Evaluating Density Functionals by Examining Molecular Structures

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A: New Tools and Methods in Experiment and Theory

Evaluating Density Functionals by Examining Molecular Structures, Chemical Bonding, and Relative Energies of Mononuclear Ru-Cl-H-PR Isomers 3

Savio J. Poovathingal, Timothy K. Minton, and Robert K Szilagyi J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b03216 • Publication Date (Web): 12 Dec 2018 Downloaded from http://pubs.acs.org on December 17, 2018

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The Journal of Physical Chemistry

Evaluating Density Functionals by Examining Molecular Structures, Chemical Bonding, and Relative Energies of Mononuclear Ru-Cl-H-PR3 Isomers Savio J. Poovathingal, Timothy K. Minton, and Robert K. Szilagyi Department of Chemistry and Biochemistry, Montana State University, Bozeman, MT 59717, USA.

Abstract. In order to define a robust level of theory using density functionals for investigating the reactivity of ruthenium complexes, we used benchmark wave function theory, with saturated basis sets to validate GGA, meta-GGA, and hyper-GGA functionals in the presence and absence of empirical dispersion and range-separated corrections. We first selected potentially suitable functionals that gave accurate predictions of the relative energetics of coordination isomers. These functionals were further evaluated for the chemical accuracy of their predicted geometric and electronic structures. For the latter, both the ionic and covalent interactions were considered. The reference level of theory for comparison was coupled-cluster perturbation theory using full treatment of singles and doubles (CCSD) with a saturated triple- quality basis set and corresponding small-core, effective core potentials for ruthenium (TZVP). Several population analysis methods were evaluated to predict the ionic interactions. We found that the atomic charges obtained from fitting the electrostatic potential provided the most reasonable estimates for the ruthenium complexes. The covalent interactions were quantified by considering the atomic compositions of Ru 4dx2-y2- and 4dz2-based frontier unoccupied orbitals. Comparison of more than two dozen functionals with reference data from high-level wave function calculations revealed trends that allowed for the formulation of an optimal hybrid density functional: PBE exchange and correlation functionals with 50% HF exchange component. This level of theory was found to reproduce the experimental structure of Ru(II) complexes. These complexes were used to investigate chemical speciation in a simplified model for an ionic liquid environment.

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1. Introduction Ruthenium-containing coordination complexes are central to dye-sensitized solar cells,1-2 organic and organometallic transformations,3-6 and supported ionic liquid phase (SILP) catalysis.7-10 Our attention is focused on SILP catalysis, where an accurate theoretical description is needed for both the ill-defined ionic liquid-vacuum interface11-14 and the speciation of Ru-containing complexes. We would like to utilize theoretical structural information to understand the catalytic mechanisms at the molecular level and thus guide the design and aid in the interpretation of future experiments. However, the use of converged ab initio wave function (WFN) methods with a high degree of electron correlation is computationally prohibitive despite their attraction for obtaining highly accurate energetic and structural information. We therefore appeal to density functional theory (DFT), as it is widely employed to study catalytic complexes because it accounts for electron exchange and correlation at a reasonable computational cost through approximate functionals of electron density. Reactive-atom scattering with mass spectrometric detection (RAS-MS)15-17 is an experimental technique that opens up new possibilities for studying catalysis at liquid-gas interfaces. RAS-MS can reveal atomic-level details of molecular mechanisms that are elusive to conventional spectroscopic techniques or chemical characterization methods. The RAS-MS experiments can be considered as a way of capturing a motion picture of chemical reactivity that provides molecular-level details like structure, surface enrichment, and interfacial dynamics.18-23 However, not all frames can be obtained experimentally. The repertoire of computational tools from empirical force fields to quantum chemical methods affords a promising approach for generating the missing frames of reactivity. The analysis of the electronic and geometric structures of each frame obtained from calculations has the potential to reveal the origins of thermodynamic driving forces and kinetic regio- or chemo-selectivity. The use of density functionals to provide the essential structural and dynamical information poses challenges because of a lack of clear guidelines for how to choose the appropriate set of functionals from a large, ever-growing, and diverse set.24-25 Ideally, for a new family of compounds, the exchange and correlation approximate functionals need to be rigorously validated against an extensive set of experimental data and, if computationally not prohibitive,

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the highest level of ab initio WFN calculations. The approach of utilizing ab inito calculations to select a functional has been successfully used for validating density functionals involving firstrow transition metals, such as Cu26 and Ni27 mononuclear complexes and Fe-S clusters,28 by the use of a variety of spectroscopic methods. Furthermore, the theoretical evaluation of functionals for 3d-transition metal chemistry found that the M05 functional had the best overall performance.29 Evaluation of functionals for Pd complexes guided by X-ray absorption spectroscopy demonstrated that the less commonly employed Becke’s “half-and-half” exchange functional and the Lee–Yang–Parr correlation functional (BHandHLYP) were the optimal density functionals.30 Previous efforts that assessed the performance of functionals for Ru complexes with C-, O-, and N- ligands did not converge to a specific optimal functional.31-33 These have relevance to biomedical and organic/organometallic applications of Ru complexes. A relevant study here is the exhaustive comparison of functionals for the second generation Grubbs catalyst (chlorophosphinoruthenium carbene complex), which found that the M06-L functional gave the best performance.34 The comprehensive energetic and structural analyses carried out for equilibrium structures in the given work make our study superior in comparison to previous single point energy calculations. Furthermore, agreement with relative energy values alone may hide important structural differences, because various metal-ligand interactions can strongly affect the ionic and covalent interactions. Therefore, a systematic evaluation of basis sets, ab initio WFN methods as a function of the completeness of capturing electron correlation, and a comprehensive set of functionals was carried out for mononuclear Ru(II) complexes with Ru–H, Ru–Cl, and Ru–PR3 ligand interactions. The evaluation of functionals was carried out by comparing their predictions to those of ab initio WFN methods using complexes with truncated phosphine (PH3) ligands. Employing the highest level of ab initio WFN theory, we carried out detailed electronic and geometric structural analyses of the model Ru(II) complexes, which was utilized in finding the most reasonable density functional that could reproduce not just the geometry and relative energies, but the ionic and covalent bonding interactions, as well. The most reasonable hybrid functional was used to obtain equilibrium structures of realistic experimental complexes and to investigate the chemical speciation of mononuclear Ru/Cl/H/PR3 complexes in a model ionic liquid solution.

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2. Computational Methods The schematic structures for the two model Ru(II) complexes and their coordination isomers are shown in Scheme 1. The structures correspond to 16-electron, coordinatively unsaturated complexes, (1) RuCl2(PR3)3 and (2) Ru(H)Cl(PR3)3, that are ready to bind -acid ligands, such as olefins. Letters following labels 1 and 2 indicate the composition of the phosphane ligands (H: PH3; Me: PMe3; Ph: PPh3; etc.) The presence of a hydride ligand is essential in hydrogenation, isomerization, oligomerization, and polymerization reactions. In addition, the formation of the Ru–H bond is a plausible event upon collision of a potential dose of H atoms with an ionic liquid interface decorated with Ru complexes in the RAS-MS experiment before the introduction of an olefin substrate.

