Modeling Ï-Bond Activations by Nickel(0) Beyond Common

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Modeling #-Bond Activations by Nickel(0) Beyond Common Approximations: How Accurately Can We Describe Closed-Shell Oxidative Addition Reactions Mediated by Low-Valent Late 3d Transition Metal? Lianrui Hu, Kejuan Chen, and Hui Chen J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.7b00708 • Publication Date (Web): 07 Sep 2017 Downloaded from http://pubs.acs.org on September 7, 2017

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Journal of Chemical Theory and Computation

Modeling σ-Bond Activations by Nickel(0) Beyond Common Approximations: How Accurately Can We Describe Closed-Shell Oxidative Addition Reactions Mediated by Low-Valent Late 3d Transition Metal? Lianrui Hu,§ Kejuan Chen,§ and Hui Chen* Beijing National Laboratory for Molecular Sciences (BNLMS), CAS Key Laboratory of Photochemistry, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China Supporting Information Placeholder ABSTRACT: Accurate modelings of reactions involving 3d transition metals (TMs) are very challenging to both ab initio

and DFT approaches. To gain more knowledge in this field, we herein explored typical σ-bond activations of H-H, C-H, CCl, and C-C bonds promoted by nickel(0), a low-valent late 3d TM. For the key parameters of activation energy (E‡) and reaction energy (ER) for these reactions, various issues related to the computational accuracy were systematically investigated. From the scrutiny of convergence issue with one-electron basis set, augmented (A) basis functions are found important, and the CCSD(T)/CBS level with complete basis set (CBS) limit extrapolation based on augmented double-ζ and triple-ζ basis pair (ADZ and ATZ), which produces deviations below 1 kcal/mol from the reference, is recommended for larger systems. As an alternative, explicitly correlated F12 method can accelerate the basis set convergence further, especially after its CBS extrapolations. Thus, the CCSD(T)-F12/CBS(ADZ-ATZ) level with computational cost comparable to the conventional CCSD(T)/CBS(ADZ-ATZ) level, is found to reach the accuracy of the conventional CCSD(T)/A5Z level, which produces deviations below 0.5 kcal/mol from the reference, and is also highly recommendable. Scalar relativistic effects and 3s3p core-valence correlation are non-negligible for achieving chemical accuracy of around 1 kcal/mol. From the scrutiny of convergence issue with N-electron basis set, in comparison with the reference CCSDTQ result, CCSD(T) is found to be able to calculate E‡ quite accurately, which is not true for the ER calculations. Using highest-level CCSD(T) results of E‡ in this work as references, we tested 18 DFT methods, and found that PBE0 and CAM-B3LYP are among the three best performing functionals, irrespective of DFT empirical dispersion correction. With empirical dispersion correction included, B97XD is also recommendable due to its improved performance.

INTRODUCTION In contrast to many rare and noble second-row (4d) and third-row (5d) transition metals (TMs), the first-row (3d) TMs are earthabundant and much cheaper. As a result, the catalytic reactions involving 3d TMs have received considerable attention in organometallic chemistry and catalysis, and witnessed great development in recent years.1-13 Despite the fact that the first-row TMs are playing increasingly important roles in catalysis, unfortunately, they have long been considered to be challenging in theoretical modeling, presumably due to their potential multi-reference character,14 which makes the accurate theoretical treatment very difficult with many commonly used approximations in quantum chemical methods. For the first-row TMs, 3d orbitals are much more compact and much smaller in size than 4s orbital. 14 The compactness of 3d orbitals leads to strong near-degeneracy effects,15 while its smaller size leads to the electrons in 3d orbital strongly repelling each other and the weak overlap interaction between the 3d orbital and the ligand orbital, both of which could strengthen the near-degeneracy effects. The strong near-degeneracy effects often lead to multi-reference character for the electronic states, which

cast serious doubt on the possibility to correctly describe these states by many single-reference approximations such as MP2 (second order Møller-Plesset perturbation theory) based on Hartree-Fock (HF) reference.14,16-18 Due to the immense success of density functional theory (DFT) methods in modeling the chemical reactions involving the TMs, particularly 4d and 5d TMs, after their wide applications over two decades, DFT methods now have become the workhorse in the electronic structure and mechanistic studies for chemical reactions involving the whole range of TMs, including 3d TMs,16,19-24 from which many efforts have been made by theoretical chemists to predict the important chemical and physical properties of the species involved in first-row transition metals. Despite that we now have enough confidence for the quality of the geometries calculated from DFT methods for TM-containing systems,25-29 their accurate energetic calculations are still an issue with much uncertainty, especially for 3d TMs.30-51 The large variations of the results often observed between different functionals and the lack of systematic approach to improve the accuracy for DFT methods also hinder our accumulation of knowledge for their performance in 3d TMs.

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Alternative to DFT methods, a useful type of ab initio methods, which are also black-box electronic structure method and hence free from the non-unique user-dependent computational settings of non-black-box methods like the active space in multireference methods, are coupled cluster (CC) methods. Two features make CC methods suitable to treat the very challenging 3d TM systems, one is the size-consistent, highly sophisticated, and efficient formalisms to account for dynamic electron correlation energy compared with the configuration interaction (CI) type methods, the other is the highly flexible and improvable form of wavefunction to treat the non-dynamic correlation energy. For example, through the CC series of CCSD, CCSDT, CCSDTQ, etc., with increasing level of excitations, systematic approaching to the full configuration interaction (FCI) limit is achieved, in which the multireference character is also treated in increasing level.52 As a result, CC methods are appealing in exploring the accuracy limit of the current ab initio methods for 3d TMs, especially for calibration purpose in relatively small systems. Among CC methods, CCSD(T) method is particularly well known and popular for its good balance between computational accuracy and cost, which leads to its wide applications in cases wherein the dynamic correlation but not the non-dynamic correlation dominates. In these systems, for example many closed-shell main group and 4d/5d TMs systems, in which the non-dynamic correlation is not severe, CCSD(T) method is considered to be quite reliable, often taken as “gold standard” in computational chemistry. However, for 3d TMs, for which non-dynamic correlation, multi-reference character, and near-degeneracy effects may play important role, it is quite unclear whether CCSD(T) is still accurate enough. In particular, for chemical reactions involving the 3d TMs, the knowledge about the effects of the following computational issues are currently lacking: (1) the convergence of one-electron basis sets (2) scalar relativistic effect; (3) 3s3p correlation effect; (4) iterative higher level of connected excitations over doubles in CC methods, i.e., the convergence of N-electron basis set. Without the knowledge about these issues, we can hardly know the reliability of the CCSD(T) method in 3d TM systems. Therefore, in this work, as a step towards more reliable ab initio calculations for 3d TMs, we selected nickel, a late 3d TM, to systematically explore these computational aspects related to the accuracy of the CCSD(T) calculations for 3d TMs. Four selected prototype oxidative addition σ-bond activations as shown in Scheme 1, for H-H/C-H/C-Cl/C-C bonds respectively, were under investigation. Their reaction barriers and reaction energies, as key kinetic and thermodynamic parameters respectively, are the two objects of our interests. These selected Ni(0)-promoted oxidative addition activations of H-H/C-H/C-Cl/C-C bonds have rich catalytic, mechanistic, and theoretical background of in chemistry. 11,53-60 These four prototypes can thus be viewed as the simplest model for a number of key σ-bond activation steps by the lowvalent late first-row transition metals. Specifically, for addressing the four ab initio computational issues outlined above, in this study we focus on the following investigations: (1) To check the basis set incompleteness error (BSIE), we did CCSD(T) calculations by employing various correlation-consistent basis sets up to augmented valence-split quintuple-ζ quality and extrapolated these data to the complete basis set (CBS) limit.61,62 (2) To evaluate the performance of the accelerated basis set convergence of explicitly correlated F12 method,63,64 which is an much less expensive alternative to the CBS extrapolation with conventional CCSD(T), we did CCSD(T)-F12b calculations and compared the results with the CCSD(T) data from very large basis set. (3) To determine the scalar relativistic effects on the calculated energetics, we tested the Douglas-KrollHess (DKH) Hamiltonian65,66 at the CCSD(T) level. (4) To critically evaluate the effect of higher-order connected excitations in CC methods beyond CCSD(T), we tested a hierarchy of CC

