A Strain-Deformation Nexus within Pincer Ligands: Application to the

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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A Strain-Deformation Nexus within Pincer Ligands: Application to the Spin States of Iron(II) Complexes James N. McPherson, Timothy E. Elton, and Stephen B. Colbran* School of Chemistry, University of New South Wales, Sydney, New South Wales 2052, Australia

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S Supporting Information *

ABSTRACT: The substitution of a pyrrolide ring for one (or more) pyridyl rings within the ubiquitous terpyridine (tpy, A) scaffold results in more open geometries of the pyridine− pyrrolide chelate ligands. DFT calculations (B3LYP-GD3BJ/ 6-31G**) demonstrate that the more open geometries of the unbound ligands are mismatched with the “pinched in” geometries required to chelate transition metal ions (e.g., Zn2+ ). The strain which builds within these ligands (ΔEL(strain)) as they bind transition metal ions can be related to changes in a single geometric parameter: the separation between the two terminal N atoms (ρ). This relationship applies more generally to other three-ringed tridentate pincer ligands, including those with different donor groups. The approach was applied to homoleptic iron(II) complexes to investigate the contribution of the steric effects operating within the ligands to the different magnetic properties, including spin crossover (SCO) activities, of these systems.

T

catalytic reactions compared to their terpyridine−metal analogues. For example, homoleptic iron(II) complexes with derivatives of ligand scaffold D− are known to be unstable in air and as such have only been partially characterized.11,12As predicted in a theoretical study,13 these complexes were experimentally determined11,12 to be high-spin (HS) configurations of iron(II), unlike terpyridyl analogues which are usually low-spin (LS) and stable.14 There is a single report of a LS [Fe(D)2] complex, which was tentatively assigned to a symmetric product observed in solution by 1H NMR studies, but the species was never isolated, nor otherwise characterized.15 The novel chemistry for metal complexes of ligands with scaffolds B−E is not surprising given the electronic and geometric properties of the five-membered pyrrolide N-donor ring differ from those of the six-membered pyridyl N-donor ring. Both the pyridine and pyrrolide rings are good σ-donor ligands. Odom recently introduced a new tool for quantitative determination of ligand donation effects to a high-valent metal ion, the ligand donor parameter (LDP), where larger LDP values correlate with weaker combined σ- and π-donor strength.16 The LDP assists prediction of useful chemical properties such as the rates of a reaction catalyzed by a series of metal catalysts in which an ancillary σ-donor ligand is varied. The LDP value for the N-donor pyrrolide ring is 13.6 kcal mol−1, about the same as fluoride ion (13.4 kcal mol−1) but larger that than for phenolate (PhO−: 12.0 kcal mol−1), t-butyl alkoxide (t-BuO−: 10.6 kcal mol−1), and dimethylamide

his work focuses on the geometric consequences of substitution of one (or more) of the six-membered rings in 2,2’:6′,2″-terpyridine (tpy, scaffold A in Figure 1), the prototypal meridional metal-binding κ3-N ligand, by a fivemembered pyrrolide ring. It is anticipated that geometric strain will build in a metal complex upon the substitution of a pyridine ring by a pyrrolide ring with consequences of fundamental importance for the electronic and, therefore, all physicochemical properties and the reactivity. Herein, a straightforward parametrization of the ligand strain within a metal complex of a three-ring, tridentate meridional ligand is developed that is demonstrated to correlate well, and most usefully, with structure determined from single crystal X-ray diffraction (SC-XRD) studies. Application to the spin states of iron(II) complexes is explored. Metal complexes of ligands based on the terpyridine scaffold A, Figure 1, are numerous and extensively studied, and their properties are well-understood.1−5 Metal−terpyridine complexes are especially sought after for their functional utility, especially as photo, magnetic, redox, and catalytic centers that can be purposefully assembled into strategic molecular, macromolecular, or supramolecular architectures for advantageous, targeted properties.6−9 Anionic analogues of the meridional, planar terpyridine ligand scaffold A in which one or more of the neutral N-donor, 6 π-electron pyridyl rings are substituted for anionic N-donor, 6 π-electron, pyrrolide rings, scaffolds B−E, are also depicted in Figure 1. The chemistry of ligands with these scaffolds was recently reviewed.10 Metal complexes of these ligands, by comparison with those with terpyridine, are sparse. However, enough is the known to demonstrate that examples of the complexes display novel physicochemical properties and © XXXX American Chemical Society

