Its Environment Engraves the Geometry of a Molecular Entity: Allyl

Article pubs.acs.org/Organometallics

Its Environment Engraves the Geometry of a Molecular Entity: Allyl Coordination within a Dicationic Ruthenium(IV) Complex Heiko Jacobsen* KemKom, 1215 Ursulines Avenue, New Orleans, Lousiana 70116, United States S Supporting Information *

ABSTRACT: The best molecular arrangements for [Ru(η5C5(CH5)5)(η3-CH2CHCHC6H5)(CH3CN)2]2+ (1) in various environments are determined. The isolated compound 1a serves as a point of reference. On the basis of crystal structure data, solid-state environments are modeled by first placing the cationic compound into the appropriate anionic environment 2a and then completing the unit cell contents by addition of the solvent molecule 3a. Density functional calculations (BP86) augmented by various dispersion corrections (BP86D2, BP86-D3, BP86-D3(BJ), BP86-dDsC) establish the computational approach for electronic structure and geometry optimization. According to the models considered, intermolecular electrostatic interactions are to a major part responsible for substantial changes in intramolecular arrangements.

■

INTRODUCTION At the present time, it appears that density functional theory (DFT)1 within the framework of Kohn and Sham2 is perceived as an independent research tool in its own right in the field of organometallics; a current account nicely illustrates the power and potential of the synergetic interplay between experiment and DFT in organic as well as organometallic transformations.3 However, the awareness is growing “that the model system used in calculations can be as important as the level of theory”.4 A case in point is the allyl coordination within the dicationic Ru(IV) complex [Ru(η5-C5(CH3)5)(η3-CH2CHCHC6H5)(CH3CN)2]2+ (1), as defined in the crystalline solid state.5 To illustrate, the molecular crystal structure of 1 together with relevant geometric data is presented in Figure 1. In a first density functional study, the geometry of 1 was optimized using nine density functionals in conjunction with three different basis sets, and it was found that all density functional methods employed resulted in an unsatisfactory description of the coordination mode of the η3-allyl unit.6 In particular, the Ru−C3 separation was overestimated by 20−50 pm. Still, one should bear in mind that an apparent DFT failure might be a simple failure of DFT due to insufficiencies in the chosen model system. The effect of the crystal environment on the solid-state structure of 1 has been assessed by semiempirical lattice energy calculations;7 not only intermolecular dispersion forces but also electrostatic interactions between crystal entities emerged as likely candidates responsible for substantial aberrations between experiment and calculation. Not too long ago, it was demonstrated that periodic density functional calculations corrected for dispersion (DFT-D3) successfully reproduce the geometry of 1 within the crystalline © XXXX American Chemical Society

Figure 1. Solid-state geometry of 1 (H atoms omitted for clarity), with relevant distances and angles.

solid state.8 Such an approach incorporates a complete description of the molecular environment of a chemical entity. It was concluded that dispersion interactions properly accounted for in the theoretical treatment are key for favorable calculations. Yet, questions remained, and it was further stated that the discrepancy between bond distances of gas-phase and solid-state structures is due to “crystal packing and the effect of the counterions, which unfortunately cannot easily be separated”.8 The present work offers a suggestion as to how the influence of the counterion under the restriction of its solidReceived: February 19, 2017

