Complicated Electronic Process of C–C σ-Bond Activation of

Article pubs.acs.org/Organometallics

Complicated Electronic Process of C−C σ‑Bond Activation of Cyclopropene by Ruthenium and Iridium Complexes: Theoretical Study Atsushi Ishikawa,†,§ Yudai Tanimura,† Yoshihide Nakao,‡ Hirofumi Sato,† and Shigeyoshi Sakaki*,‡ †

Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan Fukui Institute for Fundamental Chemistry, Kyoto University, Nishihiraki-cho 34-4, Takano, Sakyo-ku, Kyoto 606-8103, Japan

‡

S Supporting Information *

ABSTRACT: C−C σ-bond activation of cyclopropene by RuCl2(PPh3)2 and IrCl(CO)(PMe3)2 was theoretically investigated. The activation barrier and the reaction energy calculated here indicate that the reaction occurs more easily by the ruthenium complex than by the iridium complex, which is consistent with the experimental results that the Ru− vinylcarbene species is formed but the Ir−vinylcarbene is not. The valence bond analysis of the CASSCF wave function disclosed that the Ir−vinylcarbene bond is significantly weaker than that of the Ru complex because the d6 square pyramidal complex of Ru is more favorable than the d8 complex of Ir for this bonding interaction. In both the Ru and Ir systems, a precursor complex is formed by coordination of the C1C2 double bond of cyclopropene with the metal center, where C1 and C2 are sp2 carbons and C3 is an sp3 carbon. In the transition state, one C−C single bond (named C1−C3) is almost broken, but the M−C1 bond (M = Ru or Ir) and another C−C single bond (named C2−C3) are becoming stronger. When moving from the transition state to a metal−vinylcarbene product, the C1C2 double bond changes to the C1−C2 single bond with the concomitant change of the C2−C3 single bond to the C2C3 double bond. To induce these bond formation and bond breaking processes, the valence state of the metal center must change in the reaction. The promotion energy to the valence state becomes smaller in the ruthenium reaction system when going from the reactant to the product but becomes considerably larger in the iridium reaction system. This is the reason that the C−C σ-bond cleavage of cyclopropene occurs more easily in the ruthenium complex than in the iridium complex. The difference in promotion energy between the ruthenium and iridium systems is reasonably interpreted in terms of d−d orbital splitting by ligand-field and d electron number.

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to easier oxidative addition of the C−C σ-bond of cycloalkane than that of a normal alkane. In 1992, Grubbs and his coworkers reported that a ruthenium(II) complex reacts with cyclopropene to produce ruthenium vinylcarbene complex RuCl2(CH−CHCPh2)(PR3)2 (R = Ph or Cy) through C−C σ-bond cleavage, as shown by eq 2.7 This reaction is very

INTRODUCTION C−C σ-bond cleavage by a transition metal complex has been a challenging research target for a long time.1−4 This reaction is successfully performed when cycloalkane is employed as a substrate, because the release of ring strain energy is utilized for the driving force. For instance, Tipper succeeded previously in the C−C σ-bond cleavage of cyclopropane with a platinum(II) complex;5 see eq 1. A similar work was reported by Chatt and

important because the product, a ruthenium vinylcarbene complex, is employed as a catalyst for ring-opening and -closing metathesis polymerization. Because more efficient catalysts are produced from diazoalkane instead of cyclopropene nowadays,8 this reaction is not employed to synthesize the catalyst. However, this reaction is still considerably interesting from the viewpoint of σ-bond activation by a transition metal complex, as

his co-workers.6 This type of reaction is understood to be oxidative addition of a C−C σ-bond to a transition metal complex. It is believed that cycloalkane provides not only the thermodynamic driving force but also kinetically favorable factors for the reaction, because the HOMO and the LUMO of cycloalkane contain a considerably large π-orbital character. As a result, the C−C σ-bond of the cycloalkane interacts with the Pt center more easily than that of a normal alkane, which leads © 2012 American Chemical Society

Received: August 22, 2012 Published: November 19, 2012 8189

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Scheme 1. Schematic Picture of the C−C σ-Bond Cleavage of Cyclopropene

addition of a C−C σ-bond to an Ir(I) center. It is also of considerable interest to clarify the reason that the iridium complex is not reactive for the reaction of eq 2 despite its high reactivity for oxidative addition. In the present work, we theoretically investigated the C−C σ-bond cleavage of cyclopropene promoted by RuCl2(PR3)2 and IrCl(CO)(PMe3)2. Our purposes here are (i) to elucidate the reaction mechanism and the electronic process of this reaction (eq 2), (ii) to make a clear comparison of the reaction between the ruthenium and the iridium systems, (iii) to clarify the reason that the ruthenium complex is reactive for this C−C σ-bond cleavage but the iridium complex is not, and (iv) to find the important factor for this reaction. We wish to emphasize that this work presents the first theoretical understanding of the C−C σ-bond cleavage reaction of cyclopropene.

follows: (i) This reaction occurs not only via C−C σ-bond cleavage but also via complex rearrangement, leading to the formation of an interesting vinylcarbene species. (ii) The CC double bond of cyclopropene coordinates with the Ru(II) center, but the neighboring C−C single bond, which does not interact with the ruthenium center, is activated in the reaction. (iii) The other C−C single bond changes to a CC double bond and the CC double bond changes to a C−C single bond concomitantly with formation of a Rucarbene double bond; see Scheme 1. These features are completely different from those of the typical oxidative addition, eq 1. The oxidative addition of eq 1 occurs through charge-transfer interactions (CTs) of the HOMO and LUMO of the cycloalkane with the metal center. However, the C−C σ-bond cleavage of eq 2 cannot be understood with the similar CT interactions because the C−C σ-bond is activated by the reaction in spite of the absence of the direct interaction with the Ru center. This reaction is similar to pericyclic reactions such as the Cope rearrangement9 rather than oxidative addition, because one C− C σ-bond is broken and one CC double bond moves to the neighbor position (see eq 2). Also, this reaction is important for syntheses of various metal vinylcarbenes; for instance, this protocol was first applied to syntheses of vinylcarbene complexes of titanocene(II) and zirconocene(II) in 1989.10 Since then, various vinylcarbene complexes of later transition metals such as tungsten,11 rhenium,12 and ruthenium7,13 have been synthesized by this reaction. Despite its importance, changes in geometry, bonding nature, and electronic structure by this reaction have not been discussed yet. In this regard, it is worthy of elucidating the details of eq 2. Such knowledge is of considerable importance in a wide area of chemistry such as transition metal chemistry, organic and organometallic chemistry, and catalytic chemistry. Although various metal complexes can be successfully applied to this reaction,7,10−13 several exceptions were reported. For example, the Vaska-type iridium complex cannot perform this C−C σbond cleavage but produces a cyclopropene adduct; see eq 3.14

