Assessment and Application of Density Functional Theory for the

Article pubs.acs.org/JPCA

Assessment and Application of Density Functional Theory for the Prediction of Structure and Reactivity of Vanadium Complexes Brendan J. H. Sheppard,† Michael P. Shaver,‡ and Jason K. Pearson*,† †

Department of Chemistry, University of Prince Edward Island, Charlottetown, PE Canada C1A 4P3 School of Chemistry, University of Edinburgh, Joseph Black Building, David Brewster Road, Edinburgh EH9 3FJ, United Kingdom

‡

S Supporting Information *

ABSTRACT: We assess the performance of six density functionals, each paired with one of five basis sets (a total of 30 model chemistries) for the prediction of geometrical parameters in the coordination sphere of nine vanadium complexes (for a total of 270 structural analyses). We find that results are generally consistent over the range of functionals tested and that none fail drastically. For bond lengths, the model chemistry PBE0/QZVP performed the best overall (having a MAD of only 0.02 Å from experiment) yet PBE0/6-31G* provides nearly identical results. For bond angles, PBE0 also performed best overall and, when combined with the 6-31G* basis, produces one of the smallest error distributions of any model chemistry tested. We subsequently applied the PBE0/6-31G* model chemistry to understanding the mechanism of action of a [BIMPY]VCl3 catalyst in the polymerization of styrene (Sty) and vinyl acetate (VAc). Our results indicate that the [BIMPY]VCl3 catalyst operates through a unique, two-step reaction pathway: dehalogenation to form a reactive V(II) intermediate (a highly favorable process) followed by a potentially reversible OMRP to control the polymerization of vinyl acetate. Control over vinyl acetate is facilitated by both the higher reactivity of the radical species and the participation of the ester group in the trapping step. In both the Sty and VAc cases we predict relatively poor control of the polymerization with the vanadium catalyst, which is in good agreement with our experimental results.

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INTRODUCTION Vanadium is an essential element of growing importance. With multiple accessible oxidation states and a flexible coordination number and geometry, applications of vanadium in coordination chemistry, catalysis, and materials science continue to grow in both breadth and depth. The unique chemistry of vanadium has inspired extensive research into antidiabetics,1−4 coordination chemistry, especially with arylimido ligands,5,6 catalytic oxidation and epoxidation,7−9 olefin polymerization,10−13 and organometallic mediated radical polymerization (OMRP).14 Our interest in vanadium began with the discovery that bis(imino)pyridine (BIMPY = 2,6[(2,6-iPr2C6H 3)NC(Me)]2(C5H3N)) vanadium complexes were effective mediators for the controlled radical polymerization of vinyl acetate.15−17 Specifically, our experimental and computational mechanistic studies suggested that such control is derived solely from the OMRP regime, with the irreversible dehalogenation of a parent V(III) complex forming an active [BIMPY]VCl2 in situ (Scheme 1), which can reversibly trap radicals through an organometallic intermediate (process 3).15 Alternatively, we considered several other pathways including an atom transfer radical polymerization equilibrium (process 1), a formally V(III)/V(IV) equilibrium (process 2), and reversible carbon− carbon bond formation occurring via a combination of the growing free radical with a ligand-based radical (process 4). We assessed these pathways thermodynamically using molecular © XXXX American Chemical Society

modeling to understand this catalytic mechanism of action though we employed a significantly truncated ligand framework (Me[BIMPY] = 2,6-(MeNCH)2(C5H3N)) and a model chemistry that had not been extensively validated specifically for vanadium systems, raising internal questions about the veracity of these computational results. We realized during this work that there is a relative paucity of density functional theory (DFT) validation studies specifically for vanadium in a variety of coordination and oxidation states18 and thus endeavored to determine the theoretical model required to obtain reliable results in vanadium computational chemistry. Most previous validation or applications of DFT for vanadium are specific to vanadium metal,19 oxides,20−24 and/or clusters25 and may not be well representative of the geometrical and electronic diversity in vanadium coordination chemistry. Of more significant relevance is the work of Ooms et al.,26 Justino et al.,27 and Li et al.28 on heptacoordinate hydroxylamido vanadium picolinate complexes, oxoperoxo vanadium complexes of lactic acid, and divanadocene carbonyls, respectively (though only ref 27 explicitly tests more than two model chemistries). Generally speaking, each found that DFT can provide meaningful results for vanadium coordination chemReceived: April 13, 2015 Revised: July 2, 2015

