Probing Ligand Effects on the Ultrafast Dynamics of Copper Complexes via Mid-Infrared Pump Probe and 2DIR Spectroscopies

Abstract

The effects of ligand structural variation on the ultrafast dynamics of a series of copper coordination complexes were investigated using polarization-dependent mid-IR pump probe spectroscopy and two-dimensional infrared (2DIR) spectroscopy. The series consists of three copper complexes [(^R3P₃tren)Cu^IIN₃]BAr^F₄ (1^PR3 ,^R3P₃tren = tris[2-(phosphiniminato)ethyl]amine, BAr^F₄ = tetrakis(pentafluorophenyl)borate) where the number of methyl and phenyl groups in the PR₃ ligand are systematically varied across the series (PR₃ = PMe₃, PMe₂Ph, PMePh₂). The asymmetric stretching mode of azide in the 1^PR3 series is used as a vibrational probe of the small molecule binding site. The results of the pump probe measurements indicate that the vibrational energy of azide dissipates through intramolecular pathways and that the bulkier phenyl groups lead to an increase in the spatial restriction of the diffusive reorientation of bound azide. From 2DIR experiments we characterize the spectral diffusion of the azide group and find that an increase in the number of phenyl groups maps to a broader inhomogeneous frequency distribution (Δ₂). This indicates that an increase in the steric bulk of the secondary coordination sphere acts to create more distinct configurations in the local environment that are accessible to the azide group. This work demonstrates how ligand structural variation affects the ultrafast dynamics of a small molecular group bound to the metal center, which could provide insight into the structure-function relationship of the copper coordination complexes, and transition metal coordination complexes in general.

Graphical Abstract

1. INTRODUCTION

Copper coordination complexes have been extensively studied as model systems for the active sites of copper-containing enzymes, which transport and process molecular oxygen in many organisms.^1–4 Biomimetic copper coordination chemistry has thus sought to develop a comprehensive understanding of the effects imparted by the primary and secondary coordination spheres about copper ions.^2–5 The insight gained from these studies has proven to be remarkably valuable, not only for identifying disease states in metalloenzymes and developing new pharmaceuticals but also for the rational design of industrial copper based catalysts for oxidation reactions.^6,7

Previous work has revealed the pivotal role of supporting ligands in determining the reactivity and selectivity of Cu^I complexes with molecular oxygen through systematic modifications to the primary and secondary coordination spheres.^2–4 For example, studies have demonstrated that altering the steric profile,⁸ incorporating electron-donating/withdrawing substituents,⁹ and introducing intramolecular hydrogen bonds,^10,11 can impact the Cu^I/O₂ reactions. The structure-function relationship can also be established through a dynamical perspective. The interplay between ultrafast dynamics and catalytic activity has been elucidated in metalloenzymes^12–14 and their mimics^15,16, as well as catalytic transition metal complexes^17–19, demonstrating that the characterization of ultrafast dynamics can foster a better understanding of the reaction mechanism and its relationship with molecular structures.

Two-dimensional infrared (2DIR) spectroscopy has proven to be a powerful tool to probe ultrafast equilibrium dynamics of enzymes as well as models of their active sites on femtosecond to picosecond time-scales.^{13–15,17–24} Polarization-dependent mid-IR pump probe spectroscopy has also been widely used to extract the vibrational population and orientational relaxation dynamics of various systems.^25–2829 In this manuscript we apply both polarization-dependent mid-IR pump probe spectroscopy and 2DIR spectroscopy to a series of copper coordination complexes to determine how the structural variation in the secondary coordination sphere impacts the ultrafast dynamics at a small molecule binding site where a series of trigonal pyramidal Cu^I complexes bind O₂.

The series of copper complexes investigated in this work have both structural and electronic resemblance to the well-characterized tris[2-(tetramethylguanidino)ethyl]amine copper complex ([TMG₃trenCu^I]⁺, Figure 1a).^30–32 Previous studies have shown that [TMG₃trenCu^I]⁺ reacts with dioxygen at low temperatures to form an end-on copper-dioxygen adduct (Figure 1a), which remains the only η¹-cupric superoxide complex in a pseudo-C_3v geometry that has been characterized by X-ray crystallography.^31,32 In order to achieve facile modification to the secondary coordination sphere and investigate its impact on the ultrafast dynamics at the small molecule binding site, we synthesized a series of cupric azide complexes based on the ^R3P₃tren ligands recently designed by Tomson and coworkers.³³ The series consists of three complexes based on the [(^R3P₃tren)Cu^IIN₃]BAr^F₄ framework (1^PR3, ^R3P₃tren = tris[2-(phosphiniminato)ethyl]amine, BAr^F₄ = tetrakis(pentafluorophenyl)borate, Figure 1b), with varied numbers of methyl (Me) and phenyl (Ph) groups bound to the phosphorous atoms (PR₃ = PMe₃, PMe₂Ph, PMePh₂). ^R3P₃tren possesses similar donor strength as TMG₃tren, owing to the strong Brønsted basicity of the phosphinimine and guanidine fragments.^30,34 The ^R3P₃tren ligand platform also provides a similar steric profile to TMG₃tren, but one that is more easily modulated via changes to the substituents bound to phosphorous. The tunability of steric bulk in the vicinity of the small molecule binding site allows for direct observation of the relationship between ligand structure and ultrafast equilibrium dynamics. In addition to the steric effects, Tomson and coworkers found that the phosphinimine groups in the ^R3P₃tren ligand generated intramolecular electrostatic fields.³³ These electrostatic effects may also be envisioned to impact the binding and reactivity of the small molecule bound to the copper center.

Figure 1.

