Line Shape Analysis of Dynamic NMR Spectra for Characterizing Coordination Sphere Rearrangements at a Chiral Rhenium Polyhydride Complex

Sarah M. Tadros; Marina Mansour; Datta V. Naik; Gregory A. Moehring

doi:10.3791/64160

JoVE Journal > Chemistry

Química

Line Shape Analysis of Dynamic NMR Spectra for Characterizing Coordination Sphere Rearrangements at a Chiral Rhenium Polyhydride Complex

Published: July 27, 2022

doi:

10.3791/64160

Sarah M. Tadros¹, Marina Mansour¹, Datta V. Naik¹, Gregory A. Moehring¹

¹Department of Chemistry and Physics,Monmouth University

Summary

Line shape analysis of NMR spectra collected over a range of temperatures serves as a guide for the rearrangement of inner coordination-sphere atoms at a chiral, eight-coordinate, rhenium(V) polyhydride complex, ReH₅(PPh₃)₂(sec-butyl amine). Line shape analysis is also used to determine the activation parameters ΔH^‡, ΔS^‡, and ΔG^‡ for those atom rearrangements.

Abstract

Dynamic solution nuclear magnetic resonance (NMR) spectroscopy is the typical method of characterizing the dynamic rearrangements of atoms within the coordination sphere for transition metal polyhydride complexes. Line shape fitting of the dynamic NMR spectra can lead to estimates for the activation parameters of the dynamic rearrangement processes. A combination of dynamic ³¹P-{¹H} NMR spectroscopy of metal-bound phosphorus atoms with dynamic ¹H-{³¹P} NMR spectroscopy of hydride ligands may identify hydride ligand rearrangements that occur in conjunction with a phosphorus atom rearrangement. For molecules that exhibit such a coupled pair of rearrangements, dynamic NMR spectroscopy can be used to test theoretical models for the ligand rearrangements. Dynamic ¹H-{³¹P} NMR spectroscopy and line shape fitting can also identify the presence of an exchange process that moves a specific hydride ligand beyond the metal's inner coordination sphere through a proton exchange with a solvent molecule such as adventitious water. The preparation of a new compound, ReH₅(PPh₃)₂(sec-butyl amine), that exemplifies multiple dynamic rearrangement processes is presented along with line shape fitting of dynamic NMR spectra of the complex. Line shape fitting results can be analyzed by the Eyring equation to estimate the activation parameters for the identified dynamic processes.

Introduction

NMR spectroscopy is commonly used to characterize dynamic processes that occur within or between molecules. For many simple intramolecular rearrangements, estimation of ΔG^‡ is as straight-forward as measuring the frequency difference, Δν, between two resonances at the slow exchange limit and determining the coalescence temperature for those same resonances (Figure 1)¹. The relationship,

ΔG^‡ = 4.575 x 10^-3 kcal/mol x T_c [9.972 + log (T_c/Δν)]

where T_c is the coalescence temperature for a pair of resonances that represent the slow exchange form of a dynamic sample, can be used to solve for the free energy of activation for such a dynamic rearrangement. More complex dynamic systems require line shape fitting of dynamic NMR spectra or another NMR technique such as two-dimensional exchange spectroscopy (2D-EXSY) or two-dimensional rotating-frame Overhauser effect spectroscopy (2D-ROESY) to estimate activation parameters.

Figure 1: NMR spectra for a d₈-toluene solution of ReH₅(PPh₃)₂(sec-butyl amine) at two temperatures. The frequency difference between the two slow exchange doublets (lower trace, 117.8 Hz) and a coalescence temperature of 250 K (upper trace) correspond to an energy barrier (ΔG^‡) of 11.8 kcal/mol. Please click here to view a larger version of this figure.

Line shape fitting of dynamic NMR spectra is a common technique that has long been used for the estimation of activation parameters that describe dynamic rearrangements for substances with an activation energy of approximately 5 to 25 kcal/mol²^,³^,⁴^,⁵. Determination of the energy barriers to proton exchange between water and amine molecules⁶, the energy barrier to rotation about the C-N bond in dimethylformamide⁷, or the general size of organic moieties⁸ are only a few examples of the many properties that have been assessed through line shape fitting of dynamic NMR spectra. This manuscript demonstrates the use of line shape fitting to characterize the intermolecular and intramolecular dynamic processes that occur for the complex ReH₅(PPh₃)₂(sec-butyl amine). The goals of this and similar line shape fitting NMR experiments are to: 1) characterize all NMR observable intramolecular dynamic atom exchange processes if present, 2) identify and characterize NMR observable intramolecular dynamic atom exchange processes if present, 3) identify correlated intramolecular atom exchanges that occur for, in this example, both hydrogen and phosphorus atoms, and 4) for the example presented here, compare two published models for the dynamic processes that occur in the complex ReH₅(PPh₃)₂(sec-butyl amine).

Eight-coordinate rhenium(V) polyhydride systems are complex dynamic systems in which the ligands participate in multiple dynamic processes and the phosphorus atoms can participate in a single dynamic process that is a second aspect of a hydride ligand exchange process⁹^,¹⁰^,¹¹^,¹²^,¹³^,¹⁴^,¹⁵^,¹⁶^,¹⁷^,¹⁸^,¹⁹^,²⁰^,²¹^,²²^,²³^,²⁴^,²⁵^,²⁶^,
²⁷^,²⁸^,²⁹. Eight-coordinate, pseudododecahedral, rhenium(V) polyhydride complexes adopt a molecular geometry (Figure 2), which can be described as a pair of orthogonal trapezoids of ligands¹⁷^,²⁶. The vertices on the long edges of the trapezoids are commonly labelled as B sites and, in rhenium polyhydride complexes, are usually the sites occupied by neutral two-electron donor ligands such as tertiary phosphines or amine ligands. The vertices on the short edges of the trapezoids are commonly labelled as A sites and are typically occupied by anionic, two-electron donor, hydride ligands. The room temperature NMR spectra of rhenium(V) polyhydride complexes are, typically, deceptively simple due to the several dynamic processes that occur in room temperature solutions.

