Spin-Blocking Effect in CO and H2 Binding Reactions to

Aug 2, 2016 - Electronic structural analysis at the minimum-energy intersystem crossing point (MEISCP) revealed that the singly occupied molecular orb...
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Spin-Blocking Effect in CO and H2 Binding Reactions to Molybdenocene and Tungstenocene: A Theoretical Study on the Reaction Mechanism via the Minimum Energy Intersystem Crossing Point K-jiro Watanabe,†,‡ Naoki Nakatani,*,† Akira Nakayama,† Masahiro Higashi,‡ and Jun-ya Hasegawa*,† †

Institute for Catalysis, Hokkaido University, N21 W10 Kita-ku, Sapporo, Hokkaido 001-0021, Japan Department of Chemistry, Biology and Marine Science, Faculty of Science, University of the Ryukyus, 1 Senbaru, Nishihara, Okinawa 903-0213, Japan

‡

S Supporting Information *

ABSTRACT: Potential energy profiles and electronic structural interpretation of the CO and H2 binding reactions to molybdenocene and tungstenocene complexes [MCp2] (M = Mo and W, Cp = cycropentadienyl) were studied using density functional theory calculations and ab initio multiconfigurational electronic structure calculations. Experimentally observed slow H2 binding was reasonably explained in terms of the spin-blocking effect. Electronic structural analysis at the minimum-energy intersystem crossing point (MEISCP) revealed that the singly occupied molecular orbital’s π-bonding/σantibonding character in the M-CO/H2 moiety determines the energy levels of the MEISCP. Analysis of the reaction coordinate showed that the singlet-triplet gap significantly depends on the Cp-M-Cp angle. Therefore, not only the metal−ligand distance but also the Cp-M-Cp angle is an important reaction coordinate to reach the MEISCP, the transition state of H2 binding. The role of spin−orbit coupling is also discussed.

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INTRODUCTION Recently, chemical reactions with homogeneous catalysts having paramagnetic characters have received increasing attention from an interest in the ubiquitous metals due to their cost-effectiveness, availability, and environmental safety. One of the problems in the development of such a catalyst is to control the reactivity of the metal complex because intersystem crossing (ISC) occurs during the course of the reaction in many cases. Such peculiar reactivity is known as the “spin-blocking” effect1 or “two-state reactivity”.2 One of the most fundamental and substantial examples is ligand binding to low-valent transition-metal complexes.1d,e In the case of molybdenocene [MoCp2] and tungstenocene [WCp2] (Cp = cyclopentadienyl), although both CO and H2 bindings form stable complexes, the coordination kinetics are significantly different: the H2 binding occurs at much higher pressure (200 atm) than that of the CO binding reaction (1 atm).3 Because these unsaturated group 6 complexes are in the 16e triplet ground state, coordination of an additional ligand forms stable adducts in the 18e singlet ground state. Therefore, coordination of CO and H2 molecules to the ground state of [MoCp2] must involve an ISC to result in the singlet adduct. As Poli and Harvey pointed out previously, there are two substantial parameters to explain the reactivity involving ISC:1d,e one is an activation energy to lift reactant to the © XXXX American Chemical Society

energy level of the ISC point, and the other is the probability of the spin-forbidden transition between two spin states around the ISC point. The transition is driven by spin−orbit coupling (SOC) between the two states.1f Because the magnitude of the SOCs for the CO and H2 bindings must be of a similar order, the binding activity should be reasonably explained in terms of the activation energy. A pioneering work by Brintzinger and coworkers concluded that the energy level of the ISC point for the H2 binding is higher than that for the CO binding.4 However, their study was based on extended Hü ckel calculations, and more useful information should be provided for rationally understanding the geometry and electronic structure and for gaining some insight into the reactivity control of the spin-crossing reactions. In this regard, it is important to locate the ISC point, particularly as a transition state of the spin-crossing reaction.1c,d ISC takes place on a seam which is formed by the intersection of the two potential energy surfaces with different spin multiplicities. Because the surfaces are multidimensional, the intersection of ISC also constitutes a hypersurface. To locate a transition state of ISC, one has to find a minimum energy point on the intersection surface: the minimum energy intersystem Received: May 17, 2016

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DOI: 10.1021/acs.inorgchem.6b01187 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 1. Changes in geometry along the CO binding reaction (upper) and H2 binding reaction (lower). Important bond lengths (Å) and angles (deg) are also shown.

