In Search of The Bailar Twist and Rây-Dutt mechanisms that racemize chiral tris-chelates: A computational study of Sc(III), Ti(IV), Co(III), Zn(II), Ga(III), and Ge(IV) complexes of a ligand analog of acetylacetonate.

Henry S. Rzepa*^a and Marion E. Cass^b

Abstract: Two non-dissociative processes, a Bailar Twist that proceeds through a transition state of D_3h symmetry, and a Rây-Dutt Mechanism that proceeds through a transition state of C_2v symmetry, as well as dissociative/associative processes, are potential mechanisms by which the enantiomeric forms of chiral metal tris chelates can be inter-converted. We have applied density functional theory to locate the stationary points for metal tris chelates of a β-diketonate ligand analog that interconvert Δ and Λ forms via one or both of these non-dissociative pathways. Although many two dimensional static representations of the Bailar Twist and Rây-Dutt Mechanisms can be found in the chemical literature (of the type shown in Figure 1), in this communication, we present our results in the form of interactive three dimensional animations as a means of enhancing the scientific perception of these fluxional processes.

Tris-chelates are well known examples of metal complexes which can exist as separate enantiomers, belonging (if appropriately substituted) to the chiral D₃ or C₃ point groups. Analyses of how such complexes can racemize via non-dissociative ligand exchange was first presented in the late 1940s, although dissociative processes have long been proposed to be operative in isomerization/racemization mechanisms in complexes of kinetically labile metals. The two non-dissociative pathways accepted as possible mechanisms for the racemization of D₃ metal chelates (and racemization or racemization and facial-meridional isomerization C₃ metal tris chelates) are the Bailar^1a and the Rây-Dutt twist mechanisms,^1b illustrated in a two-dimensional representation in Figure 1. The Bailar Twist is a trigonal twist around the real C₃ axis of a metal tris chelate and the Rây-Dutt is a twist (sometimes referred to as a rhombic twist) around the pseudo C₃ axis. The Bailar Twist and Rây-Dutt Twist Mechanisms have been the subject of theoretical study^1-4, experimental verification^5-11, and computational analysis.^11,12

Figure 1. A 2D Illustration of the Bailar Twist and Rây-Dutt Twist Mechanisms that racemize D₃ Metal Tris Chelates or isomerize C₃ Metal Tris Chelates.

In this communication, we present our results of a computational study on a series of metal tris chelates of a simple ligand analog of the acetonylacetonate ligand, with a focus on the following aspects of non-dissociative mechanisms that racemize metal tris chelates: We have applied density functional computational techniques to systems that corroborate mechanistic proposals based on experimental observations and we have presented our computational work in the form of interactive three dimensional animations that we hope facilitates understanding.

We have previously analysed¹³ the non-dissociative mechanisms that interchange apical and equatorial atoms in AEX₅ square pyramidal molecules such as ClF₅ and IBr₅. Our analysis was considerably assisted by visual inspection of the mechanism via animation of the normal mode of the imaginary frequency of the transition state. Through visual comparison of those modes to the modes in known fluxional processes (including the Berry pseudo rotation, lever, turnstile and Bartell mechanisms which we had previously animated for pedagogic purposes¹⁴) we were able to identify combinations of shared characteristic motions. These hybrid motions that we identified in the apical/equatorial atom exchange of square pyramidal molecules we termed chimeric pseudo rotations. Here, we extend the approach of using visual three dimensional animations to an analysis of fluxional processes in D₃ 6-coordinate (octahedral) tris-chelates, examples of which are known for almost all transition and non-transition series metals.