1

2

Scheme 1: Schematic structures of coordination isomers for complexes RuCl2(PH3)3 (1H) and RuCl(H)(PH3)3 (2H). Hydrogen atoms on phosphine ligands are omitted for clarity. Framed structures indicate isomers with equilibrium structures considered in the present study; solid line: lowest energy, dashed line: intermediate energy, dotted line: highest energy. To map basis set saturation limits, we examined five basis sets with both effective core potential (ECP) and all-electron treatments. The ECP basis sets evaluated were SDD(d,f)35-38 with 155 basis functions and 283 Gaussian primitive functions (BS1), def2SVP39-40 with 153 basis functions and 283 Gaussian primitive functions (BS2), and def2TZVP41-42 with 248 basis functions and 424 Gaussian primitive functions for 88 electrons (BS4). The all-electron basis sets included DZP43-44 with 194 basis functions and 372 Gaussian primitive functions (BS3), DZP with DKH relativistic corrections45,

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(BS3+DKH), and aug-cc-VTZ basis set with diffuse

functions and DKH correction46-47 with 711 basis functions and 1555 Gaussian primitive functions (BS5). All basis sets were obtained from the EMSL Gaussian Basis Set Repository 4


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without neglecting Gaussian primitives with small coefficients;48-49 thus, the 5d/7f formalism was employed for pure d and f functions. When the 6d/10f Cartesian functions were employed for population analysis using total electron density-based population analyses, we obtained only 1-2% of an electron variation in atomic point charges or orbital composition. The exact basis set definitions are provided as Supporting Information (Tables S1-S6). The conceptually converging series of ab initio WFN methods included single-reference MP2 (with frozen core excitation space, where MOs used were 30-279 and 25-248 for 1 and 2 with HOMOs being 52 and 44, respectively), MP4 (both analytical MP4SDQ and numerical MP4), and CC (both analytical CCSD and numerical CCSD(T)). To mitigate the number of potential energy surface variables in ab initio WFN calculations, we used a reduced set of internal coordinates for all isomers where all P–H bond lengths and Ru–P–H bond angles were described by a single distance and angle variable, respectively. The definitions of the Z-matrices for 1H and 2H are provided in the Supporting Information (Table S7). The representative set of functionals classified in terms of the rungs of “Jacob’s ladder” connecting the HF world with a hypothetical “divine” functional,50, 78 are summarized in Table 1. In addition to the ab initio functionals, we also evaluated functionals with Grimme’s dispersion correction (D3) and rangeseparated hybrid (or hyper-GGA) functionals. In order to manage computational cost, all calculations with the model complexes 1 and 2 were carried out in the gas phase, while in the chemical speciation section (Section 3.3) we employ condensed-phase models. Electronic structure analyses were carried out using Mulliken (MPA),79 Weinhold (Natural population analysis, NPA, NBO version 3.1 as implemented in G16 Rev.A01),80-82 and Bader’s Atoms-in-Molecule (AIMQB Professional Version 13.02.26)83-84 population analysis methods, and Merz-Singh-Kollman electrostatic potential fit (ESP)85-86 with Universal Force Field (UFF)87 atomic radii to determine points for fitting atomic partial charges that reproduce the electrostatic potentials at these points. In order to avoid artifacts caused by basis set effects, we did not use Mulliken or Löwdin population analysis methods, especially for calculations employing large basis sets, such as BS4. Orbital compositions were determined from converged (for WFN theories) correlated total electron density, in conjunction with population analysis with increased and decreased orbital occupations to occupy and create electron holes for unoccupied (LUMOs) and occupied (HOMOs) orbitals, respectively.

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Table 1: Ordered list of density functionals, according to the rungs of “Jacob’s ladder” introduced by John Perdew,50 employed in the given study (HFX: HartreeFock exchange, DFX: density functional exchange, DFC: density functional correlation). Rung Type 1 LDA 2 GGA

Exchange Correlation S51 VWN52 53 B P8654 B53 LYP55 G96 P8654 56-57 PBE HCTH40758-60 3 meta-GGA TPSS61 M0662 M06HF63-64 53 LYP55 4 hybrid B 53 GGA B LYP55 56-57 PBE 53 B LYP55 B53 LYP55 56-57 PBE PBE56-57 PBE56-57 73 5 double B2P LYP55 76 hybrid GGA mPW2P LYP55 a

HF exchange and other corrections

27% HFX 100% HFX 20% HFX, -8% DFX, -19% DFC65 50% HFX66 25% HFX67 20% HFX, -8% DFX, -19% DFC, D368 100% HFX, -19% DFC, range separated69 range separated, LC70-72 range separated, LC,70-72 D368 50% HFX (this work) 53% HFX, 23% MP2, D374-75 55% HFX, 25% MP2, D77

Abbreviation S-VWN B-P86 B-LYP G96-P86 PBE-PBE HCTH TPSS-TPSS M06L a M06HF a B3LYP BHandHLYP PBE1PBE B3LYP-D3 CAM-B3LYP LC-PBE LC-PBE-D3 PBE(50%HF)PBE B2P-LYP-D3 mPW2PLYP-D

may also be classified as Rung 4, hybrid meta-GGA type functional.

The X-ray structures of a formally 18-electron coordinatively saturated complex [RuCl2(PMe3)4] (3Me) for cis (QAHLUI88) and trans (PENVAG89) isomers were obtained from the Cambridge Crystallographic Structural Database (CSD),90 and equilibrium structures were obtained for 3Me using the preferred hybrid functional. Additionally, we obtained equilibrium structures for related complexes: [RuCl2(PH2Ph)4] (3H2Ph, YEYSAW91), [RuCl2(P(H)Ph2)4] (3HPh2, SAYZUN92),

[RuCl2(PPh3)3]

(1Ph)

(MOZNIA,93

RUCLTP,94-95

YASFOO96)

and

[RuCl(H)(PPh3)3] (2Ph), HCPPRU97). All equilibrium structures are displayed in Figure S1. As an illustrative use of the preferred hybrid functional with direct relevance to supported ionic liquid phase catalysis experiments involving Ru-Cl-H-PR3 complexes, we investigated the chemical speciation of mononuclear Ru(II) complexes, as summarized in Scheme 2. We limit the discussion here to the reaction energies of ligand dissociation, contaminating water coordination, and H2 activation processes in Scheme 2. Although continuum models can only capture part of the solvation effects in ionic liquids, they can provide experimentally useful information on speciation of Ru-complexes (Section 3.3). Polarizable continuum models were used with integral 6


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equation formalism (PCM98), conductor-like model (CPCM99), and a “universal” solvation model based on full consideration of the solute density (SMD100). In all models, we used the published ionic liquid continuum parameters.101-103 The specific values (Table S8) used in this work correspond to the values reported for 1-ethyl-3-methylimidazolium ([emim]+) and bis(trifluoromethylsulfonyl)imide ([Tf2N]–). We chose this ionic liquid because of its relevance to planned RAS-MS experiments. The performance of the above three polarizable continuum models (PCM, CPCM, SMD) was evaluated by calculating the heat of solvation of the cation [emim]+, anion [Tf2N]–, and the neutral ion pair ([emim]+ [Tf2N]–). In Section 3.3, the gas-phase structures were refined using three different implicit condensed phase models that account for a homogeneous field of electrostatic interactions from the ionic liquid without capturing any effects from the polar and non-polar domains in ionic liquids. In addition, we considered solute/solvation corrections to the translational entropy (as a significant component to total entropy with high uncertainty) introduced by Whitesides et al.104

Scheme 2: Overview of chemical speciation pathways upon dissolution of mononuclear Ru-Cl/H-PR3 complexes in a model ionic liquid continuum (3, 1, 5, and 6), coordination of contaminating water (7), and activation by H2 (2 and 4). The evaluations of the ab initio WFN methods and density functionals, mapping the basis set saturation limit, were carried out using Gaussian09 Revision D.01,105 while the chemical speciation study with the parameterization ionic solvent continuum was completed using Gaussian16 Revision A.01.106 The visualizations and structural manipulations were done in ChemCraft V1.8 (build 489). Unless stated explicitly, all structures that are reported and discussed in this article are equilibrium structures and it was ensured that there were no imaginary normal modes. No molecular symmetry was imposed; however, in order to reduce the number of internal coordinates for high-level WFN calculations, we treated all P-H distances and

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Ru-P-H angles with shared bond length and angle variables. In all calculations, we used the tight convergence criteria for energy and density (10-8 a.u.). The integration accuracy was selected to have a pruned grid with 99 radial shells and 590 angular points. The use of a larger grid (first row atoms: 175,974; second-row atoms and beyond: 250,974) did not significantly influence the geometric and electronic structures from DFT calculations. The standard state definition was used in thermochemical calculations. 3. Results and Analysis 3.1. Comprehensive Evaluation of Wave Function Calculations for 1H and 2H. 3.1.1. Energetics of Isomers of 1H and 2H. Truncation of the phosphane (PR3) to phosphine (PH3) and description of each coordinated PH3 with a linked P-H bond and Ru–P–H angle (see supporting information for Z-matrix definitions) made geometry optimizations at the CCSD(T)/def2-TZVP level computationally feasible. This allowed for a systematic evaluation of the influence of electron-correlated methods on the structure and energetics of the isomers. For the sake of confirming basis set saturation, we evaluated the effect of basis sets on the relative energies and geometries of the coordination isomers at the reference HF electronic structure as shown in Figure S2. Comparison of relative coordination isomer energies (ESCF) obtained using BS2 and the performance of larger basis sets towards the saturation limit (right-hand side of Figure S2) suggests that BS2 may be sufficient for qualitative evaluation of energies at a minimal computational cost. The double-ξ quality all-electron basis set (BS3) exhibits mediocre performance with respect to isomer energies. The relativistic correction for BS3 (DKH, also included for BS5) shows negligible effects (< 1 kJ mol-1) on the relative energies of the isomers. Thus, we use BS4 as our approximation for the basis set saturation limit. Using the two extremes of the basis set study (BS1 and BS4), we evaluated the relative energies of the isomers for 1H and 2H as a function of increasing completeness for the treatment of electron correlation, as shown in Figure 1.

