Theoretical Study on the Two-State Reaction Mechanism for the

Article pubs.acs.org/Organometallics

Theoretical Study on the Two-State Reaction Mechanism for the Formation of a Pyridin-2-one Cobalt Complex from Cobaltacyclopentadiene and Isocyanate LingLing Lv,*,† XiaoFang Wang,† YuanCheng Zhu,† XinWen Liu,† XianQiang Huang,‡ and YongCheng Wang§ †

College of Life Science and Chemistry, Tianshui Normal University, Tianshui, Gansu 741001, People’s Republic of China Shandong Provincial Key Laboratory of Chemical Energy Storage and Novel Cell Technology, School of Chemistry & Chemical Engineering, Liaocheng University, Liaocheng 252059, People’s Republic of China § College of Chemistry and Chemical Engineering, Northwest Normal University, LanZhou, Gansu 730070, People’s Republic of China ‡

S Supporting Information *

ABSTRACT: The two-state reaction (TSR) mechanism of CpCo(C4H4) with isocyanate on the triplet and singlet potential energy surfaces has been investigated at the B3LYP level. The minimal energy crossing point (CPs) in the crossing seam between the potential energy surfaces are located using the method of Harvey et al., and possible spin inversion processes are discussed by means of spin−orbit coupling (SOC) calculations. As a result, the two distinct reaction pathways for the formation of a pyridin-2-one cobalt complex have been found. For the first pathway, there are two key crossing points along the reaction pathway. The first crossing point, CP2, exists near 1 B. The reacting system will change its spin multiplicity from the triplet state to the singlet state near this crossing region because the magnitude of the spin-multiplicity mixing (SOC1‑e,1‑center = 393.37 cm−1) increases in a small energy gap between highand low-spin states will greatly enhance the probability of intersystem crossing. The single (P1ISC) and double (P2ISC) passes estimated at CP2 are approximately 0.28 and 0.48, respectively. The second crossing point, CP3, will again change its spin multiplicity from the singlet state to the triplet state in the Co−Cγ bond activation pathway, leading to a decrease in the barrier height of 1TS(CF) from 19.5 to 9.5 kcal/mol. Thus, the reaction system will access a lower energy pathway and then move on the triplet potential energy surface as the reaction proceeds. As for the second pathway, the formation of the initial transition is a very unfavorable process kinetically. However, from the beginning of 1H, TSR is a very favorable process kinetically and thermodynamically. After passing point CP5, the triplet potential energy surface can provide a low-cost reaction pathway toward the product complex.

1. INTRODUCTION Heterocyclic compounds are very important in industrial and medicinal application, and their synthesis has been the subject of extensive experimental and computational studies.1 For the past few decades, the cyclocotrimerization of two alkynes with organic compounds containing unsaturated carbon−heteroatom bonds (CN, CO, etc.) has been a powerful and economic method to obtain six-membered heterocyclic systems.2,3 A good example is the transition-metal-catalyzed [2 + 2 + 2] cycloaddition of isocyanate with 2 equiv of an alkyne to form 2-pyridone. Pyridine derivatives were prepared from the reaction of alkynes and isocyanates using different transition metals as catalysts, such as Ni, Zr, Co, Rh, Pd, Ru, and Ta.2 Among these transition-metal catalysts, Co complexes of the type CpCoL2 (Cp = cyclopentadienyl, L = CO, PR3, alkenes) have been used extensively as excellent catalysts with high chemo-, regio-, and stereoselectivity. Recently, Kirchner and Schmid also reported their DFT studies of cyclocotrimerization of alkynes with HNCO and HN CS catalyzed by CpRuCl. It was found that in the case of © XXXX American Chemical Society

HNCO pyridin-2-ones are formed exclusively, whereas in the case of HNCS the chemoselectivity is reversed to give thiopyran-2-imines.3b Koga and co-workers3c investigated the synthetic mechanism of preparing a 2-methylpyridine Co(I) complex from cobaltacyclopentadiene and CH3CN using density functional theory (B3LYP) computations. The calculated results show that the two-state reactivity mechanism is more favorable than both the singlet- and triplet-state (single-state reactivity) mechanisms. Yamazaki and Hong reported the synthesis of pyridine derivatives via the [2 + 2 + 2] cycloaddition of phenyl isocyanate with two alkynes catalyzed by CpCo(PPh3)2 (Scheme 1).4,5 However, the title reaction in Scheme 1 was heated in a sealed tube at 135 °C for 19 h. From the reaction mixture, pyridine derivatives were isolated in only 40% yield. Although these reactions have been extensively studied using a variety of kinetic, thermodynamic, computational, and labeling techniques, the detailed Received: April 13, 2013

A

dx.doi.org/10.1021/om400301y | Organometallics XXXX, XXX, XXX−XXX

Organometallics

Article

Scheme 1. Cycloadditions with Alkynes and Isocyanates

favorable than both the singlet- and triplet-state mechanisms: A → CP1 → 3A, and then 3A + HNCO → CP2 → 1B → 1 TS(BC) → 1C → 1TS(CD) → 1D → 1TS(DE) → 1E → CP4 → 3E.

mechanism of these conversion is not yet fully established due to the complex electronic states of transition-metal compounds. We know that the chemistry of transition metals and their compounds is strongly influenced by the availability of multiple low-lying electronic states in these species.6 This means that the reactions involve several electronic states that may also have different spins and should involve spin-conserving and spininverting processes. Thus, a reaction possibly occurs on two or more potential energy surfaces (PESs) under thermal conditions, and therefore, it has to involve the electronic process of radiationless transition from one potential energy surface to another surface (this type of chemical reaction has been emphasized by Schröder, Shaik, and Schwarz7 in recent reviews of “two-state/ multiple-state (TSR/MSR)” reactivity). Moreover, reactions that involve a change in the spin state and occur on two or more PESs are known to be important in determining the outcome of chemical processes. In this case, the changes between two or more different electronic states are known to accompany the progress of the reaction and can modify the efficiency and/or selectivity of a given chemical rearrangement and can also influence a reaction from a process without change in spin state to a situation where the spin change completely determines the rate and selectivity.8 In this paper, for the title reaction (Scheme 1), our calculations took explicit account of the fact that 18-electron cobalt species exist usually as singlet ground states, whereas their 16-electron congeners prefer to be triplet states. Thus, changes in spin state along the reaction coordinate can be part of a mechanism. In addition, previous studies (CpCo + CH3CN, CpCo + alkynes, and dissociation of CO from HCo(CO)4) showed that the most favorable mechanism is the TSR (nonadiabatic) mechanism.3 These results also encouraged us to study the TSR mechanism. Although there is no appropriate computational method for calculating adiabatic spin-coupled potential energy surfaces of cobalt complexes, semiquantitative information can be gleaned from a determination of the enthalpy for accessing a crossing point at which the two spin states differ minimally in structure and energy.9 Therefore, detailed analyses of crossing points between the different potential energy surfaces are important for understanding the TSR mechanism of the reaction of cobaltacyclopentadiene with isocyanate. The aims of this study are to facilitate the understanding of the role of electronic structures on the mechanistic details at a molecular level and to clarify the dominant product channels, as well as to analyze the potential energy surface crossing scenarios.10 This kind of knowledge is essential for understanding the whole reaction mechanism and is useful for establishing an appropriate model for the title reaction processes. To our knowledge, a deep theoretical study for the formation of a pyridin-2-one cobalt complex from cobaltacyclopentadiene and isocyanates has not been reported. In the present study we discuss crossing seams, spin−orbit coupling (SOC), and possible spin-inversion processes in this intriguing chemical reaction. The results show that the TSR mechanism is more