In selecting metals for study, we confined ourselves here to diamagnetic species and excluding those metals where single electron-pair occupancy of degenerate (E) molecular orbital levels (at D_3h or D₃ symmetry) leads to Jahn-Teller like distortions from these symmetries (e.g. Mn and Cu). We also restricted our examination of the Bailar Twist and Rây-Dutt non-dissociative processes to a series of metal complexes involving a simple model analogue of the β-diketonate ligand acetonylacetonate (acac). The metal complexes of the β-diketonate ligands have been extensively studied; information on structure and reactivity^15a as well as mechanistic studies on isomerization/racemization processes^15b is available for comparison to our computational results. Furthermore, our model ligand, namely the 1,3-propanedionato, or malondialdehyde ligand (mda) has been previously used in computational models,¹⁶, and one x-ray crystal structure of a Cr(mda)₃ complex is known.¹⁷

Computational Methods

In order to achieve accurate modelling of the geometry and angular behaviour at the metal center, we used the correlation consistent-5ζ basis (and in one example when the 5ζ basis failed to converge, a 4ζ basis) on the metal itself (cc-pv5Z).¹⁸ Use of this basis on the ligands would have been prohibitive in terms of computer time, and these were instead limited to the 6-31G(d) basis. In two cases only, this combination yielded tiny negative force constants corresponding to out-of-plane ligand deformations.¹⁹ Replacing the 6-31G(d) basis on the ligand with the improved cc-pVTZ basis on the ligand removes this negative force constant, but at the expense of significantly increased processing time. Within this series, we have computationally characterized both the D_3h Bailar and C_2v Rây-Dutt diamagnetic transition states for the Sc(III), Ti(IV), Zn(II), Ga(III) and Ge(IV) tris ligand complexes at the B3LYP density functional level, including calculation of the Hessian second derivative matrix, and from this, analysis of the transition mode. Appropriate symmetry number corrections for the entropies were included.

Results and Discussion

For each M(mda)₃ complex under examination [M = Sc(III), Ti(IV), Co(III), Zn(II) Ga(III) and Ge(IV)], we computed an equilibrium geometry (presented as Enhanced Web objects, see Table 1) and then searched for a transition state of D_3h (Bailar) or C_2v (Rây-Dutt) symmetry.

All of the computed equilibrium geometries for the M(mda)₃ complexes have D₃ symmetry (Figure 2 for the general structure and see Enhanced Web Object 1 for a 3D interactive view of each computed structure and a listing of relevant bond distances and angles). The total energy as well as the free energy corrected for zero point energies and entropy are reported in our supplemental material (Web Object 3) for each structure. The computed structures compare favorably to the known structure of Cr(mda)₃¹⁷, also shown in Enhanced Web Object 1. In addition, a comparison of the structural properties of each computed M(mda)₃ complex to that of a reported x-ray crystal structure for the corresponding M(acac)₃ analog of the same metal ion²⁰, illustrates how well mda mimics the acac ligand (see Enhanced Web Object 2 for the structural comparisons). Each mda ligand, like the acac ligand, forms a planar, six-atom metal-chelate ring, and shows significant delocalization over the C-O and C-C bonds. Metal-oxygen, carbon-oxygen, and carbon-carbon bond lengths as well as O-M-O intraligand bite angles (listed in Enhanced Web Object 2) are consistent within each pair of M(mda)₃/ M(acac)₃ structures.

Figure 2. A tris metal complex of a β-diketonate ligand. Abbreviations for ligands used or referred to in this study: acetylacetonate (acac), malondialdehyde (mda), 1-Phenyl-5-methylhexane-2,4-dione (pmhd), 5-Methylhexane-2,4-dione (mhd), trifluoroacetylacetonate (tfac), benzoylacetonate (bzac), R = R' = CH₃, triacetonylmethanide-d₃ (triac-d₃).