(a) Formation of the TMG₃tren-ligated η¹-cupric superoxide complex.^31,32 (b) ^R3P₃tren-ligated cupric azide complexes that serve as thermally-robust structural models for η¹-cupric superoxide complexes.

The azide group in the 1^PR3 series was incorporated to serve as a convenient vibrational probe to detect the ultrafast dynamics at the small molecule binding site. The asymmetric stretching mode of azide has a distinct absorption feature in the ~2000 cm⁻¹ window and thus avoids the spectral overlap with ligand and/or solvent-based vibrational modes. In addition, the asymmetric stretch of azide has a high oscillator strength and sensitivity to changes in the local environment, making it widely used as a vibrational probe.^35–38 Moreover, the azide group has been used previously as a surrogate for superoxide and peroxide moieties due to the similarities in steric and electronic profiles.^10,39 Additionally, unlike cupric superoxide complexes, these cupric azide complexes are stable at room temperature and thus remain intact for the 2DIR and mid-IR pump-probe measurements.

This manuscript is outlined as follows: we first present the pump probe spectra from which we extract the vibrational population relaxation and orientational relaxation dynamics of the azide group. Applying a modified wobbling-in-a-cone analysis^40,41 we determine the degree of spatial restriction and the diffusion coefficients associated with the orientational motion of azide. We then present the 2DIR spectra of the copper complexes. The time evolution of the 2D spectral lineshape was quantified with the center line slope (CLS) parameter and the frequency frequency correlation function (FFCF) was extracted by fitting the CLS decay curves and experimental FTIR spectra.^42,43 We interpret the FFCF to gain insight into the fluctuations of the local environment at the small molecule copper-binding site.

2. EXPERIMENTAL METHODS

2.1. Sample Preparation

The synthetic protocol and structural characterization of the cupric azide complexes 1^PR3 are described in detail in Section 1 of the Supporting Information (SI). Both the steady state and ultrafast spectroscopic measurements were performed using a commercial sample cell (Harrick DLC-M25) with a 125-μm thick Teflon spacer sandwiched between two calcium fluoride windows (25 mm in diameter and 2 mm in thickness). The sample cell was placed under vacuum for at least 7 hours prior to sample preparation to remove adsorbed water. The purified complex was dissolved in anhydrous and degassed tetrahydrofuran (THF) under an inert atmosphere of N₂ in a Vacuum Atmospheres Co. glovebox. The resulting solution (ca. 12 mM) was filtered through a plug of Celite to ensure removal of any insoluble materials, and the vibrantly green filtrate was loaded into the sample cell via a syringe. The cell was then sealed with Teflon plugs which were further sealed with Parafilm before being removed from the glovebox. Control measurements were performed on free ${\text{N}}_3^{-}$ solution (ca. 12 mM) prepared by dissolving tetrabutylammonium azide (TCI Fisher) in THF under the same anhydrous conditions as the 1^PR3 series.

2.2. Linear Infrared Spectroscopy

Steady state Fourier-transform infrared (FTIR) spectra were obtained on a JASCO FT/IR-4600 spectrometer at a resolution of 1 cm⁻¹. The reported spectra are an average of 40 scans. The absorption spectrum of THF was subtracted as background. For the ultrafast measurements the optical density for the asymmetric stretching mode of azide was ~0.25 for all the samples. FTIR spectra were obtained both prior to and after the ultrafast measurements to confirm that the samples did not degrade over the course of the experiments.

2.3. Pump probe and 2DIR Experiments

To obtain a 2DIR spectrum, three laser pulses interact with the sample to generate the third-order nonlinear polarization that leads to the emission of a signal.^44,45 The first pulse creates a coherence between the ground and first vibrational excited state. After a delay time t₁, the second pulse interacts with the sample. For the azide group studied in this work, the second pulse creates a population, either on the ground state or first vibrational excited state. The system evolves in this population over the t₂ time period. Interaction of a third pulse ends the t₂ time period and initiates a second coherence that generates a macroscopic polarization in the sample leading to the emission of the signal. For the pump probe experiments the third-order nonlinear processes are similar to those of the 2DIR experiments except that the t₁ time delay is set to zero so that the first two field-matter interactions occur simultaneously.

To perform the pump probe and 2DIR measurements, 60% of the output of a commercial Ti:sapphire laser (Coherent Libra, 800 nm pulses, 100 fs duration, 1 kHz repetition rate) was directed into a two stage optical parametric amplifier (OPA, Coherent TOPAS) to generate near-IR signal and idler pulses. The signal and idler were then difference frequency mixed in a AgGaS₂ crystal (Light Conversion TOPAS DFG-1) to produce frequency-tunable mid-IR pulses. For the experiments here, the mid-IR pulses were centered at 4900 nm (2041 cm⁻¹) for measuring copper-bound azide, and 5015 nm (1994 cm⁻¹) for measuring the free azide anion. The spectral bandwidth of the mid-IR pulses was ~150 cm⁻¹ and the total power of the mid-IR pulse generated by the OPA and DFG setup was ~27 mW.

