Spectroscopic and DFT Study of RhIII Chloro Complex Transformation

Aug 21, 2017 - Moreover, the DFT calculated activation energies corroborated experimental data that the kinetic stereochemical sequence of [RhCl6]3–...
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Spectroscopic and DFT Study of RhIII Chloro Complex Transformation in Alkaline Solutions Danila B. Vasilchenko,*,†,‡ Semen N. Berdyugin,† Sergey V. Korenev,†,‡ Sean O’Kennedy,§ and Wilhelmus J. Gerber§ †

Nikolaev Institute of Inorganic Chemistry, Siberian Branch of the Russian Academy of Science, 630090 Novosibirsk, Russian Federation ‡ Novosibirsk State University, 630090 Novosibirsk, Russian Federation § Stellenbosch University, Department of Chemistry and Polymer Science, Stellenbosch 7602, Western Cape, South Africa S Supporting Information *

ABSTRACT: The hydrolysis of [RhCl6]3− in NaOH−water solutions was studied by spectrophotometric methods. The reaction proceeds via successive substitution of chloride with hydroxide to quantitatively form [Rh(OH)6]3−. Ligand substitution kinetics was studied in an aqueous 0.434−1.085 M NaOH matrix in the temperature range 5.5−15.3 °C. Transformation of [RhCl6]3− into [RhCl5(OH)]3− was found to be the rate-determining step with activation parameters of ΔH† = 105 ± 4 kJ mol−1 and ΔS†= 59 ± 10 J K−1 mol−1. The coordinated hydroxo ligand(s) induces rapid ligand substitution to form [Rh(OH)6]3−. By simulating ligand substitution as a dissociative mechanism, using density functional theory (DFT), we can now explain the relatively fast and slow kinetics of chloride substitution in basic and acidic matrices, respectively. Moreover, the DFT calculated activation energies corroborated experimental data that the kinetic stereochemical sequence of [RhCl6]3− hydrolysis in an acidic solution proceeds as [RhCl6]3− → [RhCl5(H2O)]2− → cis-[RhCl4(H2O)2]−. However, DFT calculations predict in a basic solution the trans route of substitution [RhCl6]3− → [RhCl5(OH)]3− → trans-[RhCl4(OH)2]3− is kinetically favored.

1. INTRODUCTION RhIII hydroxo complexes have attracted attention in recent years as promising catalysts for organic synthesis applications. These complexes are known to catalyze a number of addition reactions with higher efficiency in comparison to metallic rhodium or its chloro complexes.1,2 The hydroxo complexes Rh(OH)x supported on an oxide carrier were also shown to be efficient catalysts for the preparation of amides from various substrates under mild and environmentally friendly conditions.3−5 Surface-supported rhodium hydroxo complexes were also successfully applied to decrease the hematite overpotential for water oxidation.6 In the aforementioned studies hydroxo complexes were prepared from rhodium chloro complexes (RhCl3, Na3RhCl6· H2O) by treatment of these compounds with concentrated alkali (>0.1 M NaOH). Although [Rh(OH)6]3− was suggested to form under such conditions,1,2 how hydrolysis of rhodium(III) chloro complexes proceeds in an alkaline water solution was not studied in detail. Another case in point is the base hydrolysis of platinum -group-metal chloro complexes near the surface of oxide carrier supports during the preparation of heterogeneous catalysts. Some of the popular oxide carriers (Al2O3, ZrO2) have © XXXX American Chemical Society

isoelectric points higher than that of water and thus a layer of water solution near the surface of such a carrier will be sufficiently basic.7 Recently it has been shown that promotion of [PtCl6]2− hydrolysis takes place at oxide carrier surfaces, leading to the formation of supported Pt−(OH)x species8,9 which are known to be active sites for the low-temperature water-gas shift reaction.10,11 Hydrolysis of rhodium chloro complexes was studied thoroughly in acidic solutions due to the importance of this reaction for industrial applications of platinum-group-metal separation and purification.12,13 This process was found to proceed slowly, leading to an equilibrium mixture of chloro aqua complexes, and at room temperature the reaction mixture may take years to reach equilibrium.14−20 In contrast, alkali hydrolysis of rhodium chloro complexes has not been examined in detail. Titration of a potassium hexachlororhodate(III) solution by alkali produces a precipitate of RhIII hydroxide in the pH range of 5−10 which dissolves in more basic solutions, possibly forming [Rh(OH)6]3−.21,22 The homoleptic complex [Rh(OH)6]3− was isolated as its strontium Received: July 4, 2017

A

DOI: 10.1021/acs.inorgchem.7b01672 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