Figure 2: A dodecahedral coordination set (left) and the complex ReH₅(PPh₃)₂(sec-butyl amine) from the same perspective (right). The red-colored sites represent coordination sites that form a vertical trapezoid, and the blue-colored sites represent coordination sites that form a horizontal trapezoid. Please click here to view a larger version of this figure.

Complexes of the form ReH₅(PPh₃)₂(amine) are the most thoroughly studied class of rhenium polyhydride complexes with respect to dynamic processes⁹^,¹⁰^,¹²^,¹³^,¹⁶^,³⁰^,³¹. Three dynamic processes (Figure 3) have been identified for ReH₅(PPh₃)₂(amine) complexes: 1) a proton exchange between the sole B site hydride ligand and a proton from a water molecule (adventitious or intentional)⁹^,¹³, 2) a turnstile exchange of a pair of A site hydride ligands with an adjacent B site hydride ligand⁹^,¹¹^,¹³^,³⁰^,³¹, and 3) a steric inversion (or pseudorotation) that manifests itself as a pairwise exchange of the A site hydride ligands and a pairwise movement of the B site atoms to the opposite side of the rhenium center (as depicted in Figure 4)⁴^,⁵^,⁶^,⁸^,²⁶^,²⁷. The movement of B site atoms to the opposite side of rhenium is observable by dynamic NMR spectroscopy as: 1) a process that makes the inequivalent 3 and 5 protons of N = pyridine equivalent at room temperature¹⁰^,³⁰^,³¹, 2) a process that causes the E and Z isomers of N = unsymmetrically substituted aromatic amine ligands to undergo fast exchange at room temperature⁹^,¹⁰^,¹³^,³⁰^,³¹, or 3) a process that causes a fast exchange of the steric perspectives of a diastereotopic pair of phosphorus atoms with respect to a chiral center located on the amine ligand⁹^,³⁰^,³¹. The previously unreported chiral complex ReH₅(PPh₃)₂(sec-butyl amine) provides an opportunity to generally describe the methods that can be used to identify and characterize the dynamic rearrangements of rhenium polyhydride complexes.

Figure 3: Representations of the dynamic processes that are observed by NMR spectroscopy for solutions of ReH₅(PPh₃)₂(sec-butyl amine). Representation A depicts the exchange of a single proton of adventitious water for the unique B-site hydride ligand. Representation B depicts the turnstile exchange of three adjacent hydride ligands, two of which reside in A site while the third is the unique B site hydride ligand. Representation C depicts both the pairwise exchange of A site hydride ligands as well as the steric inversion of the phosphorus atoms with respect to the chiral amine ligand (N*). It should be noted that the A site hydride ligand pairwise exchange does not require a shift of the A site hydride ligands to the opposite side of the rhenium center. Please click here to view a larger version of this figure.

For chemical systems such as rhenium polyhydride complexes, which exhibit a complex set of dynamic processes, line shape fitting of dynamic NMR spectra is the most used NMR technique to characterize the processes⁹^,¹¹^,¹³^,¹⁶^,²¹^,²⁹. Two-dimensional EXSY⁹^,³² or 2D-ROESY¹¹ are alternative dynamic NMR techniques that can also be used to quantitatively characterize the dynamic processes. Two-dimensional EXSY spectra are typically measured in the slow exchange temperature domain; two-dimensional ROESY spectra are typically measured in the fast exchange temperature domain. Both two-dimensional techniques may require considerable time in the spectrometer for data acquisition, in that each of the techniques is acquiring a much larger data set, at a given temperature, than the one-dimensional data sets needed for line shape fitting analysis. Simple dynamic processes that are well understood, such as the dynamic exchange of the two methyl groups of dimethylformamide, can be readily characterized by any of the three NMR techniques. More complex systems, such as ReH₅(PPh₃)₂(sec-butyl amine), in which individual hydride ligands participate in multiple dynamic processes, or systems that are not necessarily well understood, such as a novel transition metal polyhydride complex which may or may not exchange protons between a hydride ligand and adventitious water, are more easily quantitatively characterized by the line shape fitting NMR method than by the two-dimensional NMR methods. Unlike the two-dimensional NMR methods, the line shape fitting method provides an easily interpretable visualization of the match between a tested model and the experimental data as well as visual evidence of an exchange that moves a hydride ligand beyond the inner coordination sphere of rhenium. Based upon peak heights and peak shapes in slow exchange spectra, even a complex dynamic system such as ReH₅(PPh₃)₂(sec-butyl amine) can lead to an easily tested initial set of exchange models. Additionally, when multiple theoretical models have been reported for a molecular transformation, line shape fitting of dynamic NMR spectra can allow for a visual comparison of each model versus observed spectra.

Beyond the three NMR techniques mentioned above, isotopic substitution NMR experiments involving D₂O or HD have been used to qualitatively demonstrate intermolecular exchange of atoms for complex rhenium polyhydride systems, but have not been used for quantitative characterizations⁹^,³³^,³⁴^,³⁵. Theoretical calculations present an additional method for characterizing the dynamic processes of complex dynamic systems³⁰^,³¹^,³⁶. Theoretical calculations have the advantage over line shape fitting in that they can be used to differentiate between possibilities that cannot be distinguished by line shape fitting analysis. For example, theoretical calculations have been used to describe an exchange that involves three adjacent hydride ligands on certain rhenium(V) complexes as a turnstile exchange of all three hydride ligands, rather than an alternating pair of pairwise exchanges with each pairwise exchange including a unique hydride ligand and one of two chemically equivalent hydride ligands³⁰^,³¹. The results of theoretical calculations are typically compared to experimentally observed quantitative characterizations from one of the three NMR techniques mentioned above as a check on the validity of the calculated results.