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schemes up to CCSDTQ for the smallest system in our study. From this series of CC methods along CCSD-CCSDT-CCSDTQ order, extrapolation to FCI limit estimate is possible. (5) To explore the outer-core-valence (3s3p) electron-correlation effects on the calculated energetics, we did corresponding 3s3p-correlated CCSD(T) calculations with the basis sets specially designed for this purpose, and also checked their basis set dependence. Finally, as an additional outcome of the scrutiny for the accuracy of ab initio CCSD(T) approach in 3d TM systems, we also tested the DFT performances of various commonly used functionals in these Ni(0)-mediated σ-bond activation processes by employing these ab initio calibrated data as reference. We hope this work will be helpful in the endeavor of establishing accurate and reliable computational treatment for reactions involving 3d TMs. Scheme 1. Four Selected Prototype σ-Bond (H-H/C-H/C-Cl/CC) Activations by Ni(0) Studied in This Work

COMPUTATIONAL DETAILS DFT calculations All DFT calculations were performed with Gaussian 09 program package.67 The geometries of reactant complex (RC), transition state (TS) and product complex (PC) were optimized in gas phase employing PBE0 functional with the cc-pVTZ68,69/ccpV(T+d)Z70 basis set for Ni,C,H/Cl, respectively. The identities of these stationary points were verified to have no imaginary frequency (for RC and PC) and one proper imaginary frequency (for TS). Based on these geometries, the single point DFT calculations by 18 selected functionals were done by using the aug-ccpVTZ68,69/aug-cc-pV(T+d)Z70 for Ni,C,H/Cl, respectively. The selected functionals cover a wide range, including the general gradient approximation (GGA) ones (BP8671, OLYP72,73), hybrid GGA ones (PBE074-76 B3LYP71-73,77), meta-GGA ones (M06-L78, TPSS79), hybrid meta-GGA ones (M0678,80, M06-2X78,80, BMK81, TPSSh79), long-range corrected hybrid GGA ones (LC-PBE82,83, CAM-B3LYP84, B97X85), range-separated hybrid meta-GGA one (M1186), nonseparable gradient approximation (NGA) one (N1287), range-separated hybrid NGA one (N12-SX88), and double hybrid GGA ones (B2-PLYP89, B2GP-PLYP90) Hereafter, (aug-)cc-pVXZ and (aug-)cc-pV(X+d)Z basis sets were all abbreviated as (A)XZ (X = D, T, Q, or 5). Furthermore, we tested the effect of Grimme’s DFT-D3 empirical dispersion correction with the original zero short-range damping scheme91,92 for those functionals with DFT-D3 parameters available. Since the B97X functional is not included in the DFT-D3 approach, instead we employed the corresponding B97XD functional with the empirical dispersion correction. For N12, N12-SX, and M11 that were


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recently developed without the DFT-D3 parameters, we cannot assess the effect of empirical dispersion correction. Ab initio CC calculations All ab initio single point calculations were done by employing the Molpro2010 package.93 In ab initio wavefunction methods, basis set convergence is usually slower than in DFT methods. Therefore it may require extrapolation to the CBS limit which is often useful for alleviating BSIE. The two-point CBS limit extrapolations for the total electronic energy of the valence-only correlated CCSD(T) calculations were done based on the (A)DZ(A)TZ, (A)TZ-(A)QZ, and (A)QZ-(A)5Z basis set pairs, using the formula in eq 1,94 wherein n is the cardinal number of the basis set (n = 2/3/4/5 for (A)DZ/(A)TZ/(A)QZ/(A)5Z). This formula was found to be relatively better than alternative extrapolation schemes.95 Unless otherwise specified, HF orbitals were used as reference for all the CC calculations. For C-Cl bond activation reaction (reaction 3 in Scheme 1), since HF reference has convergence problem and thus is unavailable, we employed DFT (PBE0) Kohn-Sham orbital as the reference for the CC calculations. Etotal,n = Etotal,CBS + A/(n+1/2)4

(1)

In explicitly correlated CCSD(T)-F12 calculations, we employed the CCSD(T)-F12b method with the diagonal fixed amplitude 3C(FIX) ansatz.96,97 All CCSD(T)-F12b calculations were performed with Molpro2010 using the ADZ and ATZ basis sets. Density fitting (DF) of the Fock and exchange matrices used the auxiliary basis sets of def2-AQZVPP/JKFIT98,99 for Ni, ccpVTZ/JKFIT100 for H, and aug-cc-pVTZ/JKFIT100,101 for the rest atoms. While the DF for the remaining two-electron integrals and resolution of the identity (RI) approximation employed aug-ccpVTZ/MP2FIT102 for Ni, cc-pVTZ/MP2FIT103 for H, and aug-ccpVTZ/MP2FIT103 for the rest atoms. The value of the geminal Slater exponent used is 1.4a0-1 for both the ADZ and ATZ basis sets in accord with previous investigations.104-106 For the twopoint CBS limit extrapolation of the CCSD(T)-F12b correlation energies from the ADZ-ATZ basis set pair, we employed the formula in eq 2 based on Schwenke’s scheme.62 The CCSD-F12b correlation energy and the perturbative triples contribution (T) were extrapolated separately, using the corresponding optimal parameters (pow) determined by Hill et al.107 for ADZ-ATZ basis set pair in CCSD(T)-F12b calculations. The CBS limit of the HF reference energy in the CCSD-(T)-F12b/CBS value was not obtained from extrapolation but was approximated by the SCF+CABS-singles energy108 calculated with the largest basis set (ATZ) used in CCSD(T)-F12b calculations. Of note is that for the C-Cl bond activation reaction (reaction 3 in Scheme 1), since the required HF reference is unavailable, we cannot carry out the corresponding CCSD(T)-F12b calculations. Ecorr,n = Ecorr,CBS + A/npow