2.2. Apparatus. UV−vis and reaction kinetics were recorded on a PG Instruments T60 UV−vis single-beam spectrophotometer equipped with a thermostated (±0.1 °C) cell block. Molar coefficients of extinction for [RhCl6]3−, [RhCl5(OH)]3−, and [Rh(OH)6]3− species were determined as detailed in the Supporting Information. The chloride concentration was measured with an “Anion 4100” potentiometer and Cl-selective membrane electrode, using an Ag/ AgCl electrode as reference. X-ray diffraction analysis was performed on a DRON-RM4 diffractometer (Cu Kα radiation, graphite monochromator, d001 = 3.345 Å, room temperature, polycrystalline silica used as external standard). Elemental analysis was carried out on a Thermo Scientific iCAP-6500 ICP-AES spectrometer. Raman spectra were recorded with a Triplemate SPEX spectrometer with a CCD camera and microscope for detection of the backscattering spectra with excitation by a 488 nm laser line. 2.3. Kinetic Runs. Kinetic experiments were performed by recording the optical density of K3[RhCl6] alkali solution at 523 nm for 20−25 min with 1 s time intervals in the thermostated cell described above. The ionic strength was kept constant, I = 1.1 M, with NaNO3. A mixed water solution containing NaOH and NaNO3 with corresponding concentrations was used as reference. Temperatures (5.5, 8.5, 11.7, and 15.3 °C) and rhodium (4.2, 7.6, 12.5 mM) and alkali concentrations (0.434, 0.651, 0.868, 1.085 M) were varied to obtain the matrix of experiments. For each kinetic experiment K3RhCl6·H2O was dissolved and stored in ice water (“stock solution”). A 1.5 mL portion of this solution was poured into a cuvette and thermostated at the desired temperature for 2 min, and then 1.5 mL of the previously thermostated NaOH solution with appropriate concentration was placed in the cuvette and the kinetic curve was started to record. Three to four kinetic curves were obtained using the same “stock solution”, which was kept in ice−water during the experiment. To record the chloride substitution with hydroxide, 61 mg of K2[Rh(H2O)Cl5] was dissolved in ice water in a 10 mL flask. A 1 mL portion of this solution was mixed with 1 mL of 2.18 M NaOH in a thermostated cuvette at 10.5 ± 0.1 °C, and the kinetic run was started. 2.4. Kinetic Data Processing. The rate constants for alkali hydrolysis of [RhCl6]3− were obtained by full-profile approximation of the experimental kinetic data. This was done by means of a nonlinear least-squares minimization with respect to experimental and simulated optical density at each time point by variation of four parameters: k1, k2, and the concentrations of [RhCl6]3− and [RhCl5(OH)]3− at the beginning time point t = 0 s.60 The numerical solution of the corresponding differential equation set (eq 2; see below), obtained with Python implementation of the LSODA library (“scipy.integrate.odeint” library), was used for calculation of the simulated optical density while the Broyden−Fletcher−Goldfarb−Shanno (BFGS) algorithm (“scipy.optimize.fmin_l_bfgs_b” function)27 was used for the minimization process. The standard deviation was estimated as the square root of the corresponding diagonal element of the pair correlation matrix which was calculated during the BFGS minimization procedure. 2.5. Computational Details. DFT calculations were carried out using the ORCA 3.03 software package developed by the Department of Molecular Theory and Spectroscopy at the Max Planck Institute for Chemical Energy Conversion, D-45470 Muelheim/Ruhr, Germany. Geometries were fully optimized at the scalar relativistic zero-order regular approximation (ZORA)28 level using the generalized gradient approximation (GGA) functional PBE29 and in some cases the hybrid functional B3LYP that included the D3 level of dispersion correction with zero damping.30 We also performed unrestricted PBE-D3 and B3LYP-D3 calculations to ensure that the Rh−Cl bond-breaking process was modeled correctly: i.e. (vide infra), heterolytic cleavage. These functionals were selected for their computational efficiency, good structure predictions, and in several cases chemically accurate energies even for transition-metal systems. These calculations were done with an all-electron, TZV-ZORA basis set28 for all atoms. Optimizations were done in an implicit solvent model, namely the conductor-like screening model (COSMO),31−34 with the parameters of water and only when specified were gas-phase calculations also

and barium salts that are isostructural with the corresponding aluminates ((AE)3[Al(OH)6]2, AE = Sr, Ba) with a hydrogarnet structure.23 The completely substituted complex [Rh(OH)6]3− was shown to undergo polycondensation reactions in alkali solutions to form amorphous precipitates of polymeric hydrated RhIII oxide.24 The intermediate products of this reaction were isolated by ion exchange chromatography, and it was shown that these intermediates contain bridging μ-OH ligands coordinated to two or three rhodium atoms.25 Given that RhIII hydroxo complexes are proven catalysts, a detailed investigation of [RhCl6]3− species transformations in basic media is of great interest. The main part of this work is devoted to studying RhIII chloro complex transformations in NaOH−water solutions (0.5 M < [OH−] < 2.0 M) by spectrophotometric methods. In particular we report the kinetics of chloride ligand exchange with hydroxide−water. We then performed a mechanistic density functional theory (DFT) study in order to understand the difference in rates of chloride substitution of [RhCl6]3− in acidic and basic matrices and also to account for the stereochemical course of successive chloride substitution in these matrices.

2. EXPERIMENTAL SECTION 2.1. Reagents and Solutions. The starting rhodium-containing reagent was rhodium trichloride (Joint Stock Company “The Gulidov Krasnoyarsk Non-Ferrous Metals Plant”) with 38.67% rhodium content. Solutions of hydrochloric and perchloric acids was prepared from concentrated water solutions of these acids, which are of analytically pure grade (Alfa Aesar). Sodium hydroxide solutions were prepared by dilution of carbonate-free concentrated water solutions of solid NaOH (99.99% purity, Sigma-Aldrich). The concentrations of alkali and acid solutions were determined via acid−base titration with neutral red/methylene blue indicator using potassium hydrophthalate as a primary standard. Solutions of potassium and sodium nitrates and chlorides and sodium perchlorate were prepared by dissolving the corresponding salts (analytically pure grade, Reakhim) in water. The following methods for the preparation of K3[RhCl6]·H2O and K2[Rh(H2O)Cl5] derived from procedures reported earlier16 were used. 2.1.1. Synthesis of K3[RhCl6]·H2O. A 2.49 g portion of rhodium trichloride was dissolved in 20 mL of water, and then 20 mL of concentrated hydrochloric acid and 0.5 mL of ethanol were added to the solution. This mixture was heated to boiling for 1 h to depolymerize rhodium trichloride. The solution was evaporated to 20 mL, and 5 mL of a saturated solution of potassium chloride was added. The mixture was slowly cooled to room temperature. The precipitated red crystals were filtered, washied with small amounts of cold water, ethanol, and acetone, and dried in air. Yield: 2.97 g (71%). X-ray powder diffraction evidenced a single phase, and all reflections corresponded to the theoretical diffraction pattern (PDF N 010-70-0850).26 Anal. Calcd for K3[RhCl6]·H2O: Rh, 22.82. Found: Rh, 22.95. 2.1.2. Synthesis of K2[Rh(H2O)Cl5]. A modified procedure was used in which 1.30 g of rhodium trichloride was dissolved in 20 mL of water, and then 20 mL of concentrated hydrochloric acid and 0.5 mL of ethanol were added. This mixture was heated to boiling for 1 h to depolymerize rhodium trichloride. A 1.2 g portion of potassium chloride dissolved in 5 mL of water was added to the solution, and then the mixture was slowly evaporated under an IR lamp before red crystals started to form. The mixture was slowly cooled to room temperature. The precipitated red crystals were isolated and then recrystallized from 2 M hydrochloric acid, filtered, washed with small amounts of cold water, ethanol, and acetone, and dried in air. Yield: 0.58 g (32%). X-ray powder diffraction evidenced a single phase, and all reflections corresponded to the theoretical diffraction pattern (PDF N 010-81-1210).26 Anal. Calcd for K2[Rh(H2O)Cl5]: Rh, 27.34. Found: Rh, 27.22. B

