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Comprehensive thermochemical benchmark set of realistic closed-shell metal organic reactions Sebastian Dohm, Andreas Hansen, Marc Steinmetz, Stefan Grimme, and Marek P. Checinski J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.7b01183 • Publication Date (Web): 22 Mar 2018 Downloaded from http://pubs.acs.org on March 26, 2018

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Journal of Chemical Theory and Computation

Comprehensive thermochemical benchmark set of realistic closed-shell metal organic reactions Sebastian Dohm[a], Andreas Hansen[a]*, Marc Steinmetz,[a] Stefan Grimme, [a] and Marek P. Checinski[b]*

[a] Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, Universität Bonn, Beringstraße 4, 53115 Bonn, Germany [b] CreativeQuantum GmbH, Am Studio 2, 12489 Berlin, Germany

KEYWORDS: thermochemistry benchmark, organometallic reactions, density functional theory, London dispersion interaction, local coupled cluster

ACS Paragon Plus Environment

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ABSTRACT

We introduce the new MOR41 benchmark set consisting of 41 closed-shell organometallic reactions resembling many important chemical transformations commonly used in transition metal chemistry and catalysis. It includes significantly larger molecules than presented in other transition metal test sets and covers a broad range of bonding motifs. Recent progress in linearscaling

coupled

cluster

theory

allowed

for

the

calculation

of

accurate

DLPNO-CCSD(T)/CBS(def2-TZVPP/def2-QZVPP) reference energies for 3d,4d,5d-transition metal compounds with up to 120 atoms. Furthermore, 41 density functionals, including seven GGAs, three meta-GGAs, 14 hybrid functionals, and 17 double-hybrid functionals combined with two different London dispersion corrections are benchmarked with respect to their performance for the newly compiled MOR41 reaction energies. A few wavefunction-based post-HF methods as, e.g., MP2 or RPA with similar computational demands are also tested and in total, 90 methods were considered. The double-hybrid functional PWPB95-D3(BJ) outperformed all other assessed methods with an MAD of 1.9 kcal/mol, followed by the hybrids ωB97X-V (2.2 kcal/mol), and mPW1B95-D3(BJ) (2.4 kcal/mol). The popular PBE0-D3(BJ) hybrid also performs well (2.8 kcal/mol). Within the meta-GGA class, the recently published SCAN-D3(BJ) functional as well as TPSS-D3(BJ) perform best (MAD of 3.2 and 3.3 kcal/mol, respectively). Many popular methods like BP86-D3(BJ) (4.9 kcal/mol) or B3LYP-D3(BJ) (4.9 kcal/mol) provide significantly worse reaction energies and are not recommended for organometallic thermochemistry considering the availability of better methods with the same computational cost. The results regarding the performance of different functional approximations are consistent with conclusions from previous main-group thermochemistry benchmark studies.


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Introduction

The application of quantum chemical methods to experimental, “real-life” chemical problems has become standard nowadays. Currently, Kohn-Sham Density Functional Theory (DFT)1, with its vast number of different functional approximations is the most widely used electronic structure method while coupled cluster theory with singles, doubles and perturbative triples excitations (CCSD(T)) is still the method of choice when high accuracy is needed. Within the last decade, substantial improvements have been achieved in reducing the high computational demands of CCSD(T) as, e.g., the development of the pair natural orbital based local coupled cluster methods.2,3 Moreover, with the rapid development of increasingly improved density functional approximations (DFAs) and the simultaneous growth of computing power, calculations are possible nowadays which have been unthinkable a decade ago in terms of accuracy and computing time. Particularly, the introduction of double-hybrid density functional (DHDF) methods4 led to an accuracy that could before only be reached by higher-level wavefunction (WF) based methods while the computational effort is still small enough for routine calculations of molecules with more than a hundred atoms. This situation creates a new challenge for the developer of benchmark sets, since in order to assess the accuracy of modern DFAs in a decent way, it is necessary to provide reference values for large molecules that reliably have a higher accuracy than the methods to be evaluated. Hence, it is important to approach the complete basis set limit (CBS) as close as possible when calculating reference values using e.g. the CCSD(T) method. Fortunately, local coupled-cluster methods as, e.g., the DLPNO-CCSD(T)3,55 make it possible to apply large basis sets, also for calculations on molecules with 100 atoms and more.


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Even for experienced computer chemists it is often a difficult task to assess which electronic structure method is suitable for a specific problem. The question if the chosen method will lead to the desired accuracy is crucial and can often only be achieved by the knowledge gained from appropriate benchmark studies. Frequently used benchmark sets, as, e.g., provided in the GMTKN555 meta-database, exclusively consist of molecules formed by main group elements. Transition metal test sets are rare and the included molecules are typically small. Moreover, many of the existing transition metal benchmark sets assess quantities as, e.g., bond dissociation energies of diatomic molecules,6 which do not adequately resemble typical organometallic chemistry. For example, Furche and Perdew presented a database containing 3d transition metals, which includes reaction energies6 but mostly of pure inorganic reactions as, e.g., the dissociation of the chromium dimer. Other comparable benchmark studies are restricted to only a few representative systems of smaller size. One important work improving this situation was published in 2005 by Martin and co-workers7 where various DFAs were tested on prototype reactions of Pd complexes with up to nine atoms, namely C-H and C-C bond activation reactions. Concerning the calculation of accurate reference reaction energies, they concluded that CCSD(T) is the minimum acceptable level of theory. A follow-up study of Ni and Pd complexes was conducted by Grimme and Steinmetz in 2013, 8 including also four DHDFs which were not available yet in 2005. The obtained results were consistent with those published by Martin et al.7 Up to now, the most recent and comprehensive benchmark for transition metal systems is the ccCATM/11 test set published by Wilson et. al. 9 It consists of 225 first row (3d) transition metal compounds ranging from the monohydrides to medium sized organometallics such as Sc(C5H5)3. Köhn and co-workers recently demonstrated how to arrive at accurate benchmark values for small transition metal compounds.10 The authors conducted state-of-the-art accuracy coupled


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cluster calculations close to the basis set limit including relativistic effects and multi-reference treatment. However, the study included only diatomic species and the presented methodology is not applicable to significantly larger systems of real chemical interest. As already mentioned, one way to reduce the high computational cost is to use local coupled cluster methods. The applicability of this approach to metal-organic chemistry was already demonstrated by Yao and Chen11 for 13 organometallic reactions of medium size (up to 36 atoms). Large organometallic compounds including late transition metals routinely used in homogeneous catalysis are for example included in the WCCR10 database by Reiher and coworkers.12 It consists of 10 reactions with molecules of up to 174 atoms. In the original work, only experimental reference values of partially questionable accuracy are available for the WCCR10 test set. However, this issue was resolved in a new study, which has just been completed.13 In the latter, results of local coupled-cluster and multi-reference calculations are presented, revealing the inaccuracy of the previous experimental values. These new reference values improve the WCCR10 test set to a valuable benchmark for organometallic chemistry involving larger ligands, although only ten reactions are considered. For transition metal complexes with large organic ligands typically used in organometallic chemistry, long-range London dispersion interactions become significant15. Modern quantum chemical methods as, i.e., dispersion corrected DFT (DFT-D) coupled to modern DFAs, can be used in principle in this context. The question, however, which approximation from the huge “zoo” of DFA is particularly well suited to solve transition metal related chemical problems is hard to predict presently and comprehensive benchmarking is lacking in our opinion. Nevertheless, DFT-D is already routinely applied to give additional insight into reaction


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mechanisms and underline experimental findings14,15 or make even predictions for, e.g., more efficient catalysts.16 Here we introduce a benchmark set of 41 newly compiled organometallic reactions termed MOR41. It contains significantly larger molecules than in existing compilations and moreover 13 different 3d-5d transition metals. Various common transition metal chemistry reaction motifs like complexation reactions, oxidative additions, or ligand exchanges are covered. All species are closed-shell (and neutral) to eliminate multi-reference, basis set, and convergence issues as far as possible, and to be able to conduct reliable coupled cluster reference calculations. After describing the technical details of the calculations in the next section, the test set is introduced and explained in detail. Subsequently, the generation of accurate reference reaction energies is discussed. Finally, a variety of different density functionals are benchmarked on the MOR41 set, including well known and established DFAs like PBE017 and B3LYP18,19, but also modern, state-of-the-art functionals like SCAN20,21 or ωB97X-V.22 Several MP2 based wave function methods and RPA are tested as well.