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MODELS AND COMPUTATIONAL DETAILS

Models. We employed here RuCl2(PMe3)2 and cyclopropene as models of RuCl2(PPh3)2 and 1,1-diphenylcyclopropene, which were used in the experiment.7 For the iridium reaction system, we employed IrCl(CO)(PMe3)2 because this complex was experimentally used for the reaction with 1,1-diphenylcyclopropene (eqs 3 and 4).14 We also investigated simple model complexes with MP2 to MP4(SDQ), CCSD, CCSD(T), CASSCF, and CASPT2 methods, because previous theoretical studies suggested that the multireference method must be employed for the theoretical study of carbene species;15−22 see Supporting Information pages S3 and S4. Also, remember that the multireference method was employed for the similar Cope rearrangement reaction.9c,d In the model, PMe3 was substituted for PH3 to save computational cost. The geometries of the model systems were taken to be the same as those of the real systems, where only the PH3 geometries were reoptimized. All calculations were carried out under C1 symmetry. Computations. The geometry was optimized by the DFT method with the B3LYP functional.23−25 The vibrational frequency was evaluated with the same method. The restricted and unrestricted instabilities were checked in all optimized geometries. The details of the CASSCF and CASPT2 calculations will be described below; see also Supporting Information page S3. Two basis set systems (BS-I and BS-II) were employed for calculations here: In BS-I, Los-Alamos effective core potentials (ECPs) were employed to replace core electrons of ruthenium and iridium atoms, and (341/321/31) and (341/321/21) basis sets were employed to represent valence electrons of ruthenium and iridium atoms, respectively.26 Usual 6-31G(d) basis sets were used for carbon, oxygen, chlorine, phosphorus, and hydrogen atoms.27 In BS-II, Stuttgart−Dresden−Bonn ECPs and valence basis sets (8881/7771/ 661/1) were used for ruthenium and iridium atoms.28,29 For carbon, oxygen, chlorine, phosphorus, and hydrogen atoms, cc-pVDZ basis sets were used.30 BS-I was used for geometry optimization and calculation of vibrational frequency. BS-II was used for evaluation of energy changes. Zero-point energy was evaluated with the DFT/BS-I method under assumption of a harmonic oscillator. DFT, MP2 to MP4, and CCSD(T) calculations were carried out with the Gaussian 03 program.31 CASSCF and CASPT2 calculations were performed with the MOLCAS 6.0 program.32 Valence-bond (VB)-type orbitals were employed here to analyze the electronic process of the reaction. To evaluate a VB-type orbital, the CASVB

In the presence of excess IrCl(CO)(PMe3)2, a bimetallic complex is formed via the direct insertion of IrCl(CO)(PMe3)2 into the C−C σ-bond of the cyclopropene adduct of IrCl(CO)(PMe3)2; see eq 4. This eq 4 is the usual oxidative

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Figure 1. Optimized structures of precursor complexes, transition states, and product complexes for ruthenium and iridium reaction systems. Distances in angstroms and angles in degrees. the product is responsible for the larger discrepancy in the ΔE value than in the Ea value between the CASPT2 and the other methods. The Ea and ΔE values of the realistic PMe3 system were calculated only with the DFT(B3LYP) method; see Table S1. The DFT(B3LYP)-calculated Ea and ΔE values are little different between the model and real systems except for the moderately different ΔE value of the ruthenium reaction system, suggesting that the time-consuming CASPT2 computational results of the simple model system can be successfully employed for discussion.

program implemented in MOLCAS was used,33 in which the transformation was performed so as to maximize the overlap between the CASSCF and VB-type wave functions; see Supporting Information page S3 for VB and CASVB methods. Tests of Computational Method and Model. Since the RHFUHF instability was detected in the Hartree−Fock wave function of the metal vinylcarbene complexes PRu and PIr, we had better to calculate the system with the CASSCF and CASPT2 methods. Because such calculations are time-consuming, we employed here a simple model system with the PH3 ligand. Here, we examined various computational methods such as the broken-symmetry (unrestricted) MP2 to MP4, broken-symmetry CCSD(T), broken-symmetry DFT, and CASSCF/CASPT2 methods, where the term “broken-symmetry” is omitted for brevity hereafter; see Supporting Information page S3 for RHF-UHF instability. In the CASSCF calculation, we employed an active space consisting of six electrons in six orbitals, which is described below in more detail. Among these methods, the CCSD(T) method is the most accurate when the multireference character is not large. When the multireference character is large, the CASPT2 method is the most reliable. The activation energy (Ea) and the reaction energy (ΔE) are defined as the energy differences between a precursor complex PC and a transition state TS and between PC and a product P, respectively. Important results are summarized, as follows: (i) the Ea and ΔE values somewhat fluctuate around MP3, as shown in Table S1; (ii) the MP4(SDQ)-calculated Ea and ΔE values are similar to the CCSD(T)-calculated value; (iii) the DFT(B3LYP)-calculated Ea value is similar to the CCSD(T)-calculated value, and the DFT-calculated ΔE value is not very much different from the CCSD(T)-calculated one; the deviation is 5 to 6 kcal/mol; (iv) the CASPT2-calculated Ea value is almost the same as the CCSD(T)- and DFT-calculated values in the ruthenium system and moderately smaller than the CCSD(T)and DFT-calculated values in the iridium system; and (v) the CASPT2-calculated ΔE value is considerably more negative than the CCSD(T)- and DFT-calculated values in both ruthenium and iridium systems. These results indicate that the DFT(B3LYP) method is not bad for this reaction, but the CASPT2 seems better because the RHFUHF instability is observed in the Hartree−Fock (HF) wave function of the product, as mentioned above. It is likely that this instability in