The mid-IR pulse was then split by a CaF₂ wedge (3°, ISP Optics) where the reflected portion was used as the probe pulse (~4% of the total power) and the transmitted portion was used as the pump pulse (~96% of the total power). For both the pump probe and 2DIR experiments, the pump pulse was directed into a germanium acousto-optic modulator (AOM) mid-IR pulse shaper (PhaseTech QuickShape).^46,47 For the pump probe measurements the pulse shaper was used to chop every other pump pulse, and the relative phase of two consecutive pump pulses was cycled to be 0 and π. To obtain 2DIR spectra, the pulse shaper generated two phase-locked pump pulses separated by a delay time of t₁. To obtain a 2DIR spectrum at a given t₂ time, the t₁ time was scanned from 0 to 6000 fs with the step size of 30 fs. At each t₁ time step a four-pulse phase cycling scheme was employed where the relative phase of the two pump pulses was set to be (0, 0), (π, π), (0, π), (π, 0).⁴⁸ The partial rotating frame with a frame frequency corresponding to 1800 cm⁻¹ was used.⁴⁸ For both the pump probe and 2DIR measurements, the pump pulse(s) was directed onto a mechanical delay stage (Newport ILS250CCL) to control the waiting time (t₂) between the pump and probe pulses. For a given t₂ time step, 8000 laser shots were used to generate the pump probe spectra and 8860 laser shots were used to generate the 2DIR spectra.

The polarization of the pump and probe pulses was controlled by half waveplates (Edmund 85–119) and CaF₂ holographic wire grid polarizers (Thorlabs WP25H-C) placed before the sample. For all measurements the polarization of probe pulse was set to be horizontal. For the pump probe measurements, parallel (ΔI_∥) and perpendicular (ΔI_⊥) spectra were collected by setting the polarization of the pump pulse to be either horizontal or vertical with respect to the probe pulse. For the 2DIR experiments, the pump pulse was set to the magic angle polarization to prevent influence from orientational relaxation. The pump and probe pulses were focused at the sample and subsequently collimated by a pair of off-axis parabolic mirrors (Thorlabs MPD249-P01). Before passing through the sample, the probe pulse passed through a beam splitter (Thorlabs BSW510) where 40% was reflected and directed towards the sample cell and 60% was transmitted to serve as a reference. The reference was used to characterize the laser fluctuations and increase the signal-to-noise ratio by applying a multi-channel referencing scheme based on previous work.⁴⁹ Both the reference and the probe pulses were directed into the spectrometer (Horiba iHR320) and dispersed by a grating onto a liquid-nitrogen-cooled 64×2 element mercury-cadmium-telluride (MCT) array detector coupled with an FPAS data acquisition system (Infrared Systems Development). A 150 groove/mm 4 μm blaze wavelength grating was used in the spectrometer achieving a resolution of 2 cm⁻¹.

Polarization-gated frequency resolved optical gating (PG-FROG)⁵⁰ measurements were conducted to characterize the pulses using a 2 mm thick germanium window as the nonlinear medium. From these measurements the mid-IR pulse duration was determined to be ~150 fs.

2.4. Spectroscopic Data Analysis Methods

2.4.1. Pump Probe Spectroscopy

For the pump probe measurements, two polarization configurations were employed, with the polarization of the pump pulse set to be either parallel or perpendicular to that of probe pulse. The population decay, P(t), and anisotropy decay, r(t), were extracted from the measurements according to the following expressions:^51–54

$$\text{P}(\text{t})=\frac{\mathrm{\Delta }{\text{I}}_{\Vert }(\text{t})+2\times \mathrm{\Delta }{\text{I}}_{\perp }(\text{t})}{3}$$ (1)

$$\text{r}(\text{t})=\frac{\mathrm{\Delta }{\text{I}}_{\Vert }(\text{t})-\mathrm{\Delta }{\text{I}}_{\perp }(\text{t})}{\mathrm{\Delta }{\text{I}}_{\Vert }(\text{t})+2\times \mathrm{\Delta }{\text{I}}_{\perp }(\text{t})}$$ (2)

where ΔI_∥(t) and ΔI_⊥(t) are the pump probe signals (the difference in transmitted probe pulse intensity in the presence and absence of the pump pulse) taken under parallel and perpendicular polarization conditions respectively.

The anisotropy decay reports on the molecular reorientation through its relation to the transition dipole moment correlation function:^51,52,55

$$\text{r}(\text{t})=0.4{\text{C}}_2(\text{t})$$ (3)

where C₂(t) is the second-order Legendre polynomial of the transition dipole moment correlation function: ${\text{C}}_2(\text{t})=\langle {\text{P}}_2[\widehat{\mathrm{\mu }}(\text{t})\cdot \widehat{\mathrm{\mu }}(0)]\rangle$ with $\widehat{\mathrm{\mu }}(\text{t})$ being the transition dipole moment unit vector at time t. In this work, we apply the modified wobbling-in-a-cone model to interpret the anisotropy decay. According to this model, the transition dipole moment correlation function can be expressed as a triexponential function:⁵²

$${\text{C}}_2(\text{t})=\left(1-{\text{T}}^2\right)\times \exp \left(-\frac{\text{t}}{{\text{τ}}_{\text{lib}}}\right)+{\text{T}}^2\left[{\text{S}}^2+\left(1-{\text{S}}^2\right)\exp \left(-\frac{\text{t}}{{\text{τ}}_{\mathrm{c}}}\right)\right]\times \exp \left(-\frac{\text{t}}{{\text{τ}}_{\mathrm{m}}}\right)$$ (4)

where the first term describes the rapid librational motion at early times and the second term corresponds to the biexponential decay associated with the restricted diffusive motion and overall rotation. τ_lib, τ_c, and τ_m are the time constants associated with the librational motion, restricted diffusive motion, and the complete reorientation of azide, respectively. T² and S² are the order parameters for the initial librational motion and the subsequent restricted diffusion, respectively. When the order parameters are equal to zero the system can be considered to be freely rotating in solution while a value of one corresponds to a system that does not undergo molecular reorientation. Note that although Equation 4 is a triexponential function, the time constant for the fastest component, τ_lib, can not be resolved by the current measurements, and only the order parameter T² can be determined.