Computational details Most of the DFT calculations were performed with the ORCA quantum chemistry package, version 3.0.323,24, except for the calculation of the DHDF, which were performed with ORCA version 4.0.025 to be consistent with the frozen-core treatment of the reference calculations. The Ahlrichs’-type quadruple-ζ def2-QZVPP26 basis set was used in combination with the Stuttgart/Dresden effective core potentials SD(28, MWB) and SD(60, MWB) (and matching ECP basis sets) for 4d and 5d systems,27 respectively, both obtained from the TURBOMOLE basis set library.28 Further relativistic effects not covered through ECPs are neglected. In case of


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PWRB9529 which employs RPA correlation, a modified version of TURBOMOLE 5.730 (ridft) in combination with TURBOMOLE 7.0.2 (rirpa) was employed. The calculations with the SCAN functional were carried out using TURBOMOLE 7.2-beta3. The geometries used in this benchmark

study were optimized with TURBOMOLE

7.0.2 at the TPSS-D3(BJ)

/def2-TZVP31,42,32 level of theory. The post-Hartree-Fock wavefunction methods utilized in this work are second-order Møller-Plesset perturbation theory (MP2), spin-component scaled (SCS/SOS-)MP2,33,34 and the random-phase-approximation

(RPA).35,36,37

These

computations

were

performed

with

TURBOMOLE 7.0.2.38, also employing the Ahlrichs’-type quadruple-ζ def2-QZVPP39 basis set in combination with the Stuttgart/Dresden effective core potentials for 4d/5d systems. All MP2 calculations including the MP2 part in DHDFs as well as the RPA calculations were performed using the frozen-core approximation (see the SI (Table S7) for details on the number of correlated electrons). Calculations with ORCA were converged with “TightSCF” convergence criteria (10-8 Eh total energy change between two SCF cycles), all TURBOMOLE calculations were converged to 10-7 Eh. The composite low-cost DFT-D methods B97-3c40 and PBEh-3c41 were applied as implemented in ORCA 4.0.0. All other tested DFAs were assessed with the D342 London dispersion correction in the Becke-Johnson scheme43,44 and/or the non-local (NL) density-dependent NL (VV1045,46) treatment in a non-self-consistent form, while for ωB97X-V22, the latter dispersion correction is employed self consistently. The D3 method was applied using either the standalone implementation DFTD347 or the implementation in ORCA, which was also used to calculate the NL correction. For the DOD- and DSD-DHDFs, D3 parameters were explicitly given in the


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ORCA input file. A table with the used parameters can be found in the SI (Table S12). A list of the tested DFAs is given in Table 1. For all (meta)-generalized gradient approximation (GGA) type functional, the resolution of the identity (RI-J) approximation48 was used. For all methods containing non-local Fock-exchange, the RI-approximation was also applied to the exchange part49,50 (RI-JK). For all methods with perturbative (MP2) treatment, RI was also applied in the correlation treatment.

51

The

corresponding auxiliary basis sets52,53,54 were applied as implemented in ORCA 4.0.0 and TURBOMOLE 7.0.2. Reference values for the non-relativistic, pure electronic (vibrational zero-point energy exclusive) reaction energies were calculated using DLPNO-CCSD(T)3 in its sparse maps implementation55 as available in ORCA 4.0.0 with the TightPNO56 settings and the ORCA TightSCF convergence criteria for the HF energy. A complete basis set (CBS) extrapolation using the scheme proposed by Neese and Valeev57 based on the def2-TZVPP and def2-QZVPP basis sets was carried out. The corresponding auxiliary basis sets def2-TZVPP/C and def2-QZVPP/C were employed for the DLPNO-CCSD(T) calculations. The canonical CCSD(T) aug-cc-pwCVTZ58 calculations performed for reaction (5) were also done with ORCA 4.0.0. In these calculations, all except the two 1s electrons of the manganese atoms were correlated. For all other reference calculations, the same frozen core settings and ECPs were used as describe above for the MP2-based methods (see the SI Table (7) for details).


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Table 1 All tested DFAs and dispersion correction combinations. Functional GGA B97-D BLYP BP86 mPWLYP PBE revPBE RPBE meta-GGA M06L SCAN TPSS Hybrid B1B95 B3LYP B3PW91 BHLYP CAM-B3LYP M06 M06-2X mPW1B95 PBE0 PW6B95 TPSS0 TPSSh ωB97X ωB97X-V

D3 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

NL

Reference

✓ ✓ ✓

59 60 60,61 62 63 64 65

✓

70 20 31

✓

✓ ✓

✓ ✓ ✓ ✓ a

✓

66 18,19 67 68 69 70 70 71 17 72

Functional DHDF B2GP-PLYP B2-PLYP DSD-BLYP DSD-PBEPBE DSD-PBEB95 DSD-PBEP86 DSD-SVWN DOD-PBEB95 DOD-PBEP86 DOD-PBEPBE DOD-BLYP DOD-SVWN mPW2-PLYP PBE0-2 PBE0-DH PWPB95 PWRB95

D3 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

NL

✓

Reference 74 75 76,77,78 76,77,78 76,77,78 76,77,78 76,77,78 76 76 76 76 76

✓ ✓

75 29

a) NL dispersion correction implemented selfconsistently (scNL).

73 22 22


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Description of the MOR41 set The composition of the test set aims at typical organometallic reactions including larger transition metal compounds of similar complexity, i.e., no open-shell, charged and multireference systems are included. We arrived (after considering more than 120 candidate reactions) at a statistically well-balanced set containing 41 exemplary reactions featuring typical organometallic bonding motifs. The average system size is about 33 atoms per molecule with the largest system consisting of 120 atoms. The transition metal complexes were selected with an emphasis on metals often used in catalytic processes. The chemical structures and reactions for the complete set are shown in Figure 1. It includes 10 reactions containing 3d elements (Ti, Cr, Mn, Fe, Co, Ni), 21 reactions containing 4d elements (Mo, Ru, Rh, Pd), and 10 reactions containing 5d elements (W, Ir, Pt). It covers a wide range of reaction motifs, e.g., σ-donative complexation (1-9, 16, 24, 25), π-acceptor complexation (12-14), oxidative additions (10, 11, 1723), and ligand exchange reactions (26-38). Also some other reaction types are included as an insertion reaction (15), a ring opening metathesis reaction (41), a dimerization (39), and a simplified version of the formation of Tebbes reagent79 (40). The respective reaction energies vary from 27.0 kcal/mol (11) to -65.8 kcal/mol (40) with the smallest value on an absolute scale being -1.9 kcal/mol (32). The average reaction energy is -30.0 kcal/mol. To eliminate difficulties due to static electron correlation effects, only such reactions were included for which all involved molecules are closed-shell and single-reference cases. The fractional occupation number weighted density (FOD)80,

81

as well as the T182 diagnostics was calculated for all

molecules to check for pathological cases and to ensure reliable reference calculations without significant multi-reference character. The maximum T1 value was observed for the reactant of reaction (15) ([Ni(allyl)2]) with T1 = 0.04, which is below the critical value of 0.05. The FOD


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plots were carefully analyzed, also indicating no significant multi-reference character (see the SI for further details, Fig. S2). Furthermore, an investigation of ground state multiplicities for all molecules of the MOR41 test set did not reveal energetically close open-shell states (see the SI for details). This even holds for molecules that are known to have low lying triplet states83 as e.g., ED02, because all geometries are optimized in the singlet state, and the triplet state is thereby disfavored. The Cartesian coordinates for all systems as well as all reference values are listed in the SI (Table S1) and can be downloaded from the MOR41 web-site.84 Figure 2 shows the mean average deviation (MAD) from the reference reaction energies averaged over all tested methods for each of the 41 reactions in order to reveal, whether specific reactions are particularly challenging. The spread of the average error lies within a 2σ (σ being the standard deviation) confidence interval thus showing that the MOR41 set is well balanced with reliable reference values and that most tested methods perform reasonable on this benchmark. The two reactions with large average MADs, i.e., worse results for many DFA, are number (25) and (38). The absolute reaction energy for reaction (38) is comparatively large (62.6 kcal/mol), whereas reaction (25) is primarily dispersion driven. For the latter, the average error reduces to 3.5 kcal/mol when averaging over disperion corrected methods only. For a few other reactions many tested DFAs yield larger deviations from the reference value. For the reactions (5), (15), (32), (37), and (41), large mean-absolute relative errors of >50% are observed. This is mostly due to a small reaction energy on an absolute scale (∆ER(5) = 3.7 kcal/mol,

∆ER(15) = 4.1 kcal/mol, ∆ER(32) = -1.9 kcal/mol, and ∆ER(41) = 3.2

kcal/mol). Reaction (37) is a difficult case for most DFAs without Fock exchange as will be discussed below.