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crossing point (MEISCP). The first successful implementation was achieved by Koga and Morokuma using the Lagrangian multiplier method,5 and many developments followed (for example, see ref 6 and the references therein). In the present study, we used a code developed by one of the authors7 in which a penalty function approach6f was implemented. One of our other interests is the reaction coordinate of the spin-changing reactions. In the case of an ordinary transition state in a single potential energy surface, the transition state is understood as the intersection of two diabatic energy surfaces. In most cases, one reaction coordinate, such as bond length, can explains the reactions. On the other hand, the reaction coordinate for the spin-changing reaction could utilize an additional reaction coordinate that effectively represents the relative energy of the two spin states. In our previous study on a carotenoid, the single-triplet energy gap was effectively controlled by bond length alternation8a in addition to the twisting of a carbon−carbon bond. In the case of O2 binding to a heme, a symmetric ring-shrinking mode effectively decreases the singlet−triplet gap and reduces the energy barrier to the ISC point even though the ring-shrinking mode is independent of the Fe−O2 bond length.8b It is therefore very interesting to understand the reaction coordinate of the spin-changing ligand binding to molybdenocene and tungstenocene. In this work, we focused on the CO and the H2 binding reactions with molybdenocene and tungstenocene to provide a general strategy for how we can understand the reactivity of such transition-metal complexes and clarify their mechanism on the basis of computational analyses on geometry and electronic interactions at the MEISCP. First, we theoretically investigated the potential energy profiles of the CO and H2 binding reactions to molybdenocene to discuss changes in energy and geometry, in particular around the MEISCPs. Next, we studied the ligand binding to tungstenocene and compared the magnitude of spin−orbit coupling around the MEISCP. Furthermore, we determined the reaction coordinate which plays an important role in reaching the MEISCP. Finally, the electronic structure along the reaction coordinate was investigated to clarify the origin of the ligand affinities.

COMPUTATIONAL DETAILS

Both geometry optimizations and energy evaluations were performed using density functional theory (DFT) with the M06L functional.9 To select an appropriate functional, the binding energies of CO and H2 molecules were calculated by several DFT functionals (B3LYP, B3LYP*, BHandHLYP, BLYP, LC-BLYP, M06, and M06L) and compared with those by CCSD(T). It was concluded that the M06L functional gives the closest results to CCSD(T) (see the Supporting Information for the assessments of density functionals). The basis sets we employed were Ahlrichs valence triple-ζ plus the polarization function (def2-TZVP).10 For Mo and W, 28 and 60 core electrons were replaced by the effective core potential, namely ECP28MWB and ECP60MWB,11 respectively. To obtain MEISCP structures, we carried out geometry optimization with constraint conditions in which the energy levels of the singlet and triplet states are degenerate. We also carried out CASPT2 (complete active space self-consistent field followed by the second-order perturbation theory)12 calculations for evaluation of a more accurate energy and spin−orbit coupling constant (SOC). In the CASPT2 calculations, we employed relativistic correction-consistent atomic natural orbital-type basis sets (ANORCC) with contractions [7s6p4d2f1g] for Mo, [8s7p5d3f2g] for W,13 [4s3p2d1f] for C and O, and [2s1p] for H.14 The active space of [MoCp2] consisted of three 4d orbitals, one of which is doubly occupied in the triplet spin state, one 5d orbital as a counterpart of the doubly occupied 4d orbital, and four π with the corresponding four π* orbitals from two Cp moieties; consequently, 12 electrons in 12 orbitals (12e, 12o) were considered. For the CO adduct, we added two π* orbitals of CO to the active space, and thus 12 electrons in 14 orbitals (12e, 14o) were employed. For the H2 adduct, we added the σ* orbital of H2 to the active space, and the resultant 12 electrons in 13 orbitals (12e, 13o) were employed. Natural orbitals (NOs) and their occupation numbers for these active orbitals are summarized in Figures S3−S5 for [MoCp2], [MoCp2CO], and [MoCp2H2], respectively. Scalar relativistic effect was incorporated using the second-order Douglas−Kroll−Hess integrals,15 and the spin−orbit coupling effect was evaluated with atomic mean-field integrals (AMFI).16 The basis set superposition error (BSSE) was estimated by the counterpoise correction.17 Though the solvation effect of THF (corresponding to ref 3) was also examined, we concluded that it is very small and therefore did not consider it in this work (see Figure S6 for the assessment of the solvation effect). All DFT calculations were performed using the Gaussian 09 program package (revision B-01),18 and the CASPT2 and its spin− orbit coupling calculations were carried out using the Molcas 8 program package.19 The constraint optimization was performed with B