Line shape fitting of dynamic NMR spectra takes advantage of the change in the appearance of NMR spectra that occurs when NMR-active nuclei move between different chemical environments during an NMR measurement. Slow exchange NMR spectra (spectra with independent Lorentzian resonances for each set of exchanging nuclei) occur at temperatures where the frequency difference between resonances for nuclei that exchange is large compared with the rate of exchange of the nuclei³⁷. Fast exchange NMR spectra (spectra with a single Lorentzian resonance for exchanging nuclei) occur at temperatures where the rate of exchange of the nuclei is much greater than the frequency difference between the slow exchange resonances³⁷. Intermediate exchange rates occur for temperatures between the slow exchange temperature domain and the fast exchange temperature domain³⁷. If the fundamental parameters of Larmor frequency, chemical shift of the exchanging nuclei, coupling constants (if any) for the exchanging nuclei, and relative populations of each nucleus type are known, rate constants for putative exchanges between nuclei can be determined by comparing simulated spectra to observed spectra at several intermediate temperatures. Good fits for simulations at several temperatures result in temperature and rate constant data that can be used with the Eyring equation to estimate activation parameters for the putative exchange(s). Results from the method have been found to be both accurate and reproducible.

Protocol

1. Sample preparation

Preparation of ReH₇(PPh₃)₂³⁵
1. Combine 0.15 g of sodium borohydride and 0.41 g of ReOCl₃(PPh₃)₂ in a two- or three-necked 100 mL round-bottomed flask fitted with a rubber septum and gas port, or a 100 mL Kjeldahl flask (with a side arm gas port) fitted with a rubber septum (Supplementary Figure 1).
2. Add a spin bar to the reaction vessel.
3. In a fume hood, use a piece of rubber pressure tubing to connect the gas port of the reaction vessel with one of the stopcocks of a dual glass manifold for vacuum and nitrogen gas. Connect the glass vacuum manifold to a vacuum pump with rubber pressure tubing and connect the glass nitrogen manifold to a regulated nitrogen gas cylinder.
4. Connect the exit gas from the nitrogen gas manifold to a stopcock that can be used to direct the vented gas through either a 2 cm column of mineral oil or a 2 cm column of mercury.
5. Open the tap on the nitrogen cylinder and adjust the pressure on the flowing gas to 34 pounds per square inch. Vent the nitrogen gas flow through the mercury bubbler.
6. Evacuate the gas inside the reaction vessel by adjusting the stopcock on the glass manifold to connect the vessel to the vacuum manifold. Fill the reaction vessel with nitrogen gas by changing the glass manifold stopcock so that it connects the gas manifold with the reaction vessel.
7. Repeat steps 1.1.5 and 1.1.6 two more times to completely replace the air in the reaction vessel with nitrogen gas. Chill the flask and its contents in an ice bath.
8. Add 8 mL of deoxygenated water and 8 mL of deoxygenated tetrahydrofuran to the solids in the reaction vessel via a syringe. Switch the gas-venting stopcock so that the gas vents through the mineral oil bubbler. Stir the suspension mildly in the ice bath for 15 min. Remove the reaction vessel from the ice bath after the initial 15 min of stirring.
9. Allow the mixture to continue stirring for another 45 min. Note the color of the reaction mixture as an indicator of when the reaction has completed. A tan to orange reaction mixture color (Supplementary Figure 1) indicates that the reaction has reached its end point.
10. Upon achieving an orange to tan color for the reaction mixture, filter the mixture through a 30 mL medium sintered glass funnel. Wash the recovered solid three times each with 15 mL portions of water, methanol, and ethyl ether. Dry the solid under vacuum to remove any adsorbed solvent.
  NOTE: The reaction generally produces between 0.20 g and 0.25 g of product.
Preparation of ReH₅(PPh₃)₂(sec-butyl amine)
1. Weigh 0.070 g of ReH₇(PPh₃)₂ and transfer it into a 50 mL single-necked round-bottomed flask that contains a spin bar. Fit the flask to a condenser equipped with a gas port. Deoxygenate the reaction vessel using the pump and fill method from steps 1.1.3-1.1.7.
2. Add a volume of 8 mL of deoxygenated tetrahydrofuran to the reaction vessel via a syringe by cracking the joint between the round-bottomed flask and the condenser. Add a volume of 0.2 mL of sec-butyl amine in a similar fashion. Switch the gas-venting stopcock so that the gas vents to the mineral oil bubbler.
3. Heat the reaction mixture to reflux at 65 °C with a heating mantle connected to a variable AC transformer set to 40 on a scale of 0 to 140 for 40 min. Cool the reaction mixture to a temperature that allows for convenient handling of the flask.
4. Pour the reaction mixture into 25 mL of methanol in a 125 mL Erlenmeyer flask. Stir the mixture vigorously for 5 min. Add 5 mL of water to induce the formation of a flocculent yellow precipitate.
5. Collect the yellow precipitate by vacuum filtration in a sintered glass funnel. Wash the solid with 15 mL of methanol. Dry the solid under vacuum. Following this process, typical product yield is 0.035 g.