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DOI: 10.1021/acs.jpca.5b03552 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

functionals chosen for this study include B3LYP,31,32 B3PW91,31,33 M06,34 M06-2X,34 M06-L,35 and PBE0.36−38 These were chosen on the basis of their general popularity (especially within previous work on vanadium coordination26−28) and the fact that they span a reasonable degree of “functional space”. The Minnesota functionals (M06 and M06L) were chosen because of the inclusion of transition metals in their parametrization34,35 and the PBE0 functional was chosen because it is parametrized using only fundamental physical constants and is consequently a robust density functional for a wide variety of uses. Along with these six density functionals, five basis sets were i m p l e m e n t e d : P o p l e’ s 6-3 1G * , 3 9 t h e r e l a t i v i s t i c LANL2DZ,40−43 Dunning’s correlation consistent cc-pVTZ,44 and Ahlrichs’ triple and quadruple-ζ basis sets, TZVP45 and QZVP,46 respectively. This choice spans fundamentally different flavors of basis sets, along with different levels of valence splitting, size, and effective core potentials. An all-electron geometry optimization for each combination of density functional (6) and basis set (5) was performed for each of the nine species (shown in Figure 1) for a total of 6 × 5 × 9 =

Scheme 1. Potential Controlled Radical Polymerization Pathways for [BIMPY]VC13

istry; however, as we will show, there are important and sometimes qualitative differences that can arise between well tested models and care must be taken in interpretation of the results. In our case we rely explicitly on experimental structures and mechanistic studies to offer insight on the application of DFT to vanadium coordination chemistry. In this study, we analyze the geometrical parameters of the coordination sphere of nine organovanadium complexes of which crystal structure data are available. Unfortunately, it is difficult to obtain consistent data for properties other than geometry for a variety of organovanadium complexes. We therefore confine our analysis of the test set to bond lengths and angles within the coordination sphere of the central vanadium atom. Starting from the crystal structure data, six density functionals in combination with five basis sets were applied for a total of 30 model chemistries. Subsequently, we apply our optimal methodology to the study of the vanadium-mediated controlled radical polymerization of styrene and vinyl acetate (shown in Scheme 1).15 This affords both the assessment of the theory based on agreement with our previously reported mechanistic studies and also the extension of our previous computations on truncated model ligand systems to their full molecular size, allowing us to better evaluate the proposed polymerization mechanism in conjunction with our experimental observations.

Figure 1. Structures of the nine molecules included in this study.

270 structures. Harmonic vibrational frequency calculations were performed on the structures of each molecule to ensure they represented local minima on their respective potential energy surfaces. The set of molecules used in this study are all reasonably small, monometallic vanadium complexes spanning a variety of metal−ligand bond types, geometries, charges, and oxidation states. This diversity of models and molecules affords the choice of a robust theoretical framework for the treatment of vanadium species. The oxidation states, d-electron counts, multiplicities, and metal geometries are summarized in Table 1. The absolute deviation of theoretical bond lengths from the experimental crystal structure (in Å) were determined and for molecules with multiple nonequivalent instances of the same bond type (V−Cl for example), the average of these deviations is reported and denoted the mean absolute deviation (MAD). This is also the case for bond angles in degrees. The average MAD for each functional over all basis sets is denoted the DFT MAD, and the average MAD for each basis set over all

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COMPUTATIONAL METHODS For the validation of a chosen set of model chemistries, we employed the Gaussian 0929 and Q-Chem 3.230 suites of programs. For the geometrical parameter benchmarking, all molecular species started from the crystal structure geometries obtained from the Cambridge Structural Database. The density B


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full all-electron optimization at the validated level of theory. Again, harmonic frequencies were then predicted to afford thermochemical corrections to the free energy and to confirm the nature of the stationary point.

Table 1. Summary of Molecules Included in This Work mol

ox. state

d count

multiplicity

geometry

1 2 3 4 5 6 7 8 9

3 4 4 2 3 0 −1 5 4

d2 d1 d1 d3 d2 d5 d6 d0 d1

2 2 2 4 3 2 1 1 2

tetrahedral octahedral octahedral octahedral trigonal bipyramidal octahedral octahedral square pyramidal square antiprismatic