A

DOI: 10.1021/acs.organomet.7b00127 Organometallics XXXX, XXX, XXX−XXX

Article

Organometallics

situation of charge neutrality. Of all the various choices of two anions, the anions that complete the asymmetric unit have been selected, on the basis of the shortest distance between centers of positive and negative charge. The union of these molecular entities {An−−Cat2+−An−} constitutes crystal ensemble 2. The last structure of comparison, 3a, is part of a collection of molecular entities that completes the contents of the asymmetric unit by adding an acetone solvent molecule, OC(CH3)2 (Sol). This group of four molecular entities {Sol· An−−Cat2+−An−} comprises crystal ensemble 3. To account for so-called crystal packing effects (CPE), internal coordinates of crystal ensembles 2 and 3, which define the relative position and orientation of molecular entities with respect to each other, were kept fixed during the process of geometry optimization and assigned the value found in 1x. Internal coordinates that describe the local arrangements of atoms within a molecular entity were allowed to relax and to achieve a value of minimum energy. Details of coordinate partitioning are to be found within the Supporting Information. Previous work6 established the coordination mode of the η3allyl ligand in compound 1, and in particular the Ru−C3 distance corresponding to the substituted allyl carbon, as measure of performance; Ru−Callyl distances for 1x (dXtal) and for optimized structures 1a−3a (dopt) are collected in Table 1. For each optimized structure, differences Δ(d) between calculated and measured values and their mean absolute deviation δ(Δ) are also included. Furthermore, since the internal coordinate system is chosen such that the value for the distance between atoms Ru and C3 is defined by the dihedral angle ∠(C3−C2−C1−Ru), referred to as significant torsion σ,7 values for σ and for differences Δ(σ) between calculated and measured values are added to Table 1. For an extended model of comparison, superimpositions of non-hydrogen atoms of 1 as found in the crystal 1x with optimized geometries 1a−3a, obtained from DFT and DFT-D calculations, are constructed. Resulting structural overlays are depicted in Figure 3. Mean absolute deviations of atomic positions δ(X) establish a quality criterion; their values are included in Figure 3. The Supporting Information contains relevant aspects of overlay construction, as well as a detailed overlay representation. A more detailed picture evolves when differences in internal coordinates between experiment 1x and theory 1a−3a are considered. The core Ru−N−C framework of comparison for compound 1 is outlined in Figure 4, which defines a set of representative Ru internals. The chosen selection of relevant internal coordinates comprises five bonded distances d(Ru−X), 15 bond angles ∠(Ru−X−Y) and ∠(Y−Ru−X), and 16 dihedrals ∠(Ru−X− Y−Z) and ∠(Y−Ru−X−Z). For each model system and for each computational approach, the differences in distances Δ(d), in angles Δ(ω), and in torsions Δ(σ) were considered; their mean absolute deviations δ(Δ(d)), δ(Δ(ω)), and δ(Δ(σ)) are presented in Table 2. Details are to be found within the Supporting Information. Binding Energies. The construction of crystal ensembles lends itself to a fragment approach of energy decomposition. The binding energy was analyzed using an extended transitionstate method,22 which allows one to decompose associated binding energies into a number of chemically meaningful components.23 A molecular system PQ is partitioned into two fragments P and Q that both possess the local equilibrium geometry of the

state environment might be isolated and analyzed independently.

■

COMPUTATIONAL DETAILS

DFT and DFT-D calculations for molecular systems and ensembles were carried out with the Amsterdam density functional suite of programs (ADF, version 2012.01).9 The general gradient approximation (GGA) constitutes the basic computational framework, and the functional employedBP86was chosen in analogy to previous work.7 Within the architecture of the ADF program package, such calculations are based on the local density approximation with Slater exchange10 and VWN-V correlation,11 augmented by the gradient corrections for exchange and correlation of Becke12 and Perdew,13 respectively. Molecular orbitals were expanded in an uncontracted set of Slater-type orbitals (STOs) of polarized triple-ζ quality,14 reduced to polarized double-ζ quality for H atoms. Core−shells (C, N, O, F: 1s; P: 1s2s2p; Ru: 1s2s2p3s3p3d) were treated by the frozen-core approximation.15 DFT-D calculations employed several of Grimme’s semiempirical corrections (D2,16 D3,17 D3(BJ)18) and the density dependent dispersion correction proposed by Steinmann and Corminboeuf (dDsC).19 Geometry optimizations were based on the method developed by Versluis and Ziegler20 and utilized a complete set of 3N − 6 internal coordinates (Z-matrix formalism). Graphical renditions of molecular ensembles were created with the help of the program package Jmol.21

■

RESULTS Compound 1 crystallizes together with counterions and solvent; the solid-state structure of bis(acetonitrile)(η5pentamethylcyclopentadienyl)(η3-phenylallyl)ruthenium bis (hexafluorophosphate) acetone solvate, referenced as CSD crystal structure HEQNEX, adopts the space group P1̅ with two asymmetric units per unit cell.5 Thus, the asymmetric unit of HEQNEX 1x comprises four molecular entities; their arrangement within the crystal is depicted in Figure 2.

Figure 2. Arrangement of molecular entities within the asymmetric unit of HEQNEX (H atoms omitted for clarity).