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Figure 1 The transition metal reactions included in the MOR41 test set. Their respective reference reaction energy in kcal/mol is depicted below the reaction arrow. All values are obtained at the DLPNO-CCSD(T)/TightPNO/CBS(def2-TZVPP/def2-QZVPP) level of theory except for reaction (5), where the reference value is calculated at the CCSD(T)/aug-cc-pwCVTZ level of theory.


13


12 σ-donor π-acceptor

oxidative addition ligand exchange

other

10

MAD in kcal/mol

8

6

4

2

0 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

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

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reaction number

Figure 2: MAD in kcal/mol for all reactions averaged over all tested methods (def2-QZVPP basis set, TPSS-D3(BJ)/def2-TZVP geometries). The dashed line represents the average deviation, the dotted line depicts the 2σ interval. Computation of the reference reaction energies Experimental heats of reaction are very difficult to obtain for larger transition metal reactions,85 and reliable values for most reactions included in the MOR41 test set are not known. The error bars of the experimental values can be larger than for accurate theoretical methods and additionally, most experiments are carried out in solution at finite temperatures. This leads to the need for additional thermostatistical corrections as well as an estimate for solvation contributions in order to arrive at “experimental” zero-point vibrational energy exclusive gas-phase reaction energies at 0 K needed to benchmark approximate electronic structure methods. Although “back-correcting” schemes were successfully applied in recent benchmark studies,86 it is desirable to keep the possible sources of error in the reference data as small as possible.


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Therefore, the generation of accurate gas-phase reaction energies has been one major part of our work. Their accuracy is crucial, as a doubtful reference would lead to meaningless conclusions. Since the MOR41 test set is composed of closed-shell single-reference molecules only by selection, most issues which would prevent the accurate calculation of reaction energies are already ruled out but the larger size of the involved molecules is still a challenge. The current “gold standard” of closed-shell single-reference quantum chemistry, canonical CCSD(T), is not applicable to the MOR41 set due to the unfavorable Ο(N7) scaling behavior of the computation time with system size N and the need for sufficiently large AO basis sets. Fortunately, recent developments in linear-scaling local coupled cluster theory allows for the efficient computation of systems with several hundred atoms at the local CCSD(T) level of theory.55 Specifically, the domain based local PNO method in its sparse map implementation as available in ORCA 4.0.024,23 was applied employing tight threshold values (TightPNO settings)56 to reproduce the canonical CCSD(T) energies as close as possible. Except for one reaction, the reference values were obtained at the DLPNO-CCSD(T)/TightPNO/CBS(def2-TZVPP /def2-QZVPP)//TPSS-D3(BJ)/def2-TZVP level of theory. Initial test calculations to investigate the error of the DLPNO approximation were performed with the much smaller def2-SVP26 and def2-TZVP basis set, for which canonical CCSD(T) calculations are possible in reasonable computation times, at least for some reactions of the MOR41 test set (see the SI for details, Tab. S8 and S9). They revealed in comparison to the respective DLPNO-CCSD(T) results (obtained with the same setting as used to calculate the actual reference values but the smaller def2-SVP and def2-TZVP basis sets), that the error caused by the DLPNO approximation for reaction (5) is significantly larger than for the other reactions (< 1.0 kcal/mol on average, see the SI for details). Hence, we re-calculated the reference value for reaction (5) employing the best computational


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feasible protocol, canonical CCSD(T)/aug-cc-pwCVTZ including core-valence correlation effects, which has been shown to yield accurate bond dissociation energies for diatomic molecules containing 3d transition metals containing diatomic molecules.87 Although the CBS extrapolation based on the def2-TZVPP and def2-QZVPP basis sets is expected to reduce the basis set superposition error (BSSE) to a large extent, we have check for the remaining BSSE for two exemplary cases (see the SI for details, Table S10). The conclusion from the investigation of the DLPNO error and the remaining BSSE together with neglecting relativistic and higher order correlation effects (and, except for reaction (5), also core-valence correlation), the uncertainty of the calculated reference reaction energies is estimated to be approximately +/-2 kcal/mol. Even if the error may be slightly larger for a few reactions, this will not lead to significant changes of the results of this benchmark, since the majority of the reaction energies should be well within this error bar. The estimated +/-2 kcal/mol uncertainty of the reference values is close to what is usually considered as chemical accuracy. Back-corrected “experimental” reaction energies, if available at all, often have even larger uncertainties (see the SI for a comparison, Table S11). Hence, the calculated reference reaction energies should be well suited to benchmark even the best DFAs (although a few hybrid and DHDFs closely approach the accuracy of the reference values). The DLPNO-CCSD(T)/def2-QZVPP calculations with TightPNO settings were finished within at most three weeks for the largest molecules of the test set (> 100 atoms, ~5000 basis functions). Thus, it was possible for the first time to obtain high-level reference reaction energies for a sizeable number of reactions including larger molecules which resemble closely the typical chemical problems met in organometallic chemistry. Hence, the results of the following benchmark study will allow for more realistic (and hitherto mostly missing) conclusions on which DFAs are the methods of choice for large-scale organometallic chemistry studies.


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Benchmark study on MOR41 We tested a representative set of different DFAs from the classes including seven GGAs, three meta-GGAs, 14 hybrid functionals, and 17 double-hybrid functionals. In addition, MP2, SCS-MP2, SOS-MP2 as well as the random phase approximation (RPA) were assessed. Furthermore, the recently developed low-cost composite DFT-D methods B97-3c (GGA) and PBEh-3c (hybrid) are evaluated in comparison to B3LYP, PBE and PBE0 results in obtained with small basis sets. 10.0 10

MAD in [kcal/mol]

7.7

8

7.0 6 4.9

4.7

4.9 4.4

3.7

4

3.3

2

PBEh-3c

B97-3c

WF

DHDF-DC

DHDF

Hybrid-DC

Hybrid

(meta-)GGA-DC

0 (meta-)GGA

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


Figure 3 MAD averaged over different classes of DFAs as well as the tested ‘-3c’ composite methods (def2-QZVPP basis set; TPSS-D3(BJ)/def2-TZVP geometries). All deviations are given in kcal/mol, and DC denotes dispersion corrected. The white asterisk denotes the performance of the most accurate DFA in the respective class. Moreover, two correction schemes for capturing long-range London dispersion interactions with DFAs were applied, the D3 correction with Becke-Johnson (BJ) or zero (0) damping, and the non-local dispersion correction (VV10), mostly in its non-self-consistent implementation. As


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the error statistics depicted in Figure 3 for dispersion-corrected and non-corrected methods (and the detailed statistics presented in the SI) clearly shows, employing a dispersion correction always leads to lower MADs. This also holds (although to a smaller extent) for the Minnesotatype functionals (with D3(0)), which already capture some dispersion interactions at intermediate inter-atomic distances by density dependent terms and their parameterization. Hence, mainly dispersion corrected methods will be discussed in the following. Table 2 : Statistical results of selected quantum chemical methods for the MOR41 benchmark set (def2-QZVPP basis set unless noted otherwise; TPSS-D3(BJ)/def2-TZVP geometries). All deviations are given in kcal/mol. For each class of methods, they are ordered according to decreasing accuracy (increasing RMSD). D3((BJ)): Becke-Johnson damping44, D3(0): zero-damping42, scNL: self-consistent implementation of the NL(VV10) correction. MD: Mean deviation; RMSD: root mean square deviation; MaxADev: Maximum absolute deviation. Corresponding MAD value are given in Figure 4. Functional GGA SCAN TPSS PBE revPBE M06L Hybrid ωB97X-V mPW1B95 PBE0 TPSSh PW6B95 B3LYP BHLYP M06 M06-2X B3LYP

dispersion correction

MD

RMSD

MaxADev

D3(BJ) D3(BJ) D3(BJ) D3(BJ) D3(0)