DOI: 10.1021/acs.inorgchem.6b01187 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry our program package originally coded for the minimum energy crossing point search.7

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state. The CO molecule weakly interacts with the Mo center in PCO. The energy of PCO is 2.9 kcal/mol more stable than that of [MoCp2]. The BSSE gave a minor correction of 0.2 kcal/mol in PCO, and thus the BSSE-corrected stabilization was 2.7 kcal/ mol. A CO adduct is easily formed in the triplet spin state (TCO) with a small activation barrier of 1.4 kcal/mol. The CO binding energy in the triplet spin state was estimated to be 12.8 kcal/mol. Of further interest is that the singlet spin state at the TCO geometry was found to be slightly lower in energy than that at the triplet spin state. The S-T gap of TCO was estimated to be 1.4 kcal/mol. Indeed, the MEISCP of the CO binding reaction (MCO) was found to be very close both in energy and geometry to that of TCO. Consequently, the MEISCP is easily accessible from TCO with almost no energy barrier so that the intersystem crossing takes place easily. Finally, [MoCp2CO] is formed as a stable complex in the singlet spin state (SCO). The overall binding energy was estimated to be 34.1 kcal/mol. Interestingly, the Mo-CO distance of SCO was computed to be 2.01 Å, which was slightly longer than that of TCO (1.93 Å). H2 Binding Reaction to [MoCp2]. An H2 molecule is bound to a metal center in two different manners: one is coordination in the η2−H2 fashion, and the other is coordination in the two η1−H fashion. The latter is also known as an oxidative addition reaction in which the metal center is formally oxidized and the H2 is reduced by two electrons to result in two hydride anions. H2 is a weak ligand, while a hydride ligand induces large ligand field splitting due to strong σ-donating interactions. As a result, the H2 adduct takes a low-spin state when the oxidative addition reaction occurs. Though the H2 oxidative addition to [MoCp2] can proceed, it is considerably slower than that of the CO binding reaction.3a To explore why these two reactions give completely different reaction rates and whether or not this is due to the spinblocking effect, we investigated changes in geometry and energy along the H2 binding reaction to the [MoCp2] complex and compared the results with those of the CO binding reaction. In the lower half of Figure 1, the DFT-calculated structure changes along the H2 binding reaction to [MoCp2] are summarized. The corresponding potential energy profiles for the singlet and triplet spin states are shown in Figure 2B. In the H2 binding reaction, a precursory complex PH2 was found at the Mo−H distance of 3.22 Å in the triplet spin state. It was estimated to be slightly more stable in energy by 1.9 kcal/mol (1.7 kcal/mol with the BSSE correction). In PH2, the H2 moiety is oriented to the Mo center in an on-top fashion. Unlike the CO binding reaction, no stable adduct was found in the triplet spin state. The potential energy monotonically increases toward the MEISCP (MH2), which was found at the Mo−H distances of 2.25 Å. MH2 was computed to be 10.1 kcal/ mol higher in energy from [MoCp2]. Consequently, MH2 is considered to be a transition state of the H2 binding reaction, and therefore the reaction rate must be determined by the properties of MH2. After the intersystem crossing, an oxidative addition reaction of H2 occurs to afford a dihydride complex [MoCp2(H)2] in the singlet spin state. The overall binding energy was estimated to be 25.9 kcal/mol. In the H2 binding reaction, the activation energy toward MH2 determines the rate of intersystem crossing, and the origin of the less reactive H2 binding can be understood as a spin-blocking effect. The role of the SOC effect will be discussed later.