Received: July 19, 2018

A

DOI: 10.1021/acs.inorgchem.8b02038 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 1. Drawings of ligand scaffolds comprised of three meridionally disposed, 6 π-electron, pyridine and/or pyrrolide donor rings: 2,2’:6′,2″terpyridine scaffold (A), 2-(2,2′-bipyridin-6-yl)pyrrolide scaffold (B), 2,6-di(2-pyrrolide)pyridine scaffold (C), 2,5-di(2-pyridyl)pyrrolide scaffold (D), and 5-(2-pyridyl)-2,2′-bipyrrolide scaffold (E) (not shown is the 2,2’:5′,2″-terpyrrolide scaffold as a genuine metal complex of a ligand with this scaffold is yet to be reported).

(Me2N−: 9.3 kcal mol−1) ions. Terpyridine is a redox noninnocent ligand that may act as an electron acceptor,17−23 whereas pyrrolide in distinct contrast and in keeping with its charge and raised electron density is a redox noninnocent ligand that may act as an electron donor.24−26 The differences in electronic structure upon substitution of a pyridine N-donor by a pyrrolide N-donor are exacerbated by the fact that the former is a six-membered ring whereas the latter is a five-membered ring. The geometric consequences are severe. For example, as suggested in Figure 2, such substitution

might be exploited during ligand design to target a particular function. The strategy which we employ in this work to probe the steric effects within these pyridine−pyrrolide pincer ligands was inspired by the work of Comba et al. that explored the preorganization of tetrathiamacrocyclic ligands for chelating nickel(II) or palladium(II) ions.31 Comba et al. found an empirical correlation between the changes in a structural displacement parameter from the unbound to bound ligand geometries (as determined by SC-XRD) with the difference in energies of these forms calculated using molecular mechanics (i.e., ligands which deformed less on chelation with an ion were also at similar energies in their bound or unbound conformations).31 Comba’s displacement parameter involved the sum of six different interatomic separations, and while predictive accuracy may be improved by considering additional parameters, the fewer parameters involved, the more accessible and general and therefore more useful the prediction is likely to be. At the outset, it was not clear that a single parameter would characterize ligand strain across representative ligands from all families of meridional ligand scaffolds A−E and usefully correlate with found (or predicted) structure. The effects of the differing ring donicities, geometries, and different substituents appended to a scaffold, for example, were possible sources of confounding compromise. To construct a view of ligand strain, we have used density functional theory (DFT) calculations to optimize and compare the energies and structures of free ligands (L) and their hypothetical zinc(II) complex, Zn(L)z+, in the vacuum phase. We develop a useful parametrization of ligand strain in a three-ring meridional ligand and correlation with structure that allows its estimation from the Cambridge Structural Database (CSD) data for a metal−ligand complex. We then consider ligand strain within bis(pincer)iron(II) complexes that exhibit SCO activity. Understanding and predicting SCO in metal complexes is still an important challenge, with recent reports focusing on the electronic effects of the ligands and avoiding steric considerations, by systematically modifying ligands that are structurally similar.32,33 It has long been known (and recently exploited by Shatruk and co-workers)34,35 that the magnetic properties of iron(II) complexes can be tuned through steric effects (i.e., strain).14,36−38 Others have considered the strain within the first coordination sphere of iron(II) complexes with tridentate pincer ligands and the magnetic properties which result. Halcrow, in particular, has proposed four geometric parameters from the L−Fe−L bond angles within the complexes to characterize the distortion,39 and therefore strain, of the coordination geometry around each iron(II) center, and these have now been widely accepted.39−46 Our work is related but

Figure 2. (A) Overlay of the ligand skeletons with the nitrogen atoms (depicted by dots) of the central rings eclipsed for terpyridine (A in red), dipyrrolidepyridine dianion (C2− in green), and dipyridylpyrrolide anion (D− in blue). (B) Idealized interior and exterior bond angles about the ipso-atoms of linked six- and five-membered rings.