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RESULTS AND DISCUSSION

Geometry Changes in C−C σ-Bond Cleavage of Cyclopropene Promoted by the Ruthenium and Iridium Complexes. According to previous work,14 the first step is cyclopropene coordination with a metal center to form a precursor complex. We investigated the C−C σ-bond cleavage starting from the precursor complex, as shown in Figure 1. Hereafter, we name precursor complexes PCRu and PCIr, transition states TSRu and TSIr, and vinylcarbene products PRu and PIr for the ruthenium and iridium systems, respectively, where the subscripts Ru and Ir denote the ruthenium and iridium reaction systems. As shown in Figure 1, the cyclopropene adduct RuCl2(PMe3)2(C3H4) PCRu is pseudosquare pyramidal.33 The center of the C1−C2 bond exists on the z-axis, where the C1 C2 bond is almost parallel to the P−Ru−P plane and perpendicular to the z-axis; see Scheme 1 for C1, C2, and C3 atoms. Upon coordination, the C1C2 double bond of cyclopropene is somewhat elongated by 0.096 Å, and the C1−C2−C3 and C1−C3−C2 bond angles moderately change from 65° and 51° to 62° and 55°, respectively. However, the C1−C3 and C2−C3 bond lengths are almost the same as those of free cyclopropene, as expected. When going to TSRu from PCRu, drastic changes are observed in geometry; the C1−C3 bond is substantially elongated by 0.516 Å, the C2−C3 bond becomes somewhat shorter by about 0.08 Å, and the C1−C2− 8191

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C3 angle considerably increases by 30°, whereas the C1−C2 bond length changes little. The Ru−C1 bond becomes somewhat shorter in TSRu than in PCRu by 0.145 Å, but the Ru−C2 bond is somewhat elongated by 0.122 Ǻ . These geometry changes indicate that the C1−C3 bond is nearly broken, the Ru−C1 and C2−C3 bonds are becoming stronger, and the Ru−C2 bond is becoming weaker in TSRu. In the product RuCl2(PMe3)2(CH−CHCH2), PRu, the Ru−C1 bond (1.845 Å) is much shorter than that of PCRu by 0.272 Å, suggesting that the Ru−C1 bond has the nature of a double bond. The Ru−C1 and the C2−C3 bond lengths of PRu agree well with the experimental values (1.84 and 1.35 Å, respectively) of the similar ruthenium carbene complexes.8a,34 The C2−C3 bond is much shorter than the C1−C2 bond in PRu, indicating that the C2−C3 bond becomes a double bond and the C1−C2 bond becomes a single bond. These geometrical features indicate that vinylcarbene (CH−CHCH2) is formed in the product. Similar geometry changes are observed in the reaction of IrCl(CO)(PMe3)2 except for the trigonal bipyramidal structure around the Ir center, as shown in Figure 1. In the cyclopropene adduct IrCl(CO)(PMe3)2(C3H4), PCIr, two PMe3 ligands and cyclopropene take positions on the equatorial plane and the Cl and CO ligands take positions on the pseudo-C3 axis because the anion ligand tends to take an axial position and the CC double bond tends to take an equatorial position in a d8 trigonal bipyramidal structure. This structure is often observed in a d8 five-coordinate complex. In this PCIr, the C1C2 double bond of cyclopropene is perpendicular to the Cl−Ir− CO axis and its bond length is considerably elongated by 0.130 Å, which is somewhat longer than that in PCRu. When going from PCIr to TSIr, the C1−C3 distance becomes longer and the C1−C2−C3 angle becomes much larger than those of the ruthenium system. On the other hand, the Ir−C1 bond length becomes shorter by 0.123 Å. This bond shortening occurs to a lesser extent than the Ru−C1 bond shortening. The C2−C3 bond becomes shorter by 0.108 Å, which is similar to that of the ruthenium reaction system. The product IrCl(CO)(PMe3)2(CH−CHCH2), PIr, is also trigonal bipyramidal, as expected, in which two PMe3 ligands and vinylcarbene take positions on the equatorial plane. The geometry of the vinylcarbene moiety is almost the same in both the iridium and ruthenium systems except for the M−C1 distance. Note that the Ir−C1 distance is somewhat longer than the Ru−C1 by about 0.1 Å despite almost the same Ir−C1 distance as the Ru− C1 one in the precursor complex. This result will be discussed below in relation to the difference in reactivity between the iridium and ruthenium systems. To discuss the details in geometry changes along the reaction, we evaluated the IRC (intrinsic reaction coordinate) with the DFT(B3LYP)/BS-I method; unfortunately, the IRC calculation stopped at around +3.0 and −3.0 amu1/2 Bohr; the unit “amu1/2 Bohr” is omitted for brevity hereafter. This is because the geometries at IRC = −3.0 and +3.0 are almost the same as those of the precursor and the product complexes, respectively,35 and hence the energy gradient becomes too small to determine the reaction coordinate; see Figure S1 in the Supporting Information for the geometries at IRC = +3.0 and −3.0. Changes in energy and important geometrical parameters relative to those of PCRu and PCIr are displayed against the IRC in Figure 2, where IRC = 0.0 corresponds to the transition state, TSRu and TSIr. The Ru−C2 and C1−C3 bonds become gradually longer, while the Ru−C1 bond becomes gradually

Figure 2. Changes in energy and important geometrical parameters along the IRC of the ruthenium and iridium reaction systems.