The degree of spatial restriction associated with the librational motion and diffusive motion can be quantified by the corresponding order parameters and cone semiangles:⁵²

$${\text{T}}^2=2.5\left({\text{a}}_1+{\text{a}}_2\right)={\left[\frac{1}{2}\left(\text{cos}{\mathrm{\theta }}_{\text{lib}}\right)\left(1+\cos {\text{θ}}_{\text{lib}}\right)\right]}^2$$ (5)

$${\text{S}}^2=\frac{{\text{a}}_2}{{\text{a}}_1+{\text{a}}_2}={\left[\frac{1}{2}\left(\cos {\text{θ}}_{\mathrm{c}}\right)\left(1+\cos {\text{θ}}_{\mathrm{c}}\right)\right]}^2$$ (6)

$${\text{T}}^2{\text{S}}^2=2.5{\text{a}}_2={\left[\frac{1}{2}\left(\cos {\text{θ}}_{\text{tot}}\right)\left(1+\cos {\text{θ}}_{\text{tot}}\right)\right]}^2$$ (7)

where a₁ and a₂ are the amplitudes of the biexponential anisotropy decay. θ_lib and θ_c are the cone semiangles associated with the librational motion and restricted diffusion respectively. θ_tot denotes the total cone semiangle combining contributions from the librational motion and restricted diffusion.

The time constant associated with the restricted orientational diffusion, τ_c, can be obtained from the anisotropy decay time constants ${\text{τ}}_{\mathrm{c}}={\left({\text{t}}_{\text{or},1}^{-1}-{\text{t}}_{\text{or},2}^{-1}\right)}^{-1}$. From θ_c, S², and τ_c, the diffusion coefficient for restricted reorientation within the cone can be calculated as:⁵²

$${\text{D}}_{\mathrm{c}}=\frac{{\text{x}}_{\mathrm{c}}^2{\left(1+{\text{x}}_{\mathrm{c}}\right)}^2\left\{\ln \left[\frac{\left(1+{\text{x}}_{\mathrm{c}}\right)}{2}\right]+\frac{\left(1-{\text{x}}_{\mathrm{c}}\right)}{2}\right\}}{{\text{τ}}_{\mathrm{c}}\left(1-{\text{S}}^2\right)\left[2\left({\text{x}}_{\mathrm{c}}-1\right)\right]}+\frac{\left(1-{\text{x}}_{\mathrm{c}}\right)\left(6+8{\text{x}}_{\mathrm{c}}-{\text{x}}_{\mathrm{c}}^2-12{\text{x}}_{\mathrm{c}}^3-7{\text{x}}_{\mathrm{c}}^4\right)}{24{\text{τ}}_{\mathrm{c}}\left(1-{\text{S}}^2\right)}$$ (8)

where x_c = cosθ_c. For the complete reorientation of azide, the time constant τ_m is equivalent to the longer time constant t_or,₂ of the anisotropy decay, and the corresponding diffusion coefficient D_m can be calculated as:⁵²

$${\text{D}}_{\mathrm{m}}=\frac{1}{6{\text{τ}}_{\mathrm{m}}}.$$ (9)

2.4.2. Two-dimensional Infrared (2DIR) Spectroscopy

2DIR spectroscopy is a powerful tool for investigating the time evolution of the local environment surrounding a vibrational probe.⁴⁴ Depending on the system, changes in the local environment can arise from solvent rearrangements^56–58 or molecular structural dynamics^59,60. The fluctuations in the local environment can act to perturb the potential energy surface of a vibrational probe, resulting in the modulation of its vibrational frequency. This process is known as spectral diffusion.⁴⁴ The frequency fluctuations can be used as a reporter for changes in the local environment. The amplitude and time-scale of the frequency fluctuations can be characterized by the frequency frequency correlation function (FFCF).⁴⁴ The FFCF is defined as FFCF(t) = 〈δω(t)δω(0)〉 where δω(t) = ω(t) − 〈ω〉 is the difference between the instantaneous vibrational frequency at time t and average frequency. The FFCF can be described by the following expression:^42,44

$$\text{FFCF}(\text{t})=\frac{\text{δ}(\text{t})}{{\text{T}}_2}+\sum _i{\mathrm{\Delta }}_i^2\exp \left(-\frac{\text{t}}{{\text{τ}}_i}\right)$$ (10)

where Δ_i and τ_i are the amplitude and correlation time of the i-th component of the frequency fluctuation. T₂ is the homogeneous dephasing time that has contributions from pure dephasing time ${\text{T}}_2^{*}$, finite vibrational lifetime T₁, and orientational relaxation time ${\text{T}}_{\text{or}}:\frac{1}{{\text{T}}_2}=\frac{1}{{\text{T}}_2^{*}}+\frac{1}{2{\text{T}}_1}+\frac{1}{3{\text{T}}_{\text{or}}}$. Here T_or can be approximated by τ_m extracted from the anisotropy measurements. The total homogeneous line broadening Γ₂ is related to T₂ by the expression: Γ₂ = 1⁄(π T₂).