of a pyrrolide for pyridyl ring should always lead to an increase in the separation of the two terminal N donor atoms and an increase in the bend angle of the ligand (here defined as the angle between the two inter-ring bond vectors). Upon binding to a metal ion, the ligand will then “pinch in” to optimize the M−N distances. The minimum system energy, and the final observed structure, corresponds to the compromise that reaches best M−N bonding with least ligand strain. Stresses and strains within coordination complexes have been of much interest, particularly in the context of the entatic state principle (i.e., the energization due to a misfit between ligands and metal ions which results in a net lowering of the relative transition state energy) which has been reviewed comprehensively.27,28 Most studies have focused on examining the immediate coordination geometry of a given metal center and its deviations from the geometry “preferred” by the metal ion (i.e., by examining the M−L bond lengths and angles and comparing them to some reference datum), although such approaches are complicated by the selection of such a “preferred” reference geometry.27,29 Computational methods have been used to probe the overall energies of complex molecules, for example, Kroll et al. demonstrated by DFT and spectroscopic methods that the geometric differences (strain) alone between a pair of pentadentate ligands resulted in a weakening of the ligand field by ∼20−30 kJ mol−1 in their iron(II) complexes, with the more flexible (and stronger field) ligand forming a spin crossover (SCO) active iron(II) complex.30 Such approaches are often complicated by solvent or co-ligand interactions, which must be deconvoluted from the overall energies in order to arrive at key parameters that B


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Inorganic Chemistry

A, z = 2; L = B, z = 1; L = C, z = 0; L = D, z = 1; L = E, z = 0) were performed using the B3LYP functional48−50 with the 6-31G** basis set.51 Dispersion corrections were included by adding the D3 version of Grimme’s dispersion with Becke−Johnson damping.52 The geometry optimizations were followed by calculation of vibrational frequencies at the B3LYP level. Positive vibrational frequencies indicated that the coordinates for each structure were energy minima. Previous studies have shown that this combination of theory and basis set provides accurate structural information with complexes of similar size and composition.53−57 Calculations without an empirical dispersion correction returned similar results (see Table S1). Single-point energy calculations (B3LYP/6-31G**) for the strained geometries were performed after the Cartesian coordinates of the ligand atoms were harvested from the theoretical [Zn(L)]z+ structures described above. The geometry of the ligand was then allowed to relax, although the inter-ring N−C−C−N torsion angles were constrained to 0.0°. The same method was employed for structures from experimental SC-XRD data; however, prior to the single-point energy calculation of the strained (coordinated) geometry, the atomic positions of the H atoms were first optimized (B3LYP/6-31G**) with the heavy atom (N, C, O, P, and S) positions fixed. Solid-State Structural Analysis. The Cartesian coordinates of the ligand atom positions from experimental SC-XRD structures were harvested from searches of the CSD and are listed with their Cambridge Crystallographic Data Centre (CCDC) identifier code and a citation to the original report (Tables S3 and S4). H atoms are not directly observed during SC-XRD structure determinations; their positions are typically fixed at positions inferred from neighboring heavier atoms. If left untreated then the crystallographically fixed H atom positions within the ligand structures contribute significant error in subsequent energy calculations. To find more appropriate H atom positions, prior to the initial single-point energy calculations of the “strained” geometries, the positions of all heavy atoms (i.e., non-H atoms) were fixed, and those of the H atoms were optimized (B3LYP/6-31G**). For analysis of the homoleptic iron(II) complexes (Table S5), the ρL(coord) parameter was measured directly from the SC-XRD solidstate structure prior to a single DFT geometry optimization (B3LYP/ 6-31G**) calculation for each ligand (again with N−C−C−N interring torsion angles constrained to 0°) to afford ρL(relax).

tells the other half of the story: what happens to the ligand as it binds these centers.

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EXPERIMENTAL SECTION

Parameterization of Ligand Geometric Structure. The following parameters are used to define the deformation upon binding of a tridentate κ3-N ligand to a metal ion: Bend angle (θ/°): the angle between the two bond vectors from the innermost ring to its two outer substituent rings, as shown in blue in Figure 3.