We computationally characterized a transition state of D_3h symmetry and of C_2v symmetry for each of the Sc(III), Ti(IV), Zn(II), Ga(III) and Ge(IV) species. Computed energies are given in Table 2. The results, as well as a discussion of how our computational results compare to published mechanistic studies, are presented individually vida infra for each species. In contrast to the results for Sc(III), Ti(IV), Zn(II), Ga(III) and Ge(IV), we were unable to locate a transition state of D_3h or C_2v symmetry for the Co(III) species. A stationary state of C_2v symmetry collapsed to yield a five coordinate intermediate (see discussion below), consistent with the proposal by Holm and coworkers that Co(III) tris chelates of examined β-diketonate ligands exhibited behavior characteristic of isomerization/racemization through a dissociate mechanism proceeding through a five coordinate species.³

^aFree energy corrected for zero point energies and entropy. ^bBasis set: cc-pV5Z(5d,7f) on the metal center¹³, 6-31G(d) on the ligands. A more extensive table of the energies and computational parameters can be found in Web Object 3. ^ccc-pV5ζ on central atom, cc-pVTZ on ligands.

Given that metal acetylacetonate complexes have C-O and C-C bond lengths consistent with delocalized electron density, and given that the M(acac)₃ complexes undergo reactions normally associated with aromatic compounds such as electrophilic aromatic substitution, we calculated the nucleus Independent chemical shift (NICS) value at and above the center of the metal-mda ring in each structure to ascertain if this was useful in understanding the aromaticity in these molecules. The NICS(1) and/or NICS(2) values (1 Å and 2 Å respectively above the centroid of a ring) are useful in predicting aromaticity in organic and organometallic complexes²¹. More recently, researchers have begun to calculate NICS(1) and/or NICS(2) to estimate the aromaticity of coordination complexes²². All of the ground state geometries we computed in this study gave NICS(2) values close zero (± 2 ppm), indicative of non-aromatic rings (NICS(1) values show slightly more contribution from the σ-derived ring currents). Apparently all the empty orbitals available on all the metals used in this study are sufficiently mismatched in energy for effective π delocalization.

Sc(III)L₃: The D_3h transition state for the Sc(mda)₃ complex has a similar barrier (ΔG^‡ = 7.7 kcal mol^-1, 32.1 kJ/mol) to that of the C_2v transition state (Δ G^‡ = 7.3 kcal mol^-1, 29.3 kJ/mol). For each of the two computed transition states, a single imaginary frequency was found: 60i cm^-1 for the D_3h Bailar TS (with an A₁" irreducible representation) and 45i cm^-1 for the C_2v Rây-Dutt TS (with an A₂ irreducible representation). With such low energy barriers for both transition states, these Sc(III) complexes would be predicted to thermally racemize well below room temperature (although dissociative pathways may well also occur in solution and we have not computationally explored these types of pathways). An animation of the Bailar twist and of the Rây-Dutt mechanism for the racemization of Sc(mda)₃ is visually identical to that of Ga(mda)₃ shown in Enhanced Web Object 4 and Enhanced Web Object 5 respectively. An experimental study found that the Sc(III) tris complex of the pmhd β-diketonate ligand (Figure 1 R = CH-(CH₃)₂ and R' = CH₂-C₆H₅) exhibited fast fluxional behavior in the ¹H NMR spectrum in chlorobenzene, and at temperatures as low as -95^oC in dichloromethane.⁴ The fluxional behavior was suggested to be facile but non-dissociative, since addition of aliquots of alternatively substituted β-diketonates did not yield ligand exchange isomers.⁴ Our computed barriers and pathways are consistent with these experimental results.

[Ti(IV)L₃]⁺:

The Ti(IV) complex is very similar to the SC(III) system; the only significant difference is that the loss of entropy at either of the two transition states is slightly greater, indicating tighter binding for the cationic system.