(2)

To assess the scalar-relativistic effects, we used the DouglasKroll relativistic one-electron integrals with a second order Douglas-Kroll-Hess (DKH) Hamiltonian65,66 and employed aug-ccpVTZ-DK69,109 (denoted ATZ-DK) basis set for all atoms in CCSD(T) method. Except CCSD and CCSD(T), all higher-order CC calculations, including CCSDT, CCSDT(Q), and CCSDTQ methods, were performed with MRCC program110 interfaced to Molpro2010. Due to the extremely high computational cost of these methods, especially for CCSDTQ, many of these higherorder CC calculations are not feasible with large basis sets and molecules. Therefore, for these CC calculations, we only employed cc-pVDZ basis set for the smallest model of H-H activation reaction (reaction 1 in Scheme 1). Based on the CCSD,

CCSDT, and CCSDTQ series, an estimate of FCI limit was obtained by using a continued fraction (cf) extrapolation.111,112 The Ni 3s3p outer-core-valence electron-correlation correction was determined by the difference of two CCSD(T) single point calculations with and without 3s3p electrons correlated, using the same basis sets of cc-pwCVTZ69/cc-pVTZ (wTZ) and cc-pwCVQZ69/cc-pVQZ (wQZ) for Ni/rest atoms. Using these data, then two-point extrapolation to the CBS limit was performed on the basis of eq 3 proposed by Truhlar.113 The predetermined optimal parameter β (3.05) by Neese et al. was used with the cardinal number n = 3 and 4 for wTZ and wQZ basis sets.114 Ecorr,n = Ecorr,CBS + A/nβ

(3)

Combining the valence-only electron-correlation calculation and Ni 3s3p core-valence electron-correlation calculation, our final reference value of Efinal is the sum of these two parts as in eq 4, wherein Efinal was obtained from the valence-only correlated CCSD(T) calculations with AQZ-A5Z CBS limit extrapolation by eq 1, and E3s3p was obtained from CCSD(T) Ni 3s3p outercore-valence electron-correlation correction with wQZ-wQZ CBS limit extrapolation by eq 3. Efinal = ECBS + E3s3p

(4)

RESULTS AND DISCUSSION

Figure 1. Transition state geometries (bond distances labeled in Å) optimized at the PBE0/TZ level for the four selected oxidative addition reactions in Scheme 1 by Ni(0) for σ-bond activations of (1) HH in H2, (2) C-H in CH4, (3) C-Cl in CH3Cl, and (4) C-C in C2H6.

Activation energy (E‡) and reaction energy (ER) are the two central objects under study in this work. For the four selected prototype Ni(0)-promoted oxidative addition σ-bond activation reactions in Scheme 1, the DFT-optimized structures of the corresponding transition states with the key bond distances labeled are depicted in Figure 1. Based on these geometries, below we start to explore various computational issues related to the accuracy of the ab initio CC calculations.

Convergence of valence-correlated basis sets To investigate the convergence of valence-correlated basis set in CC calculations, we did CCSD(T) calculations using two series of correlation-consistent basis sets of DZ-TZ-QZ-5Z and ADZ-ATZ-AQZ-A5Z. The calculated E‡ and ER of reactions 1-4 are summarized in Table 1, and their convergence behaviors are also shown in Figure 2, along with the corresponding CBS limit extrapolation data.



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Table 1. CCSD(T)-calculated E‡ and ER (in kcal/mol) of Reactions 1-4 from Various Valence-Correlated Basis Sets and Their CBS Limitsa

E (1) ‡

E‡(2) E‡(3) E‡(4)

(A)DZ

(A)TZ

(A)QZ

(A)5Z

CBSD-Tb

CBST-Qc

CBSQ-5d

-0.07 (0.01) 7.70 (7.34) 11.45 (9.91) 12.41 (10.71)

0.67 (1.16) 5.83 (6.31) 9.47 (9.81) 11.43 (10.87)

1.29 (1.52) 5.58 (5.80) 9.64 (9.90) 11.36 (11.07)

1.55 (1.66) 5.45 (5.57) 9.85 (10.02) 11.18 (11.13)

0.93 (1.57) 5.18 (5.95) 8.78 (9.77) 11.09 (10.93)

1.65 (1.72) 5.43 (5.50) 9.73 (9.95) 11.32 (11.19)

1.76 (1.77) 5.35 (5.38) 10.02 (10.12) 11.04 (11.18)

ER(1)

-4.85 -2.77 -1.59 -1.09 -2.04 -0.91 -0.68 (-4.72) (-2.04) (-1.21) (-0.92) (-1.10) (-0.73) (-0.69) ER(2) -4.99 -5.35 -4.89 -4.66 -5.48 -4.62 -4.48 (-5.25) (-4.41) (-4.41) (-4.46) (-4.11) (-4.40) (-4.50) ER(3) -39.70 -39.27 -37.72 -36.76 -39.12 -36.83 -35.98 (-39.87) (-36.58) (-36.37) (-36.05) (-35.42) (-36.25) (-35.79) ER(4) -19.21 -17.40 -16.53 -16.30 -16.77 -16.02 -16.11 (-20.15) (-17.72) (-16.64) (-16.33) (-16.87) (-16.02) (-16.08) a Values in parentheses are from the corresponding augmented (A) basis sets. b CBS limit from (A)DZ-(A)TZ extrapolation. c CBS limit from (A)TZ-(A)QZ extrapolation. d CBS limit from (A)QZ-(A)5Z extrapolation.