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Figure 1: Convergence of relative electronic energies (gas phase, ESCF, kJ mol-1) between the trans- and the cis-1H isomers (solid symbols), basal,cis and apical-(H) 2H (hollow symbols) isomers as the completeness of electron correlation (small and large symbols connected with thin and thick lines denote results obtained with BS1 and BS4, respectively). The relative energies were calculated from the differences between the energies of trans and cis isomers for 1H, indicating that the trans isomer is more stable at the HF level. However, the first electron-correlated method (MP2) reverses this order, as the cis isomer becomes more stable at any correlated method (Figure 1). Geometry optimizations of 2H predict the apical-(H) isomer (Scheme 1) as the most stable complex using all ab initio WFN methods. The small valence basis sets (BS1 and BS2) with small-core ECPs show a significant difference in the relative energies for 2H. Figure 1 indicates that the MP2 level is already sufficient for 2H (upper traces in Figure 1). However, the need for a higher level of theory was observed (lower traces in Figure 1) for 1H. At the HF level, the relative energies predicted using BS4 were 6 and 17 kJ mol-1 higher compared to BS1 for 1H and 2H. The difference between predictions of the two basis sets becomes more pronounced by the inclusion of gradually higher-level electron correlation for 1H. Particularly, at the CCSD level of theory, the BS1 calculation switches the relative order of cis and trans isomers. This result underscores the need for evaluating basis set saturation at the correlated level and not just at the HF limit. The convergence of the WFN level of theory was shown to be achieved already at the CCSD level with respect to the CCSD(T) level. Given the maximum 4 kJ mol-1 difference for both complexes between the analytical CCSD versus

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numerical CCSD(T), we consider the optimal representation of the basis set saturated, correlated post-HF level of theory to be CCSD/BS4 (def2TZVP) for geometric and electronic structure calculations. This level of theory has several advantages. The analytical second derivatives allow for the analysis of the correlated electron density and quantitatively defining ionic and covalent interactions in terms of natural orbital population analysis. The relative energies, molecular geometries, and electronic structures obtained at the CCSD/BS4 level can be considered as the reference for strategic selection of the most desirable set of density functionals.

3.1.2

Geometric Structure of Complexes 1H and 2H. The evaluation of all stationary isomers

summarized in Scheme 1 at the highest level of theory used (CCSD/BS4) resulted in equilibrium structures (Figure 2) without imaginary normal modes. The optimized atomic Cartesian coordinates and internal coordinates are provided in the Supporting Information (Tables S9 and S10). For both complexes, only the square pyramidal coordination environment gave stationary equilibrium structures without imaginary normal modes and all trigonal bipyramidal structures isomerized to square pyramidal coordination geometry even with the use of the simplified set of internal coordinates. In the case of 1H, the optimized structures at the highest level of theory demonstrate the concept of cis influence, where the σ-donor ligands prefer the adjacent positions to maximize their covalent interactions. Comparing the cis and trans isomers, the Ru–Cl distances only differ by 0.01 Å, while the Ru–P distances vary by as much as 0.06 Å. Since the apical interaction is approximately perpendicular (within 4-6º) with respect to the basal atoms, the axial Ru–P remains relatively unchanged (0.01 Å) between the two isomers. However, the shorter basal distances in cis-1H will have a greater interaction with the donut lobes of the 4dz2 orbital, which elongates the apical Ru–P distance. The metal-ligand (M–L) σ-interactions do not result in deviations greater than 3º from the ideal angles in the base of the square pyramidal coordination environment. Another small deviation from ideality is the out-of-plane positions of the Ru (see italicized number under the Ru center in Figure 2), which are 0.18 and 0.17 Å for cis and trans1H isomers, respectively. This allows for mixing of metal and ligand orbitals to maximize the covalent M–L interactions and increases the ligand field stabilization.

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Figure 2: Summary of equilibrium structures with key internal coordinates (bold: bond lengths in Å, regular: bond angles in º, and italics: out-of-plane position of Ru in Å) calculated at the CCSD/BS4 level of theory (gas phase) for 1H and 2H (H atoms on phosphine ligands were omitted for clarity). Relative energy values shown here correspond to ESCF, and zero point energy corrected values are given in parentheses. Tables S9 and S10 summarize the atomic positional and internal coordinates, respectively. The presence of the hydride ligand in 2H introduces a peculiar distortion to the Ru coordination environment. This is also seen below in the orbital contour plots, which is the sign of an exclusive σ-overlap between the H 1s and the appropriate Ru 4d orbitals. Furthermore, 2H manifests a richer stereochemistry than 1H for the Ru coordination environment. All square pyramidal isomers (Scheme 1) were identified as stationary structures. The lowest energy structure has an apical hydride ligand with a considerably distorted (113º) Cl–Ru–H bond angle relative to an ideal perpendicular basal/apical angle. As a result, the complementary H–Ru–P

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angle decreases and the trans P–Ru–P angle bends toward the chloride ligand by 10º relative to the ideal 180º. The Ru out-of-planarity defined by the centroid of the [ClP3] plane is 0.13 Å, which is similar to 1H. The other isomer with the apical chloride ligand is the highest in energy by more than 100 kJ mol-1. While the overall geometries of the apical-(H) and apical-(Cl) isomers are similar, a distinct difference is observed in the interaction of the chloride and hydride ligands. For the latter, the apical chloride can only interact through a -overlap, which in addition to the less efficient 3p/4d overlap versus 1s/4d, reduces the complex stability. The stability of the hydride complex in the apical position, which is opposite to the vacant coordination site, where a π-acid ligand (example olefin) can coordinate and display olefin insertion or a hydride transfer reaction is further supported by the existence of crystallographically characterized, five coordinate Ru-Cl-H-PR3 complexes such as 2Ph.97 The basal,cis and basal,trans isomers of 2H (Scheme 1) are energetically located approximately halfway between the apical isomers with an energetic difference of 8 kJ mol-1. This can be correlated with the cis-influence of strong σ- and -donor ligands in comparison to the σ-donor phosphanes. The distortion of the basal isomers is considerably less than the apical isomers with a notable variation of the Ru–Cl bond lengths as a function of ligands in the trans position. The difference in Ru-Cl distances is greater than in Ru–H by 0.06 Å among the basal,cis and basal,trans-2H isomers, which indicates that the hydride ligand is a better donor than a phosphane ligand. Despite the negative charge and commonly considered covalent M–Cl interactions, the chloride appears to be the weakest donor from the comparison of the Ru–P distances in the basal,cis isomer. The P trans to the hydride ligand has the longest Ru–P bond length while the P trans to the chloride has the shortest Ru–P bond length. Overall, from the comparison of Ru–P distances, we conclude that the chloride ligand will likely be labile in the lowest energy isomer, apical-(H) 2H, which is favorable for the activation of 2H and opens additional coordination sites for substrate substitutions. 3.1.3

Electronic Structure Analysis of 1H and 2H. The atomic charges and compositions of

frontier orbitals are key electronic structural features to understand the trends in the relative stability of coordination isomers, distortions, and structural perturbations. These structural features define the ionic and covalent nature of M–L bonding that manifests in the overall ground state electronic structure. Since the energetic differences among the coordination isomers

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for 2H are large, electronic structure calculations were carried out only for the lowest energy isomer, apical-(H)-2H. The trans isomer of 1H may contribute up to 10% of the molecular properties in a temperature range of room temperature to the boiling point of most ionic liquids containing [emim]+ cation (up to 250 oC);107 therefore, both cis- and trans-1H isomers were included in the electronic structure analysis. Table 2: Electrostatic potential derived charges (ESP) using the Merz-SinghKollman algorithm and the Universal Force Field atomic radii87 defining points for fitting atomic partial charges for the energetically preferred cis- and trans-1H and apical-(H)-2H isomers in gas phase. All other population analysis results are shown in Supporting Information (Table S11). Ru Cl(basal) Cl(basal) P(apical) P(basal) P(basal) Ha a

cis-1H trans-1H +0.76 +0.94 -0.50 -0.57 -0.50 -0.56 -0.09 -0.21 -0.15 -0.27 -0.16 -0.26 +0.07 +0.10

Ru Cl(basal) H(apical) P(trans to Cl) P(basal) P(basal) Ha

apical-(H) 2H +0.31 -0.69 -0.15 +0.11 -0.05 -0.06 +0.04

averaged value for all PH3 ligands.