shorter, as the reaction proceeds from IRC = −3.0 to +3.0. These changes correspond to the formation of the RuC1 double bond and the breaking of the Ru−C2 and C1−C3 bonds in the reaction. The C2−C3 bond becomes somewhat shorter, but the C1−C2 bond becomes somewhat longer when going from IRC = −3.0 to +3.0, which corresponds to the change of the C2−C3 single bond to the C2C3 double bond and that of the C1C2 double bond to the C1−C2 single bond. These geometry changes are consistent with the reaction of eq 2; see also Scheme 1. Important here is that all these geometry changes gradually occur during the reaction and no characteristic change is found around the transition state, indicating that the electronic structure also gradually changes during the reaction. Energy Changes by the C−C σ-Bond Cleavage. In the real system, the Ea and ΔE values were calculated only with the DFT(B3LYP) method, because other methods are timeconsuming. As mentioned above, the comparison between the real and simple model systems suggests that the CASPT2calculated values of the model system are useful in discussing the energy changes. Apparently, the Ea value of the ruthenium system is considerably smaller than that of the iridium system, and the ΔE value of the ruthenium system is much more negative than that of the iridium system in both the simple model and real systems. These Ea and ΔE values indicate that this C−C σ-bond activation reaction occurs more easily in the ruthenium system than in the iridium system, which agrees with the experimental facts that the reaction occurs readily in the ruthenium system but does not in the iridium system.7,14 Electronic Structure of the Vinylcarbene Complex. We briefly investigate here the electronic structure of the metal− vinylcarbene product, because the Hartree−Fock wave function exhibits instability in this product; see Supporting Information 8192

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In this reaction, various events are involved, as shown in Scheme 1: (i) the C1−C3 bond is broken concomitantly with the conversion of the C1C2 double bond to the C1−C2 single bond; (ii) the C2−C3 single bond changes to a C2C3 double bond; and (iii) the M−C2 bond is broken and simultaneously the MC1 double bond is formed. It is expected that many kinds of singlet coupling occur in this reaction, as shown in Scheme 2.

pages S3 and S4 for several theoretical terms such as biradicaltype open-shell, broken-symmetry, CASSCF(4 in 4), etc. We analyzed Kohn−Sham orbitals of PRu and PIr calculated by the DFT(B3LYP) method; see Figure 3 for PRu and Supporting

Scheme 2. Possible Distribution of Unpaired Electrons around the Transition State

Figure 3. π-Type molecular orbitals of PRu (isovalue = 0.08 au) calculated by the DFT(B3LYP) and CASSCF(4 in 4) methods. Number represents occupation number of the CASSCF natural orbital.

For such complicated bond breaking and formation processes including various singlet couplings, the valence bond wave function is expected to provide a clear understanding. However, the conventional VB method is too expensive to apply to the transition metal complex due to the heavy computational cost.37 To avoid this difficulty, the VBtype orbitals are reconstructed from the CASSCF wave function with the CASVB method proposed by Cooper and co-workers,37−43 which has been applied to chemical reactions of organic molecules.44−46 The CASSCF calculation was carried out with an active space consisting of six electrons in six MOs. These six MOs correspond to the bonding and antibonding MOs in the Ru− C1, Ru−C2, and C1−C3 moieties;47 note that this active space contains that of the CASSCF calculation of the ruthenium− vinylcarbene complex discussed above. Figure 4 shows

Information Figure S2 for PIr. The Hartree−Fock method presents similar MOs; see Figure S3. In both PRu and PIr, two π-type MOs with no node and one node are found in the occupied level, while two π*-type MOs with two and three nodes are found in the unoccupied level. These MOs are similar to those of butadiene.36 The broken-symmetry Hartree−Fock (UHF)/BS-II method provides lower total energy than the RHF method by 5.8 and 8.6 kcal/mol for PRu and PIr, respectively. The spin density of the UHF wave function suggests that the metal−vinylcarbene moiety takes a biradicaltype open-shell singlet electronic structure in PRu and PIr; see Supporting Information Figure S4. Considering the biradical character, we further investigated PRu and PIr with the CASSCF(4 in 4) method, where we employed an active space consisting of four electrons in two sets of π- and π*-MOs of the MCH−CHCH2 moiety. We denote this active space as (4 in 4) hereafter. The natural orbitals and their occupation numbers of the ground state are summarized in Figure 3; see also Figure S3. These natural orbitals (φ1π to φ4π) are essentially the same as Kohn−Sham orbitals. Their occupation numbers suggest that the electron excitation from φ2π to φ3π somewhat contributes to the total wave function. Consistent with this occupation number, the main configuration is a closed-shell singlet with a weight of 90.0% to which the second (0.04%) and the third leading (0.03%) electron configurations moderately contribute to the total wave function. These second and third leading terms, which correspond to the φ2π → φ 3π two-electron and one-electron excitations, respectively, induce the biradical character in the MCH− CHCH2 moiety. Although their weights are not large, the occupation number of the φ3π is considerably larger than zero and that of φ2π is considerably smaller than 2.0, suggesting that the biradical character should be properly considered in PRu and PIr. Electronic Process of the C−C σ-Bond Cleavage. To clarify the reason that the reaction occurs easier in the ruthenium system than in the iridium system, it is necessary to elucidate the electronic process of this C−C σ-bond cleavage.

Figure 4. CASSCF(6 in 6) natural orbitals and their occupation numbers of TSRu (isovalue = 0.08 au).

important natural orbitals at the transition state; the natural orbitals φ1TS, φ2TS, and φ3TS correspond to the Ru−C1, the Ru−C2, and the C1−C3 σ-bonding MOs, respectively. Their occupation numbers are moderately smaller than 2.00. The φ4TS, φ5TS, and φ6TS correspond to the antibonding MOs of the Ru−C1, the Ru−C2, and the C1−C3 σ-bonds, respectively. Their occupation numbers are not very large but not negligibly small; they are 0.08, 0.16, and 0.11, respectively. These results indicate that the Ru−C2 and the C1−C3 bonds are becoming 8193

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Figure 5. CASVB orbitals and their overlaps along the IRC of the ruthenium reaction system.

