DFT and CASPT2 Study on the Mechanism of Ethylene Dimerization

ARTICLE pubs.acs.org/JPCA

DFT and CASPT2 Study on the Mechanism of Ethylene Dimerization over Cr(II)OH+ Cation Zhen Liu, Lei Zhong, Yun Yang, Ruihua Cheng, and Boping Liu* State Key Laboratory of Chemical Engineering, East China University of Science and Technology, 130 Meilong Road, 200237, Shanghai, China

bS Supporting Information ABSTRACT: In this work, the ethylene coordination and dimerization mechanism over Cr(II)OH+ cation were systematically investigated using density functional theory (DFT) and complete active space second-order perturbation theory (CASPT2). It was found that Cr(II)OH+ cation can coordinate with up to four ethylene molecules which gives seven possible stable Cr(II)OH+ 3 (C2H4)n (n = 1
4) π-complexes. We investigated whether ethylene dimerization over Cr(II)OH+ cation proceeds through either a carbene mechanism or a metallacycle mechanism. The potential energy surfaces were characterized using four different functionals (M06L, BLYP, B3LYP, and M06). It was found that the potential energy profiles calculated at the M06 level agreed well with the CASPT2 energy profiles. Since the intermediates involved in the proposed catalytic cycles showed different ground spin states, a reaction pathway involving a spin crossing between two potential energy surfaces was observed. The minimum-energy crossing points (MECPs) that connect the two potential energy surfaces were successfully located. The two-state metallacycle reaction pathway with the formation of chromacyclopentane as the rate-determining step was found to be energetically more favorable than the carbene reaction pathway. 1-Butene was formed from the chromacyclopentane by a twostep reductive elimination pathway through a chromium(IV) hydride intermediate.

1. INTRODUCTION In the gas phase, transition-metal contained ions are effective catalysts for the activation of simple hydrocarbons.1
3 It is straightforward to study the mechanisms of metal-mediatedreactions in the gas phase, unlike those in the condensed phase, as these studies one may work directly at the molecular level and not be interrupted by the environments.4 Consequently, during the last three decades, chromium-based ions have attracted a lot of attention in the field of the gas-phase catalytic reactions.5
16 In particular, chromium oxide cations are much more effective catalysts in the gas phase. Kang and Beauchamp investigated alkene oxidation by CrO+ and found that CrO+ exhibits a good activity as well as a good selectivity.10 Schwarz and co-workers reported that OCrO+ is an efficient catalyst for the oxidation of methane and benzene molecules.11 These gas-phase ionic reaction systems are not only well-suited for the experimental investigations on the mechanisms but also useful for theoretical calculations to gain deeper insight into the mechanisms of these reactions.17
25 Shiota and Yoshizawa theoretically investigated the methane-to-methanol conversion by all the first transition metal oxide ions (MO+s) and found that methane hydroxylation by CrO+ is facilitated by a nonadiabatic transformation.24 Scupp and Dudley studied the reactions of CrO+ with ethylene using various theoretical methods and found acetaldehyde is the major product.25 Surprisingly, most of the gas-phase studies, both experimental and theoretical, have centered on small hydrocarbon oxidation r 2011 American Chemical Society

by chromium oxide cations, while only a few studies have focused on ethylene coordination and polymerization on chromium ions. Transition-metal ethylene bonds in Cr(C2H4)n+ (n = 1
2) have been detected by guided ion beam mass spectrometry26,27 and have also been examined using theoretical calculations.28 Hanmura et al. investigated the reactions of ethylene molecules on various chromium ions in the gas phase and found two ethylene molecules adsorbed on Cr(II)OH+ cation under multiple collision conditions followed by dimerization into 1-butene on the basis of their experimental and theoretical investigations.12,13 However, in their theoretical studies, only several stationary points were calculated and the whole reaction pathway was not considered. In our opinion, the Cr(II)OH+ cation could be a simple and ideal homogeneous cluster model for further theoretical investigation on the initiation mechanism for ethylene dimerization. Furthermore, an understanding of the formation of the first Cr
C bond may also shed some lights on the initiation mechanism for ethylene polymerization on the chromium-based Phillips catalyst.29
31 Since spin-crossing reactions have been observed for most chromium ion catalyzed reactions,19
25 the calculations on the system require a theoretical method capable of describing spininversion energies accurately. Density functional theory (DFT) Received: November 21, 2010 Revised: June 2, 2011 Published: June 07, 2011 8131

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The Journal of Physical Chemistry A is well-known for the computational speed and reasonably good accuracy in the description of many chemical problems.32 However, special care and careful calibration are required when selecting a DFT functional to describe reactions involving a spin-crossing transformation.33 The newly developed hybrid meta-GGA functional M06 and the pure local density functional M06L are recommended for the description of the transition-metal contained systems.34 Furthermore, for a system with near-degenerate states, it is always necessary to perform a multiconfigurational self-consistent field (MCSCF) calculation to evaluate the electron correlations, while the electron dynamical correlation could be captured by complete active space second-order perturbation theory (CASPT2).35,36 In this work, the ethylene coordination and dimerization over Cr(II)OH+ cation were systematically investigated using DFT and the complete active space SCF (CASSCF)/ CASPT2 approach. The Cr(II)OH+ cation was found to be able to coordinate with up to four ethylene molecules, resulting in the formation of seven Cr(II)OH+ 3 (C2H4)n (n = 1
4) Cr
ethylene π-complexes. When starting from the most stable complexes, which contain one or two coordinated ethylene molecules, a two-state metallacycle reaction pathway for ethylene dimerization catalyzed by the Cr(II)OH+ cation was found to be energetically preferable to a carbene reaction pathway.