Co(III)L₃: True D_3h or C_2v transition states for the tris mda complex of Co(III) were not locatable. The stationary state of C_2v symmetry 60.4 kcal mol^-1 above the equilibrium D₃ geometry had B₂ and A₂ imaginary modes. Whilst the latter is the Rây-Dutt mode, the former corresponds to asymmetric Co-O stretching of the unique ligand. Following the Rây-Dutt mode results in complete fission of one Co-O bond to give a 5-coordinate intermediate 39.4 (ΔG 34.5) kcal mol^-1 above the equilibrium D₃ geometry (using a 4ζ basis on the metal; the corresponding 5ζ basis proved unconvergeable). This corresponds to a dissociative process for Λ and Δ interconversion, albeit one that is only accessible with high energy input. This intermediate is shown in Enhanced Web Object 6. The absence of a low energy pathway for thermal isomerization is consistent with the experimental observation that the Λ and Δ forms of the analogous Co(acac)₃ complex are isolable and stable to racemization at room temperature.¹⁰ Furthermore, an extensive mechanistic study based on an analysis of the temperature dependent reaction rates of isomerization and racemization for Co(mhd)₃ (Figure 1, R = CH-(CH₃)₂ and R' = CH₃) monitored by proton NMR and CD spectroscopy indicates that this process involves bond rupture to generate a five-coordinate species⁴. The barriers for these isomerization and racemization processes (tabulated in Table 3 for comparison, along with values for isomerization and racemization in other similar Co(III) β-diketonates^4-6) agree reasonably well with theory. It is noteworthy however that our calculated ΔS^‡ for the dissociative process (+13.7 cal K^-1 mol^-1) is rather larger than that derived from kinetic measurement (~+6-9 cal K^-1 mol^-1), which implies that in practice, the 5-coordinate intermediate may be more highly solvated than the D₃ ground state.

Table 3. Experimentally Measured Activation Parameters for Relevant Systems
System	Processes Observed	Reported Activation Energies are in kcal mol-1, entropies in cal K-1 mol-1	Comments	Ref
Co(III) Systems
	Co(mhd)3 Isomerization cis-trans trans-cis Racemization for cis for trans	ΔG‡Calc 293K = 30.4, ΔH‡ = 32.9, ΔS‡ = 8.7 ΔG‡Calc 293K = 30.8, ΔH‡ = 32.6, ΔS‡ = 6.3 ΔG‡Calc 293K = 29.4, ΔH‡ = 29.9, and ΔS‡ = 1.5 ΔG‡Calc 293K = 29.6, ΔH‡ = 31.6, and ΔS‡ = 6.8	Bond Rupture Mechanism (proceeding through a five coordinate intermediate) is proposed Measurements of temperature dependent rates using proton NMR and CD Spectroscopy Solvent: Chlorobenzene	4
	Co(tfac)3 Isomerization	ΔG‡455K = 26.8, ΔS‡ = 8.6	Barrier Determined from Coalescence of 19F NMR Signals Solvent: Chloroform	6
Ga(III) Systems
	Ga(pmhd)3 Isomerization/Racemization	ΔG‡Calc 293K = 18.6, ΔH‡ = 19.4, and ΔS‡ = 2.9	Non-dissociative Twist Mechanisms are Proposed to be most consistent with experimental observations Measurements by proton NMR Analysis of Temperature Dependent Line Broadening Solvent: Chlorobenzene	5
	Ga(tfac)3 Isomerization/Racemization	ΔG‡335K = 17.5	Barrier Determined from Coalescence of 19F NMR Signals Solvent: Chloroform	6
	Ga(L)3 Intramolecular Racemization Intramolecular Isomerization	ΔG‡295 = 14 kcal/mol (60 kJ/mol) in D2O ΔG‡327 = 16 kcal/mol (67 kJ/mol) in DMSO-d6 Barrier for Isomerization (Rây-Dutt) is larger than that for Racemization Computed Barrier for the Bailar Twist: ΔE = 12.7 kcal/mol (53 kJ/mol) Computed Barrier for the Rây-Dutt: ΔE = 16 kcal/mol (67 kJ/mol)	The Bailar Twist was shown both experimentally and computationally to be the dominant process No observed ligand exchange was used to confirm that racemization processes are intramolecular Barrier Determined Experimentally from Coalescence and Line Shape Analysis of VT 1H NMR	10 11
	Ga(fox)3 Isomerization/Racemization Bailar ≈ Rây-Dutt	ΔG‡293K = 14.4, ΔH‡ = 16.9, and ΔS‡ = 6.7	Proposed Mechanism: Bailar and Rây-Dutt Measurements Temperature Dependent Line Broadening of 19F-NMR signals and use of 2D EXSY 19F-NMR Cross Peak Intensities Solvent: DMF	7