2. Acquisition and analysis of NMR spectra

Measurement of dynamic NMR spectra
1. Prepare an NMR sample with approximately 8 mg of the complexReH₅(PPh₃)₂(sec-butyl amine) in about 0.8 mL of d₈-toluene. Insert the sample into the instrument.
2. Click on the File tab and select novo from the choices that appear to open a dialog box that is used to build an NMR experiment.
3. Build a ¹H experiment by completing the following steps.
  1. Assign a folder name for the new experiment by completing the Name input box with a unique file name. Assign an experiment number such as 1 for the ¹H experiment in the EXPNO box.
  2. Assign a process number of 1 for the experiment in the PROCNO box. Assign the folder into a directory using the dropdown list for DIR. Identify the solvent that the instrument will lock on from the dropdown Solvent choices.
  3. Choose the directory that contains the parameters for the ¹H experiment from the dropdown list of directories in Experiment Dirs. Select the Proton experiment from the choices in the dropdown Experiment list, and (optional) add a title for the data in the Título fill in box.
  4. Enter an Eda command in the command line and adjust the parameters as needed to meet the descriptions of the experiment provided in the second paragraph of the Discussion section below.
4. Click on the Window tab, select New Window from the list, and repeat Steps 2.1.3.1-2.1.3.8 to prepare a ¹H-{³¹P} experiment using an EXPNO value of 2 to differentiate the experiment from the ¹H experiment built previously.
5. Click on the Window tab, select New Window from the list, and repeat Steps 2.1.3.1-2.1.3.8 to prepare a ³¹P-{¹H} experiment using an EXPNO value of 3 to differentiate the experiment from the ¹H and ¹H-{³¹P} experiments built previously (see Supplementary Table 1 for detailed parameter information).
6. Enter a Lock command in the command line and select the d₈-toluene choice from the list. Click OK to accept the solvent choice. Enter an Atma command in the command line, if necessary, because of a variable nucleus X-band probe, to minimize reflected energy at the Larmor frequencies for ¹H and ³¹P on the instrument.
7. Enter a Ro command on the command line, type a value of 20 into the box, and click on the Start rotation button. Enter a Shim command on the command line. Choose an appropriate autoshim routine such as Topshim from the list of shim routines and click the Start button.
8. Enter an Rga command on the command line. Choose the Automatic Receiver Adjust selection and click OK. In turn, measure the three spectra of the sample at room temperature using 64 scans for each spectrum with a Go command on the command line.
9. Transform the data from an experiment into a spectrum with an Efp command entered in the command line.
10. Adjust the phasing of the spectrum using the following commands.
  1. Click on the Phase tab followed by a click on the Adjust Phase tab. Hover the cursor over the 0 button on the phasing toolbar and hold the left mouse button down so that the 0 button turns to green.
  2. With the left mouse button held down, roll the mouse forward or backward until the baseline is flat over the entire spectrum and all of the resonances are displayed as absorbances (peaks rise above the baseline).
  3. If the baseline cannot be made flat with only the 0 button, adjust the 1 button as described in steps 2.1.10.1 and 2.1.10.2 as well as the 0 button, until the baseline is flat for the entire spectral window.
  4. Save the phase adjustment with the data by clicking on the Save and Return button on the phasing toolbar.
11. Adjust the number of scans for each measurement, as needed, based upon the signal-to-noise ratio in the spectrum, keeping in mind that signal-to-noise typically decreases at lower temperatures due to de-coalescence of the signals into individual resonances (Figure 4).
12. Prepare the spectrometer for temperature control as per instructions from the vendor. Enter a flow rate of 200 L/h for the cooling gas and a target temperature of 290 K for the probe. Allow the spectrometer to stabilize at the target temperature for 2 min. Increase the cooling gas flow rate, if needed, to 210 or 220 L/h to stabilize the temperature.
13. Shim the sample at 290 K as in Step 2.1.7. Change the file name for each of the previously measured spectra by adding the temperature to the end of the file name (Steps 2.1.2 and 2.1.3.1) and acquire a set of three spectra at 290 K.
14. Increase the cooling gas flow rate by ≥ 30 L/h, as needed to stabilize at the next temperature, and decrease the target temperature by 10 K. Allow the spectrometer to stabilize at the next temperature for 2 min and then shim the sample as in Step 2.1.7. Measure the set of three spectra.
15. Repeat Steps 2.1.13 and 2.1.14 as needed to acquire spectra down to the lowest temperature desired.
  NOTE: A temperature of 200 K is usually sufficient for a complete set of data that is suitable for determining the activation parameters for the dynamic processes of the sample.
16. Warm the sample back to room temperature in increments of 10 K. Stabilize the temperature for 2 min at each temperature before warming the sample again to prevent damage to the glass liner of the probe.
Line shape analysis of the measured spectra
1. Within the NMR program click on the command bar at the top left of thewindow and select Open from the dropdown menu. Select Open NMR data stored in standard format. Click OK to open the file explorer window for the program.
2. Navigate to the folder for the data to be analyzed by line shape fitting. Select the file number that corresponds to the spectrum to be analyzed and click the Display button. The spectrum (if previously processed) or the free induction decay (FID) curve is displayed in the NMR software.
3. Process the FID if necessary, by entering an Efp command (exponential multiplication, Fourier transformation, and phase correction) in the command line. Adjust the phase of the spectrum (Step 2.1.10).
4. Adjust the baseline of the spectrum; if it is not flat across the entire spectrum then level with the 0-intensity line, as follows.
  1. Click the Process tab and then click the Baseline tab. Hover the cursor over the A button. Depress the left mouse button and roll the mouse forward or backward to level the red adjustment line with the left (downfield) end of the spectrum.
  2. If the baseline is still not level with the red adjustment line, repeat the process with the remaining letter buttons until the red adjustment line fits the baseline of the spectrum. Use the save and return button to save the adjustment when the red adjusted baseline matches the actual baseline.
5. Select the Analyze tab within the NMR software. Within the analyze options, select the Line Shapes choice followed by the Fit Dynamic NMR Models choice.
6. The spectrum is now displayed in the line shape fitting module window. Use the toolbars above the spectrum to adjust how the spectrum is displayed. The window to the left of the spectrum handles the line shape fitting of the spectrum.
7. Adjust the spectrum display with the Smooth Zoom Tool so that the portion of the spectrum to be fitted is displayed in the spectrum window. Use the Shift Spectrum Left and Right toolbar button to center a portion of the spectrum in the display window.
8. Access the chemical shift window for line shape fitting by selecting the Spectrum tab in the line shape fitting window.
9. Click on the Edit Range button. Enter the upper and lower chemical shifts for line shape fitting and click the OK button to accept those limits.
10. Start a model for line shape fitting by clicking on the Spin System tab in the line shape fitting window. Click on the Add button to allow for the building of a model spin system.
11. Unselect LB (for line broadening) and enter the value for line broadening manually with the mouse and the LB button on the line shape fitting toolbar.
12. Add the first nucleus into the model by clicking on the Nucleus tab followed by clicking on the Add button. A set of default values will appear for Nucleus 1. Adjust the chemical shift for Nucleus 1 by entering a value for chemical shift in the Nu(iso) box or with the chemical shift tool on the line shape fitting toolbar.
  NOTE: If the selection box is left in the checked form, the chemical shift of this nucleus will be varied to achieve the best fit. Unchecked variables will not be varied in the line fitting process.
13. Use the Pseudospin box for Nucleus 1 to input the number of equivalent nuclei for Nucleus 1 with each spin 1/2 nucleus equivalent to 0.5 in counting. Enter the sum of the spins into the Pseudospin box in order to account for all equivalent nuclei.
14. Use the In Molecule box to accommodate models that require more than a single molecule to participate in a dynamic process. Assign resonances that arise from different molecules to separate molecules using designations such as 1, 2, etc. for different molecules. For resonances that arise from a single molecule, assign 1 for all In Molecule values.
15. Add the second and all subsequent nuclei to the model by clicking on the Nucleus tab followed by clicking on the Add button. Include spin-spin coupling between nuclei by either entering the coupling in the appropriate JN box (where N is the nucleus with which the nucleus that is added is coupled, N = 1, 2, …) or by adjusting the Scalar coupling button on the line shape fitting toolbar.
16. Begin the process of describing the atom exchanges by clicking on the Reaction tab. Click on the check box if the rate constant for the exchange is to be varied in line shape fitting. Enter the number of nuclei to be exchanged (number with respect to their identifying tabs such as Nucleus 1 and Nucleus 2) into the Exchanges box for the first exchange in the model.
17. Describe the exchanges to be tested in the boxes below the Exchanges box. Define the exchanges between Nucleus tabs in the boxes below. A two Nucleus exchange would be entered as Nucleus 1 to Nucleus 2 and Nucleus 2 to Nucleus 1. Ensure that exchanges are cyclic in that if a nucleus is moved from Nucleus 1, another nucleus has to be moved into Nucleus 1.
18. Use the Exchange speed button on the line shape fitting toolbar to change the initial value of k in order to iteratively adjust the value of k, even if the check box is selected for the rate constant.
19. Add more exchanges to the model by clicking on the Reaction tab followed by clicking on the Add button. Add exchanges to the model as needed. Use the tools on the line shape fitting toolbar to adjust the starting variables, including spectrum intensity to a good match for the spectrum to be fit.
20. Begin iterative line shape fitting by clicking on the Start the Spectrum Fit button on the line shape fitting toolbar. Continue iterative fitting until no change is found in the best overlap between spectrum and model or until 1000 iterations are reached. If fitting stops at 1000 iterations, continue further iterations with the Start the Spectrum Fit button. The model spectrum is displayed with the actual spectrum for comparison.
21. Record the best fit values from the appropriate tabs. Save the best fit spectrum by clicking on the Spectrum tab in the line shape fitting window followed by clicking on the Save button.
  NOTE: The best fit spectrum will be saved in the same folder as was used to collect the data. The best fit spectrum will be distinguished from the original data by being saved with a different processing number that is input when the save occurs.
22. Save the model used for the line shape fitting by clicking on the Main tab followed by clicking on the Save button. Enter a name for the model.