1.65 1.76 0.93

-0.07

-1 -2 (A)DZ

(A)TZ (A)QZ

(A)5Z CBS(I) CBST-Q T-QCBS(III) Q-5 CBSD-T CBS CBSQ-5 D-T CBS(II)

7.7

7 7.34

6.31

6 5.83 5

-0.73 -0.68 -1.21 -0.92 -1.10 -0.69 -0.91 -1.09 -2.04 -1.59 -2.04

-2 -3

-2.77

-4

5.18

5.50 5.38 5.43

5.35

5.5

9.91 9

(A)DZ (A)TZ (A)QZ (A)5Z CBS(I) CBST-Q CBS(III) CBSD-T CBS(II) CBSQ-5

Ni+H2

9.77 9.95 10.02 9.73

9.85

(A)DZ (A)TZ (A)QZ (A)5Z CBS CBS(I) CBS(II)CBS(III) CBST-Q T-Q CBS CBSQ-5 Q-5 CBS D-T CBS D-T

(A)DZ (A)TZ (A)QZ (A)5Z CBS CBS(I) D-T CBST-Q CBS(III) CBSQ-5 Q-5 D-T CBS(II)

-2 -1.1 -3 -4 -5 -6

-4.4 -4.11 -4.40 -4.41 -4.41 -4.46 -4.48 -4.99 -4.62 -4.50 -4.5 -4.89 -4.66 -5.25 -5.35 -5.48

Ni+CH4

12 11 10

12.41 11.43 11.36 11.18 11.09 11.32 11.18 11.19 11.07 11.13 11.04 10.93 10.7110.87

9 (A)DZ (A)TZ (A)QZ (A)5Z CBS CBS(I) CBS(II) T-Q CBS(III) Q-5 D-T CBS CBSQ-5

-36

-36.58

-36.37

-37

-36.05

-35.42 -35.79 -36.25 -35.98

-36.76

-38 -39

Ni+C2H6

(4b)

XZ AXZ

-35

-40

(A)DZ (A)TZ (A)QZ (A)5Z CBS(I) CBST-QCBS(III) CBSQ-5 CBSD-T CBS(II)

13

Ni+CH3Cl

(3b)

XZ AXZ

-7

-4.85

9.47

9.64

XZ AXZ

14

8.78

-4.72 -5

10.02

9.81 9.90

10

Ni+CH4

ER(2)/kcal mol-1

0 -1

5.45

5.95

9.9 10.12

8

(2b)

XZ AXZ

5.58

5.57

11.45

11 5.8

4 Ni+H2

(1b)

5.80

12

E‡(4)/kcal mol-1

1.29 1.55

8

(4a)

XZ AXZ

13

-36.83

-39.7

-39.12

-39.27

-16 -17 -18

-37.72

(A)DZ (A)TZ (A)QZ (A)5Z CBS(I) CBSQ-5 CBSD-T CBS(II) CBST-QCBS(III)

Ni+CH3Cl

-16.53 -17.40 -19.21

-16.64

-16.30 -16.33

-16.02 -16.08 -16.77 -16.02 -16.11 -16.87

-17.72

-19 -20

-39.87

XZ AXZ

-15

ER(4)/kcal mol-1

0.67

0.01

1.66 1.57 1.72

(3a)

XZ AXZ

9


1.16 1

1.52

1.77



2

0

(2a)

XZ AXZ

3

ER(3)/kcal mol-1

1

(1a)

ER(1)/kcal mol-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

-20.15

(A)DZ (A)TZ (A)QZ (A)5Z CBS(I) CBST-QCBS(III) CBSD-T CBS(II) CBSQ-5

Ni+C2H6

Figure 2. The convergence behaviors of CCSD(T)-calculatedE‡ and ER (in kcal/mol) of reactions 1-4 with various valence-correlated basis sets and their CBS limit extrapolations.

From Figure 2, is can be seen that except the smallest (A)DZ basis set in some cases such as (2b) and (3a), along both two basis series of DZ-TZ-QZ-5Z and ADZ-ATZ-AQZ-A5Z, the calculated CCSD(T) energies exhibit fine monotonic convergence behavior with the increasing cardinal number. This simply guarantees that larger basis set gives closer results to the basis-converged ones. It is notable that augmented basis set (AXZ) is not always more accurate than the corresponding non-augmented one (XZ), as seen in (2a) and (4b) in Figure 2. CBS limit extrapolations, which were often used to alleviate BSIE, do improve the results. The CBS limit extrapolations based on (A)XZ-(A)(X+1)Z basis pair always give better results than the (A)(X+1)Z data before extrapolation, but with the similar exceptions of (A)DZ-(A)TZ CBS extrapolations in (2b) and (3a) of Figure 2 due to the abnormal results from (A)DZ basis. As a result, the triple-ζ basis set (A)TZ appears to be a minimum for a safe CBS extrapolation in CC calculations. Excluding the abnormal (A)DZ results mentioned above, the quality of (A)XZ-(A)(X+1)Z CBS extrapolation is often close to or even better than that from (A)(X+2)Z without extrapolation, such as in (1a) and (1b) of Figure 2. From Figure 2, of note is that the CBS limits from QZ-5Z

and AQZ-A5Z extrapolations are essentially identical, with their differences below 0.05 kcal/mol for almost all systems except reaction 3, for which the two CBS limits are also very small of only 0.1 and 0.2 kcal/mol for E‡ and ER, respectively, as seen in (3a) and (3b) in Figure 2. These results indicate that for basis set large enough (such as 5Z), augmented diffuse functions are not important any more and negligible. Hereafter, we take the highestlevel CBS(AQZ-A5Z) value as a reference for BSIE issue. Table 2 summarizes the mean absolute deviations (MADs) and maximum absolute deviations (MaxDs) of various basis sets for E‡ and ER. From the larger statistical deviations for ER than for E‡ in almost all cases, we can see apparently that ER is more difficult to model accurately than E‡. For E‡, (A)TZ alone already can produce MADs and MaxDs below ~1 kcal/mol. While if MADs and MaxDs below 1 kcal/mol for both E‡ and ER are required, we have to use basis set up to AQZ, or do CBS limit extrapolations based on ADZ-ATZ basis pair, with the latter being apparently more affordable. According to MADs and MaxDs, the performances of various basis sets follow this order (decreasing performance): CBSQ-5 > (A)5Z ≈ CBST-Q > (A)QZ >


-16.3 -17.4

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Table 2. Statistical Deviations (MAD and MaxD, in kcal/mol) of CCSD(T)-calculated E‡ and ER from the referencea (A)DZ (A)TZ (A)QZ (A)5Z CBSD-Tb CBST-Qc CBSQ-5d 1.68 0.61 0.34 0.14 0.62 0.18 0.07 MAD (1.10) (0.54) (0.25) (0.11) (0.34) (0.09) (0.00) E‡ 2.32 1.1 0.48 0.27 1.34 0.39 0.14 MaxD (1.96) (0.93) (0.42) (0.19) (0.57) (0.17) (0.00) 2.92 1.93 0.92 0.44 1.59 0.33 0.06 MAD (3.23) (0.97) (0.44) (0.20) (0.49) (0.17) (0.00) ER 4.16 3.48 1.93 0.97 3.33 1.04 0.19 MaxD (4.08) (1.64) (0.58) (0.26) (0.79) (0.46) (0.00) a Values in parentheses are from the corresponding augmented (A) basis sets, reference values are taken from CCSD(T)/CBS data based on AQZ-A5Z extrapolations. b CBS limit from (A)DZ-(A)TZ extrapolation. c CBS limit from (A)TZ-(A)QZ extrapolation. d CBS limit from (A)QZ-(A)5Z extrapolation. Table 3. E‡ and ER (in kcal/mol) Calculated at the CCSD(T)-F12b and CCSD(T) Level with ADZ and ATZ Basis Sets and the Corresponding CBS Limit Data E‡/CCSD(T)