Complex Geometries. Atomic positions obtained from 1x provided the starting point for further refinement. Compound 1 was placed into various environments, and its geometry was optimized in DFT and DFT-D calculations. The first structure of comparison, 1a, refers to the isolated dication [Ru(Cp*)(η3CH2CHCHPh)(MeCN)2]2+ (Cat2+) in vacuo. The next structure of comparison, 2a, relates to the dication surrounded by two PF6− anions (An−). This extension establishes a B

DOI: 10.1021/acs.organomet.7b00127 Organometallics XXXX, XXX, XXX−XXX

Article

Organometallics

Table 1. Ru−Callyl Distances d and Significant Torsions σ for 1x and for DFT and DFT-D Optimized Structures 1a−3a, and Differences Δ(d) and Δ(σ) between Theory and Experiment, and Mean Absolute Distance Deviations δ(Δ)a 1x 1a

2a

3a

a

Xtal DFT DFT-D2 DFT-D3 DFT-D3(BJ) DFT-dDsC DFT DFT-D2 DFT-D3 DFT-D3(BJ) DFT-dDsC DFT DFT-D2 DFT-D3 DFT-D3(BJ) DFT-dDsC

d(Ru−C1)

Δ(d1)

d(Ru−C2)

Δ(d2)

d(Ru−C3)

Δ(d3)

δ(Δ)

σ

Δ(σ)

218.1 221.3 221.2 222.5 221.9 220.8 222.5 221.4 222.6 221.6 221.3 222.3 221.1 222.2 221.6 220.8

3.2 3.1 4.4 3.8 2.7 4.4 3.3 4.5 3.5 3.2 4.2 3.0 4.1 3.5 2.7

218.9 226.8 222.4 224.0 223.9 223.3 221.2 218.8 220.0 219.7 219.5 220.8 218.6 219.9 219.2 219.1

7.9 3.5 5.1 5.0 4.4 2.3 −0.1 1.1 0.8 0.6 1.9 −0.3 1.0 0.3 0.2

238.2 266.9 248.4 253.9 254.1 252.6 239.1 232.2 235.2 234.4 234.5 237.9 231.9 234.7 233.0 233.5

28.7 10.2 15.7 15.9 14.4 0.9 −6.0 −3.0 −3.8 −3.7 −0.3 −6.3 −3.5 −5.2 −4.7

13.3 5.6 8.4 8.2 7.2 2.5 3.1 2.9 2.7 2.5 2.1 3.2 2.9 3.0 2.5

66.4 77.5 70.8 73.2 72.7 72.2 67.1 65.1 65.8 65.5 65.7 66.5 65.0 65.5 65.0 65.3

11.2 4.4 6.8 6.3 5.9 0.7 −1.2 −0.5 −0.9 −0.6 0.1 −1.4 −0.9 −1.4 −1.1

Distances are given in pm and angles in deg.

Table 2. Mean Absolute Deviations of Differences δ(Δ) between Experiment and Calculation for Selected Bonded Distances Δ(d), Bonded Angles Δ(ω), and Bonded Torsions Δ(σ)a 1a

2a

Figure 3. Superposition of non-hydrogen atoms of 1 between experiment 1x and calculation 1a−3a, with mean absolute deviations of atomic positions δ(X) (in pm).

3a

a

DFT DFT-D2 DFT-D3 DFT-D3(BJ) DFT-dDsC DFT DFT-D2 DFT-D3 DFT-D3(BJ) DFT-dDsC DFT DFT-D2 DFT-D3 DFT-D3(BJ) DFT-dDsC

δ(Δ(d))

δ(Δ(ω))

δ(Δ(σ))

9.1 3.8 6.0 5.3 4.7 2.5 2.1 2.1 1.9 1.7 2.2 2.2 2.0 2.1 1.8

3.1 2.2 2.4 2.3 2.3 1.8 2.7 2.4 2.3 2.2 2.0 3.0 2.7 2.7 2.4

10.5 21.3 18.6 14.9 16.7 12.0 11.3 11.4 13.4 11.9 11.3 12.2 12.4 10.5 16.9

Distances are given in pm and angles in deg.

