Phase Transition-Metal Polyolefin Catalysis Leanne D Chen, James Joseph Lawniczak, Feizhi Ding, Peter J

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Subscriber access provided by Caltech Library Quantum Electronic Structure Embedded Mean-Field Theory for Solution- Phase Transition-Metal Polyolefin Catalysis Leanne D Chen, James Joseph Lawniczak, Feizhi Ding, Peter J. Bygrave, Saleh Riahi, Frederick R. Manby, Sukrit Mukhopadhyay, and Thomas Francis Miller J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.0c00169 • Publication Date (Web): 22 May 2020 Downloaded from pubs.acs.org on May 26, 2020

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1 2 3 4 5 6 7 8 Embedded Mean-Field Theory for 9 10 11 Solution-Phase Transition-Metal Polyolefin 12 13 14 15 Catalysis 16 17 18 : : : ; 19 Leanne D. Chen, James J. Lawniczak, Feizhi Ding, Peter J. Bygrave, Saleh 20 ¶ , 21 Riahi,: Frederick R. Manby,; Sukrit Mukhopadhyay, and Thomas F. Miller III˚ : 22 23 24 :Division of Chemistry and Chemical Engineering, California Institute of Technology, 25 26 Pasadena, CA 91125, USA 27 28 ;Centre for Computational Chemistry, University of Bristol, Bristol BS8 1TS, United 29 30 Kingdom 31 32 ¶The Dow Chemical Company, Midland, MI 48674, USA 33 34 35 E-mail: [email protected] 36 37 38 Abstract 39 40 41 Decreasing the wall-clock time of quantum mechanics/molecular mechanics (QM/MM) 42 calculations without sacrificing accuracy is a crucial prerequisite for widespread sim- 43 44 ulation of solution-phase dynamical processes. In this work, we demonstrate the use 45 46 of embedded mean-field theory (EMFT) as the QM engine in QM/MM molecular dy- 47 48 namics (MD) simulations to examine polyolefin catalysts in solution. We show that 49 50 employing EMFT in this mode preserves the accuracy of hybrid-functional DFT in 51 52 the QM region, while providing up to 20-fold reductions in the cost per SCF cycle, 53 54 thereby increasing the accessible simulation time-scales. We find that EMFT repro- 55 duces DFT-computed binding energies and optimized bond lengths to within chemical 56 57 58 59 1 60 ACS Paragon Plus Environment Journal of Chemical Theory and Computation Page 2 of 37

1 2 3 accuracy, as well as consistently ranking conformer stability. Furthermore, solution- 4 5 phase EMFT/MM simulations provide insight into the interaction strength of strongly 6 7 coordinating and bulky counterions. 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 2 60 ACS Paragon Plus Environment Page 3 of 37 Journal of Chemical Theory and Computation

1 2 3 Introduction 4 5 6 Catalyst design in transition-metal catalysis typically requires extensive experimental opti- 7 8 mization to achieve desired product characteristics.1 Efficient catalysts – many of which have 9 10 complex ligand structures – are often difficult and expensive to synthesize. To circumvent 11 12 the bottleneck this presents in research and development efforts, advances in computational 13 14 methods can help accelerate the identification of promising ligands.2 De novo catalyst design 15 16 is challenging due to the subtle interplay of electronic and steric effects on the performance of 17 18 the catalyst under specific reaction conditions. Further complicating catalyst design are the 19 20 important effects of solvent, conformational flexibility, and counterions at finite temperature 21 22 and concentration.3 New methods are needed to provide reliable computational insight into 23 24 the effective design of catalysts in their solvation environment. 25 26 The combined quantum mechanics/molecular mechanics (QM/MM) method4,5 has proven 27 28 effective in a variety of applications including biological reactions6–11 and solution-phase 29 30 chemistry,12–16 due to its ability to address both dynamical effects in multi-scale systems 31 32 along with local bond-making and bond-breaking events. The cost of a single QM/MM MD 33 34 step is usually dominated by that of the force evaluation for the QM region, since the MM in- 35 36 teractions have a simple analytic form. Therefore, managing the cost of the QM calculation 37 38 is an important objective for the development of computationally efficient solution-phase 39 40 QM/MM simulations. 41 42 Quantum embedding offers an appealing strategy for reducing the computational costs 43 44 associated with the QM regions while preserving its accuracy. For example, wavefunction- 45 46 in-(density functional theory) quantum embedding methods17–20 provide high (i.e., coupled- 47 48 cluster theory) accuracy in the QM region at a significant reduction in cost versus a full 49 50 wavefunction-method description,21,22 although this approach remains too costly for widespread 51 52 use in QM/MM MD simulations. 53 54 In the current work, we employ an alternative quantum embedding approach in the QM 55 56 region, specifically embedded mean-field theory (EMFT),23,24 which provides a high-quality 57 58 59 3 60 ACS Paragon Plus Environment Journal of Chemical Theory and Computation Page 4 of 37

1 2 3 mean-field description (such as DFT with a hybrid functional using a large atomic-orbital 4 5 basis set) for a subsystem of the QM region, while the remainder of the QM region is 6 7 described using a less costly mean-field method (such as DFT with a GGA functional using 8 9 a small atomic-orbital basis set). A key advantage of the method is that it does not require 10 11 specification of link atoms that connect the subsystems, nor does it require specification of the 12 13 number of subsystem spin states or the number of electrons per subsystem. Previous work has 14 15 shown that EMFT can be much more accurate than both the point-charge25 and ONIOM26,27 16 17 schemes for subsystem embedding, particularly for systems that involve partitioning across 18 19 delocalized covalent bonds.23,28 EMFT has additionally been benchmarked for open-shell 20 21 systems,23 for deprotonation reactions,29 and for the linear-response description of excited 22 23 states.30 As we will show, this leads to tangible advances in terms of the information we can 24 25 glean in the application area we study. 26 27 Polyolefins are the most widely used class of polymers31 whose industrial importance is in 28 29 part due to the tunability of their mechanical and physical properties, such as elasticity and 30 31 opacity. Precise control of these macroscopic properties requires an atomic-scale mapping of 32 33 the barriers of the elementary steps in the polymerization mechanism (Figure 1),32 where the 34 35 goal is to design molecular catalysts that offer superior control of product selectivity over their 36 37 heterogeneous analogues.33 Nuclear magnetic resonance (NMR) studies have suggested that 38 39 configurational sampling of the solvent and counterion degrees of freedom near the catalyst 40 41 play a crucial role in its functionality,34 which necessitates the application of dynamic rather 42 43 than static modeling techniques. A chemically accurate description of the electronic structure 44 45 near the active site is necessary to reliably describe reactivity at the active site. For these 46 47 reasons, QM/MM studies have typically been used to study transition-metal catalysts in 48 49 solution.35–40 In this work, we show that replacing DFT with EMFT for the QM subsystem in 50 51 these solution-phase QM/MM simulations of organometallic compounds largely preserves the 52 53 accuracy of the description for these organometallic compounds while substantially improving 54 55 computational efficiency. 56 57 58 59 4 60 ACS Paragon Plus Environment Page 5 of 37 Journal of Chemical Theory and Computation

1 2 3 The current work focuses on four archetypal Group (IV) molecular catalysts for olefin 4 5 polymerization (Figure 2), which include both metallocene and post-metallocene structures. 6 7 Catalyst 1 is a constrained geometry complex (CGC) of the metallocene class of polyolefin 8 9 catalysts.41,42 Catalyst 2 is a post-metallocene structure, where the reaction of interest in 10 11 this case is the binding of propylene to the Hf4` active site.43 The competition between the 12 13 binding of ethylene and propylene in the polymerization process influences the branching 14 15 ratio in the final product, which influences its bulk material properties. Catalyst 3 and 16 17 Catalyst 4 are also post-metallocene structures, which have been previously reported to 18 19 produce olefin block copolymers with favorable elastomeric properties.44 (The full chemical 20 21 names of the catalysts are provided in the Supporting Information.) 22 23 24 25 26 Computational Methods 27 28 29 Density functional theory (DFT) is widely used for ab initio simulations because of its balance 30 45–48 31 between accuracy and computational cost. For organometallic compounds in particular, 32 33 various DFT studies have demonstrated the importance of using hybrid exchange correla- 34 49–52 35 tion functionals which include some fraction of exact Hartree-Fock exchange, although 36 37 such hybrid functionals are typically more computationally expensive than those that em- 38 53 39 ploy the generalized gradient approximation (GGA) alone. Embedded mean-field theory 40 23,24 41 (EMFT) seeks the best of these two worlds — hybrid functional-like predictions at a 42 43 computational cost similar to that of the GGA, yielding experimentally relevant quantities 44 28 45 with chemical accuracy. EMFT is a simple, self-consistent method that provides a high- 46 47 level DFT (or other mean-field) description on a subset of the system and a lower-level DFT 48 23 49 (or other mean-field) description on the remainder. 50 54 51 All DFT and EMFT calculations reported here are performed using the entos package. 52 55 53 For the B3LYP functional used in the paper, the VWN3 local correlation energy is em- 54 55 ployed. We employ the density-corrected implementation of the method (DC-EMFT) to 56 57 58 59 5 60 ACS Paragon Plus Environment Journal of Chemical Theory and Computation Page 6 of 37