Reaction

ER/CCSD(T)

ATZ

CBSD-T

ADZ

ATZ

CBSD-T

ADZ

ATZ

CBSD-T

ADZ

ATZ

CBSD-T

0.01

1.16

1.57

0.89

1.40

1.72

-4.72

-2.04

-1.10

-2.73

-1.17

-0.27

2

7.34

6.31

5.95

7.28

5.92

5.17

-5.25

-4.41

-4.11

-3.76

-4.19

-4.41

4

10.71

10.87

10.93

11.77

11.15

10.95

-20.15

-17.72

-16.87

-17.87

-16.83

-16.11

(2a)

1.52

1.57

1.72

1.77

0 0.01 -1

7.34

7 7.28

6.31 5.8

6

5.92

5.95 5.57

5

-2

5.5

13

5.38

12 11.77 11.15

11 10

5.17

A5Z CBS CBS(I) CBS(II)CBS(III) T-Q CBSQ-5 D-T D-T CBS Ni+H2

CCSD(T) CCSD(T)-F12b -1.17

0 -1

-1.21 -2.73

(2b)

-0.27

-0.92

-0.73

-0.69

-1.1

-2.04

-4 -5 -4.72

-3

AQZ

ADZ

A5Z CBS CBS(I) CBS(II)CBS(III) T-Q CBSQ-5 D-T CBS Ni+CH4

(3b)

-15

-3.76 -4.19 -4.41

-5

-4.11 -4.41

-4.46

-4.41

-4.4

-4.5

-5.25

AQZ

CBST-Q CBSQ-5 A5Z CBS CBS(I) D-T CBS(II)CBS(III) Ni+H2

-17

ATZ

AQZ

A5Z CBS(I) CBST-Q CBSQ-5 CBSD-TCBS(II)CBS(III) Ni+C2H6

-16.11

-16.83 -16.64

-17.87

-18

-16.02 -16.08

-16.33 -16.87

-17.72

-19 -20

-7 ATZ

10.95 11.07 11.13 10.93 11.19 11.18

CCSD(T) CCSD(T)-F12b

-16

-4

-6

ATZ


-2

-3

ADZ

ADZ

ER(4)kcal mol-1

AQZ

ER(2)/kcal mol-1

(1b)

ATZ

10.71 10.87

9

4 ADZ

-2

8


14 E‡(4)/kcal mol-1

1.16

1.66


1.72

1.4

(3a)


9

2 1 0.89

ER/CCSD(T)-F12b

ADZ


3 E‡(1)/kcal mol-1

E‡/CCSD(T)-F12b

1

(1a)

ER(1)/kcal mol-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

-21 ADZ

ATZ

AQZ

A5Z CBS CBS(I) CBST-Q CBSQ-5 D-T CBS(II)CBS(III) Ni+CH4

-20.15 ADZ

ATZ

AQZ

A5Z CBS CBS(I) CBST-Q CBSQ-5 D-T CBS(II)CBS(III) Ni+C2H6

Figure 3. E‡ and ER (in kcal/mol) of reactions 1, 2, and 4 calculated by CCSD(T)-F12b with ADZ and ATZ basis sets (and the CBS limit extrapolation thereof), in comparison to CCSD(T) results with various AXZ basis sets and CBS limit extrapolations.

CBSD-T > (A)TZ > (A)DZ. Statistically, augmented (A) basis set AXZ are always better than the corresponding non-augmented XZ one, with only one exception of MAD from ADZ for ER. Considering the small MaxD of 0.79 kcal/mol and acceptable computational cost, CBS(ADZ-ATZ) could be the level of choice for relatively large systems.

Performance of explicitly correlated F12 approach As a computationally efficient approximation, explicitly correlated F12 approach has often been found to greatly enhance the basis set convergence in CC methods,96,97,115-117 which makes it possible to use relatively small basis set to accurately treat the otherwise computationally unfeasible large systems. Therefore, it is interesting to know the performance of the explicitly correlated F12 approach for 3d TM systems with relatively small ADZ and

ATZ basis sets. In Table 3 and Figure 3, for all reactions except reaction 3 (due to unavailable HF reference), we listed E‡ and ER calculated at the CCSD(T)-F12b level with ADZ and ATZ basis sets, as well as the corresponding CBS limit extrapolations. The deviations, MADs, and MaxDs relative to the reference (CCSD(T)/CBS(AQZ-A5Z)) are collected in Tables 4 and 5 for E‡ and ER, respectively. In previous work for main group systems, results of CCSD(T)-F12b/AXZ (denoted as F12b/AXZ) were found to be able to improve the CCSD(T)/AXZ results by two in cardinal number, i.e., CCSD(T)-F12b with ADZ and ATZ basis sets can reach the AQZ and A5Z quality of the CCSD(T) results, respectively96,97. However, from Figure 3 to compare CCSD(T)-F12b with the conventional CCSD(T) method for our investigated 3d TM systems, the improvement to such an extent is true only in



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 13

Table 4. Deviations (D), MaxD, and MAD of E‡ (in kcal/mol) Calculated by CCSD(T)-F12b and Conventional CCSD(T) Methods from Referencea ADZ

ATZ

AQZ

A5Z

CBSD-T

CBST-Q

F12b/ADZ

F12b/ATZ

D(1) -1.76 -0.61 -0.25 -0.11 -0.20 -0.05 -0.88 -0.37 D(2) 1.96 0.93 0.42 0.19 0.57 0.12 1.90 0.54 D(4) -0.47 -0.31 -0.11 -0.05 -0.25 0.01 0.59 -0.03 MaxD 1.96 0.93 0.42 0.19 0.57 0.12 1.90 0.54 MAD 1.40 0.62 0.26 0.12 0.34 0.06 1.12 0.31 a Reference values are taken from CCSD(T)/CBS data based on AQZ-A5Z extrapolations.

F12b/CBSD-T -0.05 -0.21 -0.23 0.23 0.16

Table 5. Deviations (D), MaxD, and MAD of ER (in kcal/mol) Calculated by CCSD(T)-F12b and Conventional CCSD(T) Methods from Referencea ADZ

ATZ

AQZ

A5Z

CBSD-T

CBST-Q

F12b/ADZ

F12b/ATZ

D(1) -4.03 -1.35 -0.52 -0.23 -0.41 -0.04 -2.04 -0.48 D(2) -0.75 0.09 0.09 0.04 0.39 0.10 0.74 0.31 D(4) -4.07 -1.64 -0.56 -0.25 -0.79 0.06 -1.79 -0.75 MaxD 4.07 1.64 0.56 0.25 0.79 0.10 2.04 0.75 MAD 2.95 1.03 0.39 0.17 0.53 0.07 1.52 0.51 a Reference values are taken from CCSD(T)/CBS data based on AQZ-A5Z extrapolations.