1.0 1.0 -0.3 0.1 -3.1

4.5 4.5 5.0 5.5 6.3

14.1 16.6 15.8 14.6 14.2

scNL D3(BJ) NL D3(BJ) D3(BJ) NL D3(BJ) D3(0) D3(0) -

-1.2 -0.8 -0.2 1.1 -2.5 -1.4 -0.1 -4.7 -5.2 9.5

2.8 3.1 3.1 3.8 3.8 4.2 7.4 7.4 8.3 14.8

8.2 9.4 9.9 13.8 7.9 14.8 13.5 21.7 21.5 38.5


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Functional DHDF PWPB95 PBE0-DH DOD-PBEB95 MPW2PLYP DSD-PBEB95 B2PLYP PWRB95 DSD-PBEP86 Wavefunction RPA SCS-MP2 SOS-MP2 MP2 Low-cost B97-3c PBEh-3c B3LYP/def2-SVP

dispersion correction

MD

RMSD

MaxADev

D3(BJ) NL D3(BJ) D3(BJ) D3(BJ) D3(BJ) NL D3(BJ)

-0.7 0.8 0.1 -0.9 -0.1 0.3 3.3 1.1

2.6 3.3 3.5 3.6 3.8 4.3 4.3 5.5

8.8 8.3 10.3 10.6 12.7 13.9 10.8 17.7

-

-4.2 -2.6 -4.2 0.5

5.1 9.3 8.4 13.9

10.1 34.6 33.5 36.8

D3(BJ) D3(BJ) -

-1.0 0.8 6.5

6.0 6.4 9.1

16.9 14.7 29.9

Figure 3 shows that the tested DFAs perform on average as expected according to the picture of "Jacob’s Ladder"88,89 and resemble closely the results for the extensive GMTKN55 main group benchmark set.5 Table 2 shows further statistical results for selected methods. The full table with detailed information for all 90 tested methods is given in the SI. The RMSD values in Table 2 show the same trend as the MAD values depicted in Figure 4. On average, the RMSD is about 20% bigger than the MAD, thus indicating a statistically well behaving benchmark set without significant outliers.


19


10

8

D3 NL

GGA

3.9 8.5

D3 NL

hybrid

6.8

7

6.2

8

3.2

5.6

4 2.4

3

2.9

4.0 2.8

2.2 2.4

3.1

3.1

2.7

2.8

3.9

4.1

4.2

camB3LYP

4.9

5

B3PW91

4

4.9

4.2 3.8

4.1 3.8

5.9

3.9 5.2

3.1 4.9

TPSS0

4.8 3.3

6.2

PW6B95

6

MAD in [kcal/mol]

MAD in [kcal/mol]

6

4.2

2.6

2 2

6

12

D3 NL

DHDF

wavefunction

4.9

5

10.5

low-cost 9.1

10

4

2.9 2.7

2.8

2.8

3.3 2.9

4.0

2.7 3.5

3.5

3.7

4.0

4.0

3.7

MAD in [kcal/mol]

3.3

3

M06-2X

BHLYP

M06

ωB97x

B3LYP

B1B95

TPSSh

PBE0

MPW1B95

RPBE

MPWLYP

B97-D

BLYP

M06-L

BP86

revPBE

TPSS

PBE

0 SCAN

0

ωB97x-v

1

3.0

1.9

2

8 6.7 6.1

6

4.9 4.4

4.5

4

1 2

B3LYP /def2-SVP

PBEh-3c

B97-3c

MP2

SCS-MP2

SOS-MP2

0 RPA

DSD-BLYP

DSD-SVWN

DSD-PBEP86

DOD-BLYP

DSD-PBEPBE

DOD-PBEPBE

B2GPPLYP

DOD-PBEP86

PBE0-DH

PWRB95

DSD-PBEB95

B2PLYP

DOD-SVWN

DOD-PBEB95

MPW2PLYP

0 PWPB95

MAD in [kcal/mol]

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 20 of 45

Figure 4: Mean absolute deviations (MADs) of (meta-)GGAs, hybrid functionals, DHDFs and wavefunction/low-cost composite methods for MOR41 (def2-QZVPP basis set except for the low-cost methods; TPSS-D3(BJ)/def2-TZVP geometries). Dispersion corrections are always applied but not denoted explicitly (cf. Table 2 for details). The tested (meta-)GGA functionals have an average MAD of 4.7 kcal/mol. The wellestablished TPSS-D3(BJ) method performs well in this class of DFAs with an MAD of 3.3 kcal/mol. It is only slightly outperformed by the recently developed strongly constrained and appropriately normed (SCAN) meta-GGA functional by Perdew et. al.,20,21 which reaches an


20

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MAD of 3.2 kcal/mol if the D3(BJ) dispersion correction is added. In general, and consistent with "Jacob’s Ladder",88,89 meta-GGAs as SCAN and TPSS yield more accurate results than the tested pure GGAs, although the meta-GGA M06L, which was suggested as being particularly suitable for transition metal thermochemistry,90,91 does not perform convincingly on MOR41 (MAD of 4.9 kcal/mol). Analogously to the results for GMTKN55, revPBE-D3(BJ) with an MD of approximately zero (MAD = 3.8 kcal/mol) is the best among all tested GGA functionals but PBE performs almost equally well with a slightly larger MD of -0.3 kcal/mol. (MAD = 3.8 kcal/mol) A clear improvement is obtained with hybrid DFAs. The average MAD is reduced to 3.7 kcal/mol. The best tested hybrid functional is ωB97X-V with an MAD of 2.2 kcal/mol, very closely followed by mPW1B95-D3(BJ) (MAD 2.4 kcal/mol) and PBE0-NL (MAD 2.4 kcal/mol). While the good performance of ωB97X-V and mPW1B95-D3(BJ) for metalorganic chemistry is a new result of the present study, PBE0-D3(BJ) was already known to be a good and robust DFA for this type of chemistry.8 The hybrid functionals BHLYP-D3(BJ) and M06-2X-D3(0) including large amounts of Fock-exchange (50% and 54%, respectively) perform worse with an MAD of 6.2 kcal/mol and 6.8 kcal/mol, respectively, and M06-2X-D3(0) has by far also the largest mean signed deviation among all tested hybrid DFAs. It systematically underestimates the reaction energies by more than 5 kcal/mol. Despite their good performance for small molecule transition metal benchmark sets,11

M06-2X-D3(0)

and

M06-D3(0)

cannot

be

recommended

for

computational

thermochemistry of larger transition metal complexes with significant intramolecular dispersion interactions. In particular, the maximum absolute deviation is significantly larger (about 20 kcal/mol) in comparison to less parameterized hybrid functionals (about 10 kcal/mol). Without


21


Page 22 of 45

the D3(0) correction, the errors are even larger (see SI). The popular B3LYP functional performs reasonably when combined with the NL dispersion correction and its MAD of 3.1 kcal/mol is near the average MAD of all tested hybrid functionals. Going to double-hybrid functionals, the best performing DFA is PWPB95-D3(BJ) (MAD 1.9 kcal/mol) nearly approaches the accuracy of the reference values and being also one of the most robust among all tested methods. It performs significantly better than the average of the tested DHDFs (3.3 kcal/mol) and its generally good performance is in agreement with the conclusions of a benchmark on smaller Ni and Pd based transition metal catalysts, where PWPB95-D3(BJ) was also found to be the best DHDF for closed-shell metal-organic chemistry. The PWRB95 functional, specially designed as a computationally less demanding alternative for this type of chemistry, includes RPA instead of MP2 correlation. It performs reasonably accurate (MAD 3.5 kcal/mol) but involves a much smaller computational effort compared to the other DHDF due to the use of a GGA type reference function for the RPA treatment. For the largest molecule, PWRB95 was approximately eight times faster than, e.g., B2PLYP. Not

surprisingly

for

transition

metal

chemistry,

the

MP2

methods

(average

MAD = 7.8 kcal/mol) could not reach the accuracy of good DFAs. As expected, the best result among the tested wavefunction based correlation methods was obtained for RPA (MAD = 4.5 kcal/mol). Considering, however, the somewhat higher computational demands compared to similarly accurate hybrid DFAs, it cannot be recommended in general. The tested composite low-cost methods B97-3c and PBEh-3c have to be discussed separately, since they are applied with their method-specific optimized small (def2-mSVP or mTZVP) basis sets. With an MAD of 4.4 kcal/mol and 4.9 kcal/mol, respectively B97-3c and PBEh-3c perform well compared to large basis set DFA treatments. Due to the relatively small (but well balanced) basis


