Bond Energies in Models of the Schrock ... - ACS Publications

ARTICLE pubs.acs.org/JPCC

Bond Energies in Models of the Schrock Metathesis Catalyst Monica Vasiliu, Shenggang Li, Anthony J. Arduengo, III, and David A. Dixon* Chemistry Department, The University of Alabama, Shelby Hall, Box 870336, Tuscaloosa, Alabama 35487-0336, United States

bS Supporting Information ABSTRACT: Heats of formation, adiabatic and diabatic bond dissociation energies (BDEs) of the model Schrock-type metal complexes M(NH)(CRR0 )(OH)2 (M = Cr, Mo, W; CRR0 = CH2, CHF, CF2) and MO2(OH)2 compounds, and Brønsted acidities and fluoride affinities for the M(NH)(CH2)(OH)2 transition metal complexes are predicted using high level CCSD(T) calculations. The metallacycle intermediates formed by reaction of C2H4 with M(NH)(CH2)(OH)2 and MO2(OH)2 are investigated at the same level of theory. Additional corrections were added to the complete basis set limit to obtain near chemical accuracy ((1 kcal/mol). A comparison between adiabatic and diabatic BDEs is made and provides an explanation of trends in the BDEs. Electronegative groups bonded on the carbenic carbon lead to less stable Schrock-type complexes as the adiabatic BDEs of MdCF2 and MdCHF bonds are much lower than the MdCH2 bonds. The Cr compounds have smaller BDEs than the W or Mo complexes and should be less stable. Different M(NH)(OH)2(C3H6) and MO(OH)2(OC2H4) metallacycle intermediates are investigated, and the lowest-energy metallacycles have a square pyramidal geometry. The results show that consideration of the singlet
triplet splitting in the carbene in the initial catalyst as well as in the metal product formed by the retro [2 þ 2] cycloaddition is a critical component in the design of an effective olefin metathesis catalyst in terms of the parent catalyst and the groups being transferred.

’ INTRODUCTION There is substantial interest in olefin metathesis by transition metal complexes due to the importance of being able to manipulate C
C bonds catalytically and the applicability of this reaction in medicine, biology, and material sciences. Catalytic olefin metathesis has become an increasingly indispensable tool in organic chemistry ranging from the synthesis of macrocyclic rings to olefin polymerization. The importance of the metathesis reaction in chemistry was recognized by the 2005 Nobel Prize in Chemistry.1
3 An olefin metathesis reaction is a [2 þ 2] type cycloaddition reaction between a transition metal alkylidene complex (A) and an olefin (B) with formation of a new olefin (E) and reformation of the metal catalyst (D) in the retro [2 þ 2] type reaction 1. Chauvin was the first one to propose the olefin metathesis mechanism, which involves the formation of a metallacycle (C) as an intermediate or as a transition state.4 Schrock’s W- and Mo-based catalysts, which are air sensitive, are generally more active than the air-stable “first-generation” Grubbs’ Rubased catalysts which tend to have a higher functional group tolerance and are more robust under some laboratory conditions. The “secondgeneration” Grubbs catalysts show much higher activity than the “firstgeneration” and have activities comparable to the Schrock catalysts.5,6

We are interested in the relationship between homogeneous and heterogeneous catalysts. The basic structure of a Schrock-type r 2011 American Chemical Society

catalyst M(NR)(CR0 2)(OR00 )2 (M = Cr, Mo, W) (see the example Schrock catalyst F7 in reaction 2 with M = W) is very similar to the high metal oxidation state MO2-, MO3-, and MO2(OH)2-based clusters (structure H, reaction 2), which we have been studying computationally8
13 to better understand their role in heterogeneous catalysis. Structure G (reaction 2) is the simplified model system that we can use to study the fundamental thermochemistry of Schrock catalysts. We will describe our work on models of the Grubbs catalyst in a subsequent publication.

There have been a number of previous computational studies which focus on olefin metathesis reactions14
19 and the electronic structures20
28 of molybdenum, tungsten, and even chromium-derived catalysts. Most of these calculations are at the density functional theory (DFT) level. Eisenstein and co-workers have used DFT to map out the reaction pathways for Re-, Mo-, and W-based olefin metathesis reactions with a focus on catalysts bonded to silica.29 Important results from this work include the role of the different substituents on the O and N as Received: March 21, 2011 Revised: April 22, 2011 Published: June 02, 2011 12106

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well as the need to prepare the catalyst for the addition of the olefin to a vacant site on the metal. In addition, these authors showed that the initial approach of the olefin was an important feature of the reaction and that the reactions for the W and Mo systems similar to ours (with an alkyl replacing one of the OR groups) have essentially no barrier and are dominated by the formation of the metallacycle. Thus, the reactions are dominated by the free energy of complexation and the loss of the degrees of freedom of the free particles in the complex. It is now possible to use high level molecular orbital theory methods with extensive treatments of the correlation energy and with basis sets extrapolated to the complete basis set (CBS) limit to predict the thermodynamic properties of transition metal containing molecules.9 As part of our study of high oxidation state catalysts, in the current paper we have predicted and compared the bond dissociation energies (BDEs) and heats of formation of the model compounds M(NH)(CRR0 )(OH)2 (G, (2)) and also MO2(OH)2 (H, (2)) for M = Cr, Mo, and W to better understand the energetics underlying their catalytic behavior. We also investigated the role of ligand electronegativity on the carbene by studying the BDEs of the complexes M(NH)(CHF)(OH)2 and M(NH)(CF2)(OH)2. These values provide a base set of thermodynamic values which can be used for the prediction of the properties of more realistic complexes. Our focus is on the generation of the initial catalyst and its properties. The initial complexation reaction of the olefin with the catalyst can be considered as the addition of a Lewis acid (the metal complex) to a Lewis base (the olefin).29a Thus the Lewis acidity of the metal complex is of interest, especially as it allows the catalyst to be compared to other transition metal compounds in terms of Lewis acid strength. The gas-phase fluoride affinities (FAs) provide a measure of the Lewis acidity30 and are defined as the negative of the enthalpy of reaction 3. AF
f A þ F


ð3Þ

The reaction energetics of the four-membered metallacycle intermediates formed by reacting M(NH)(CH2)(OH)2 or MO2(OH)2 (M = Cr, Mo, W) with C2H4 (reactions 4 and 5) provide more details about the initial complexation reaction. Depending on the orientation of the addition of the C2H4 molecule (from the CNO or COO face) on the four-coordinate pseudotetrahedral Schrock-type catalyst, different metallacycle conformers can form in the C2H4 addition reaction. Experimental work has shown that the four-membered cycles can be trigonal bipyramidal (TBP) or square pyramidal (SP), depending on a variety of factors.7,31