Figure 4: A comparison of ³¹P-{¹H} signal intensities for a single sample of ReH₅(PPh₃)₂(sec-butyl amine) in d₈-toluene. A representative demonstration of the difference in signal intensities between a fast exchange single phosphorus resonance and a pair of phosphorus resonances near the coalescence temperature for those resonances. Please click here to view a larger version of this figure.

3. Determination of activation parameters from an Eyring plot ¹

Enter data from line shape fitting for one modelled dynamic process into a spreadsheet with the independent variable entered as 1/T and the dependent variable entered as ln(k/T).
Insert a scatter plot of the data into the spreadsheet. Add a trend line through the data. Use the slope and intercept of the trend line to solve for ΔH^‡ and ΔS^‡. The slope of the trend line is -ΔH^‡/R while the intercept of the trend line is ΔS^‡/R + 23.76.
Solve for ΔG^‡ at a given temperature using the relationship
ΔG^‡_(T) = ΔH^‡ – TΔS^‡.
NOTE: For a simple exchange of two nuclei with resonances that coalesce, a check of the values of ΔH^‡ and ΔS^‡ can be performed by comparing ΔG^‡ calculated at the coalescence temperature with the value of ΔG^‡ that arises from the slow exchange frequency difference between resonances and the coalescence temperature.

Representative Results

The characterizations of both rhenium polyhydride products described in this manuscript are best accomplished by ¹H-{³¹P} and ³¹P-{¹H} NMR spectroscopy. In a room temperature d₆-benzene solution, the hydride ligand resonance of ReH₇(PPh₃)₂ appears as a binomial triplet at δ = -4.2 ppm with ²J_PH = 18 Hz by ¹H NMR spectroscopy (Supplementary Figure 2). The same d₆-benzene solution will exhibit a singlet resonance at δ = 31.4 ppm by ³¹P-{¹H} NMR (Supplementary Figure 3). In a d₈-toluene solution, the hydride ligand ¹H-{³¹P} NMR resonance of ReH₅(PPh₃)₂(sec-butyl amine) appears as a broad singlet at δ = -4.83 ppm (Supplementary Figure 4). The same d₈-toluene solution will exhibit a singlet resonance at δ = 47.3 by ³¹P-{¹H} NMR spectroscopy (Supplementary Figure 5). Common impurities that can occur for either sample are ReH₅(PPh₃)₃ (δ_hydride = -4.73; ²J_PH = 18.8 Hz, quartet; δ_phosphorus= 34.16 measured in d₈-toluene) and Re₂H₈(PPh3)₄ (δ_hydride = -4.93; ²J_PH = 9.3 Hz, pentet; δ_phosphorus= 42.79 measured in d₆-benzene).