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RESULTS AND DISCUSSION Assessment of DFT for Vanadium. Reading Strip Charts. The results of this work are illustrated in Figures 2 and 3 by means of strip charts analogous to those reported by Sherrill et al.49 They are divided into six sections, one for each density functional, and each section is subdivided into five strips, one for each basis set. The strips are made up of color coded vertical lines representing different bond lengths (Figure 2) or bond angles (Figure 3). Each colored line corresponds to the MAD for that bond length or angle at the model chemistry described by that strip. When reading these charts, one looks for narrow sets of strips concentrated close to zero, indicating the model chemistry performed consistently well for all bond lengths or angles. Vanadium−Ligand Bond Lengths. Vanadium−carbon bonds are present in 1, 6, and 7. Complexes 6 and 7 are geometrically similar but vary in their electronic structure whereas 1 possesses a single η5 cyclopentadienyl ligand (Cp). For the vanadium−carbon interatomic distances within the Cp ligand, each was measured and averaged over the five Cp carbon atoms, as was done by Truhlar in his study on cyclopentadienyl systems.50 The MADs for vanadium−carbon bond lengths are represented in Figure 2 by black vertical lines. Over all the functionals tested, PBE0 produced the lowest DFT

functionals is denoted the basis set MAD (BS MAD). Full tables of bond lengths and angles are available in the Supporting Information. Due to convergence issues, four of the structures could not be optimized using the extensive QZVP basis and are thus not included in this benchmark. The missing structures are molecule 2 M06-L/QZVP, molecule 3 M06-2X/QZVP, and molecule 4 B3LYP/QZVP and M06/ QZVP. On the scale of the 6 × 5 × 9 = 270 structures, these 4 do not significantly affect the conclusions of our study. For the investigation of the polymerization pathways we began with the optimized structures from ref 15 and reoptimized using our validated model (details on the model chemistry presented below) including harmonic frequency prediction for thermochemical energetics and PES validation. Subsequently, we extended the truncated ligand framework to the full BIMPY system and optimized the external ligand framework (holding the immediate vanadium coordination sphere fixed) with a semiempirical PM347,48 model prior to a

Figure 2. Mean absolute deviation of vanadium−ligand bond lengths (in angstroms). Refer to the subsection Reading Strip Charts above for an explanation of how these data are presented. C


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The Journal of Physical Chemistry A Table 2. Absolute Errors for Vanadium−Ligand Bond Lengths (Å) basis set

B3LYP

B3PW91

M06

M06-2X

M06-L

PBE0

BS MAD

6-31G* LANL2DZ cc-pVTZ TZVP QZVP DFT MAD

0.040 0.056 0.047 0.048 0.041 0.047

0.029 0.045 0.033 0.032 0.030 0.034

0.026 0.043 0.029 0.031 0.029 0.031

0.033 0.050 0.037 0.038 0.034 0.039

0.032 0.051 0.036 0.038 0.034 0.038

0.025 0.042 0.028 0.028 0.024 0.029

0.031 0.048 0.035 0.036 0.032

Figure 3. Mean absolute deviation of vanadium−ligand bond angles in degrees. B3LYPillVP ∠SVS bond angle, 4.68°, and M06-L/6-31G* ∠NVC bond angle, 4.0°, were omitted from the figure as they are significantly larger than the other data. Dashed lines indicate an overlap of the respective colors. Refer to the subsection Reading Strip Charts above for an explanation of how these data are presented.

over all the BS MADs, LANL2DZ outperformed the rest with a value of 0.011 Å. Complex 9 contains vanadium−sulfur bonds (yellow vertical lines in Figure 2) and has an eight-coordinate metal center with four bidentate ligands arranged roughly tetrahedrally around the central vanadium atom. Though the PBE0 functional again predicted the lowest DFT MAD at 0.061 Å, this is still more than double the magnitude of many of the MADs for the other bond types. The lowest MAD was 0.043 Å from PBE0/ccpVTZ. The largest MAD was produced by B3LYP/LANL2DZ with a value of 0.150 Å. Complexes 1, 4, 5, and 8 exhibited vanadium-halogen bonds (including chlorine and bromine). 8 was the only species in the test set containing vanadium−bromine bonds. It is a tetrabromovanadium complex so the values reported are an average of the four vanadium−bromine bonds. These data are represented as orange vertical lines in Figure 2. The effective core potentials of LANL2DZ did not perform particularly well for the relatively heavy bromine atoms in this case as the BS MAD for LANL2DZ is more than double that of some of the other basis sets and nearly 6 times larger than 6-31G*. When coupled with 6-31G*, all of the density functionals perform well, particularly so for PBE0 and M06, and we note a consistent trend emerging with these model chemistries. Again, these two density functionals produced the lowest DFT MADs with 0.032 and 0.035 Å, respectively. The vanadium−chlorine bonds in 1, 4, and 5 were most accurately modeled by the M06 density functional and MADs for this bond length are represented in Figure 2 by green vertical lines. It can be seen