1

2. COMPUTATIONAL DETAILS 2.1. Geometrical Optimization. Computations were carried out using the Gaussian 03 program package.11 Energies and geometries of the reaction intermediates and the transition states were calculated using density functional theory (DFT) with the B3LYP level. Unrestricted wave functions were used for all open-shell species. The triple-ζ 6-311+G(d) basis set of Pople and co-workers12 was used for C, N, O and H, and the standard Stuttgart/Dresden (SDD) effective core potential (ECP) together with the associated (8s7p6d1f) primitive set13 resulting in a (311111|22111|411|1)[6s5p3d1f] contraction was used to describe the 3s, 3p, 3d, and 4s electrons of Co. However, the nature of the “exact”, Hartree−Fock, and exchange parts of the DFT functional has a strong influence on computed spin-state splitting. In particular, it is strong for compounds of the elements in the first transition row, which is presumably related to the large exchange interactions between compact 3d orbitals. For this reason, at the “nonlocal” functional BP86 and hybrid functional BHandHLYP levels, single-point energy calculations were performed using the larger 6-311++G(d,p) basis set for all of the atoms. In addition, the PCM approach for accounting for solvent effects (singlepoint calculations with benzene as solvent) was applied at the B3LYP/ 6-311++G(d,p) level,3a but no significant changes of the relative energies were observed (see the Supporting Information). Previous investigations of transition-metal compounds employing the B3LYP functional by other groups14 and us15 indicated that this approach shows a very promising performance to predict properties such as bond dissociation energies, geometries, and harmonic frequencies with an accuracy comparable to that obtained from highly correlated wave function based ab initio methods. Frequency calculations were performed at the B3LYP/6-311+G(d) + SDD level to confirm the nature of the stationary points and to obtain zero-point energies (ZPE). The transition-state structures all represent saddle points, characterized by one negative eigenvalue of the Hessian matrix. Then the intrinsic reaction coordinate (IRC) was calculated and used to track the minimum energy path from transition states to the corresponding minima, to probe the reaction path, and to check if the correct transition state was located. The minimal energy crossing points (CPs) in the crossing seam between the singlet and triplet potential energy surfaces were optimized using the code developed by Harvey and co-workers.10 The vibrational analyses at these points were executed within the (3N − 7)-dimensional hypersurface of the crossing seam.9 2.2. Spin−Orbit Coupling Calculations. Spin−orbit coupling (SOC) matrix elements were calculated between triplet and singlet complete-active-space configuration iteration (CASCI) wave functions with respect to the full Pauli−Breit Hamiltonian SOC operator, Ĥ SO(BP), which consists of the one-electron and two-electron terms,16−18 as given in eq 1, where the summation is over nuclei (A) and electrons (i and j). The r̂j × p̂i product is the orbital angular momentum operator Iî , while Ŝi is the corresponding spin operator. The first term in eq 1 accounts for the one-electron interaction that each electron samples by “revolving” about all nuclei. The second term corresponds to the interaction of the angular momentum of an electron with the spins of other electrons. B


Organometallics

Article

Figure 1. Optimized geometries and selected bond distances (in Å) of the intermediates and transition states along the singlet and triplet surfaces of the CpCoC4H4 (A) with HNCO reaction via the N orientation at the B3LYP/6-311+G(d)+SDD level of theory. ⎛Z ⎞ α2 [∑ ∑ ⎜ A ⎟Sî ·IiÂ − Ĥ SO(BP) = 2 i A ⎝ riA3 ⎠

⎛1⎞ ⎟(rĵ × pi ̂ )(Sî + 2Sĵ )] 3 ⎝ riA ⎠

The SOC constant is relevant to the electronic factor of the rate of the intersystem crossing, as determined by Landau−Zener theory. The SOC matrix elements in eq 2 were evaluated at the singlet/triplet state averaged complete active space self-consistent field wave function CASSCF(8,7) (eight electrons in seven orbitals) with the effective core potential (ECP) basis set proposed by Stevens and co-workers19 using the second-order configuration interaction (SO-CI) method.20 Since the orbital sets of the singlet and triplet states must share a common set of frozen-core orbitals to calculate the SOC matrix elements, we employed the wave function of the triplet state as a reference state for the singlet CI wave function as well as the triplet wave function.

∑⎜ i≠j

(1)

α2 e 2h = 2 4πme2c 2 The root-mean-squared value of the SOC constant is defined as eq 2.

soc = (

∑

∑

Ms = 0, ±1 k = x , y , z

M

⟨3ψ s|Ĥ SO(BP)|1ψ ⟩k2 )1/2 (2) C


Organometallics

Article

Figure 2. Optimized geometries and selected bond distances (in Å) of the intermediates and transition states along the singlet and triplet surfaces of the CpCoC4H4 (A) with HNCO reaction via the C orientation at the B3LYP/6-311+G(d)+SDD level of theory.

than the singlet state, 1A, by about 17.4 kcal/mol. Relaxation to the triplet ground state of this coordinatively unsaturated species is facilitated by the presence of a minimum energy crossing point (CP1) of the singlet and triplet surfaces located at 1.3 kcal/mol (BP86, −3.1 kcal/mol, BHandHLYP, −0.9 kcal/mol; see Figure 4) relative to the singlet complex; therefore, it is reasonable to believe that the change in the spin state will occur readily, which is in accordance with previous calculations.3c 3.1. Reaction of HNCO with Cobaltacyclopentadiene via the Orientation of N toward the Co Center. 3.1.1. Initial Complexes. On the singlet potential surface, the first step of the reaction is coordination of the HNCO molecule to the Co center of CpCo(C2H4), producing an initial η1-N CpCo(C2H4)(HNCO) complex. Our optimization led to the local minimum of cobaltacyclopentadiene isocyanate complex 1B in Figure 1, in which the N atom of isocyanate coordinates to the Co atom with a Co−N bond length of 2.027 Å. 1 B is13.2 kcal/mol more stable than 1A + HNCO. However, for the triplet states, since the initial cobaltacyclopentadiene has a triplet spin ground state and a HNCO singlet state, the reaction begins on the triplet surface. We tried to find a corresponding 3B intermediate, but the results show that the optimization process cannot be converged, which suggested that there is no reaction pathway giving the intermediate 3B. These results show that a crossing and spin inversion process