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 Figure 1: Initial steps leading up to the catalytic cycle of a Group (IV) metal-catalyzed oleﬁn 41 polymerization, including abstraction of an alkyl group (represented as R) by an oxidizing activator 42 reagent to form the catalytically-active resting state (Step 1), binding of the ﬁrst monomer to 43 44 the resting state species (Step 2), and insertion of bound monomer into the initial alkyl (here, 45 n-propyl) ligand (Step 3). Afterwards, monomer binding and insertion into the growing polymer 46 chain repeat until termination. 47 48 49 50 51 52 53 54 55 56 57 58 59 6 60 ACS Paragon Plus Environment Page 7 of 37 Journal of Chemical Theory and Computation

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 Figure 2: Transition-metal polyoleﬁn catalysts considered here (resting state depicted). (a) 42 Catalyst 1 is a metallocene complex belonging to the constrained geometry complex (CGC) class. 43 44 (b) Catalyst 2 is a post-metallocene catalyst containing bisphenol ligands. (c) Catalyst 3 is a post- 45 metallocene FI-type catalyst containing Schiﬀ base amines. (d) Catalyst 4 is a post-metallocene 46 catalyst with a pyridyl-amido motif. 47 48 49 50 51 52 53 54 55 56 57 58 59 7 60 ACS Paragon Plus Environment Journal of Chemical Theory and Computation Page 8 of 37

1 2 3 prevent unphysical collapse of the electronic density.24 The exact-exchange contributions to 4 5 the coupling between the high- and low-level subsystems are treated using the EX0 scheme.23 6 7 For the predictions of catalyst conformer stability, configurational sampling was performed 8 9 using thermostatted molecular dynamics on the GFN1-xTB56 potential using the entos pack- 10 11 age.54 A linear cooling schedule from 800 K to 100 K was used, with a total sampling time 12 13 of 70 ps and time step of 1 fs. Sampled configurations were subsequently optimized using 14 15 (B3LYP/Def2-SVP). 16 17 QM/MM simulations are carried out by interfacing entos 54 with the GROMACS 2018.1 18 19 molecular dynamics software.57 The toluene solvent is described using the modification of 20 21 the OPLS-AA58 force-field by Caleman and coworkers,59 60 and σ and values for the tita- 22 23 nium atom are taken from Cu2` in the OPLS-AA database. Partial charges of the metal 24 25 complex are obtained from Mulliken population analysis61 performed on the complex us- 26 27 ing (B3LYP/Def2-SVP). The force-field parameters for borate counterions, including methyl 28 29 [tris(pentafluorophenyl)]borate, tetrakis(pentafluorophenyl)borate, and BF – , are obtained 30 4 31 from a previous study.62 GROMACS parameter and topology files employed in this study 32 33 are provided in the Supporting Information. 34 35 QM/MM simulations are carried out with electrostatic interactions calculated using 36 37 the reaction-field-zero method.63 The charge-group cutoff scheme is used, with the solvent 38 39 molecules comprised of neutral charge groups and with the catalyst and counterion com- 40 41 prised of charge groups with net charges. Electrostatic coupling between the QM and MM 42 43 particles is evaluated through the electrostatic embedding scheme. Other non-bonded inter- 44 45 actions between the QM and MM particles are calculated using the Lennard-Jones potential 46 47 with parameters provided in the Supporting Information. 48 49 All covalent bonds in the solvent and counteranion structures are constrained using the 50 51 LINCS algorithm.64 The leap-frog integrator is used with a 1 fs time step. Periodic boundary 52 53 conditions (PBCs) are used, with a 1.2 nm cutoff for electrostatic and vdW interactions. The 54 55 electrostatic cutoff is applied with respect to the distance between the geometrical (i.e., un- 56 57 58 59 8 60 ACS Paragon Plus Environment Page 9 of 37 Journal of Chemical Theory and Computation

1 2 3 mass weighted) centers of the charge groups. When employed, the Nosé-Hoover thermostat65 4 5 and the Parrinello-Rahman barostat66 are utilized with a temperature of 298 K, a pressure 6 7 of 1 bar, and a damping time constant of 1 ps. 8 9 The initial configurations for the QM/MM simulations are prepared as follows: The 10 11 solvated catalyst and counterion were initialized from a pre-equilibrated simulation cell, 12 13 obtained using the solvate utility within the GROMACS package,67 and performing a 1 14 15 ns isothermal-isobaric (NpT ) equilibration using fully classical MD. For the Cl– , BF – , 16 4 17 CH B(C F ) – and B(C F ) – simulations, the number of solvent molecules is respectively 18 3 6 5 3 6 5 4 19 196, 196, 193, and 195. During this initial equilibration, the cubic simulation cell adopts 20 21 a sidelength of approximately 3.3 nm centered around the catalyst. The system was then 22 23 equilibrated for 5 ps in the NpT ensemble using the GFN1-xTB/MM potential, then for at 24 25 least 5 ps in the NVT ensemble using the EMFT/MM potential, before performing produc- 26 27 tion runs in the NVE ensemble using the EMFT/MM potential. Each QM/MM production 28 29 run has a simulation time of at least 30 ps. 30 31 32 33 34 Results and Discussion 35 36 37 Benchmarking EMFT Accuracy and Cost 38 39 40 We begin by benchmarking the accuracy and efficiency of EMFT for the prediction of struc- 41 42 ture and reactivity of the archetypal Group (IV) olefin polymerization catalysts shown in 43 44 Figure 2. In particular, we focus on monomer binding energies, resting-state bond lengths, 45 46 and relative-energy rankings of a resting-state conformer using EMFT. 47 48 For DFT calculations, we specify the exchange correlation functional and basis set with 49 50 the standard nomenclature (functional/basis set). For EMFT, we specify the level of theory 51 52 via ((high-level)-in-(low-level)); for example, ((B3LYP/Def2-SVP)-in-(PBE/6-31G)) denotes 53 54 the use of EMFT with the B3LYP functional and Def2-SVP basis for the high-level subsystem 55 56 and the PBE functional and 6-31G basis for the low-level subsystem. 57 58 59 9 60 ACS Paragon Plus Environment Journal of Chemical Theory and Computation Page 10 of 37

1 2 3 Substrate binding energies 4 5 6 The binding of a monomer substrate is an important elementary step in the overall poly- 7 8 merization mechanism (Figure 1). We compare the binding energy values obtained by EMFT 9 10 ((B3LYP/Def2-SVP)-in-(PBE/6-31G)) to those calculated using high-level DFT (B3LYP/Def2- 11 12 SVP) and low-level DFT (PBE/6-31G). Additionally, we investigate the convergence of 13 14 EMFT binding energy values to the high-level DFT result, as a function of high-level sub- 15 16 system size. To calculate the binding energy using DFT or EMFT, we take the diﬀerence 17 18 between the single-point energies of the bound intermediate product and the resting state 19 20 and unbound ethylene reactants (Step 2, Figure 1). The unbound ethylene monomer is 21 22 treated with (B3LYP/Def2-SVP) for EMFT and high-level DFT, and with (PBE/6-31G) for 23 24 low-level DFT. All calculations are performed at geometries that are optimized at the B3LYP 25 26 level of theory; these structures for both the resting-state and substrate-bound intermediates 27 28 for all four catalysts are provided in the Supporting Information. 29 30 For EMFT energy evaluations of the resting state and bound intermediate catalyst struc- 31 32 tures, the partitioning of the system is illustrated in Figure 3 and Figure 4. For each catalyst, 33 34 four subsystem sizes are explored using EMFT. To compactly label the high-level regions for 35 36 each subsystem size, we assign each atom a label from 1–4 in the resting state structure of 37 38 the catalyst (Figure 3), with hydrogen atoms atoms sharing the index of the heavy atom to 39 40 which they are bonded. Hence, a partitioning scheme X P t1, 2, 3, 4u deﬁnes the high-level 41 42 subsystem as all atoms which have an index value less than or equal to X. For example, 43 44 partitioning scheme 2 places both the blue (label 1) and green (label 2) atoms in the high- 45 46 level subsystem. The atomic labelling for the resting states as shown in Figure 3 extend to 47 48 the bound intermediate; as shown in Figure 4, the monomer substrate in the unbound and 49 50 bound intermediate structure is always included in the high-level subsystem. 51 52 53 54 55 56 57 58 59 10 60 ACS Paragon Plus Environment Page 11 of 37 Journal of Chemical Theory and Computation