MAD (0.019 Å), though M06 was very close (0.020 Å). In considering specifc model chemistries, PBE0/cc-pVTZ and TZVP were both on average within 0.013 Å of experimental values. PBE0 and M06 paired with 6-31G* produced a similar MAD of only 0.014 Å. All BS MADs were below 0.030 Å with 6-31G* being the lowest at 0.020 Å. Vanadium−nitrogen bond lengths were most accurately predicted by the M06-L density functional. MADs of this bond length are represented in Figure 2 by blue vertical lines. In general, the three Minnesota functionals performed well for this bond type with DFT MADs of 0.038, 0.034, and 0.032 Å for M06, M06-2X, and M06-L, respectively. Comparatively, B3LYP produced a DFT MAD of 0.066 Å, the worst overall. The specific model chemistry M06-L/QZVP produced the lowest MAD overall at 0.017 Å. Both 2 and 3 contain vanadium−oxygen single bonds, and the MADs for these are represented in Figure 2 by red vertical lines. All density functionals tested produced bond lengths to within 0.021 Å on average for this bond type. Again, however, PBE0 performs well with a DFT MAD value of 0.009 Å followed closely by M06 (0.010 Å). In terms of the BS MADs, they are all within 0.009 Å of each other implying that the choice of basis set is less important than the functional here. Vanadium−oxygen π bonds were the only bond lengths best reproduced by the B3LYP density functional in our study; however, all the density functionals in this study modeled this bond type, on average, accurate to less than two hundredths of an angstrom, with the exception of M06-2X. Their MADs are represented with purple vertical lines in Figure 2. Interestingly, D


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accuracy is an important feature of a good density functional. The PBE0 functional was most consistent, producing a DFT MAD of 1.57° and there was only slight variance between basis sets. The remaining complexes having bond angles containing nitrogen are 3, 4, and 5. Mean absolute deviations for ∠NVN angles from 4 and 5 are presented in Figure 3 with blue vertical lines. The model chemistry B3LYP/TZVP performed well for this parameter, producing a MAD of 0.14°. 3 is the only molecule in the test set with ∠NVO and LOVO angles. Due to the symmetry in this molecule, the MADs for these two angles are identical, as can be seen in Figure 3 by the overlapping red and cyan vertical lines (shown as dashed lines in the figure). For both the bond angles PBE0/LANL2DZ performed well (MAD of 0.80°) in addition to PBE0/QZVP and B3LYP/QZVP. The density functional with the lowest DFT MAD here was B3PW91 with a value of 1.21°. In this case, the LANL2DZ basis set performed particularly well as it outperformed all other basis sets by at least 0.2° and was less than half the BS MAD of 6-31G* and cc-pVTZ. PBE0 outperformed the other functionals for the ∠OVO angles present in 2 and 3 (DFT MAD of 1.64°). The MADs for this bond type are in Figure 3 represented by yellow vertical lines. The closest match to experimental data came from B3PW91 with the 6-31G* basis set, recording a MAD of 1.29°. The other chalcogen-containing bond angle was the ∠SVS angle exhibited in 9. The MADs for ∠SVS angles in this system are represented by gray vertical lines in Figure 3. M06-2X performed best for this parameter; however, PBE0 was essentially equivalent. B3LYP performed well with the exception of B3LYP/TZVP which predicted bond angles with errors greater than 4°. Considering the halogens, complexes 1, 4, and 5 all contain ∠NVCl angles and the MADs are presented in Figure 3 with black vertical lines. The best results here come from the M06-L functional (DFT MAD of 0.95°) and the choice of basis set is not so important here as the BS MADs are all within 0.08° of each other with the exception of LANL2DZ. The only complex in the test set to contain a bromine atom is 8, and thus it is the only molecule to contain the two bond angles ∠OVBr and ∠BrVBr. These are represented by magenta and brown vertical lines in Figure 3, respectively. This structure has high symmetry and thus is a relatively simple case for theory. All the density functionals produced DFT MADs within 0.3° of experiment with a maximum MAD still falling within a half of a degree. B3LYP paired with 6-31G* predicted the ∠OVBr bond angle exactly to fit experiment. The Minnesota functionals performed the worst for this bond angle; however, the MADs are certainly acceptable and an order of magnitude less than those of many other bond angle types. The BS MADs varied by no more than a third of a degree with 6-31G* and TZVP both predicting bond angles on average to within 0.1° from crystal structure. As seen in Figure 3, the brown vertical lines for ∠BrVBr nearly always overlap the magenta lines for ∠OVBr. Figure 3 represents MADs for ∠ClVCl angles with vertical orange lines. This bond type is found in three species: 1, 4, and 5. It should be noted that in 4 the chlorines are trans to each other, making them a relatively simple case for theory by symmetry. Due to this, the MADs for 4 are nearly zero every time, with a maximum MAD of 0.02°. Over the three molecules, all the density functionals with the exceptions of