For the qualitative interpretation of the nonzero SOC interaction, we also used ROHF orbitals21 generated at the triplet state as orbitals from which CASCI wave functions were constructed (see text for details). All SOC calculations were performed with the GAMESS program package.22

3. RESULTS AND DISCUSSION The optimized geometries in the triplet and singlet electronic states are depicted in Figures 1 and 2. In order to keep the discussion more simple, each species is labeled using letters with the superscript 1 or 3 as spin multiplicity. The calculated potential energy profiles for the singlet and triplet states are shown in Figures 3−5. Generally accepted initial reaction steps are shown in Scheme 2. In the restricted to closed-shell species, featuring CpCo(PH3)2 as a model precatalyst and ethyne as a model reagent, initially one and then two alkyne moieties displace sequentially two phosphines from the metal to form alkyne complexes a and then b. Bis-alkyne complex b undergoes spontaneous oxidative coupling to give the corresponding coordinatively unsaturated Cp-cobaltacyclopentadiene A. It is an important intermediate in the formation of many organic compounds; therefore, the transformation of bis(η2-acetylene) cobalt to cobaltacyclopentadiene has been studied experimentally as well as theoretically. In our study at the B3LYP level, the triplet state of CpCo(C4H4), 3A, was calculated to be more stable D


Organometallics

Article

Figure 3. Potential energy diagram (energies in au include zero-point energy at the B3LYP/6-311+G(d) +SDD level) along the reaction pathway CpCo(C4H4) + HNCO → CpCo + H4C4N(H)CO, in the singlet and triplet states. Relative energies are given in kcal/mol. Singlet spin surfaces are indicated by light blue lines and triplet spin surfaces by deep blue lines.

Figure 4. Proposed two-state potential energy diagrams along the favorable reaction pathways from our calculations (energies in au include zero point energy at the B3LYP/6-311+G(d) +SDD level). Relative energiesare given in kcal/mol with both BP86 (blue) and BHandHLYP (red). S = 0 light blue; S = 1 blue. E


Organometallics

Article

Figure 5. Potential energy diagram (energies in au include zero point energy at the B3LYP/6-311+G(d)+SDD level) along the reaction pathway CpCo(C4H4) + HNCO → CpCo + H4C4N(H)CO, in the singlet and triplet states. Relative energies are given in kcal/mol with both BP86 (blue) and BHandHLYP (red). Singlet spin surfaces are indicated by light blue lines and triplet spin surfaces by deep blue lines.

Scheme 2. Mechanism for Cp-cobaltacyclopentadiene

using the code of Harvey et al.10 The significant crossing of the singlet and triplet surfaces occurs in the vicinity of the 1B complex. The structure and energy of CP2 are given in Figure 6 and Table 1 at the B3LYP level of theory, respectively. The CP2 structure is very similar to 1B, in which the Co−N, N−C, and C−O bond distances are 2.099, 1.232, and 1.191 Å, respectively. CP2 corresponds to a late crossing point, leading to an intersystem crossing barrier height of 8.4 kcal/mol relative to that of 3A + HNCO at the B3LYP/6-311+G(d)+SDD level. It plays a significant role in mediating the two surfaces. Geometry optimization on the singlet potential energy surface starting at this CP2 structure leads to the 1B complex, suggesting that if the crossover occurs in this region of configurational space, then formation of the 1B intermediate will be favored. Within the crossing seam, the CP point is a minimum, and the spin hopping easily takes place because the Franck−Condon principle requires that it has the same energies and geometries. Therefore, the reaction system will access a lower energy singlet pathway by changing its spin multiplicities at the CP point. However, what kind of mechanism (nonadiabatic or adiabatic) takes place, which will depend on the magnitude of the transition probability? Among the factors that affect the magnitude of the transition probability is the spin−orbit coupling (SOC) interaction

may take place to reach the singlet encounter complex 1B reaction pathway. 3.1.2. Surface-Crossing Behavior. Spin inversion is a nonadiabatic process,23 and we need to inspect crossing seams on the singlet and triplet potential energy surfaces to know the mechanism of intersystem crossing (ISC). A spin change can be thought of as occurring when the motion of the atoms of the molecule brings the system into the region where the two surfaces cross, and spin− orbit coupling then enables a “hop” from one surface to the other. Moreover, for the transition-metal compounds, spin−orbit coupling can be very strong so that a better or at least equally good description of the electronic structure in the crossing region involves electronic states and potential energy surfaces of a mixed spin character, arising from an avoided crossing of the pure spin states.9 For this reason, finding the crossing point gives very valuable information as to the relative energy of the regions a spin-forbidden two-state reaction must necessarily pass through. The potential energy surfaces are multidimensional and therefore cross in many different points; one wishes to find the minimum energy crossing points between them. However, CP is not a stationary point on either of the individual spin surfaces and the common programs cannot find this point in a practical way for an organometallic system. In this paper, CPs are identified by F


Organometallics

Article

Figure 6. B3LYP optimized minimum energy crossing point (CP) between singlet and triplet surfaces (bond lengths in Å).

Table 1. Single-Point Energies Eelec (au) for the Minimum Energy Crossing Point Species Calculated at the B3LYP/ 6-311+G(d)+SDD Level species

spin state

ZPEa

Eelec

Eelec+ZPEb

CP1

singlet triplet singlet triplet singlet triplet singlet triplet singlet triplet

0.146010 0.145472 0.169990 0.169628 0.170834 0.171642 0.175773 0.175474 0.173424 0.173540

−494.176754 −494.176052 −662.932062 −662.930194 −662.921417 −662.924052 −663.010367 −663.014954 −662.950893 −662.954949

−494.030744 −494.030580 −662.762072 −662.760566 −662.750583 −662.752410 −662.834594 −662.839480 −662.777469 −662.781409

CP2 CP3 CP4 CP5 a

Zero point vibrational energies. bZPE corrections have been taken into account. Figure 7. Active orbitals in the vicinity of the CP2 crossing seam at the ROHF level and the orbital diagram of the important singlet and triplet configurations (blue). In order to save space, the nonactive orbitals (LUMO) are omitted. The numbers in parentheses are CI (configuration interaction) coefficients.

between the states.24 Therefore, the strength of the SOC and the energy gap are the keys to understanding the mechanism. Let us then discuss the SOC interaction. 3.1.3. Spin−Orbit Coupling (SOC) Discussion in the CP Region. The requirement for a successful surface hopping is that there is significant coupling between the two states. Thus, the extent of the nonadiabatic coupling in this formally spinforbidden process was investigated using the Pauli−Breit spincoupling operator (see calculation details). As the overall spin momentum is not conserved, ISC has to be promoted by SOC, where the orbital angular momentum can absorb the momentum change associated with the spin flip. The ROHF orbitals for the construction of the triplet and singlet CASCI wave functions to be used in the SOC evaluation have been generated in the CP2 region by triplet ROHF calculations. At least six active orbitals, as given in Figure 7 (in order to save space, the nonactive orbital LUMO is omitted), are found to be essential to reproduce the qualitative trends of SOC in the 3A + HNCO → 1B step. These orbitals form a basis for a subsequent SOCI.