’ COMPUTATIONAL METHODS Equilibrium geometries and harmonic vibrational frequencies were first calculated at the DFT level with the B3LYP32,33 and BP8634,35 exchange-correlation functionals. We used the aug-ccpVDZ basis set for all first row atoms36 and the pseudopotential (PP) based aug-cc-pVDZ-PP basis sets for the transition metals37 in the DFT optimization and frequency calculations. The above combination of basis sets will be denoted as aX, where X = D, T, Q, etc. For Cr, 10 electrons in the 1s2s2p orbitals are modeled by the PP; for Mo, 28 electrons in the 1s2s2p3s3p3d orbitals are modeled by the PP; and for W, 60 electrons in the 1s2s2p3s3p3d4s4p4d4f orbitals are modeled by the PP. In these cases, the (n
1)s2(n
1)p6 electrons with n = 4, 5, and 6 for M = Cr, Mo, and W, respectively, are included in the valence space at the DFT level. The same valence space is used in the Hartree
Fock self-consistent field calculations that provide the starting wave functions for the CCSD(T) calculations. Single-point CCSD(T)38 calculations were performed with the aug-cc-pVnZ and aug-cc-pVnZ-PP basis sets for n = D, T, Q at the above B3LYP geometries, where the electrons in the 1s orbitals for the first row elements (C, N, O, F), the 3s3p orbitals for Cr, the 4s4p orbitals for Mo, and the 5s5p orbitals for W were not correlated initially but are included in the Hartree
Fock calculations. The open-shell calculations were done with the R/UCCSD(T) approach where a restricted open shell Hartree
Fock (ROHF) calculation was initially performed and the spin constraint was then relaxed in the coupled cluster calculation.39 In addition, the development of the correlation-consistent basis sets, which allows for the extrapolation of the electronic energy to the CBS limit, has proven critical for reaching chemical accuracy in the calculated energetics.40 Thus, the CCSD(T) energies with n = D, T, Q were extrapolated to the complete basis set (CBS) limit using a mixed Gaussian/exponential formula (eq 6)41 EðnÞ ¼ ECBS þ A exp½
ðn
1Þ þ B exp½
ðn
1Þ2  ð6Þ The cardinal numbers for the n = D, T, Q basis sets are 2, 3, and 4. Our recent studies on the group 6 transition metal trioxide clusters have shown that the effect of the choice of the cardinal numbers in this extrapolation scheme is fairly small.12 Core
valence correlation corrections (ΔECV) were calculated at the CCSD(T) level with the aug-cc-pVTZ basis set for H, the augcc-pwCVTZ basis set for the first row atoms,42 and the aug-ccpwCVTZ-PP basis set for the transition metals;37 these basis sets will be denoted as awCVTZ-PP. For first row atoms, the core
valence correction accounts for the electron correlation effect of the 1s2 electrons interacting with themselves and their interaction with the valence electrons, whereas for the transition metal atoms, it accounts for the correlation of the (n
1)s2(n
1)p6 electrons 12107

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with n = 4, 5, and 6 for M = Cr, Mo, and W, respectively, with themselves and with the original valence electrons. Scalar relativistic corrections (ΔESR) for the nonmetal atoms (these corrections are incorporated into the pseudopotential on the transition metal atoms) were calculated as the expectation values of the mass-velocity and Darwin operators (MVD) from the Breit
Pauli Hamiltonian43 for the CISD (configuration interaction with single and double excitations) wave function with the aT basis set. The above approach is based on the development of methods for the accurate prediction of the heats of formation for a wide range of compounds at The University of Alabama, Washington State University, and Pacific Northwest National Laboratory.44 For the calculation of the total atomization energies (TAEs) of the parent molecules, additional calculations were done at the CCSD(T) level with the second-order Douglas
Kroll
Hess Hamiltonian45 and the aug-cc-pwCVTZ-DK basis set (the augcc-pVTZ-DK basis set for H).37,46,47 These basis sets will be collectively denoted as awCVTZ-DK. For the first row elements, these DK basis sets were obtained by augmenting the cc-pVTZDK basis set with the diffuse and/or tight functions from the augcc-pVTZ basis set for H and the aug-cc-pwCVTZ basis set for other first row elements. For W, additional high angular momentum functions (2f2g1h) were added to the aug-cc-pwCVTZDK basis set to include the 4f14 electrons in the core
valence calculations (see below). These calculations are to correct for errors associated with the use of the effective core potential (ECP) and the above MVD approach, following our previous work.9 The scalar relativistic correction is defined by eq 7. ΔERel ¼ ΔESR þ ΔEPP, corr ¼ ΔEawCVTZ-DK
ΔEawCVTZ-PP

ð7Þ

where ΔEawCVTZ-DK and ΔEawCVTZ-PP are the valence electronic energy differences calculated at the CCSD(T)-DK/awCVTZDK and CCSD(T)/awCVTZ-PP levels, respectively; ΔESR is the above MVD correction; and ΔEPP,corr is the pseudopotential correction. In addition, the core
valence correction was also calculated at the CCSD(T)-DK/awCVTZ-DK level, which was used to calculate the TAEs instead of using that calculated at the CCSD(T)/awCVTZ-PP level. This is necessary to obtain very accurate TAEs based on our recent work, but the difference in calculated core
valence corrections from the above two approaches is much smaller for other properties such as clustering energies, fluoride affinities, and electron affinities on the basis of our recent work.9,13,48 The atomic spin
orbit corrections (SO) were calculated from the experimental values for the ground states of the atoms.49 The ground state of Cr and Mo are the 7S3 state, so there is no spin
orbit correction for them. For W, we calculated the TAE to the first excited state (7S3), which has no spin
orbit correction, and then used the experimental correction of 8.44 kcal/mol to get the TAE with respect to the ground state (5D0) of W. The TAEs at 0 K were calculated from eq 8.

∑D0, 0K ¼ ΔECBS þ ΔERel þ ΔECV þ ΔEZPE þ ΔESO

ð8Þ

Heats of formation at 0 K were calculated from the above calculated TAEs and the experimental heats of formation of the atoms at 0 K from the JANAF Tables (58.98 ( 0.02 kcal/mol for O, 169.98 ( 0.1 kcal/mol for C, 112.53 ( 0.02 kcal/mol for N, 18.47 ( 0.07 kcal/mol for F, 51.63 ( 0.001 kcal/mol for H, 94.5 ( 1.0 kcal/mol for Cr, 157.1 ( 0.9 kcal/mol for Mo, and 203.1 ( 1.5 kcal/mol for W).50 Heats of formation at 298 K were calculated by following the procedures outlined by Curtiss et al.51

Bond dissociation energies (BDEs) for the MdO, M
O(H), MdCRR0 (CRR0 = CH2, CHF, CF2), and MdN(H) bonds in the parent molecules were calculated in a similar fashion as the TAEs except that ΔECV was calculated at the CCSD(T)/awCVTZ-PP level. The heats of formation of the metal-containing fragments were then calculated from the BDEs and the heats of formation of the parent molecules. This approach was necessary to avoid evaluating the computationally expensive core
valence correction for the TAEs for the radicals at the CCSD(T)-DK/awCVTZ-DK level. The molecular spin
orbit corrections to the BDEs were calculated using two different methods. The first method uses the spin
orbit approach and the scalar two-component zero-order regular approximation (ZORA)52 as implemented in the ADF program at the BLYP/TZ2P level. The calculated bond energy difference between ZORA and ZORA þ SO is the spin
orbit correction. The second method uses the SO
DFT approach53 as implemented in the NWChem program at the B3LYP/aD level with the pseudopotentials including the spin
orbit components.54 The energy difference between DFT and DFT þ SO is the SO correction. The molecular spin
orbit corrections for the BDEs were not included as they are small, mostly less than 0.5 kcal/mol (see Supporting Information). Theoretical pKa values in aqueous solution were calculated by combining the CCSD(T) gas-phase acidities with self-consistent reaction field55 calculations using the COSMO approach and parametrization.56 The aqueous deprotonation Gibbs free energy (solution free energy) (ΔGaq) was calculated from the gas-phase free energy and the aqueous solvation free energy. The solvation energy is calculated as the sum of the electrostatic energies (polarized solute
solvent) and the nonelectrostatic energies. A dielectric constant of 78.39 corresponding to that of bulk water was used in the COSMO calculations at the B3LYP/aD level using the gas-phase geometries obtained at this level. The pKa values in aqueous solution were calculated using eq 9 pKa 0 ¼ pKa ðHAÞ þ ΔGaq =ð2:303RTÞ