ΔEsnap = ΔE int + ΔE Pauli + ΔEelstat = ΔEelstat + ΔE orb (1)

The beneficial orbital interaction energy ΔEint results from an extension of the orbital space when the electronic structure of the final molecule is established. It includes interactions between occupied orbitals on one fragment with unoccupied orbitals on the other fragment, as well as intrafragmental polarization: that is, mixing of occupied and virtual orbitals within the same fragment. The energy requirement due to an adjustment of the occupied orbital space as a response to interfragmental electron repulsion is interpreted as a consequence of Pauli’s exclusion principle and denoted as ΔEPauli. The last term, ΔEelstat, captures the electrostatic interaction between bond-forming fragments. To emphasize particular aspects of binding, the three fundamental contributions might be grouped together in various ways;25 here, ΔEelstat is isolated,

Figure 4. Core Ru−N−C framework of 1.

overall system. Kohn−Sham orbitals for fragments P and Q are calculated that reflect an electronic structure suitable for binding. These two fragments so prepared are united to the molecular system PQ; the change in energy associated with this process, referred to as snapping energy ΔEsnap,24 comprises three essential components (eq 1): C

DOI: 10.1021/acs.organomet.7b00127 Organometallics XXXX, XXX, XXX−XXX

Article

Organometallics and the remaining two terms are merged into the combined orbital term ΔEorb (eq 1). The snapping energy reflects the main component of the binding energy between chemical entities; the bond energy is obtained when the corresponding bond snapping energy BEsnap is corrected by necessary preparation energies.26 For DFT-D calculations, BEsnap is augmented by a change in dispersion energy ΔEdisp, obtained as the difference between dispersion contributions to the total system, EPQdisp, and to individual fragments, EPdisp and EQdisp (eq 2). BEsnap = −ΔEsnap − ΔEdisp

Table 4. Total Hirshfeld Charges qH‑tot and Partial Hirshfeld Charges qH−X on Atoms C1−C3 (see Figure 1) for Compounds 1a−3a (in au) 1a

2a

(2)

The binding energy for crystal ensembles 2 describes the formation of a charge-neutral system from a ruthenium dication and hexafluorophosphate anions (eq A). The binding energy for crystal ensembles 3 is obtained by consideration of a twostep process, initiated by the formation of a charge-neutral intermediate (eq A) and completed by addition of a solvent molecule (eq B). Cat2 + + {An−···An−} → {An−−Cat2 +−An−}

3a

Results for binding energy decomposition of 2 and 3 are presented in Table 3. Table 3. Contributions to Intermolecular Binding Energies (in kJ/mol) for Crystal Ensembles 2 and 3 (in Italics) Obtained from DFT and DFT-D Calculations DFT DFT-D2 DFT-D3 DFT-D3(BJ) DFT-dDsC

−928 −929 −944 −952 −942 −952 −939 −949 −938 −948

−14 −12 −9 −6 −10 −6 −10 −8 −10 −8

qH−C1

qH−C2

qH−C3

−0.0739 −0.0688 −0.0700 −0.0702 −0.0712 −0.0719 −0.0710 −0.0716 −0.0728 −0.0719 −0.0732 −0.0734 −0.0737 −0.0733 −0.0745

−0.0414 −0.0384 −0.0387 −0.0388 −0.0390 −0.0498 −0.0507 −0.0503 −0.0499 −0.0501 −0.0508 −0.0520 −0.0510 −0.0513 −0.0513

0.0172 0.0025 0.0100 0.0088 0.0065 −0.0306 −0.0365 −0.0341 −0.0339 −0.0344 −0.0325 −0.0376 −0.0348 −0.0362 −0.0357

tends to overestimate dispersion effects in transition-metal complexes. The extension of the cationic model system as to include intermolecular electrostatic interaction due to the anionic environment leads to a significant improvement. For systems 2a, DFT, with a deviation of 0.9 pm, closely approaches the experimental distance, while DFT-D methodologies produce a critical distance d(Ru−C3) that now is shorter than the measured value. As might have been expected, DFT-D2 calculations yield the shortest separation. Completion of the contents of the asymmetric unit results in cations 3a. This addition only causes a minor change in d(Ru− C3). For all types of calculations, the critical distance is further reduced by only about 0.5 pm; to judge the influence of solvent, the criterion for comparison needs to be expanded. If the critical distance is understood to include all Ru−C allyl separations, and if the mean absolute deviation of the three Ru−Callyl distances δ(Δ) is chosen as the criterion of comparison, a constant improvement in δ(Δ) is observed for DFT in the progression 1a to 2a to 3a. The inclusion of an anionic environment causes major changes, while the addition of a solvent molecule leads to further refinement. While all DFT-D calculations result in shortened Ru−Callyl separations under the influence of an anionic environment, they still benefit from the expansion 1a to 2a in terms of δ(Δ). The addition of acetone again results in small changes in δ(Δ) for compound 3a, yet there seems to be no consistency among the various DFT-D approximations. On the basis of the value of δ(Δ), the density-dependent dispersion correction dDsC, aimed at a balanced description of both intermolecular and intramolecular weak interactions,28 constitutes the most suitable approach. The decomposition of intermolecular binding energies of crystal ensembles 2 and 3 together with an inspection of partial atomic charges at the critical Callyl atoms offers an explanation for the observed trends in d(Ru−C3). To no surprise, the intermolecular DFT binding energies in compounds 2 and 3 are dominated by electrostatic interactions with only a negligible amount due to combined orbital interactions, and one might have guessed that DFT-D calculations append a sizable dispersion contribution to the total binding energy. Be that as it may, this increase in binding energy does not remain