The SOC matrix elements between the singlet state and the triplet state in the CP2 region are indicated in Table 2. In order to assess the relative importance of the one- and two-center SOC interactions, we have calculated them using the full Pauli−Breit method. The following can be seen from Table 2. (i) The SOC generated in CP2 was dominated by a one-center interaction, while two-center interactions nearly cancel out. At the same time, the one- and two-electron contributions have different signs, the latter being ca. 7−14% of the former. This recurring result supports the general view that the two-electron part acts as a screening factor on the one-electron SOC interaction.17 (ii) The spin transition contributions from the triplet state to the singlet state are strong because of the larger SOC values: SOC1‑e,1‑center = 393.37 cm−1. According to the SOC operator, G


Organometallics

Article

Table 2. Calculated SOC Matrix Elements (cm−1) of Singlet and Triplet States in the CP2 Crossing Point ⟨HSO⟩r

⟨S1 = 0; Ms,1k|HSO|S2 = 1; Ms,2k⟩a

r=z

⟨Ms,1 = 0|HSO|Ms,2 = 0⟩ = 32.55 one and two centers ⟨Ms,1 = 0|HSO|Ms,2 = 1⟩ = −193.73; 135.46 ⟨Ms,1 = 0|HSO|Ms,2 = −1⟩ = −193.73; −135.46 ⟨Ms,1 = 0|HSO|Ms,2 = 0⟩ = 32.64 one center ⟨Ms,1 = 0|HSO|Ms,2 = 1⟩ = −194.38; 135.79 ⟨Ms,1 = 0|HSO|Ms,2 = −1⟩ = −194.38; −135.79

r = x, y r = x, y r=z r = x, y r = x, y a

center

SOCfull

SOC1e

335.89

390.47

2

|1ψ ⟩ =

fk = λ ZW ⟨dxz|hk̂ |dxy⟩ − 2−1/2λ d z2dxy⟨d z 2|hk̂ |dxz⟩

363.93

⎛ α2 + 2−1/2λ d yzπN⟨d yz|hk̂ |dxz⟩⎜⎜hk̂ = 2 ⎝

393.37

k

(5)

(6)

where η is the Ms-dependent weighing factor and θ = α and/or β. In this case, for the triplet state, the fundamental open-shell configuration has one dominant coefficient, i.e. C0 = 0.97 ≈ 1, while the coefficient for the singlet state is λZW = 0.89. For ⟨S1 = 0; Ms,1k|HSO|S2 = 1; Ms,2k⟩ matrix elements, the calculated SOC matrix elements come mainly from the dxz → dxy spin flip. Therefore ⟨dxz|ICo, k|dxy⟩⟨θxz|Sk|θxy⟩ = dxz|ICo, x|dxy⟩⟨α|Sx|β⟩ + ⟨dxz|ICo, y|dxy⟩⟨α|Sy|β⟩ + ⟨dxz|ICo, z|dxy⟩⟨α|Sz|α⟩

(7)

Here, using the transformation properties of the d atomic orbitals under the operation of the Ix,y,z operators, only the first term is nonzero. An illustration is given in Figure 7, where the two orbitals are dxz and dxy, and the electron shift from dxy to dxz creates an angular momentum in the Ix direction, resulting in the SOC matrix element ⟨Ms,1 = 0|HSO|Ms,2 = ± 1⟩ = −194.38 cm−1 (see Table 2). Similarly, the second term, ⟨dz2|ĥk|dxz⟩ in eq 5, will lead to a larger SOC matrix element in the Iy direction. However, for the third term, the direct conversion from T1 is inhibited because of the incompatibility of the two electronic states. This state must execute a metal Co to ligand HNCO electron transfer, thereby formally oxidizing the metal and reducing the ligand when SOC occurs in the Iz direction. The final feature of the calculation that requires understanding is the variation of the SOC matrix element along the 3A + HNCO → 1B step. Considering the orbital contribution of HNCO for the SOC matrix element, the SOC matrix element is given as

(3a)

(0)

⟩ = |d z 2 d̅ z 2d yz d̅ yzπCπ ̅ C d̅ xz d̅ xy⟩

A

k ZA*IÂ ⎞⎟ rA3 ⎠⎟

⟨SOC⟩ = ηC0λ ZW ∑ ξCo⟨dxz|ICo, k|dxy⟩⟨θxz|Sk|θxy⟩

|3ψ ⟩ = 2−1/2(|d z 2 d̅ z 2d yz d̅ yzπCπ ̅ C d̅xzdxy⟩

|ψ

∑

The first term is the most important aspect due to the two mutually perpendicular orbitals in the corresponding integral part providing a significant one-center contribution to the SOC, and the 1dxzdxz wave function is the dominant configuration with a weight of about λZW = 0.89. Therefore, to further understand the efficient SOC, it is very important that the SOC matrix element ⟨dxz|hk̂ |dxy⟩ is discussed. The function f k consists of a sum of molecular orbital (MO) integrals multiplied by a configuration mixing coefficient (λ). Because the SOC constant (ζCo, which depends on the effective nuclear charge Z*A exerted on the valence electrons) is 1 order of magnitude greater than the SOC values for the N, C, and O atoms, it is a reasonable approximation to consider only the Co contribution when discussing spin−orbit mixing with the singlet state. Thus

(1)

3 (−1)

2

(4)

we can easily discover that the transition-metal center has a relatively large SOC due to a high nuclear charge (heavy-atom effect).25 (iii) The x, y components couple spin-sublevels (substates), which differ by ±1 unit from the Ms quantum number, while the z component couples substates with ΔMs = 0. (iv) The SOC interactions will lead to x and y components of the larger SOC matrix element; this is due to symmetry selection rules (a nonzero maximum angular momentum expectation value is obtained when the orbitals are mutually perpendicular). To further understand the electronic structure of CP2, we analyzed the origin of the nonzero SOC interaction by using the one-electron SOC operator. Interestingly, the CP2 showed significant multireference character for the singlet state (see Figure 7). At the CAS(8,7) level, the dominant determinants of the MCSCF wave functions have CI coefficients of 0.97 and 0.05 for the triplet state and 0.89, 0.12, and −0.21 (configurations of less than 0.1 have not been listed) for the singlet state. These indicate that multireference methods are important for the analysis of the CP2. Therefore, the permissible approximation of the triplet wave function by a single configuration (0.97) enables us to analyze the SOC matrix elements. The triplet T1 wave function of the CP2 can be satisfactorily expressed in eqs 3a−3c: i.e., a single covalent configuration formally described as 3dxzdxy. On the other hand, the singlet S0 wave function is given by the superposition of two covalent configurations (the two electrons occupied the different d orbitals) and one zwitterionic configuration (where the two electrons occupy the same dxz orbital), as shown in eq 4, in which i = 1dz2dxy and 1dyzπN (see Figure 7). The weights of the three configurations are 0.89, −0.21, and 0.12, respectively. The 1dxzdxz zwitterionic configuration wave function is the dominant configuration with a weight of about 0.89 at around the CP2 region. The permissible approximation of the triplet wave function by a single configuration enables us to analyze the SOC matrix element in a simple formula. Nonzero elements of the k components (k ≅ x, y, and z) of the SOC matrix, ⟨3ψ|Ĥ SO|1ψ⟩k, are always proportional to the function, f k, as given in eq 5, where λ is the configuration mixing coefficient, ĥk is a monoelectronic Hamiltonian, and ZA* is the effective nuclear charge.