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 Figure 3: Deﬁnition of the high-level subsystem by atomic labeling (shown for resting state 41 structures) for EMFT partitioning. For a partitioning scheme X indexed as 1, 2, 3, 4, the atoms 42 43 with indices of less than or equal to X are in the high-level region, and the remaining atoms are 44 in the low-level region; moieties indicated in black are in all cases treated at the low level. For 45 each atom that is joined by bonds containing diﬀerent colors, the label corresponding to the lower 46 index is used. All implicit hydrogen atoms share the index of the atom to which they are bonded. 47 For example, partitioning scheme 2 places the blue- and green-labeled atoms in the high-level 48 49 subsystem, and the remaining atoms in the low-level subsystem. 50 51 52 53 54 55 56 57 58 59 11 60 ACS Paragon Plus Environment Journal of Chemical Theory and Computation Page 12 of 37

1 2 3 4 5 6 7 8 9 10 11 12 Figure 4: Illustration of the partitioning for the minimal high-level subsystem (Figure 3, X “ 1) 13 for the resting state, ethylene-bound intermediate, and propylene-bound intermediate, respec- 14 tively. The high-level subsystem (represented in red) always contains at least the metal, n-propyl 15 16 group, and if present in the structure, the bound monomer. 17 18 19 Binding energies for ethylene (black dots) and propylene (gray dots) are plotted as a 20 21 function of the number of atoms in the high-level subsystem (Figure 5). All binding energies 22 23 are reported relative to the ethylene binding energy calculated by low-level DFT (PBE/6- 24 25 31G). On each plot, the first point corresponding to zero atoms in the high-level subsystem 26 27 is obtained from the low-level DFT (PBE/6-31G) energy, and the last point corresponding 28 29 to the inclusion of all atoms in the high-level subsystem is obtained from the high-level 30 31 (B3LYP/Def2-SVP) energy. The four intermediate points indicate the EMFT energy cal- 32 33 culated using increasing sizes of the high-level subsystem. To indicate the target range of 34 35 chemical accuracy, the light and dark green bar indicates ˘1 kcal/mol deviation from the 36 37 high-level DFT (B3LYP/Def2-SVP) propylene and ethylene binding energy, respectively. 38 39 EMFT-calculated ethylene and propylene energies converge to the high-level DFT result 40 41 for all four catalysts (Figure 5). For all four of the catalyst systems, the minimal subsystem – 42 43 including the growing polymer chain, the metal center, and the unbound or bound monomer 44 ´1 45 – is sufficient to obtain the energy of ethylene and propylene binding to within „1 kcal mol 46 47 of the high-level calculation on the full system. For some intermediate subsystem sizes, the 48 ´1 49 error is slightly larger than 1 kcal mol , but in general the deviations are modest. Notably, 50 51 this effect holds for large catalysts, including the largest catalyst studied (Catalyst 3, with 52 53 127 atoms in the resting state form), for which the computational speed-ups will be greatest 54 55 using EMFT. It is particularly encouraging that EMFT consistently provides good accuracy 56 57 58 59 12 60 ACS Paragon Plus Environment Page 13 of 37 Journal of Chemical Theory and Computation

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 Figure 5: Ethylene and propylene binding energies relative to the low-level calculated ethylene 43 binding energy (PBE/6-31G), as a function of the number of atoms in the high-level subsystem 44 of the resting state structure. On each plot, from left to right is shown the full low-level DFT 45 46 (PBE/6-31G), EMFT ((B3LYP/Def2-SVP)-in-(PBE/6-31G)) using partitioning schemes in Fig- 47 ure 3, and full high-level DFT (B3LYP/Def2-SVP). The number of atoms in each case coincide 48 with the subsystem partitionings indicated in Figure 3. 49 50 51 52 53 54 55 56 57 58 59 13 60 ACS Paragon Plus Environment Journal of Chemical Theory and Computation Page 14 of 37

1 2 3 across all four catalyst systems, which vary with respect to the transition metal and ligand 4 5 scaﬀold. 6 7 Figure 6 addresses the accuracy with which EMFT predicts the relative binding energy of 8 9 ethylene versus propylene in the four catalyst systems, a quantity that is of central interest 10 11 in determining selectivity with respect to unwanted side-products during polyoleﬁn catalysis. 12 13 In all four cases, EMFT is performed using the smallest and least computationally expensive 14 15 high-level subsystem considered (partitioning scheme 1). Comparing these EMFT results 16 17 with respect to high-level DFT, it is clear that the lower-cost EMFT method accurately 18 19 predicts ethylene and propylene binding energies across all four catalysts. 20 21 22 23 8 )

24 1 B3LYP 25 6 EMFT 26 27 4

28 2 29 30 0 31 32 2 33 34 4

35 6 36 Binding Energy Difference (kcal mol 37 8 38 1 2 3 4 39 Catalyst 40 41 Figure 6: Difference in ethylene vs. propylene binding energy (ethylene – propylene) for Catalyst 42 1 (Ti4+), Catalyst 2 (Hf4+), Catalyst 3 (Zr4+), and Catalyst 4 (Hf4+). The differences in binding 43 energies is evaluated with both DFT (B3LYP/Def2-SVP) and EMFT ((B3LYP/Def2-SVP)-in- 44 ´1 45 (PBE/6-31G)) using the minimal subsystem partitioning (Figure 3, X “ 1). A 1 kcal mol error 46 bar is included for comparing the DFT and EMFT binding energy differences. 47 48 49 50 51 Predicting conformer stability 52 53 An important capability in computational screening is the ability to predict the structure 54 55 and relative energy of the most stable conformers. We investigate the distribution of con- 56 57 58 59 14 60 ACS Paragon Plus Environment Page 15 of 37 Journal of Chemical Theory and Computation

1 2 3 formers for resting state of Catalyst 3, which consists of a trigonal bipyramidal geometry 4 5 with 2 oxygen ligands, 2 nitrogen ligands, and an n-propyl ligand. Three unique isomers 6 7 are considered (Isomers 1–3, Figure 7), based on the orientation of the bonding connectivity 8 9 at the metal site. We consider four low-energy conformers associated with each isomer, ob- 10 11 tained via simulated annealing (see Computational Methods). Speciﬁcally, an independent 12 13 simulated annealing trajectory was performed for each of the three isomers of Catalyst 3, 14 15 and from each trajectory, the four lowest-energy distinct structures that were obtained after 16 17 local minimization using high-level DFT (B3LYP/Def2-SVP) were included in this analysis. 18 19 All structures are provided in the Supporting Information. For all calculations reported in 20 21 this section, ((B3LYP/Def2-SVP)-in-(PBE/6-31G)) EMFT is performed using the smallest 22 23 and least computationally expensive high-level subsystem considered (partitioning scheme 24 25 1). 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 15 60 ACS Paragon Plus Environment Journal of Chemical Theory and Computation Page 16 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Figure 7: Three isomers of the Catalyst 3 resting state. Isomers 1–3 are displayed above, with 24 25 diﬀerent arrangements of the nitrogen- and oxygen-based ligands at the axial and equatorial sites. 26 The n-propyl ligand is held at the equatorial position in all cases. 27 28 29 Figure 8a presents the correlation between the relative conformer energies computed 30 31 using high-level DFT versus EMFT, for structures optimized using high-level DFT. As is 32 33 clear from the plot, the prediction of conformer energy rankings from EMFT is excellent, 34 35 with the rank-ordering of the 12 conformers – including those across isomers and with a 36 37 given isomer – being correctly predicted using EMFT. We further note that the overall R2 38 39 value of the correlation is 0.994, and that for every structure except the highest energy one, 40 41 the EMFT relative energy predictions coincide with the high-level DFT prediction to within 42 43 1 kcal/mol (indicated by the shaded region). 44 45 Figure 8b then tests the degree to which the optimization of the geometries using EMFT 46 47 (versus high-level DFT) eﬀects the quality of the conformer energy ranking. Each of the 48 49 twelve conformer structures that were initially optimized using high-level DFT were subse- 50 51 quently optimized using EMFT, and the energy of high-level DFT energy (at the high-level 52 53 DFT optimized geometry) is correlated against the EMFT energy (at the EMFT optimized 54 55 geometry). For all cases the error between the DFT and EMFT energy is less than 2 56 57 58 59 16 60 ACS Paragon Plus Environment Page 17 of 37 Journal of Chemical Theory and Computation