While Table S11 summarizes the atomic point charges for all population analysis methods employed, the displayed atomic charges in Table 2 were obtained by using atomic radii from Universal Force Field87 to generate a set of points that are used to fit the molecular electrostatic potential (ESP). This population analysis method provided the most reasonable values with respect to metal-ligand electron donation as a result of electronegativity differences and bond polarities. The atom-centered point charges are valuable in molecular mechanical force field parameterization, which is a key step in carrying out molecular dynamics simulations of ionic liquid solutions with dissolved Ru complexes. The generally preferred Bader’s AIM analysis gave unreasonable values for P (greater than +2 e- charge with attached H charges greater than 0.5 e-). This discrepancy may stem from the non-trivial electron density distributions owing to the ionic and covalent nature of P–H bonds (P–H versus P––H+ versus P+–H-). Weinhold’s NPA charges describe the Ru center (less than -1 e- charge) to be nucleophilic when using the extended valence orbital set definition [4d 5s 4p]. The Mulliken (MPA) charges cannot describe the polarized M–L ligand bonds because of the symmetrical atomic boundaries of electron density.

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The formal charges of the Ru centers in complexes 1H and 2H are +2, while the effective ESP charge is reduced to approximately +0.8 in 1H and closer to the formally metallic state of 0 in 2H (+0.3). These differences are an indication of the presence of highly covalent M–L bonds. The chloride ligands lose 0.5 and 0.4 e- in 1H, while they retain only 0.3 e- in 2H due to shared electron density with the electrophilic Ru center. As discussed earlier (see geometrical structures section), the hydride ligand donates the most electron density (~0.9 e-), which implies that its electronic structure is closer to a hydrogen atom than to a hydride ligand. This makes the Hligand amenable to homolytic reactivity. Despite the PRu donation, the P center is nucleophilic, with the charge ranging from -0.05 to -0.26 e-. The exception is the PH3 ligand trans to chloride in 2H, where it gains a slightly positive (+0.1 e-) charge. This latter anomaly has already been rationalized above when considering Ru–Cl, Ru–H, and Ru–P bond lengths, as the chloride is a weaker donor than PH3. The significant polarity of the P–H bond is likely the source of the failure of the AIM population analysis, which gives a high positive charge for the P centers. In ESP analysis, the entire PH3 ligand’s charge becomes positive: 0.07–0.13, 0.04–0.11, and 0.05–0.22 e- for cis-, trans-1H, and 2H, respectively. The emergence of the positive charge on the P-ligand is a result of the covalent Ru–P bonding. The measure of bond covalency can be better gauged by molecular orbital compositions. Given the 4d6 electron configuration of the Ru(II) ion and the square pyramidal coordination environment, ligand field theory dictates that the lowest unoccupied molecular orbitals (LUMOs) should be 4dx2-y2 and 4dz2. However, the [Cl2P3] and [ClHP3] asymmetrical ligand-environment and the out-of-planarity of the Ru center by 0.1-0.2 Å further split and mix the Ru 4d orbitals. In addition, symmetry-adapted linear combinations of ligand-based orbitals are interspersed among the Ru-based orbitals. The use of electronic structure as a tool to validate density functionals requires analyzing the composition of frontier, metal-based orbitals. The results support and further explain earlier discussions about geometric structural features.

14


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cis-1H 4dx2-y2 *

4dz2 *

unoccupied occupied

4dxy

4dxz

4dyz

trans-1H 4dx2-y2 *

4dz2 * unoccupied occupied

4dxy

4dxz

4dyz

apical (H)-2H 4dx2-y2 *

4dz2 * unoccupied occupied

4dxy

4dxz

4dyz

Figure 3: Frontier natural molecular orbital contour plots (at 0.04 e-/Å3 level) of the Ru-based 4d orbitals for the energetically preferred isomers of complexes 1H and 2H derived from the gas phase CCSD/BS4 electron density.

15



Table 3: Frontier molecular orbital energies (at the reference HF level, gas phase), orbital occupations (at the CCSD level, gas phase) from the natural atomic orbital analysis, and their compositions (metal and ligand covalency according to a general M–L unoccupied, antibonding orbital definition 𝜑 √1 𝛼 𝜙 𝛼𝜙 / / ) for energetically preferred isomers of complexes 1H and 2H. cis-1H

trans-1H

apical-(H)-2H

LUMO+4 LUMO HOMO HOMO-1 HOMO-3 LUMO+4 LUMO HOMO HOMO-1 HOMO-5 LUMO+3 LUMO HOMO HOMO-1 HOMO-2

EHF, eV occ., eRu, % Cl, % H, % PH3, % 3.3 0.05 54 26 – 20 1.3 0.06 61 11 – 28 -9.4 1.94 42 49 – 9 -9.7 1.94 55 31 – 15 -10.1 1.95 35 53 – 12 3.4 0.05 57 16 – 17 1.5 0.05 61 22 – 27 -9.4 1.94 24 73 – 2 -9.4 1.94 74 3 – 23 -11.2 1.95 15 76 – 8 3.5 0.05 57 13 2 29 1.8 0.06 56 5 24 15 -9.2 1.94 67 16 0 17 -9.3 1.94 35 51 1 13 -10.0 1.95 35 38 0 28

Figure 3 displays the contour plots for Ru 4d-based frontier orbitals. Table 3 presents the corresponding numerical results for the atom-based, orbital composition analysis. Considering the relationships of E(dx2-y2) = +9.14 Dq and E(dz2) = +0.86 Dq for the idealized square pyramidal coordination environment,108 the 10Dq values can be estimated to be at most 4.6, 4.7, and 5.3 eV, respectively, corresponding to a strong-field description as expected for second row organometallic complexes. The non-zero occupation numbers from the natural orbital analysis of the correlated electron density indicate non-negligible mixing of excited states as the occupation numbers deviate from their ideal values of 2.0 and 0.0. The value of 0.05 e- does not justify the need for a computationally prohibitive multi-reference treatment (at least 24 electrons, 15 orbitals for 1H and 20 electrons, 13 orbitals for 2H are needed). However, the electronic structure of the complexes may pose a limitation on the single-reference treatment of the employed WFN theories as well as for density functionals. The orbital contour plots in Figure 3 reveal a considerably cleaner M–L bonding picture for the trans-1H isomer because of its higher symmetry. The interspersed occupied orbitals of those

16


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listed in Table 3 are composed of a symmetry-adapted combination of ligand-based orbitals mixed with Ru 5p contributions. Unexpectedly, we find that the unoccupied frontier orbitals with P–H * character contains a considerable amount of 4d contributions. This is an indication of the presence of RuPH3 back-donation (of ca, 0.3 e–, unoccupied orbitals not shown). The backdonation is reduced because of the electron richness of the P center in comparison to the phosphine, while the opposite applies for aryl phosphanes. The possibility of mixing metal and ligand orbitals (5px+5py and 5px-5py combinations) in cis-1H explains a small but significant stabilization relative to the trans-1H isomer. In the following discussion, we focus on the unoccupied Ru-based 4d orbitals in Table 3, which can be considered as a direct representation of covalent M–L bonding. The occupied orbitals (HOMOs) in Table 3 qualitatively show similar covalent electronic structure; however, the bonding picture is less clean than the unoccupied orbitals, which can be characterized by absorption spectroscopic techniques. As discussed during the geometry analysis, the Ru–Cl, Ru– H, and the Ru–P bonds are highly covalent. This is indicated by the metal character of the antibonding, unoccupied basal and apical -orbitals varying between 54% and 61% in all three Ru complexes (Table 3). The charge of the Ru center is effectively reduced by 0.39–0.46 erelative to its formal oxidation state as a result of the covalent M–L bonds. Using the example of the LUMO and LUMO+3 in apical-(H)-2H complex, the best donor is the hydride ligand (24 and 2%) followed by a phosphane ligand (15 and 29% for all three ligands), while the chloride ligand provides the least donation (5 and 13%) despite its negative charge. This can be rationalized with its higher electronegativity in comparison to the P and H centers. Importantly, these orbital compositions provide a way to validate electronic structures from an approximate density functional calculation. In addition, they lay down the groundwork for probing the electronic structure experimentally by X-ray absorption spectroscopy at the Ru L-, Cl K-, and P K-edges109 where differences of 5% in orbital compositions are significant and experimentally measurable.