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Inorganic Chemistry done. All of the obtained structures were characterized as potential energy surface (PES) minima by analyzing the Hessian matrix.35−39 In a similar manner transition states were identified by analyzing the Hessian matrix: i.e., one negative frequency was obtained where the ligand vibrational motion is to and from with respect to the metal center. The domain-based local pair natural orbital coupled-cluster singles doubles triples DLPNO−CCSD(T) method was implemented in ORCA 4.0.0.40 The TightPNO settings (TCutPairs = 10−5, TCutPNO = 10−7, TCutMKN = 10−3) was implemented along with ExtremeSCF convergence criteria. The basis set used for the DLPNO-CCSD(T) calculations was a def2-QZVPPD41,42 and def2-QZVPP/C43 auxiliary basis set with def2/JK44 and ECPs for rhodium45 as automatically included in the basis set. All DLPNO-CCSD(T) calculations also included the conductor-like polarizable continuum model (CPCM).

Figure 2. (a) Change in the absorption spectrum of K3RhCl6 solution in 1.0 M NaOH (C(Rh) = 10−2 mM) as a function of time during the first 20 min from the moment of preparation. (b) Rh−Cl MLCT band dynamics registered at 260 nm for the same solution (T = 20 °C).

3. RESULTS AND DISCUSSION 3.1. Substitution of Chloride Ligands in [RhCl6]3−. General Description. Addition of NaOH to a K3RhCl6 solution at approximately 30 °C leads to a relatively fast color change from red to yellow (Figure S1 in the Supporting Information). This change was monitored using UV−vis spectroscopy, and Figure 1 represents the evolution of a 3.85

Figure 3. UV−vis spectrum of (1) solution 1 (see text for details) and (2) [Rh(H2O)6]2(SO4)3 in NaOH−water solution (C(NaOH) = 1.0 M).

the spectra of this solution and solution 1 were found to be identical (Figure 3). On the basis of these results it is concluded that the [Rh(OH)6]3− anion is the sole product generated in solution 1. In an earlier study14 [Rh(OH)6]3− was reported to be isolated from a basic solution, originally containing rhodium chloro complexes, as a Sr3[Rh(OH)6]2 salt with a hydrogarnet type mineral crystal structure: e.g., (Sr or Ba)3[Al(OH)6]2. Indeed, addition of strontium nitrate to solution 1 immediately leads to precipitation of a yellow solid. From X-ray powder diffraction data, it is evident that this precipitate is amorphous and cannot be identified as Sr3[Rh(OH)6]2. However, from ICP-AES elemental analysis the following results were obtained: (i) “all” of the rhodium precipitated out of solution 1 and (ii) the Rh to Sr ratio in the yellow solid is 2:3, corresponding to the stoichiometry of the desired salt (Table S1 in the Supporting Information). Hydroflux46 recrystallization of the solid product precipitated from a concentrated KOH/NaOH solution ([KOH] = [NaOH] = 5.0 M) yields fine crystalline material with the aforementioned hydrogarnet structure (see Figure S2 in the Supporting Information). The Raman spectrum of this crystalline sample of Sr3[Rh(OH)6]2 salt exhibits two sharp bands around 500 cm−1 corresponding to Rh−O stretching vibrations (Figure S3 in the Supporting Information). The Raman spectrum obtained of the initially isolated precipitate from solution 1 contains the aforementioned bands, albeit broader, at analogous wavenumbers. Therefore, this precipitate can be characterized as a disperse sample of the Sr3[Rh(OH)6]2 salt containing small crystallites

Figure 1. Change in the absorption spectrum of K3RhCl6 solution in 1.0 M NaOH (C(Rh) = 3.85 mM) solution as a function of time during the first 30 min from the moment of preparation (T = 20 °C). Time intervals between spectra are 1 min.

mM solution of K3RhCl6 in 1.0 M NaOH during the first 30 min. One can note a rapid decrease in absorbance at 523 nm and the corresponding hypsochromic shift of RhIII d−d transition bands by approximately 110 nm with the appearance of apparent isosbestic points (vide infra) at 327, 400, 430, and 473 nm. Additionally, the Rh−Cl charge transfer band in the UV range of the spectrum disappears during this process (Figure 2). The spectral evolution can be explained by the substitution of chloride ligands present in the RhIII coordination sphere with OH− ligands, which induces a larger crystal field splitting in comparison with chloride and is the cause of the mentioned hypsochromic shift of d−d transition bands. The substitution process is complete after approximately 20 min at room temperature, as no further spectral changes were observed. In previous work it was postulated (mainly on the basis of EXAFS data)1 to be the result of complete conversion to the [Rh(OH)6]3− complex, but this was not proved. To test this hypothesis, a solution of K3[RhCl6] in 1 M NaOH was prepared and kept at room temperature for 30 min, after which the UV−vis spectrum was recorded (Figure 3; hereinafter referred to as solution 1). We then prepared a [Rh(OH)6]3− solution independently by dissolving [Rh(H2O)6]2(SO4)3 in a 1.0 M NaOH solution, and C

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Inorganic Chemistry in an amorphous environment that results in broadening of Raman bands and XRD reflexions. Treatment of solution 1 with Sr(NO3)2 results in quantitative precipitation of Rh, and this allows for the measurement of the chloride concentration in the resulting mother liquor. According to potentiometric measurements (see the Supporting Information for details) the solution contain 5.95 ± 0.06 chloride ions per rhodium center, which indicates complete substitution. On the basis of the aforementioned spectral and analytical data it can be inferred that solution 1 contains rhodium exclusively as the [Rh(OH)6]3− complex (reaction 1). [RhCl 6]3 − + 6OH− → [Rh(OH)6 ]3 − + 6Cl−

Figure 4. Time dependence of D523 for (1) K3[RhCl6] and (2) K2[Rh(H2O)Cl5] solutions in NaOH−water (T = 8.5 °C, C(NaOH) = 1.0 M, C(Rh) = 7.6 mM).