ð9Þ

where ΔGaq is the solution free energy; R is the gas constant; and T = 298 K is the temperature. We report our pKa values relative to known standards including phosphoric acid, nitric acid, or acetic acid (HA) depending on the size of the ΔGgas.70 The calculated pKa of HNO3 using this approach is in error by 0.7 pKa units, that of CH3COOH by
2.8 pKa units, and that of H3PO4 by
1.4 pKa units. The molecular DFT calculations were performed with the Gaussian 03 program package.57 The SO
DFT calculations were performed with the NWChem 5.1 program package.58 The ZORADFT calculations were performed with the ADF 2008.01 program package.59 The CCSD(T) calculations were performed with the MOLPRO 2006.1 program package.60 The calculations were performed on the Opteron-based dense memory cluster (DMC) and Itanium 2-based SGI Altix supercomputers at the Alabama Supercomputer Center, the Xeon-based Dell Linux cluster at the University of Alabama, the local Opteron-based and Xeon-based Penguin Computing Linux cluster, and the Opteron-based Linux cluster at the Molecular Science Computing Facility from the Pacific Northwest National Laboratory.

’ RESULTS Equilibrium Geometries and Vibrational Frequencies of Parent Complexes. The M(NH)(CRR0 )(OH)2 (M = Mo, W;

CRR0 = CH2, CHF, CF2) metal complexes are pseudotetrahedral

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Table 1. Calculated Bond Length (Å) for M(NH)(CRR0 )(OH)2 (M = Cr, Mo, W; CRR0 = CH2, CHF, CF2) at the B3LYP/aD Level molecule 1

Cr(NH)(CH2)(OH)2 ( A/C1) 1

MdCRR0

MdN(H)

M
O(H)

1.769

1.598

1.780/1.774

Table 2. Calculated Harmonic Vibrational Frequencies in cm
1 for Metal
Oxygen, Metal
Nitrogen, and Metal
Carbon Stretchesa in M(NH)(CRR0 )(OH)2 (M = Cr, Mo, W; CRR0 = CH2, CHF, CF2) at the B3LYP/aD Level molecule

MdCRR0

MdN(H)

M
O(H)

Cr(NH)(CHF)(OH)2 ( A/C1)

1.804

1.604

1.786/1.780

Cr(NH)(CH2)(OH)2

843

1078

688 (s), 695 (as)

Cr(NH)(CF2)(OH)2 (1A/C1)

1.838

1.606

1.781/1.781

Cr(NH)(CHF)(OH)2

825

1062

683 (s), 662 (as)

Mo(NH)(CH2)(OH)2 (1A0 /Cs)

1.883

1.725

1.919

Cr(NH)(CF2)(OH)2

662

1054

662 (s), 670 (as)

Mo(NH)(CHF)(OH)2 (1A0 /Cs) Mo(NH)(CF2)(OH)2 (1A0 /Cs)

1.908 1.931

1.730 1.728

1.915 1.917

Mo(NH)(CH2)(OH)2

808

1013

685 (s), 688 (as)

Mo(NH)(CHF)(OH)2

792

1001

678 (s), 681 (as)

W(NH)(CH2)(OH)2 (1A0 /Cs)

1.893

1.738

1.915

Mo(NH)(CF2)(OH)2

638

1004

653 (s), 632 (as)

W(NH)(CHF)(OH)2 (1A0 /Cs)

1.913

1.741

1.911

W(NH)(CF2)(OH)2 (1A0 /Cs)

1.923

1.740

1.913

W(NH)(CH2)(OH)2 W(NH)(CHF)(OH)2

816 783

1021 1011

690 (s), 690 (as) 691 (s), 689 (as)

W(NH)(CF2)(OH)2

630

1014

702 (s), 699 (as)

with Cs symmetry, and the M = Cr complexes have C1 symmetry. The — NMC angles are smaller than the ideal tetrahedral angle of 109.5 by ∼7 for CRR0 = CH2 and by up to 12 for CRR0 = CHF or CF2. The — NMO bond angles are larger by up to 10 for CRR0 = CHF and CF2 and 7 for CRR0 = CH2 (Supporting Information). The MO2(OH)2 complexes are also pseudotetrahedral with C2 symmetry and are less distorted (1
2) from a tetrahedral structure than the M(NH)(CRR0 )(OH)2 complexes (Supporting Information). The calculated bond lengths for the MdO and M
O(H) bonds for M = W and Mo in the MO2(OH)2 complexes are comparable and longer as compared to those for M = Cr. A similar trend was observed for the calculated bond lengths of M(NH)(CRR0 )(OH)2 complexes (Table 1). The r(M
O(H)) in M(NH)(CRR0 )(OH)2 are up to 0.02 Å longer as compared to the MO2(OH)2 complexes. Substitution of H by the more electronegative F in CRR0 leads to a lengthening of the MdCRR0 bond from RdR0 dH to RdR0 dF by 0.07, 0.05, and 0.03 Å for Cr, Mo, and W, respectively. The MdN(H) and M
O(H) bond lengths are little affected by the different substitutions for R and R0 . The calculated geometries of the M(NH)(CRR0 )(OH)2 complexes with M = W and Mo are in good agreement with previous calculations for CRR0 = CH220
22 and with experimental X-ray structures of different substituted Schrock-type Mo and W complexes.31b,c,f The calculated MdCRR0 , MdNH, and M
O(H) vibrational frequencies are given in Table 2 for the M(NH)(CRR0 )(OH)2 complexes. The stretching frequencies for the bonds to the Cr complexes are calculated to be higher as compared to the W and Mo complexes consistent with the differences in the bond lengths. The M
O(H) stretching frequencies are similar for the MO2(OH)2 (Supporting Information) and M(NH)(CRR0 )(OH)2 complexes and mix with the bending frequencies. For MdCRR0 , the frequencies are in the order CF2 < CHF < CH2, and the MdCF2 stretches are much smaller (150 to 190 cm
1) than the MdCH2 and MdCHF stretches. The MdN(H) stretching frequencies are dependent on the transition metal and are not strongly affected by the nature of R and R0 , although the MdN(H) stretching frequencies for the CH2 complexes are larger than the frequencies in the CF2 and CHF complexes. Heats of Formation of Parent Complexes. The heats of formation at 0 and 298 K of M(NH)(CRR0 )(OH)2 and MO2(OH)2 (M = Cr, Mo, W; CRR0 = CH2, CHF, CF2) are given in Table 3 with the various electronic structure components used to calculate them given as Supporting Information. To improve our estimate of the calculated zero-point energies, the effect of

a

s, symmetric; as, asymmetric.