17



3.2. Comprehensive Evaluation of Density Functionals for 1H and 2H. 3.2.1

Energetics of Isomers for 1H and 2H. The relative energies, coordination geometries,

ionic character, and covalent bonding of the isomers of 1H and 2H allow for a holistic evaluation of the density functionals. We evaluated eighteen strategically chosen density functionals as shown in Table 1. We utilized the saturated basis set (BS4) to evaluate the optimized equilibrium geometries and electronic structures of gas phase models and compared with the equilibrium structures and energetics obtained from ab initio WFN theory, CCSD/BS4. Due to the poor performance in predicting relative energies, we omitted considering the MP2 results as a suitable reference WFN theory.

Figure 4: Comparison of the performance of a series of density functionals in gas phase calculations with respect to error (ESCF) in relative isomer energies. The relative energies obtained from DFT calculations are compared with CCSD/BS4 results (gas phase) for 1H (for panel A) and 2H (panels B-D). Figure S3 provides a comparison on the same energetic scale. Arrows highlight trends for hybrid functionals based on BLYP (red) and PBE (green) set of functionals. (Note to the editor: please consider this as a whole page figure as suggested by Reviewer 2) 18


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The variations of relative isomer energies (ESCF) calculated using density functionals in comparison to the CCSD/BS4 reference level (Figure 1) are summarized in Figure 4 for the optimized 1H (Figure 4A) and 2H (Figures 4B-4D) complexes. Most density functionals predict the cis isomer of complex 1H to be more stable (right-hand side of Figure 4A) compared to the trans isomer, consistent with the prediction of correlated ab initio WFN calculations. Some hybrid functionals with a considerable HF exchange term get the relative cis and trans isomer energies incorrect for 1H (left-hand side of Figure 4A). For both complexes, the double-hybrid functionals underperform in predicting the relative energies because of the inferior performance of the MP2 level of theory (Figure 1). Overall, hybrid functionals appear to perform better than pure functionals, which is consistent with previous findings for transition metals, particularly for Ru complexes.34, 31-33 The overall performance of the functionals indicates a significant influence of the coordination environment and ligand composition on various trends. A specific trend can be recognized for 1H that provides guidance for obtaining functionals that reproduces ab initio data for Ru-Cl-H-PR3 complexes. We observe that the introduction of Hartree-Fock exchange (HFX) reduces the error in the relative energies of the isomers in 1H. Specifically, if we consider the series BLYP, B3LYP, and BHandHLYP (red arrows in Figure 4), which contain 0%, ca. 20%, and 50% HFX, the relative energies of isomers (trans-cis) monotonically decrease (13, 7, and -4 kJ mol-1, respectively; see Figure S3 in Supporting Information). A similar monotonically decreasing trend is observed for the Perdew-BurkeErnholtz exchange and correlation functionals for pure PBE and PBE1PBE (25% HFX). Consequently, we find that the hybrid functional PBE with 50% HFX, PBE(50%HF)PBE, provides the closest agreement with the ab initio WFN energies. The deviation of the relative energy predicted from PBE(50%HF)PBE for 1H is shown on top of Figure 4A. Admittedly, the above trend breaks down somewhat for 2H. For the basal,cis isomer, most of the functionals perform well. The addition of HFX appears to be saturating at levels represented by B3LYP and PBE1PBE functionals (~18-25%). The basal,trans isomer behaves even more erratically, as all functionals except for M06L underestimate the relative isomer energies. The addition of HFX is detrimental to this agreement. The deviation from the relative CCSD/BS4 values is even more exaggerated for the apical-(Cl) isomer. Among all trends, PBE(50%HF)PBE provides a desirable performance for all isomers of 2H, since the deviation of PBE(50%HF)PBE/BS4 from

19



CCSD/BS4 calculation in relative isomer energies is at most 2 kJ mol-1. As discussed later, this agreement is rooted in the improved electron density (ionic and covalent bonding) obtained by this hybrid functional in comparison to other functionals that were investigated. This “half-andhalf” mixing of density functional and HF exchange is not unexpected since this composition of hybrid functional has been successful in describing the X-ray absorption spectroscopic features and reactivity110-111 of chloropalladium complexes. Notably, we observe that the empirical dispersion correction (Grimme’s D3 parameters68) provides only marginal improvement (2–4 kJ mol-1), while the range-separated hybrid causes a more significant contraction of the spread (up to 14 kJ mol-1) of relative isomer energies. We took advantage of the considerable efficiency and straightforwardness of evaluating relative isomer energies in narrowing down the most likely candidates for those density functionals that might also predict accurate molecular structures. Furthermore, some of the corrections employed in DFT (dispersion, for example) only affect the total energy associated with the density, but not the density itself. We arbitrarily choose the deviation of 5 kJ mol-1 as an energy window for DFT to reproduce the conceptually converged, highest level WFN theory (CCSD). It is important to emphasize that the final selection was based on the simultaneously acceptable agreement with respect to energetics, geometric structure, ionic and covalent interactions as detailed below. 3.2.2

Geometric Structure of Complexes 1H and 2H. We evaluated a series of functionals that

reproduced relative isomer energies within ±5 kJ mol-1 of the WFN reference. For complex 1H, the functionals are BLYP, B3LYP (with and without empirical dispersion correction or range separation), long-range corrected PBE functional (with and without empirical dispersion correction), and M06HF. The four isomers of the 2H narrow the promising functionals to BP86, G96P86, PBE, PBE1PBE, and LC-ωPBE (Figure S3). The intersection of the two sets of functionals defines the PBE, PBE1PBE, PBE(50%HF)PBE, and LC-ωPBE series. In addition, we also evaluated the geometric and electronic structures obtained by BLYP, B3LYP, and M06HF functionals as controls. These functionals provide good agreement with CCSD/BS4 results for only one of the Ru complexes (1H or 2H); thus, they help us to understand why the PBE series provides good performance for both 1H and 2H.

20


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Table 4: Ranges of root mean square (RMS) errors in listed DFT calculations (all using BS4, gas phase) in reproducing the molecular geometry (bond lengths l and bond angles θ; see also Tables S12A and S12B), atomic point charges (q; see also Tables S13A and S13B), and orbital covalency (2, defined by the amount of ligand 3p of Cl– and PH3 and 1s of H– characters of the Ru 4d-based, unoccupied frontier orbitals according to a general M–L bonding definition 𝜑 √1 𝛼 𝜙 𝛼𝜙 / / ) for all energetically relevant isomers of 1H and 2H with stationary structure relative to the reference WFN level (CCSD/BS4, gas phase). The RMS errors are computed using the listed DFT functional and the reference WFN values. The ranges reflect the variations in the RMS errors. A smaller value for the lower limit in the range shown here indicates better agreement between the DFT and WFN calculations. Tables S12-S14 contain the absolute values from the DFT functionals (panels A) and the deviation from reference WFN level for molecular geometries, atomic point charges, and orbital covalency (panels B). Density Functionals PBE PBE1PBE PBE(50HF%)PBE LC-ωPBE BLYP B3LYP M06HF

Geometry l, Å θ,º 0.01–0.03 0.9–4.0 0.01–0.02 0.3–1.3 0.02 0.3–2.1 0.02 0.1–1.6 0.02–0.03 0.8–3.2 0.01–0.02 0.3–1.6 0.03–0.04 1.0–2.4

Electronic structure q, e– 2, % 11–19 0.07–0.10 10–19 0.05–0.08 11–17 0.02–0.09 8–15 0.05–0.09 10–16 0.05–0.09 10–17 0.03–0.04 16–36 0.08–0.14