(1)

It was previously reported that in alkaline solutions the [Rh(OH)6]3− species forms polynuclear species with bridging OH groups.24,25 Due to charge transfer within Rh(μ-OH)Rh fragments these polynuclear species can be detected by an increase in absorption in the UV range as a function of time. Our preliminary experiments show that the rate of polycondensation strongly depends on temperature and below 20 °C no signs of polycondensation is observed for at least 5 h and reagent concentrations of C(Rh) = 1−20 mM,= and C(NaOH) = 0.4−2 M. It should be noted that, at a concentration of NaOH as low as 0.1 M, rhodium is partially deposited in the form of the amorphous hydroxide Rh(OH)3·xH2O (Figure S1 in the Supporting Information). To avoid this complication, further studies (section 3.2) were carried out at C(NaOH) above 0.4 M. Reaction 1 is relatively fast for a RhIII (d6) center, which is known for its kinetic inertness with respect to ligand exchange reactions. In contrast, hydrolysis of K3RhCl6 under acidic conditions is significantly slower at the same temperature (equilibration takes 1−2 years) and yields an equilibrium mixture of different chloro aqua complexes.14−20 The reactivity of [RhCl6]3− in alkaline solutions can be attributed to hydroxo ligands, which are known to cause labilization of inert transition-metal complexes toward substitution reactions.47,48 In order to obtain a better understanding of hydroxo ligand induced labilization of RhIII ligand exchange, the kinetics of reaction 1 was studied by UV−vis spectroscopy and the mechanism of ligand exchange modeled using DFT. 3.2. Ligand Substitution Kinetics for the Transformation of [RhCl6]3− into [Rh(OH)6]3−. The UV−vis spectral changes during ligand substitution (Figure 1) exhibit apparent isosbestic points at wavelengths where the molar extinction coefficients of [RhCl6]3− and [Rh(OH)6]3− are the same. Zooming in on any one of these isosbestic points reveals that initially the spectra do not cross exactly but shift each time, albeit by a very small amount for the first couple of minutes, identified as region 1 below; after this period the crossing points remain the same as the reaction progresses. This implies that for the first part of the reaction one or more of the [RhCl6−n(OH)n]3− (n = 1−5) species are also present above the detection limit of the instrument. Bearing this in mind, we assume the rate-determining step of reaction 1 to be the substitution of the first chloride ligand in [RhCl6]3− to form the [RhCl5(OH)]3− species. To confirm this assumption, base hydrolyses of K2[RhCl5(H2O)] and K3[RhCl6] under identical conditions were studied by monitoring the optical density at 523 nm (Figure 4) as a function of time. [RhCl5(H2O)]3− deprotonates under such basic conditions (>0.4 M NaOH), and thus kinetic traces for K2[RhCl5(H2O)] and K3[RhCl6] are

actually the transformations of [RhCl5(OH)]3− and [RhCl6]3− respectively. This experiment confirms that chloride ligands in [RhCl5(OH)]3− undergo substitution at least 10 times faster than in [RhCl6]3− and emphasizes again the strong labilization effect of hydroxo ligands. Formation of [RhCl5(OH)]3− from [RhCl6]3− is the rate-determining step of reaction 1, while further rapid substitution steps from [RhCl5(OH)]3− to [Rh(OH)6]3− can be effectively considered as a single step. From these observations it is clear that the [RhCl6−n(OH)n]3− (n = 2−5) species are present in negligible or undetectable amounts during the reaction. Reaction 1 can thus be described by Scheme 1 and eq 2, where all steps are considered as pseudo Scheme 1. Kinetic Model of [RhCl6]3− Base Hydrolysis (Reaction 1)

first order in an excess of hydroxide, DΣ = D([RhCl6]3−) + D([RhCl5(OH)]3−)+ D([Rh(OH)6]3−), and 1 = [RhCl6]3−, 2 = [RhCl5(OH)]3−, and 3 = [Rh(OH)6]3−. As the free chloride concentration only arises due to substitution, the contribution of anation to the reaction rates is negligible and all steps are modeled as irreversible. We also point out that curve 1 in Figure 4 cannot be fitted with a single exponential, whereas curve 2 can. The fact that curve 2 (Figure 4) can be fitted with a single exponential is further validation that substitution steps from [RhCl5(OH)]3− to [Rh(OH)6]3− can be effectively considered as a single step. dD Σ = k1[1](ε2 − ε1) + k 2[2](ε3 − ε2) dt d[1] = −k1[1] dt d[2] = k1[1] − k 2[2] dt d[3] = k 2[2] dt

(2)

In a series of kinetic measurements solutions of K3[RhCl6] and NaOH were mixed and reaction 1 was followed at 523 nm and at least 50-fold excess of [OH−] over the rhodium concentration was used in order to permit pseudo-first-order kinetics if hydroxide coordinates directly to the metal center. To prevent polycondensation, all experiments were conducted D

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Inorganic Chemistry bellow 20 °C. One “stock solution” of K3[RhCl6] was used to record three to four curves, and a typical example of kinetic traces obtained for one of the “stock solutions” is illustrated in Figure 5. The kinetic traces in Figure 5 do not overlay and

Table 1. Rate Constant Values Calculated from Experimental Data for Solutions with Varied Rhodium Concentrationa

a

C(Rh), mmol dm−3

k1, 10−4 s−1

k2, 10−3 s−1

4.0 7.6 12.5

3.2 ± 0.1 3.4 ± 0.1 3.3 ± 0.1

5.20 ± 0.07 5.21 ± 0.05 5.25 ± 0.08

Conditions: T = 11.7 °C, C(NaOH) = 0.651 M.