1 2 3 kcal/mol. The correlation remains excellent (R2 “ 0.997), and the relative ranking of the 4 5 conformer remains perfect (with the exception of two nearly iso-energetic conformers of iso- 6 7 mer 2). These results suggest that EMFT provides a powerful tool for screening catalyst 8 9 conformers, without the need for high-level DFT geometries or even single-point energies. 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Figure 8: Comparison of DFT and EMFT energy rankings of the 12 conformers obtained by 33 simulated annealing. The blue circles correspond to conformers of Isomer 1, the red squares to 34 those of Isomer 2, and the green triangles to those of Isomer 3. The gray bar represents a 1 35 ´1 36 kcal mol error bar at the diagonal. (a) DFT vs. EMFT energy for DFT-optimized conformer 37 geometries. (b) DFT energy of DFT-optimized conformer geometries vs. the EMFT energy of 38 the EMFT-optimized conformer geometries. 39 40 41 42 43 Predicted geometries 44 45 From an energy perspective, Figure 8b indicates that EMFT provides a satisfactory de- 46 47 scription of the optimized geometry for the catalyst resting state, which tends to be the 48 49 most abundant species in catalytic mechanism.68 We now further investigate the quality 50 51 of the EMFT-optimized structures for the catalyst resting state across all Catalysts 1-4. 52 53 For each resting state structure of the catalysts, geometry optimization was performed with 54 55 high-level DFT (B3LYP/Def2-SVP), EMFT ((B3LYP/Def2-SVP)-in-(PBE/6-31G)), using 56 57 58 59 17 60 ACS Paragon Plus Environment Journal of Chemical Theory and Computation Page 18 of 37

1 2 3 the minimal partitioning scheme 1, and low-level DFT (PBE/6-31G). 4 5 For Catalyst 1, Table 1 presents representative bond lengths obtained via geometry op- 6 7 timization using EMFT, in comparison to the corresponding values obtained using both the 8 9 low-level and high-level DFT methods. The rows of the table are grouped into distances 10 11 between atoms that are within the high-level region of the EMFT description (top unshaded 12 13 block), distances between atoms that span the high- and low-level regions (shaded block), 14 15 and distances between atoms that are within the low-level region of the EMFT descrip- 16 17 tion (bottom unshaded block). Corresponding tables for Catalysts 2–4 are provided in the 18 19 Supporting Information. 20 21 The general expectation of EMFT is for bonds within the high-level subsystem to be 22 23 described at the quality of the high-level DFT; this is largely borne out in Table 1 by the 24 25 fact that the difference between the EMFT and high-level DFT bond lengths (EMFT – 26 27 B3LYP) for atoms within the high-level region are smaller than the corresponding difference 28 29 between EMFT and the low-level DFT bond lengths (EMFT – PBE). Similarly, the there 30 31 is an expectation for bonds within the low-level subsystem to be described by EMFT at the 32 33 quality of the low-level DFT; this is again supported by the data in Table 1 by the fact 34 35 that the difference between the EMFT and low-level DFT bond lengths (EMFT – PBE) 36 37 for atoms within the low-level region are smaller than the corresponding difference between 38 39 EMFT and the high-level DFT bond lengths (EMFT – B3LYP). For bonds that span the 40 41 high- and low-level subsystems, it is seen in the table that these distances are generally more 42 43 consistent with the description of the low-level DFT theory, as is expected; nonetheless, we 44 45 find some cases, like the Ti–N bond length, where the description of the atoms spanning the 46 47 high- and low system deviates substantially from both the high- and low-level DFT methods. 48 49 Figure 9 summarizes the results in Table 1 and generalizes them to Catalysts 2–4. In 50 51 Figure 9a, we plot the root-mean-square-error (RMSE) for the difference between EMFT- 52 53 optimized bond lengths and either high-level or low-level DFT-optimized bond lengths for 54 55 atoms contained within the high-level region of the minimal EMFT partitioning. In Figure 56 57 58 59 18 60 ACS Paragon Plus Environment Page 19 of 37 Journal of Chemical Theory and Computation

1 2 3 Table 1: For Catalyst 1, bond lengths are compared between EMFT ((B3LYP/Def2-SVP)- 4 in-(PBE/6-31G)), high-level DFT (B3LYP/Def2-SVP), and low-level DFT (PBE/6-31G). 5 6 The minimal subsystem partitioning is used for EMFT (Figure 3, X “ 1). Columns are 7 grouped according to bonds located within the high-level subsystem (top unshaded block), 8 across the high- and low-level subsystems (shaded block), or within the low-level subsystem 9 (bottom unshaded block). Duplicate names for atoms are given superscript indexing for 10 differentiation. The bond length computed by EMFT, the difference between the EMFT 11 12 and PBE-calculated bond lengths (EMFT – PBE), and the difference between the EMFT 13 and B3LYP-calculated bond lengths (EMFT – B3LYP) are presented. 14 15 First Atom Second Atom EMFT (Å) EMFT – PBE (Å) EMFT – B3LYP (Å) 16 Ti C(n-Pr)1 2.071 ´0.010 ´0.005 17 C(n-Pr)1 C(n-Pr)2 1.513 0.012 0.001 18 ´ ´ 1 19 Ti C(ring) 2.229 ´0.013 ´0.002 20 Ti C(ring)2 2.362 0.005 0.010 21 Ti C(ring)3 2.557 0.023 0.065 22 Ti C(ring)4 2.515 0.021 0.068 23 5 24 Ti C(ring) 2.281 ´0.009 0.018 25 Ti N 1.790 ´0.102 ´0.104 26 N Si 1.899 0.012 0.085 27 N C(t-Bu) 1.510 0.001 0.015 28 Si C(ring)1 1.927 ´0.004 0.018 29 30 31 9b, we present the corresponding results for bond lengths involving atoms that lie within 32 33 the low-level region of the EMFT partitioning. For Catalyst 1, these results are obtained 34 35 from the data reported in Table 1, and for Catalysts 2–4, the data are obtained from the 36 37 corresponding tables in the Supporting Information. It is clear that for all four catalysts, 38 39 the EMFT-optimized geometries yield a description of atoms within the high-level region 40 41 that is more consistent with the high-level DFT description (panel a), whereas the atoms 42 43 with low-level region are more closely described at the level of the low-level DFT (panel 44 45 b). These results clearly illustrate that EMFT provides improved accuracy in the high-level 46 47 region while describing the remainder of the system at the quality of the low-level DFT 48 49 theory. 50 51 52 53 54 55 56 57 58 59 19 60 ACS Paragon Plus Environment Journal of Chemical Theory and Computation Page 20 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Figure 9: Root-mean-square error (RMSE) of bond lengths between EMFT and full-DFT geom- 20 etry optimized structures for representative bonds that are (a) inside the high-level subsystem or 21 (b) outside the high-level subsystem. The minimal subsystem partitioning is used for EMFT 22 (Figure 3, X “ 1). 23 24 25 Cost Analysis 26 27 28 The preceding results have shown that even with the minimal number of atoms in the 29 30 high-level region (partitioning 1), EMFT provides a description across all four catalysts con- 31 32 sidered here that is within chemical accuracy for substrate binding, reliable for resting-state 33 34 conformer stability ranking, and yields optimized geometries that are consistent with the 35 36 high-level DFT method around the catalyst active site. Furthermore, as has been empha- 37 38 sized in previous work,23,28 the use of EMFT brings substantial reductions in computational 39 40 cost in comparison to using the high-level DFT method for the full system. The reduced cost 41 42 of EMFT comes from both the reduced size of the basis set in the low-level region, as well as 43 44 the lower cost of evaluating the low-level DFT exchange correlation function for the atoms 45 46 in the low-level region. Speciﬁcally, in the current applications, the use of EMFT reduced 47 48 the need for evaluating exact exchange contributions to only the atoms within the high-level 49 50 subsystem. 51 52 Table 2 compares timings for EMFT ((B3LYP/Def2-SVP)-in-(PBE/6-31G)) in compar- 53 54 ison to high-level DFT (B3LYP/Def2-SVP) and low-level DFT (PBE/6-31G) applied to the 55 56 full system. In all cases, EMFT is performed using the minimal partitioning (partitioning 57 58 59 20 60 ACS Paragon Plus Environment Page 21 of 37 Journal of Chemical Theory and Computation