2. COMPUTATIONAL DETAILS All DFT calculations have been carried out using the Gaussian 09 package.37 For clarity, the five groups of basis sets employed in DFT calculations are denoted as follows: BS1 (6-31G(d,p) for H, C, O, and Cr), BS2 (6-31G(d,p) for H, C, and O, LANL2DZ for Cr), BS3 (6-311G for H, C, and O, LANL2TZ for Cr), BS4 (6311G(3df,3pd) for H, C, and O, LANL2TZ(f) for Cr), and BS5 (6-311++G(3df,3pd) for H, C, and O, LANL2TZ(f) for Cr). The CASSCF/CASPT2 computations were performed using the MOLCAS 7.0 package.38,39 In these calculations a large ANORCC40,41 (atomic natural orbital—relativistic with core correlation) basis set with triple-ζ quality (ANO-RCC-VTZP) was used on Cr, while the double-ζ quality basis set (ANO-RCC-VDZP) was used on H, C, and O. This group of basis sets is henceforth referred to as BS6. 2.1. Cr(II)OH+
Ethylene π-Complexes. We first determined that the quintet is the ground spin state of the Cr(II)OH+ cation using a CASSCF/CASPT2 method. In searching for stable configurations of Cr(II)OH+
ethylene π-complexes, geometry optimizations were conducted first at the B3LYP/BS2 level for a number of possible initial geometries. Eight stable configurations (5EA1a, 5EA1b, 5EA2a, 5EA2b, 5EA3a, 5EA3b, 5EA4, and 5EA5) were obtained for the quintet Cr(II)OH+ cation with up to 5 coordinated ethylene molecules. To check for basis set superposition error (BSSE) in the calculation of the binding energies, B3LYP geometry optimizations were further performed with the other 4 different basis sets (BS1, BS3, BS4, and BS5) for all eight geometries. BSSE effects were then evaluated with the CP (counterpoise) method as implemented in the Gaussian 09 package.37 The complex 5EA5, which contains 5 coordinated ethylene molecules, collapsed during optimizations using a basis set of triple-ζ quality (BS3, BS4, and BS5) and is thus only presented in the Supporting Information. The most reliable results were obtained with the largest triple-ζ basis set (BS5), and so it was employed for all the following mechanistic DFT calculations. Uncorrected binding energy (BDE) and BSSE corrected binding energy (BDE C ) were calculated using the following

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formulas: BDE ¼ E½CrðIIÞOH+ 3 ðC2 H4 Þn 
E½CrðIIÞOH+ 
nE½C2 H4  ðn ¼ 1
4Þ BDEC ¼ EBSSE ½CrðIIÞOH+ 3 ðC2 H4 Þn 
E½CrðIIÞOH+ 
nE½C2 H4  ðn ¼ 1
4Þ where E[Cr(II)OH+ 3 (C2H4)n] and E[Cr(II)OH+] are the total energies of the Cr(II)OH+ 3 (C2H4)n and Cr(II)OH+ cations in their quintet ground states, respectively, while EBSSE[Cr(II)OH+ 3 (C2H4)n] is the BSSE-corrected total energy of Cr(II)OH+ 3 (C2H4)n and E[C2H4] is the total energy of C2H4 in its singlet ground state. Four DFT functionals B3LYP,42,43 BLYP,42,44 M06,45,46 and M06L,45,46 were used to compute the BDE of a Cr(II)OH+ 3 (C2H4)2 adduct for which the experimental result is available.13 Subsequent single point CASPT2 calculations were carried out on the basis of the DFT optimized geometries of Cr(II)OH+ 3 (C2H4)2. The active space includes two sets of π, π* orbitals on the ethylene molecules, the Cr
O σ bonding orbital, the Cr
O σ* antibonding orbital, the O lone pair orbital with its corresponding virtual orbital, and four singly occupied 3d orbitals on Cr (See Figure S5 in the Supporting Information for the 12 orbitals included in the active space). Hence, a CAS(12,12) calculation was conducted by distributing 12 active electrons in the 12 active orbitals. 2.2. Two-State Reaction Mechanisms. Previous calculations by Hanmura et al. were performed using the quintet spin multiplicity and did not consider the possibility of a spin-crossing phenomenon.13 We found that a spin crossing does indeed take place in the proposed reaction intermediates (see Table S2 in the Supporting Information). Consequently, assuming spin conservation seems somewhat arbitrary, which is unable to give a reasonable mechanistic description for the ethylene dimerization catalyzed by the Cr(II)OH+ cation, we therefore performed detailed investigations of both the high- and low-spin potential energy surfaces. The reaction pathway that involves a mixing of both spin states is thus determined. Starting from the complexes with coordination with one or two ethylene monomers, the reaction may follow either a carbene pathway or a metallacycle pathway, as shown in Scheme 1. All the calculations in this section were first performed at the B3LYP/BS5 level of theory. The DFT functional effect on the prediction of the ground spin states of the intermediates and on the description of the potential energy surfaces of the reaction was then evaluated by reperforming the calculations using the BLYP, M06 and M06L functionals as implemented in Gaussian 09.37 Throughout we have employed harmonic vibrational frequency calculations to confirm that structures have been properly optimized and intrinsic reaction coordinate (IRC) calculations, which test whether or not the transition state is directly connected to the reactant and product states, to test the veracity of the transition states. The tight convergence criteria were selected for all calculations consisting of threshold values of 0.00001 au, 0.00004 au for root-mean-square (rms) force and rms displacement, respectively. Meanwhile, a self-consistentfield (SCF) density convergence threshold value of 1  10
11 was specified. A larger DFT integration grid (keyword: int=ultrafine) was used together with these tight convergence criteria in order to obtain more reliable results. The methodology developed by Harvey and co-workers41 was employed to 8132

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Scheme 1. Two-State Reactivity for Dimerization of Ethylene Catalyzed by the Cr(II)OH+ Cation

Table 1. Geometrical Features and Charge Distribution of the Multiple States of Cr(II)OH+ Determined at the CASPT2/BS6 Level of Theorya NBO charge spin multiplicity

Cr
O

Cr
O
H

Cr

atomic spin density

O

H

Cr

O

H

rel total energy

singlet

1.716

136.2

1.479


0.856

0.377

0

0

0

70.0

triplet

1.720

140.3

1.515


0.896

0.381

1.935

0.060

0.005

52.0

quintet

1.744

136.0

1.547


0.921

0.374

3.961

0.034

0.005

0

a

The Cr
O distance is expressed in angstroms. The Cr
O
H angle is in degrees. NBO charges and the Mulliken spin density of Cr are also listed. The total energy of the quintet state is taken as a reference. Energies are in kcal/mol.

locate minimum energy crossing points (MECPs) between high- and low-spin surfaces. The quadratic convergence SCF method (keyword: scf=qc) was employed whenever the SCF failed to convergent. Because entropy contributions at 298 K do not change the reaction profile, only the electronic total energies are discussed in the description of the reaction mechanisms. The free energies are also shown in parentheses along the reaction pathway. CASSCF/CASPT2 single point energy calculations have been performed for the geometries obtained from optimizations with all the four DFT functionals at the BS5 level. In order to obtain a reasonable energy comparison along the reaction pathway, a CAS(2,2)/CASPT2 calculation was performed on ethylene, a CAS(4,4)/CASPT2 calculation was performed on 1-butene, CAS(8,8)/CASPT2 calculations were performed on Cr(II)OH+ cation (A0), CAS(10,10)/CASPT2 calculations were performed on A1, A5 and TS[A1
A5], and CAS(12,12)/ CASPT2 calculations were performed on all the other geometries. Since the numerical-gradient calculation needed in the CASPT2 geometry optimization is prohibitively expensive, crossing points located at DFT level were reoptimized at the CASSCF level, after which CASPT2 energy calculations were performed on the CASSCF optimized geometries.