anharmonic corrections was included by scaling the OH and CH stretches by 0.981 and the NH stretch by 0.982. The scaling factor was obtained by dividing the average of the experimental and theoretical values by the theoretical value61 for H2O, CH4, and NH3 using the B3LYP/aD harmonic frequencies where the experimental frequencies62 include anharmonic corrections. The core
valence corrections to the TAEs calculated at the CCSD(T)DK/awCVTZ-DK level are less than 3 kcal/mol with the largest correction found for Cr(NH)(CH2)(OH)2. The core
valence corrections are slightly higher for CRR0 = CH2 than for CHF and CF2. Core
valence corrections at the CCSD(T)/awCVTZ-PP level differ by up to 4 kcal/mol as compared to the core
valence corrections at the CCSD(T)-DK/awCVTZ-DK level for M = Cr, differ by up to 2 kcal/mol for M = Mo, and are almost identical for M = W complexes (see Supporting Information for the core
valence corrections at the CCSD(T)/awCVTZ-PP level of the parent compounds). Relativistic corrections (ΔERel) are less than 2 kcal/mol with the largest predicted for WO2(OH)2. These relativistic corrections increase the heats of formation of M = Mo complexes and decrease the heats of formation of M = Cr and M = W complexes (see Supporting Information). The calculated heats of formation for M(NH)(CRR0 )(OH)2 and MO2(OH)2 should have an accuracy similar to those calculated for MO3 which were found to be within the experimental error bars.9 We expect the calculated heats of formation to be good to (2 kcal/mol with most of this limit coming from the errors in the heats of formation of the atoms and the extrapolation procedure. The heats of formation of various metal-centered radicals and MO(CH2)(OH)2 are also included for use in calculating the bond dissociation energies, and those for the excited states of the metal fragments are given in the Supporting Information. Bond Dissociation Energies in the Parent Complexes. We define two types of BDEs:63,64 (1) adiabatic, dissociating to the ground states of the separated species, and (2) diabatic, dissociating to electronic configurations appropriate for forming the appropriate bonds in the parent molecule. The adiabatic and diabatic BDEs may be equal depending on the nature of the electronic states of the products. The diabatic BDE is always equal to or higher than the adiabatic BDE, and the difference between the adiabatic and diabatic BDEs corresponds to any reorganization energy of the product(s). The basis set extrapolation effects at the CCSD(T) level from an aT to CBS for the adiabatic BDEs are less than 3 kcal/mol. The relativistic corrections for the BDEs are less than 1 kcal/mol with the exception of 12109

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Table 3. Heats of Formation at 0 and 298 K (ΔHf,0K and ΔHf,298K, kcal/mol) for the Ground States of the Metal-Containing Fragments of the M(NH)(CRR0 )(OH)2, MO2(OH)2, MO(CH2)(OH)2, and Metal Fragments (M = Cr, Mo, W; CRR0 = CH2, CHF, CF2)a ΔHf,0Kb

molecule

ΔHf,298Kc

ΔHf,0Kb

ΔHf,298Kc

ΔHf,0Kb

ΔHf,298Kc

MdCr

MdCr

MdMo

MdMo

MdW

MdW


171.8


174.9


201.4


204.1


216.7


219.2

M(NH)(CH2)(OH)2


45.9


50.0


49.9


53.8


61.2


65.1

M(NH)(CHF)(OH)2


92.8


96.3


93.9


97.3


102.8


106.2

M(NH)(CF2)(OH)2


145.9


149.0


147.3


150.2


154.3


157.2

MO(OH)2 MO2(OH)


129.2
102.5


130.7
103.9


107.3
103.6


109.0
105.1


114.2
108.9


116.2
110.3

MO2(OH)2

M(NH)(CH2)(OH)

24.5

21.9

39.0

36.0

38.0

35.1

M(NH)(CHF)(OH)


22.6


24.7


5.2


7.8


3.9


6.4

M(NH)(CF2)(OH)


77.6


79.1


60.6


62.6


57.7


59.7

M(NH)(OH)2


65.0


67.2


41.6


44.3


49.1


51.8

M(CH2)(OH)2


42.9


45.8


15.2


17.9


16.3


19.0

M(CHF)(OH)2


87.1


89.1


56.1


58.4


54.6


56.7

M(CF2)(OH)2 MO(CH2)(OH)2


142.8
116.9


144.4
120.2


110.2
118.9


112.1
121.3


101.4
128.5


103.1
131.7

a Defined as the energy difference between the ground states of the atoms (7S3 for M, 3P2 for O, 2S1/2 for H, 3P0 for C, 4S3/2 for N, 2P3/2 for F) and the complex. b ΔHf,0K = ΣΔHf,0K(atoms)
ΣD0,0K where ΔHf,0K is 58.98 ( 0.02 kcal/mol for O, 169.98 ( 0.1 kcal/mol for C, 112.53 ( 0.02 kcal/mol for N, 18.47 ( 0.07 kcal/mol for F, 51.63 ( 0.001 kcal/mol for H, 94.5 ( 1.0 kcal/mol for Cr, 157.1 ( 0.9 kcal/mol for Mo, and 203.1 ( 1.5 kcal/mol for W. c ΔHf,298K = ΔHf,0K þ ΔH0Kf298K
ΣΔH0Kf298K(atoms) where ΔH0Kf298K is 1.04 kcal/mol for O, 0.25 kcal/mol for C, 1.04 kcal/mol for N, 1.05 kcal/mol for F, 1.01 kcal/mol for H, 0.97 kcal/mol for Cr, 1.10 kcal/mol for Mo, and 1.19 kcal/mol for W. ΔH0Kf298K for the metal complexes is calculated at the B3LYP/aD level.

Table 4. CCSD(T)/CBS Adiabatic and Diabatic Bond Dissociation Energies at 0 K in kcal/mol (ΔE0K) for the MdO bonds in MO2(OH)2 and MO(CH2)(OH)2 (M = Cr, Mo, and W) and Singlet
Triplet Energy Differences at 0 K in kcal/mol (ΔES-T) for MO(OH)2 and M(CH2)(OH)2 typea

ΔE0Kb

ΔES-Tc

CrO2(OH)2 f O (3P2) þ CrO(OH)2 (3A00 )

ad, dia

102.0

13.2 (T)

MoO2(OH)2 f O (3P2) þ MoO(OH)2 (3A)

ad, dia

153.1

2.4 (T)

WO2(OH)2 f O (3P2) þ WO(OH)2 (1A1)

ad

161.4

12.8 (S)

WO2(OH)2 f O (3P2) þ WO(OH)2 (3A)

dia

174.6

CrO(CH2)(OH)2 f O (3P2) þ Cr(CH2)(OH)2 (3A)

ad, dia

133.0

MoO(CH2)(OH)2 f O (3P2) þ Mo(CH2)(OH)2 (3A)

ad, dia

162.7

2.7 (T)

WO(CH2)(OH)2 f O (3P2) þ W(CH2)(OH)2 (1A1) WO(CH2)(OH)2 f O (3P2) þ W(CH2)(OH)2 (3A)

ad dia

171.2 181.1

9.9 (S)

reaction

a

19.7 (T)

ad, adiabatic; dia, diabatic. b Equation 8. c The ground state is specified in the parentheses (S, singlet; T, triplet).