RESULTS AND DISCUSSION

In this section, we first show the potential energy profiles of the CO and H2 binding reactions to [MoCp2] via the MEISCP. Next, we studied the same reactions to [WCp2] and the SOC values to discuss the spin-blocking effect in more detail. On the basis of the so-called “meta-intrinsic reaction coordinate (IRC)” calculations, i.e., the steepest decent reaction coordinate search from the initial coordinate,18 we analyzed important geometrical parameters controlling the intersystem crossing reaction. Finally, we discuss why H2 binding is much slower than CO binding from the viewpoint of the electronic structure. CO Binding Reaction to [MoCp2]. The CO molecule is a characteristic ligand widely used in inorganic and organometallic chemistry. Due to its strong π-back-donating interaction to d-orbitals of a metal center, the CO ligand strongly binds to various metal complexes, and the CO-bound complex usually takes the low-spin state because of its large ligand-field splitting. The CO binding reaction to the [MoCp2] complex occurs easily to afford a CO-adduct [MoCp2CO] as the singlet ground state. Here, we investigated an energy profile along with the CO binding reaction to the [MoCp2] complex in the singlet and triplet spin states based on the DFT level of theory. The result is compared with that of the H2 binding reaction in a later section. In Figure 1, the DFT-calculated structural changes for CO binding are summarized. The corresponding potential energy profiles of the singlet and triplet spin states are shown in Figure 2A. The ground state of the reactant complex [MoCp2] was found to be the triplet spin state. At the same structure, the singlet spin state was computed to be 30.5 kcal/mol higher in energy than the triplet ground state. A precursory complex PCO was found at the Mo-CO length of 3.58 Å in the triplet spin

Figure 2. Potential energy profiles of the (A) CO and (B) H2 binding reactions to [MoCp2] in the singlet spin state (green) and the triplet spin state (magenta). C

DOI: 10.1021/acs.inorgchem.6b01187 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Comparison with [WCp2] and SOC. Next, we compared the CO and H2 binding reactions of [MoCp2] with those of [WCp2]. The magnitude of the SOC around the MEISCP was also compared. To the best of our knowledge, there was no clear experimental data comparing the reactivity of [MoCp2] and [WCp2]. Therefore, the present comparison could be useful for discussing the relative reactivity of [WCp2] and the role of the SOC. The basic aspects of the CO and H2 binding reactions to [WCp2] were found to be almost the same as those to [MoCp2]. The overall binding energies were computed to be 40.8 and 38.3 kcal/mol for the CO (Figure 3A) and H2 (Figure