+ |d z 2 d̅ z 2d yz d̅ yzπCπ ̅ Cdxz d̅xy⟩)

2

i=1

To account for one- and two-electron interactions.

|3ψ ⟩ = |d z 2 d̅ z 2d yz d̅ yzπCπ ̅ Cdxzdxy⟩

∑ λi|1Ψcov(i)⟩ + λZW |d z d̅ z d yzd̅ yzπCπ ̅ Cdxzd̅xz⟩

(3b)

⟨SOC⟩r = 0.5λC0[md (cCoc′Co )ζCo + (c HNCOc′HNCO )ζHNCO]md = 1,

(3c) H

3, 2

(8)


Organometallics

Article

3.1.5. Formation of a Pyridin-2-one Cobalt Complex. From the discussion above, it is clearly shown that the triplet surface intersystem can efficiently cross to the singlet state to form complex 1B. 1B isomerizes to the side-on complex 1C through 1 TS(BC) with an energy barrier of 2.5 kcal/mol. From 1C, the reaction can proceed in two possible pathways, as seen in Figures 3 and 4. The first pathway is the formation of the N−Cα bond. According to the results presented in Figures 3 and 4, N−Cα bond formation in 1C takes place quite easily via the transition state 1TS(CD), with the barrier being only −1.2 kcal/mol. Structure 1TS(CD) is a real transition state with one imaginary frequency of 319i cm−1 corresponding to the N−Cα stretch. Going from 1C to 1TS(CD), the N−Cα bond is shortened from 2.845 to 2.115 Å. The second pathway originating at complex 1C is the Co−Cγ cleavage process through the transition state 1TS(CF), leading to 1F. In 1F, the longer Cγ−Cδ bond of 1.367 Å suggests that this bond interacts with the Co atom, to make 1F an 18-electron Co complex. The puckered structure of 1F is also ascribed to this interaction. The transition state 1TS(CF) has one imaginary frequency of 293i cm−1 corresponding to the expected components of the vibration reaction coordinate: i.e., breaking of the Co − Cγ bond. The Co−Cγ bond is stretched from 1.998 Å in 1C to 2.881 Å in 1TS(CF). As seen from Figure 1, 1TS(CF) has a trans configuration in the Cγ−Cδ bond, while in the other intermediate structures this bond has a cis configuration (optimizations are very difficult to converge). This would be why the activation barrier is high. The calculated barrier height is 19.5 kcal/mol relative to structure 1C. A pronounced difference in comparison with N−Cα bond activation is that it has a high activation barrier of the Co−Cγ activation transition state, which may lead to the low efficiency. In order to understand the factors controlling the N−Cα and Co−Cγ cleavage processes, the energies to distort reactant fragments to the transition-state geometry (the distortion energy) and the energies of interaction between these distorted reactant intermediates and transition states (the interaction energy) were analyzed. Such an analysis is also known as the activation strain model.27 It is related to the deformation/interaction method developed by Morokuma et al.,28 which has been elaborated and applied to some systems. Thus, the activation energy ΔE⧧ is decomposed into the distortion energy (ΔE⧧dist(TS), required to distort the reactant fragments CpCo(C4H4) + HNCO into the TS geometry; it should be noted that the initial CpCo(C4H4) and HNCO structures are our zero reference for the calculated distortion energies of the transition states and therefore the ⧧ interaction energies ΔEint( 1 C) of the distorted fragments, CpCo(C4H4) + HNCO, cannot be ignored in the intermediate 1 C) and the stabilizing transition state (TS) interaction energies (ΔE⧧int(TS), gained upon allowing the distorted fragments to interact), namely

Here, we have already considered the nonvanishing spin factor (0.5); in the present case, the triplet configuration has one dominant coefficient, i.e. C0 ≈ 1. The md parameters are the coefficients of the angular momentum expectation values, while the cc′ factors are products of the MO coefficients for a given atom. Equation 8 provides a basis for understanding the SOC matrix element. Obviously, the HNCO term contributes to the SOC matrix element, but to a lesser extent than the Co term because ζCo is far larger than ζHNCO. Thus, to a rough approximation, the SOC matrix element will be determined by the variation of two main factors: the delocalization of the MO’s as accounted for by the cCoc′Co MO coefficient term and the ROHF configuration coefficient, λ, of the singlet state. One can see from Figure 7, from the dxy orbital to the dxz orbital, the MO coefficient, c′Co becomes larger, while the delocalization of Co becomes weaker, and the singlet state is dominated by a primary configuration, as the CP step possesses a significant SOC matrix element. In addition, an illustration is given in Figure 7, where the two MOs are dxz and dxy and the electron shift from dxy to dxz creates an angular momentum in the x direction. By a choice of the centers to be matched by the orbital rotation, here it is seen that the rotations are both in the same direction;18 as such, CP will produce a significant one-center SOC interaction. Therefore, this will enhance the probability of intersystem crossing from the triplet to the singlet state. 3.1.4. Estimation of the Probability of Intersystem Crossing (ISC) in the CP2 Region. In order to obtain more reliable results, we have computed the probability of intersystem crossing (ISC) within the limits of currently available theories. The probability of ISC for a molecule passing through a triplet−singlet crossing can be calculated from Landau−Zener theory.26 The Landau− Zener equations for the probability of single (PISC 1 ) and double (PISC ) passes through the crossing point are shown in eqs 9 2 and 10: P1ISC = 1 − P LZ

(9)

P2ISC = (1 + P LZ)(1 − P LZ)

(10)

where ⎛ 2πH 2 12 P LZ(E − Ec) = exp⎜⎜ − F ℏΔ ⎝

⎞ ⎟⎟ 2(E − Ec) ⎠ μx

Here, H12 is the spin−orbit coupling-derived off-diagonal Hamiltonian matrix element between the two electronic states and ΔF is the relative slope of the two surfaces at the crossing seam. The reduced mass of the system as it moves along the hopping coordinate x is μx, Ec is the energy of the CP, and E is the total internal energy. The CP provides a natural choice for the hopping coordinate, as the gradients on the two surfaces at the CP are either parallel or antiparallel and are orthogonal to the seam of crossing. Within the seam, the CP is a minimum. Thus, using Landau−Zener theory, the calculated values of ΔF and μx (the reduced mass of the distortion coordinate) are 0.02327 hartree bohr−1 and 6.18 ISC amu for the CP2, respectively. The probabilities of PISC 1 and P2 −1 passes estimated at MECP (SOCfull = 335.89 cm ) are approximately 0.28 and 0.48, respectively. The high probability in the crossing region indicates that the triplet surface intersystem crossing to the singlet state would be clearly very efficient.