weaker, but the RuC1 double and the C2−C3 π-bonds are not yet formed in TSRu. The VB-type orbitals ψ1 to ψ6 obtained from the CASSCF(6 in 6) wave function are shown in Figure 5, where the geometry was taken from the IRC calculation. The important overlap integrals are also shown in Figure 5, where the positive and the negative values indicate bonding and antibonding interactions, respectively, and a large value represents a strong interaction; see Supporting Information Figure S5 for the VB-type orbitals of the iridium system. First, we will discuss the bond-breaking process in the reaction. In the reactant, the C1−C3 σ-bond is mainly constructed by the ⟨ψ1|ψ2⟩ bonding overlap, where the overlap integral between ψ1 and ψ2 is represented by ⟨ψ1|ψ2⟩ for brevity. The directions of ψ1 and ψ2 change little when going to IRC = 0.0 from IRC = −3.0. After TSRu, the ψ1 becomes a sp2type p orbital of the C3 atom, and simultaneously the ψ2 changes its direction toward the Ru atom. These direction changes are consistent with the changes in orbital overlaps, as follows: The overlap integral ⟨ψ1|ψ2⟩ is large (0.78) at IRC = −3.0, but gradually decreases to 0.57 when going to IRC = 0.0. Then, it considerably decreases to a small value (0.17) at IRC = +1.0 and finally to a negligibly small value (−0.09) at IRC = +3.0. These changes correspond to the C1−C3 bond breaking in the reaction. The above results indicate that the C1−C2 bond breaking occurs after TSRu, though the C1−C2 distance is considerably elongated at TSRu. The ⟨ψ3|ψ4⟩ overlap, whose value is about 0.50 at IRC = −3.0, contributes to the Ru−C1 bonding interaction before TSRu. This overlap is considerably smaller than the ⟨ψ1|ψ2⟩ overlap at IRC = −3.0. This is not surprising because the ⟨ψ1|ψ2⟩ overlap corresponds to the C1− C3 single bond and the ⟨ψ3|ψ4⟩ overlap corresponds to the Ru− C1 bond. Since the ⟨ψ5|ψ6⟩ overlap also corresponds to the interaction between the C1C2 double bond and the ruthenium center, the ⟨ψ3|ψ4⟩ and ⟨ψ5|ψ6⟩ overlaps are similar to each other (0.51) at IRC = −3.0. However, the ⟨ψ5|ψ6⟩ overlap decreases very much to 0.19 when going to IRC = +1.0 and finally becomes nearly zero at IRC = +3.0, while the ⟨ψ3|ψ4⟩ overlap changes little in the reaction. These changes correspond to the fact that the Ru−C2 bond is broken but the

Ru−C1 bond is kept in the reaction. The ⟨ψ3|ψ5⟩ overlap is 0.48 at IRC = −3.0, little changes at TSRu, but then starts to decrease around IRC = 0.0 to 1.0, and finally decreases to 0.24 at IRC = +3.0, indicating that the C1−C2 π-bond breaking occurs after TSRu. However, it does not become negligibly small at IRC = +3.0, suggesting that the C2 p orbital (ψ5) still keeps some conjugation with the C1 p orbital (ψ3) at IRC = +3.0; note that the C1 p orbital interacts with the Ru dπ orbital (ψ4) and simultaneously forms a π-conjugation with the C2 p orbital in PRu. Then, we will discuss the bond formation process in the reaction. Though the ⟨ψ2|ψ6⟩ overlap is very small (−0.04) at IRC = −3.0, it considerably increases around IRC = +1.0 and finally reaches a significantly large value of 0.43 at IRC = +3.0. This change corresponds to the Ru−C1 bond formation in the reaction; see the ψ2 and ψ6 orbitals at IRC = +3.0 in Figure 5. Since the ⟨ψ3|ψ4⟩ overlap corresponding to the Ru−C1 bond is kept during the reaction, as discussed above, the large value of this ⟨ψ2|ψ6⟩ indicates that one more Ru−C1 bonding interaction is formed in the product. Because of this new bonding interaction, the Ru−C1 bond is understood to be a double bond in PRu, which is the origin of the short Ru−C1 distance in PRu, as mentioned above. The ψ1 is a σ orbital on the C3 at IRC = −3.0, but becomes a pπ orbital around IRC = 0.0 to +1.0. Consistent with this direction change, the ⟨ψ1|ψ5⟩ is small at IRC = −3.0 but becomes considerably large (0.65) at IRC = +3.0. This increase in the ⟨ψ1|ψ5⟩ overlap corresponds to the formation of the C2−C3 π-bond. It is noted that the ⟨ψ5|ψ6⟩ overlap decreases and the ⟨ψ2|ψ6⟩ and ⟨ψ1|ψ5⟩ overlaps increase around IRC = 0.0 to +1.0. These changes indicate that the Ru− C2 bond is gradually broken and the C2−C3 π-bond and the RuC1 double bond are gradually formed after the transition state.48 Almost the same changes in VB orbitals are observed in the iridium system; see Supporting Information Figure S5. The direction changes in the ψ4 and ψ6 can be understood in terms of the hybridization change of metal d orbitals: At IRC = −3.0, the ψ4 and ψ6 have a large component in the yz-plane, which leads to the large ⟨ψ3|ψ4⟩ and ⟨ψ5|ψ6⟩ overlaps. After TSRu, however, the directions of these ψ4 and ψ6 significantly change, and finally large components are observed in the xz8194

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Scheme 3. Changes in Valence-Orbital Overlaps

plane at IRC = +3.0. This fact suggests that the 4dz2 − 4dyz hybridization participates in bonding interactions at IRC = −3.0, but the 4dz2 − 4dzx hybridization participates at IRC = +3.0. When the dyz and dzx orbitals are close in energy, such hybridization change readily occurs. However, if not, the hybridization change occurs with difficulty. This strongly suggests that the energy difference among metal d orbitals deeply relates to the Ea value; if such hybridization change easily occurs, the activation barrier is small. This will be discussed in the next section. In summary, the CASVB orbitals constructed from the CASSCF(6 in 6) wave function provide a clear understanding of the C−C σ-bond cleavage followed by the bond-rearrangement processes, as shown in Scheme 3: (i) The C1−C3 bond becomes somewhat weaker in the transition state and is almost broken after the transition state, as shown by the considerable decrease of ⟨ψ1|ψ2⟩ after the transition state. (ii) This leads to the formation of unpaired electrons on the C1 and C3, as represented by the ψ1 and ψ2 orbitals; see Scheme 3A. (iii) The ψ1 begins to overlap with the ψ5 to form the C2−C3 π-bond around IRC = 0.0 to +1.0, which is shown by the increase of ⟨ψ1|ψ5⟩; see Scheme 3B. (iv) The ψ5 overlaps with the ψ6 to form the M−C2 bonding interaction in the reactant (Scheme 3C), but changes its bonding partner to the ψ1 around IRC = 0.0 to +1.0 to form the C2−C3 π-bond in the product (Scheme 3B). (v) The ψ6 loses the bonding partner around IRC = 0.0 to +1.0 but finds a new partner ψ2 around there to form a new Ru−C1 bonding interaction; see Scheme 3C. (vi) The ⟨ψ3|ψ4⟩ overlap, corresponding to the M−C1 bonding interaction, is kept in the reaction (Scheme 3D), and hence, the increase of the ⟨ψ2|ψ6⟩ overlap leads to the formation of the RuC1 double bond. From the above discussion, the hybridization of metal d orbitals should change in the reaction to induce the bonding changes of (iii) to (v), as follows: In the precursor complex, cyclopropene coordinates with the metal center. To form this metal−cyclopropene bonding interaction, the 4dz2 − 4dyz hybridization must occur to form the Ru−C1 and Ru−C2 bonds;48 remember that the C1C2 double bond of cyclo-