SOC values at MCO and MH2 of the Mo complex were computed to be 96 and 42 cm−1, respectively, while those of the W complex were 226 and 209 cm−1, respectively. For CO binding, the SOC value of the W complex is twice that of the Mo complex. For H2 binding, the SOC of the W complex is at most four times larger than that of the Mo complex. On the other hand, the activation energy of MH2 is very similar in the two cases (12.0 kcal/mol in the Mo case and 12.5 kcal/mol in the W case). These results confirmed that the trend of CO and H2 binding to the W complex should be similar to that of the Mo complex. The overall reaction rate must be determined by a product of the Boltzmann factor (depending on the spin-blocking barrier in an exponential manner) and the spin-transition probability (depending on the SOC value in a square manner). The spinblocking barrier of 0.3 kcal/mol of the CO binding reaction can easily be achieved by thermal fluctuation, and therefore intersystem crossing in the CO binding reaction depends on only the SOC value. On the other hand, because the energy barrier of 12 kcal/mol gives a much smaller Boltzmann factor in the MH2 geometry than that in the MCO geometry, the H2 binding reaction must be much slower than the CO binding reaction. It should be noted that the 12 kcal/mol activation energy is not very large for common chemical reactions occurring in the same spin state. However, because the intersystem crossing involves a spin-forbidden transition, the probability of intersystem crossing is in general very small. Thus, the product of the Boltzmann factor and the probability of intersystem crossing results in a very small reaction rate in the H2 binding reaction. Consequently, the H2 binding reaction to [MoCp2] or [WCp2] is a typical spin-blocked reaction. Structural Parameters Controlling the MEISCP. In this subsection, we clarify what kinds of geometrical parameters control stability and electronic structure of the MEISCP in the H2 binding reaction (MH2). This is the most essential part of this paper, and our strategy can provide an idea of how to control the rate of chemical reaction involving ISC. The Cartesian force acting on each atom was calculated for the MH2 structure. The largest force acts on the Mo atom in either the singlet or triplet spin state (see Figure 5). Interestingly, the force at the Mo atom induces geometrical changes not only for the Mo−H2 distance but also for the position of the Mo center relative to the two Cp rings. We carried out meta-IRC calculations along with these two forces as follows: from MH2 to PH2 (the left-hand side of Figure 6A), we calculated the MEP according to the force in the triplet spin state, and the energy in the singlet spin state was evaluated along the triplet-state reaction coordinate. From MH2 to SH2 (the right-hand side of Figure 6A), we calculated MEP according to the force in the singlet spin state, and the energy in the triplet spin state was evaluated along the singlet reaction coordinate. After the structural investigation, we found that the Mo−H distance and the Cp-Mo-Cp angle described well the structural changes according to the forces at the MEISCP. Therefore, for each singlet and triplet state, the potential energy curves along the meta-IRC were replotted on these two-dimensional planes, as shown in Figure 6B. The result clearly indicates that the decrease of the Cp-Mo-Cp angle (corresponding to opening two Cp moieties) is coupled with the decrease of the Mo−H distance around the MEISCP, as we expected.

Figure 3. Potential energy profile of the (A) CO and (B) H2 binding reactions to [WCp2] in the singlet spin state (green) and the triplet spin state (magenta).

3B) binding reactions to [WCp2], respectively. In the triplet spin state, the energy barrier of the MEISCP was calculated to be very small (only 0.3 kcal/mol) for CO binding, while a somewhat large energy barrier (12.5 kcal/mol) was found for H2 binding. From these results, the reaction rate of the H2 binding in [WCp2] is expected to be smaller than that of the CO binding due to the spin-blocking effect as well as the [MoCp2] complex. As a general trend, heavier elements have larger SOC values and higher transition probabilities in reactions involving the ISC point. We cannot easily rule out the possibility that the magnitude of the SOC causes the difference between the Mo and W complexes. To evaluate the SOC values, we carried out CASPT2 calculations along with the reaction coordinate obtained by the meta-IRC-type calculation. This enables us to trace the minimum-energy path (MEP) on the potential energy surface across the MEISCP, as discussed later in more detail. We also checked that the DFT-calculated potential energy curve agreed very well with the CASPT2-calculated curve along the reaction coordinate (see Figure S7). Figure 4 summarized the SOC values along the CO and H2 binding reactions to the [MoCp2] and [WCp2] complexes. The D

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Figure 4. Changes in the SOC values between the T1 and S0 states for the CO (left, black) and H2 (right, red) binding reactions to (A) [MoCp2] and (B) [WCp2].