(B)

ΔEorb

qH‑tot 2.00 2.00 2.00 2.00 2.00 1.513 1.499 1.496 1.502 1.504 1.196 1.186 1.181 1.187 1.187

(A)

{An−−Cat2 +−An−} + Sol → {Sol·An−−Cat2 +−An−}

ΔEelstat

DFT DFT-D2 DFT-D3 DFT-D3(BJ) DFT-dDsC DFT DFT-D2 DFT-D3 DFT-D3(BJ) DFT-dDsC DFT DFT-D2 DFT-D3 DFT-D3(BJ) DFT-dDsC

ΔEdisp

BEsnap

−62 −63 −61 −67 −52 −58 −42 −47

942 941 1014 1025 1013 1026 1001 1015 990 1003

Fragment Charge Densities. The concept of charge distribution is central to binding interaction within an ionic crystal. Hirshfeld’s quantitative description for charge densities of bonded-atom fragments27 seems to provide an adequate definition of charge for the current problem. Relevant Hirschfeld charges qH are collected in Table 4.

■

DISCUSSION In accord with previous work,6,8 the length of separation between atoms Ru and C3 (see Figure 1) serves as the critical distance and as the first measure of comparison. Values for d(Ru−C3) of compound 1athe isolated dicationpresented in Table 1 confirm previous reports: DFT grossly overestimates this critical distance d(Ru−C3) by about 30 pm. While inclusion of intramolecular dispersion notably reduces the critical distance, the discrepancy in d(Ru−C3) remains in a range of about 10−16 pm and does not meet the common expectations of the performance of DFT. The fact that DFT-D2 calculations give rise to the smallest gap between atoms Ru and C3 has been noted and explained in previous work;8 DFT-D2 D

DOI: 10.1021/acs.organomet.7b00127 Organometallics XXXX, XXX, XXX−XXX

Article

Organometallics

reproduced, results for soft internal coordinates such as torsions and dihedrals fall short in reaching acceptable agreement. In particular, torsions around the nitrogen centers display the largest deviations. One should keep in mind that the selected surroundings for the ruthenium dication complete the first and closest coordination sphere only. While this chosen environment adequately captures the bonding situation around the transition-metal center, soft internal coordinates of peripheral groups of atoms are likely to be affected by an extended secondary coordination sphere. An inspection of intermolecular forces within the molecular surroundings of the crystal obtained from semiempirical lattice energy calculations lead to the conclusion that interactions between entities that do not share a common asymmetric unit might also influence the structure of units of interest.7 The peripheral discrepancies, reflected in Table 2 and observed in Figure 3, are most likely due to protracted interactions. One should further keep in mind that the importance of any counterions is well-known, and for solution chemistry, the ion pair concept is well understood.33 Ion−ion interactions have also been employed to model relative stabilities of cationic coordination isomers in a crystalline environment.34 While this approach allows one to judge relative stabilities, it was pointed out that a gas-phase interaction between two charged species does not produce reliable absolute values for a cation in the solid state.34 But, if the ionic arrangement is enforced to obey the translational symmetry of the crystal, the results presented in this work indicate that a quantitative comparison can be achieved. Finally, we point out that the results of the present work appear to be of a general nature and are independent of the choice of density functional adapted for dispersion. For the interested reader, details and results of some additional calculations are supplied as Supporting Information.