Line shape fitting is generally straight-forward for dynamic ³¹P-{¹H} NMR spectra of rhenium polyhydride complexes that do not exhibit E and Z isomers¹⁰. The best fit simulations and ³¹P-{¹H} NMR spectra for the complex ReH₅(PPh₃)₂(sec-butyl amine) for several temperatures are shown in Figure 5. Only one model is needed to exchange phosphorus atoms on such complexes. When the phosphorus nuclei exhibit spin-spin coupling, as is the case with the complex ReH₅(PPh₃)₂(sec-butyl amine), that coupling must be included in the model for good results. To simulate ³¹P-{¹H} NMR spectra measured at the coalescence temperature and above, the temperature dependence of the chemical shift difference between the two resonances must be tracked and used to estimate the chemical shifts of the nuclei at the coalescence temperature and above (Figure 6). Additionally, NMR spectra measured at temperatures near the freezing point of the solvent may exhibit broadening of resonances due to increased solvent viscosity and precipitation of the analyte. Spectra that exhibit such resonance broadening should not be included in determination of the rate constants that are subsequently used in Eyring plot determinations.

Figure 5. The ³¹P-{¹H} NMR spectra (black traces) and best fit simulations (red traces) for a d₈-toluene solution of ReH₅(PPh₃)₂(sec-butyl amine). The black traces show the coalescence of the two resonances that arise from the diastereotopic phosphorus atoms into a single resonance at higher temperatures. The red traces show a good match of the simulated spectra that arise from line shape fitting and the observed data. Please click here to view a larger version of this figure.

Figure 6. A plot of the temperature dependence of the difference in chemical shifts between the two ³¹P-{¹H} resonances. An extrapolation of this line allows for estimation of the chemical shifts of the individual resonances at higher temperatures. Please click here to view a larger version of this figure.

Line shape fitting of the hydride region of dynamic ¹H-{³¹P} NMR spectra is more challenging than line shape fitting for phosphorus resonances. Line shape fitting of hydride resonances requires more nuclei and more exchange models. Common hydride ligand exchange models that have been used for rhenium(V) polyhydride complexes include: 1) exchange between a pair of adjacent hydride ligands¹⁶, 2) a turnstile exchange of three adjacent hydride ligands⁹^,¹¹^,¹³^,³⁰^,³¹, 3) exchange between a specific hydride ligand and a proton from water⁹^,¹³, and 4) pairwise exchange of the A site hydride ligands on one side of rhenium with the A site hydride ligands on the other side of rhenium⁹^,¹³^,³¹. The latter exchange has been reported as a second aspect of the associated interconversion of E and Z phosphorus resonances or with the steric inversion of diastereotopic phosphorus resonances¹³. As such, the activation parameters and the rate constants for the latter hydride ligand exchange (if it occurs) should reflect the same values for the associated dynamic phosphorus process.

Line shape fitting can be used to test theoretical models of hydride ligand exchanges¹³. As with the phosphorus resonances mentioned above, the temperature dependence of the hydride resonances that will be modelled has to be determined so that chemical shifts can be adjusted for temperature drift. Figure 7 shows the temperature dependence that was observed for the hydride resonances of an ReH₅(PPh₃)₂(sec-butyl amine) sample in d₈-toluene as well as the best linear fit equations for that drift. The models for line shape fitting of ¹H-{³¹P} NMR spectra used chemical shifts that were calculated for each resonance even when the resonance frequency could be determined directly from the spectrum. Chemical shifts of the hydride resonances were not treated as variable when line shape fitting the hydride region of dynamic ¹H-{³¹P} NMR spectra. Figure 8 compares the results of line shape fitting, based on a pairwise exchange of A site hydride ligands, a turnstile exchange of three adjacent hydride ligands, and a proton exchange between one proton of water and hydride ligand H4, with the observed hydride region of a series of ¹H-{³¹P} NMR spectra collected from 225 K to 240 K.

Figure 7. Best fit lines for the temperature dependence of each ¹H-{³¹P} NMR hydride resonance. The chemical shifts calculated from the best linear fits were used in the models for line shape fitting of the observed spectra. Please click here to view a larger version of this figure.

Figure 8. The hydride region of ¹H-{³¹P} NMR spectra (black traces) and best fit simulations (red traces) for a solution of ReH₅(PPh₃)₂(sec-butyl amine). The spectra were measured on a d₈-toluene solution. Please click here to view a larger version of this figure.

Figure 9 displays best fits for two models of hydride ligand exchange for ReH₅(PPh₃)₂(amine) complexes in the hydride region of the 225 K ¹H-{³¹P} NMR spectrum for a sample of ReH₅(PPh₃)₂(sec-butyl amine) in d₈-toluene. The line shape fits are based upon theoretical models of hydride ligand exchange for the compound ReH₅(PPh₃)₂(pyridine)³⁰^,³¹. Two aspects of the best fit spectra are important. First, the blue traces represent the best fits of the spectrum line shape based entirely on the reported exchange models. The blue traces indicate that a proton exchange between a specific hydride ligand and a proton from beyond the inner coordination sphere is missing. For this example, ReH₅(PPh₃)₂(sec-butyl amine) complex, the missing exchange includes a proton from adventitious water along with the unique B site hydride ligand. Second, the red traces indicate that when a proton exchange with water is included with either theoretical model, a good line shape may or may not be obtained. For the complex ReH₅(PPh₃)₂(sec-butyl amine), Model A generates the better fit for the observed spectrum. A comparison of rate constants for the steric inversion of diastereotopic phosphorus atoms with the rate constants for an associated hydride ligand rearrangement in each model also favors Model A over Model B (Table 1).

Figure 9. A comparison of two models for the rearrangement of hydride ligands at ReH₅(PPh₃)₂(amine) complexes without proton exchange. Both models were tested with the inclusion of an exchange of a specific hydride ligand with a proton from water (red traces) and without such a proton exchange (blue traces). The black traces are the measured ¹H-{³¹P} NMR spectrum of ReH₅(PPh₃)₂(sec-butyl amine) at 225 K. The model used to produce the A traces includes a pairwise exchange of A site hydride ligands. The model used to produce the pair of B traces includes a basal turnstile exchange of hydride ligands. Please click here to view a larger version of this figure.