In 2DIR spectra, spectral diffusion can be observed as a lineshape change, from which the FFCF can be extracted.^61,62 In this work we use the center line slope (CLS) method to characterize the spectral diffusion process and extract the FFCF. To obtain the CLS from a 2DIR spectrum at a given t₂ time, we first take slices parallel to the ω₃ axis over an ω₁ frequency range spanning the desired peak. Then the maxima along the ω₃ axis are determined by fitting each slice with two Gaussian functions to account for the center frequencies for the 0 → 1 and 1 → 2 transitions, respectively. The center frequency for the 0 → 1 transitions is recorded for each 𝜔₁ frequency. The resulting data points are then fit with a linear function, and the slope of this line is referred to as the center line slope (CLS). This process is then performed for 2DIR spectra at different t₂ times to obtain the CLS as a function of t₂, CLS(t₂). The CLS(t₂) has been shown to be directly proportional to normalized FFCF under the short time approximation.^42,43 The value of the CLS is less than unity and will decay from the initial value to zero when the vibrational oscillator has sampled all the possible configurations of the local environment and thus the vibrational frequency has completely lost the correlation with its initial value. The difference between the initial value of the CLS and unity reveals the contribution of the homogeneous component to the linewidth broadening.⁴²

2.5. DFT Calculations

Geometry optimizations were performed with the Gaussian 16 software package⁶³ using the B3LYP functional and 6–31G(d) basis set for carbon, nitrogen, phosphorus, and hydrogen atoms, and LANL2DZ pseudopotential for copper.⁶⁴ The THF solvation effects were taken into account by using the polarizable continuum model. Vibrational analysis was conducted at the same level of theory with the same basis set and pseudopotential and used to confirm the optimized structure. The molecular volumes were obtained for the optimized structures. The optimized geometries and calculated vibrational frequencies associated with azide are reported in Section 2 of the SI.

3. RESULTS AND DISCUSSION

3.1. Linear Infrared Spectroscopy

Figure 2 displays the normalized FTIR spectra of azide bound to the three different copper complexes (1^PMe3, red line; 1^PMe2Ph, green line; 1^PMePh2, blue line) dissolved in THF. For comparison the normalized FTIR spectrum of the free ${\text{N}}_3^{-}$ anion dissolved in THF is also plotted in Figure 2 (yellow line). The FTIR spectra exhibit one main transition in the 1960–2080 cm⁻¹ region assigned to the asymmetric stretching mode of azide. The asymmetric stretching mode of free ${\text{N}}_3^{-}$ absorbs at 1995 cm⁻¹ and has a weak shoulder on the low frequency edge of the peak around 1982 cm⁻¹ which is attributed to the bending hot band.^65,66 For the copper-bound azide, the asymmetric stretch is blue shifted with respect to free ${\text{N}}_3^{-}$ with an absorption occurring at ~2046 cm⁻¹. The blue shift can be explained by considering the two resonance structures of the azide group: N⁻ = N⁺ = N⁻ ↔ N ≡ N⁺ − N²⁻. Binding to the copper breaks the symmetry of azide and increases the contribution from the resonance structure with triple bond character,^67,68 thus resulting in an increase of the vibrational frequency by ~50 cm⁻¹.^29,69

Figure 2.

Background-subtracted and normalized FTIR spectra of the azide asymmetric stretching mode for 1^PMe3 (red), 1^PMe2Ph (green), 1^PMePh2 (blue) and the free ${\text{N}}_3^{-}$ anion (yellow) dissolved in THF.

Comparing the FTIR spectra of the three copper complexes we find that the absorption frequency and spectral broadening vary with phosphine ligand substitution. Modest increases in the absorption maxima are observed with the addition of phenyl groups, with the absorption maxima for 1^PMe3, 1^PMe2Ph, and 1^PMePh2 occurring at 2045, 2046, 2047 cm⁻¹, respectively. This trend could arise from the electron-withdrawing effects of the phenyl groups enhancing the positive charge at copper which would be expected to further stabilize the triple bond-containing resonance form of azide.

In addition to the variation in transition frequencies, a change in the linewidth is also observed. The full width at half-maximum (FWHM) exhibits an increasing trend among the three copper complexes, from 10 cm⁻¹ for 1^PMe3, to 13 cm⁻¹ for 1^PMe2Ph, and to 15 cm⁻¹ for 1^PMePh2. For comparison the FWHM of free ${\text{N}}_3^{-}$ anion is 11 cm⁻¹, lying between the FWHM of 1^PMe3 and 1^PMe2Ph. The difference in the linewidth indicates a change associated with the vibrational dephasing, which has contributions from the pure homogeneous dephasing, vibrational lifetime, and inhomogeneous dephasing.^44,70 To unravel the different contributions to the line broadening mechanism we apply ultrafast polarization dependent mid-IR pump probe spectroscopy and 2DIR spectroscopy to the 1^PR3 series.

3.2. Pump Probe Spectroscopy

Polarization dependent pump probe experiments were performed to determine how the structural variation of the ligand affects the vibrational energy dissipation and orientational relaxation of the copper-bound azide group in the 1^PR3 series. The same measurements were performed on the free ${\text{N}}_3^{-}$ ion that serves as a control.

Figures 3(a) and (b) display the pump probe spectra of the azide group of 1^PMe3 measured under parallel and perpendicular polarization conditions. The positive signal arises from the 0 → 1 transitions. The negative signal, red-shifted due to the vibrational anharmonicity, arises from the 1 → 2 transitions. The dashed vertical lines denote the frequency at which the time traces are taken, and the values of ΔI_∥(t) and ΔI_⊥(t) are plotted in Figure 3(c) as a function of waiting time. The pump probe spectra for 1^PMe2Ph, 1^PMePh2, and free ${\text{N}}_3^{-}$ under parallel and perpendicular polarizations as well as the corresponding time traces are presented in Figure S15 of the SI. In general, these spectra are similar to those reported in Figure 3, but with different center frequencies that evolve with different time constants. All the population and anisotropy decays discussed below were obtained according to Equation 1 and Equation 2 where ΔI_∥(t) and ΔI_⊥(t) were taken at the center frequency of the 0 → 1 transition for each sample. Data analysis was performed starting at 500 fs to avoid contributions from pulse overlap and coherent artifacts.

Figure 3.