3. RESULTS AND DISCUSSION In this work, we present a detailed investigation of the Cr(II)OH+ 3 (C2H4)n (n = 1
4) π-complexes and the two-state catalytic cycle for ethylene dimerization. The ground spin state of Cr(II)OH+ cation was first determined using the CASSCF/ CASPT2 approach. Then, the basis set effects were examined through a comparison of the BDEs for Cr(II)OH+ 3 (C2H4)n (n = 1
4) π-complexes calculated at the B3LYP level of theory using 5 different basis sets (see Table S1 in the Supporting Information). Particularly, the binding energy for Cr(II)OH+ 3 (C2H4)2 was calculated using 4 DFT functionals (B3LYP, BLYP, M06, and M06L) and using the CASPT2 approach. Having validated the methodology, we then examined the two-state reaction mechanism that starts from the Cr(II)OH+ 3 (C2H4)n (n = 1
2) π-complexes for ethylene dimerization catalyzed by Cr(II)OH+ cation. Both the BDE of Cr(II)OH+ 3 (C2H4)2 and the reaction energy profiles calculated at the M06/BS5 level of theory are in good agreement with those obtained by CASPT2 calculations. Hence, we only discuss the results computed at the M06/BS5 level of theory but provide optimized geometries and energy profiles obtained with B3LYP/BS5, BLYP/BS5, and M06L/BS5 in the Supporting Information. Finally, a comparison between the DFT and CASPT2 results for the prediction of the 8133

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Table 2. Binding Energiesa (Relative to Free Ethylenes and Ground-State Cr(II)OH+) for the Quintet States of Cr(II)OH+ 3 (C2H4)n (n = 1
4) Adducts Calculated at the B3LYP/BS5 Level of Theory
BDE
ΔH298K
ΔG298K
BDEC
ΔHC298K
ΔGC298K 5

38.8

34.0

25.3

37.4

32.5

23.8

5

40.9

36.1

28.3

38.9

34.1

25.7

5

64.8

58.5

41.1

61.1

54.8

37.5

5

66.3

60.0

42.1

63.0

56.6

38.8

5

78.2

70.1

42.4

73.3

65.3

37.7

5

80.5

72.4

43.7

75.6

67.6

38.9

5

87.0

77.4

39.6

80.7

71.1

33.5

EA1a EA1b EA2a EA2b EA3a

Figure 1. Selected active orbitals (8 in 8) for the CASPT2 optimization of quintet Cr(II)OH+ (0.04 au
3/2 isovalue).

EA3b EA4

BDEs are given in terms of total energy. ΔH298K is the enthalpy change at 298 K. ΔG298K is the free energy change at 298 K. BSSE-corrected values are marked with a superscript “C” on the top-right corner. Energies are in kcal/mol. a

most facile reaction pathway for ethylene dimerization catalyzed by Cr(II)OH+ cation is discussed. 3.1. Cr(II)OH+ Cation. Table 1 shows that the quintet is the ground spin state for the Cr(II)OH+ cation at the CASSCF/ CASPT2 level of theory. Contour plots for the orbitals selected in the active space are depicted in Figure 1. The active space includes four Cr 3d singly occupied orbitals (15a, 16a, 17a, and 18a), the Cr
O σ bonding orbital (14a) (and its bonding counterpart 19a), and the O lone pair orbital (13a) (and its corresponding virtual orbital 20a). The Cr
O bond lengths in the singlet, triplet and quintet states are predicted to be 1.716, 1.720, and 1.744 Å, respectively. The computed Mulliken spin density (MSD) on Cr is 3.961 au, which is slightly lower than the 4 for the quintet state of the Cr(II)OH+ cation. This may be caused by delocalization of the 3d electrons of the chromium. The low spin states of the Cr(II)OH+ cation are higher in energy relative to the quintet state (1
5ΔE = 70.0 kcal/mol; 3
5ΔE = 52.0 kcal/mol). The interactions between transition metals and ethylene can usually be described by the Dewar
Chatt
Duncanson model.47,48 In this model, the orbital between the carbon atoms of ethylene donates electron density into an empty metal d-orbital, while the metal donates electrons back from a filled d-orbital into the empty π* antibonding orbital of the ethylene. The frontier orbitals of chromium in the Cr(II)OH+ cation are ready to interact with ethylene molecules through the donation and back-donation interaction resulting in the formation of the multiple Cr(II)OH+
ethylene π-complexes. 3.2. Cr(II)OH+
Ethylene π-Complexes. Table 2 lists the BDEs and the BSSE-corrected BDEs computed at the B3LYP/ BS5 level of theory (See Table S1 in the Supporting Information for BSSEs evaluated with all five groups of basis sets). The optimized geometrical features of Cr(II)OH+ 3 (C2H4)n (n = 1
4) are shown in Figure 2. The BSSE-corrected BDEs for the ethylene-coordinated π-complexes 5EA1a, 5EA1b, 5EA2a, 5 EA2b, 5EA3a, 5EA3b, and 5EA4 are 37.4, 38.9, 61.1, 63.0, 73.3, 75.6, and 80.7 kcal/mol, respectively. The CdC bond in the coordinated ethylene is elongated generally compared to the CdC bond in the unperturbed ethylene molecule (CdC bond length of the free ethylene is 1.325 Å calculated at the B3LYP/BS5 level). By removing the BSSEs, the calculated enthalpy changes at 298 K are 32.5 kcal/mol for 5EA1a and 71.1 kcal/mol for 5EA4, respectively. All 7 complexes are predicted to be stable configurations. However, the entropic contribution to the formation of π-complexes becomes apparent when the coordination number is larger than 2. In particular, Table 2 shows that the free energy change at 298 K for the complex with 3 coordinated ethylenes (5EA3a or 5EA3b) is almost identical to that of the complex with