Temperature (K)	k Steric inv. (Hz)	k Pairwise (Hz)	k Basal (Hz)
225	94.5	88.2	6.6
230	131.3	151.3	28.4
235	236	219.3	46.1
240	376.4	324.2	66.4

Table 1. A comparison of rate constants for phosphorus atom steric inversion with pairwise exchange of the A site hydride ligands and with the basal turnstile exchange of hydride ligands. All simulations of hydride resonances included an exchange of protons between adventitious water and the unique B site hydride ligand.

Activation parameters for each modelled dynamic process of Model A can be estimated from Eyring plots (Figure 10 and Figure 11, Supplementary Figure 6, and Supplementary Figure 7). Eyring plots of dynamic ³¹P-{¹H} rate constants have the advantage over Eyring plots of dynamic ¹H-{³¹P} rate constants in that only one model is needed to describe phosphorus atom exchanges. Having a single model for phosphorus atom exchange means that there is no confounding of the phosphorus atom exchange results, unlike hydride ligand exchanges which have multiple exchange models that involve the same atoms. Dynamic ³¹P-{¹H} NMR data is also generally available for a larger range of temperatures than for dynamic ¹H-{³¹P} NMR data which means more data points for the Eyring plot.

Figure 10. Eyring plot from the line shape fitting of ³¹P-{¹H} NMR spectra for a d₈-toluene solution of ReH₅(PPh₃)₂(sec-butyl amine). The trend line shows that the rate constants that arise from line shape fitting of the ³¹P-{¹H} NMR spectra at several temperatures fit the Eyring equation well. Please click here to view a larger version of this figure.

Figure 11. Eyring plot from the pairwise exchange of A site hydride ligands. The data arises from line shape fitting of ¹H-{³¹P} NMR spectra measured on a d₈-toluene solution of ReH₅(PPh₃)₂(sec-butyl amine). Please click here to view a larger version of this figure.

Supplementary Figure 1: An example of the end point color for the reaction of ReOCl₃(PPh₃)₂ with sodium borohydride to form ReH₇(PPh₃)₂. The color of the reaction, as shown in the Figure, is the best indication that the reaction between ReOCl₃(PPh₃)₂ and sodium borohydride, in tetrahydrofuran and water, has gone to completion. Please click here to download this File.

Supplementary Figure 2. The ¹H NMR hydride resonance for a sample of ReH₇(PPh₃)₂ dissolved in d₆-benzene. The ¹H NMR spectrum of a sample can be used to readily identify the product of a reaction as a genuine sample of ReH₇(PPh₃)₂. Please click here to download this File.

Supplementary Figure 3. The ³¹P-{¹H} NMR spectrum of a sample of ReH₇(PPh₃)₂ dissolved in d₆-benzene. The ³¹P-{¹H} NMR spectrum can be used to qualitatively characterize a sample of ReH₇(PPh₃)₂, and such a spectrum provides a convenient check for impurities in the sample. Please click here to download this File.

Supplementary Figure 4. The room temperature ¹H NMR hydride resonance for a sample of ReH₅(PPh₃)₂(sec-butyl amine) dissolved in d₈-toluene. The small spike on the upfield shoulder of the peak is due to an impurity of Re₂H₈(PPh₃)₄. Please click here to download this File.

Supplementary Figure 5. The ³¹P-{¹H} NMR spectrum of a sample of ReH₅(PPh₃)₂(sec-butyl amine) dissolved in d₈-toluene. The ³¹P-{¹H} NMR spectrum of a sample can be used to qualitatively identify a sample of ReH₅(PPh₃)₂(sec-butyl amine) and to check for impurities. Please click here to download this File.

Supplementary Figure 6. Eyring plot from the turnstile exchange of two A site hydride ligands with an adjacent B site hydride ligand. The data arises from line shape fitting of ¹H-{³¹P} NMR spectra measured on a d₈-toluene solution of ReH₅(PPh₃)₂(sec-butyl amine). Please click here to download this File.

Supplementary Figure 7. Eyring plot from the exchange of protons between adventitious water and the unique B site hydride ligand. The data arises from line shape fitting of ¹H-{³¹P} NMR spectra measured on a d₈-toluene solution of ReH₅(PPh₃)₂(sec-butyl amine). Please click here to download this File.

Supplementary Table 1. NMR experiment parameters. Please click here to download this Table.

Discussion

There are four items in the preparation of ReH₇(PPh₃)₂ that can impact the quantity and purity of the material that is produced. First, the use of an ice bath during the first 15 min of the reaction is important to remove heat from the reaction that occurs between sodium borohydride and water. Higher initial temperatures lead to a decreased yield of the ReH₇(PPh₃)₂ product due to formation of the thermal decomposition product Re₂H₈(PPh₃)₄. Second, the color of the reaction mixture is more important than the amount of time for the reaction. When the reaction mixture has gone to completion, the mixture will have a tan to orange color. Any shade of green in the reaction mixture indicates that the reaction must proceed further. If necessary, additional sodium borohydride can be added to the reaction mixture after 1.5 h in case the mixture still has a green color. Third, the washing step is crucial for ensuring a high purity product from the reaction. A thorough water wash ensures that inorganic products such as sodium chloride and sodium borate are washed away from the product. The ethyl ether washes are crucial for removing colored rhenium polyhydride impurities that are always produced in the reaction such as ReH₅(PPh₃)₃ and Re₂H₈(PPh₃)₄. Finally, the tetrahydrofuran solvent must be peroxide free, which can be accomplished either by using freshly distilled solvent or by storing the solvent under an atmosphere of nitrogen.