Figure 3. Top: The bend angles (θ, blue) and terminal N···N separations (ρ, red) as measured in this study for terpyridine (tpy, A) above and dipyridyl pyrrolide (D−) below as examples. Bottom: The deviation from planarity (μrms) was measured by the root-meansquare of the distances (μ, values as shown in Å) of each ring C or N atom to the mean plane through them (shown in violet) as shown, for the exemplar theoretical [Zn(D)]+ complex, with the Zn(II) and H atoms omitted for clarity.

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RESULTS AND DISCUSSION A zinc(II) ion was used to template ligands A−E2− into strained theoretical coordination geometries. The zinc(II) ion was removed, and the ligand’s energy was calculated (B3LYP/ 6-31G**) before the ligand was allowed to “relax.” The changes in geometric parameters were compared to the energy stabilization, and trends observed from this training set were then compared to solid state data obtained from the CSD. DFT Geometry Optimizations. A hypothetical complex of each parent ligand (all substituents are H atoms) with the

Terminal N···N donor separation (ρ/Å): the interatomic separation of the two terminal N donor atoms, as shown in red in Figure 3. Twisting, torsion and/or puckering out of the ligand plane (μrms/ Å): the root mean squared (rms) deviation (Å) of all ring C and N atoms from the mean plane through them, as shown in Figure 3. DFT Calculations. DFT calculations were performed with the Gaussian 2009 software package.47 Vacuum-phase geometry optimizations for free ligand HD, and the zinc complexes [Zn(L)]z+ (L =

Table 1. Predicted (B3LYP+GD3BJ/6-31G**) Zn−N Distances (Å) and N−Zn−N Bond Angles (deg) for the Hypothetical [Zn(L)]z+ Speciesa Zn−N(t) [py/pyr] 2+

[Zn(A)]

1+

[Zn(B)]

[Zn(C)] [Zn(D)]1+ [Zn(E)]

1.978 1.995 1.878 1.899 2.016 2.013 1.912

[py] [py]b [pyr] [pyr] [py] [py]b [pyr]

Zn−N(c) [py/pyr]

N(t)−Zn−N(c)

N(t)−Zn−N′(t)

1.993 [py] 1.929 [py]

83.41 81.71b 85.82 84.13 83.85 83.03b 86.78

166.83 167.53

1.946 [py] 1.864 [pyr] 1.889 [pyr]

168.26 158.77 158.86

L is the parent ligand from scaffolds A−E, Figure 1. bFor nonsymmetric ligands B− and E2−, distances and angles involving pyridyl (py) N atoms are given first, followed by those involving the pyrrolide (pyr) N atoms. a

C


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Inorganic Chemistry

state of the free ligand (no constraints). Thus, ΔEL(strain) is an underestimation of the true strain energy, except when the global minimum energy conformation of the ligand exactly matches the constrained syn,syn conformation (see Figure S1). Estimation of Geometric Deformation Parameters. The three geometric parameters used to define the deformation of a ligand upon binding to a metal ion (θ/°, ρ/Å and μrms/Å) are summarized in Figure 3, while Scheme 1 presents a graphical summary of the methodology employed to obtain these geometric parameters. The changes in geometric parameters (Δθ and Δρ) were normalized against the values for the relaxed ligand (θL(relax) or ρL(relax) respectively) such that the relative deformations are independent from the size of the ligand. The geometric parameters for relaxed syn,syn conformers of ligand scaffolds A−E which were studied in this work are summarized in Tables S2 and S3 for the coordination complexes of these ligand scaffolds. Hypothetical ZnL Complexes and Ligands. As examples, Figure 4 presents overlaid views of the DFT-