propene exists on the yz-plane. In the ruthenium vinylcarbene product, on the other hand, the metal d orbitals overlap with the C1 sp2 orbital and the C1 p orbital. To form such bonding interactions, the 4dz2 − 4dzx hybridization must occur; remember that the C1 p orbital is parallel to the x-axis. In other words, the 4dz2 − 4dyz hybridization of the cyclopropene adduct must change to the 4dz2 − 4dzx one in the vinylcarbene product. This is a key factor for the difference in reactivity between the ruthenium and iridium systems, which will be discussed below. Comparison between Ruthenium and Iridium Systems. Despite the similarities in geometry changes and the bonding characters between the iridium and ruthenium systems, the Ea is much larger and the ΔE is much less exothermic in the iridium system than those of the ruthenium system. It is of considerable importance to elucidate the reasons for the larger Ea and the smaller exothermicity in the iridium system than in the ruthenium system. We inspected the VBtype orbitals in Figures 5 and S5 and found that the ⟨ψ2|ψ6⟩ overlap is somewhat smaller in the iridium system than in the ruthenium system around IRC = 0.0 to +3.0; see also Figure 6. The other overlaps are not much different between these two systems. This means that the Ir−C1 bonding interaction formed by the reaction is somewhat weaker than the Ru−C1 bonding interaction. Actually, the Ir−C1 bond is somewhat longer than the Ru−C1 bond in the vinylcarbene product, as discussed

Figure 6. ⟨ψ2|ψ6⟩ overlap along the IRC of the iridium reaction system. 8195

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above. To provide the good ⟨ψ2|ψ6⟩ overlap, the ψ6 must extend toward the ψ2 orbital. In the ruthenium system, the ψ6 extends toward the ψ2, whereas the direction of the ψ6 deviates somewhat from the ψ2 in the iridium system, as shown in Scheme 4. This is the reason that the ⟨ψ2|ψ6⟩ overlap is small in the iridium system.

occupied in a formal sense. This electronic state does not correspond to a ground state but an excited state, which we name “cyclopropene valence state” hereafter. Similarly, the dz2 and dzx must be singly occupied to form the valence state in the product, which is named “vinylcarbene valence state”. The promotion energies to these valence states are important to induce the hybridization. We carried out the state-averaged CASSCF(8 in 9) and multistate CASPT2 calculations of the metal moieties RuCl2(PH3)2 and IrCl(CO)(PH3)2 to evaluate the promotion energies to these valence states. In this CASSCF calculation, 8 roots were solved and density matrices of the lower 6 states are averaged, where a level shift of 0.2 au was employed in the PT2 calculation; see Supporting Information page S4 for state-averaged CASSCF and the level shift. In RuCl2(PH3)2, the ground state corresponds to the (4dxy)2(4dyz)2(4dz2)2(4dzx)0(4dx2−y2)0 electron configuration in a formal sense. The first excited state is assigned as the vinylcarbene valence state, because the 4dz2 and 4dzx orbitals are singly occupied. This state is energetically higher than the ground state by 1.1 and 5.1 kcal/mol by the multistate CASSCF and CASPT2 methods, respectively; see Figure 7. The cyclopropene valence state is calculated at the fifth excited state, in which the 4dz2 and 4dyz orbitals are singly occupied. This state is much higher in energy than the vinylcarbene valence state by 20.9/19.4 kcal/mol at the multistate CASSCF/ CASPT2 levels; see Figure 7. These results indicate that the hybridization change in the reaction is downhill, which is

Scheme 4. Comparison of ψ2 and ψ6 between the Ruthenium and Iridium Systems at IRC = +3.0 Geometry

The next issue is to find the reason that the direction of the ψ6 changes well toward the ψ2 orbital in the ruthenium system but does not in the iridium system when going from the cyclopropene adduct to the vinylcarbene product. As discussed above, the dz2 − dyz hybridization must change to the dz2 − dzx one when going from the cyclopropene adduct to the vinylcarbene product. It is likely that if this hybridization easily changes, the direction of the ψ6 easily changes toward the ψ2 orbital. For the dz2 − dyz hybridization in the valence state of the cyclopropene adduct, these two orbitals must be singly

Figure 7. Natural orbitals, their occupation numbers, and promotion energies to a valence state in the metal moieties of ruthenium and iridium reaction systems (CASSCF(8 in 9)/BS-II, isovalue = 0.08 au). (a) Five metal d orbitals are selected. (b) The CASSCF/CASPT2 calculated values (in kcal/mol). (c) The 5dxy − 5dyz and 5dyz + 5dxy somewhat mix with 5dzx and (5dx2 + 6s), leading to a complex shape of orbitals. 8196

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consistent with the small Ea and the large exothermic ΔE values in the reaction by the ruthenium complex; see Table 1.