1 2 3 1). For each of the catalysts, timings are reported for the energy calculation such that 11 4 5 atoms are described in the high-level region (e.g. metal, propyl side-chain). All calculations 6 7 were done on 16-core Intel Skylake dual-CPUs with a clock speed of 2.1 GHz. 8 9 As is seen from Table 2, EMFT yields a cost reduction that ranges from a factor of 4 for 10 11 the smallest catalyst (Catalyst 1) to a factor of „20 for the largest catalysts (Catalysts 2 12 13 and 3). In general, the EMFT cost is only slightly increased relative to that for the low-level 14 15 DFT method. Furthermore, the number of self-consistent ﬁeld iterations needed for EMFT 16 17 is similar to the standard DFT methods. These results, in combination with the previously 18 19 shown benchmarks of EMFT accuracy, illustrate that the method preserves accuracy of the 20 21 high-level DFT method while providing vast reductions in computational cost. 22 23 Table 2: For the resting state structures of Catalysts 1–4, energy calculation tim- 24 25 ings for EMFT ((B3LYP/Def2-SVP)-in-(PBE/6-31G)) in comparison to high-level DFT 26 (B3LYP/Def2-SVP) and low-level DFT (PBE/6-31G) applied to the full system. EMFT 27 calculations employ the minimal high-level subsystem partitioning. Timings reported using 28 16-core Intel Skylake dual-CPUs with a clock speed of 2.1 GHz. 29 30 Catalyst Settings SCF Time (s) Cycles Total SCF Time (s) 31 32 High-Level DFT 1.0 18 18.6 33 1 EMFT 0.4 21 8.4 34 Low-Level DFT 0.3 22 5.7 35 High-Level DFT 33.1 20 662.8 36 37 2 EMFT 1.4 20 27.9 38 Low-Level DFT 1.1 20 22.6 39 High-Level DFT 25.1 19 477.8 40 3 EMFT 1.3 22 28.3 41 Low-Level DFT 1.1 25 26.5 42 43 High-Level DFT 13.3 19 251.9 44 4 EMFT 0.9 19 18.0 45 Low-Level DFT 0.8 20 14.8 46 47 48 49 50 51 52 53 54 55 56 57 58 59 21 60 ACS Paragon Plus Environment Journal of Chemical Theory and Computation Page 22 of 37

1 2 3 Application of EMFT for QM/MM Simulations 4 5 6 To illustrate the applicability of EMFT for the simulation of condensed phase reactions asso- 7 8 ciated with these homogeneous catalysts, we present EMFT/MM simulations (i.e., QM/MM 9 10 simulations with EMFT used for the QM region) of ethylene binding to Catalyst 1. We 11 12 model the ion-pairing of this cationic catalyst with four different counterions ranging from 13 – – 14 small, strongly-coordinating anions Cl and BF4 to sterically-bulky, weakly-coordinating 15 – – 16 anions CH3B(C6F5)3 and B(C6F5)4 . Particular focus is given to the way in which the 17 18 cationic catalyst interacts with counterions of varying size, given the crucial role that the 19 20 counterion plays in catalyst efficiency.69 21 22 EMFT/MM simulations are performed using EMFT ((B3LYP-D3/Def2-SVP)-in-(PBE- 23 24 D3/6-31G)) with the minimal high-level subsystem partitioning and using the D3 dispersion 25 26 correction in both the high- and low-level regions.70 The ethylene-bound Catalyst 1, with 61 27 28 atoms, is included in the EMFT region while the counterions and solvent (193–196 toluene 29 30 molecules) are treated within the MM region, as illustrated in Figure 10. Full calculation 31 32 details are provided in the Computational Methods section. 33 34 As a demonstration of robustness, Figure 11 illustrates the energy conservation of mi- 35 36 crocanonical EMFT/MM trajectories for each of the four considered counterions. In each 37 38 case, we show that there is minimal drift in the total energy, which is plotted relative to the 39 40 average kinetic energy for the system of the entire trajectory. The small fluctuations and 41 42 drift of the total energy in these plots over 30 ps indicates the good energy conservation of 43 44 the EMFT/MM trajectories. 45 46 We qualitatively assess the strength of the interaction between the cationic catalyst and 47 48 the anionic counterion using the radial distribution function (RDF) for the two species. 49 50 Specifically, Figure 12 plots the RDF with respect to the distance between the Ti atom of 51 52 Catalyst 1 and the center-of-mass of each of the four considered counterions from separate 53 54 EMFT/MM simulations. 55 56 It is clear that the EMFT/MM simulations lead to qualitatively different RDF profiles 57 58 59 22 60 ACS Paragon Plus Environment Page 23 of 37 Journal of Chemical Theory and Computation

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 Figure 10: Snapshots of the QM and MM subsystems used in the EMFT/MM simulations. 41 Catalyst 1 complex is presented as a balls-and-stick model, with Ti, Si, N, C, and H atoms 42 43 colored in red, yellow, blue, cyan, and white, respectively. Toluene molecules (solvent) are – – 44 shown using blue lines. From a–d respectively, the counteranions of interest, Cl , BF4 , – – 45 CH3B(C6F4)3 , and B(C6F5)4 , are depicted with a transparent ball-and-stick structure. 46 Each simulation is solvated in toluene with 193 to 196 molecules in a periodic simulation 47 cell. 48 49 50 51 52 53 54 55 56 57 58 59 23 60 ACS Paragon Plus Environment Journal of Chemical Theory and Computation Page 24 of 37

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 Figure 11: Energy conservation plots for EMFT/MM trajectories for Catalyst 1 with solvent 43 44 and various counterions (indicated in each panel) in the NVE ensemble. The gray line 45 indicates pEptq ´ Eavgq{pKEavgq, while the black line indicates the cumulative average of the 46 same quantity. 47 48 49 50 51 52 53 54 55 56 57 58 59 24 60 ACS Paragon Plus Environment Page 25 of 37 Journal of Chemical Theory and Computation

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Figure 12: RDF for the distance between Catalyst 1 and its counterion in the four 24 EMFT/MM simulations computed between 15–30 ps.(a) Close contact between the small 25 counterions (blue circle) and the metal binding site leads to dissociation of ethylene (green 26 triangle) from the catalyst (red semicircle). (b) Ethylene remains bound to the metal binding 27 site in the presence of bulky counterions. 28 29 30 for the smaller (Figure 12a) versus bulkier (Figure 12b) counteranions. The small, strongly 31 32 coordinating counterions chloride (Cl– ) and tetrafluoroborate (BF – ) are on average more 33 4 34 closely associated with Catalyst 1 than the bulkier counterions. Specifically Cl – and BF – 35 4 36 counteranions are located at „ 2.5 Å from the Ti atom, which is 4 Å closer than that of 37 38 CH B(C F ) – and B(C F ) – . 39 3 6 5 3 6 5 4 40 The close binding of the chloride and tetrafluoroborate ions to the catalyst has direct 41 42 consequences for the reactivity of the catalyst in solution. In the EMFT/MM simulations 43 44 performed with these smaller counterions, the ethylene substrate that is originally bound 45 46 to the catalyst is displaced from the binding site within 10 ps, driven by the formation of 47 48 the close contact of these counterions with the Ti atom. Schematically, this is shown in 49 50 Figure 12a cartoon with the counterion (blue circle) displacing the substrate (green triangle) 51 52 from the catalyst (red semicircle) binding site. Conversely, in the EMFT/MM simulations 53 54 involving the larger counterions CH B(C F ) – and B(C F ) – , the ethylene substrate re- 55 3 6 5 3 6 5 4 56 mains coordinated to the Ti atom of Catalyst 1. Experimentally, it is also known that the 57 58 59 25 60 ACS Paragon Plus Environment Journal of Chemical Theory and Computation Page 26 of 37