2 coordinated ethylenes (5EA2a or 5EA2b). Therefore, Cr(II)OH+
ethylene π-complexes with up to 2 coordinated ethylenes are the most stable species at room temperature that could be experimentally detected. The dissociation energy of Cr(II)OH+ 3 (C2H4)2 was previously determined experimentally by Hanmura et al.13 (see Table 3). Table 3 also lists the computed BDEs for 5EA2b, the most stable configuration with 2 coordinated ethylenes, calculated with 4 different DFT functionals. The corresponding geometrical parameters for 5EA2b are shown in Figure S2 in the Supporting Information. The calculated BDEs for Cr(II)OH+ 3 (C2H4)2 are 66.3 kcal/mol (B3LYP), 71.4 kcal/mol (M06), 64.3 kcal/mol (BLYP), and 77.4 kcal/mol (M06L). The difference between these BDEs can be understood from a geometrical point of view. The M06L functional predicts slightly shorter bond lengths and more compact configuration, while BLYP tends to give a complex with longer bond lengths and a more open geometry. The two hybrid functionals, meanwhile, give configurations with moderate bond lengths and coordination distances. It is of interest to note that the BDEs computed with CASPT2 single point energy calculations on the basis of the four DFT optimized geometries are 69.3 kcal/mol (CASPT2//B3LYP), 69.1 kcal/mol (CASPT2//M06), 68.9 kcal/mol (CASPT2//BLYP), and 68.6 kcal/ mol (CASPT2//M06L). The BSSE induced by BS5 in the computed BDEs of Cr(II)OH+ 3 (C2H4)2 is about 3 kcal/mol for all four DFT functionals. In summary, 7 kinds of Cr(II)OH+
ethylene π-complexes have been obtained at the B3LYP/BS5 level and the Cr(II)OH+ 3 (C2H4)n (n = 1
2) species have been determined to be the most stable complexes at room temperature. At the BS5 level, the calculated BDEs for 5EA2b with four different DFT functionals are between 64.3 and 77.4 kcal/mol, while the CASPT2 single point energies are almost identical for all the DFT optimized geometries. It is worth noting that the CASPT2 BDE computed for 5EA2b is only about 4 kcal/mol lower than that detected experimentally (72.9 ( 5.1 kcal/mol13) and is within the experimental error bar. The BDE computed using M06/BS5 is generally consistent with that obtained by CASPT2 calculations. 3.3. Ethylene Dimerization over the Cr(II)OH+ Cation. To understand the mechanism for ethylene dimerization catalyzed by Cr(II)OH+ cation, we have evaluated the feasibility of the initiation and dimerization steps following either a carbene mechanism or a metallacycle mechanism. The quintet has been determined as 8134

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Figure 2. Geometrical features of the ethylene-coordinated complexes (from 5EA1a to 5EA4) optimized at the B3LYP/BS5 level of theory. Bond lengths are in angstroms. Angles are in degrees.

Table 3. Binding Energiesa (Relative to Free Ethylenes and Ground-State Cr(II)OH+) for the Quintet State of Cr(II)OH+ 3 (C2H4)2 Adduct Calculated at Various Levels of Theory B3LYP

M06

BLYP

M06L

exptb


BDE

66.3

71.4

64.3

77.4

72.9 ( 5.1


BDEC

63.0

67.6

61.1

73.1


BDE*

69.3

69.1

68.9

68.6

a

BDEs are given in terms of total energy. BSSE-corrected values are marked with a superscript “C” on the top-right corner. CASPT2 energies computed for the various DFT optimized geometries are marked with a superscript “*” on the top-right corner. b The experimental value is taken from ref 13 and converted to kcal/mol for clarity. All the DFT energies are computed at the BS5 level. Energies are in kcal/mol.

the ground spin state for the Cr(II)OH+ cation and the ethylene π-complexes. However, the key intermediates, chromium carbene spices for the carbene mechanism and chromacyclopentane for the metallacycle mechanism, prefer to be in a triplet spin state (see Table S2 in the Supporting Information). Consequently, a mechanism involving a two-state reactivity must be considered in order to obtain a correct understanding for ethylene dimerization over Cr(II)OH+ cation. We first present the calculations at the M06/BS5 level of theory. The most feasible reaction pathways for the carbene mechanism and the metallacycle mechanism are compared by means of the M06 and CASPT2 energies. The effects of DFT functionals on the most plausible reaction pathway are discussed finally. All the M06/BS5 geometries involved in the reaction pathway are graphically presented in the following section. 3.3.1. Carbene Mechanism for Ethylene Dimerization over Cr(II)OH+ Cation. The optimized geometrical features and the energetic data, obtained using a hybrid meta-GGA functional

M06, for ethylene dimerization through the carbene mechanism are presented in this section. The key intermediate, the chromium carbene species, could be generated either through an intramolecular hydrogen transfer in the monoethylene
Cr π-complex or through an ethylene assisted intramolecular hydrogen transfer in the bis-ethylene
Cr π-complex. The potential energy surfaces (PESs) for the carbene mechanism for ethylene dimerization over the Cr(II)OH+ cation are shown in Figure 3, while all the intermediates are depicted in Figure 5. 5A0 can either interact with one ethylene to give a monoethylene
Cr complex 5A1 or it can interact with two monomers to yield a bis-ethylene
Cr complex 5A2. Both of these processes are exothermic: calculations at the M06/BS5 yield enthalpies of reaction 39.1 and 71.4 kcal/mol, respectively. For 5A1, a donation
back-donation interaction leads to a moderate elongation of the CdC double bond length by 0.030 Å. The average Cr
C distance in 5A2 is longer than that in 5A1 by 0.035 Å, which is indicative of a slightly weaker interaction between the activated ethylene molecules and the chromium center in 5A2. The energy gap was determined for the starting species (3
5ΔEA1 = 22.2 kcal/mol, 3
5ΔEA2 = 15.3 kcal/mol, at the M06/BS5 level), which is indicative of the quintet ground spin state for the ethylene coordinated complexes. Therefore, the first barrier presented on the carbene pathway is the crossing to the triplet surface through an MECP (5
3CP1 for A1 and 5
3CP2 for A2). The MECP (5
3CP1) for the triplet and quintet potential energy surfaces was located 0.5 kcal/mol higher than the triplet 3A1 and 22.7 kcal/mol higher than the quintet 5A1. The overall activation barrier for intramolecular hydrogen shift is therefore 72.0 kcal/ mol and involves a transition from 5A1 to 3A5. The Cr
C bond length is 1.779 Å in 3A5, which shows a double metal
carbon bond character. Coordination of a second ethylene to 3A5 to form ethylene coordinated carbene species 3A6 is predicted to be a fast reaction with a high exothermicity of 40.1 kcal/mol. As 8135

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Figure 3. Potential energy surfaces for the two-state reaction for ethylene dimerization catalyzed by Cr(II)OH+, via a carbene mechanism determined at the M06/BS5 level of theory. The triplet surface is shown in blue while the quintet surface is shown in black. Gibbs free energy changes at 298.15 K are also reported in parentheses. Energies are in kcal/mol and relative to 5A2 and free ethylenes.