⧧ ⧧ ≠ ΔE ⧧ = ΔEdist(TS) − ΔE int( + ΔE int(TS) 1 C)

These are shown schematically in Figure 8. The calculated results are summarized in Table 3. Interestingly, for the 1TS(CD) transition state, the activation distortion energies (ΔE⧧dist(TS)) of HNCO and CpCo(C4H4) were very small, while their interaction was calculated to be strong at −116.3 kcal/mol. Thus, the lowering of the activation barriers is caused by the 1TS(CD) interaction ΔE⧧int(TS) becoming more stabilizing, which will lead to the nonbarrier process. To facilitate the fragment interactions in 1TS(CF), the pyridone ring I


Organometallics

Article

reaction coordinate at 3TS(DE) is mainly the Cα−N bond stretching. At 3TS(DE) the Cα−N bond (2.034 Å) is about 39.7% shorter than that (2.841 Å) in 3D; IRC calculations starting from 3TS(DE) to 3E showed that, after the Cα−N bond is formed, the Co−N bond is broken and after that 3E is obtained (during the course of the reaction, the pyridone ring rotates to reach the η2-pyridine complex). In the 1D → 1E step, the pyridinone complex 1D is more stable than the 1F intermediate by 11.7 kcal/mol. This high stability is ascribed to the formation of the η4-pyridin-2-one ligand, in which a new σ bond with a bond length of 1.441 Å is formed. In 1D, pyridin-2-one coordinates to the Co atom in an η4 manner to avoid the formation of a 20-electron species. As a result, significant bond alternation is seen in the pyridine ring, and the uncoordinated Cβ−Cγ bond has a double-bond character with a short bond distance of 1.342 Å. The C and N atoms of HNCO remain in interaction with the Co atom in 1D. However, there is a more stable isomer of the η4-pyridin-2-one complex 1E in which the C and N atoms from the isocyanate molecule do not coordinate to the Co atom. Pyridin-2-one has already formed in 1D, and if the ligand exchange takes place in 1D, the catalytic reaction will proceed. Finally, we turn to the formation of 3E from 1E. A second crossing point, CP4, is located by using the methods of Harvey et al. The structure of CP4 is shown in Figure 6. The geometrical parameters of CP4 are indeed very similar to those of 1E (Figure 1 and 6), with an energy of 2.5 kcal/mol relative to that of 1E (ΔECP4‑1E = 2.5 kcal/mol). The one-center SOC value is 225.3 cm−1 in CP4; the large values of the singlet and triplet SOC will be more efficient in CP4 from the viewpoint of the spinforbidden transition. We also note that the main contribution to the SOC between the singlet and triplet state comes from the ⟨dyz|Ĥ SO|dxz⟩k component (see Scheme 3a). A nonzero maximum angular momentum expectation value is obtained when the orbitals are mutually perpendicular. Therefore, the triplet state is generated from the singlet at CP4 by electron shifts from dyz to dxz, which lead to the d-AO matrix elements, ⟨dyz|Iz|dxz⟩, and z components of angular momentum. As a result, we expect that it should generate a large one-electron one-center SOC interaction, which is also conceptually verified by an analysis of the spin densities, as shown in Scheme 3b,c. The two activation electrons are localized on the Co atom according to the DFT calculations, as indicated by spin densities of 1.99 (the triplet state) and α − β = 0.03 (the singlet state). These calculations show that SOC induces a spin multiplicity mixing; the magnitude of the spin multiplicity mixing increases in a small energy gap between singlet and triplet states will greatly enhance the probability of the intersystem crossing. From the discussion above, it is clearly shown that the singlet surface intersystem crossing to the triplet state to form 3E would be very efficient. 3.2. Reaction of HNCO with Cobaltacyclopentadiene via the Orientation of C toward the Co Center. The calculated potential energy profiles for the singlet and triplet states are shown in Figure 5. The corresponding optimized geometries are depicted in Figure 2. As can been seen from Figure 5, singlet Cp-cobaltacyclopentadiene 1A relaxes to the triplet ground state via CP1 and then reacts with HNCO to form the transition state, 3TS(GH). 3TS(GH) is characterized as a transition structure by one imaginary frequency of 345.66i, and the vibrational vector corresponds to the expected components of the N−Cγ reaction coordinate. This step needs to overcome a large activation energy of 43.7 kcal/mol, which also indicates a very unfavorable process kinetically. As for the singlet potential surface, it is very similar to the triplet state, and there is a high

Figure 8. Distortion/interaction model for the singlet transition states, 1 TS(CD) and 1TS(CF).

Table 3. Distortion/Interaction (kcal/mol, without Zero Point Vibrational Energies) Analysis of TSs Involving 1 TS(CD) and 1TS(CF) ΔEdist

ΔEint

TS

ΔE⧧

HNCO

CpCoC4H4

TS

TS(CD) 1 TS(CF)