1 2 3 toluene solvent will compete with the ethylene substrate for binding, although this not seen 4 5 on the timescales of these simulations.71 The simulations indicate that olefin binding (Step 6 7 2, Figure 1) is strongly influenced by the strength of the interaction between the counte- 8 9 rion and metal complex. The results presented here are consistent with previous literature 10 11 demonstrating that bulkier counteranions increase the efficiency of the catalyst by binding 12 13 more weakly to the catalyst, thus promoting monomer binding and polymerization at the 14 15 cationic active site.62,69,72,73 16 17 18 19 20 Conclusion 21 22 23 We have developed a framework for combined EMFT and QM/MM MD simulations. Our 24 25 benchmarks indicate that for the wide range Group (IV) transition-metal polyolefin cata- 26 27 lysts, using a minimal high-level region for EMFT reproduces the energetic and structural 28 29 properties obtained by high-level DFT on the entire system. According to the timing data 30 31 provided in Table 2, EMFT is able to reduce the cost of DFT calculations from a factor of 4 32 33 up to a factor of 20 per SCF iteration while maintaining the accuracy of the high-level DFT 34 35 (hybrid functional). EMFT/MM simulations of counteranion binding to the cationic catalyst 36 37 demonstrate energy conservation within the range expected given the truncated treatment 38 39 of electrostatics, and provide insights into the nature of counteranion binding as a function 40 41 of counteranion size. Our results indicate that ethylene binding to the activated catalyst is 42 43 significantly influenced by the interaction between the counterion and metal complex. Close 44 – – 45 contact between the counterion and metal complex (i.e. Cl and BF4 ) leads to dissociation 46 47 of ethylene from the catalyst binding site. 48 49 Understanding the detailed role of the solvent and counterion environment is critical for 50 51 reliable prediction of catalytic activity, and hence for the design of new catalysts. While con- 52 53 ventional QM/MM simulations using hybrid DFT in the QM region are often unaffordable, 54 55 the EMFT embedding scheme provides the desired level of accuracy at greatly reduced com- 56 57 58 59 26 60 ACS Paragon Plus Environment Page 27 of 37 Journal of Chemical Theory and Computation

1 2 3 putational cost, by tuning in the exact exchange treatment to just a small number of atoms 4 5 in the immediate vicinity of the active transition-metal center. This is a key step on the 6 7 path towards widespread use of QM/MM simulation for discovery of new transition-metal 8 9 catalysts, both for polyolefin catalysis, and more widely. 10 11 12 13 14 Acknowledgement 15 16 17 This work was carried out with financial support within the University Partnership Initiative 18 19 from the Dow Chemical Company. This material is based upon work supported by the Na- 20 21 tional Science Foundation Graduate Research Fellowship under Grant No. DGE–1144469. 22 23 24 25 Supporting Information 26 27 28 The attached compressed folders contain the following data: (1) XYZ coordinate files for the 29 30 resting state and monomer-bound catalyst structures, (2) DFT-optimized structures of the 31 32 Catalyst 3 conformers, (3) EMFT-optimized structures of the Catalyst 3 conformers, and 33 34 (4) GROMACS files for the QM/MM study. 35 36 This information is available free of charge via the Internet at http://pubs.acs.org. 37 38 39 40 41 Authorship 42 43 44 L.C. and J.L. are co-first authors. 45 46 47 48 References 49 50 51 (1) Poree, C.; Schoenebeck, F. A Holy Grail in Chemistry: Computational Catalyst Design: 52 53 Feasible or Fiction? Acc. Chem. Res. 2017, 50, 605–608. 54 55 56 (2) Busico, C. Ziegler-Natta catalysis: Forever young. MRS Bull. 2013, 38, 224–228. 57 58 59 27 60 ACS Paragon Plus Environment Journal of Chemical Theory and Computation Page 28 of 37

1 2 3 (3) Chen, C. Designing catalysts for oleﬁn polymerization and copolymerization: Beyond 4 5 electronic and steric tuning. Nat. Rev. Chem. 2018, 2, 6–14. 6 7 8 (4) Warshel, A.; Levitt, M. Theoretical studies of enzymic reactions: Dielectric, electro- 9 10 static and steric stabilization of the carbonium ion in the reaction of lysozyme. J. Mol. 11 12 Biol. 1976, 103, 227–249. 13 14 15 (5) Warshel, A.; Karplus, M. Calculation of ground and excited state potential surfaces of 16 17 conjugated molecules. I. Formulation and parametrization. J. Am. Chem. Soc. 1972, 18 19 94, 5612–5625. 20 21 22 (6) Woods, C. J.; Shaw, K. E.; Mulholland, A. J. Combined Quantum Mechanics/Molecular 23 24 Mechanics (QM/MM) Simulations for Protein–Ligand Complexes: Free Energies of 25 26 Binding of Water Molecules in Inﬂuenza Neuraminidase. J. Phys. Chem. B 2014, 119, 27 28 997–1001. 29 30 31 (7) Gong, W.; Wu, R.; Zhang, Y. Thiol Versus Hydroxamate as Zinc Binding Group in 32 33 HDAC Inhibition: An Ab Initio QM/MM Molecular Dynamics Study. J. Comput. 34 35 Chem. 2015, 36, 2228–2235. 36 37 (8) Ugur, I.; Marion, A.; Aviyente, V.; Monard, G. Why Does Asn71 Deamidate Faster 38 39 Than Asn15 in the Enzyme Triosephosphate Isomerase? Answers from Microsecond 40 41 Molecular Dynamics Simulation and QM/MM Free Energy Calculations. Biochemistry 42 43 2015, 54, 1429–1439. 44 45 46 (9) David, R.; Jamet, H.; Nivière, V.; Moreau, Y.; Milet, A. Iron Hydroperoxide Interme- 47 48 diate in Superoxide Reductase: Protonation or Dissociation First? MM Dynamics and 49 50 QM/MM Metadynamics Study. J. Chem. Theory Comput. 2017, 13, 2987–3004. 51 52 53 (10) Ranaghan, K. E.; Morris, W. G.; Masgrau, L.; Senthilkumar, K.; Johannissen, L. O.; 54 55 Scrutton, N. S.; Harvey, J. N.; Manby, F. R.; Mulholland, A. J. Ab Initio QM/MM 56 57 58 59 28 60 ACS Paragon Plus Environment Page 29 of 37 Journal of Chemical Theory and Computation

1 2 3 Modeling of the Rate-Limiting Proton Transfer Step in the Deamination of Tryptamine 4 5 by Aromatic Amine Dehydrogenase. J. Phys. Chem. B 2017, 121, 9785–9798. 6 7 8 (11) Steinmann, C.; Olsson, M. A.; Ryde, U. Relative Ligand-Binding Free Energies Calcu- 9 10 lated from Multiple Short QM/MM MD Simulations. J. Chem. Theory Comput. 2018, 11 12 14, 3228–3237. 13 14 15 (12) Ortuño, M. A.; Vidossich, P.; Ujaque, G.; Conejero, S.; Lledós, A. Solution dynamics 16 17 of agostic interactions in T-shaped Pt(II) complexes from ab initio molecular dynamics 18 19 simulations. Dalton Trans. 2013, 42, 12165–12172. 20 21 22 (13) Shen, L.; Yang, W. Quantum Mechanics/Molecular Mechanics Method Combined with 23 24 Hybrid All-Atom and Coarse-Grained Model: Theory and Application on Redox Po- 25 26 tential Calculations. J. Chem. Theory Comput. 2016, 12, 2017–2027. 27 28 29 (14) Wood, G. P. F.; Sreedhara, A.; Moore, J. M.; Wang, J.; Trout, B. L. Mechanistic In- 30 31 sights into Radical-Mediated Oxidation of Tryptophan from ab Initio Quantum Chem- 32 33 istry Calculations and QM/MM Molecular Dynamics Simulations. J. Phys. Chem. A 34 35 2016, 120, 2926–2939. 36 37 (15) Zvereva, E. E.; Katsyuba, S. A.; Dyson, P. J.; Aleksandrov, A. V. Solvation of Palladium 38 39 Clusters in an Ionic Liquid: A QM/MM Molecular Dynamics Study. J. Phys. Chem. 40 41 C 2016, 120, 4596–4604. 42 43 44 (16) Hofer, T. S.; Hünenberger, P. H. Absolute proton hydration free energy, surface po- 45 46 tential of water, and redox potential of the hydrogen electrode from ﬁrst principles: 47 48 QM/MM MD free-energy simulations of sodium and potassium hydration. J. Chem. 49 50 Phys. 2018, 148, 222814. 51 52 53 (17) Manby, F.; Stella, M.; Goodpaster, J.; Miller, T. F., III A Simple, Exact Density- 54 55 Functional-Theory Embedding Scheme. J. Chem. Theory Comput. 2012, 8, 2564–2568. 56 57 58 59 29 60 ACS Paragon Plus Environment Journal of Chemical Theory and Computation Page 30 of 37