zinc(II) ion without coligands was chosen for modeling to minimize the electronic (symmetric d10 ion)and steric (no other ligands) influences on the structure. The Zn−N and N− Zn−N bond lengths and angles obtained are summarized in Table 1. All Zn−N(pyrrolide) bonds were shorter (1.864− 1.912 Å) than Zn−N(pyridyl) bonds (1.929−2.016 Å). The longest Zn−N(t) (t = terminal, outer ring) and the shortest Zn−N(c) (c = central, inner ring) bonds were 2.016 and 1.864 Å, respectively, predicted for [Zn(D)]1+ with a central pyrrolide donor. The three ligands with six-membered pyridyl cores (A, B−, and C2−) had N(t)−Zn−N′(t) bond angles within 167.5 ± 0.8°, while those for D− and E2− with fivemembered pyrrolide cores were less obtuse, within 158.8 ± 0.1°. Calculation of the Internal Ligand Strain. Ligand strain energies are here defined as the rise in energy of a ligand as a consequence of binding to a metal ion. The ligand strain energies were calculated using a strategy similar to those reported by Comba et al.,31 Combariza and Vachet,58 and Wolney et al.,59,60 and are summarized graphically in Scheme 1. Single-point energy calculations (B3LYP/6-31G**) were Scheme 1. Graphical Representation of the Methodology Employed for Estimation of the Internal Ligand Strain Energy and Geometric Parameters Describing Ligand Deformation for Ligands in Hypothetical [Zn(L)]z+ Complexes (Top) and for Ligands in Complexes Harvested from Experimental SC-XRD Structural Data (Bottom)

Figure 4. Binding with a metal ion (divalent 3d10 zinc) is predicted to induce various degrees of strain within the ligands: overlaid images of the DFT-optimized geometries for the complex ([Zn(L)]z+, pink) and relaxed ligand (syn,syn-L, blue) for L = A, z = 2; L = C2−, z = 0; L = D−, z = 1. Note the considerable deviation from planarity in the complex of the ligand with a central five-membered ring (D−).

optimized structures for the relaxed geometries for ligands A, C2−, and D− (shown in blue) and their hypothetical zinc(II) complexes (shown in pink). The geometric parameters and strain energies (the difference between the energy of each ligand in its coordination geometry and that of the same ligand after relaxation, as described above) are summarized in Table 2 (see Table S2 for the geometric parameters for the relaxed ligands). Except for the [Zn(A)]2+ (A = tpy) structure, the relative changes in N···N separations (13.0 ≤ Δρ/ρL(relax) ≤ 31.4%) were greater than the bend angle deformations (13.3 ≤ ̈ to changes in the Δθ/θL(relax) ≤ 22.2%), and the latter are naive external ring angles about the ipso atoms. We therefore determine ρ to be the most sensitive “catch-all” parameter to describe geometric change within the ligand after binding to a metal ion. Ligands A−C2− with central six-membered pyridyl rings were generally predicted to deform less (Δρ/ρL(relax) between 13.0−25.5%) and remain planar (μrms = 0, see Figure 4) than ligands D− or E2− with pyrrolide cores (Δρ/ρL(relax) between 25.5−31.4%), which were also predicted to twist and bend out of plane (with Δμrms between 0.236−0.266 Å, see Figure 4) when coordinated to a zinc(II) center. For ligands A−C2−, both the relative degree of deformation (Δρ/ρL(relax) = 13.0, 19.2, and 25.5%) and ligand strain energy (ΔEL(strain) = 38, 67, and 113 kJ mol−1) associated with chelation of the zinc(II) center increases with the number of flanking pyrrolide rings (0, 1, and 2 for A, B− and C2−, respectively) in the ligand scaffold. We offer a 2-fold explanation. First, as discussed above, shorter Zn−Npyr bonds

performed on the ligand L having the geometry found in the [Zn(L)]z+ complex, i.e., all ligand atoms in the complex were fixed in position, the Zn2+ ion removed, and the energy, ΔEL(coord), calculated. Next, the ligand was allowed to relax during a geometry optimization with the inter-ring N−C−C− N torsion angles fixed at 0° so that the meridional, tridentate (syn,syn) conformations were optimized. The calculation (B3LYP-6-31G**) of the electronic energy of the resulting geometry affords an energy, ΔEL(relax), for the relaxed, but syn,syn-conformer of the ligand L. Thus, the “internal ligand strain energy” is given by eq 1. ΔE L(strain) = ΔE L(coord) − ΔE L(relax)

(1)

As defined, the ligand strain energy, ΔEL(strain), is not the entire strain energy that builds within each ligand as it distorts and binds to a metal ion. The true strain energy is the difference in global energy minima for the coordinated and entirely relaxed D