Zn(II)L₃]^-: The D_3h and C_2v transition states for the [Zn(mda)₃]^- anion have relatively low and very similar energy barriers (for the D_3h Bailar TS ΔG^‡ = 10.8 kcal mol^-1 and for the C_2v transition state ΔG^‡ = 10.0 kcal mol^-1. With such low energy barriers, these Zn(II) complexes would be expected to racemize well below room temperature. For each of the two computed transition states, a single imaginary frequency was found: 70.7i cm^-1 for the Bailar TS of D_3h symmetry and 58.2i cm^-1 for the Rây-Dutt C_2v. Animations of the Bailar twist and the Rây-Dutt mechanism for the racemization of the Zn complex is again is visually identical to that of Ga(mda)₃ shown in Enhanced Web Object 4 and Enhanced Web Object 5 respectively.

Ga(III)L₃: The results of our computational study are perhaps the most interesting for the Ga(III) species of the mda ligand. As with the Sc(III) and Zn(II) complexes, the D_3h and C_2v transition states have fairly similar energy barriers (ΔG^‡ = 20.6 kcal mol^-1 for the D_3h Bailar TS and ΔG^‡ = 19.3 kcal mol^-1 for the C_2v Rây-Dutt transition state). Unlike the Zn(II) and Sc(III) homologues however, the energy barriers fall within a range that is both high enough to prevent immediate and complete racemization under reasonable experimental conditions, yet low enough to access without thermal degradation. In an experimental study of line broadening in the resonances of the Ga(pmhd)₃ complex measured in between 31^o and 105^oC the fluxional processes were determined to involve both isomerization and inversion of absolute configuration.⁵ Furthermore, experiments carried out with the similar Ga(triac-d₃)₃ complex measured bond rupturing linkage isomerization reactions to proceed at 1/800 of the reaction rate of the isomerization/racemization, allowing the authors to rule out a fluxional process involving bond rupture. Collectively these experimental observations led the authors to support a fluxional twist mechanism that occurred along the real C₃ (Bailar Twist) and pseudo C₃ (Rây-Dutt) axes.⁵ The barrier for the collective twist processes is reported in Table 3 for comparison along with that for Ga(tfac)₃⁶, bearing in mind that the fluorinated β-diketonates have been reported to have lower barriers for isomerization/racemization reactions than their alkyl analogs.⁵

In a recent set of experiments, Raymond and his coworkers were able to experimentally observe the racemization of Δ and Λ-trans- tris(2,3-dihyroxy-N-tert-butyl-N'-benzylterephthalamide)Ga(III) via VT ¹H NMR. The experimentally determined activation barrier for the Bailar Twist (ΔG^‡₂₉₅ = 14 kcal/mol (60 kJ/mol) in D₂O) is lower than that observed for isomerization processes that would proceed via a Rây-Dutt.¹⁰ Computational studies confirmed the Bailar to have a lower activation barrier relative to the Rây-Dutt for this GaL₃ complex and gave excellent agreement with experimentally determined results.¹¹

In another recent publication, 2D EXSY and Dynamic ¹⁹F-NMR was used to examine the fluxional processes for the meridional isomer of the Ga(III) complex of the unsymmetrical chelate fox (5-fluoro-8-hydroxyquinoline). The minor facial (cis) isomer has C₃ symmetry. Line shape analysis for the ¹⁹F signals undergoing exchange, as well as cross-peak intensities in the 2D-EXSY spectrum, were used to calculate the activation barriers for twist mechanisms. The authors suggest that two non-dissociative mechanisms (Rây-Dutt and Bailar) have identical values for ΔH^‡ (Table 3),⁷ differing only in ΔS^‡ effectively corresponding to a rate difference of 2.1. Their experiment proves conclusively that a Rây-Dutt mechanism must operate; their inference of an (equal) kinetic contribution from a Bailar mechanism is less direct.⁷