and the energy gap (S-T gap) for [MoCp2]. Energy contributions from each geometrical parameter to reach the MH2 can be obtained from the energy differences: 1 − [MoCp2] for the Cp-Mo-Cp angle, 2 − 1 for the Mo−H distance, and 3 − 2 for the others. The ratio for each contribution relative to the S-T gap of [MoCp2] (30.5 kcal/mol) was estimated and is shown in Figure 8. It is of considerable interest that the CpMo-Cp angle gives the main contribution to reduce the S-T gap. A decrease in the Cp-Mo-Cp angle (i.e., opening two Cp rings) considerably stabilizes the singlet spin state by 20.0 kcal/ mol while somewhat destabilizes the triplet spin state by 3.8 kcal/mol; thus, 78.0% of the S-T gap can be reduced by the CpMo-Cp angle. A decrease in the Mo−H distance destabilizes both the singlet and triplet spin states by 1.4 and 6.0 kcal/mol, respectively, and thus reduces 14.9% of the S-T gap. Therefore, the Cp-Mo-Cp angle and the Mo−H distance both contribute to reducing the S-T gap and, in total, 92.9% of the contribution comes from these two parameters. These results clearly indicated that the Cp-Mo-Cp angle is the most effective parameter to change the reactivity of [MoCp2] and/or [WCp2]. This is consistent with the previous experimental and theoretical studies about ansa-metallocene complexes;20 the C−H oxidative addition reaction is more preferable to the ansatungstenocene complex than the reductive elimination reaction. An important hint to understand why the Cp-Mo-Cp angle contributes to decreasing the S-T gap can be found from the singlet (S0) geometry of [MoCp2]. As shown in Figure 9, the Cp-Mo-Cp angle of [MoCp2] was optimized to be 148.8° in the singlet spin state, which was considerably more acute than that in the triplet (T1) geometry and even more acute than that of MH2 (see Figure 1). Therefore, changing the Cp-Mo-Cp angle indeed stabilizes the singlet spin state of the [MoCp2] complex itself. Of further interest is that the S-T gap at the singlet geometry of [MoCp2] was found to be already very

Figure 5. DFT-calculated Cartesian forces acting on each atom in the MH2 structure. Triplet spin state (left). Singlet spin state (right).

Next, we carried out the energy decomposition analysis to quantitatively analyze how much these structural parameters affect the energies of the singlet and triplet spin states. The structural changes to reach MH2 in the H2 binding reaction were decomposed into (1) opening two Cp rings (decrease of the Cp-Mo-Cp angle), (2) binding of H2 molecule (decrease of the Mo−H distance), and (3) others to reach MH2 (Scheme 1). For 1, a partial geometry optimization in the triplet spin state was carried out where the Cp-Mo-Cp angle was fixed to that of MH2. For 2, we optimized the geometry where the Mo−H distance was fixed to that of MH2 in addition to the Cp-Mo-Cp angle. For 3, all the other parameters were changed to those of MH2. It should be noted that there is another way to decompose the reaction coordinate: change the Mo−H distance first and then change the Cp-Mo-Cp angle. In this case, however, the Cp-MoCp angle was already changed when we performed a partial geometry optimization even if we only fixed the Mo−H distance to that of MH2. Thus, the geometrical parameter can only be purely decomposed in that order: changing the Cp-MoCp angle before the Mo−H distance. Figure 7 shows the potential energy changes in the singlet and triplet spin states E

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Figure 8. Ratio for each contribution of the Cp-Mo-Cp angle and Mo−H distance to decrease the S-T gap toward MH2.

Figure 9. Optimized geometry of [MoCp2] in the triplet (T1, left) and singlet spin state (S0, right). Important structural parameters are also shown in the figure.

gives an important contribution and why CO and H2 binding are so different. Geometry and Reactivity from the Electronic Structure Viewpoint. Figure 10 shows the natural orbital of

Figure 6. Minimum-energy paths from [MoCp2] to MH2 in the triplet spin state (magenta) and from MH2 to SH2 in the singlet spin state (green) according to meta-IRC calculations. Potential energies plotted by (A) a mass-weighted reaction coordinate (amu) and (B) by Mo−H distance and Cp-Mo-Cp angle.