The left-hand side columns of Table 4 summarize the range of root-mean-square (RMS) values for bond lengths (l) and bond angles () in basal-cis, basal-trans, apical-(H), basal-cis, basaltrans, and apical-(Cl) isomers. Tables S12A lists the absolute values from the DFT calculations. Table S12B lists each deviation in internal coordinates of the molecular Z matrices relative to the CCSD/BS4 results. Overall, the deviations in bond lengths and angles for all the selected functionals in Table 4 do not allow for an unambiguous differentiation among the shortlisted functionals. Bond lengths are reproduced within 0.04 Å in RMS values. It is interesting to note that the subset of chosen density functionals generally underestimate the bond lengths (Table S12A) indicating more covalent bonding than required to reproduce the CCSD/BS4 orbital densities (see below). The exceptions are those containing LYP correlational functionals, where maximum and minimum deviations are between +0.01 and +0.03 Å (Table S12A). This behavior for LYP functionals has been previously described for [4Fe-4S] clusters.112 Most functionals predict the bond angles accurately except PBE and M06HF functionals, where the RMS values

21



are 4º or greater (Table S12B). No clear systematic trend can be observed, as the compositions of the functionals change and the maximum and minimum deviations are generally symmetrical with only a few exceptions (Table S12B). The LYP functionals tend to fare worse than PBE functions (BLYP vs. PBE, B3LYP vs. PBE1PBE). The M06HF functional underperforms in predicting the geometric structure despite reasonable agreement in relative isomer energies. The deviations in bond lengths and angles obtained from the equilibrium structures using the M06HF functional are significantly higher than the hybrid PBE-series. 3.2.3

Electronic Structure Analysis of Complexes 1H and 2H. The ionic contributions to the

electronic structure were quantified by the ESP derived charges shown in Table S13A for the isomers basal-cis and basal-trans of 1 and apical-(H) of 2. In contrast to the geometric structure, there are recognizable trends indicating improvement in the electronic structure as we move from the pure PBE GGA functional to the validated PBE(50HF%)PBE functional. The atomic charges exhibit higher sensitivity in 1H versus 2H (Table S13B). Smaller values for the lower limits of ranges shown in middle columns of Table 4 indicate better agreement between the DFT and WFN calculations. We considered a RMS variation of 0.01 e– to be significant, given that these values were calculated from considering 18 individual charge differences (Tables S13A) for each level of theory. The PBE(50%HF)PBE functional provides the lowest RMS values in Ru, Cl, H, and P charges; thus, it describes the ionic metal-ligand bonding interactions closest to the reference CCSD/BS4 level. While all functionals show outliers (Table S13B), the Ru charge is universally underestimated, and the chloride atomic charge is overestimated for 1H. This is a sign of overly covalent Ru–Cl bonding except for PBE(50HF%)PBE, LC-ωPBE, and M06HF. For all functionals, the hydride charge in 2H is overestimated by up +0.05 e. The B3LYP functional is notable since it gives one of the closest predictions of the ionic character of the electronic structure for both complexes despite its inferior performance in both energetics and internal coordinates. All density functionals show a distribution of the ionic character of the Ru– Cl bond with respect to reproducing chloride effective charge. In all cases, the chloride charge is less negative compared to the CCSD/BS4 calculations, which indicates excessive covalency for the Ru–Cl bond. The hydride description appears to be reasonable, but the phosphane ligands are more electrophilic than in the reference WFN. Overall, the RMS values in Table S13B provide a rationale for the use of the PBE(50HF%)PBE functional with respect to M–L ionic bonding

22


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interactions. The changes as a function of the amount of HF exchange (PBEPBE(50%HF)PBE or BLYPB3LYP) indicate a convergent behavior of the ionic electronic structure. In contrast to the atomic charges, the covalent contributions (2 in Table 4, and 2(Cl), 2 (PH3), 2(H) in Tables S14A and S14B) to metal-ligand bonding are more convoluted as they are expressed by orbital compositions of the lowest unoccupied frontier molecular orbitals shown in Tables S14A and S14B. The Kohn-Sham orbital contributions underestimate the Ru character in the unoccupied orbitals and some of the occupied orbitals in comparison to the CCSD/BS4 values from Table 3. This is a signature of an overly covalent description (2 is greater in DFT than in reference CCSD calculations) by all the selected functionals. The trends are peculiar, as the LC-ωPBE functional provides the best reproduction of the CCSD/BS4 orbital densities. However, the selected PBE(50HF%)PBE functional provides an improved covalent M–L bonding for 2H in comparison to any of the pure GGA functionals when individual orbital compositions are considered (Table S14B). The pure GGA functionals (PBE or BLYP) provide the expected energetic order of metal-based frontier occupied and unoccupied orbitals. As the amount of HF exchange is increased to ~25% (PBE1PBE and B3LYP) and then to ~50% (PBE(50%HF)PBE) the limitation of the electronic structure analysis becomes apparent, as the virtual orbitals become highly mixed with Ru 5s and 5p contributions that hinder a straightforward comparison of results obtained at the ab initio CCSD level with those of a given hybrid functional. The total electron density difference between CCSD and the PBE(50%HF)PBE functional revealed the fundamental origin of the differences between the reference ab initio WFN method and the most reasonable density functional theory for Ru-Cl-H-PR3 complexes. This difference also provides a route towards introducing modifications to the functionals that may lead to improvements in the performance of DFT calculations. The WFN and DFT electron densities were calculated from single point energy calculations using the optimized CCSD/BS4 geometry and subtracted from each other. The differences in electron density contours are shown in Figures 5A-5F. At low contour levels (Figures 5A and 5D) the lack of electron density (blue lobes) appears in the core regions of the Ru and the Cl centers. Consequently, excess electron density appears (red lobes, Figures 5B and 5E), between the atoms (along with the covalent bonds) in the valence region of the electron density, which manifests in overly covalent M–L 23



bonding in both complexes (Figures 5C and 5F). Thus, adjustment in the core potential and the corresponding valence basis set may open a pathway for further improving the already reasonable agreement between the selected hybrid functional (PBE(50HF%)PBE) and the reference WFN theory (CCSD).

A

B

C

D

E

F

Figure 5: Difference in electron density (0.01, 0.005, and 0.0025 e- Å-3 contour levels from left to right columns, respectively) between PBE(50%HF)PBE/BS4 and CCSD/BS4 theory for gas phase models basal,cis-1H (panels A-C) and apical-(H) 2H (panels D-F). The atomic positions are obtained at the CCSD/BS4 level of theory (gas phase). Blue and red lobes indicate deficient and excess electron density at the DFT level, respectively. As has been demonstrated, systematic comparison of representative density functionals for each rung of Perdew’s “Jacob’s ladder” for density functionals shows that the hyper-GGA hybrid functional PBE(50%HF)PBE provides the best performance. It results, simultaneously, in the lowest error individually, or cumulatively as RMS values, in relative coordination isomer energies, molecular geometries, ionic and covalent metal-ligand interactions when benchmarked against the results of CCSD/BS4 calculations. Therefore, PBE(50%HF)PBE is our preferred functional to study Ru-Cl-H-PMe3 complexes. 3.3. A Representative Application of the PBE(50HF%)PBE/BS4 Level of Theory. The selected hybrid density functional, PBE(50HF%)PBE with a saturated, triple- basis set containing polarization functions, was utilized to provide initial insights into the chemical speciation pathways described in Scheme 2. In addition, the crystal structures of both cis- and