that nearly all the model chemistries produced vanadium− chlorine bond lengths to within 0.050 Å with the exception being B3LYP/LANL2DZ, with a MAD of 0.053 Å. M06/ccpVTZ and B3PW91/TZVP both perform well with a MAD of 0.017 Å; however, six other model chemistries produced bond lengths less than 0.020 Å from the experimental value. Vanadium−Ligand Bond Lengths Summary. Table 2 shows the average of each model chemistry over all bond types as well as the DFT MADs and BS MADs. This table gives a quantitative measure of which density functional, basis set, and model chemistry most accurately predicted vanadiumligand bond lengths. It is useful to compare Table 2 and Figure 2. There is not a large difference between the performance across the set and, depending upon the requirements of a given simulation, all may be acceptable. It is clear though that the PBE0 functional outperformed the others as it is the only functional with a DFT MAD under 0.030. It is also expected that such geometrical parameters would be less sensitive to a change in model chemistry than the underlying electronic structure, and therefore, it is important to have a model chemistry that consistently produces the best structural parameters with minimal computational effort. Furthermore, when comparing the data in Table 2 and Figure 2, one notices that certain outliers are “averaged out” when looking broadly across the results. For example, specific errors for several model chemistries approached 0.15 Å (i.e., B3LYP/LANL2DZ), which can be up to a 10% error in some cases. In addition to low errors reported in Table 2, it is important to have a narrow distribution of data in Figure 2. Fortunately, there are several model chemistries that meet such criteria. Specifically, PBE0/QZVP predicted the bond lengths closest to experiment with an average MAD of 0.024 Å and the narrowest distribution of errors overall (none greater than 0.05 Å). PBE0/6-31G*, however, has an average MAD negligibly higher (and a similar error distribution in Figure 2), and because 6-31G* is a significantly smaller basis set, PBE0/631G* is clearly recommended for vanadium−ligand geometries. The choice of 6-31G* over QZVP is further supported by comparing their respective BS MADs, where we find that over all compounds and functionals, 6-31G* outperformed QZVP by 0.001 Å. Vanadium−Ligand Bond Angles. Molecules 6 and 7 are structurally the same, both being V(CO)6; however, they are electronically different such that 6 is neutral whereas 7 is an anion. The MADs for the ∠CVC angles in these molecules are presented in Figure 3 with purple vertical lines. Most of the MADs for this bond angle type are in the 2.5° to 3° range; however, closer analysis of the angles in 6 vs 7 shows that the neutral 6 was modeled significantly worse than the anionic 7. Some of the model chemistry MADs for 6 were greater than 4° and as high as 4.96° in M06-L/cc-pVTZ. The MADs of the anion ranged only from 1.63° to 1.70°, meaning that the choice of model chemistry here had very little effect. Data for the ∠NVC angles are represented in Figure 3 with light green vertical lines. This bond angle is only found in complex 1; however, the data presented are the average MAD for the ∠NVC bond angle to every carbon in the Cp ring. All model chemistries for this bond angle performed to roughly within 2° of experiment with the best being M06-LIQZVP with a MAD of 0.89°. M06-L was in general more variable than other methods as it produced both the best and worst results for ∠NVC angles of 0.89° and 4.07°. This variability makes it difficult to suggest it as an ideal model chemistry as consistent E


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The Journal of Physical Chemistry A Table 3. Absolute Errors for Vanadium−Ligand Bond Angles (deg) basis set

B3LYP

B3PW91

M06

M06-2X

M06-L

PBE0

basis set MAD

6-31G* LANL2DZ cc-pVTZ TZVP QZVP DFT MAD

1.36 1.23 1.53 1.61 1.33 1.41

1.25 1.32 1.41 1.24 1.23 1.29

1.50 1.34 1.55 1.43 1.44 1.45

1.58 1.47 1.79 1.66 1.38 1.57

1.84 1.47 1.63 1.49 1.36 1.56

1.31 1.18 1.37 1.23 1.23 1.27

1.47 1.33 1.55 1.44 1.33

complex. Previous work in our group15 has indicated that the controlled reversible polymerization of vinyl acetate could be achieved via a reactive V(II) intermediate and reversible OMRP; however, the theoretical work was performed on a significantly truncated ligand system. In the present work, we seek both to apply a more thoroughly validated model chemistry to the system in question and to extend our calculations to the full bis(imino)pyridine ligand BIMPY52 (BIMPY = 2,6-[(2,6-iPr2C6H3)NC(Me)]2(C5H3N)) ligand, from which our experimental results are based. This will allow us not only to probe the effect of increasing ligand size but also to further validate our PBE0/6-31G* model for reaction energetics by qualitatively assessing the predicted thermochemistry in comparison to the known experimental properties. To that end, processes 1−4 (Scheme 1) were investigated computationally using both the full and truncated Me[BIMPY] ligand system, where Me[BIMPY] = 2,6-(MeNCH)2(C5H3N) supporting the various vanadium complexes and [CH3CHPh]• (Sty•) or [CH3CHOCOCH3]• (VAc•) radicals. Comparing the enthalpies and free energies of the reactant and product species for each process affords valuable insight into the viability of each potential reaction pathway. The overall thermochemistry calculated for the complexes is provided in Table 4, and a