Scheme 1

Figure 10. NOs of the triplet (left) and singlet (right) geometry of [MoCp2]. Orbital energies, which were estimated from corresponding canonical orbitals, were introduced for a better interpretation of the electronic structure.

[MoCp2] from CASSCF (12e, 12o) calculations. For a better understanding, orbital energies of canonical molecular orbitals (CMOs) were assigned to each NO because we found that the CMOs possessed features similar to those of NOs in this system. In the T1 geometry, 4dx2−y2 and 4dz2 orbitals are almost degenerated, and therefore two spins occupy these two orbitals so that the triplet spin state is stabilized by a typical ferromagnetic interaction. In the S0 geometry, however, these two orbitals are split into the lower and higher energy levels due to the interactions with π and π* orbitals of two Cp rings, as shown in Scheme 2. In this way, the closed-shell singlet spin

Figure 7. Energy changes in the triplet (magenta) and singlet (green) spin states along with the decomposition scheme as defined in Scheme 1. Changes in the S-T gap are also shown as a black line (values in parentheses).

small (2.2 kcal/mol). A later section discusses the electronic structural origins for the reasons why the Cp-Mo-Cp angle F

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back bonding orbital is unoccupied, while in the triplet spin state, one of the π-bonding orbitals is doubly occupied and nonbonding 4dx2−y2 orbital and another π-back bonding orbital are singly occupied. Consequently, both the singlet and the triplet spin states are stabilized by π-back bonding interactions because no antibonding orbital is occupied. This is the essential reason why the CO binding reaction easily occurs with [MoCp2]. In MH2, 4dz2 and 4dxy orbitals of the Mo center interact with the σ- and σ*-orbitals of H2, respectively. This interaction results in two bonding orbitals and the corresponding two antibonding orbitals. The 4dx2−y2 orbital remains as a nonbonding orbital (Figure 11B). In the singlet spin state of MH2, the 4dxy-σ*(H2) bonding orbital is doubly occupied, which contributes to the formation of a stable adduct. This is a common feature of oxidative addition reactions in which a metal center is formally oxidized and an H2 molecule is formally reduced. In the triplet spin state of MH2, however, two unpaired electrons occupy the nonbonding 4dx2−y2 orbital and the 4dz2-σ (H2) antibonding orbital. Thus, stabilization from the bonding interaction is partially canceled because of the destabilization from the antibonding interaction. This is an essential difference in the mechanisms of the CO and the H2 binding reactions to [MoCp2]. Therefore, the H2 binding reaction needs a relatively large activation energy to achieve the MEISCP structure. Finally, on the basis of the orbital interaction analysis, we discuss the change in the magnitude of SOC in the course of the CO and the H2 binding reactions (Figure 4). In the case of H2 binding, the calculated SOC value significantly changes, while only a moderate change was observed for the CO case. To reveal this difference, we focused on three factors which mainly contribute to the SOC values: (a) populations of spins on the metal center, (b) weight and character of the main configuration of each of singlet and triplet spin state, and (c) the directions of the angular momentum vectors from the orbital pictures.1f We analyzed the changes in a and b and concluded that contributions to the SOC value from them are relatively small toward the binding reaction (Figure S8 and S9). Therefore, we discuss herein the contribution from c in more detail. In the present case, the expectation value of the L × S coupling roughly depends on the characters of the singly occupied molecular orbitals (SOMOs) in the triplet spin state. In MCO, the π-bonding interaction between the Mo 4dxz and C 2pz orbitals has angular momentum roughly along the z direction (Scheme 3A). The L × S coupling between this orbital and the nonbonding 4dx2−y2 orbital gives a nonzero coupling element vertical to the coordination bond. In MH2, on the other hand, antibonding interaction between Mo 4dz2 and H2 σ-orbitals has angular momentum roughly along the xdirection (Scheme 3B). The L × S coupling between this orbital and the nonbonding 4dx2−y2 orbital gives a nonzero coupling element parallel to the coordination bond. Consequently, the SOC value is not significantly influenced by the Mo-CO coordinate, while it is highly influenced by the Mo−H2 coordinate.