Figure 4. Triplet and quintet potential energy surfaces for ethylene dimerization catalyzed by Cr(II)OH+, via a metallacycle mechanism determined at the M06/BS5 level of theory. The triplet surface is shown in blue while the quintet surface is shown in black. Gibbs free energy changes at 298.15 K are also reported in parentheses. Energies are in kcal/mol and relative to 5A2 and free ethylenes.

mentioned above, 3A6 could also be prepared directly from the bis-ethylene
Cr complex (5A2) through the MECP (5
3CP2). The overall activation barrier for this process is 66.6 kcal/mol, and the hydrogen transfer is facilitated by the second coordinated ethylene molecule by 5.4 kcal/mol. The insertion of the coordinated ethylene into the Cr
C bond proceeds through a much lower energy barrier by 3.1 kcal/mol, and the resulting formation of 3A7 is exothermic by 7.1 kcal/mol. The 3A7 species was determined to be the ground state lying 6.5 kcal/mol lower in energy than its analogue on the quintet potential energy surface. The regeneration of the carbene active site to give 3A8 is disfavored both kinetically (activation energy of 45.8 kcal/mol) and thermodynamically (endothermicity of 6.9 kcal/mol). The 1-butene coordinated species 3A9 was obtained through 2,3hydrogen transfer with an activation energy of 21.4 kcal/mol.

For 3A9, the terminal double bond is still relatively long (C(1)
C(2), 1.415 Å) and the Cr
C(1) distance is in the range for a single metal
carbon bond (2.024 Å). This suggests that the interaction between the terminal C
C bond and chromium is still strong in the triplet state. It is noteworthy that 3A9 can relax to the quintet ground spin state 5A9 very easily through an MECP (3
5CP3) that lies only 0.03 kcal/mol above 3A9. As shown in Figure 6, the geometrical parameters for the MECP (3
5CP3) are very close to those of 3A9 (in Figure 5). The Cr
C(1) distances (2.024 Å in 3A9; 2.015 Å in the MECP (3
5CP3)) are almost identical to the Cr
C(2) distances (2.010 Å in 3A9; 1.999 Å in the MECP (3
5CP3)) for both structures. Finally, the coordinated 1-butene complex 5A9 was found to be the ground spin state and to be more stable than its triplet analogue 3A9 by 21.1 kcal/mol. The terminal C(1)
C(2) bond 8136

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Figure 5. Optimized geometries for all the structures on the potential energy surfaces for ethylene dimerization over Cr(II)OH+ cation, via both a metallacycle reaction pathway and a carbene reaction pathway determined at the M06/BS5 level. *3A6 and 3TS[A6-A7] were optimized with a constrained distance (see Supporting Information for detailed discussion). Bond lengths are in angstroms. Angles are in degrees.

Figure 6. Structures of MECPs associated with triplet
quintet spin crossing, determined at the M06/BS5 level. Bond lengths are in angstroms. Angles are in degrees.

length is 1.350 Å, which is indicative of a slightly perturbed double bond character. As discussed above, two reaction pathways leading to ethylene coordinated carbene species 3A6 are available when one starts from the ethylene coordinated species in their ground spin state

(5A1 and 5A2). This kind of transformation proceeds through an MECP (5
3CP1 for 5A1 f 3A6, 5
3CP2 for 5A2 f 3A6) between the high- and low-spin potential energy surfaces. The overall activation energies for the intramolecular hydrogen transfers are 72.0 and 66.6 kcal/mol for mono- and bis-ethylene coordinated species, respectively. CASPT2//M06 energies showed an activation barrier of 67.2 kcal/mol for the intramolecular hydrogen transformation of 5A1 f 3A6 and 66.2 kcal/mol for 5A2 f 3 A6 (see Figure S22 in the Supporting Information). Therefore, the formation of ethylene coordinated carbene species 3A6 is facilitated by the second coordinated ethylene by 5.4 kcal/mol at M06/BS5 level, and 1.0 kcal/mol at CASPT2/BS6 level (single point energies on M06/BS5 geometries). 3.3.2. Metallacycle Mechanism for Ethylene Dimerization over Cr(II)OH+ Cation. The optimized geometrical features and the energetic data, obtained with the hybrid meta-GGA functional M06, for metallacycle initiation associated with the ethylene dimerization over Cr(II)OH+ cation are presented in this section. In the first step, the interaction between the ethylenes and Cr(II)OH+ cation results in the formation of ethylene binding 8137

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Figure 7. Potential energy surfaces for the most feasible two-state reaction pathways for ethylene dimerization catalyzed by Cr(II)OH+, via both a carbene mechanism and a metallacycle mechanism determined at the M06/BS5 level of theory. The computed CASPT2//M06 energies are reported in square brackets. Also shown are the crossing points optimized at CASSCF level. The triplet metallacycle reaction pathway is depicted in blue, while the triplet carbene reaction pathway is shown in dark red. The quintet parts are in black. Energies are in kcal/mol and relative to 5A2. Bond lengths are in angstroms. Angles are in degrees.

π-complexes, as discussed above. From the mechanistic point of view, the reaction may proceed through one ethylene binding to the Cr(II)OH+ cation to generate a monoethylene
Cr complex A1. A second ethylene could then coordinate with the chromium active center to yield a bis-ethylene
Cr complex A2. During the second stage, the key intermediate chromacyclopentane A3 could be formed through an MECP (5
3CP2), which connects the triplet and quintet potential energy surfaces. Next, the 1-butene coordinated species A9 is formed through a chromium hydride spices A4. The potential energy surfaces (PESs) for the metallacycle mechanism for ethylene dimerization over Cr(II)OH+ cation are shown in Figure 4, while all the optimized geometries are shown in Figure 5. Starting from a bis-ethylene
Cr complex (5A2), the oxidative coupling requires 36.2 kcal/mol of activation energy and is highly endothermic by 35.4 kcal/mol on the quintet potential energy surface. However, this transformation is facilitated by the presence of an MECP (5
3CP2) between the triplet and quintet potential energy surfaces located 0.2 kcal/mol higher than the triplet 3A2 and 15.5 kcal/mol higher than the quintet 5 A2. Therefore, crossing to the triplet surface through the MECP (5
3CP2) opens a facile reaction pathway for the transformation from a bis-ethylene
Cr complex to the ground spin state of chromacyclopentane 3A3. The whole activation energy barrier for the two-spin-state reaction is 27.3 kcal/mol and is endothermic by 19.9 kcal/mol. The triplet species 3A3 is more stable than 5 A3 by 15.5 kcal/mol. Therefore, it is reasonable to believe that the spin crossing will occur readily. For 3A3, the Cr
H distance of 1.956 Å indicates a β-hydrogen agostic interaction, as shown in Figure 5. We failed to locate a transition state on the triplet surface for the one-step β-hydrogen transfer to the terminal C(4) to yield a 3A9 species. A hydride transfer that proceeds through a two-step reaction pathway was confirmed at the M06/BS5 level of theory. In the first step, the β hydrogen is abstracted by the chromium to yield a chromium hydride species 3A4. In the transition state 3TS[A3
A4], the Cr
H distance is 1.580 Å and the C(1)
C(2) distance is 1.352 Å, which are indicative of β-hydrogen transfer and the formation of a terminal C(1)dC(2) double bond. An activation barrier of 14.6 kcal/mol was computed for the hydride transformation along with an endothermicity of 12.1 kcal/mol. Reductive elimination through the migration of the hydride to the terminal