Polarization dependent pump probe spectra of the copper-bound azide group of 1^PMe3 dissolved in THF measured under (a) parallel and (b) perpendicular polarization conditions. (c) The time traces taken at 2046 cm⁻¹ (denoted as dashed lines superposed on the pump probe spectra) are plotted for the parallel and perpendicular polarization conditions.

3.2.1. Population Relaxation Dynamics.

Figure 4 displays the population decay traces of the copper-bound azide for the 1^PR3 series and free ${\text{N}}_3^{-}$ in THF. Through comparison of the traces we find that the population relaxation of copper-bound azide is faster than that of free ${\text{N}}_3^{-}$ and that the three copper complexes exhibit similar decay traces. To extract the time constants for population relaxation the traces are fit with exponential functions. A single exponential function can describe the population decay of the copper-bound azide whereas a biexponential function is required to fit the population decay of free ${\text{N}}_3^{-}$. The extracted fitting parameters are reported in Table 1. The different fitting functions for free and bound azide reflect differences in the underlying mechanism of population relaxation. To interpret the population relaxation we compare our results to previous studies by Vöhringer et al.⁶⁷ and Park et al.⁷¹ Vöhringer et al. characterized the vibrational relaxation of ferric azide complexes as well as free ${\text{N}}_3^{-}$, where both systems were solvated by acetonitrile (ACN).⁶⁷ Park et al. characterized the vibrational relaxation of metal azide ion pairs solvated by DMSO.⁷¹

Figure 4.

Normalized population decay P(t) of the asymmetric stretching mode of the azide group in 1^PMe3 (red circle), 1^PMe2Ph (green star), 1^PMePh2 (blue triangle) and free ${\text{N}}_3^{-}$ anion (yellow diamond) in THF. Solid curves are single exponential fits for the 1^PR3 series and a biexponential fit for free ${\text{N}}_3^{-}$.

Table 1.

Extracted population decay times (T₁), and the best fit parameters for the anisotropy decay. The error bars report the 95% confidence intervals.

	Population Decay	Anisotropy Decayc
	T1 (ps)	a1	t1,or (ps)	a2	t2,or (ps)
1PMe3	4.82 ± 0.03a	0.06 ± 0.02	3.1 ± 0.8	0.28 ± 0.02	21 ±2
1PMe2Ph	4.42 ± 0.02a	0.05 ± 0.01	2.5 ± 0.7	0.30 ± 0.01	37 ± 5
1PMePh2	4.57 ± 0.02a	0.02 ± 0.01	2.7 ± 1.8	0.32 ± 0.01	59 ± 12
Free ${\text{N}}_3^{-}$	2.3 ± 0.4 (7%)b 15.5 ± 0.2 (93%)b	0.18 ± 0.01	1.2 ± 0.1	0.10 ± 0.01	6.4 ± 0.4

^aPopulation decay of the 1^PR3 series is fit with a single exponential function.

^bPopulation decay of free ${\text{N}}_3^{-}$ is fit with a biexponential function, and the values in parentheses are the amplitude percentage for eachcomponent.

^cThe anisotropy decay was fit with the following expression: $\text{r}(\text{t})={\text{a}}_1\exp \left(-\frac{\text{t}}{{\text{t}}_{1,\text{or}}}\right)+{\text{a}}_2\exp \left(-\frac{\text{t}}{{\text{t}}_{2,\text{or}}}\right)$.

In the current work, we find the population of the asymmetric stretch of free ${\text{N}}_3^{-}$ solvated by THF decays with a fast component of 2.3 ps and a slower component of 15.5 ps. Our results are comparable to those of free ${\text{N}}_3^{-}$ in ACN (4.0 ps and 18.0 ps).⁶⁷ In accord with previous studies⁶⁷, we assign the 2.3 ps decay component to intramolecular vibrational energy redistribution (IVR) and the 15.5 ps component to vibrational energy relaxation to solvent modes. More specifically, the IVR process of free ${\text{N}}_3^{-}$ arises from vibrational energy redistribution of the asymmetric stretching mode, ν_asym, among the combination band of the symmetric stretching mode, ν_sym, and the bending mode, ν_bend, and the energy mismatch is compensated by the low-frequency solvent modes.⁶⁷

As for the copper-bound azide, we only resolve one component in the population decay with a time constant of 4.8 ps for 1^PMe3, 4.4 ps for 1^PMe2Ph, and 4.6 ps for 1^PMePh2. These time constants are consistent with the slower 4.4 ps component reported for the ferric azide complexes in ACN.⁶⁷ For the ferric azide complexes Vöhringer et al.⁶⁷ assigned the 4.4 ps component to vibrational energy dissipation to the solvent’s vibrational modes, and its acceleration upon complexation was attributed to an increase in the spectral overlap between the asymmetric stretching band of azide and the ACN solvent.⁶⁷ In the current work, the copper-azide complexes are solvated by THF, which has an absorption around 1971 cm⁻¹. The blue shift in the asymmetric stretching mode of azide bound to the copper complex results in a decrease in the spectral overlap with the THF solvent mode. Thus, increased spectral overlap with solvent modes is not responsible for the shorter vibrational lifetime observed for the copper-azide complexes studied here. Additional insight can be gained by comparing to previous work by Park et al., where it was found that the population decay of the azide asymmetric stretching mode is faster for free ${\text{N}}_3^{-}$ when compared to various metal-azide contact ion pairs.⁷¹ The metal cation of the ion pair was thought of as blocking the relaxation pathway to the solvent bath.⁷¹ As for the copper complexes studied in this manuscript, the bound azide group is isolated from the THF solvent molecules by the bulky phosphine ligands, and yet the vibrational relaxation of bound azide is still accelerated in contrast to the metal-azide ion pairs⁷¹. The discussion above indicates that the population relaxation of the copper-bound azide does not arise from the vibrational energy being dissipated into the solvent modes, but rather the intramolecular vibrational modes of the copper complexes.