Our computational results on Ga(mda)₃ compare favorably to the experimental results discussed above. (See Enhanced Web Object 4 and Enhanced Web Object 5 for visualizations of the Bailar Twist and Rây-Dutt Mechanisms for Ga(mda)₃). A possible exception is the computed entropy of activation. Whereas the measured values are positive (+3-7 cal K^-1 mol^-1), the computed values are somewhat less (Rây-Dutt; -2.4, Bailar, 0.0 cal K^-1 mol^-1). We also note that throughout the series Sc(III)-Co(III)-Zn(II)-Ga(III), the free energy barrier for the Rây-Dutt process is uniformly less than that for the Bailar. In the specific case of Ga(III), the value of ΔG^‡(Rây-Dutt) - ΔG^‡ (Bailar) is about 1.3 kcal mol^-1, which corresponds to a rate factor of about 9 less for the Bailar and therefore suggest a possibility that there is in fact little or no contribution from the Bailar process for the Ga(III) fluxional process for this β-diketonate complex.

[Ge(IV)L₃]⁺:

The cationic Ge(IV) system completes the trend, revealing the largest barriers in the series. The imaginary modes also have the largest values in the series.

Trends and Comparison to Predicted Results

Theory predicts that as the "normalized bite" (b, See Figure 3) of a metal chelate complex decreases (either within a series of metal ligand complexes of the same metal, or within a series of metal ligand complexes of the same ligand), intramolecular mechanisms for racemization/isomerization should become more favorable.^3,11 Complexes with smaller b values for the ground state structures are distorted towards the trigonal prismatic transition state of D_3h or C_2V symmetry, therefore lowering the activation barrier for the intramolecular rearrangement. The normalized bite size has been reported to be a better predictor of the barrier to intramolecular rearrangement, because the distance between ligating atoms within a given chelate ring (d_A-A) is not invariant across a series of metal complexes of that same ligand.^3,11 In addition it has been proposed that metal ions with empty or partially empty d orbitals (eg V^V, Ti^IV, V^III, etc) are favorably distorted towards trigonal prismatic geometries to optimize ligand-to-metal σ and π bonding.¹¹ These metal complexes have lower barriers to intramolecular isomerization, which is correctly predicted by the normalized bite size (b) and incorrectly predicted by the metal to donor atom (d_M-A) bond distance alone.

Figure 3. Parameters measured to predict the relative magnitude of the barriers to intramolecular rearrangement and the relative barriers to Bailar vs Rây-Dutt Twist Mechanisms: b = the normalized bite size = the distance between the two ligating atoms within the same chelate ring (d_A-A) divided by the metal-donor atom bond distance (d_M-A). Some analyses examine the ratio of d_A-A to l_A-A (the ligand-to-ligand hard sphere distance) as a predictor of preferred intramolecular rearrangement mechanism.

Theory also predicts that the Bailar Twist intramolecular rearrangement mechanism has a lower activation barrier relative to the Rây-Dutt mechanism as b decreases across a series of metal ligand complexes. Three sets of authors give different values for b as a cut off for when the Bailar Twist becomes the predominant intramolecular rearrangement mechanism. Beguin states that "when this value is less than 1.5, the Bailar twist is energetically preferred over a Rây-Dutt twist." ⁷, Montgomery reports that "compounds with a relatively small b value (b/M-L < 2^1/2) will choose the Bailar Twist over the Rây-Dutt"¹² and Kepert's original work proposes that in complexes of "ligands with normalized bites below approximately 1.3....the twist about the C₃ axis will be favored".³