occupied, but the 4dx2−y2 and 4dzx orbitals are unoccupied in the ground state, because the 4dx2−y2 orbital is destabilized by the antibonding interaction with two Cl and two PH3 ligands and the 4dzx orbital is destabilized by the antibonding interaction with the doubly occupied Cl pz orbital. In the cyclopropene valence state, the 4dz2 and 4dyz must be singly occupied, but in the vinylcarbene valence state the 4dz2 and 4dzx orbitals must be singly occupied. Because of the antibonding interaction with the Cl pπ orbital, the 4dzx exists at higher energy than the 4dyz orbital, as shown in Scheme 5. As a result, the hybridization change from the cyclopropene valence state to the vinylcarbene valence state induces considerable energy stabilization. This is the reason for the large exothermicity of the Ru reaction system. In d8 IrCl(CO)(PH3)2, which is a part of the trigonal bipyramidal structure, the 5dy2−z2, 5dxy, 5dzx, and 5dyz are doubly occupied but the 5dx2 + 6s is unoccupied;49 see ref 50 for 5dx2. In the cyclopropene valence state, the 5dyz and 5dx2 + 6s must be singly occupied, while in the vinylcarbene valence state the 5dzx and 5dx2 + 6s must be singly occupied. The 5dyz exists at much higher energy than the 5dzx because of the bent P−Ir−P angle; remember that the phosphine lone pair orbitals destabilize the 5dyz orbital, as shown in Scheme 6. Thus, the

Table 1. Activation Energies (Ea) and Reaction Energies (ΔE) of Ruthenium and Iridium Reaction Systemsa (in kcal/ mol) ruthenium reaction method Model System DFT(B3LYP)b CCSD(T)b CASSCF(6 in 6) CASPT2 Real System DFT(B3LYP)b a

iridium reaction

Ea

ΔE

Ea

ΔE

30.72 29.38 33.33 30.33

−25.63 −31.44 −44.96 −38.60

43.53 47.32 39.61 40.98

−8.53 −3.19 −23.09 −15.99

30.73

−30.94

43.58

−8.47

b

BS-II was used for all calculations. Broken-symmetry method was employed.

In IrCl(CO)(PH3)2, the ground state corresponds to the (5dy2−z2)2(5dxy)2(5dzx)2(5dyz)2(5dx2 + 6s)0 electron configuration. The cyclopropene valence state is calculated as the first excited state, which is higher than the ground state by 36.6/ 32.2 kcal/mol at the multistate CASSCF/CASPT2 levels; see Figure 7. The vinylcarbene valence state is calculated at the fifth excited state,49 which is energetically much higher than the cyclopropene valence state by 44.6/42.5 kcal/mol at the multistate CASSCF/CASPT2 levels. These results indicate that the hybridization change in the reaction is significantly uphill, indicating that the hybridization change is very difficult in the iridium system. As a result, the reaction of the iridium complex occurs with larger Ea and much less exothermic ΔE values than those by the ruthenium complex. The next is to clarify the reason that the promotion energy for the vinylcarbene valence state is much larger in the iridium reaction system than in the ruthenium system. The reason is easily understood based on the schematic d−d orbital splitting by the ligand-field theory, as shown in Scheme 5; in d6 squareplanar RuCl2(PH3)2, the 4dxy, 4dyz, and 4dz2 orbitals are doubly

Scheme 6. Energy Splitting between 5dzx and 5dyz Orbitals of IrCl(CO)(PMe3)2

5dyz − (5dx2 + 6s) hybridization needs a smaller promotion energy than the 5dzx − (5dx2 + 6s) hybridization, and hence the vinylcarbene valence state exists at considerably higher energy than the cyclopropene valence state in the iridium product. This is the reason that the hybridization change is downhill in the ruthenium system but highly uphill in the iridium system. On the basis of the above results, it should be concluded that the d orbital splitting by ligand-field and d-electron number determine how easily the hybridization changes and also how easily the C−C σ-bond of cyclopropene is activated by the transition metal complex.

Scheme 5. Ground State, Cyclopropene Valence State, and Vinylcarbene Valence State of Ru and Ir Systemsa

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CONCLUSIONS In this work, the C−C σ-bond activation of cyclopropene by RuCl2(PPh3)2 and IrCl(CO)(PMe3)2 was theoretically investigated mainly with the broken-symmetry DFT and the CASSCF/CASPT2 methods. In this reaction, (i) the CC double bond of cyclopropene, which coordinates with the metal center, is not activated but changes to a C−C single bond, (ii) the neighboring C−C single bond that does not interact with the metal center is activated, and (iii) another C−C single bond changes to a CC double bond. This reaction mechanism is completely different from the σ-bond activation of strained cycloalkane via the oxidative addition to the transition metal

a

In the valence states of IrCl(CO)(PH3)2, several d orbitals induce mixing with each other; φd1 = 5dyz + (5dx2 + 6s), φd2 = 5dyz − (5dx2 + 6s), φd3 = 5dxy + 5dyz, φd4 = 5dzx + (5dx2 + 6s), φd5 = 5dyz − 5dxy, and φd6 = (5dx2 + 6s) − 5dzx; see Figure 7 and Supporting Information page S5. 8197