WO2(OH)2 which has a ΔERel =
1.8 kcal/mol. The core
valence corrections are also less than 1 kcal/mol for M = W and Mo complexes and 1
3 kcal/mol for M = Cr. Thus, the core
valence corrections can be as large as the basis set extrapolation from aT to the CBS value (see Supporting Information). The calculated MdO BDEs for the ground states of MO2(OH)2 and MO(CH2)(OH)2 are given in Table 4. The adiabatic and diabatic BDEs are the same for M = Cr and Mo. For M = W, the diabatic WdO BDE is higher for MO2(OH)2 by 13.2 kcal/mol and for MO(CH2)(OH)2 by 9.9 kcal/mol than the adiabatic value because the ground state of MO(OH)2 is a singlet (1A1), whereas it is a triplet (3A) for M = Cr and Mo. The adiabatic MdO BDEs increase from Cr to W with the largest increase being that from Cr to Mo. For MoO(OH)2, there is a small triplet
singlet gap of 2.4 kcal/mol, and for WO(OH)2, the singlet
triplet gap is 12.8 kcal/mol. For M(CH2)(OH)2, the

ground state for Cr is a triplet with the singlet about 20 kcal/mol higher in energy. The triplet
singlet gap decreases to ∼3 kcal/mol for M = Mo, and for M = W the singlet is the ground state with the triplet 10 kcal/mol higher in energy. The M
O(H), MdN(H), and MdCRR0 BDEs for the Schrock-type compounds are given in Tables 5 to 7. For the M
O(H) BDEs, the products are both doublets so the adiabatic and diabatic values (Table 5) are the same. The Cr
O(H) BDEs are all just less than 80 kcal/mol and do not particularly depend on whether the parent has two CrdO bonds or has Cr(NH)(CRR0 ) bonds. There is also little dependence on the nature of R and R0 within 2 kcal/mol with the substitution pattern of R = R0 = F having a BDE about 2 kcal/mol smaller. The Mo
O(H) BDEs are larger than the Cr
O(H) BDEs and show more dependence on the substituents with the parent with two ModO bonds having a BDE about 10 kcal/mol larger than the parent with 12110

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Mo(NH)(CRR0 ) bonds. Again, there is little dependence on the nature of R and R0 . The W
O(H) BDEs are again larger and follow the same trends as for the Mo
O(H) BDEs. As expected, the smallest MdN(H) adiabatic BDE (Table 6) is for M = Cr and the largest for M = W. For M = Cr and Mo, the metal fragments have a triplet ground state, and for M = W, the metal fragment has a singlet ground state. The ground state of NH is a triplet, so the adiabatic and diabatic BDEs are the same for M = Cr and Mo and are different for M = W. The MdN(H) BDEs are not strongly dependent on the nature of the R and R0 on the CRR0 moiety for M = Cr and Mo. For M = W, the presence of the CF2 fragment stabilizes the WdN(H) bond by about 8 kcal/mol. The MdCRR0 (CRR0 = CH2, CHF, and CF2) BDEs for M(NH)(CRR0 )(OH)2 are listed in Table 7. The R = R0 = H adiabatic BDEs are the largest, and the R = R0 = F adiabatic BDEs are the smallest. Again, the MdCRR0 BDEs increase from Cr to W consistent with what is predicted for the MdO BDEs. For CrdCH2, the adiabatic and diabatic BDEs are the same because the Cr fragment has a triplet ground state as does the CH2 fragment. For M = Mo and W, the Mo and W fragments are singlets as are Table 5. Adiabatic Bond Dissociation Energies at 0 K (ΔE0K, kcal/mol) for the M
OH Bonds in M(NH)(CRR0 )(OH)2 and MO2(OH)2 (M = Cr, Mo, W; CRR0 = CH2, CHF, CF2) Calculated at the CCSD(T) Level Using Equation 9 ΔE0K

reaction 2 0

CrO2(OH)2 f OH ( Π) þ CrO2(OH) ( A ) Cr(NH)(CH2)(OH)2 f OH (2Π) þ Cr(NH)(CH2)(OH) (2A0 )

78.7 79.5

Cr(NH)(CHF)(OH)2 f OH (2Π) þ Cr(NH)(CHF)(OH) (2A0 )

79.2

2

Cr(NH)(CF2)(OH)2 f OH (2Π) þ Cr(NH)(CF2)(OH) (2A0 ) MoO2(OH)2 f OH (2Π) þ MoO2(OH) (2A) Mo(NH)(CH2)(OH)2 f OH (2Π) þ Mo(NH)(CH2)(OH) (2A0 )

77.3 106.9 97.9

Mo(NH)(CHF)(OH)2 f OH (2Π) þ Mo(NH)(CHF)(OH) (2A0 ) 97.8 Mo(NH)(CF2)(OH)2 f OH (2Π) þ Mo(NH)(CF2)(OH) (2A0 )

95.7

WO2(OH)2 f OH (2Π) þ WO2(OH) (2A) W(NH)(CH2)(OH)2 f OH (2Π) þ W(NH)(CH2)(OH) (2A0 )

116.9 108.3

W(NH)(CHF)(OH)2 f OH (2Π) þ W(NH)(CHF)(OH) (2A0 )

108.0

W(NH)(CF2)(OH)2 f OH (2Π) þ W(NH)(CF2)(OH) (2A0 )

105.7

those of the CHF and CF2 fragments, so the adiabatic BDEs differ from the diabatic BDEs for R = H, R0 = F, and R = R0 = F. We calculated the singlet
triplet splittings in the carbenes and in the metal fragments (Supporting Information). Methylene (CH2) has a triplet ground state (3B1) with an excited state (1A1) 9.1 kcal/mol higher in energy in excellent agreement with experiment65 and our previous calculations.66 The ground state of fluorocarbene (CHF) is a singlet (1A0 ) with the triplet excited state (3A00 ) 14.6 kcal/mol higher in energy, and difluorocarbene (CF2) has an even more stable singlet ground state (1A1) which is 56.5 kcal/mol lower in energy than its excited state (3B1). Our calculated values are in good agreement with most of the experimental and theoretical results for the singlet
triplet splittings of CF2 and CHF67,68 and the most recent value of 55.7 kcal/mol for CF2 at the CAS-BCCC4 level.69 For the Mo fragment, the singlet ground state is less than 1 kcal/mol below the triplet excited state. The singlet
triplet splitting for the W fragment is 13.8 kcal/mol with a singlet ground state. The adiabatic BDEs for the MdCRR0 bonds increase from Cr to W and decrease from R = R0 = H to R = R0 = F. The changes in the MdCRR0 BDEs with fluorine substitution are comparable for the different metals with the difference between the MdCH2 and MdCF2 BDEs ranging from 48 kcal/mol for M = W to 41 kcal/mol for M = Cr. The lowest overall MdCRR0 BDE is 34 kcal/mol for Cr(NH) (CF2)(OH)2. The MdCH2 BDEs in MO(CH2)(OH)2 are also listed in Table 7. Similar to the other calculated BDEs, the MdCH2 BDEs in MO(CH2)(OH)2 increase from Cr to W. For M = Cr and Mo, the adiabatic and diabatic BDEs are the same, and for M = W the diabatic BDE is 13.1 kcal/mol higher than the adiabatic BDE. Lewis Acidity (Fluoride Affinity) of Parent Complexes. The fluoride affinities for six different addition sites to the Schrock catalyst model M(NH)(CH2)(OH)2 were optimized at the DFT (B3LYP/aD, see Supporting Information) level with single point energies calculated at the CCSD(T)/aD level (Table 8). The energy of the strongest Lewis acid site was further studied with energies at the CCSD(T)/CBS level (Structure A). The structures of the F
adducts for Mo are shown in Figure 1. The sites clearly have different Lewis acidities by up to 8 kcal/mol for M = Mo and W and by up to 13 kcal/mol for M = Cr. Structures A, B, and C have the F
adding trans to the NH group and mostly differ in the orientation of the OH groups.