22

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sets, the calculations need only a fraction of computation time compared to the large def2QZVPP calculations. On [email protected] compute cluster nodes, the average wall time per molecule of the MOR41 test set amounts to only 1.7 min for B97-3c, 56 min for the GGA functionals, 234 min for hybrid functionals, and 364 min for DHDFs. This means, compared to GGAs, hybrid functionals are about four times and DHDF about 6.5 times more expensive on this set, respectively. Hence, the performance of B97-3c is really promising for large scale computational studies of this type of chemistry. For comparison, a few other commonly used DFA/basis set combinations as, e.g., B3LYP/small basis were tested. Since the frequently applied 6-31G* Pople basis set92 is not available for all transition metals, these calculations were carried out using the comparably small def2-SVP basis set. While the computation time is very similar to PBEh-3c, B3LYP clearly performs worse with an MAD of 9.1 kcal/mol (MaxDev = 29.9 kcal/mol) if no dispersion correction is added (the MAD including D3(BJ) is 5.1 kcal/mol). PBE-D3(BJ)/def2-TZVP (MAD = 5.0 kcal/mol) performs slightly worse than B97-3c (MAD = 4.4 kcal/mol), whereas PBE0-D3(BJ)/def2-SVP (MAD = 4.7 kcal/mol) performs slightly better than the comparable PBEh-3c composite method (MAD = 4.9 kcal/mol), which can be attribute to the larger amount of Fock exchange (42%) in PBEh-3c as opposed to 25% in PBE0. Note, that the respective dispersion-uncorrected results yield significantly larger MADs (7.6 kcal/mol for PBE/def2TZVP and 5.5 kcal/mol for PBE0/def2-SVP, respectively). Hence, according to previous studies on main group chemistry93, we discourage the usage of dispersion uncorrected B3LYP/6-31G* or similar dispersion uncorrected DFA/small basis set combinations for metal organic chemistry of larger molecules. However, it should be also noted, that B3LYP with the def2-QZVPP basis set yields an even larger MAD = 11.4 kcal/mol and hence it can be concluded that dispersion


23


Page 24 of 45

uncorrected B3LYP calculations should be avoided in general for larger molecule transition metal chemistry. As already illustrated in Figure 2, no significant differences in the accuracy of the tested methods concerning the different reaction types were observed. For some specific reactions however, the absolute deviations are significantly larger, e.g., for reactions (37) and (38). The cleavage of the η6-bound benzene ligand appears to be more difficult for GGAs and meta-GGAs. The overall trend among the functional classes is, however, also reproduced for these reactions (averaged MADs for (meta-)GGA = 13.8 kcal/mol, hybrid functionals = 8.5 kcal/mol, and DHDF = 6.3 kcal/mol), although the error for reaction (37) of the (meta-)GGAs is of the same size as the reference value itself (-14.0 kcal/mol). Hybrid and double hybrid functionals that generally perform well for the MOR41 test set are also able to accurately describe this difficult reaction. The deviation of ωB97X-V is only 1.4 kcal/mol and 2.0 kcal for PWPB95-D3(BJ)), respectively, thus showing that both a good exchange-correlation kernel including a balanced percentage of Fock exchange and an accurate description of dispersion interactions are needed to correctly describe this reaction with density functional methods. On the other hand, even large systems can be calculated accurately with GGAs, e.g., reaction (24) with the product consisting of 120 atoms. Here the dispersion correction is of special importance due to its large relative contribution to the reaction energy (e.g., -34.9 kcal/mol for B3LYP-D3(BJ)), but the chemical transformation occurring in this reaction seems to be much easier to describe correctly for all classes of DFAs (averaged MAD = 9.8 kcal/mol). The dependency of the deviations on the system size was investigated exemplarily for the B3LYP functional. The change in the reaction dispersion energy (∆EDisp) was taken as a measure of the system size. However, plotting (∆EB3LYP-D3(-BJ) – ∆EReference) vs. ∆EDisp shows no correlation between both. A further


24

Page 25 of 45

investigation comparing the average MADs for the five largest and five smallest reactions of the MOR41 test set did also not reveal a dependency of the DFA performance on the system size. Details on these investigations can be found in the SI (Fig. S1). Figure 4 contains results for a few DFAs with the density dependent NL (VV10) dispersion correction which can be directly compared to the corresponding D3 contribution for the same underlying DFA. For two GGAs (revPBE and PBE), the DHDFs, and most of the hybrids, the D3 and NL models perform very similar. Only for B3LYP, B3PW91, BLYP, and RPBE, the NL scheme outperformed the D3(BJ) correction and in fact, the B3PW91-NL and B3LYP-NL hybrid DFT methods yield quite small MADs of about 3 kcal/mol. revPBE-D3(BJ) SCAN-D3(BJ) ωB97x-V PWPB95-D3(BJ) RPA

Probability [arbitrary units]

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


-15

-10

-5

0 5 Deviation [kcal/mol]

10

15

20

Figure 5: Normal distribution of the deviations from coupled-cluster reference data for the best performing method in each class of DFAs for the MOR41 set (def2-QZVPP basis set; TPSS-D3(BJ)/def2-TZVP geometries). The overall performance of the tested density functional methods resembles Perdew’s metaphoric picture of "Jacob’s Ladder". Focusing on the best functionals in each class, it can be clearly seen from Figure 5, that these DFAs perform as expected for their class, i.e., DHDFs are


25


Page 26 of 45

the most accurate DFAs, hybrids are better than meta-GGAs, and the latter are an improvement compare to pure GGAs. This is in accordance with the results of extensive benchmark studies for main group chemistry as, e.g., the GMTKN55 set5. Obviously, the MOR41 set behaves similar to main group chemistry, which is partly due to the restriction to single-reference closed-shell systems but can also be attributed to the large organic ligands involved. The fact that 4d/5d element containing molecules, which are usually considered as being electronically “simpler” than 3d-species, dominate MOR41 likely also contributes to this result. To elaborate on this, the MOR41 test set was divided in two subsets, one containing all 3d-species and one with all reactions containing 4d/5d-elements (see Table S13 of the SI for an overview of the corresponding MADs). It turned out that, in general, both subsets behave very similar. If averaged over all (meta-)GGAs, the MAD is 5.0 kcal/mol for the 3d reactions compared to 4.6 kcal/mol for the 4d/5d subset. For hybrid functionals, the difference even vanishes with 3.7 kcal/mol. It is noteworthy that methods which involve MP2 correlation seem to have systematic problems for the 3d-subset, most likely originating from a smaller energy denominator in the MP2 expressions. The MAD of 10.7 kcal/mol averaged over all assessed MP2 type methods for the 3d-subset is substantially larger than for the 4d/5d subset (MAD = 5.8 kcal/mol). This effect (although weakened) also shows up for the majority of the DHDFs. The average MAD rises from 2.9 kcal/mol for the 4d/5d subset to 4.6 kcal/mol for the first-row transition metals. Since this effect is not apparent in the RPA calculation (MAD = 4.7 kcal/mol for 3d and MAD = 4.4 kcal/mol for 4d/5d-subset), it is not surprising that PWRB95, which uses RPA correlation instead of MP2, outperforms the other functionals on the 3d-subset (MAD = 1.9 kcal/mol for 3d and MAD = 4.0 kcal/mol for 4d/5d-subset). Nevertheless, conclusions should be


26

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drawn with caution, since the MAD of the 3d subset is dominated by only two reactions, namely the nickel containing reactions (3) and (15).

Summary and conclusions The new MOR41 metal-organic thermochemical benchmark set presented in this paper attempts to create more realistic model systems of larger size and more diverse reaction types but still allowing the calculation of reasonably accurate reference values. The utilized DLPNO-CCSD(T)/TightPNO/CBS(def2-TZVPP/def2-QZVPP) protocol turned out to be a viable reference method for this purpose, since the estimated uncertainty of the respective reaction energies is only approximately 2 kcal/mol. This is supported from previous experience on similar compounds83 and by comparing the coupled cluster results to available accurate experimental values. The MOR41 set was used to benchmark various DFAs as well as some MP2 and related methods. It can be concluded, that many DFAs are able to accurately calculate reaction energies involving large organometallic systems. Methods with small statistical errors and no significant outliers are identified in each class of DFAs. In general, methods that do not or only partially account for intramolecular London dispersion effects (i.e., when dispersion corrections are not applied) fail to describe the reactions accurately. Preliminary results achieved with the recently proposed charge-dependent D494 dispersion correction model showed that the MADs can be slightly further reduced thus indicating that the dispersion contribution of the transition metal atom in typical complexes is significant but not very large. The slightly better results obtained with the density dependent VV10 dispersion correction compared to those from the D3 model supports this conclusion.