Rodger and Johnson developed a modified form of Kepert's geometric analysis to predict relative rates and preferred reaction pathways for these intramolecular processes. Like Kepert, they examined the unfavorable energy change associated with metal-ligand (d_M-A) bond stretching that must occur to pass through the transition state, offset by a smaller energy change in dispersion stabilization from the interaction of ligand nearest neighbor atoms to predict which non-dissociative mechanism is more favorable. A value is calculated for the ratio of the distance between two ligating atoms within the same chelate ring (d_A-A) to the ligand-to-ligand hard sphere distance (l_A-A where a "reasonable estimate of l can be made by measuring the shortest nearest neighbor distance of the reactant (usually between two atoms related by the 3-fold axis of the complex)"²) (Again See Figure 3). A molecule with a small value of the ratio of d_A-A/l_A-A (near 0.5) is predicted to proceed via a Bailar Twist, whereas a molecule with a large ratio of d_A-A/l_A-A (near 1.5) will proceed via a Rây-Dutt Mechanism. A molecule with an intermediate ratio of d_A-A/l_A-A (near 1.0) will proceed through either mechanism "as there will be little difference between the energies of the two structures."² Thus two schemes have been put forward to assess reaction rates and pathways in the fluxional processes of metal tris chelates; Kepert compares values of b (the normalized bite) and Roger and Johnson compare values of d_A-A/l_A-A. Since different authors reference different assessment schemes, we have included both in order to compare our computational data to experimental results and to other computational results.

A number of studies have been published on the intramolecular rearrangements of metal complexes of the β-diketonates, tropolonates, catecholates and dithiocarbamates (Scheme 1). Consistent with theory, general trends show that β-diketonates have larger normalized bite values (b near 1.4) and have slower rates of racemization/isomerization than the tropolonates (with b values near 1.3) or catecholates (with b values ranging from 1.26 to 1.34). The dithiocarbamates (with b values near 1.2) are experimentally observed to have the fastest rates of racemization/isomerization within this series chosen for comparison.

Some experimental studies have been able to distinguish between Bailar and Rây-Dutt twists and as Raymond points out, this "experimental differentiation...can be difficult".¹¹ In 1996 and 2006, the Raymond group reported experimental findings which showed preference of a Bailar twist over the Rây-Dutt in the intramolecular rearrangements of metal complexes of substituted catecholates (these complexes have b values ranging from 1.26 to 1.34)^10,11. Their results were supported by computation of the activation barriers for the different twist mechanisms.¹¹ Earlier, an experimental study of racemization/isomerization rates for metal complexes of tropolonate ligands (b near 1.3) showed a low temperature racemization process to be most consistent with a Bailar Twist and a higher temperature process correlated to isomerization via a Rây-Dutt mechanism.^8a