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Inorganic Chemistry

Table 2. Relative Deformations (Δθ/θL(relax)Δρ/ρL(relax) and Δμrms) and Calculated Coordination Strain Energies (B3LYP/631G**) for Ligand Backbones from Vacuum-Phase [Zn(L)]z+ Geometries (B3LYP+GD3BJ/6-31G**) complex 2+

[Zn(A)] [Zn(B)]+ [Zn(C)] [Zn(D)]+ [Zn(E)]

ligand

θ (deg)

Δθ/θL(relax) (%)

ρ (Å)

Δρ/ρL(relax) (%)

Δμrms (Å)

ΔEL(strain) (kJ mol−1)

A B− C2− D− E2−

98.1 96.3 94.0 105.0 101.9

13.3 17.3 21.7 18.9 22.2

3.929 3.850 3.777 3.963 3.858

13.0 19.2 25.5 25.5 31.4

0 0 0 0.236 0.266

38 67 113 118 170

were predicted than Zn−Npy across all theoretical [Zn(L)]z+ complexes studied, which results in greater contraction of θ and ρ. This is compounded by the more “open” relaxed ligand geometries (θL(relax): 113.3, 116.4, and 120.0° for A, B−, and C2−, respectively) which result from alleviation of steric demands at the back of the ligands as the six-membered pyridyl rings are replaced by five-membered pyrrolide rings. We note that θL(relax) for C2− was equal to the ideal value (120°) for a generic six-membered ring. These trends also hold for ligands with pyrrolide cores (relative deformations and ligand strain energies increase from 25.5 to 31.4% and from 118 to 170 kJ mol−1, respectively, for D− and E2−) although at much wider θ (and therefore larger ρ) due to the wider ideal bend angle (144°) for a fivemembered core. For these ligands, additional modes of deformation are also predicted, such as twisting and puckering of the rings (Δμrms = 0.236 and 0.266 Å for D− and E2−, respectively) due to the geometric consequences of the short central Zn−Npyr bonds (100°) associated with five-membered cores already discussed above. Correlation of Ligand Strain Energy and Deformation. A simple relationship between the coordination strain and changes in our easily measured geometric parameters was sought. The goodness of fits was evaluated by the residual rootmean-square value (rmsresidual =

Figure 5. Fitting of ligand strain energy against relative ligand deformation (Δρ/ρL(relax)) for vacuum-phase theoretical [Zn(L)]z+ complexes (training set) in black. Data from selected solid state SCXRD structures of complexes (accessed from the CSD, see Table S3) are shown as empty triangles: L = A (red); L = (C2)2− (purple), L = (C3)2− (mustard); L = D− (green) and L = (D2)− (blue); where H2C2 = 2,6-bis(5-methyl-3-phenyl-pyrrol-2-yl)pyridine;68 H2C3 = 2,6-bis(indol-2-yl)pyridine;67 and HD2 = methyl 4-methyl-2,5-bis(pyrid-2yl)pyrrole-3-carboxylate.26

{ ∑ (actual value − predicted value)2 /n} , where n = 5 is the number of observations in this case). The strain energies are presented in Figure 5 (as squares) against the relative change in terminal N···N donor separation (Δρ/ρL(relax)). Fitting these data by linear regression analysis (and enforcing that 0 deformation equates to 0 strain energy) results in the trend defined by eq 2, which is also shown as the black trendline in Figure 5, with standard error in the slope of just under 10%.

ΔE L(strain) = (460 ± 37)

Δρ ρL(relax)