an independent addition but is accompanied by a further increase in ΔEelstat. Structural consequences become apparent when partial charges of compounds 2a and 3a are compared with those of the isolated system 1a. Despite the fact that in all compounds the transition metal carries a positive partial charge, not all atoms within a cationic compound share this same charge distinction. For the allyl centers in compound 1a, a buildup of negative charge at atoms C1 and C2 is observed, which is not found for atom C3 that adjacent to the aromatic phenyl ringshows a small positive charge. The electrostatic repulsion between atoms Ru and C3 together with an electrostatic attraction between the remaining Callyl atoms and the transition-metal center might induce an elongation of the d(Ru−C3) distance. While compounds 2a and 3a maintain their cationic character within their respective crystal ensembles, their overall charge deviates from the expected value. In comparison to the isolated complex 1a, decreases in charge by about 0.50 and 0.80 au are seen for compounds 2a and 3a, respectively. This redistribution of charge also influences the polarization of the Callyl atoms; a significant change is observed for the critical atom C3 that now carries a negative charge. The presence of an anionic environment converts the repulsive interaction between atoms Ru and C3 into an attractive interaction and, as a consequence, induces shrinkage in the Ru to C3 separation. At the same time, the decrease in d(Ru−C3) bond length is accompanied by an increase in extended separation between negatively charged peripheral centers of the ruthenium complex and the fluorophosphate entities, which would strengthen intermolecular binding. Additional intermolecular dispersive attractions enhance this effect, as seen in the increase in ΔEelstat for DFT-D calculations. Hence, it looks as if intermolecular dispersion corrections applied to a cationic system within an anionic environment unduly enhance components of intramolecular interaction energies. Similar observations were made for nonmetal bonding with anionic electron donors29 and in the context of a solution environment, be it for folding energies of molecules with long alkyl chains30 or for ligand substitution energies of transitionmetal complexes.31 Overall, a suitable model system should put an emphasis on the balance between intermolecular and intramolecular electrostatic interactions, and for calculations of copper borates under periodic boundary conditions, it was observed that the inclusion of dispersion plays a minor role, reflecting how the full solid-state environment might balance intramolecular dispersion.32 Although qualitative in nature, a more general perspective is obtained by inspection of superimposed structures (Figure 3). While all computational approaches seem to satisfactorily reproduce ligand geometries as well as placement of Cp* units, larger discrepancies occur when the relative positioning of phenyl groups and acetonitrile ligands is evaluated. This shortcoming is reflected in the mean absolute deviations δ(X). While the extended anionic environment significantly improves the quality of DFT calculations, only small improvements are observed for DFT-D approaches. Consideration of the solvent molecule has no significant influences on DFT results but affects to a small extent the outcome of DFT-D calculations. This first assessment is clarified by an inspection of selected internal coordinates that define the coordination of the relevant ligands to the transition-metal center (Table 2). While ruthenium bond distances and bond angles are satisfactorily

■

SUMMATION In the construction of a model for a chemical entity that is part of an extended chemical system, intermolecular interactions between the entity of interest and its surroundings might significantly influence its intramolecular interactions. For a molecular entity within a crystalline environment, it is important to restrain the relative position and orientation of molecular units within a chosen model system according to the constraints of the crystal. For an ionic system, while added dispersion corrections refine and enhance the quality of the computational model, it is the inclusion of intermolecular electrostatic interactions that causes substantial intramolecular changes. This finding is in accord with a previous report “that care should be taken when applying “semiempirical” dispersion corrections in structure optimizations”.35 Overall, the outcome of the present work supports the notion that the model system used in calculations can be as important as the level of theory.4

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.organomet.7b00127. Cartesian coordinates, internal coordinates, total binding energies, and convergence criteria for reference strucE

DOI: 10.1021/acs.organomet.7b00127 Organometallics XXXX, XXX, XXX−XXX

Article

Organometallics

■

(26) Jacobsen, H.; Ziegler, T. Comments Inorg. Chem. 1995, 17, 301− 317. (27) Hirshfeld, F. L. Theoret Chim Acta 1977, 44, 129−138. (28) Corminboeuf, C. Acc. Chem. Res. 2014, 47, 3217−3224. (29) Bauzá, A.; Alkorta, I.; Frontera, A.; Elguero, J. J. Chem. Theory Comput. 2013, 9, 5201−5210. (30) Yang, L.; Adam, C.; Nichol, G. S.; Cockroft, S. L. Nat. Chem. 2013, 5, 1006−1010. (31) Jacobsen, H.; Cavallo, L. ChemPhysChem 2012, 13, 562−569. Jacobsen, H.; Cavallo, L. ChemPhysChem 2012, 13, 1405−1406. (32) Collins, L. R.; Rajabi, N. A.; Macgregor, S. A.; Mahon, M. F.; Whittlesey, M. K. Angew. Chem., Int. Ed. 2016, 55, 15539−15543. (33) Marcus, Y.; Hefter, G. Chem. Rev. 2006, 106, 4585−4621. (34) Aullón, G.; Esquius, G.; Lledós, A.; Maseras, F.; Pons, J.; Ros, J. Organometallics 2004, 23, 5530−5539. (35) Weymuth, T.; Couzijn, E. P. A.; Chen, P.; Reiher, M. J. Chem. Theory Comput. 2014, 10, 3092−3103.