Table 2. Rate Constants k1 and k2a

Figure 5. Kinetic traces depicting the change in absorbance (λ 523 nm) for solutions with C(Rh) = 7.6 mM, C(NaOH) = 1.085 M, and T = 8.5 °C: (a) prepared from fresh K3RhCl6 “stock solution”; (b) “stock solution” of K3RhCl6 was kept for ∼20 min at 0 °C; (c) “stock solution” of K3RhCl6 kept for ∼40 min at 0 °C; (d) “stock solution” of K3RhCl6 kept for ∼60 min at 0 °C . Area I corresponds to a fast depletion of [RhCl5(OH)]3− (k2); area II is the rate-limiting step of interconversion of [RhCl6]3− to [RhCl5(OH)]3−. Experimental data are presented as circles, and full-profile fits are given as colored curves.

T, °C

C(NaOH), M

8.5 11.7 15.3 5.5 8.5 11.7 15.3 5.5 8.5 11.7 15.3 5.5 8.5 11.7 15.3

0.434 0.434 0.434 0.651 0.651 0.651 0.651 0.868 0.868 0.868 0.868 1.085 1.085 1.085 1.085

k1, 10−4 s−1 1.5 2.4 4.4 1.1 1.9 3.3 5.4 1.5 2.25 4.01 6.8 2.0 3.0 5.4 9.0

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.05 0.1 0.1 0.1 0.2 0.1 0.3 0.1 0.06 0.04 0.3 0.1 0.06 0.1 0.1

k2, 10−3 s−1 2.71 4.45 7.40 2.03 3.01 5.22 8.50 2.3 3.40 5.71 9.39 2.66 4.1 6.50 11.3

± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.03 0.05 0.03 0.06 0.02 0.07 0.08 0.1 0.05 0.02 0.03 0.05 0.1 0.03 0.2

a Every value is averaged over three values for solutions with C(Rh) = 4.0, 7.6, and 12.5 mM.

[RhCl5(OH)]3− (region I in Figure 5) its concentration should attain a steady-state value and the rate of reaction 1 from this point will be determined by the rate-limiting step with rate constant k1 region II in Figure 5). Indeed, the calculated distribution of species vs time (Figure 6) illustrates that after

decrease in absorbance each time the experiment is repeated. This phenomenon is caused by the generation of [RhCl5(H2O)]2− species in the “stock solution” due to aquation of initial [RhCl6]3− leading to a change in solution composition with time even when this solution is kept in ice− water. Thus, after addition of NaOH there are two RhIII species in solution, namely [RhCl5(OH)]3− and [RhCl6]3−, whose ratio changes during the experimental timeline. Generally, the curves in Figure 5 consist of two areas: area I mainly corresponds to fast depletion of [RhCl5(OH)]3− present initially in the stock solution, and area II is when [RhCl5(OH)]3− initially present is depleted and the rate-limiting step, i.e. interconversion of [RhCl6]3− to [RhCl5(OH)]3−, is the cause of slower absorbance change with time. This feature of the system allows for the calculation of both rate constants k1 and k2 at the same time. Moreover, given that all the substitution reactions are pseudo first order, initial Rh species concentrations will not influence calculated rate constants. Analysis of the data was performed using full-profile fitting of the numerical solution of the set of eq 2 to experimental curves. For the nonlinear least-squares fits the Python implementation of the BFGS method was used with the following experimentally determined extinction coefficients: 117, 96.5, and 5 L mol−1 cm−1 for [RhCl6]3−, [RhCl5(OH)]3−, and [Rh(OH)6]3−, respectively (λ 523 nm). From Figure 5 it is seen that the model fits the experimental data well. Calculated rate constants k1 and k2 do not vary as a function of rhodium concentration (see example in Table 1), and therefore the averaged constants as a function of temperature and hydroxide concentration are given in Table 2. As the k2/k1 ratio for all experimental conditions is about 15−20, it is observed that after a period of a fast consumption of

Figure 6. Evolution of concentrations of rhodium species in alkali− water media calculated from obtained k1 and k2 values. Conditions: C(Rh) = 7.6 mM, C(NaOH) = 1.085 M, T = 8.5 °C (freshly prepared solution). Legend: (1) [Rh(OH) 6 ] 3− ; (2) [RhCl 6 ] 3− ; (3) [RhCl5(OH)]3−.

about 500 s the concentration of [RhCl5(OH)]3− is negligible and proposed steady-state conditions are reached. Moreover, region I corresponds to the aforementioned isosbestic point drift and after consumption of [RhCl5(OH)]3− the isosbestic point positions are stable during the course of further reaction. From the linear Eyring plots the activation parameters for k1 and k2 were estimated and are given in Tables S4 and S5 in the Supporting Information. It is assumed that the transmission coefficient in the Eyring equation is equal to unity. As ΔH† and E