Table 6. CCSD(T) Adiabatic and Diabatic Bond Dissociation Energies at 0 K (ΔE0K, kcal/mol) for the MdNH Bonds in M(NH)(CRR0 )(OH)2 (CRR0 = CH2, CHF, CF2; M = Cr, Mo, W) and Singlet
Triplet Energy Differences at 0 K (ΔES-T, kcal/mol) for the Metal-Containing Fragments reaction

a

typea

ΔE0Kb

ΔES-Tc 19.7 (T)

Cr(NH)(CH2)(OH)2 f NH (3Σ) þ Cr(CH2)(OH)2 (3A)

ad, dia

89.1

Cr(NH)(CHF)(OH)2 f NH (3Σ) þ Cr(CHF)(OH)2 (3A)

ad, dia

91.7

20.2 (T)

Cr(NH)(CF2)(OH)2 f NH (3Σ) þ Cr(CF2)(OH)2 (3A) Mo(NH)(CH2)(OH)2 f NH (3Σ) þ Mo(CH2)(OH)2 (3A)

ad, dia ad, dia

89.2 120.7

18.3 (T) 2.7 (T)

Mo(NH)(CHF)(OH)2 f NH (3Σ) þ Mo(CHF)(OH)2 (3A)

ad, dia

123.9

2.7 (T)

Mo(NH)(CF2)(OH)2 f NH (3Σ) þ Mo(CF2)(OH)2 (3A)

ad, dia

123.2

4.3 (T)

W(NH)(CH2)(OH)2 f NH (3Σ) þ W(CH2)(OH)2 (1A1)

ad

130.9

9.9 (S)

W(NH)(CH2)(OH)2 f NH (3Σ) þ W(CH2)(OH)2 (3A)

dia

140.8

W(NH)(CHF)(OH)2 f NH (3Σ) þ W(CHF)(OH)2 (1A0 )

ad

134.3

W(NH)(CHF)(OH)2 f NH (3Σ) þ W(CHF)(OH)2 (3A)

dia

143.7

W(NH)(CF2)(OH)2 f NH (3Σ) þ W(CF2)(OH)2 (1A0 ) W(NH)(CF2)(OH)2 f NH (3Σ) þ W(CF2)(OH)2 (3A)

ad dia

139.0 142.6

9.3 (S) 3.7 (S)

ad, adiabatic; dia, diabatic. b Equation 8. c The ground state is specified in the parentheses (S, singlet; T, triplet). 12111

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Table 7. CCSD(T) Adiabatic and Diabatic Bond Dissociation Energies at 0 K (ΔE0K, kcal/mol) for the MdCRR0 Bonds in M(NH)(CRR0 )(OH)2 (CRR0 = CH2, CHF, CF2; M = Cr, Mo, W), MdCH2 Bonds in MO(CH2)(OH)2, and Singlet
Triplet Energy Differences at 0 K (ΔES-T, kcal/mol) for the Metal-Containing Fragments typea

bond energy reaction

a

ΔE0Kb

ΔES-Tc

Cr(NH)(CH2)(OH)2 f CH2 (3B1) þ Cr(NH)(OH)2 (3A)

ad, dia

75.0

12.2 (T)

Mo(NH)(CH2)(OH)2 f CH2 (3B1) þ Mo(NH)(OH)2 (1A1)

ad

102.3

0.7 (S)

Mo(NH)(CH2)(OH)2 f CH2 (3B1) þ Mo(NH)(OH)2 (3A)

dia

103.0

W(NH)(CH2)(OH)2 f CH2 (3B1) þ W(NH)(OH)2 (1A1)

ad

106.0

13.8 (S)

W(NH)(CH2)(OH)2 f CH2 (3B1) þ W(NH)(OH)2 (3A) Cr(NH)(CHF)(OH)2 f CHF (1A0 ) þ Cr(NH)(OH)2 (3A)

dia ad

119.8 62.6

12.2 (T)

Cr(NH)(CHF)(OH)2 f CHF (3A00 ) þ Cr(NH)(OH)2 (3A)

dia

77.2

Mo(NH)(CHF)(OH)2 f CHF (1A0 ) þ Mo(NH)(OH)2 (1A1)

ad

87.2

Mo(NH)(CHF)(OH)2 f CHF (3A00 ) þ Mo(NH)(OH)2 (3A)

dia

102.5

W(NH)(CHF)(OH)2 f CHF (1A0 ) þ W(NH)(OH)2 (1A1)

ad

88.5

W(NH)(CHF)(OH)2 f CHF (3A00 ) þ W(NH)(OH)2 (3A)

dia

116.9

Cr(NH)(CF2)(OH)2 f CF2 (1A1) þ Cr(NH)(OH)2 (3A)

ad

33.9

12.2 (T)

Cr(NH)(CF2)(OH)2 f CF2 (3B1) þ Cr(NH)(OH)2 (3A) Mo(NH)(CF2)(OH)2 f CF2 (1A1) þ Mo(NH)(OH)2 (1A1)

dia ad

90.3 59.0

0.7 (S)

Mo(NH)(CF2)(OH)2 f CF2 (3B1) þ Mo(NH)(OH)2 (3A)

dia

116.2

W(NH)(CF2)(OH)2 f CF2 (1A1) þ W(NH)(OH)2 (1A1)

ad

58.4

W(NH)(CF2)(OH)2 f CF2 (3B1) þ W(NH)(OH)2 (3A)

dia

128.6

CrO(CH2)(OH)2 f CH2 (3B1) þ CrO(OH)2 (3A00 )

ad, dia

81.7

MoO(CH2)(OH)2 f CH2 (3B1) þ MoO(OH)2 (3A)

ad, dia

105.6

2.4 (T)

WO(CH2)(OH)2 f CH2 (3B1) þ WO(OH)2 (1A1)

ad

108.3

12.8 (S)

WO(CH2)(OH)2 f CH2 (3B1) þ WO(OH)2 (3A)

dia

121.4

0.7 (S) 13.8 (S)

13.8 (S) 13.2 (T)

ad, adiabatic; dia, diabatic. b Equation 8. c The ground state is specified in the parentheses (S, singlet; T, triplet).

Table 8. CCSD(T)/aD Fluoride Affinities at 298 K (FA298K, kcal/mol) for Different Addition Sites of the M(NH)(CH2)(OH)2 (M = Cr, Mo, W) metal

A

B

C

D

E

F

Cr

55.6

50.6

53.3

52.7

51.6

53.9a

Mo

62.3

54.5

58.3

57.6

58.9

56.8

W

69.4

62.8

66.1

63.8

65.4

62.0

The T1 value for the fluorine binding to the F site with M = Cr at the CCSD(T)/aD level was calculated to be larger than 0.1. The FA for the F site with M = Cr was estimated by taking the DFT B3LYP value and adding to it 18.2 kcal/mol which is the average of the differences between the CCSD(T)/aD and B3LYP/aD values of all of the other isomers. a