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complex (eq 1) but similar to pericyclic reactions such as Cope rearrangement.9 All the computational results indicate that the reaction occurs more easily by the ruthenium complex with smaller Ea and larger exothermic ΔE values than those by the iridium complex, which is consistent with the experimental results that the C−C σ-bond activation of cyclopropene is performed easily by the ruthenium system but not by the iridium system. The VB-type wave function indicates that the Ir−vinylcarbene bond is significantly weaker than the Ru−vinylcarbene bond, because the d6 square pyramidal complex of Ru is more favorable than the d8 complex of Ir for this bond formation. Important features of this reaction are summarized, as follows: (i) The C1−C3 σ-bond is broken to afford two σ-type singly occupied orbitals on the C1 and C3 atoms. (ii) The σtype singly occupied orbital on the C3 changes to a pπ-type orbital in the reaction and begins to overlap with the C2 pπ-type orbital to form the C2−C3 π-bond around the transition state. (iii) Simultaneously, the M−C2 bonding interaction is weakened, and hence, the metal d orbital employed for the M−C2 bond begins to overlap with the singly occupied pπ orbital on the C1 that is formed by the C1−C3 σ-bond breaking. This leads to the M−C1 π-bond formation. (iv) Because the M−C1 σ-bond is kept during the reaction, the formation of the M−C1 π-bonding interaction in addition to the M−C1 σbonding interaction leads to the formation of the MC1 double bond. In other words, the C1−C3 single bond is easily broken because two unpaired electrons formed by the C1−C3 bond breaking can easily find bonding partners with the help of d orbitals of the metal center. In the cyclopropene adduct, the 4dz2 − 4dyz hybridization must occur, while in the vinylcarbene product the 4dz2 − 4dzx hybridization must occur. These valence-state electron configurations correspond to the excited states of RuCl2(PMe3)2 and IrCl(CO)(PMe3)2. We evaluated the promotion energies to these states by the multistate CASSCF/CASPT2 method, where the metal moiety was taken from the precursor complex. In the ruthenium system, the vinylcarbene valence state is more stable than the cyclopropene valence state by 21.5/19.4 kcal/mol. This indicates that the 4dz2 − 4dyz hybridization changes to the 4dz2 − 4dzx one with energy stabilization. In the iridium system, on the other hand, the cyclopropene valence state is considerably more stable than the vinylcarbene valence state by 44.6/42.5 kcal/mol, suggesting that the 5dyz − (5dx2 + 6s) hybridization changes to the 5dzx − (5dx2 + 6s) one with considerable energy destabilization. This is the reason for the larger Ea and the smaller exothermic ΔE values in the iridium system than in the ruthenium system. It is important to elucidate the reason that such a difference in hybridization is present between the ruthenium and iridium systems. We can easily understand the reason based on the d orbital splitting by ligand-field and the d electron numbers. These explanations suggest that the d6 square pyramidal complex is reactive for this type of C−C σ-bond activation, but the d8 trigonal bipyramidal one is not. This type of C−C σ-bond activation of cyclopropene occurs through complicated electronic processes. Our work presents the first clear understanding of this reaction based on the CASVB method. We believe that this understanding is useful for discussing the similar σ-bond activation reaction.

Article

ASSOCIATED CONTENT

S Supporting Information *

Full representation of ref 31, brief explanation for theoretical and computational terminologies used in this work (pages S3 and S4), brief discussion of theoretical studies of carbine species, comparisons of various computational methods, geometry and energy changes in the local minimum structure of the ruthenium system, geometry of IRC = −3.0 and +3.0 for the iridium reaction systems, π-type molecular orbitals of PIrcalculated DFT, CASSCF, and broken-symmetry Hartree− Fock (HF) methods, spin density-calculated broken-symmetry HF method, VB-type orbital changes in the reaction of the iridium system, and natural orbitals and their occupation numbers of the ground and valence state in the square planar iridium complex, Cartesian coordinates of compounds and transition states. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address §

Quantum Chemistry Research Institute, Goryo-zaka, Katsura, Nishikyo-ku, Kyoto 615−8245, Japan. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is financially supported by Grants-in-Aid from the Ministry of Education, Culture, Science, Sport, and Technology through Grants-in-Aid of Specially Promoted Science and Technology (No. 22000009). We wish to thank the computer center of Institute for Molecular Science (IMS, Okazaki, Japan) for kind use of their computers.

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REFERENCES

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(42) Hirao, K.; Nakano, H.; Nakayama, K.; Dupuis, M. J. Chem. Phys. 1996, 105, 9227−9239. (43) Nakano, H.; Nakayama, K.; Hirao, K. J. Mol. Struct. (THEOCHEM) 1999, 461, 55−69. (44) Karadakov, P. B.; Cooper, D. L.; Gerratt, J. J. Am. Chem. Soc. 1998, 120, 3975−3981. (45) Karadakov, P. B.; Cooper, D. L.; Gerratt, J. Theor. Chem. Acc. 1998, 100, 222−229. (46) Blavins, J. J.; Karadakov, P. B.; Cooper, D. L. J. Org. Chem. 2001, 66, 4285−4292. (47) The present active space is reasonable, as follows: It contains the C1−C3 σ and σ* MOs, C1−C2 π and π* MOs, and two important d orbitals of Ru in the reactant and C2−C3 π and π* MOs, two p orbitals of C1, and two important d orbitals of Ru in the product. C1−C2 and C2−C3 σ-bonds are not explicitly included in the active space, because these are not broken during the reaction. Also, their σ-bonding and σ*antibonding MOs exist at a very low energy and a very high energy, respectively. The present CASSCF calculation shows that the valence orbitals calculated with the CASVB smoothly change when going from the reactant to the product; see Figure 5. Also, the CASPT2 presents similar energy changes to those of DFT(B3LYP) and CCSD(T) except for somewhat different reaction energy of the Ir system; see Table 1. (48) Note that the C1−C2 bond is not represented by the usual σ and π double bond but by the two bent (banana-type) bonds. This description of the double bond has long been discussed;37,38 for instance, see the CASVB study of ethylene.46 Here, we do not discuss this description because it is not the present purpose. (49) In the cyclopropene valence state of IrCl(CO)(PR3)2, the mixing between 5dyz and (5dx2 + 6s) provides two valence orbitals, 5dyz + (5dx2 + 6s) and (5dx2 + 6s) − 5dyz; see Figure 7. In the vinylcarbene valence state, 5dzx + (5dx2 + 6s) and (5dx2 + 6s) − 5dzx are valence orbitals; see Figure 7. These are a little bit different from those of RuCl2(PR3)2, the reason for which is not clear at this moment. It is also noted that the 6s orbital seems to participate in the valence state, as shown by the natural orbitals of Figure 7. Such 6s orbital mixing is not surprising because the 6s plays an important role as a valence orbital in general. (50) As well known, dx2−y2 and dz2 are represented as follows: dx2−y2 = (x2−y2)R(r) and dz2 = (2z2−x2−y2)R(r), where R(r) is an appropriate function of an electron−nucleus distance r. This means that we had better use the designation dx2 when the x component is much larger than y and z components in the d orbital; dx2 = (2x2−y2−z2)R(r). In such case, another component should be described as dy2−z2; dy2−z2 = (y2−z2)R(r). See the 5dx2 + 6s orbital of the IrCl(CO)(PH3)2 in Figure 7. This orbital expands along the x-axis, but its shape does not correspond to a pure 5dx2 because of the mixing of the 6s orbital.

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