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Inorganic Chemistry ΔS† values are not sufficiently influenced by the concentration of hydroxide (Tables S4 and S5), the mean values are used for further discussion: ΔH†(k1) = 105 ± 4 kJ mol−1, ΔS†(k1) = 59 ± 10 J K−1 mol−1, ΔH†(k2) = 96 ± 4 kJ mol−1, ΔS†(k2) = 49 ± 10 J K−1 mol−1. The positive values of ΔS† for k1 and k2 suggests that ligand exchange proceeds via a dissociative (D) mechanism. In addition, in support of the dissociative pathway is the good agreement of k1 and ΔH† calculated here in a basic solution with those found in previous studies regarding [RhCl6]3− aquation in an acidic media where a limiting D mechanism has been proposed to be operative according to the volume of activation (ΔV†) measurements.18,19 Formation of [RhCl5(OH)]3− species may proceed via two different ways (Scheme 2). The first is direct interaction

different for the two systems described above or that for the same reaction mechanism the reaction Gibbs activation energy (ΔG†) is significantly lower for the latter case. Seven-coordinate RhIII species are unlikely to form; coupled with the anticipated Coulombic repulsion between [RhCl6]3− and hydroxide, associative (A) and interchange associative (IA) mechanisms are considered to be implausible. Moreover, in computational studies51−53 where A, IA, and interchange dissociation (ID) ligand exchange mechanisms are proposed the incoming ligand is either neutral or is oppositely charged with respect to the complex. In our [RhCl6]3− and hydroxide system the rate of chloride substitution also depends on the free hydroxide concentration, which implies that ID in addition to a pure dissociation (D) mechanism must also be taken into account. To ascertain how the different ligands (Cl−, OH−, and H2O) influence chloride substitution reaction energy barrier heights, we start with the D mechanism, shown in Scheme 3, using the

Scheme 2. Routes of [RhCl5(OH)]3− Formation

Scheme 3. Chloride Substitution via a Dissociative Mechanism in [RhCl5L]x−, Where L = Cl−, OH−, H2O and x = 2, 3

between [RhCl6]3− and OH−. The second is aquation of [RhCl6]3− followed by deprotonation of the [RhCl5(H2O)]2− aqua complex (pKa = 7.3).49 From Scheme 2 the rate constant (k1) can be expressed as k1 = k OH[OH−] + kH2O

complexes [RhCl6]3−, [RhCl5(OH)]3−, and [RhCl5(H2O)]2− as test cases. The rate-limiting step for the D mechanism (vide infra) is the first transition state (TS) energy barrier, and therefore only the first portion of the D mechanism will be focused on, i.e. steps 1 and 2 of Scheme 3. The DFT-calculated equilibrium geometries using the PBED3 functional of [RhCl6−n(OH)n]3− and [RhCl6−n(H2O)n]n−3 (n = 0−6) are shown in Figure 7 and Figures S7 and S8 in the Supporting Information. A comparison of calculated bond lengths with known crystal structures are given in Table 3, where it is noted that good agreement between theory and experiment is obtained. The good agreement of the computational methodology with respect to the obtained geometries offers assurance that DFT-calculated geometries of species for which there are no experimental crystal structure data with which to compare are indeed accurate. The Rh−Cl bond lengths for the series of complexes [RhCl5L]3−/2− that are trans to a L = Cl−, OH−, or H2O ligand (Figure 9) are 2.385, 2.444, and 2.325 Å, respectively. When OH− is bound to RhIII, the trans Rh−Cl bond lengthens and hence weakens in comparison to [RhCl6]3−, and vice versa when water is bound, the trans Rh−Cl bond contracts and increases in strength in comparison to [RhCl6]3−. These trends in bond length and hence bonding strength persist for the series of [RhCl6−n(OH)n]3− and [RhCl6−n(H2O)n]n−3 (n = 0−6) complexes. There are several cases in which a correlation between bond strength and reaction rate has been found: i.e., a stronger M−L bond would decrease the rate of exchange for that ligand.54,55 This would suggest that substitution of chloride is faster for the set of [RhCl6−n(OH)n]3− anionic complexes and slower for the corresponding set of [RhCl6−n(H2O)n]n−3 complexes where OH− or H2O is trans to the leaving Cl−, in agreement with experiment, and provides evidence for the D mechanism. We therefore proceeded to evaluate the influence of coordinated ligands on activation energies for the three complexes [RhCl6]3−, [RhCl5(OH)]3−, and [RhCl5(H2O)]2−,

(3) −

The dependence of k1 on [OH ] is fitted well with a straight line where the y axis interception points vary around (5−10) × 10−5 s−1 (Figure S6 and Table S6 in the Supporting Information), which are somewhat smaller than reported values for the [RhCl6]3− aquation rate constant kH2O (4 × 10−4 s−1 for 15 °C).19 However, extrapolation into regions of low [OH−] is questionable, as [RhCl5(OH)]3− and [RhCl5(H2O)]2− species are both present. In addition the system was studied here at [OH−] above 0.4 M to avoid rhodium being partially deposited as Rh(OH)3·xH2O(s). The hypothesis that introduction of hydroxide into the coordination sphere increases the rate of subsequent Cl− substitution corroborates well with the fact that the calculated k2 value is 15−20 times greater than k1. To obtain a better understanding of the aforementioned OH-induced labilization, we carried out a systematic DFT study. 3.3. Mechanistic DFT Study of [RhCl6]3− Ligand Exchange. The stepwise substitution of chloride with water into the kinetically inert [RhCl6]3− complex anion is relatively slow in an acidic solution. The half-life (t1/2) for the first chloride substitution is approximately 5 min, and each substitution thereafter takes approximately 10 times longer, such that on estimation it would take 1 year to form the [Rh(H2O)6]3+ complex in an acidic solution at 298 K and 1 bar pressure.50 In contrast, in a basic aqueous solution only the first chloride substitution with hydroxide parallels that with water in an acidic solution in terms of the reaction duration, to form the [RhCl5(OH)]3− complex, after which complete conversion to the [Rh(OH)6]3− species occurs within 30 min (Figure 1). The relatively large difference in subsequent ligand substitution rate may indicate that the ligand substitution mechanisms are F

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Figure 7. DFT (PBE-D3) optimized equilibrium structures of (a) [RhCl6]3−, (b) [RhCl5(OH)]3−, and (c) [RhCl5(H2O)]2−.