Structures D and E have the F
adding trans to an OH group and again differ mostly in the orientation of the OH groups. The same type of study was done for the MO2(OH)2 complexes, and the Lewis acidities for the five sites' results are given in the Supporting Information. They behave in a similar fashion with smaller energy differences. Table 9 lists the fluoride affinities, a measure of the Lewis acidity, of the Schrock-type metal complexes and MO2(OH)2 for the most Lewis acidic site. The core
valence and scalar relativistic corrections are small, less than 0.6 and 0.3 kcal/mol, respectively. Also the variation in the basis set extrapolation effects from aT to CBS is not more than 2 kcal/mol (see Supporting Information). The FAs of MO2(OH)2 are calculated to be higher than the FAs of M(NH)(CH2)(OH)2, with the smallest difference for M = Cr, Cr
O(H) > CrdCH2. The MdNH BDE remains the largest for Mo and W; however, for Mo, the MdCH2 is slightly above the M
O(H) bond energy, and the order reverts back to that of Cr for W with the W
O(H) and WdCH2 bonds of comparable energy. The MdCH2 BDEs are 14, 19, and 25 kcal/mol less than the MdNH BDEs for M = Cr, Mo, and W, respectively. The adiabatic MdO BDEs in MO(CH2)(OH)2 are calculated to be larger by 44, 42, and 40 kcal/mol for M = Cr, Mo, and W, respectively, as compared to MdNH BDEs in M(NH)(CH2)(OH)2. Similarly, the MdO BDEs in MO2(OH)2 are larger than the MdCH2 BDEs in MO(CH2)(OH)2 by 20, 47, and 53 kcal/ mol for M = Cr, Mo, and W, respectively. The MdCH2 BDES in MO(CH2)(OH)2 can be compared to those in M(NH)(CH2)(OH)2 to determine the effect of substitution of dNH for dO. The effect is largest for Cr with substitution of dNH for dO reducing the CrdCH2 BDE by 7 kcal/mol and smallest for W where the substitution reduces the BDE by only 2 kcal/mol. The BDEs for MdCH2 for M = Mo and W are just above 100 kcal/mol, and the two values are comparable. The MdCRR0 BDEs drop by 15 kcal/mol for Mo and by 18 kcal/mol for W when an F is substituted for one H on the CH2 group. Substitution of a second F to form CF2 leads to a substantial decrease in the MdCF2 BDE by about 30 kcal/mol to a value near 60 kcal/mol. The F can be considered to be a representative electrophilic substituent. This σ-withdrawing and π-donating substituent substantially stabilizes the singlet ground state of the carbene so that the metal carbene BDE becomes weaker. The weaker MdCRR0 bond when R and/or R0 is a σ-withdrawing and πdonating substituent does not readily form, and hence one cannot use this type of catalyst for olefin metathesis reactions involving such substituents. In fact, Grubbs and co-workers in a different catalyst system (Grubbs “second-generation”) bearing a CF2 unit showed that such a metal
CF2 complex does not function as a catalyst for olefin metathesis.73 Similarly, one notes that the imidazol(in)ylidene ligand present in Grubbs “secondgeneration” catalysts and beyond is not transferred in the olefin metathesis reaction consistent with the large singlet
triplet splitting in such carbenes.74 The weaker MdCF2 bond arises because there is very little electron density available for backbonding from the “out of plane” orbital on the carbene moiety. The CrdCRR0 bonds are quite weak, ranging from 75 kcal/mol for R = R0 = H to 35 kcal/mol for R = R0 = F. Hence, it is unlikely that one can use Cr with these types of substituents for a metathesis catalyst due to the weak bonds to the carbene. Further insight into the MdCRR0 BDEs comes from considering the differences in the adiabatic and diabatic BDEs. The adiabatic and diabatic BDEs for MdCH2 are comparable for M = Cr and Mo, and for M = W, the difference is about 14 kcal/ mol. The differences between the adiabatic and diabatic MdCRR0 BDEs become larger as R and R0 become more electronegative. The diabatic MdCH2 and MdCHF BDEs are about the same for a specific metal, and there is an increase of 12
14 kcal/mol for the MdCF2 diabatic BDE. Thus, the diabatic BDEs are comparable within 15 kcal/mol independent of substituent for a given metal. This is similar to what has been found in comparing other adiabatic and diabatic BDEs, for example, in the CdC bonds in C2H4 and C2F4.63 By using the experimental heats of formation of C2F4 and C2H4,50 the adiabatic CdC BDE in C2F4 is 64.8 kcal/mol as compared to the BDE in C2H4 of 173.2 kcal/mol, a difference of 108.4 kcal/mol. The adiabatic BDE in C2H4 is the same as the

ARTICLE

diabatic value, and the diabatic BDE in C2F4 is 177.6 kcal/mol, essentially the same as the value in C2H4. Thus, the BDEs in terms of the actually binding configurations are comparable in C2H4 and C2F4, very similar to what we find for the MdCRR0 bonds. The results strongly suggest that the carbene centers involved need to have triplet ground states or at least a small singlet
triplet splitting if the singlet is the ground state. The typical alkyl or aryl substituents on the carbene center or on the olefin meet this criterion. However, substituents which stabilize the singlet ground state of the carbene such as F will lead to catalysts that are nonfunctioning. This is not just for the reactant carbene but also for carbene products after metathesis. Our results show that consideration of the singlet
triplet splitting in the carbene is a critical component in the design of an effective olefin metathesis catalyst in terms of the parent catalyst and the groups being transferred. These concepts are consistent with the properties of spin-philicity and spin-donicity derived from density functional theory75,76 recently used to explain the singlet
triplet gaps in carbenes and their heavier homologues.77 These quantities in their simplest form for the vertical singlet
triplet splitting are related to the HOMO
LUMO gap in the singlet carbene.75 We can correlate the calculated BDEs with the bond distances and stretching frequencies. The MdCRR0 BDE in M(NH)(CRR0 )(OH)2 decreases in the order CH2 > CHF > CF2, which is consistent with the order of the calculated bond distances (CH2 < CHF < CF2) and stretching frequencies (CH2 > CHF > CF2). The MdN(H) and M
O(H) BDEs, bond distances, and stretching frequencies in M(NH)(CRR0 )(OH)2 are much less affected by the nature of R and R0 in CRR0 . The calculated MdCRR0 BDEs are much smaller than those for MdN(H) and MdO BDEs, consistent with the longer bond lengths and lower stretching frequencies for MdCRR0 . The Lewis acidity based on the calculated FAs of these species provides information on the ability of the transition metal complex to bind a Lewis base such as the reactant olefin. The Lewis acidities as determined by the FAs are much lower than those for MO3 whose FAs were calculated to be 124.5, 137.2, and 147.4 kcal/mol at the B3LYP level with a triplet zeta basis set for M = Cr, Mo, and W, respectively.11 The moderate Lewis acidity of the transition metal complex coupled with steric constraints prevents a weak Lewis acid
base complex from forming as we have not found any precomplexes that are bound with a moderately short M
C2H4 distance for the Schrock catalyst. If the Lewis acidity is increased and the steric constraints removed as would occur for WO3 (trigonal pyramidal), the C2H4 complexation energy is
43.8 kcal/mol (CCSD(T)/aug-cc-pVTZ-PP level þ ZPE). The MO2(OH)2 species weakly bind C2H4 via the protons on the OH’s. As discussed below, the MO2(OH)2 species are very strong Brønsted acids consistent with this type of binding. We focused on the addition of C2H4 only with M(NH)(CH2)(OH)2 because, as discussed above, the reaction with the CHF or CF2 is not likely to occur because of instability of the initial catalyst complex. The C2H4 undergoes a [2 þ 2] cycloaddition with the MdCH2 or MdO bond leading to the formation of the M(NH)(OH)2(C3H6) or MO(OH)2(OC2H4) intermediate. In our degenerate reaction case for CH2, the ethylene and the Schrock-type metal complex are regenerated. For the MO2(OH)2 reaction, formaldehyde and MO(CH2)(OH)2 are formed via a retro [2 þ 2] reaction. The reaction energies for MO2(OH)2 þ C2H4 f MO(CH2)(OH)2 þ CH2O are 19.1, 43.0, and 49.4 kcal/mol for M = Cr, Mo, and W, respectively. 12116