Figure 8. Energy gaps between the low- and high-spin configurations of A2, A5, A7, and A9, determined using four different DFT functionals (B3LYP, BLYP, M06, and M06L). Energies computed at the CASPT2// M06 level are also reported. Energies are in kcal/mol. The dashed line is only a guide for the eye.

carbon C(4) can then take place with an exothermicity of 21.5 kcal/mol. The transition state 3TS[A4
A9] lies 7.5 kcal/mol above 3A4 and has one imaginary frequency of 794 cm
1 which corresponds to the transfer of the hydrogen to the terminal C(4). The chromium hydride distance in 3TS[A4
A9] is only slightly elongated by 0.002 Å compared to that in the 3A4 species, which indicates how close the transition state is to the reactant 3A4. The relaxation of 3A9 to its quintet ground spin state is similar to that discussed in the carbene pathway. 3.3.3. A Comparison between the Two Mechanisms. The most facile of the two mechanisms for ethylene dimerization over Cr(II)OH+ cation is shown in Figure 7. Also shown are the two crossing points, which are connecting between the low- and highspin potential energy surfaces and optimized at the CASSCF/BS6 level. The crossing point for the formation of the metallacyclopentane species 3A3 was located only 0.2 kcal/mol above the triplet 3A2 at the M06/BS5 level. When 5
3CP2 was reoptimized at the CASSCF level, it showed very different geometrical features compared to the M06/BS5 structure. For the M06/ BS5 structure, both coordinated ethylenes were activated identically (both CdC bonds were elongated to 1.369 Å). In the structure obtained at the CASSCF level, meanwhile, one of the ethylene molecules was activated considerably (the C(3)dC(4) bond elongated to 1.432 Å), but the other ethylene remained 8138

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Table 4. Relative Total Energiesa (kcal/mol) for the Stationary Points on the PES of Ethylene Dimerization over Cr(II)OH+ Cation at Various Levels of Theory for the Metallacycle Pathway B3LYP 5

M06

BLYP

M06L

Table 5. Geometrical Parametersa for the MECP(5-3CP2) Associated with the Bis-ethylene-Coordinated Complex A2 on the Triplet and Quintet Potential Energy Surfaces

CASPT2//M06

B3LYP

M06

BLYP M06L

CASSCF

Cr
O

1.734

1.715

1.756

1.737

1.735

Cr
O
H

138.5

136.1

139.3

139.2

134.6 2.439/2.031

A2

0.0

0.0

0.0

0.0

0.0

5
3

20.4

15.5

12.1

11.6

22.0

Cr
C(1)/C(4)

2.195

2.143

2.230

2.160

3

19.5

15.3

7.9

6.7

11.5

C(2)
C(3)

2.933

2.830

3.303

2.899

3.238

3

35.8

27.3

22.6

17.2

27.4

C(1)
C(2)/C(3)
C(4)

1.364

1.369

1.376

1.368

1.347/1.432

3

30.0

19.9

17.5

9.6

21.7

3

44.6

34.5

29.3

23.5

35.5

3

37.5 46.6

32.0 39.5

23.1 34.5

20.6 29.4

30.8 42.7

A9

15.9

10.46

9.8

2.3

13.9

3
5

18.8

10.49

9.8

2.6

16.4


4.7


10.3


11.6

CP2

A2 TS[A2-A3] A3 TS[A3-A4] A4 TS[A4-A9]

3 3

CP3

5

A9


8.1


10.6

a

All DFT energies are computed at BS5 level. CASPT2 energies are computed with BS6 on the geometries obtained at the M06/BS5 level. The total energy of 5A2 is taken as a reference. Energies are in kcal/mol.

almost unaffected. Furthermore, the energy at this point was 10.5 kcal/mol above 3A2. The energy gain can be understood from the much activated ethylene in the structure optimized at the CASSCF level. From this activated complex one may either generate the ethylene coordinated carbene species 3A6 through chromium assisted intramolecular hydrogen transfer or form a metallacyclopentane species 3A3 through an oxidative coupling reaction. However, the first of these processes has a prohibitively high energetic cost (66.6 kcal/mol at the M06/BS5 level and 66.2 kcal/mol at CASPT2 level). Therefore, the formation of the metallacyclopentane species 3A3, which involves an energetic cost of only 27.3 and 27.4 kcal/mol at the M06/BS5 and CASPT2 levels respectively, is more likely. In summary, for the ethylene dimerization catalyzed by the Cr(II)OH+ cation, the metallacycle pathway is energetically much more favorable than the carbene route. Starting from a bisethylene
Cr π-complex 5A2, the chromacyclopentane 3A3 is formed by an oxidative coupling reaction through a spin-crossing transition to the triplet ground state. The reaction then proceeds through a two-step reductive elimination to generate a triplet 1-butene coordinated complex 3A9, which is followed by another spin-crossing transition to the quintet ground spin state yielding 5 A9. The formation of the chromacyclopentane 3A3 is the ratedetermining step for the two-state reaction. The detachment of the 1-butene from Cr(II)OH+ is highly endothermic (52.6 kcal/ mol at M06/BS5 level). Hence, the 1-butene coordinated product Cr(II)OH+ 3 (C4H8) is predicted to be a stable complex and also possible for the experimental observations.13 These findings suggest a metallacycle initiation for ethylene dimerization over Cr(II)OH+ cation. This agrees with both the theoretical investigations49
51 and proposals on the basis of experimental observations52 for the initiation mechanism of ethylene polymerization on the chromium-based Phillips catalyst. 3.3.4. The Effect of DFT Functionals on the Prediction of the Two-State Reaction Pathway. To determine the effect of DFT functionals on the results, the energy gaps between the high- and low-spin configurations of A2, A5, A7, and A9 were computed using four different functionals (M06L, BLYP, B3LYP, and M06). Furthermore, CASPT2 single point energy calculations were performed on the geometries obtained from all four DFT

a

Distances are in angstroms. Angles are in degrees.