27


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A comparison with the results of other studies revealed some generally recommendable DFAs. For the meta-GGA class, we suggest to use the recently published SCAN-D3(BJ) functional and TPSS-D3(BJ) as an alternative. Also considering the convincing results in the recent GMTKN55 study, our recommendation for a modern hybrid is ωB97X-V. The well-known PBE0-D3(BJ) also performs very well for the MOR41 benchmark and is only outperformed by ωB97X-V and mPW1B95-D3. The comparison of the results for the minimal parameterized PBE0 and highly parameterized M06/M06-2X methods shows the risk of applying strongly fitted DFAs to systems which are not comparable to the molecules used in their training/fitting set. The good performance of mPW1B95-D3 is a bit surprising and more experience has to be gained whether this holds in general. It was, however, also one of the well performing hybrid DFA for the large GMTKN55 main group chemistry benchmark. The PWPB95-D3(BJ) double-hybrid functional, which was already found to be especially suitable for transition metal thermochemistry in 2013,8 here also outperformed all other tested methods and is the method of choice when very high accuracy is desired. Keeping the slower basis set convergence of DHDF in mind, it is a trade-off in terms of accuracy vs. computation time when comparing the best hybrid functionals to the best DHDFs since hybrids generally provide reasonable results already at a triple-zeta basis set level. Although

some

GGAs

perform

remarkably

well

for

MOR41,

we

recommend

PWPB95-D3(BJ), or hybrid functionals like ωB97X-V or PBE0-D3(BJ) for the calculation of thermodynamic properties of closed-shell metalorganic systems without significant multireference character. If the systems show moderate amounts of static correlation or the computation time is a limiting factor, meta-GGAs like SCAN-D3(BJ) or TPSS-D3(BJ) can be used as faster and robust alternatives, particularly when combined with finite temperature DFT80.


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For explorative studies, the recently developed fast B97-3c composite method allows the screening of many compounds or the calculation of even larger systems, respectively. It features a 30+ times reduction of computational effort compared to GGA functionals in the large def2-QZVPP basis set but still yields an accuracy comparable to that of many tested methods. It was possible to obtain high-level reference reaction energies for a sizeable number of reactions including larger molecules which resemble much closer the typical chemical problems met in organometallic chemistry. The results of the benchmark study allowed for more realistic conclusions on which DFAs are to be used in large-scale organometallic chemistry studies. Regarding the performance of the various tested DFA, the conclusions are very consistent to those from previous main-group chemistry benchmarks, which is a new, may be somewhat expected, but nevertheless important result. Ongoing work will focus on larger open-shell transition metal complexes involving an increasing amount of static correlation effects as well as strong London dispersion interactions.

AUTHOR INFORMATION Corresponding Author Andreas Hansen*: [email protected] Marek P. Checinski*: [email protected] Marc Steinmetz (present address): Institut für Kognitionswissenschaft, Universität Osnabrück, Wachsbleiche 27, 49090 Osnabrück, Germany

ACKNOWLEDGMENT


29


Page 30 of 45

We thank the Agence Nationale de la Recherche and the “Deutsche Forschungsgemeinschaft” (DFG) for funding this work in the framework of the COCOORDCHEM joint ANR-DFG project, project and the BMWi for further financial support (project KF3341401RR4). We thank C. Bauer for technical help with the canonical CCSD(T) calculations and E. Caldeweyher for proofreading the manuscript.

SUPPORTING INFORMATION

•

Description of the reactions of the MOR41 set, calculated energies for all reactions and tested methods, details on the frozen-core approximation used in correlated calculations, DFT-D3 parameters for DSD- and DOD-DHDFs (PDF)

•

Investigation of the local error and the BSSE in the DLPNO-CCSD(T) calculations, comparison to experimental reaction energies, comparison of the performance for 3d and 4d/5d transition metal complexes, investigation of the ground-state multiplicities, dependence of the functional performance on the system size, investigation of the fractional occupation number weighted density (PDF)

•

Cartesian coordinates of all optimized structures of the MOR41 test set (ZIP)

The Supporting Information is available free of charge on the ACS Publications website at http://pubs.acs.org

References 1 Kohn, W. Nobel Lecture: Electronic Structure of Matter—wave Functions and Density Functionals. 1999, 71, 1253–1266.


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22 Mardirossian, N.; Head-Gordon, M. ωB97X-V: A 10-Parameter, Range-Separated Hybrid, Generalized Gradient Approximation Density Functional with Nonlocal Correlation, Designed by a Survival-of-the-Fittest Strategy. Phys. Chem. Chem. Phys. 2014, 16, 9904–9924. 23 Neese, F. The ORCA Program System. WIREs Comput. Mol. Sci. 2012, 2, 73–78. 24 ORCA–An Ab Initio, Density Functional and Semiempirical Program Package, V. 3.0 (Rev. 3); F. Neese, Max– Planck Instiut für Chemische Energiekonversion, Mülheim a.d. Ruhr (Germany), 2013. 25 ORCA – an ab initio, density functional and semiempirical program package, V. 4.0.0; F. Neese, MPI für Chemische Energiekonversion, Mülheim a. d. Ruhr, Germany, 2017. 26 Weigend, F.; Ahlrichs, R. Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy. Phys. Chem. Chem. Phys. 2005, 7, 3297–3305. 27 Peterson, K. A.; Figgen, D.; Goll, E.; Stoll, H.; Dolg, M. Systematically Convergent Basis Sets with Relativistic Pseudopotentials. II. Small-Core Pseudopotentials and Correlation Consistent Basis Sets for the Post-D Group 16– 18 Elements. J. Chem. Phys. 2003, 119, 11113–11123. 28 Turbomole basis set library (ftp://ftp.chemie.uni-karlsruhe.de/pub/basen/). 2017. 29 Grimme, S.; Steinmetz, M. A Computationally Efficient Double Hybrid Density Functional Based on the Random Phase Approximation. Phys. Chem. Chem. Phys. 2016, 18, 20926–20937. 30 TURBOMOLE 5.9, R. Ahlrichs, et al., Universität Karlsruhe, 2008. See http://www.turbomole.com. 31 Tao, J.; Perdew, J. P.; Staroverov, V. N.; Scuseria, G. E. Climbing the Density Functional Ladder: Nonempirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids. Phys. Rev. Lett. 2003, 91, 146401. 32 Schäfer, A.; Huber, C.; Ahlrichs, R. Fully Optimized Contracted Gaussian Basis Sets of Triple Zeta Valence Quality for Atoms Li to Kr. J. Chem. Phys. 1994, 100, 5829–5835. 33 Grimme, S. Improved Second-Order Møller–Plesset Perturbation Theory by Separate Scaling of Parallel-and Antiparallel-Spin Pair Correlation Energies. J. Chem. Phys. 2003, 118, 9095–9102. 34 Grimme, S.; Goerigk, L.; Fink, R. F. Spin-Component-Scaled Electron Correlation Methods. WIREs Comput. Mol. Sci. 2012, 2, 886–906. 35 Bohm, D. A Suggested Interpretation of the Quantum Theory in Terms Of “ hidden” variables. I. Phys. Rev. 1952, 85, 166. 36 Bohm, D.; Pines, D. A Collective Description of Electron Interactions: III. Coulomb Interactions in a Degenerate Electron Gas. Phys. Rev. 1953, 92, 609–625. 37 Langreth, D. C.; Perdew, J. P. The Exchange-Correlation Energy of a Metallic Surface. Solid State Commun. 1975, 17, 1425–1429. 38 TURBOMOLE 7.0.1, R. Ahlrichs, et al., Universität Karlsruhe, 2016. See http://www.turbomole.com. 39 Weigend, F.; Ahlrichs, R. Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy. Phys. Chem. Chem. Phys. 2005, 7, 3297–3305. 40 Brandenburg, J. G.; Bannwarth, C.; Hansen, A.; Grimme, S. B97-3c: A Revised Low-Cost Variant of the B97-D Density Functional Method. J. Chem. Phys. 2018, 148, 64104. 41 Grimme, S.; Brandenburg, J. G.; Bannwarth, C.; Hansen, A. Consistent Structures and Interactions by Density Functional Theory with Small Atomic Orbital Basis Sets. J. Chem. Phys. 2015, 143, 54107. 42 Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132, 154104.