poorer correlations (rmsresidual= 29.9 kJ mol−1 for Δθ/θL(relax) alone, or 16.1 kJ mol−1 with Δμrms included). Complexes and Ligands from the CSD. To test the generality of the trends observed for the data on the hypothetical [Zn(L)]z+ species (eqs 1 and 2), “experimental” data was sought. Twenty solid-state structures of metal complexes of tridentate pyridine−pyrrolide ligands were selected from the CSD. To challenge our methodology, a range of metal coordination geometries (octahedral, trigonal bipyramidal, and square planar), and metal centers (mostly transition metals of various oxidation states but also two lead(IV) structures from the same unit cell) were deliberately selected. No structures were available through the CSD for ligand scaffolds B− or E2−,10 so our “experimental” study was limited to derivatives of A, C2−, and D−. The ligand strain energies and the ligand deformation parameters were determined as graphically summarized in Scheme 1. All data obtained are summarized in Table S3. The calculated ligand strain energy from the solid state structural data was in poorer agreement to eq 3 (rmsresidual = 15.0 kJ mol−1) than for the theoretical vacuum-phase [Zn(L)]z+ training set. This was not particularly surprising. The largely unpredictable intermolecular interactions inherent in crystal packing61 may also contribute to deviations from coplanarity of the aromatic ligand ring systems. For example,

kJ mol−1 (2) −1

The rmsresidual was improved from 17.7 kJ mol for eq 2 to 11.9 kJ mol−1 when the Δμrms parameter was included (eq 3), albeit with a large increase in error. It can be concluded that the out-of-plane deformations (twisting, puckering, and torsion) make significant but somewhat unpredictable (given the large error) contributions to the buildup of strain within these ligands. ΔE L(strain) = (395 ± 44)

Δρ ρL(relax)

+ (127 ± 66) Δμrms kJ mol−1

(3)

Analyses involving the relative bend angle deformations (Δθ/ θL(relax)) were also investigated (see Figure S2), but resulted in E


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Inorganic Chemistry

metal binding therefore involves a smaller relative geometric deformation. Beyond Pyridyl−Pyrrolide Pincer Ligands. To push the generality of the approximation of ligand strain energy by the terminal donor atom separation, nine tridentate pincer ligands, with different donor atoms and ring systems, were selected from the CSD (Figure 6 and Table S4). Other 5−6−5 and 6−

neither of the solid-state structures of HD in the literature are coplanar (μrms = 0.112 and 0.169 Å for the structures with CCDC codes QOBREF62 and QOBREF01,63 respectively), unlike the vacuum-phase optimized geometry (μrms = 0).10 In contrast, the correlation of eq 2 to the solid-state data (rmsresidual = 12.0 kJ mol−1) was an improvement over our theoretical vacuum-phase training set. As shown in Figure S2, the relationship between ΔEL(strain) and Δθ/θL(relax) (rmsresidual = 14.2 kJ mol−1) was also stronger than that when Δμrms was included (rmsresidual = 17.4 kJ mol−1). Therefore, we present the relative change in terminal N···N donor separations (Δρ/ ρL(relax)) as the preferred metric parameter for approximating ligand coordination strain as defined herein, due to both ease of measurement and goodness-of-fit (with lowest rmsresidual). The calculated coordination strain from the solid-state data are plotted against Δρ/ρL(relax) in Figure 5 (triangles). Going forward, it emphasized that our analysis suggests an ∼10% error for eq 2. Complexes of D− (green and blue triangles, Figure 5) developed greater ligand strain energy (75−121 kJ mol−1) than those of A (red triangles in Figure 5, 25−59 kJ mol−1) with those of C2− intermediate (purple and mustard triangles in Figure 5, 57−103 kJ mol−1), consistent with the trends observed in the vacuum-phase training set discussed above. Within the octahedral, homoleptic [M(A)2](ClO4)2 complexes (CCDC codes: M = Fe(II), DANMOU;64 M = Ru(II), BENHUZ;65 and M = Os(II), GOGDOV66), the terpyridyl chelate ligands are the least strained in the ruthenium(II) complexes (∼25 kJ mol−1), while the osmium(II) and iron(II) structures are strained to similar degrees (41 and 52 kJ mol−1 for iron, 47 and 58 kJ mol−1 for osmium). Interestingly, the terpyridyl (A) ligand in Colbran’s heteroleptic octahedral [Ru(A)(D2)][PF6] complex (CCDC code: LOGKUP)26 is also more strained (∼60 kJ mol−1) than that in the homoleptic [Ru(A)2]2+ system (CCDC code: BENHUZ).65 The C2− ligand derivatives had similar deformations and strains in high valent trigonal bipyramidal lead(IV) complexes (Δρ/ρL(relax) = 13.1−13.5%, ΔEL(strain) = 72−76 kJ mol−1, CCDC code: ALILUC)67 to those in Milsmann’s octahedral zirconium(IV) photosensitizer (Δρ/ρL(relax) = 13.4−14.1%, ΔEL(strain) = 57−66 kJ mol−1, CCDC code: YAHBIV).68 The lower coordination number square planar palladium(II) complex was more strained (Δρ/ρL(relax) = 20.7%, ΔEL(strain) = 103 kJ mol−1, CCDC code: XOVFIX).69 Within the set of complexes of derivatives of D−, an additional observation is worth noting. The octahedral ruthenium(II) and square planar palladium(II) complexes of unsubstituted D− (green triangles, Figure 5) were both more deformed and more strained (Δρ/ρL(relax) = 21.7 and 23.9% and ΔEL(strain) = 88 and 120 kJ mol−1 for complexes with CCDC codes AYOSUE70 and TELPUX,63 respectively) than similar complexes of Colbran’s substituted (D2)− derivative (blue triangles in Figure 5, Δρ/ρL(relax) = 13.7−16.1%; ΔEL(strain) = 75−91 kJ mol−1 for complexes with CCDC codes LOGKUP, LOGLEA and LOGKOJ).26 Since binding of these dipyridylpyrrolide ligands to a metal typically brings the N-donor atoms of the outer rings closer (i.e., ρL(coord) < ρL(relax)), the introduction of bulky inner ring substituents (the 3-methyl ester and 4-methyl pyrrolide substituents for D2) will serve to “pre-organize” the ligand into its coordinated geometry. Thus, ρL(relax) = 5.322 Å for unsubstituted D− versus 4.879 Å for Colbran’s (D2)− (see Table S2), and