B3LYP and M06-2X predicted bond angles to less than a degree from experiment. A ∠ClVC angle is present in 1 and the MAD for this parameter is averaged over ten ∠ClVC angles (two chlorine atoms and five carbon atoms in the Cp ring). The data for this parameter are presented in Figure 3 by dark green vertical lines. It can be seen that M06-L performed very well (DFT MAD of 1.55°) in comparison to the other functionals that predict bond angles to have greater than 2° MADs from the crystal structure. Vanadium−Ligand Bond Angle Summary. For quantitative analysis of overall bond angle performance, all the MADs for each model chemistry have been averaged in Table 3. Not surprisingly, the results are similar to those for the bond length parameters above. In general, there is not a large difference across the entire set; however, there are some functionals that exhibit significant outliers for some parameters (i.e., B3LYP, M06-L, and M06-2X). The three density functionals with the lowest DFT MADs were PBE0, B3PW91, and B3LYP with values of 1.27°, 1.29°, and 1.41° respectively. Again, we note that the PBE0 functional demonstrates superior performance for our test set. Additionally, inspection of Figure 3 illustrates that the PBE0/6-31G* model chemistry is again particularly robust, having all data points close to or within 2.5° of experimental structural parameters (a characteristic rarely matched across the rest of the model chemistries). Considering that PBE0/6-31G* was the superior choice in the case of both bond lengths and angles, it is particularly well suited to the structural prediction of vanadium complexes of a variety of ligands, coordination numbers, and oxidation states. This method not only produced the lowest MADs across our entire test set but also exhibited the narrowest distribution of errors according to Figures 2 and 3. When the relatively inexpensive cost of this method is taken into consideration, it is a particularly conclusive result. Though we can be relatively sure that the 6-31G* basis set falls well short of the basis set limit, in this context it offers a convenient and reliable cancellation of errors when paired with the PBE0 functional. We decided to explore the effects of empirical dispersion corrections, and to do so we applied the Becke−Johnson empirical dispersion correction51 to the PBE0/6-31G* model and reoptimized the PBE0/6-31G* geometries. We find that most of the bond lengths in the vanadium coordination sphere change (as compared to the original PBE0/6-31G* geometries) by less than 0.003 Å and the largest difference observed was 0.06 Å. We therefore conclude that such corrections are probably not necessary in the context of vanadium complexes. Optimized geometries for these and all other models employed in the current work are provided in the Supporting Information. Application to the Controlled Radical Polymerization Pathways of [BIMPY]VCl3. We then applied the PBE0/631G* model chemistry to the study of the controlled radical polymerization of both vinyl acetate and styrene by a vanadium

Table 4. Summary of Overall Gas-Phase Reaction Enthalpies (kcal/mol) and Free Energies (at 298 K) for Each Process in Scheme 1 reaction process process process process process process process process process process process process process process process process process process

a

1 (Sty) 2 (Sty) 3a (Sty) 3b (Sty, a) 3b (Sty, e) 4 (Sty, py, R) 4 (Sty, py, S) 4 (Sty, im, R) 4 (Sty, im, S) 1 (Vac) 2 (VAc) 3a (VAc) 3b (VAc, a) 3b (VAc, e) 4 (VAc, py, R) 4 (VAc, py, S) 4 (VAc, im, R) 4 (VAc, im, S)

ΔG (Me[BIMPY]/ B3LYP)b

ΔG (Me[BIMPY]/ PBE0)

ΔG ([BIMPY]/ PBE0)

−12.90 n/a −12.90 19.93 21.59 28.58 29.92 6.40 3.99 −24.11 n/a −24.11 8.09 3.91 18.42 14.36 −7.16 −8.99

−14.55 n/a −14.55 13.98 17.47 16.65 18.09 −8.03 −9.63 −24.34 n/a −24.34 3.97 −0.59 7.79 3.89 −18.61 −20.41

−14.75 n/a −14.75 32.45 24.23 23.18 23.37 n/a 15.77 −24.53 n/a −24.53 17.20 9.91 14.82 7.61 4.69 3.80

a

Sty = styrene, VAc = vinyl acetate, a = axial coordination, e = equatorial coordination, R/S = enantiomer formed upon radical addition, py = attack at pyridine carbon, im = attack at imine carbon. b From ref 15. F