Scheme 2

state is stabilized to be the ground state. In the MEISCP, these orbital interactions in the S0 structure are weakened and closer to those in the T1 structure. To estimate the change in the orbital interactions due to the Cp-Mo-Cp bending at the MEISCP structure, we carried out single point calculations for ligand-free [MoCp2]. The atomic coordinates for the [MoCp2] part were taken from those of MCO or MH2, and the structures are named here as M−CO and M−H2, respectively. The results were compared with those of MCO and MH2 to understand the change in the orbital interactions due to the ligand association. In the MCO structure, typical π-back-donating interactions, π*(CO)-4dxy and π*(CO)-4dxz, are observed. The 4dx2−y2 orbital remain being a nonbonding orbital (Figure 11A). In the singlet spin state, one of the π-back bonding orbitals and nonbonding 4dx2−y2 orbital are doubly occupied, and another π-

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CONCLUSIONS The CO and H2 binding reactions to [MCp2] (M = Mo and W) were theoretically studied by means of the DFT and CASPT2 calculations. Because the ground state of these

Figure 11. Orbital interaction between the [MoCp2] moiety and ligand in MCO (A) and MH2 (B). The orbital energies of CASSCF CMOs were assigned to the corresponding NOs. G

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DFT-optimized structures for the CO and the H2 binding reactions, assessments of the DFT functionals, NOs and occupation numbers of the CASSCF calculations, solvation effect of THF, CASPT2-calculated potential energy curves around the MEISCP of the H2 binding reaction, and analyses of the changes in the SOC values (PDF)

Scheme 3

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Prof. H. Nagashima for fruitful discussions about experimental backgrounds of metal inorganic and organometallic chemistry. This work was financially supported by JST-CREST, JSPS KAKENHI (Grants JP15H05805, JP15K06563, JP15K20832, JP15H03770, JP26810008, and JP16H00778) and the FLAGSHIP2020 (priority study 5) program from MEXT. Parts of the computations were carried out at RCCS (Okazaki, Japan) and ACCMS (Kyoto University).

metallocenes has triplet spin multiplicity, the reaction pathway involves the intersystem crossing. Consequently, the energy level of the MEISCP is an essential determinant for understanding the reactivity. On the basis of the calculated potential energy profile, we successfully interpreted the origin of the significant difference in the reactivity between CO and H2 binding. In the CO case, the energy minimum of the triplet [MCp2CO] is very close to that of the MEISCP. In the H2 case, however, the energy of the MEISCP was about 12 kcal/mol higher than that of the triplet [MCp2H2], indicating that the MEISCP corresponds to the transition state. This reaction is therefore classified as a typical case of the spin-blocking effect. We conducted detailed analyses of the geometry and electronic structure of the MEISCP and revealed that the CpM-Cp angle is the most important structural parameter to control the energy barrier of intersystem crossing in the H2 binding reaction. Further analysis clarified that the singlet− triplet energy gap is very sensitive to the Cp-M-Cp angle. It should be noted that the reaction coordinate other than the metal−ligand distance is important for the ligand binding via ISC. Because similar conclusions were obtained in our previous studies,8 the importance of the gap-controlling coordinate should be emphasized. In addition, we found that the calculated SOC values considerably decrease over the course of the H2 binding reaction. Because the nonzero L × S coupling element appears parallel to the coordination bond, it is highly influenced by the bonding interaction. Consequently, both the energy barrier and the SOC value work for blocking the H2 binding reaction. Although this is a very simple and well-known reaction in inorganic and organometallic chemistry, the idea and strategy that we presented here would be of great use to predict and control the reactivity of various chemical reactions involving intersystem crossing.

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DOI: 10.1021/acs.inorgchem.6b01187 Inorg. Chem. XXXX, XXX, XXX−XXX