Figure 6. Calculated coordination strain energies (B3LYP/6-31G**) for other “pincer”-type ligands against the relative change in terminal donor atom separations (Δρ/ρL(relax)) from structures obtained from the CSD (shown with metal centers labeled and donor atoms colored blue, nitrogen; gray, carbon; orange, phosphorus; yellow, sulfur). The trend-line, ΔEL(strain) = 460(Δρ/ρL(relax)), obtained from results for the training set of pyridyl−pyrrolide pincers A−E2− and their Zn2+ complexes, is shown in black. Predicted strain energies that agree with the model are illustrated in black, while those showing clear error are shown in red.

6−6 ring systems with imine (pyridyl or pyrazolyl), carbenes, or cyclometalated phenyl rings agreed well with eq 2 (with residual error values 4.9 Å) for SCO-inactive HS iron(II) complexes (Table S5, entries 29−32), where the metal−ligand bonding was insufficient to overcome the restrictions imposed by ligand geometry, the Fe−N bonds lengthen to minimize the strain within the ligand well below that predicted by eq 5. In contrast, the HS configurations of the two SCO-active complexes studied with ρL(relax) ∼ 5.0 Å (Table S5, entries 22, 25, and 26) were in good agreement with eq 5. That these particular iron(II) complexes are SCOactive despite long ρL(relax) values is indicative of stronger metal−ligand bonding; indeed, the difference ligand field stabilization energy is at the cusp of compensation for the internal ligand strain for the LS state. Therefore, their HS states follow eq 5. Finally, although the application of eqs 4 and 5 followed by a comparison with experimental data generates plots such as illustrated in Figure 8 that well rationalize spin state and SCO behavior, this explanation all comes after the fact, a posteriori, it is not predictive. A prediction of the spin state or SCO behavior for a particular complex demands a considerably more sophisticated methodology involving the full and difficult calculation of the optimum geometry, energy and entropy for both spin states. Such methodologies, while possi-

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b02038. DFT and SC-XRD analyses; diagrams of all pincer ligands investigated; Cartesian coordinates from the output of DFT calculations (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

James N. McPherson: 0000-0003-0628-7631 Stephen B. Colbran: 0000-0002-1119-4950 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the Australian Research Council for funding (Grant No. DP160104383) and the School of Chemistry, UNSW Sydney for supporting this research. J.N.M. and T.E.E. are grateful for the receipt of Australian Postgraduate Awards. H


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Inorganic Chemistry

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