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43 Becke, A. D.; Johnson, E. R. A Density-Functional Model of the Dispersion Interaction. J. Chem. Phys. 2005, 123, 154101. 44 Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the Damping Function in Dispersion Corrected Density Functional Theory. J. Comput. Chem. 2011, 32, 1456–1465. 45 Vydrov, O. A.; Voorhis, T. V. Nonlocal van Der Waals Density Functional: The Simpler the Better. J. Chem. Phys. 2010, 133, 244103. 46 Hujo, W.; Grimme, S. Performance of the van Der Waals Density Functional VV10 and (hybrid)GGA Variants for Thermochemistry and Noncovalent Interactions. J. Chem. Theory Comput. 2011, 7, 3866–3871. 47 https://www.chemie.uni-bonn.de/pctc/mulliken-center/software/dft-d3/get-the-current-version-of-dft-d3/ 48 Eichkorn, K.; Treutler, O.; Öhm, H.; Häser, M.; Ahlrichs, R. Auxiliary Basis Sets to Approximate Coulomb Potentials. Chem. Phys. Lett. 1995, 240, 283–290. 49 Früchtl, H. A.; Kendall, R. A.; Harrison, R. J.; Dyall, K. G. An Implementation of RI–SCF on Parallel Computers. Int. J. Quantum Chem. 1997, 64, 63–69. 50 Weigend, F. A Fully Direct RI-HF Algorithm: Implementation, Optimised Auxiliary Basis Sets, Demonstration of Accuracy and Efficiency. Phys. Chem. Chem. Phys. 2002, 4, 4285–4291. 51 Feyereisen, M.; Fitzgerald, G.; Komornicki, A. Use of Approximate Integrals in Ab Initio Theory. An Application in MP2 Energy Calculations. Chem. Phys. Lett. 1993, 208, 359–363. 52 Weigend, F. Accurate Coulomb-Fitting Basis Sets for H to Rn. Phys. Chem. Chem. Phys. 2006, 8, 1057–1065. 53 Hättig, C. Optimization of Auxiliary Basis Sets for RI-MP2 and RI-CC2 Calculations: Core–valence and Quintuple- Basis Sets for H to Ar and QZVPP Basis Sets for Li to Kr. Phys. Chem. Chem. Phys. 2005, 7, 59–66. 54 Hellweg, A.; Hättig, C.; Höfener, S.; Klopper, W. Optimized Accurate Auxiliary Basis Sets for RI-MP2 and RICC2 Calculations for the Atoms Rb to Rn. Theor. Chem. Acc. 2007, 117, 587–597. 55 Riplinger, C.; Pinski, P.; Becker, U.; Valeev, E. F.; Neese, F. Sparse maps—A Systematic Infrastructure for Reduced-Scaling Electronic Structure Methods. II. Linear Scaling Domain Based Pair Natural Orbital Coupled Cluster Theory. J. Chem. Phys. 2016, 144, 24109. 56 Pavošević, F.; Peng, C.; Pinski, P.; Riplinger, C.; Neese, F.; Valeev, E. F. SparseMaps—A Systematic Infrastructure for Reduced Scaling Electronic Structure Methods. V. Linear Scaling Explicitly Correlated CoupledCluster Method with Pair Natural Orbitals. J. Chem. Phys. 2017, 146, 174108. 57 Neese, F.; Valeev, E. F. Revisiting the Atomic Natural Orbital Approach for Basis Sets: Robust Systematic Basis Sets for Explicitly Correlated and Conventional Correlated Ab Initio Methods? J. Chem. Theory Comput. 2010, 7, 33–43. 58 Prascher, B. P.; Woon, D. E.; Peterson, K. A.; Dunning, T. H.; Wilson, A. K. Gaussian Basis Sets for Use in Correlated Molecular Calculations. VII. Valence, Core-Valence, and Scalar Relativistic Basis Sets for Li, Be, Na, and Mg. Theor. Chem. Acc. 2010, 128, 69–82. 59 Grimme, S. Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction. J. Comput. Chem. 2006, 27, 1787–1799. 60 Becke, A. D. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys. Rev. A 1988, 38, 3098–3100. 61 Perdew, J. P. Density-Functional Approximation for the Correlation Energy of the Inhomogeneous Electron Gas. Phys. Rev. B 1986, 33, 8822–8824. 62 Adamo, C.; Barone, V. Exchange Functionals with Improved Long-Range Behavior and Adiabatic Connection Methods without Adjustable Parameters: The mPW and mPW1PW Models. J. Chem. Phys. 1998, 108, 664–675.


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82 Lee, T. J.; Taylor, P. R. A Diagnostic for Determining the Quality of Single-Reference Electron Correlation Methods. Int. J. Quantum Chem. 2009, 36, 199–207. 83 Harvey, J. N.; Aschi, M. Modelling Spin-Forbidden Reactions: Recombination of Carbon Monoxide with Iron Tetracarbonyl. Faraday Discuss. 2003, 124, 129. 84 https://www.chemie.uni-bonn.de/pctc/mulliken-center/software/mor41/ 85 Hyla-Kryspin, I.; Koch, J.; Gleiter, R.; Klettke, T.; Walther, D. Reassessment of the Electronic and Molecular Structure, Bonding, and Stability of Zerovalent Nickel Acetylene Complexes by the Density Functional Method. Organometallics 1998, 17, 4724–4733. 86 Hansen, A.; Bannwarth, C.; Grimme, S.; Petrović, P.; Werlé, C.; Djukic, J.-P. The Thermochemistry of London Dispersion-Driven Transition Metal Reactions: Getting the “Right Answer for the Right Reason.” ChemistryOpen 2014, 3, 177–189. 87 Cheng, L.; Gauss, J.; Ruscic, B.; Armentrout, P. B.; Stanton, J. F. Bond Dissociation Energies for Diatomic Molecules Containing 3d Transition Metals: Benchmark Scalar-Relativistic Coupled-Cluster Calculations for 20 Molecules. J. Chem. Theory Comput. 2017, 13, 1044–1056. 88 Perdew, J. P.; Ruzsinszky, A.; Tao, J.; Staroverov, V. N.; Scuseria, G. E.; Csonka, G. I. Prescription for the Design and Selection of Density Functional Approximations: More Constraint Satisfaction with Fewer Fits. J. Chem. Phys. 2005, 123, 62201. 89 Kurth, S.; Perdew, J. P.; Blaha, P. Molecular and Solid-State Tests of Density Functional Approximations: LSD, GGAs, and Meta-GGAs. Int. J. Quantum Chem. 1999, 75, 889–909. 90 Averkiev, B. B.; Truhlar, D. G. Free Energy of Reaction by Density Functional Theory: Oxidative Addition of Ammonia by an Iridium Complex with PCP Pincer Ligands. Catal. Sci. Technol. 2011, 1, 1526. 91 Gusev, D. G. Assessing the Accuracy of M06-L Organometallic Thermochemistry. Organometallics 2013, 32, 4239–4243. 92 Ditchfield, R.; Hehre, W. J.; Pople, J. A. Self-Consistent Molecular-Orbital Methods. IX. An Extended GaussianType Basis for Molecular-Orbital Studies of Organic Molecules. J. Chem. Phys. 1971, 54, 724–728. 93 Kruse, H.; Goerigk, L.; Grimme, S. Why the Standard B3LYP/6-31G∗ Model Chemistry Should Not Be Used in DFT Calculations of Molecular Thermochemistry: Understanding and Correcting the Problem. J. Org. Chem. 2012, 77, 10824–10834. 94 Caldeweyher, E.; Bannwarth, C.; Grimme, S. Extension of the D3 Dispersion Coefficient Model. J. Chem. Phys. 2017, 147, 34112.