tures 1a, 2, 3, superimposition information, and extended sets of internal coordinates (PDF) All computed molecule Cartesian coordinates (XYZ)

AUTHOR INFORMATION

Corresponding Author

*E-mail for H.J.: [email protected]. ORCID

Heiko Jacobsen: 0000-0003-0721-8726 Notes

The author declares no competing financial interest.

■

ACKNOWLEDGMENTS The Louisiana Optical Network Initiative (LONI) and the Modeling Laboratory for Nanostructures and Catalysis (MoLNaC) are gratefully acknowledged for granting access to their computational facilities.

■

REFERENCES

(1) Hohenberg, P.; Kohn, W. Phys. Rev. 1964, 136, B864−B871. (2) Kohn, W.; Sham, L. Phys. Rev. 1965, 140, A1133−A1138. (3) Sperger, T.; Sanhueza, I. A.; Schoenebeck, F. Acc. Chem. Res. 2016, 49, 1311−1319. (4) Vidossich, P.; Lledós, A.; Ujaque, G. Acc. Chem. Res. 2016, 49, 1271−1278. (5) Fernández, I.; Hermatschweiler, R.; Breher, F.; Pregosin, P. S.; Veiros, L. F.; Calhorda, M. J. Angew. Chem., Int. Ed. 2006, 45, 6386− 6391. (6) Calhorda, M. J.; Pregosin, P. S.; Veiros, L. F. J. Chem. Theory Comput. 2007, 3, 665−670. (7) Jacobsen, H. J. Chem. Theory Comput. 2011, 7, 3019−3025. (8) Moellmann, J.; Grimme, S. Organometallics 2013, 32, 3784−3787. (9) te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. J. Comput. Chem. 2001, 22, 931−967. Fonseca Guerra, C.; Snijders, J. G.; te Velde, G.; Baerends, E. J. Theor. Chem. Acc. 1998, 99, 391−403. http://www. scm.com (accessed 4/17/2017). (10) Slater, J. C. Phys. Rev. 1951, 81, 385−390. (11) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200− 1211. (12) Becke, A. D. Phys. Rev. A: At., Mol., Opt. Phys. 1988, 38, 3098− 3100. (13) Perdew, J. P. Phys. Rev. B: Condens. Matter Mater. Phys. 1986, 33, 8822−8824. (14) Van Lenthe, E.; Baerends, E. J. Comput. Chem. 2003, 24, 1142− 1156. (15) Baerends, E. J.; Ellis, D. E.; Ros, P. Chem. Phys. 1973, 2, 41−51. (16) Grimme, S. J. Comput. Chem. 2006, 27, 1787−1799. (17) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. J. Chem. Phys. 2010, 132, 154104. (18) Grimme, S.; Ehrlich, S.; Goerigk, L. J. Comput. Chem. 2011, 32, 1456−1465. (19) Steinmann, S. N.; Corminboeuf, C. Chimia 2011, 65, 240−244. Steinmann, S. N.; Corminboeuf, C. J. Chem. Theory Comput. 2011, 7, 3567−3577. (20) Versluis, L.; Ziegler, T. J. Chem. Phys. 1988, 88, 322−328. (21) Jmol: an open-source Java viewer for chemical structures in 3D; http://www.jmol.org/ (accessed 04/17/2017). (22) Ziegler, T.; Rauk, A. Theor. Chim. Acta 1977, 46, 1−10. (23) Ziegler, T.; Rauk, A. Inorg. Chem. 1979, 18, 1558−1565. Ziegler, T.; Rauk, A. Inorg. Chem. 1979, 18, 1755−1759. (24) Jacobsen, H.; Ziegler, T. J. Am. Chem. Soc. 1994, 116, 3667− 3679. (25) Jacobsen, H.; Fink, M. J. Inorg. Chim. Acta 2007, 360, 3511− 3517. F

DOI: 10.1021/acs.organomet.7b00127 Organometallics XXXX, XXX, XXX−XXX