Table 3. Rh−Cl and Rh−O Distances in [RhClnL6−n] (L = H2O, OH−) Complexes Obtained from X-ray Diffraction Analysis of Monocrystals and Calculated with DFT Using the PBE-D3 Functionala Rh−Cl (Å)

Rh−O (Å) DFT

n(Cl−)

XRD aqua

6 5

2.3556 2.30 (trans) 2.34 (cis)57 2.30 (cis)58

4 3, fac 3, mer

aqua 2.39 2.32 2.38 2.36 2.30 2.35 2.30

(cis) (trans) (cis) (cis)b (trans)c

DFT hydroxo

XRD aqua

2.39 (cis) 2.44 (trans)

2.0951

2.15

2.03

2.0352

2.01 2.12 2.06 (cis) 2.13 (trans) 2.01−2.04

2.03 2.08 (cis) 2.03 (trans)

2.45 2.39 (cis) 2.44 (trans) 2.0159

0

aqua

hydroxo

The trans and cis markers point to the position of the given ligand with respect to the same type of ligand. bRefers to two Cl− ligands in the xy plane opposite to each other. cRefers to one Cl− ligand in the z plane opposite to H2O or OH−. a

[RhCl5(H2O)]2− trans analogue and for [RhCl5(OH)]3− approximately 20 kJ mol−1 higher in comparison to the [RhCl5(OH)]3− trans analogue. These results not only explain why Cl− substitution is relatively slow in an acidic solution and relatively rapid in a basic solution but also yield insight into the stereochemical route of successive Cl− substitution by either H2O or OH−. It is well-known from experimental data that when successive Cl− substitution of [RhCl6]3− takes place with H2O in an acidic solution the following sequence occurs: [RhCl 6]3− → [RhCl5(H2O)]2− → cis-[RhCl4(H2O)2]−.18,19 Consistent with bonding strength considerations and the computed ΔH† energy barriers (Figure 8), the formation of the trans-[RhCl4(H2O)2]− species is orders of magnitude slower than that for cis[RhCl4(H2O)2]− and accounts for the experimentally observed substitution sequence. In contrast, when successive Cl− substitution of [RhCl6]3− takes place with “OH−”, our computational results, from a kinetic perspective and bonding strength considerations, yields the sequence [RhCl6]3− → [RhCl5(OH)]3− → trans-[RhCl4(OH)2]3−: i.e., the trans−mer route instead of the cis−fac route. The possible five-coordinate species that can form by chloride elimination from [RhCl6]3−, [RhCl5(OH)]3− and [RhCl5(H2O)]2−, are illustrated in Figure 9. In all cases the geometries of the five-coordinate species are slightly distorted square pyramidal even when the geometry optimization starts from a trigonal-bipyramidal (tbp) configuration. Moreover, the H2O or OH− ligands can either be present in the xy plane of the square or be present in the z plane of the pyramid. For the [RhCl4(H2O)]− complex the standard reaction Gibbs (ΔG°rxn) energy is 45 kJ mol−1 higher in energy when the H2O ligand is present in the z plane of the pyramid (Figure 9b), in comparison to when it is present in the xy plane of the square

where chloride, hydroxide, or water is trans to the leaving chloride ligand in one set and for another set of calculations where hydroxide or water is cis to the leaving chloride ligand. Several relaxed and rigid linear transit DFT (PBE-D3, B3LYPD3, UPBE-D3, UB3LYP-D3) calculations (Figure 8) were performed where the Rh−Cl bond length was systematically increased in order to identify possible TS structures. After which, those identified structures, for the trans cases, were resubmitted for a TS search where the found TSs have one degree of freedom where the leaving ligand vibrates to and from the metal center shown in Figure S9 in the Supporting Information. In general the rigid linear transit scan (Figure 8) potential energy surface (PES) energies at the maxima are approximately 10−20 kJ·mol−1 higher in compared to their relaxed scan analogues. This is due to the RhCl4L moiety of the complex that does not undergo any geometric “relaxation” during the rigid linear transit calculation, resulting in higher electronic energies. When Cl−, H2O, or OH− is coordinated trans to the leaving Cl− ligand, shown in Figure 8a, the ΔH† barrier for Cl− substitution concerning the [RhCl5(OH)]3− complex is approximately 11 kJ mol−1 lower in comparison to [RhCl6]3−, which qualitatively agrees with our experimental findings that chloride substitution is much more rapid when hydroxide is present in the primary coordination sphere. Moreover, the ΔH† barrier to substitute the Cl− situated trans to H2O in the [RhCl5(H2O)]2− complex (Figure 8a), is approximately 66 and 77 kJ mol −1 larger in comparison to [RhCl6 ] 3− and [RhCl5(OH)]3−, respectively. When H2O or OH− is cis to the leaving Cl− ligand, the ΔH† energy barrier for Cl− substitution concerning [RhCl5(H2O)]2− (Figure 8b) is approximately 50 kJ mol−1 lower in comparison to the G

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(Figure 9c). In contrast, for the [RhCl4(OH)]2− complex ΔG°rxn is 5 kJ mol−1 lower in energy when the OH− ligand is present in the z plane of the square (Figure 9d), in comparison to when it is present in the xy plane of the pyramid (Figure 9e). Moreover, the two energetically favored five-coordinate complexes (Figure 9c,d) form when Cl− is removed cis with respect to H2O in the [RhCl5(H2O)]2− complex and trans with respect to OH− in [RhCl5(OH)]3−, which corresponds with the routes of lowest energy activation barriers (Figure 8). As the five-coordinate species are square-pyramidal, the incoming water ligand will enter in the same position as the Cl− leaving ligand, forming the cis-[RhCl4(H2O)2]− species in an acidic solution and the trans-[RhCl4(OH)2]3− species in a basic solution: i.e., retention of configuration. These observations combined with activation energy barriers (Figure 8) and considerations to bonding strength convincingly explain in our opinion the relative rates with respect to each other and stereochemical route of Cl− exchange in an acidic and in a basic solution proposed. For completeness we also performed a rigid linear transit scan to estimate the ΔH† barrier when water coordinates to the five-coordinate square-pyramidal [RhCl5]2− species (Figure S10 in the Supporting Information). As expected, the approximate ΔH† for this bond formation step of 6−9 kJ mol−1 is approximately 10 times smaller in comparison to Rh−Cl bond dissociation (Figure 8) and hence is not the rate-limiting step as inferred above. The computed ΔH† barrier with DFT (PBE-D3) for the first chloride substitution of [RhCl6]3− is approximately 48 kJ mol−1 less than that found experimentally (Table S7 in the Supporting Information). Moreover, essentially the same result is obtained when using a hybrid functional (B3LYP-D3) and unrestricted Kohn−Sham functionals (UPBE-D3, UB3LYP-D3; Figure S12 in the Supporting Information). From this we can at least conclude that the bond dissociation process is modeled correctly as heterolytic cleavage. All of these calculations were done using COSMO to simulate the solvent; therefore, we ran several rigid linear-transit DFT PBE-D3 calculations for Rh−Cl dissociation in the gas phase, using [RhCl 6 ] 3− and [RhCl5(OH)]3− as test cases, to ascertain how the solvent affects the computed ΔH† barrier heights (Figure 10).