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Figure 4. Reaction coordinate diagram, multiplicities (M), ΔG values, and optimized structures of processes 1−4 involving the styrene radical. The 2,6-(iPr)2C6H3 group has been truncated to a single C atom for clarity.

observe a significant destabilization upon radical attack. With the exception of processes 1/3a, all others are predicted to be less thermodynamically favored for the full BIMPY ligand systems due to sterics. Process 1/3a, a vanadium delahogenation formally establishing an atom transfer radical polymerization equilibrium, does not involve a significant change in sterics or in bond type about vanadium, and therefore, its exothermicity is remarkably consistent across the model chemistries and ligands. It is thermodynamically favored by ≈24 kcal/mol with VAc• and by ≈14 kcal/mol with Sty•, the difference being predominantly due to the difference in stability of the free radical. Again we see that regardless of monomer, it would not be feasible for a reversible halogen transfer to facilitate the controlled radical polymerization (process 1). Process 2, as in the case of our previous work, seems highly unlikely to occur. The trapping of an alkyl radical by the parent Me [BIMPY]VCl3 complex would require a seven-coordinate vanadium organometallic and is not predicted to be thermodynamically viable in this case as all attempts to optimize a stable stationary point structure failed, and in each case the optimization proceeded to remove the radical from the vanadium center. This is not to say that a seven-coordinate vanadium is entirely infeasible, as we note that process 3 with vinyl acetate involves the ester carbonyl group in chelating to the metal center which stabilizes the trapped vinyl acetate

reaction coordinate diagram for the various mechanistic possibilities is shown in Figures 4 and 5. Both the R and S products resulting from Sty• or VAc• addition were calculated, as slight differences in energies were noted due to differences in steric interactions between the two potential products. In comparison to our previous results at the B3LYP/ LACVP*31,39−43 level, all processes for the truncated model systems are predicted to be more exergonic with the PBE0/631G* method. On average, the free energy changes are predicted to be about 8 kcal/mol lower with PBE0/6-31G*. Most significantly, the species having a formally covalent V− N,C linkage have been stabilized to the greatest extent, likely due more to the increased flexibility of the basis for the vanadium atom than the choice of functional. Generally, PBE0/ 6-31G* predicts somewhat shorter bond lengths within the vanadium coordination sphere (Supporting Information). For the study of the full BIMPY ligand structures, we began with the optimized truncated models and appended the correct molecular extensions followed by a semiempirical PM3 relaxation47,48 of the ligand while holding the immediate coordination sphere of the V atom fixed. The subsequent structures were then fully reoptimized using the PBE0/6-31G* model chemistry. The thermodynamics were then afforded by a standard harmonic frequency analysis. Table 4 lists the relative free energies for each relevant process predicted for the full BIMPY ligand systems. In accord with the significantly expanded size of the diisopropylbenzene substituents, we G


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Figure 5. Reaction coordinate diagram, multiplicities (M), ΔG values, and optimized structures of processes 1−4 involving the vinyl acetate radical. The 2,6-(iPr)2C6H3 group has been truncated to a single C atom for clarity.

and VAc stationary structures provides a reasoning for this differentiation (Figures 4 and 5). Participation of the ester carbonyl group in chelating to the metal center stabilizes the trapped vinyl acetate species and makes V−C bond formation more thermodynamically favorable. Chelation of this carbonyl group to the metal center has been previously reported for calculations on the Co(acac)2 system, with a six-coordinate dormant species proposed.53 These results support this vanadium catalyst operating through a unique, two-step reaction pathway: dehalogenation to form a reactive V(II) intermediate (a highly favorable process) followed by a potentially reversible OMRP to control the polymerization of vinyl acetate. Control over vinyl acetate is facilitated by both the higher reactivity of the radical species and the participation of the ester group in the trapping step. In both the Sty and VAc cases we predict relatively poor control of the polymerization with the vanadium catalyst, which is in good agreement with our experimental results15 and further validates our chosen PBE0/6-31G* model for work with vanadium complexes. Again, it seems that the PBE/6-31G* model provides a convenient and fortuitous cancellation of errors in the context of vanadium chemistry. It is, however, important to note that, because we are working with a relatively small basis set and chemical systems that may benefit from a more elaborate electronic structure model, one should not stray too