35

CO 1)

OC OC

Cr

CO

CO CO

+

1 CO 2 3 Fe 2) + CO 4 OC CO 5 6 CO 7 Ni 3)8 + CO 9 OC 10 11 Co 4)12 + 13 14 H 15 16OC Mn CO 5) + CO 17OC CO 18 19 CO 20 OC CO Cr 6)21 + OC CO 22 23 24 P(iPr)3 25 CO W 7)26OC + CO 27 P(iPr)3 28 29 30 CO Ph3P Ir 8)31 + Cl PPh3 32 33 34 35 Cl Rh PPh3 9) + PPh3 36 37 38 39 40 10) + Rh 41 OC 42 43 44 45 46 N N 11) 47 48 Pd 49 Me I 50 51 CO 52 53 OC CO Cr 12) CO 54 OC 55

CO

Journal ofCO Chemical Theory and Computation OC Cr

OC

-43.1

CO

Rh

13)

+

Page 36 of 45

C2H4

CO CO

OC

-46.6

Ph CO

CO

-27.6

tBu

CO

OC

+ CO2

N

N

Ni

N

+ NHC-tBu

Cl

CO

p-Tol

Pd

-39.8

CO

Cl tBu

N

P(tBu)2

CO

H 17)

N

CO + MeOH

Ru

N

-16.1

OC

CO

W

H2

NEt2

CO

Ph3P

CO

Ir

H

PPh3

Cl

H

-18.7

PMe3

Ir

+ MeI

-34.2

Me3P

PPh3

Rh

PPh3

Cl

Me

CO

CO

Cl

Cl PMe3

Ir

+ AcI

-40.1

Me3P

Ac

CO

CO

Cl

Cl PMe3

Ir

+ AcCl

-30.2

Me3P

Rh OC

H C3H7

21) Me

PMe3

Ir

Ac

CO

-22.6

PMe3

Ir

Cl 20) Me3P

C3H8

PMe3

Ir

I 19) Me3P

H H2

Cl I

18) Me3P

H

-17.2

CO

NEt2

Cl

P(iPr)3

H2

Ru

MeO

P(iPr)3

-16.2

tBu

N

P(tBu)2

CO

H2

H2

tBu

p-Tol

Cr

OC

-23.2

N

tBu

tBu

Pd

CO H2

O

-4.1

CO

OC

O

O

Ni

16)

Mn

OC

+3.7

Ni

-52.0

O

CHO CO

+ COD

O

15)

Co

-62.5

H

Ni O

CO CO

OC

P

14)

CO Ni

Ph

P

CO

CO

Ph

Ph

CO

Fe

Rh

-43.2

CO

CO

N

N

Me

Me

N

N

Me

I Rh

+ MeI

OC + C2H6

N

N

27.0

I

Pd

Me Me

Me

I

-15.1

Rh

Ac

I

N

N

Me

Me

N

Me

N

Me I OC

CO +

C2H4

OC

-29.8

OC

CO Ir

ACS Paragon Plus tBu S S tBu 22) Environment CO Cr

OC

CO

Ir

OC

CO

CO Ir

+ I2

-35.9

tBu S

S tBu Ir

OC

CO I

Cl

Cl

Page 37 of 45

23) Me3P

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

Ir

Journal of Chemical Theory and Computation I

PMe3

+ I2

-55.0

Ir

Me3P

CO

+

PCy3

Ph

N

N

Cl

O

+

COD

O

-1.8

Rh

Cl

Ru

Cl

-41.6

O

Mes

+

PCy3

Cl

-45.9

33)

N

Mes

Ph

Cl

N

Me3P Me3P

PMe3 + PhOH

Ru

Me3P

Me3P

-10.7 PMe3

Mes

Ru

Ph

34)

Me3P Me3P

Ru

Me3P

+ PhSH

-25.6

Ru

Me3P

PMe3

Cl

-36.4

Me3P

+ COD

Ru

35)

Cl

Me3P

Me3P

+ dmpm

-21.8

Cl

Me2P

Mo

+ dmpe Cl

-36.3

Me2P

Me

-28.3

Me2P

PMe2

39)

+ 3 MeCN

Mo OC OC

CO

-14.0

Pt

Pt

-14.9

Me

Me Pt

Py2P

PPy2

Me

Me Pt

+ dppv

-29.9

Ph2P

CO

Mo

MeCN

CO

+

benzene

Mo OC OC

CO

Me3P

+ 3 PMe3

-64.4

2

+ COD

CO

Mo

Me3P

CO

+

benzene

PMe3 OC

Rh

Ti

Rh

-63.9

CO

+

CO

Cl Rh Cl

OC

CO

Al

Cl

Me

Me + dpype

MeCN

NCMe

Cl

40) Me

+ C2H4

CO 38)

Cl

Pt

+ dmpe

I

CO

Me

Me

+ C2H4

SePh

-39.8

CO

Pt

PMe3 H

I

+ COD

Ru PMe2

Me3P

Cl

37)

Ru

Ru

Mo

+ I2

+ C2H4

+ COD

Ru PMe2

-30.9

+ C2H4

SPh

Me3P

PMe3

36)

Ru

+ PhSeH

PMe3 H

PMe3

Ru

Me3P

PMe3 H

PMe3

PMe3 Ru PCy3

+ 2 PMe3

Ru

Me

2 C2H4

OPh

PMe3

Me

+

Rh

PMe3

Ph

PCy3

Ru

Cl

O

PCy3

Ru

Cl

32)

CO

PCy3 Cl

PMe3

I

+ COD

Ti

-65.8

Cl Cl

41) + COD ACSPPh Paragon Plus Environment 2

Al Cl

PCy3 PCy3

Ru

-3.2

Cl

Ru Cl

4


MAD in kcal/mol 12 σdonor πacceptor

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

10

8

6

4

2

0

oxidative addition ligand exchange

reaction number

other

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 38 of 45


10.0

(meta−)GGA

4.7

1 2 (meta−)GGA−DC 3 4 5 6 Hybrid 7 8 Hybrid−DC 9 10 11 12 DHDF 13 14 DHDF−DC 15 16 17 18 WF 19 20 21 22 B97−3c 23 ACS Paragon Plus Environment 24 25 PBEh−3c 26

10

8

6

4

2

0

MAD in [kcal/mol] Page 39 Journal of 45of Chemical Theory and Computation

7.7

3.7

4.9

3.3

7.0

4.4

4.9

4.9

5.9

B97−D

4.9

3.9 5.2

BLYP

4.2 3.8

M06−L

4.1 3.8

BP86

4.8 3.3

PBE

GGA

Page 403.9 of 45 8.5

6.2

RPBE


MPWLYP

revPBE

3.2

TPSS

MAD in [kcal/mol]

8 1 2 3 6 4 5 6 4 7 8 9 2 10 11 12 0 13 14 15 16 17


D3 NL

SCAN

10

8 Page D3 41 of 45


hybrid

6.8 6.2

3.1 4.1

4.2

4.2

camB3LYP

ωB97x

2.8

3.9

B1B95

2.7

2.8

M06−2X

BHLYP

M06


B3LYP

TPSS0

2.6

PW6B95

2.4

3.1

TPSSh

2.4

PBE0

2.2

3.1

5.6

4.9

B3PW91

2.9

4.0

MPW1B95

MAD in [kcal/mol]

16 2 35 4 54 6 73 8 92 10 111 12 0 13 14 15 16 17

ωB97x−v

7

NL

6

5

4

3

2

D3 NL

1.9

PWPB95

1

0

MAD in [kcal/mol] Journal of Chemical Theory and Computation Page 42 of 45

2.7

1 MPW2PLYP 2 3 DOD−PBEB95 4 B2PLYP 5 6DOD−SVWN 7 8 DSD−PBEB95 9 10 PWRB95 11 PBE0−DH 12 13 DOD−PBEP86 14 15B2GPPLYP 16 DOD−PBEPBE 17 18DOD−BLYP 19 DSD−PBEPBE 20 21 DSD−PBEP86 22 23DSD−BLYP ACS Paragon Plus Environment 24 DSD−SVWN 25 26 2.8

2.9

2.8 2.9

3.0

3.3

3.5

DHDF

2.7

3.3

3.5 3.7 3.7 4.0 4.0 4.0 4.9

12 Page 43 of 45

low−cost

6.7


4.9

B3LYP /def2−SVP

MP2

SCS−MP2

4.5

B97−3c

4.4

PBEh−3c

6.1

SOS−MP2

MAD in [kcal/mol]

1 2 8 3 4 5 6 6 7 4 8 9 10 2 11 12 0 13 14 15 16 17

10.5

9.1

RPA

10


wavefunction


revPBED3(BJ) SCAND3(BJ) ωB97xV PWPB95D3(BJ) RPA

Probability [arbitrary units]

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 44 of 45

15

10

5

0 5 Deviation [kcal/mol]


10

15

20

0

M R

Page 45 Journal of 45 of Chemical Theory and Computation −5

−10

1 2 3 4

ΔE [kcal/mol]

−15 −20 −25 −30


[Ru(PCy3)(=CHPh)Cl2] + PCy3

−35 −40

GGA Hybrid WF DHDF DLPNO−CCSD(T)

[Ru((PCy3)2(=CHPh)Cl2]

Comprehensive Thermochemical Benchmark Set ... - ACS Publications

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