Figure 8. (a) DFT (PBE-D3) relaxed scan linear transit electronic energy of [RhCl6]3−, [RhCl5(OH)]3−, and [RhCl5(H2O)]2− as a function of Rh−Cl bond length where Cl − , H 2 O, and OH − coordinated trans to the leaving Cl− ligand and (b) DFT (PBE-D3) rigid scan linear transit electronic energy where H2O and OH− coordinated cis and trans to the leaving Cl− ligand. All energies are scaled relative to the electronic energy of the respective complexes in their ground state equilibrium geometry.

Figure 9. DFT (PBE-D3) optimized equilibrium structures of the possible 5-coordinate RhIII intermediate complex species that can form. H

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Finally, given the qualitative (DFT PBE-D3) and quantitative (DLPNO-CCSD(T)) agreement between experiment and theory concerning the rates of ligand substitution for the [RhCl6−n(OH)n]3− and [RhCl6−n(H2O)n]n−3 (n = 0−2) systems and the qualitative agreement concerning the stereochemical sequence of ligand exchange are in our opinion consistent with the proposed D mechanism of ligand exchange.

4. CONCLUSIONS In summary, both experimental kinetic data and DFT calculation results confirm the labilization of the Rh III coordination sphere toward substitution reactions when a hydroxo ligand(s) is coordinated. As it evident from DFT calculations, hydroxo ligands not only affect activation energy parameters but also control the stereochemical route of ligand exchange reactions. For chemically accurate dissociation energies it was necessary to supplement the DFT calculations with DLPNO-CCSD(T) to better account for electron correlation. In this context reported catalytic properties of supported RhIII hydroxo complexes can be connected with the hydroxo ligand(s) that induce a high rate of ligand substitution, which plays a key role in catalysis mediated by transition-metal complexes. Moreover, from spectroscopic data it is clear that RhIII polynuclear species are easily formed in water-alkaline solutions subjected to heating. The influence of such polynuclear species on catalyst performance is not fully understood at this point in time, and therefore conditions must be thoroughly controlled during preparation and operation of these systems.

Figure 10. DFT (PBE-D3) rigid linear transit electronic energy of [RhCl6]3− and [RhCl5(OH)]3− as a function of Rh−Cl bond length where OH− is coordinated trans to the leaving Cl− ligand.

Comparison of Figures 8b and 10 reveals several differences: (i) the ΔH† barrier is now significantly smaller at approximately 34 and 10 kJ mol−1, respectively, and (ii) the formed fivecoordinate species plus free chloride is now energetically favored above the six-coordinate parent compound in contrast to experiment. Without the inclusion of a solvent model the PES is not even qualitatively the correct shape. Accurate hydration energy is shown here to be crucial, and hence the neglect of explicit water molecules may contribute largely to the mismatch between theory and experimental ΔH†. However, the energy difference of ΔH† between theory and experiment is also likely due to the fact that the DFT methodology, in particular the functionals chosen for their computational efficiency (PBE-D3 and B3LYP-D3), cannot account correctly for the exchange-correlation energy in this system. Rotzinger46 strongly advocates the use of higher levels of theory such as configurational interaction (CI) which uses multiple Slater-type determinants that can accurately take into account correlation energy (dynamic and static). To test this, a recently developed wave functional method was employed known as DLPNOCCSD(T), which can recover 99.9% of electron correlation (dynamic and static). We first did a geometry optimization using DLPNO-CCSD(T) of [RhCl6]3− and found almost identical bond lengths in comparison to PBE-D3: i.e., 2.386 and 3.388 Å. We did not reoptimize the TS of chloride dissociation of [RhCl6]3−, given the good agreement of ground state geometry found between DLPNO-CCSD(T) and PBE-D3 for [RhCl6]3−, as discussed above, and only a single point DLPNOCCSD(T) calculation was done using the PBE-D3 TS. Analysis of the natural orbital occupation of both ground and transition state structures of [RhCl6]3− revealed that occupation numbers were either very close to 0 or 2, from which it is concluded that static correlation is negligible in our system: i.e., only dynamic correlation is of concern here. The difference in electronic energy between the ground state and TS was found to be 97.14 kJ mol−1, which agrees well with the experimental value of 105 ± 4 kJ mol−1 and is just outside the experimental error range. This result confirms the importance of accurately taking correlation energies into account. We are currently pursuing this line of inquiry and the computation of the ID mechanism.

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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.7b01672. Text, figures, and tables as described in the text (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail for D.B.V.: [email protected]. ORCID

Danila B. Vasilchenko: 0000-0002-4233-2105 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Russian foundation for basic research grant 16-03-00549 A. D.B.V. thanks the Ministry for Education and Science of the Russian Federation for the award of a fellowship of the President of the Russian Federation for young scientists. The authors wish to acknowledge Ilya Kochetygov for help with X-ray powder diffraction, Dr. Boris Kolesov for Raman spectroscopy, and Dr. Al’fia Tsygankova for ICP-AES analysis.

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REFERENCES

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DOI: 10.1021/acs.inorgchem.7b01672 Inorg. Chem. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.inorgchem.7b01672 Inorg. Chem. XXXX, XXX, XXX−XXX