Among the three copper complexes studied here (1^PR3), there is not a significant difference in their vibrational lifetimes, indicating that the coupling between the azide asymmetric stretching mode and the other intramolecular vibrational modes is not affected by the structural changes in the secondary coordination sphere. One possible reason for the absence of a fast decay component, which was previously observed and attributed to IVR for the ferric azide complexes,⁶⁷ is that this component may become too fast to be resolved for the 1^PR3 series. Another possibility is that the time constants for IVR among the azide modes and vibrational energy relaxation involving the supporting ligand’s vibrational modes are similar, thus rendering the two components inseparable. Analysis of the DFT calculated frequencies shows that the energy gap between ν_asym and the sum of ν_sym and ν_bend is similar for copper-bound azide and free ${\text{N}}_3^{-}$, and thus favors the latter possibility. A detailed discussion is presented in Section 2.4 of the SI.

3.2.2. Orientational Relaxation Dynamics.

The anisotropy decays for the copper-bound azide and free ${\text{N}}_3^{-}$ anion are plotted in Figure 5. The anisotropy decay of free ${\text{N}}_3^{-}$ shows an initial rapid decay followed by a longer timescale component that approaches zero within the time window probed. Compared to free azide, the copper complexes rotate relatively slowly in the solution due to their larger molecular volumes, and thus the orientational relaxation dynamics of bound azide cannot be fully characterized within the 13 ps time window probed. Though not fully decayed, the anisotropy of the copper complexes show clear differences, with an increase in the number of phenyl groups mapping to a slower anisotropy decay of the azide group. This suggests that the peripheral groups bound to phosphorous in ^R3P₃tren influence the orientational relaxation dynamics of the copper-bound azide on the picosecond timescale.

Figure 5.

Anisotropy decay r(t) of the azide group of 1^PMe3 (red circle), 1^PMe2Ph (green star), 1^PMePh2 (blue triangle) and free ${\text{N}}_3^{-}$ anion (yellow diamond) in THF. Solid curves are biexponential fits to the data.

To extract the timescales for molecular reorientation we fit the anisotropy decays with biexponential functions. We note that the anisotropy decays of 1^PMe2Ph and 1^PMePh2 can also be well fit with a single exponential and a constant offset term. However, we choose to use a biexponential function to model the anisotropy decay for all the samples in order to obtain a comparative physical picture of the orientational relaxation dynamics for the copper-bound azide. A detailed discussion for choosing the biexponential fitting function for all samples and the examination of slow time constants is provided in Sections 4 and 6 of SI. The fitting parameters are summarized in Table 1 and the curves representing the best fits are plotted in Figure 5 as solid lines. We note that the optimized parameters were obtained using the corresponding normalized population decay as a weighting function in the fitting process to account for the signal decay associated with the vibrational lifetime (see Section 7 of SI for more details).

Table 1 shows the extracted parameters obtained from fitting the anisotropy decays. We find that the time constants for the fast ~3 ps decay component are not distinguishable within experimental error. However, differences are observed in the slower time component where the time constant nearly doubles in going from 1^PMe3 to 1^PMe2Ph and almost triples when comparing 1^PMePh2 with 1^PMe3. The relative contribution of the slow component (a₂/(a₁ + a₂) ) also increases from 82% for 1^PMe3, to 86% for 1^PMe2Ph, and to 94% for 1^PMePh2. As for free ${\text{N}}_3^{-}$, both the fast and slow anisotropy decay components are accelerated when compared with the copper-bound azide and the slower component has a much smaller contribution (36%) to the overall decay.

We apply a modified wobbling-in-a-cone model^40,41 to the anisotropy data to quantitatively characterize the degree of spatial restriction and extract the diffusion coefficients. This model was initially developed to interpret the fluorescence depolarization data of molecules embedded in biomembranes,^40,41 and was later generalized to nuclear magnetic resonance data^72,73 and mid-infrared anisotropy measurements in various systems.^25,71,74 According to this model, the faster component of the anisotropy decay is associated with the restricted orientational motion of the transition dipole moment within a cone shaped space, and the slower component is associated with the complete reorientation. We note for each of the four samples, the sum of amplitudes (a₁+a₂, Table 1) is less than 0.4, the theoretical initial value of the anisotropy decay in an isotropic medium. We attribute the initial decrease in the anisotropy to the ultrafast librational motion of the azide group that is not resolved by our measurements. Previous studies have observed short-time librational motion preceding the diffusive orientational relaxation in several different systems.^74–77 Although we do not resolve the time constants for the initial decay, the spatial restriction of this librational motion can be estimated from the ratio of the theoretical r=0.4 value at zero time and the experimentally extrapolated anisotropy value at zero time (a₁+a₂, Table 1) using a modified wobbling-in-a-cone model developed by Fayer et al.⁵²

Applying the modified wobbling-in-a-cone analysis we extract the cone semiangles θ_lib, θ_c, and θ_tot to characterize the spatial restriction, and τ_c, D_c, τ_m, D_m to characterize the timescale and speed for the orientational relaxation dynamics of both free and bound azide. The results (summarized in Table 2) indicate that the total cone semiangles exhibit a decreasing trend across the series with θ_tot = 27° for 1^PMe3, θ_tot = 24° for 1^PMe2Ph, and θ_tot = 21° for 1^PMePh2, where the error bars (reporting 95% confidence intervals) have some overlap. The θ_tot values quantify the overall degree of spatial restriction (Eq. 7), with contributions from both the librational motion and restricted diffusive reorientation. Below we consider the two different contributions to gain further insight into the restricted orientational relaxation.