dx.doi.org/10.1021/jp202668p |J. Phys. Chem. C 2011, 115, 12106–12120

The Journal of Physical Chemistry C Our calculated geometry parameters for the M(NH)(OH)2(C3H6) SP and TBP conformers of the metallacycle intermediates can be compared with the available structural data for olefin metathesis intermediates.7,31 For the SP metallacycles with M = W and Mo, the experimental r(M
C2) values are about 2.77
2.79 Å, and the experimental — C1MC3 and — C2C3C4 angles are 63
65 and 93
104. There is a good agreement between the calculated and experimental geometry parameters for the M = W and Mo metallacycles. Similarly, for the TBP conformers, the experimental r(M
C2) values are about 2.3
2.4 Å; the — C1MC3 and — C2C3C4 angles are 82
84 and 116
121; and our calculated geometry parameters for M
TBP2 are in good agreement with the experimental values, especially considering the differences in the substituents. For Cr, there are no experimental data, so our values should serve as reliable estimates for the geometries of these species. In both M(NH)(OH)2(C3H6) and M(O)(OH)2(OC2H4) SP structures, the dNH or dO occupies the axial position as expected. The reaction energy to form the lowest-energy SP metallacycle for Cr(NH)(CH2)(OH)2 is the least negative, and that for W is the most negative with the Mo complexation energy being only 3 kcal/mol less negative than for M = W. This correlates with the ordering of the Lewis acidities as determined by the fluoride affinities. The Cr compounds will not form many complexes at 298 K on the free energy scale, whereas it is still favorable to form the complexes for M = Mo and W. Experimental studies have shown that the nature of the substituents on the initial metal carbene and the olefin can change the relative energies of the SP and TBP structures.7,31 Thus, electron-withdrawing groups on the alkoxide, for example, OCMe(CF3)2, stabilize a TBP geometry, and electron-donating groups such as O-t-butyl stabilize the SP geometry.7,31a,31d,31e The substituents of the olefin can lead to an SP geometry (β-t-butyl) or to the TBP geometry (β-SiMe3) of the metallacycle.31b,d The nature of the transition metal also affects the geometry with the SP geometry predominant for Mo and both the SP and TBP found for W when OR = OAr.31c We predict for M(NH)(OH)2(C3H6) that the energy between the M
SP1, M
SP2, and M
TBP2 conformers is M
O(H) > MdCRR0 , except for the ModCH2 BDE which is just above Mo
O(H). The following conclusion can be drawn from the MdCRR0 BDEs. The MdCRR0 BDEs increase in the order CF2 < CHF < CH2 showing that the CF2 and CHF Schrock-type complexes are much less stable than CH2 complexes. The σwithdrawing and π-donating substituent (F) substantially stabilizes the singlet ground state of the carbene so that the metal carbene BDE becomes much weaker. The weaker MdCRR0 bond when R and/or R0 are a σ-withdrawing and π-donating substituent should not readily form in either the starting catalyst or the metal product generated by the retro [2 þ 2] cycloaddition; hence, this type of catalyst cannot readily be used for olefin metathesis reactions involving carbenes and/or olefins with such substituents. The singlet
triplet/triplet
singlet splitting in the carbene is thus a critical component in the design of effective olefin metathesis catalysts in terms of the parent catalyst and the groups on the olefins being transferred. The results strongly suggest that the carbene centers involved in the metathesis reactions need to have triplet ground states or a small singlet
triplet splitting if the singlet is the ground state to form good MdC bonds. In addition, the results show that the weaker CrdC bonds make it unlikely that Cr compounds will serve as good catalysts for olefin metathesis reactions using the Schrock-type substituents. The M(NH)(CH2)(OH)2 and MO2(OH)2 model compounds are predicted to be medium to weak Brønsted acids and modest Lewis acids. The moderate Lewis acidity coupled with the steric constraints present in the parent M(NH)(CH2)(OH)2 with no substituents on N, C, or O was shown to not be large enough for C2H4 to form more than a very weak van der Waals type complex with M(NH)(CH2)(OH)2. Thus the formation of the metallacycle will proceed via a direct addition of the olefin to the catalyst without the formation of a precomplex. In the reaction of M(NH)(CH2)(OH)2 or MO2(OH)2 complexes with ethylene, distorted trigonal bipyramidal (TBP) or square pyramidal (SP) metallacycles are formed as intermediates. Both MO(OH)2(OC2H4) and M(NH)(OH)2(C3H6) metallacycles prefer the SP geometries: M
SP4 and, respectively, M
SP1 with the dO or dNH in the axial position. The energies of the SP and TBP complexes are reasonably close in the unsubstituted metallacycle so that substituents on O, N, or C can change the relative energies of the conformers as is found experimentally. The Brønsted acidity calculations show that if one were to make a catalyst soluble in aqueous solution that the carbene hydrogens on the CH2 on the complex are not very acidic so that it may be possible to design such catalysts.

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’ ASSOCIATED CONTENT

bS

Supporting Information. Calculated geometry parameters and vibrational frequencies for MO2(OH)2; calculated bond angles for M(NH)(CRR0 )(OH)2 (M = Cr, Mo, W; CRR0 = CH2, CHF, CF2) at the B3LYP/aD Level; valence electronic energy contributions to the total atomization energies and total atomization energies for MO2(OH)2, MO(CH2)(OH)2, and M(NH)(CRR0 )(OH)2 at the CCSD(T) level; bond dissociation energies for MO2(OH)2 and M(NH)(CRR0 )(OH)2 at the CCSD(T) level; heats of formation and bond dissociation energies at B3LYP/aD and BP86/aD levels; total atomization energies and heats of formation for CRR0 at the CCSD(T) level; total atomization energy and heat of formation of MoO2 at the CCSD(T) level; Brønsted acidities, and fluoride affinities for MO2(OH)2 and M(NH)(CRR0 )(OH)2 at the CCSD(T) level; brønsted acidities, and fluoride affinities for MO2(OH)2 and M(NH)(CRR0 )(OH)2 at the MP2 and DFT levels; fluoride affinities for different F
adducts of MO2(OH)2 and M(NH)(CRR0 )(OH)2; solvation energy contributions; solution energetics and pKa values; heats of formation for the excited states of M(NH)(CRR0 )(OH)2 and MO2(OH)2 at the CCSD(T) level; molecular spin orbit corrections calculated with the ZORA and SO
DFT approaches; calculated geometry parameters for the metallacycles at the MP2/aT level; calculated vibrational frequencies for the metallacycles at the B3LYP/aD level; calculated reaction energies for the metallacycles at the CCSD(T), B3LYP/aD, and BP86/aD levels; and optimized Geometries at the B3LYP/aD and MP2/aT levels. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Fax: 205-348-4704.

’ ACKNOWLEDGMENT This work was supported by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, U.S. Department of Energy (DOE), under grant no. DE-FG02-03ER15481 (catalysis center program), and by the National Science Foundation. D. A. Dixon is indebted to the Robert Ramsay Endowment and A. J. Arduengo, III to the Saxon Chair Foundation, both of the University of Alabama, for partial support. Part of this work was performed at the W. R. Wiley Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by DOE’s Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory, operated for the DOE by Battelle. ’ REFERENCES (1) Chauvin, Y. Angew. Chem., Int. Ed. 2006, 45, 3740. (2) Schrock, R. C. Angew. Chem., Int. Ed. 2006, 45, 3748. (3) Grubbs, R. H. Angew. Chem., Int. Ed. 2006, 45, 3760. (4) H
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