species and makes V−C bond formation more thermodynamically favorable (see below). Process 4 was again investigated by targeting two potential alkylation sites on the bis(imino)pyridine framework representing attack at the electrophilic pyridyl and imine carbons, respectively. We find that attack at the imine carbon is more favorable in all cases; however, it is interesting to note that in the full BIMPY system imine attack is significantly more destabilized compared to the truncated model relative to attack at the pyridyl carbon. This effect of steric crowding near the vicinity of the isopropylphenyl substituents results in process 4 (both imine and pyridine) being thermodynamically disfavored in all cases and lessens the gap between the thermodynamics of pyridyl and imine attack observed for the truncated ligands. In fact, such steric crowding rendered it impossible to locate a product of the styrene radical attack at the imine carbon in the R stereochemistry theoretically. As in our previous study,15 this work supports process 3 as a viable option to control the radical polymerization of vinyl acetate, albeit with less than desirable control. A relatively small differential of ≈10 kcal/mol separates the parent [BIMPY]VCl2 complex and the [BIMPY]VCl2(VAc) organometallic, suggesting that this process may be reversible. This computational study also supports the disparity in control over styrene and vinyl acetate polymerizations, as the [BIMPY]VCl2 Sty• reaction is endergonic by 24 kcal/mol. Comparing the Sty H


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available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b03552.

far from the PBE0/6-31G* model and expect to get reliable results.

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CONCLUSION In this study we tested the accuracy of six density functionals, each paired with one of five basis sets (a total of 30 model chemistries) for the prediction of geometrical parameters in the coordination sphere of nine vanadium complexes (for a total of 270 structural analyses). Each bond length and bond angle was measured and averaged over all the bond types and molecules to afford a broad comparison to experimental crystal structural parameters. We find that results are generally consistent over the range of functionals tested and that none fail catastrophically. However, the PBE0 functional was clearly the best performing functional in the set tested. For bond lengths, the model chemistry PBE0/QZVP performed the best overall (having a MAD of only 0.024 Å from experiment), yet PBE0/631G* makes use of a much smaller basis set than QZVP and provides nearly identical results. For bond angles, PBE0 was still the best density functional overall and, when combined with the 6-31G* basis, produces one of the smallest error distributions of any model chemistry tested. Due to the low computational cost and ease of convergence, we recommend PBE0/6-31G* as the low-cost model chemistry of choice for organo-vanadium complexes. We subsequently applied the PBE0/6-31G* model chemistry to understanding the mechanism of action of a [BIMPY]VCl3 catalyst in the polymerization of styrene and vinyl acetate. Apparently, using a less validated methodology (B3LYP/ LACVP*) on a truncated model system (Me[BIMPY]VCl3) fortuitously yielded a reaction coordinate that aligned reasonably well with experimental observations.15 In the current work, we employ a more appropriate methodology to the same truncated ligand system, yet the thermodynamics are significantly more exergonic, even suggesting competition between carbon−carbon bond formation at the ligand and the (expected) dehalogenation of the parent Me[BIMPY]VCl3. This points to the inaccuracies introduced by using a truncated ligand set, which are corrected by considering the full [BIMPY] ligand framework. With the full 2,6-[(2,6-iPr2C6H3)N C(Me)]2(C5H3N) vanadium complexes, we predict a significant destabilization of all product species with the exception of the [BIMPY]VCl2 intermediate and the loss of Cl is once again the preferred process by a significant margin. Subsequent capture of the carbon at the vanadium center (process 3b), however, is now significantly higher in free energy, meaning that the control would not be ideal and this far better aligns with experimental observations of low conversions and nonideal dispersities. Energies between a termination reaction (attack at the backbone) are now closer to the deactivation, meaning that the catalyst death from this type of reaction is accessible (along with standard PVAc termination reactions) linking to the low overall conversion observed experimentally.

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AUTHOR INFORMATION

Corresponding Author

*J. K. Pearson. E-mail: [email protected]. Phone: +1 902 566 0934. Fax: +1 902 566 0632. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the Natural Sciences and Engineering Research Council (NSERC) of Canada and the Canada Foundation for Innovation (CFI) for funding that supported this work. Computational facilities are provided by the Atlantic Computational Excellence Network (ACEnet), the regional high-performance computing consortium for universities in Atlantic Canada. ACEnet is funded by CFI, the Atlantic Canada Opportunities Agency (ACOA), and the provinces of NewFoundland & Labrador, Nova Scotia, and New Brunswick. The authors also thank Dr. Jason Masuda for providing experimental structural data.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

Optimized structural parameters for all molecules in Figure 1 for all model chemistries employed herein are available in the Supporting Information. Additionally, we provide all computational outputs for optimizations and frequency calculations for each relevant species in the controlled radical polymerization pathways of [BIMPY]VCl3. The Supporting Information is I


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Assessment and Application of Density Functional Theory for the

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