1 2 3 (18) Lee, S. J. R.; Welborn, M.; Manby, F. R.; Miller, T. F., III Projection-Based 4 5 Wavefunction-in-DFT Embedding. Acc. Chem. Res. 2019, 52, 1359–1368. 6 7 8 (19) Chulhai, D.; Goodpaster, J. Projection-Based Correlated Wave Function in Density 9 10 Functional Theory Embedding for Periodic Systems. J. Chem. Theory Comput. 2018, 11 12 14, 1928–1942. 13 14 15 (20) Bennie, S.; van der Kamp, M.; Pennifold, R.; Stella, M.; Manby, F.; Mulholland, A. A 16 17 Projector-Embedding Approach for Multiscale Coupled-Cluster Calculations Applied 18 19 to Citrate Synthase. J. Chem. Theory Comput. 2016, 12, 2689–2697. 20 21 22 (21) Zhang, X.; Bennie, S.; van der Kamp, M.; Glowacki, D.; Manby, F. R.; Mulholland, A. J. 23 24 Multiscale analysis of enantioselectivity in enzyme-catalysed ’lethal synthesis’ using 25 26 projector-based embedding. R. Soc. Open Sci. 2018, 5, 171390. 27 28 29 (22) Barnes, A.; Kaminski, J.; Borodin, O.; Miller, T. F., III Ab Initio Characterization of 30 31 the Electrochemical Stability and Solvation Properties of Condensed-Phase Ethylene 32 33 Carbonate and Dimethyl Carbonate Mixtures. J. Phys. Chem. C 2015, 119, 3865–3880. 34 35 (23) Fornace, M. E.; Lee, J.; Miyamoto, K.; Manby, F. R.; Miller, T. F., III Embedded 36 37 Mean-Field Theory. J. Chem. Theory Comput. 2015, 11, 568–580. 38 39 40 (24) Ding, F.; Manby, F. R.; Miller, T. F., III Embedded Mean-Field Theory with Block- 41 42 Orthogonalized Partitioning. J. Chem. Theory Comput. 2017, 13, 1605–1615. 43 44 45 (25) Bakowies, D.; Thiel, W. Hybrid Models for Combined Quantum Mechanical and Molec- 46 47 ular Mechanical Approaches. J. Phys. Chem. 1996, 100, 10580–10594. 48 49 50 (26) Dapprich, S.; KomÃąromi, I.; Byun, K.; Morokuma, K.; Frisch, M. J. A new ONIOM 51 52 implementation in Gaussian98. Part I. The calculation of energies, gradients, vibrational 53 54 frequencies and electric ﬁeld derivatives1Dedicated to Professor Keiji Morokuma in 55 56 celebration of his 65th birthday.1. J. Mol. Struct.:THEOCHEM 1999, 461-462, 1 – 21. 57 58 59 30 60 ACS Paragon Plus Environment Page 31 of 37 Journal of Chemical Theory and Computation

1 2 3 (27) Vreven, T.; Byun, K. S.; KomÃąromi, I.; Dapprich, S.; Montgomery, J. A.; Mo- 4 5 rokuma, K.; Frisch, M. J. Combining Quantum Mechanics Methods with Molecular 6 7 Mechanics Methods in ONIOM. J. Chem. Theory Comput. 2006, 2, 815–826, PMID: 8 9 26626688. 10 11 12 (28) Jiang, H.; Kammler, M.; Ding, F.; Dorenkamp, Y.; Manby, F. R.; Wodtke, A. M.; 13 14 Miller, T. F., III; Kandratsenka, A.; Bünermann, O. Imaging covalent bond formation 15 16 by H atom scattering from graphene. Science 2019, 364, 379–382. 17 18 19 (29) Lee, S. J.; Miyamoto, K.; Ding, F.; Manby, F. R.; Miller, T. F. Density-based errors 20 21 in mixed-basis mean-field electronic structure, with implications for embedding and 22 23 QM/MM methods. Chem. Phys. Lett. 2017, 683, 375 – 382, Ahmed Zewail (1946- 24 25 2016) Commemoration Issue of Chemical Physics Letters. 26 27 28 (30) Ding, F.; Tsuchiya, T.; Manby, F. R.; Miller, T. F. Linear-Response Time-Dependent 29 30 Embedded Mean-Field Theory. J. Chem. Theory Comput. 2017, 13, 4216–4227, PMID: 31 32 28783359. 33 34 35 (31) Kaminsky, W. Trends in Polyolefin Chemistry. Macromol. Chem. Phys. 2008, 209, 36 37 459–466. 38 39 (32) Rappé, A. K.; Skiff, W. M.; Casewit, C. J. Modeling Metal-Catalyzed Olefin Polymer- 40 41 ization. Chem. Rev. 2000, 100, 1435–1456. 42 43 44 (33) Coates, G. W. Precise Control of Polyolefin Stereochemistry Using Single-Site Metal 45 46 Catalysts. Chem. Rev. 2000, 100, 1223–1252. 47 48 49 (34) Landis, C. R.; Sillars, D. R.; Batterton, J. M. Reactivity of Secondary Metallocene 50 51 Alkyls and the Question of Dormant Sites in Catalytic Alkene Polymerization. J. Am. 52 53 Chem. Soc. 2004, 126, 8890–8891. 54 55 56 57 58 59 31 60 ACS Paragon Plus Environment Journal of Chemical Theory and Computation Page 32 of 37

1 2 3 (35) Woo, T. K.; Margl, P. M.; Ziegler, T.; Blöchl, P. E. Static and ab Initio Molecular 4 5 Dynamics Study of the Titanium(IV)-Constrained Geometry Catalyst (CpSiH NH)Ti- 6 2 7 R+. 2. Chain Termination and Long Chain Branching. Organometallics 1997, 16, 3454– 8 9 3468. 10 11 12 (36) Margl, P. M.; Deng, L.; Ziegler, T. Cobalt(II) Imino Pyridine Assisted Ethylene Poly- 13 14 merization: A Quantum-Mechanical/Molecular-Mechanical Density Functional Theory 15 16 Investigation. Organometallics 1999, 18, 5701–5708. 17 18 19 (37) Lanza, G.; Fragalà, I. L.; Marks, T. J. Ligand Substituent, Anion, and Solvation Ef- 20 21 fects on Ion Pair Structure, Thermodynamic Stability, and Structural Mobility in “Con- 22 23 strained Geometry” Olefin Polymerization Catalysts: an Ab Initio Quantum Chemical 24 25 Investigation. J. Am. Chem. Soc. 2000, 122, 12764–12777. 26 27 28 (38) Lanza, G.; Fragalà, I. L.; Marks, T. J. Energetic, Structural, and Dynamic Aspects of 29 30 Ethylene Polymerization Mediated by Homogeneous Single-Site “Constrained Geome- 31 32 try Catalysts” in the Presence of Cocatalyst and Solvation: An Investigation at the ab 33 34 Initio Quantum Chemical Level. Organometallics 2002, 21, 5594–5612. 35 36 37 (39) Solans-Monfort, X.; Clot, E.; Copéret, C.; Eisenstein, O. Understanding Structural 38 39 and Dynamic Properties of Well-Defined Rhenium-Based Olefin Metathesis Cata- 40 41 lysts, Re(”CR)(=CHR)(X)(Y), from DFT and QM/MM Calculations. Organometallics 42 43 2005, 24, 1586–1597. 44 45 (40) Yang, S.-Y.; Ziegler, T. Combined Car–Parrinello QM/MM Dynamic Study on 46 47 the Propagation and Termination Steps of Ethylene Polymerization Catalyzed by 48 49 [Cp2ZrR(µ-Me)B(C6F5)3] (R = Me, Pr). Organometallics 2006, 25, 887–900. 50 51 52 (41) Devore, D. D.; Timmers, F. J.; Hasha, D. L.; Rosen, R. K.; Marks, T. J.; Deck, P. A.; 53 54 Stern, C. L. Constrained-Geometry Titanium(II) Diene Complexes. Structural Diversity 55 56 and Olefin Polymerization Activity. Organometallics 1995, 14, 3132–3134. 57 58 59 32 60 ACS Paragon Plus Environment Page 33 of 37 Journal of Chemical Theory and Computation