F12b/CBSD-T 0.42 0.09 -0.03 0.42 0.18

Table 6. Nonrelativistic, Scalar Relativistic E‡ and ER (in kcal/mol), and Relativistic Corrections (E‡ and ER) Calculated by CCSD(T) Reaction

Nonrelativistic

Relativistic

Nonrelativistic

Relativistic

ER /ATZ

ER /ATZ-DK

ER

-2.04

-4.92

-2.88

E /ATZ

E /ATZ-DK

E

1

1.16

0.12

-1.05

2

6.31

5.01

-1.30

-4.41

-8.14

-3.73

3

9.52

9.91

0.38

-37.59

-40.42

-2.83

4

10.87

10.47

-0.40

-17.72

-21.71

-3.99

‡

‡

one example of reaction 4, i.e., result of F12b/ATZ for E‡, which is close to the quality of CCSD(T)/A5Z, as shown in (3a) of Figure 3. For most other cases in Figure 3, F12b/ADZ and F12b/ATZ are only better than CCSD(T)/ADZ and CCSD(T)/ATZ, respectively. This performance of F12 method can also be seen from the order of MADs (over reactions 1, 2, and 4, in kcal/mol) of the CCSD(T)-F12b and CCSD(T) results: (1) for E‡, 1.40 (ADZ) > 1.12 (F12b/ADZ) > 0.62 (ATZ) > 0.34 (CBSD-T) > 0.31 (F12b/ATZ) > 0.26 (AQZ) > 0.16 (F12b/CBSD-T) > 0.12 (A5Z) > 0.06 (CBST-Q); (2) for ER, 2.95 (ADZ) > 1.52 (F12b/ADZ) > 1.03 (ATZ) > 0.53 (CBSD-T) > 0.51 (F12b/ATZ) > 0.39 (AQZ) > 0.18 (F12b/CBSD-T) > 0.17 (A5Z) > 0.07 (CBST-Q). As also seen from this MAD sequence, CCSD(T)-F12b/CBS data based on ADZ-ATZ basis pair are better than CCSD(T)/AQZ, closer to the CCSD(T)/A5Z in quality, but less accurate than CCSD(T) at CBS(ATZ-AQZ) level. Considering the obviously better performance of F12b/CBSD-T over CBSD-T, and their comparable computational costs, F12b method at this level, which can reduce the MADs and MaxDs below 0.5 kcal/mol as shown in Tables 5 and 6, is certainly recommendable for replacing the conventional CCSD(T) method at CBS(ADZ-ATZ) level when HF reference is available.

Scalar relativistic effects As presented in Table 6, by using the second-order DKH Hamiltonian in CCSD(T) calculations, we have investigated the scalar-relativistic effects on E‡ and ER of reactions 1-4. The calculated relativistic contributions (E‡ and ER) to E‡ and ER indicate that the scalar-relativistic effects are generally

‡

smaller for the activation energy than for the reaction energy. The size of scalar-relativistic corrections are typically ~1 kcal/mol for E‡, but are about 2~4 kcal/mol for ER. Since scalar-relativistic effects are largely independent on electronic structure methods, it was not considered in all method comparisons in this work.

Convergence of high-order CC methods Recently, high-order CC methods have attracted considerable attentions in generating highly accurate interaction energies.118-123 However, due to its extremely high computational scaling,112 high-order CC method such as CCSDTQ can only be applied to the smallest TM model systems and atoms.124-127 Therefore, using high level CCSDTQ method to evaluate the performances of CCSD(T) method has been scarcely carried out for the TM complexes. In the four reactions under study, CCSDTQ is only feasible for reaction 1 of smallest model using our current computational resources. To check the reliability of CCSD(T) method in the Ni(0)-promoted -bond activation reactions, as presented in Table 7, we calculated E‡ and ER at CCSD, CCSD(T), CCSDT, CCSDT(Q), and CCSDTQ level with DZ basis set, and estimated the extrapolated FCI limit. In Figure 4, we plot calculated E‡ and ER of reaction 1 using these CC methods relative to their corresponding CCSDTQ values. It is clear that there exists good convergence along the hierarchy of CCSD-CCSDT-CCSDTQ levels. The estimated FCI limits are only 0.03 and 0.01 kcal/mol away from the CCSDTQ data for E‡ and ER, respectively. This indicates that taking CCSDTQ result as a benchmark is a reasonable choice.


Page 7 of 13

Table 7. E‡ and ER (in kcal/mol) of Reaction 1 Calculated with DZ Basis Sets at Various CC Levels. E‡

ER

CCSD

-3.30

-9.28

CCSD(T)

-0.07

-4.85

CCSDT

0.28

-1.80

CCSDT(Q)

-0.96

-2.75

CCSDTQ

0.39

-1.34

FCI

0.36

-1.35

(a) 2

‡ E‡-ECCSDTQ

0

-0.46 -2 -4

0

-0.11

-0.03

-1.35 -3.69

-6 -8 CCSD

CCSD(T)

CCSDT CCSDT(Q) CCSDTQ

FCI

Ni+H2

(b) 2 0

ER-ER,CCSDTQ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0

-0.46 -2

-0.01

-1.41

-4

-3.51

-6 -8

-7.94

CCSD

CCSD(T)

CCSDT CCSDT(Q) CCSDTQ

FCI

Ni+H2 Figure 4. E‡ and ER (in kcal/mol) of reaction 1 calculated by various CC methods with DZ basis set, relative to CCSDTQ value.

For CCSD(T) method, we can see that in E‡ calculation it is quite close to CCSDTQ reference by less than 0.5 kcal/mol. In ER calculation, however, the large difference of ~3.5 kcal/mol from CCSDTQ reference casts substantial doubt on the accuracy and reliability of CCSD(T). So this result indicates that the accuracy of “gold standard” CCSD(T) method could not be enough for the ER calculations of Ni(0)-promoted -bond activations. This is in line with the recent findings of other authors about the inadequate accuracy of CCSD(T) for bond dissociation energies in 3d TM systems.44 Notably, the computationally more expensive CCSDT(Q) method performs worse than CCSDT, and in E‡ case even worse than CCSD(T), which hardly makes CCSDT(Q) a sound method of choice. Interestingly, among CCSD(T), CCSDT, and CCSDT(Q), CCSDT is the most accurate one, which is only inferior to the much more expensive CCSDTQ method. Before we close this CC section, it is necessary to point out that due to the closed-shell character of the Ni(0) systems under study (Table S1 in the SI), the implications herein might not be applicable to openshell 3d TM systems with substantial multi-reference character.