24


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trans- [RuCl2(PMe3)4] (3Me, Scheme 2) are available from the CSD database; thus, we could also confirm the chemical accuracy of the selected hybrid density functional from gas phase calculations for realistic Ru coordination complexes without any simplification in the ligand environment. The cis isomer was found to be 5 kJ mol-1 more stable than the trans isomer for 3Me, similar to the truncated 1H (6 kJ mol-1). The RMS deviations between the calculated and experimental values for bond lengths and bond angles involving the Ru center are typically 0.01 Å and 1º with maximum deviation for Ru–Cl (0.03 Å) and Cl–Ru–Cl (3º). The deviations for all structural parameters are shown in Table S15. Excellent agreement was obtained even without considering crystal-packing interactions. The RMS deviations in C–H bond lengths (~0.1 Å) indicate that the atomic positions of the H atoms in the crystal structure were not rigorously refined in the experimental work. Figure S1 contains the optimized structures for all examples of Ru-Cl-H-PR3 complexes with experimental crystal structures at the PBE(50%HF)PBE/BS4 level(see Methods section for the list of complexes). It is worth mentioning that the Ru–H distance in 2Ph97 deviates rather significantly (calc. 1.57 Å; exp. 1.49 Å) while the rest of the M– L distances are within 0.03 Å. In order to obtain experimentally meaningful values for the Gibbs free energy (ΔGrxn) and enthalpy (ΔHrxn) of reaction for the pathways considered in Scheme 2, we switch from gas phase to condensed phase models. We first evaluated the performance of the ionic liquid [emim]+[NTf2]– polarizable continuum parameters. Consideration of the implicitly solvated solvent ions [emim]+ and [NTf2]–, as well as their neutral ion pair, clear differences (Table S16) were observed among the three solvation models considered in the given study. The integral equation formalism (PCM) and polarizable conductor calculation (CPCM) models give positive values for the heat of solvation and free energy for the neutral ion pair ([emim]+[NTf2]–) when the non-electrostatic cavitation, repulsion, and dispersion terms are considered. These interactions cannot be omitted given that the third model (SMD) intrinsically contains a nonelectrostatic term. On the contrary, the SMD model gives a negative free energy of solvation for all species considered in Scheme 2. Therefore, in the main manuscript, we only report the reaction free energy values obtained at the PBE(50%HF)PBE/def2TZVP/SMD([emim]+[NTf2]–) level, while all other results are reported in Tables S17-S18. The standard state free energy values were corrected for the difference in translational entropy in the gas phase versus the ionic liquid solution by employing Whitesides’s correction104 for an approximately 3 mM 25



Page 26 of 47

concentration of dissolved Ru complexes 1-7 and corresponding dissociating and coordinating ligands. Table 5: Gibbs free energy (ΔGrxn in kJ mol-1) changes for speciation pathways shown in Scheme 2 in the SMD condensed phase model at the PBE(50%HF)PBE/def2TZVP level. See Table S8 for ionic liquid continuum parameters. Values given in parentheses were obtained by taking into account translational entropy corrections due to the 3 mM solutions of [Ru] complexes and their ligands, which is an anticipated solute concentration in the envisioned RAS-MS experiments. The reaction enthalpy values and specific results for the PCM and CPCM continuum models are presented in Tables S17-S18. isomers Reaction 3Me → 1Me + PMe3

cis 8 (0)

trans 0 (-8)

1Me + H2O → 7Me

9 (17)

27 (35)

1Me → 5Me a + PMe3

55 (46)

140 (131)

1Me → 6Me+ a + Cl–

46 (37)

92 (83)

1Me + H2 → 2Me + HCl

88 (88)

74 (74) b

1Me + H2 → 4Me + Cl2 a

398 (398)

387 (387)

cis and trans isomerism is defined for the in-plane phosphane ligands; b the apical-(H) isomer was used instead of the trans-2Me; in both 3Me and 1Me, the dissociation of the weakest, axial PMe3 ligand with the longest Ru–P bond was considered.

In all the continuum model calculations that we carried out, the gas phase structures were refined using the implicit condensed phase model (Table S8) that accounts for a homogeneous field of electrostatic interactions from the ionic liquid and some of the non-electrostatic contributions; however, no effects from the polar and non-polar domains in ionic liquids were captured. The values for thermodynamic state functions at standard conditions in the SMD model of the ionic solvent phase for both cis and trans isomers are summarized in Table 5 (gas phase results are shown in Table S17 and the values for PCM and CPCM are summarized in Table S18) for the step-wise reactions defined in Scheme 2. All continuum models predict nearly spontaneous dissociation of a phosphane ligand in 3Me to give 1Me from ΔGrxn values close to zero. This indicates that the first phosphane ligand likely dissociates in ionic liquids, which is an experimentally relevant conjecture. This result predicts the simultaneous presence of free phosphane ligand and coordinatively unsaturated Ru complex in an ionic liquid. The ΔGrxn for the dissociation of the second phosphane from 1Me resulting in 5Me ranges from 46 to 140 kJ

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mol-1 for the cis and trans isomers, respectively. This is likely a non-spontaneous process. This result would suggest the use of a coordinatively unsaturated 16-electron complex (such as 1Me) as a pre-catalyst in order to avoid facing complex scattering product distributions resulting from chemical speciation. When considering the presence of contaminating water molecules, addition of H2O to 1Me is the next most favorable process, with associated free energy changes ranging from 9–35 kJ mol-1. With a more complete modeling of ionic liquids (explicit solvation that recaptures missing interactions), the free energy differences may decrease further and indicate a spontaneous process. Thus, water contamination will likely act as inhibitor to the presence of the coordinatively unsaturated, reactive Ru complex.

However, the envisioned RAS-MS

experiments would be performed under vacuum, mitigating the interference from H2O contamination. As these experiments would focus on olefin hydrogenation, the thermodynamic analysis was extended to investigate the hydrogenation of 1Me that may result in either a mono(2) or dihydride (4) species. This reaction also establishes a connection between the two Rucomplexes (1 and 2) used in the training set of the method development section. The free energies of the last two reactions in Table 5 (see also Tables S17-S18) indicate the preferred formation of a monohydride complex (2Me) versus dihydride (4Me) by a significant 310 kJ mol-1, primarily due to the approximately 200 kJ mol-1 greater bond strength107 of Cl2 than HCl. In order to illustrate the benefit of using a density functional theory validated by high-level WFN calculations, Table S19 presents the results obtained at the BP86/BS2 level that can cause enthalpy and free energy deviations of -38 to +10 kJ mol-1 and +68 to +80 kJ mol-1 in reactions involving neutral and charged species, respectively; employing the same condensed phase model (SMD). The numbers shown in Table 5 may further change by considering an adequate explicit solvation model for ionic liquids that has the potential to capture the long-range order and ordered solvation shells. However, the mere size of these explicitly solvated systems render these calculations computationally prohibitive at either the WFN or DFT levels. A QM/MM approach would have to be undertaken to describe solvation. This work has provided the foundation for the QM part; however, further efforts would be needed to develop the missing MM parameters for Ru complexes with high chemical accuracy.

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4. Discussion The two representative complexes [RuCl2(PR3)3] and [Ru(H)Cl(PR3)3] for the Ru-Cl-H-PR3 coordination environment have provided us with the ability to complete a systematic evaluation of both wave function and density functional theories. These complexes are notable because of their bias for chemical reactivity because they do not obey the 18-electron rule. As such, they are coordinatively unsaturated which makes them ideal candidates for catalysts. Truncation of the phosphane ligand to PH3 allowed for computationally non-prohibitive structural optimization at the CCSD(T) level of theory with a triple- quality saturated basis set. This is a key compositional feature of the studied complexes that allowed us to obtain energetics, as well as geometric, and electronic structural features at the accepted highest level of theory for a singlereference ab initio WFN method. We unexpectedly found that MP2 level is not an acceptable approximation for considering the effects of electron correlation in relative isomer energies. Computations at the multi-reference level were not feasible for these complexes because of the sizeable active space needed to capture M–L bonding fully. Moreover, the electronic structure analysis suggested that a multi-reference treatment may not be warranted. Consideration of both trigonal bipyramidal and square pyramidal coordination environments for the dichloro- and chlorohydridotrisphosphinoruthenium(II) complexes resulted in equilibrium structures for square pyramidal complexes with cis arrangement of the chlorides in [RuCl2(PR3)3] and at the apical-hydride position in [Ru(H)Cl(PR3)3].] The experimentally characterized cis/trans isomerism of [RuCl2(PR3)4] is well reproduced within 4-6 kJ mol-1, favoring the cis isomer. The M–L distances provide a window into the ionic and covalent bonding differences among the phosphane, chloride, and the hydride ligands. The Ru–P bond lengths greatly vary for apical positions (2.15-2.25 Å) and basal positions (2.21-2.36 Å) depending on the coordination environment. The Ru–Cl bond lengths (2.37-2.39 Å) are independent of their location and the coordination environment. There was a clear difference between the apical and basal Ru–H distances (1.55 and 1.61-1.62 Å, respectively). The angular internal coordinates of the square pyramidal coordination environment were close to the ideal values except for the apical hydride ligand, which had considerable bend away from the ideal apical axis that maximized the -interaction with the lobes of a t2g-type Ru 4d orbital.