1 2 3 (42) Woo, T. K.; Margl, P. M.; Lohrenz, J. C. W.; Blöchl, P. E.; Ziegler, T. Combined Static 4 5 and Dynamic Density Functional Study of the Ti(IV) Constrained Geometry Catalyst 6 7 (CpSiH NH)TiR+. 1. Resting States and Chain Propagation. J. Am. Chem. Soc. 1996, 8 2 9 118, 13021–13030. 10 11 12 (43) Zhou, Z.; Stevens, J. C.; Klosin, J.; Kümmerle, R.; Qiu, X.; Redwine, D.; Cong, R.; 13 14 Taha, A.; Mason, J.; Winniford, B.; Chauvel, P.; Montañez, N. NMR Study of Isolated 15 16 2,1-Inverse Insertion in Isotactic Polypropylene. Macromolecules 2009, 42, 2291–2294. 17 18 19 (44) Arriola, D. J.; Carnahan, E. M.; Hustad, P. D.; Kuhlman, R. L.; Wenzel, T. T. Catalytic 20 21 Production of Oleﬁn Block Copolymers via Chain Shuttling Polymerization. Science 22 23 2006, 312, 714–719. 24 25 26 (45) Becke, A. D. Density-functional thermochemistry. III. The role of exact exchange. J. 27 28 Chem. Phys. 1998, 98, 5648–5652. 29 30 31 (46) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti correlation-energy 32 33 formula into a functional of the electron density. Phys. Rev. B 1988, 37, 785–789. 34 35 (47) Vosko, S. H.; Wilk, L.; Nusair, M. Accurate spin-dependent electron liquid correlation 36 37 energies for local spin density calculations: A critical analysis. Can. J. Phys. 2011, 58, 38 39 1200–1211. 40 41 42 (48) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. Ab initio calculation 43 44 of vibrational absorption and circular dichroism spectra using density functional force 45 46 ﬁelds. J. Phys. Chem. 1994, 98, 11623–11627. 47 48 + 49 (49) Ricca, A.; Bauschlicher, C. W. J. Successive Binding Energies of Fe(CO)5 . J. Phys. 50 51 Chem. 1994, 98, 12899–12903. 52 53 54 (50) Musaev, D. G.; Morokuma, K. Structure, Stability, and Bonding of Transition- 55 56 57 58 59 33 60 ACS Paragon Plus Environment Journal of Chemical Theory and Computation Page 34 of 37

1 2 3 Metal–Boryl Complexes. A Molecular Orbital Study. J. Phys. Chem. 1996, 100, 6509– 4 5 6517. 6 7 8 (51) Froese, R. D. J.; Musaev, D. G.; Morokuma, K. Theoretical Study of Substituent Eﬀects 9 10 in the Diimine–M(II) Catalyzed Ethylene Polymerization Reaction Using the IMOMM 11 12 Method. J. Am. Chem. Soc. 1998, 120, 1581–1587. 13 14 15 (52) Froese, R. D. J.; Musaev, D. G.; Morokuma, K. Theoretical Studies of the Factors 16 17 Controlling Insertion Barriers for Oleﬁn Polymerization by the Titanium-Chelating 18 19 Bridged Catalysts. A Search for More Active New Catalysts. Organometallics 1999, 20 21 18, 373–379. 22 23 24 (53) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made 25 26 Simple. Phys. Rev. Lett. 1996, 77, 3865–3868. 27 28 29 (54) Manby, F.; Miller, T.; Bygrave, P.; Ding, F.; Dresselhaus, T.; Batista-Romero, F.; 30 31 Buccheri, A.; Bungey, C.; Lee, S.; Meli, R.; Miyamoto, K.; Steinmann, C.; Tsuchiya, T.; 32 33 Welborn, M.; Wiles, T. entos: A Quantum Molecular Simulation Package. 2019, 34 35 (55) Vosko, S. H.; Wilk, L.; Nusair, M. Accurate spin-dependent electron liquid correlation 36 37 energies for local spin density calculations: a critical analysis. Can. J. Phys. 1980, 58, 38 39 1200–1211. 40 41 42 (56) Grimme, S.; Bannwarth, C.; Shushkov, P. A Robust and Accurate Tight-Binding Quan- 43 44 tum Chemical Method for Structures, Vibrational Frequencies, and Noncovalent Inter- 45 46 actions of Large Molecular Systems Parametrized for All spd-Block Elements (Z = 47 48 1âĂŞ86). J. Chem. Theory Comput. 2017, 13, 1989–2009. 49 50 51 (57) Berendsen, H. J. C.; van der Spoel, D.; van Drunen, R. GROMACS: A message-passing 52 53 parallel molecular dynamics implementation. Comput. Phys. Commun. 1995, 91, 43– 54 55 56. 56 57 58 59 34 60 ACS Paragon Plus Environment Page 35 of 37 Journal of Chemical Theory and Computation

1 2 3 (58) Jorgensen, W. L.; Tirado-Rives, J. Potential energy functions for atomic-level simula- 4 5 tions of water and organic and biomolecular systems. J. Proc. Natl. Acad. Sci. 2005, 6 7 102, 6665–6670. 8 9 10 (59) Caleman, C.; van Maaren, P. J.; Hong, M.; Hub, J. S.; Costa, L. T.; van der Spoel, D. 11 12 Force Field Benchmark of Organic Liquids: Density, Enthalpy of Vaporization, Heat 13 14 Capacities, Surface Tension, Isothermal Compressibility, Volumetric Expansion Coef- 15 16 ficient, and Dielectric Constant. J. Chem. Theory Comput. 2012, 8, 61–74, PMID: 17 18 22241968. 19 20 21 (60) virtualchemistry. http://virtualchemistry.org/. 22 23 24 (61) Mulliken, R. S. Electronic Population Analysis on LCAOâĂŞMO Molecular Wave Func- 25 26 tions. I. J. Chem. Phys. 1955, 23, 1833–1840. 27 28 29 (62) Rowley, C. N.; Woo, T. K. Counteranion Effects on the Zirconocene Polymerization Cat- 30 31 alyst Olefin Complex from QM/MM Molecular Dynamics Simulations. Organometallics 32 33 2011, 30, 2071–2074. 34 35 (63) van Gunsteren, W. F.; Berendsen, H. J. C.; Rullmann, J. A. C. Inclusion of reaction 36 37 fields in molecular dynamics. Application to liquid water. Faraday Discuss Chem Soc. 38 39 1978, 66, 58–70. 40 41 42 (64) Hess, B.; Bekker, H.; Berendsen, H. J. C.; Fraaije, J. G. E. M. LINCS: A linear con- 43 44 straint solver for molecular simulations. J. Comput. Chem. 1997, 18, 1463–1472. 45 46 47 (65) Evans, D. J.; Holian, B. L. The Nosé-Hoover thermostat. J. Chem. Phys. 1985, 83, 48 49 4069–4074. 50 51 52 (66) Parrinello, M.; Rahman, A. Polymorphic transitions in single crystals: A new molecular 53 54 dynamics method. J. Appl. Phys. 1981, 52, 7182–7190. 55 56 57 58 59 35 60 ACS Paragon Plus Environment Journal of Chemical Theory and Computation Page 36 of 37

1 2 3 (67) Lindahl, E.; Hess, B.; van der Spoel, D. GROMACS 3.0: a package for molecular 4 5 simulation and trajectory analysis. J. Mol. Model. 2001, 7, 306–317. 6 7 8 (68) Malinoski, J.; White, P.; Brookhart, M. Structural Characterization of [κ2-(t- 9 2 + - 10 Bu)2PCH2PC(O)C6PH5P]PdMe(η P-C2H4) BAr4 : A Model for the Catalyst Resting 11 12 State for Ethylene Polymerization. Organometallics 2003, 22, 621–623. 13 14 15 (69) Chen, Y.-X.; Stern, C. L.; Yang, S.; Marks, T. J. Organo-Lewis Acids As Cocat- 16 17 alysts in Cationic Metallocene Polymerization Catalysis. Unusual Characteristics of 18 19 Sterically Encumbered Tris(perfluorobiphenyl)borane. J. Am. Chem. Soc. 1996, 118, 20 21 12451–12452. 22 23 24 (70) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio 25 26 parametrization of density functional dispersion correction (DFT-D) for the 94 elements 27 28 H-Pu. The Journal of Chemical Physics 2010, 132, 154104. 29 30 31 (71) Collins, R. A.; Russell, A. F.; Mountford, P. Group 4 metal complexes for homogeneous 32 33 olefin polymerisation: a short tutorial review. Appl. Petrochem. Res. 2015, 5, 153–171. 34 35 (72) Roberts, J. A. S.; Chen, M.-C.; Seyam, A. M.; Li, L.; Zuccaccia, C.; Stahl, N. G.; 36 37 Marks, T. J. Diverse Stereocontrol Effects Induced by Weakly Coordinating Anions. 38 39 Stereospecific Olefin Polymerization Pathways at Archetypal Cs- and C1-Symmetric 40 41 Metallocenium Catalysts Using Mono- and Polynuclear Halo-perfluoroarylmetalates as 42 43 Cocatalysts. J. Am. Chem. Soc. 2007, 129, 12713–12733. 44 45 46 (73) Riddlestone, I. M.; Kraft, A.; Schaefer, J.; Krossing, I. Taming the Cationic Beast: 47 48 Novel Developments in the Synthesis and Application of Weakly Coordinating Anions. 49 50 Angew. Chem. 2018, 57, 13982–14024. 51 52 53 54 55 56 57 58 59 36 60 ACS Paragon Plus Environment Page 37 of 37 Journal of Chemical Theory and Computation

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