Outer-core-valence 3s3p electron correlation effects In Table 8 we listed the CCSD(T) results of outer-corevalence 3s3p electron correlation effects on E‡ and ER via two

consecutive basis sets wTZ and wQZ, and the CBS limits extrapolated thereby. It can be seen that in many cases, Ni 3s3p electron correlation is substantially affected by BSIE, which necessitates the CBS limit extrapolation adopted here. For instance, the sign of the 3s3p electron correlation corrections for ER (ER,3s3p) are reversed from wTZ to CBS(wTZ-wQZ) levels for reactions 1, 3, and 4, whereby the values of ER,3s3p are changed by as large as ~1 kcal/mol. As seen in Table 8, at our highest CBS(wTZ-wQZ) level, the largest magnitudes of 3s3p electron correlation effects for E‡ and ER (E‡3s3p and ER,3s3p) both come from reaction 2, which are -1.01 and -0.65 kcal/mol, respectively. Notably, this size of 3s3p correlation effect by Ni(0) is comparable to the corresponding 5s5p correlation CCSD(T) computational data in C-H activation by Pt(0), the congener of Ni.128

DFT calibration Since DFT methods currently are the most widely used theoretical modeling approach for chemical reactions involving 3d TMs, it would be helpful to know their performances for selecting a better approximate functional from the various commonly used ones. Taking the high level reference values (E‡final) in Table 8, which were obtained from the CCSD(T)/CBS(AQZ-A5Z) level for valence electron correlation combined with Ni 3s3p corevalence correlation at the CCSD(T)/CBS(wTZ-wQZ) level, we try to figure out which DFT method performs best for these four Ni(0)-promoted reactions. Due to the possible relatively large error of CCSD(T) method in ER calculations, we only consider E‡ for the DFT calibration below. Without DFT empirical dispersion correction, the deviations of DFT-computed E‡ from the references are summarized in Table 9 and shown in Figure 5a. As seen from Table 9, among all 18 tested functionals, the magnitudes of MADs span a range from ~1 kcal/mol to ~4 kcal/mol, with the smallest MAD of 1.27 kcal/mol from PBE0 and the largest MAD of 3.79 kcal/mol from B2GP-PLYP. There are ten MADs below 2 kcal/mol, in the increasing order of PBE0 < CAM-B3LYP < M11 < N12-SX < OLYP < B3LYP ≈ LC-PBE < B97X < N12 < TPSSh. Among them, PBE0, CAM-B3LYP, M11, and N12-SX give the better performance than the others, with their MADs below 1.5 kcal/mol. The two tested double-hybrid functionals (B2GP-PLYP and B2PLYP) perform worst, with B2GP-PLYP generating the only MUD value larger than 3 kcal/mol. This is in line with the extremely poor performance of double-hybrid meta-GGA levels in nickel-containing molecules.38,129 From the mean signed deviations (MSD) in Table 9 and Figure 5a (red bar), it can be seen that pure-GGA functionals BP86, OLYP, and TPSS systematically underestimate E‡ (MAD and MSD with opposite signs and equal magnitudes), whereas B97X systematically overestimates E‡. Except these functionals, all other ones do not show systematic error so that they can both overestimate and underestimate E‡ of the four reactions under study. After inclusion of DFT empirical dispersion corrections, the deviations of DFT-computed E‡ by 15 functionals (M11, N12, and N12-SX are not included in the DFT-D3 approach) are summarized in Table 10 and shown in Figure 5b. As shown in Figure 5, generally the changes of MUDs after adding the DFT empirical dispersion correction are quite small, probably due to the fact that no bulky ligands are involved. This result also implies that DFT empirical dispersion correction is not the central issue for improving the performance of DFT methods for 3d TM systems. Two exceptions of relatively large changes in MUDs are the largest decrease with B97XD by 0.41 kcal/mol and the largest increase with OLYP-D3 by 0.74 kcal/mol. With the empirical dispersion correction, the functionals with MUD less than 2 kcal/mol are in this MUD-increasing order of B97X < PBE0 < CAM-B3LYP < LC-PBE < B3LYP < TPSSh, with the first three functionals having best performances by bearing MUDs below 1.5 kcal/mol.



Table 8. 3s3p Outer-core-valence Electron Correlation Corrections and Corrected E‡ and ER (in kcal/mol) Calculated by CCSD(T) method. Reaction

E‡3s3p wTZ

E‡3s3p wQZ

E‡3s3p CBS

E‡CBS (AQZ-A5Z)

E‡final

ER,3s3p wTZ

ER,3s3p wQZ

ER,3s3p CBS

ER,CBS (AQZ-A5Z)

ER,final

1 2 3 4

-0.43 -0.67 -0.06 -0.04

-0.19 -0.87 -0.11 -0.01

-0.02 -1.01 -0.15 0.01

1.77 4.37 9.97 11.19

1.75 4.37 9.95 11.20

-0.71 -0.91 -0.37 -0.91

-0.17 -0.76 0.05 -0.30

0.21 -0.65 0.36 0.13

-0.69 -4.50 -35.79 -16.08

-0.48 -5.15 -35.43 -15.95

Table 9. Deviations (D), MAD, and MSD of DFT-computed E‡ (in kcal/mol) without DFT empirical dispersion correction from the Reference CC Data E‡final. B2GP-

B2-

CAM-

M06

M06

PLYP

PLYP

B3LYP

BMK

BP86

B3LYP

-2X

-L

M06

OLYP

PBE0

TPSSh

TPSS

B97X

LC-PBE

M11

N12

SX

D(1)

-1.13

-0.78

-0.84

-1.29

-1.78

-0.50

-0.54

-1.37

0.83

-0.96

-1.06

-1.82

-2.07

0.07

-0.34

-1.93

-0.24

-1.52

D(2)

8.59

7.02

2.36

5.02

-1.33

3.62

7.07

1.96

4.91

-0.46

2.02

0.02

-1.36

4.68

3.16

1.20

1.07

1.62

D(3)

3.98

2.90

0.21

-0.57

-1.88

0.52

-0.61

-2.00

-1.60

-0.32

-0.61

-1.58

-2.22

0.86

0.47

-1.02

-2.54

-0.65

D(4)

1.46

0.29

-3.01

-2.64

-4.90

-0.51

-1.69

-2.77

-1.91

-4.58

-1.40

-3.96

-5.35

1.14

2.46

-1.09

-3.47

-1.91

MSD

3.23

2.36

-0.32

0.13

-2.47

0.78

1.06

-1.04

0.56

-1.58

-0.27

-1.83

-2.75

1.69

1.44

-0.71

-1.30

-0.61

MAD

3.79

2.75

1.60

2.38

2.47

1.29

2.48

2.03

2.31

1.58

1.27

1.84

2.75

1.69

1.61

1.31

1.83

1.42

N12-

Table 10. Deviations (D), MAD, and MSD of DFT-computed E‡ (in kcal/mol) with DFT empirical dispersion correction from the Reference CC Data E‡final. B2GP-