levels. No significant differences were observed in the CASPT2 energies computed for these different geometries (see Figure S8 in the Supporting Information). Therefore, only the CASPT2// M06 energies are discussed here, and the CASPT2//B3LYP, CASPT2//BLYP, and CASPT2//M06L energies are given in the Supporting Information. Figure 8 shows that the amount of exact exchange has a noticeable effect on the prediction of the energy gap between two spin states. For A2, A7, and A9, all four functionals predict similar trends and that the high-spin state (quintet state) lies lower in energy for A2 and A9, while A7 prefers a triplet ground state. For A5, the energy gap between two spin states (3
5ΔEA5) is
4.9 kcal/mol computed with M06L, but 5.7 kcal/mol when computed with B3LYP. Meanwhile, BLYP and M06 predict the two states of A5 to be very close in energy. However, the triplet ground spin state of 3A5 was confirmed through a CASPT2 calculation (3
5ΔEA5 was predicted to be
11.3 kcal/mol with CASPT2// M06). Table 4 lists the relative energies for the stationary points on the most facile metallacycle reaction pathway, calculated using four DFT functionals and the CASPT2 method. It shows that the first spin
orbit induced crossing occurs shortly after the formation of the bis-ethylene
Cr π-complexes 5A2. The MECP (5
3CP2) lies 0.2
4.9 kcal/mol above 3A2 at different DFT levels, and 10.5 kcal/mol above 3A2 at the CASPT2 level. Table 5 lists the geometrical features associated with this structure and shows that the structures obtained using the M06L and B3LYP functionals for the MECP (5
3CP2) are quite similar. However, BLYP tends to give a much more open configuration with slightly longer coordination distances. In contrast, M06 predicts a slightly tighter geometry than the other three functionals. All four DFT functionals predict a geometry of 5
3CP2 with two ethylene molecules activated simultaneously. However, the MECP (5
3CP2) optimized using the CASSCF method is very different. The spin crossing occurs in a complex in which the π
π double bond in one of the ethylene molecules is greatly perturbed, while the other is almost unaffected. The activation energy for the transformation of bis-ethylene
Cr π-complexes 5A2 to a chromacyclopentane 3A3 thus depends dramatically on the choice of DFT functional. The energetic barrier for ring formation is predicted to be relatively small at the M06L level (17.2 kcal/ mol), but B3LYP predicts this barrier to be almost two times as large (35.8 kcal/mol). It is worth noting that M06 shows an energetic barrier of 27.3 kcal/mol for the ring formation, which is almost identical to that predicted by the CASPT2 method (27.4 kcal/mol). In the following step, these four functionals give similar energies for two-step β-hydrogen transfer process. For the 1-butene coordinated species 3A9, the relaxation to the quintet ground spin state through the MECP (3
5CP3) is ready 8139

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Table 6. Geometrical Parametersa for the MECP(3-5CP3) Associated with the 1-Butene-Coordinated Complex A9 on the Triplet and Quintet Potential Energy Surfaces

a

B3LYP

M06

BLYP

M06L

CASSCF

Cr
O

1.709

1.711

1.734

1.720

1.730

Cr
O
H

134.3

129.6

135.4

134.6

133.9

Cr
C(1)

2.004

2.015

2.065

2.039

1.993

Cr
C(2)

1.994

2.001

2.063

2.040

1.980

C(1)
C(2)

1.426

1.419

1.426

1.412

1.492

Distances are in angstroms. Angles are in degrees.

Table 7. Dissociation Energiesa (kcal/mol) for 1-Butene from Cr(II)OH+ Cation
D0


ΔG298K

B3LYP

50.6

38.1

M06

52.6

40.4

M06L

59.1

47.0

BLYP CASPT2//M06

48.9 47.9

36.9

D0 is given in terms of total energy. ΔG298K is the free energy change at 298 K. Energies are in kcal/mol. a

to occur. The MECP (3
5CP3) was found to be very close in energy to the triplet 3A9 at the M06, M06L, and BLYP levels. B3LYP predicts a slightly higher energy for 3
5CP3 (2.9 kcal/ mol above 3A9), which is in good agreement with CASSCF/ CASPT2 energy (2.5 kcal/mol above 3A9). The geometrical parameters of the MECP (3
5CP3) are listed in Table 6. There is good agreement between the bond lengths at the MECP (3
5CP3) for the hybrid functionals B3LYP and M06. However, the pure density functionals tend to give a slightly larger distance between the coordinated 1-butene and the chromium center. The CASSCF method gives a tight coordinated configuration with a greatly elongated double bond in 1-butene. The final desorption of 1-butene from the chromium center is determined to be highly endothermic. The dissociation energies and the free energy changes are listed in Table 7. This step is associated with an energy gain of 50.6, 52.6, 59.1, 48.9, and 47.9 kcal/mol for the calculations with the B3LYP, M06,M06L,BLYP and CASPT2// M06 methods, respectively. 1-Butene dissociation results in an increase of entropy, which lowers the free energy change at 298 K for about 12 kcal/mol at each DFT level. For both the metallacycle and carbene pathways, all four functionals predict a similar reaction profile on each single potential energy surface. However, the reaction potential energy profile varies for the different DFT functionals when 5A2 is taken as the resting state (see Figure S7 in the Supporting Information). The potential energy profile predicted at the M06/BS5 level is quite similar to that computed at the CASPT2/BS6//M06/BS5 level. The CASPT2 energy profiles calculated on the four groups of DFT predicted geometries are almost identical (see Figure S8 in the Supporting Information). It is possible to accurately explore the reaction energy profile by computing the CASPT2 energies with a reasonable large basis set (BS6) on the DFT optimized structures. All four DFT functionals and the CASPT2 level demonstrate that the metallacycle reaction pathway is much more energetically favorable than the carbene pathway.