For a complex of interest such as ReH₅(PPh₃)₂(sec-butyl amine), which contains organic-type protons, hydride ligands, and diastereotopic phosphorus atoms, three different variable temperature series of experiments are informative: 1) a series of ¹H NMR spectra, 2) a series of ¹H-{³¹P} NMR spectra, and 3) a series of ³¹P-{¹H} NMR spectra. Each of the three different spectra can be acquired sequentially at each temperature of interest. All the dynamic NMR spectra of interest for a complex can be collected on a single NMR sample. The two proton spectra can be measured with 32 K data points for a window of 24 ppm, at 400 MHz, centered at 0 ppm. The phosphorus spectrum can be measured with 32 K data points with a window of 100 ppm, at 162 MHz, centered at 20 ppm. Measuring spectra at temperatures separated by 10 K is usually sufficient for most applications, but increments of 5 K temperature differences obviously produce more data, which can be useful in providing data for an Eyring equation determination of activation parameters. A typical temperature series from room temperature down to 200 K, in increments of 10 K, requires at least consecutive 4 h on the spectrometer. The 4 h include: the time to set up the heat exchanger and bottled nitrogen for the temperature controller, time for setting up the three experiments that will be measured at each temperature, time to measure room temperature spectra and examine the quality of the sample, time to decrease the temperature in increments of 10 K and stabilize at each temperature, time to shim the sample at each temperature and measure the spectra of interest, and time to warm the sample and spectrometer back to room temperature in increments of 10 K with at least 2 min intervals to stabilize the instrument before again increasing the temperature. Obviously going to lower temperatures or decreasing the temperature increments to 5 K will increase the time required on the spectrometer.

The parameters used for each of the three NMR series in this investigation can be found in the supporting materials. While NMR parameters can be changed during a temperature series, it makes for better comparisons of spectra measured at different temperatures if the spectra are all measured with the same parameters. For ReH₅(PPh₃)₂(sec-butyl amine) and similar complexes, the temperature series begins in the fast exchange domain. Resonances arising from exchanging nuclei appear as coalesced resonances. Typically, signal-to-noise ratio for the exchanging nuclei will be larger at room temperature and will reach a minimum at a temperature near the coalescence temperature. Due to the changing nature of signal-to-noise, it is best if the signal-to-noise ratio is much better than marginal for the room temperature spectra. Additionally, the acquisition window must be set large enough to include all the resonances that will occur in the slow exchange spectrum.

Complexes of the form ReH₅(PPh₃)₂(amine) which include an unsymmetrically substituted aromatic amine such as 3-picoline exhibit E and Z isomers⁹^,¹⁰. At lower temperatures where dynamic rearrangements are slowed, phosphorus resonances from both isomers can be observed. Coalescence of these resonances corresponds to observing an average signal from the two interconverting isomers. Since the free energy of the two isomers are not necessarily the same, the phosphorus resonances that arise from these isomers will not necessarily have the same intensities. The line shape fitting software allows for each phosphorus atom in the model to occur in different molecules with different populations. This feature of the line shape fitting software allows for the line shape fitting of ³¹P-{¹H} NMR spectra that arise from samples that include E and Z isomers.

Line shape fitting of the hydride region of the ¹H-{³¹P} NMR spectra can be challenging because the individual hydride ligands may participate in multiple dynamic processes. It can be helpful when a chiral center is present, such as occurs with ReH₅(PPh₃)₂(sec-butyl amine), to compare rate constants for phosphorus atom rearrangement with rate constants for the hydride ligand rearrangements, in order to test whether a hydride ligand rearrangement and a phosphorus atom rearrangement are different manifestations of a single molecular rearrangement. Furthermore, proton exchanges, such as between a hydride ligand and an adventitious water proton (a common occurrence for rhenium polyhydride complexes)⁹^,¹³^,³⁴ which move a hydride ligand beyond the inner coordination sphere of the metal center, should be readily apparent in line shape fitting as an inability to produce a good fit using models that include only intramolecular hydride ligand exchanges (Figure 9)¹³.

Rhenium polyhydride complexes serve as pre-catalysts for the transformation of small molecules²³^,³⁸^,³⁹^,⁴⁰^,⁴¹^,⁴²^,⁴³^,⁴⁴^,⁴⁵^,⁴⁶^,⁴⁷^,⁴⁸^,⁴⁹^,⁵⁰^,⁵¹. The specific mechanisms for catalytic cycles, though, are generally not well understood. The low activation energy dynamic processes of such complexes essentially confound all of the atom resonances in room temperature NMR spectra, making the chemical properties of individual atoms in specific locations impossible to follow. Dynamic NMR spectroscopy can allow for the identification of some chemical properties of a specific hydride ligand⁹^,¹³. Catalytic steps with activation energies within the range of 5 to 25 kcal/mol may be apparent with line shape fitting of dynamic NMR spectra of such catalytic systems. Dynamic NMR spectroscopy can also lead to an understanding of dynamic properties, which may lead to rational design of transition metal polyhydride complexes with restricted dynamic properties. Complexes with restricted dynamic properties should allow for room temperature NMR investigations of chemical properties of specific atoms in specific coordination sites and lead to insight into catalytic cycles that start with transition metal polyhydride complexes.

Declarações

The authors have nothing to disclose.

Acknowledgements

The authors thank the Department of Chemistry and Physics and the Creativity and Research Grant Program (Naik, Moehring) at Monmouth University for financial support of this work.

Materials

Bruker Avance II 400 MHz NMR spectrometer	Bruker Biospin		The instrument includes a two channel probe (1H and X) with the X channel tunable from 162 MHz to 10 Mhz. The instrument is also VT capable with a dewar and heat exchanger for VT work.
d₈-toluene	MilliporeSigma	434388
Powerstat variable transformer	Powerstat
sec-butyl amine	MilliporeSigma	B89000
Sodium borohydride	MilliporeSigma	452882
Tetrahydrofuran	MilliporeSigma	186562
Thermowell C3AM 100 mL	Thermowell
Topspin 3.0 or 4.1.4 with dNMR	Bruker Biospin		Data was acquired with Topspin version 3.0 and data handling was performed on a second computer that was running Topspin version 4.1.4..
Trichlorooxobis(triphenylphosphine) rhenium(V)	MilliporeSigma	370193
Vacuubrand PC3000 vacuum pump with a CVC 3000 controller	Vacuubrand

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Tadros, S. M., Mansour, M., Naik, D. V., Moehring, G. A. Line Shape Analysis of Dynamic NMR Spectra for Characterizing Coordination Sphere Rearrangements at a Chiral Rhenium Polyhydride Complex. J. Vis. Exp. (185), e64160, doi:10.3791/64160 (2022).