an ethylene complex 6 CHZ-CHz H 2CyCH2 I \ H-Pd-PHj I H Pd-PHj I I H H 5 6 POTENTIAL-ENERGY SURFACES Table 2. Barrier for p-elimination and insertion reactions in kcal mol-1 method p-elimination insertion H.F.R. 11.0 8.0 M P2 2.8 5.8 has been found to be on a smooth continuation of the agostic H**-M interaction and to have a low barrier.The basis sets used are valence double-zeta and core minimal for Pd 3-21G for atoms in the ethyl group and STO-2G for the PH group. The geometry optimization was carried out at the H.F.R. level. The optimized structure of the intermediate 5 is shown in fig. 8. The PdCC angle is 88O the Pd*..H distance is short (2.13 A) and the CH distance directly involved in the interaction 1.13 A is 0.05 A longer than other CH distances in the same ethyl group. All these features as before point to a direct Pd*.*H interaction. A comparison between this three-coordinate Pd intermediate and the six-coordinate Ti complex discussed in section 4.1 indicates that the ethyl group in this complex is more deformed than in the Ti complex despite the smaller electron deficiency in the former (electron count 14) than in the latter (electron count 12).This suggests that the presence oi’ three-coordination in a Pd d8complex which prefers four-coordination provides an empty ‘site’ convenient for interaction and is a factor favouring the agostic interaction. The optimized structure for the /?-elimination product 6,given in fig. 8 is that of a typical ethylene complex. The geometry of the transition state for /?-elimination is shown also in fig. 8. The Pd...H distance 1.65 A is closer to that of the product (1.59 A) than that of the reactant (2.13 A). The C-C distance 1.40 A is closer to the 1.34 A of the product than the 1.53 A of the reactant. These results indicate that /?-elimination has a ‘late’ transition state.Note also that the Pd-C bond is not as stretched as in the product which suggests that this transition state is ‘tight’ as well as being ‘late’. Table 2 shows the barrier heights for /?-elimination and its reverse the insertion reaction calculated with the H.F.R. and MP2 methods at H.F.R.-optimized geometries. The reaction in either direction has a rather low barrier suggesting the reversibility of the /?-elimination/insertion.16 Experimentally an equilibrium between ethyl complexes and ethylene complexes has also been observed in some cases.17 A low activation enthalpy for the insertion reaction has been observed in an Rh complex.lS Our calculated results for a model Pd complex suggest that such a facile /?-eliminationlinsertion may be taking place via an intermediate having an agostic hydrogen.It has been shown experimentally that when the ethyl group has electronegative substituents the /?-elimination reaction is suppressed. The geometry optimization for Pd(CH,CHF,)(PH,)(H) Pd(CH,CF,)(PH,)(H) and the transition state connecting the two gives an undistorted difluoroethyl group in the reactant intermediate and a high barrier. The electron-withdrawing fluorine atom on the /3 carbon makes the electron-donating ability of the CH bond too small for a favourable agostic interaction. 5. CONCLUDING REMARKS Thanks to the development of the energy-derivative method and other advances in theory and coding the way in which quantum chemists explore multidimensional potential hypersurfaces has changed dramatically.With these new developments K. MOROKUMA K. OHTA N. KOGA S. OBARA AND E. R. DAVIDSON quantum chemists can carry out chemistry. We no longer have to be bound to unrealistically simplified model compounds or model reactions. Rather we can deal with realistic if not real reactants and reactions with reasonable reliability and confidence. In the coming years molecular-orbital calculations may help an experimentalist to conceive a non-existing molecule and examine its structure stability reactivity and other properties theoretically before he/she actually goes to the laboratory to synthesize it. One may also be able to design or control a chemical reaction leading to a specific product by calculating the transition states and barriers of reactions and by evaluating alternatives.The design of homogeneous catalysts by changing the metals and ligands on the computer and finding a most promising route might be feasible. We are grateful to Dr Kazuo Kitaura who is a coauthor of one of the papers on which the presented work is based. Numerical calculations were carried out at the Computer Centre of I.M.S. E. R. D. was a visiting professor at I.M.S. when the work presented here was carried out. P. Pulay in Applications of Electronic Structure Theory ed. H. F. Schaefer (Plenum Press New York 1977) p. 153 and references therein; A. Komornicki K. Ishida K. Morokuma R. Ditchfield and M. Conrad Chem. Phys. Lett. 1977 45 595; S. Kato and K. Morokuma Chem. Phys. Lett. 1979 65,19;J.D. Goddard N. C. Handy and H. F. Schaefer,J. Chem. Phys. 1979,71,1525;B. R. Brooks W. L. Laidig P. Saxe J. D. 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