B2-

CAM-

M06

M06

PLYP

PLYP

B3LYP

BMK

BP86

B3LYP

-2X

-L

M06

OLYP

PBE0

TPSSh

TPSS

B97X

PBE

D(1)

-1.13

-0.78

-0.83

-1.29

-1.78

-0.50

-0.54

-1.37

0.83

-0.93

-1.06

-1.80

-2.07

-0.44

-0.33

D(2)

8.58

7.01

2.35

5.00

-1.31

3.61

7.07

1.97

4.92

-1.60

2.02

0.10

-1.34

3.77

3.16

D(3)

3.90

2.81

0.11

-0.85

-2.01

0.44

-0.59

-1.97

-1.50

-1.19

-0.62

-1.34

-2.25

0.41

0.39

D(4)

1.42

0.24

-3.07

-2.74

-4.89

-0.58

-1.70

-2.77

-1.92

-5.55

-1.44

-4.14

-5.33

-0.37

2.39

MSD

3.19

2.32

-0.36

0.03

-2.50

0.74

1.06

-1.04

0.58

-2.32

-0.28

-1.80

-2.75

0.84

1.40

MAD

3.76

2.71

1.59

2.47

2.50

1.28

2.48

2.02

2.29

2.32

1.29

1.84

2.75

1.25

1.57

(b) 5

B97X

LC-PBE

PBE0

M06

M06-2X

BMK

M06-L

TPSSh

TPSS

-4

OLYP

-3

CAM-B3LYP

-2

B3LYP

-1

B2-PLYP

B97X TPSS

-4

TPSSh

-3

OLYP

-2

N12-SX

0 M11 N12

0 LC-PBE

1

PBE0

1

M06

2

M06-L

2

BMK

3

BP86 CAM-B3LYP M06-2X

3

-1

MSD DFT D3(0) MUD DFT D3(0) MAD

4

BP86

MSD DFT MAD MUD DFT

4

LC-

B2GP-PLYP

(a) 5

B2GP-PLYP B2-PLYP B3LYP

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-5

-5

Figure 5. Statistical deviations (MAD, MSD, in kcal/mol) of calculated E‡ of reactions 1-4 by various DFT methods (a) without and (b) with DFT empirical dispersion correction, taking E‡final as reference.

Overall, considering both with and without empirical dispersion correction, PBE0 and CAM-B3LYP are recommendable for reaction barrier calculations of σ-bond activations by low-valent Ni. With empirical dispersion correction included, B97XD is also recommended. Interestingly, the good performance of PBE0 found here is consistent with the previous work of Martin et al. on σ-bond activations by Pd(0),130 and of Grimme et al. on similar

bond activations by Ni(0) and Pd (0),129 as well as our own work on C-H activation by Pt(0),131 all of which are group 10 TMs.


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CONCLUSIONS

ASSOCIATED CONTENT

In this study, to know how accurately we can model closed-shell oxidative addition reactions mediated by low-valent late 3d transition metals, we theoretically investigated the Ni(0)-promoted σbond activations of H-H, C-H, C-Cl, and C-C bonds. Our systematic investigation of activation energy (E‡) and reaction energy (ER) mainly focuses on ab initio coupled cluster (CC) methods (in particular CCSD(T)) and DFT methods, which covers many accuracy-related computational issues including: (a) convergence of one-electron and N-electron basis sets, (b) accuracy of the explicitly correlated F12 method, (c) the scalar relativistic effects, (d) outer-core-valence (3s3p) electron-correlation effects, (e) DFT calibration. Our key discoveries are as follows. (1) Except the smallest double-ζ (A)DZ basis set in some cases, good one-electron basis set convergence behaviors were observed for both E‡ and ER of all reactions along the (A)DZ(A)TZ-(A)QZ-(A)5Z basis set series in valence-correlated CCSD(T) calculations. Unless using very large basis set like 5Z, augmented (A) diffuse functions are important to improve the convergence of correlation consistent basis set, especially in CBS limit extrapolation. Considering balance between the good basis set convergence to below 1 kcal/mol and computational cost, CBS limit extrapolated from ADZ-ATZ basis pair can be recommended for the relatively larger systems of 3d TMs. (2) Compared to the conventional CCSD(T) method, the explicitly correlated CCSD(T)-F12 method can accelerate the convergence of one-electron basis set, albeit to a less extent in our 3d TM systems than that reported before for main group elements.93,94 As an more accurate alternative to the CBS(ADZ-ATZ) level of conventional CCSD(T) method, CCSD(T)F12b/CBS(ADZ-ATZ) level with comparable computational cost is recommended for larger systems, since it performs better than the more expensive conventional CCSD(T)/AQZ level, and reaches an accuracy close to the conventional CCSD(T)/A5Z level. (3) The scalar-relativistic effects are generally smaller for E‡ than for ER. Typically, the size of scalar-relativistic corrections are ~1 kcal/mol for E‡, but are about 2~4 kcal/mol for ER. The outer-core (3s3p) electron-correlation effects are usually not large for E‡ and ER, being as large as ~1 kcal/mol. However, their basis set dependence is significant to change the signs of the 3s3p correlation corrections in some cases, which necessitates additional basis set convergence consideration like the CBS limit extrapolation. In general, the scalar-relativistic and 3s3p correlation effects should be considered if chemical accuracy is required. (4) For N-electron basis set convergence issue, our testing calculations on Ni(0)-promoted H-H bond activation employing a series of CC schemes show good convergence along the hierarchy CC levels of CCSD-CCSDT-CCSDTQ line. CCSDTQ is extremely close to the estimated FCI limit and hence can serve as a benchmark. CCSD(T) is quite accurate in E‡ calculation by having deviation of less than 0.5 kcal/mol from CCSDTQ reference, but its ER calculations is less reliable, with deviation of more than 3 kcal/mol. For improving the accuracy, CCSDT performs better than more expensive CCSDT(Q), which is not recommended. (5) Using the more reliable CCSD(T) references of E‡ from our highest level treatments of valence-only and 3s3p corevalence correlations, the best performing DFT functionals from the 18 tested ones are PBE0 and CAM-B3LYP, generally with and without DFT empirical dispersion correction. With empirical dispersion correction included, B97XD is also recommendable.

Supporting Information Two tables, and Cartesian coordinates of all the optimized structures. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Author Contributions §L.H.

and K.C. contributed equally.

Notes The authors declare no competing financial interests.

ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (NSFC, Nos. 21473215, 21290194, 21221002), and Institute of Chemistry, Chinese Academy of Sciences.

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