−1.0 19.1

8.8 11.3

−0.4 52.8

−116.3 −151.9

1

1

C

−106.9 −106.9

is largely deformed with a large deformation energy of 52.8 kcal/mol. For most of the compounds, decomposition of the distortion energies into their bending and stretching components confirmed that the origin of their difference is due to the stretching of the Co−Cγ bond in 1TS(CF) and the bending of the Co(C4H4) ring in 1TS(CD). Moreover, the interaction between the deformed fragments in 1TS(CF) is very strong, with the largest interaction energy of −151.9 kcal/mol, but it cannot compensate for the energy difference between the distortion energies of the HNCO and CpCo(C4H4) fragments and the intermediate reactant 1C interaction. Therefore, the 1TS(CF) transition state is much more unstable, leading to a high activation energy of 19.5 kcal/mol. Obviously, the interaction energies may control the N−Cα bond formation process, while the Co−Cγ bond activation is controlled by the fragment distortion energies in 1TS(CF). In addition, we noted that there is a third crossing point, CP3, between the singlet and triplet potential surfaces (see Figure 4) in the region from 1C to 3D. The structure of CP3 is depicted in Figure 6. This point is geometrically closer to 1TS(CF). The large difference is due to the fact that the Co−Cγ bond length is 2.493 Å in CP3 but 2.191 Å in 1TS(CF). This crossing point is the important aspect in this reaction pathway because the molecular system could change its spin multiplicity from the singlet state to the triplet state near this crossing region, leading to a decrease in the barrier height of 1TS(CF) from 19.5 to 9.5 kcal/mol at the B3LYP/6-311+G(d)+SDD level. Thus, the reaction system will access a lower energy pathway by changing its spin state via the CP3 point and then move on the triplet potential energy surface as the reaction proceeds. In the triplet pathway, an azacobaltacycloheptatrienone ring in 3D is close to a planar structure, in contrast to its puckered structure in the corresponding singlet intermediate 1F (see Figure 1). The d orbital, which is unoccupied in 1F and accepts electrons from the Cγ−Cγ bond, is singly occupied in 3D. Consequently, the interaction is absent or very weak in 3D. This high stability of 3D can be ascribed to the strong Co−N bond (1.838 Å) in 3D, which is 0.059 Å shorter than the Co−N bond (1.897 Å) in 1F. The transition state, 3TS(DE), connects 3D and 3E with a larger energy barrier of 14.8 kcal/mol. The J


Organometallics

Article

Scheme 3

calculations. All structures of the triplet and singlet potential energy surfaces have been determined and characterized at the DFT-B3LYP/6-311+G(d) level. Crossing points between the potential energy surfaces are located using the method of Harvey et al., and possible spin inversion processes are discussed by means of spin−orbit coupling (SOC) calculations. The SOC between the triplet and singlet states was calculated using the SO-CI method with the converged ROHF wave function with the GAMESS program package. As a result, the initial singlet state of CpCo(C2H4), 1A, will readily relax to the triplet ground state, 3A, through a spin flip in the minimum energy crossing point (CP1) located at 1.3 kcal/mol (see Figures 3 and 4) relative to the singlet complex. From the beginning of cobaltacyclopentadiene, 1A or 3A, two distinct reaction pathways for the formation of pyridin-2-one cobalt complex have been found. The calculated results show that the most favorable mechanism is the TSR nonadiabatic mechanism in Figures 4 and 5. For the first pathway for the orientation of N toward the Co center, as shown in Scheme 4, there are three main crossing points (CP2, CP3, and CP4) between the singlet and triplet potential surfaces along the reaction pathway, and the reacting system should change its spin multiplicity in these crossing points. The first crossing point, CP2, exists near 1B, which is the important aspect in this reaction pathway due to a large spin-change-induced barrier of 8.4 kcal/mol. Spin−orbit coupling (SOC) is discussed in the vicinity of the CP2, and the reacting system will change its spin multiplicity from the triplet state to the singlet state near this crossing region because the magnitude of the spin-multiplicity mixing (SOC1‑e,1‑center = 393.37 cm−1) increasing in a small energy gap between high- and low-spin states will greatly enhance the probability of intersystem crossing. The single (P1ISC) and double (P2ISC) passes estimated at CP2 are approximately 0.28 and 0.48, respectively. From 1C, the reaction splits into two paths: Co−Cγ bond activation and the N−Cα bond formation. The Co−Cγ bond activation pathway will again

barrier of 45.9 kcal/mol. We know the frontier molecular orbitals are the main participants in the interactions of the reactants, and the donor/acceptor orbital overlaps dominate the reaction pathway. The molecular orbitals of HNCO show that the HNCO HOMO is a π orbital, which is dominantly N and O in character. The LUMO is a π* orbital with orbital contributions from N, C, and O, which is antibonding in character for both the C−N and C−O bonds. Thus, for the transition state, the middle C atom coordination configuration likely causes the difficulty in electron transfer, while terminal nitrogen coordination is favorable due to a good overlap of the HOMO of HNCO with the Co empty d orbitals. Unlike the singlet state, the triplet system apparently cannot form a stable insertion intermediate, 3H, while it will possibly access a lower energy pathway by changing its spin states via the crossing point. However, unfortunately, this crossing point cannot be located using the method of Harvey et al.,10 as mentioned previously. 1 H needs an activation energy of 0.9 kcal/mol to transform to the intermediate 1I through 1TS(HI), with a large exothermicity of 16.8 kcal/mol. From 1H to 1I, we find another crossing point, CP5 (see Figure 6), after 1TS(HI), the relative energy being −15.8 kcal/mol, with a large one-electron one-center SOC interaction of 304.7 cm−1. This crossing seam will lead to spin inversion from the singlet to the triplet state, by which the exothermicity required for the formation of 3I can be increased from 16.8 to 27.4 kcal/mol. Obviously, the 3I formation is a very favorable process kinetically and thermodynamically. Therefore after passing point CP5, the triplet potential energy surface can provide a low-cost reaction pathway toward the product complex. Then the 3I → 3E step is calculated to be strongly exothermic by 35.9 kcal/mol and has a small barrier of 2.8 kcal/mol.

4. CONCLUSION In this study, the reactions of cobaltacyclopentadiene with the HNCO molecule have been studied using theoretical K


Organometallics

Article

Scheme 4. Two-State Reactivity Mechanisma

research. This research was supported by TianShui Normal University by a grant of “QingLan” talent engineering funds.