The normalized bite for our computed equilibrium geometry mda complexes as well as the ratios of d_A-A/l_A-A, and the difference in metal ligand bond distances between the equilibrium geometry and computed transition states (Δd_M-A) are presented in Table 4. We observe that as the normalized bite increases, the activation barriers for both the Bailar Twist and Rây-Dutt Mechanisms increase, and are larger than those observed for metal complexes of the tropolonates, catecholates, or dithiocarbamates with smaller values of b. Our computed activation barriers indicate that of our model complexes favor the Rây-Dutt Twist over the Bailar Twist, although the two mechanisms have similar energy barriers as predicted by theory (with d_A-A / l_A-A values near 1.0 and relatively large values of the normalized bite that are near or greater than 1.3)^2,3. The computed change in the metal ligand bond distance (Δd_M-A) for the molecule to move through the transition state is smaller for the Rây-Dutt Twist over the Bailar Twist also consistent with lower energy barriers for the Rây-Dutt Mechanism. We also observe that as b increases within our series from Sc(III) (b = 1.31) < Ti(IV) (b = 1.33) < < Zn(II) (b = 1.39), < Ga(III) (b = 1.43), Ge(IV) (b = .46), the relative difference in the activation barriers between the Bailar and Rây-Dutt Mechanisms increase: Sc(III) (ΔΔG^‡ = 0.4 kcal/mol) < Ti(IV) (ΔΔG^‡ = 0.8 kcal/mol) ~ Zn(II) (ΔΔG^‡ = 0.8 kcal/mol) < Ga(III) (ΔΔG^‡ = 1.3 kcal/mol) < Ge(IV) (ΔΔG^‡ = 2.5 kcal/mol), again consistent with theoretical predictions. Within our series of examined complexes of the mda ligand, comparison of b, d_A-A/l_A-A, and ΔΔG^‡ values correctly predict the general trends however our results suggest that the Zn(mda)₃^- monoanion should have a higher barrier than we have found computationally. Our computed activation barrier for the Zn(II) complex is closer to that of the Sc(III) or Ti(IV) complex although the value of b is more similar to that of our Ga(III) complex. Ligand-ligand repulsions increase as the charge on the complex increases³ and should favor distortion towards octahedral geometry which would also increase (rather than decrease) the barrier for an intramolecular rearrangement that procedes via a trigonal prismatic transition state. Futhermore, Raymond et al propose that complexes with filled or partially filled d orbitals should not favor distortion toward the trigonal prismatic transition state which would lower the activation barrier.¹¹ We do not understand at this point why the computed activation barriers for intramolecular rearrangements in Zn(mda)₃^- are so low.

^a Shannon, R. D.; Acta Crystallogr, A32, 1976 p. 751-767.
^b Distances and angles were measured in Gaussview from the M(mda)₃ Gaussian output files. (Also see Enhanced Web Object 1 for M(mda)₃ structures and Enhanced Web Object 2 for structural comparisons to the known M(acac)₃ crystal structures).
^c Each Rây-Dutt TS has two 4 short and 2 longer M-O distances. The average is taken over all six distances.

Conclusions

The original suggestions for two different dynamic processes for the non-dissociative ligand permutation in some octahedral transition metal complexes were made more than half a century ago. Arguments have been put forward which suggest that the preferred pathway can be predicted by calculating either the normalized bite or the ratio of the donor-to-donor atom distance within one chelate, to the donor-to-donor atom distance of donor atoms in adjacent chelates (d_A-A/l_A-A). Theory predicts that metal tris chelate complexes with a normalized bite above 1.3 should favor a Rây-Dutt over a Bailar Twist intramolecular rearrangement and that complexes with d_A-A/l_A-A ratios near 1 (as is the case for all of our model complexes in this study, see Table 4) should show only a small preference for racemization via one pathway over the other. Our computational study is consistent both with these theoretical predictions and within the trends of experimentally observed data for several metal ligand complexes. We find (a) That Sc(mda)₃, [Ti(mda)₃]⁺, and [Zn(mda)₃]^- should be highly fluxional molecules, with low barriers to Δ and Λ interconversion. (b) That across the series of mda complexes from Sc(III) to Ge(IV), the Rây-Dutt energy is consistently, but only slightly, lower than that of the Bailar process and (c) that the barriers for intramolecular rearrangement increase as the normalized bite increases within this same series, which is also consistent with experimental observations. We also find (d) That the dynamic process for Co(mda)₃ specifically involves dissociative exchange via a 5-coordinate Co(III) intermediate (more precisely, this is probably an intermediate on the total energy potential surface, and more speculatively with a transition state for dissociation existing only on the free energy potential surface). This is consistent with experimental observations for the tris-β-diketonates of Co(III) and consistent with our finding that the computed barriers for intramolecular rearrangement in Co(mda)₃ are significantly higher than those available through the dissociative mechanism.

Acknowledgements

MEC, the Charles "Jim" and Marjorie Kade Professor of the Sciences, would like to thank the Kades for their generous support of Carleton College. MEC and HSR thank Bob Hanson of St. Olaf College for consultation while producing interactive images.

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