4. CONCLUSIONS In this work, the mechanism of ethylene coordination and dimerization over the Cr(II)OH+ cation have been systematically investigated using both DFT and the CASPT2 methods. The effects of basis set and DFT functional on the calculations have also been considered. The performance of 5 groups of basis sets has been evaluated in the calculations of the BDEs of 7 stable configurations Cr(II)OH+ 3 (C2H4)n (n = 1
4) with up to 4 ethylene molecules adsorbed on the chromium center. The Cr(II)OH+ 3 (C2H4)n (n = 1
2) species are the most stable complexes at room temperature and could be experimentally observable. We also calculated BDEs for the Cr(II)OH+ 3 (C2H4)2 π-complex using 4 DFT functionals (M06L, BLYP, B3LYP, and M06) with a very large triple-ζ basis set (BS5). The calculated CASPT2 BDEs for the B3LYP, M06, BLYP, and M06L structures were found to be 69.3, 69.1, 68.9, and 68.6 kcal/mol, respectively. The BDE computed at the M06/BS5 level is 71.4 kcal/mol (67.6 kcal/mol with BSSE correction), which is very close to that computed at the CASPT2 level. Both high- and low-spin potential energy surfaces have been characterized in detail at the M06/BS5, BLYP/BS5, B3LYP/ BS5, and M06L/BS5 levels of theory. Along the ethylene dimerization pathway, the quintet ground state of the bisethylene
Cr π-complex is transformed into the triplet ground state of the chromacyclopentane product, and therefore spin crossing must occur. A two-state metallacycle reaction pathway involving the formation of chromacyclopentane as the ratedetermining step has been found to be more energetically favorable than the carbene reaction pathway. The energy barrier for the rate-determining step is 27.3 kcal/mol calculated at the M06/BS5 level of theory. The CASPT2//M06 single point energy calculations predict a similar activation barrier for this transformation (27.4 kcal/mol). In general, the M06 functional agrees with the CASPT2 method for the prediction of the energy profile for ethylene dimerization catalyzed by Cr(II)OH+ cation. B3LYP meanwhile lifts the potential energy profile by about 10 kcal/mol, while BLYP and M06L lower the potential energy profile by about 5 and 10 kcal/mol, respectively. Therefore, M06 is suggested to be a suitable hybrid DFT functional for studying the two-state reaction catalyzed by the Cr(II)OH+ cation as accurate prediction for the energy gap between the low- and high-spin states is necessary in order to describe the reaction mechanisms. Although some energetic discrepancies have been observed for the different DFT levels, the metallacycle reaction pathway for ethylene dimerization over Cr(II)OH+ cation is always much more energetically preferable to the carbene pathway. The first Cr
C bond forms through the formation of a fivemembered chromacyclopentane species via an MECP (5
3CP2) that allows the system to cross from the high-spin potential energy surface to the low-spin potential energy surfaces. 1-Butene is then generated from the chromacyclopentane through a two-step reductive elimination pathway that involves a chromium(IV) hydride intermediate. Thus far, the initiation mechanism for ethylene dimerization over the Cr(II)OH+ cation has been elucidated. This mechanistic study may also shed some light on the initiation mechanism for ethylene polymerization on the chromium-based Phillips catalyst. 8140

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’ ASSOCIATED CONTENT

bS

Supporting Information. BSSE effects evaluation; groundspin state determination of all the intermediates involved in the catalytic reaction pathway; the potential energy surfaces determined at BLYP/BS5, B3LYP/BS5, M06L/BS5 levels of theory; the CASPT2 energy profiles; the Cartesian coordinates and the total energies at M06L/BS5, BLYP/BS5, B3LYP/BS5, M06/BS5 levels of theory. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Tel: 0086-21-64253627. Fax: 0086-21-64253627. E-mail: boping@ ecust.edu.cn.

’ ACKNOWLEDGMENT This work is financially supported by the National Natural Science Foundation of China (No. 20744004 and No.20774025), the research program of the State Key Laboratory of Chemical Engineering, Shanghai Pujiang Talent Plan Project (08PJ14032) and the Program of Introducing Talents of Discipline to Universities (B08021). We thank Prof. J. N. Harvey and Prof. T. J. Dudley for their kind suggestions to locate the minimum-energy crossing points (MECP) between two different potential energy surfaces. We thank Prof. L. Gagliard and Dr. G. Li Manni for their kind suggestions on performing CASPT2 calculations. We thank Dr. G. Tribello for language improvement. ’ REFERENCES (1) Bohme, D. K.; Schwarz, H. Angew. Chem., Int. Ed. 2005, 44, 2336. (2) Roithova, J.; Schroder, D. Chem. Rev. 2010, 110, 1170. (3) Schroder, D.; Schwarz, H. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 18114. (4) Eller, K.; Schwarz, H. Chem. Rev. 1991, 91, 1121. (5) Gianotto, A. K.; Hodges, B. D. M.; Benson, M. T.; Harrington, P. de B.; Appelhans, A. D.; Olson, J. E.; Groenewold, G. S. J. Phys. Chem. A 2003, 107, 5948. (6) Gianotto, A. K.; Hodges, B. D. M.; Harrington, P. de B.; Appelhans, A. D.; Olson, J. E.; Groenewold, G. S. J. Am. Soc. Mass Spectrom. 2003, 14, 1067. (7) Hop, C. E. C. A.; McMahon, T. B. J. Am. Chem. Soc. 1992, 114, 1237. (8) Kang, H.; Beauchamp, J. L. J. Am. Chem. Soc. 1986, 108, 7502. (9) Mazurek, U.; Schroder, D.; Schwarz, H. Eur. J. Inorg. Chem. 2002, 1622. (10) Kang, H.; Beauchamp, J. L. J. Am. Chem. Soc. 1986, 108, 5663. (11) Fiedler, A.; Kretzschmar, I.; Schroeder, D.; Schwarz, H. J. Am. Chem. Soc. 1996, 118, 9941. (12) Hanmura, T.; Ichihashi, M.; Monoi, T.; Matsuura, K.; Kondow, T. J. Phys. Chem. A 2004, 108, 10434. (13) Hanmura, T.; Ichihashi, M.; Monoi, T.; Matsuura, K.; Kondow, T. J. Phys. Chem. A 2005, 109, 6465. (14) Limberg, C.; Koppe, R.; Schnockel, H. Angew. Chem., Int. Ed. 1998, 37, 496. (15) Mandich, M. L.; Steigerwald, M. L.; Reents, W. D., Jr. J. Am. Chem. Soc. 1986, 108, 6197. (16) Walba, D. M.; DePuy, C. H.; Grabowski, J. J.; Bierbaum, V. M. Organometallics 1984, 3, 498. (17) Veliah, S.; Xiang, K.-H.; Pandey, R.; Recio, J. M.; Newsam, J. M. J. Phys. Chem. B 1998, 102, 1126. (18) Wang, X.; Andrews, L. J. Phys. Chem. A 2006, 110, 10409.

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