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In addition to the assumed ionic interactions between the Ru center and the chloride and hydride ligands, the electronic structure analysis revealed considerably covalent M–L bonds that reduce the Ru electrophilicity relative to its formal +2 charge. The covalent M–L bonds have the following order: hydride ligand, apical phosphane, basal phosphane, and chloride ligands. Despite the high numerical value of the bond covalency, the orbital overlap between Ru 4d and ligand 1s (H), 3p (Cl/P) orbitals is limited, which contributes to a modest M–L bond strength. The chemical speciation analysis of the [RuCl2(PMe3)4] complex in a model ionic liquid showed that the phosphane and chloride ligands may dissociate by mild activation that creates a coordinatively unsaturated and a highly reactive 14-electron, square planar Ru(II) complex. The given work does not include the thermodynamics of each Ru-ligand bond; however, through the electronic structure analysis, we evaluated the exact nature of the ground state from both ionic and covalent bonding interactions. The varied ligand environment provided an initial survey for the change in the ground state electronic structure on going between two different Ru-H/Cl-PR3 complexes. Further studies involving olefin coordination and complex dimerization are planned to validate, and as needed, expand the scope of, the selected hybrid DFT method. Moreover, upon the availability of reactivity data from future RAS-MS experiments, we will be in a position to extend the current study towards compositionally ill-defined, reactive species, such as the above-mentioned 14-electron complex. Another important result of our study is the selection of a hybrid density functional, PBE(50%HF)PBE, which was strategically chosen from many-well performing functionals. This functional reproduces both the electronic and geometric structures as defined by the reference WFN theory, CCSD. The preferred functional allows for reliable theoretical calculations of relevant Ru complexes to map the potential energy surface for olefin coordination, hydrogenation, and polymerization reactions. We wish to highlight that the selection of a sound functional for Ru-complexes is not trivial, as witnessed by earlier studies. Laury and Wilson compared the enthalpy of formation for various second-row transition metals and found significant improvement with the addition of HFX to the PBE functional.31 Specifically, the mean absolute deviation for PBE1PBE in relative energy was one third of that for the pure the PBE functional, with a similar trend for B3LYP (hybrid GGA) and BLYP (pure GGA).31 Paranthaman et al. observed similar improvements between the pure and hybrid functionals for

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tri-metallic Ru systems.33 Sun et al. assessed the performance for σ-bond activation of various Ru and Rh complexes and found that PBE1PBE provided the best agreement for reaction energies and a deviation of about 2 kcal mol-1 for the activation energies.32 It is important to emphasize that previous efforts commonly used single point energy calculations for comparison of relative energies, while we used optimized structures at all levels because the structures of complexes can vary significantly between functionals. Our approach of utilizing trends by adjusting HF exchange terms appears to be consistent with past studies. Hence, through a systematic approach of increasing the amount of HF exchange, we could obtain a density functional that most reasonably reproduced the relative isomer energies, bond lengths, angles, ionic character, and covalent electronic structure relative to the reference ab initio theory. Zhao et al. performed an exhaustive comparison of density functionals to predict the bond dissociation energy of the Ru-containing, second-generation Grubbs catalyst and found that PBE and PBE1PBE had inferior performance to M06-L.34 We can explain the different conclusion of our work by considering the limitation of using single point energy calculations for predicting bond dissociation energies using optimized geometries obtained at a different level of theory. We found that the M06-HF functional provides reasonable agreement with the relative energies; however, it provides inferior performance with respect to geometric and electronic structures. In addition, Laury and Wilson found that the mean absolute deviation is reduced by 8 kJ mol-1 for M06-L when equilibrium structures were used.31 Hence, the poor performance of PBE1PBE observed by Zhao et al. is likely a consequence of computing energies using non-equilibrium structures. From an experimental perspective, our results indicate that bombarding an ionic liquid interface containing a chlorophosphinoruthenium complex with a beam of H2 molecules will likely lead to a hydride containing complex that can be validated by the detection of HCl escaping from the interface. The key to this reaction is the amount of Ru complex located at the interface, which can be tuned by the nature of the phosphane ligand. Although the SMD model has a modest treatment of non-electrostatic terms, linear solvation parameters (H-bond donor/acceptor strength, aromaticity, and electronegative halogenicity) and surface tension, we wish to emphasize that all ionic liquid continuum models employed were implicit solvation modes that predominantly account for electrostatic interactions. However, ionic liquids have well-defined

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lattice-like structures, which could have additional thermodynamic driving forces that influence the Ru-complex partitioning at the interface, resulting in complex reactivity that results in the solvation behavior at the vacuum-liquid interface being different from the bulk behavior. These processes may be studied by molecular beam experiments and molecular mechanical and quantum chemical integrated molecular dynamics calculations. 5. Conclusion In addition to the specific insights about structure and reactivity of Ru-Cl-H-PR3, we found a convergent behavior of the energetic, geometric, and electronic structures obtained from density functional theory and high level, correlated post-HF ab initio wave function calculations. Given the past successes for Cu, Ni, and Fe-containing systems, the strategy undertaken here is a promising approach for benchmarking, improving, and developing basis sets or density functionals. The detailed energetic, geometric, and electronic structure analyses carried out on a representative set of complexes for the Ru-Cl-H-PR3 coordination complex at both wave function and density functional levels provide an abundant reference set for developing semiempirical density functional tight-binding and empirical force field parameters for QM/MM molecular dynamics and Monte-Carlo simulations. In our study, we achieved the highest-level (CCSD/def2TZVP-level) molecular structural description of dichlorotrisphosphino- and chlorohydridotrisphoshinoruthenium(II) complexes for all coordination isomers. The structural knowledge at the highly correlated post-HF level was transferred to the realm of density functionals by selecting a hybrid functional, PBE(50%HF)PBE and the same basis set, which provides optimal performance in terms of relative isomer energies, bond lengths, angles, atomic charges, and orbital compositions. This allows us to map potential energy surfaces of catalytic cycles, define experimental nonobservables, transient intermediates, and transition states at a fraction of the computational cost and without truncation of the ligand environment. As an initial inquiry, we gained insights into the chemical speciation of the structurally characterized RuCl2(PMe3)4 complex towards the formation of coordinatively unsaturated reactive and hydride complexes. The chemical speciation study is a prelude to obtaining new insights into the hydrogenation reactivity and activation of coordinatively saturated Ru/Cl/PR3 complexes in an ionic liquid environment.

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AUTHOR INFORMATION Corresponding Author. * (R.K.Sz.) E-mail: [email protected] ASSOCIATED CONTENT Supporting information. Basis set definitions, Z-matrix definitions, optimized Cartesian coordinates at CCSD/BS4 level, internal coordinates calculated by various density functionals, results of population analyses, comparison of relative isomer energies on a common energy scale, and thermochemical functions for gas phase reaction pathways. Additional electronic supporting information (ESI) is provided as a dataset at DOI 10.5281/zenodo.1478258. ORCID: Savio J. Poovathingal: 0000-0001-7350-5104 Timothy K. Minton: 0000-0003-4577-7879 Robert K. Szilagyi: 0000-0002-9314-6222 *Notes. The authors declare no competing financial interest.

ACKNOWLEDGMENT This work has been supported by the U.S. National Science Foundation (CHE-1566616). Computational efforts were made possible by the Hyalite High-Performance Computing System, operated and supported by University Information Technology Research Cyberinfrastructure at Montana State University. REFERENCES (1) Kontos, A. G.; Stergiopoulos, T.; Likodimos, V.; Milliken, D.; Desilvesto, H.; Tulloch, G.; Falaras, P., Long-term thermal stability of liquid dye solar cells. J. Phys. Chem. C 2013, 117, 8636–8646. (2) Jella, T.; Srikanth, M.; Soujanya, Y.; Singh, S. P.; Giribabu, L.; Islam, A.; Han, L.; Bedja, I.; Gupta, R. K., Heteroleptic Ru(II) cyclometalated complexes derived from benzimidazole-phenyl carbene ligands for dye-sensitized solar cells: An experimental and theoretical approach. Mater. Chem. Front. 2017, 1, 947–957. (3) Naota, T.; Takaya, H.; Murahashi, S.-I., Ruthenium-catalyzed reactions for organic synthesis. Chem. Rev. 1998, 98, 2599–2660.

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Evaluating Density Functionals by Examining Molecular Structures

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