■

a

(1) (a) Vollhardt, K. P. C. Angew. Chem., Int. Ed. Engl. 1984, 23, 539. (b) Braunstein, P.; Nobel, D. Chem. Rev. 1989, 89, 1927. (2) (a) Saito, S.; Yamamoto, Y. Chem. Rev. 2000, 100, 2901. (b) Galan, B. R.; Rovis, T. Angew. Chem., Int. Ed. 2009, 48, 2830. (c) Varela, J. A.; Saà, C. Chem. Rev. 2003, 103, 3787. (c) Heller, B.; Hapke, M. Chem. Soc. Rev. 2007, 36, 1085. (d) Ozaki, S. Chem. Rev. 1972, 72, 457. (3) (a) Dalton, D. M.; Oberg, K. M.; Yu, R. T.; Lee, E. E.; Perreault, S.; Oinen, M. E.; Pease, M. L.; Malik, G.; Rovis, T. J. Am. Chem. Soc. 2009, 131, 15717. (b) Schmid, R.; Kirchner, K. J. Org. Chem. 2003, 68, 8339. (c) Dahy, A. A.; Yamada, K.; Koga, N. Organometallics 2009, 28, 3636. (4) Hong, P.; Yamazaki, H. Tetrahedron Lett. 1977, 15, 1333. (5) Hong, P.; Yamazaki, H. Synthesis 1977, 50. (6) (a) Armentrout, P. B. Annu. Rev. Phys. Chem. 1990, 41, 313. (b) Armentrout, P. B. Science 1991, 251, 175. (c) Rue, C.; Armentrout, P. B. J. Chem. Phys. 1999, 110, 7858. (7) Schroder, D.; Shaik, S.; Schwarz, H. Acc. Chem. Res. 2000, 33, 139. (8) (a) Fiedler, A.; Schroder, D.; Shaik, S.; Schwarz, H. J. Am. Chem. Soc. 1994, 116, 10734. (b) Shaik, S.; Danovich, D.; Fiedler, A.; Schroder, D.; Schwarz, H. Helv. Chim. Acta 1995, 78, 1393. (c) Fiedler, A.; Schroder, D.; Zummack, W.; Shaik, S.; Schwarz, H. Inorg. Chim. Acta 1997, 259, 227. (d) Hirao, H.; Kumar, D.; Que, L.; Shaik, S. J. Am. Chem. Soc. 2006, 128, 8590. (e) Yarkony, D. R. J. Phys. Chem. 1996, 100, 18612. (9) Harvey, J. N.; Poli, R.; Smith, K. M. Coord. Chem. Rev. 2003, 238− 239, 347. (10) Harvey, J. N.; Aschi, M.; Schwarz, H.; Koch, W. Theor. Chem. Acc. 1998, 99, 95. (11) Frisch, M. J. et al. Gaussian 03 (Revision-E.01); Gaussian Inc., Pittsburgh, PA, 2003. (12) Frisch, M. J.; Pople, J. A.; Binkley, J. S. J. Chem. Phys. 1984, 80, 3265. (13) (a) Dunning, T. H., Jr.; Hay, P. J. In Modern Theoretical Chemistry; Schaefer, H. F., III, Ed.; Plenum: New York, 1976; Vol. 3, pp 1−28. (b) Andrae, D.; Haeussermann, U.; Dolg, M.; Stoll, H.; Preuss, H. Theor. Chim. Acta 1990, 77, 123. (14) (a) Cho, H. G.; Andrew, L. J. Phys. Chem. A 2006, 110, 3886. (b) Straub, B. F. J. Am. Chem. Soc. 2002, 124, 14195. (c) Filatov, M.; Shaik, S. J. Phys. Chem. A 1998, 102, 3835. (15) (a) Wang, Y. C.; Zhang, J. H.; Geng, Z. Y. Chem. Phys. Lett. 2007, 446, 8. (b) Liu, Z. Y.; Wang, Y. C.; Geng, Z. Y.; Yang, X. Y. Chem. Phys. Lett. 2006, 431, 223. (c) Wang, Y. C.; Wang, Q.; Geng, Z. Y.; Lv, L. L.; Si, Y. B.; Wang, Q. Y.; Liu, H. W.; Cui, D. D. J. Phys. Chem. A 2009, 113, 13808. (d) Lv, L. L.; Wang, Y. C.; Geng, Z. Y.; Liu, H. W. Organometallics 2009, 28, 6160. (16) Fedorov, D. G.; Koseki, S.; Schmidt, M. W.; Gordon, M. S. Int. Rev. Phys. Chem. 2003, 22, 551. (17) Danovich, D.; Shaik, S. J. Am. Chem. Soc. 1997, 119, 1773. (18) Danovich, D.; Marian, C. M.; Neuheuser, T.; Peyerimhoff, S. D.; Shaik, S. J. Phys. Chem. A 1998, 102, 5923. (19) Matsushita, T.; Asada, T.; Koseki, S. J. Phys. Chem. A 2006, 110, 13295. (20) Koseki, S.; Schmidt, M. W.; Gordon, M. S. J. Phys. Chem. 1992, 96, 10768. (21) (a) Salem, L.; Rowland, C. Angew. Chem., Int. Ed. 1972, 11, 92. (b) Isobe, H.; Yamanaka, S.; Kuramitsu, S.; Yamaguchi, K. J. Am. Chem. Soc. 2008, 130, 132. (22) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S.; Windus, T. L.; Dupuis, M.; Montgomery, J. A., Jr. J. Comput. Chem. 1993, 14, 1347. (23) Harvey, J. N. Phys. Chem. Chem. Phys. 2007, 9, 331. (24) Hirao, H.; Kumar, D.; Que, L., Jr.; Shaik, S. J. Am. Chem. Soc. 2006, 128, 8590. (25) Dede, Y.; Zhang, X. H.; Schlangen, M.; Schwarz, H.; Baik, M. H. J. Am. Chem. Soc. 2009, 131, 12634.

Triplet species and pathways appear in blue and singlet states in red.

change its spin multiplicity from the singlet state to the triplet state near CP3, leading to a decrease in the barrier height of 1 TS(CF) from 19.5 to 9.5 kcal/mol. Thus, the reaction system will access a lower energy pathway and then move on the triplet potential energy surface as the reaction proceeds. However, N−Cα bond formation in 1C takes place quite easily via the transition state 1TS(CD), with the nonbarrier being only −1.2 kcal/mol. As for the second pathway (see Figure 8), formation of the bicyclic carbene intermediate 1H by C attack of the HNCO molecule needs to overcome a large activation energy of 45.9 kcal/mol, which also indicates a very unfavorable process kinetically. We find another crossing point, CP5 (see Figure 6), from 1H to 1I, which will lead to spin inversion from the singlet to the triplet state and is a very favorable process kinetically and thermodynamically. After passing point CP5, the triplet potential energy surface can provide a low-cost reaction pathway toward the product complex.

■

ASSOCIATED CONTENT

* Supporting Information S

Table S1, giving the total energies E (au) for the optimized species calculated at the B3LYP/6-311+g(d)+SDD and B3LYP/6-311++G(d,p) solvent effects (benzene as solvent) level, Table S2, giving single-point energies E (au) at the BP86/ 6-311++G(d,p) and BHandHLYP/6-311++G(d,p) levels, and Table S3, giving XYZ coordinates of optimized geometries. This material is available free of charge via the Internet at http://pubs.acs.org.

■

REFERENCES

AUTHOR INFORMATION

Corresponding Author

*L.L.: tel, 18793855301; e-mail, [email protected]/lvling100@ 163.com. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We wish to thank the National Natural Science Foundation of China (Grant No. 21263022) and the University Research Fund of Gansu Province Financial Department for support of this L


Organometallics

Article

(26) (a) Zener, C. Proc. R. Soc. London, Ser. A 1932, 137, 696. (b) Zener, C. Proc. R. Soc. London, Ser. A 1933, 140, 660. (27) (a) Schoenebeck, F.; Houk, K. N. J. Am. Chem. Soc. 2010, 132, 2496. (b) Gorelsky, S. I.; Lapointe, D.; Fagnou, K. J. Am. Chem. Soc. 2008, 130, 10848. (28) (a) Kitaura, K.; Morokuma, K. Int. J. Quantum Chem. 1976, 10, 325. (b) Morokuma, K. J. Chem. Phys. 1971, 55, 1236.

M


Theoretical Study on the Two-State Reaction Mechanism for the

Recommend Documents