Table 2.

Parameters calculated from the wobbling-in-a-cone analysis. The errors in this table are propagated from those in Table 1. The details of error estimation are presented in Section 9 of the SI.

	θlib (°)	θc (°)	θtot (°)	τc (ps)	Dc (10−3 ps−1)	τm (ps)	Dm (10−3 ps−1)
1PMe3	19 ± 4	20 ± 3	27 ± 2	3.7 ± 1.1	9.4 ± 3.6	21 ± 2	8.0 ± 0.8
1PMe2Ph	17 ± 3	18 ± 2	24 ± 2	2.6 ± 0.8	10.9 ± 3.8	37 ± 5	4.5 ± 0.6
1PMePh2	18 ± 3	12 ± 3	21 ± 2	2.8 ± 2.0	4.4 ± 3.8	59 ± 12	2.8 ± 0.6
Free ${\text{N}}_3^{-}$	27 ± 1	45 ± 1	51 ± 1	1.5 ±0.1	97 ± 7	6.4 ± 0.4	26 ± 2

The values contained within Table 2 show that the three copper complexes have indistinguishable (within experimental error) librational cone semiangles of θ_lib ~18°. The similar θ_lib values are consistent with similar binding of the azide groups to the different copper complexes. From DFT calculations the copper azide complexes have comparable Cu-N bond lengths (2.03 Å for 1^PMe3 and 1^PMe2Ph, 2.01 Å for 1^PMePh2) and Cu-N-N binding angles (126° for 1^PMe3 and 1^PMePh2, 125° for 1^PMe2Ph). In addition, the Cu-N-N bending force constants calculated from the Hessian matrix based on the Seminario method⁷⁸ using VFFDT software⁷⁹ are similar among the three copper complexes (67.9 kcal/(mol·rad²) for 1^PMe3, 66.0 kcal/(mol·rad²) for 1^PMe2Ph and 1^PMePh2). These calculations suggest that the coordination bond strength of azide to the copper atom is similar across the 1^PR3 series, thereby corroborating the experimentally observed invariance of θ_lib among the three copper complexes.

Comparing the diffusive cone semiangles (θ_c) a trend is observed wherein θ_c decreases from θ_c = 20° for 1^PMe3, to θ_c = 18° for 1^PMe2Ph, and further to θ_c = 12° for 1^PMePh2, with the error range of 1^PMe3 overlapping with that of 1^PMe2Ph. For the copper-bound azide, the orientational diffusion arises from the randomization of the transition dipole driven by the interactions with its immediate local environment, namely the peripheral phosphinimine ligands and solvent molecules. The decreasing trend of θ_c indicates a greater spatial restriction on the diffusive reorientation of the azide group which arises from the steric hinderance of the bulky phenyl groups. A possible explanation for the smaller difference between θ_c of 1^PMe3 and 1^PMe2Ph can be made through considering the DFT-optimized molecular structures of the copper complexes (Figure 6). For 1^PMe2Ph the phenyl groups are oriented away from the copper center in order to reduce the steric hinderance. We note that the DFT structures report on the optimized geometries, and in solution the PMe₂Ph group can rotate along the N-P bond so that the phenyl groups can lie in closer proximity to the bound azide. Nevertheless, for comparative purposes we focus on the optimized DFT structures (Fig. 6). When considering the optimized DFT structures, the local steric environment experienced by the bound azide in 1^PMe2Ph is comparable to that of 1^PMe3, resulting in a similar θ_c between 1^PMe3 and 1^PMe2Ph. Apart from the angular displacement about the optimized orientation of the azide group as depicted with a blue total cone in Figure 6(a), the azide group can also undergo rotation about the Cu-N bond (N is the binding nitrogen atom of azide). Thus the total cone in Figure 6(a) only represents a simplified physical picture of the restricted orientational motion of the copper-bound azide.

Figure 6.

DFT-optimized structures for 1^PMe3 (left), 1^PMe2Ph (middle), and 1^PMePh2 (right). A schematic librational cone (grey) and total cone (blue) for the restricted reorientation of bound azide are depicted for 1^PMe3. The transition dipole moment of azide’s asymmetric stretching mode is schematically shown as a solid arrow for 1^PMe3. The atoms are color coded: red for copper, blue for nitrogen, orange for phosphorus, green for carbon, and light grey for hydrogen.

The time constant τ_c and diffusion coefficient D_c associated with the restricted orientational diffusion are also reported in Table 2. Among the three copper complexes, τ_c and D_c cannot be distinguished within experimental error. The large error bars associated with τ_c and therefore D_c are due to the large error bars of t₁,or that result from the limited detection time window. The time constants associated with the complete orientational relaxation of azide, τ_m, increase from 21 ps for 1^PMe3, to 37 ps for 1^PMe2Ph, and further to 59 ps for 1^PMePh2. We note that these values are lower limits as demonstrated in Section 6 of SI. The corresponding diffusion coefficients D_m calculated from these lower limits show a clear decreasing trend, which is consistent with the orientational diffusion coefficients of the copper complexes estimated with the Debye-Stokes-Einstein equation^74,80,81, ${\text{D}}_{\mathrm{m}}^{\text{DSE}}$ (Section 5 of SI).

As for free ${\text{N}}_3^{-}$, it undergoes a restricted orientational motion with an overall cone semiangle of θ_tot = 51°. The librational and diffusive cone angles are both larger than their counterparts in the copper complexes. The constrained orientational motion of free anions has been observed previously and its origin has been attributed to the solute-solvent interactions.^71,82 The D_c of free ${\text{N}}_3^{-}$ is about an order of magnitude larger than those of the copper-bound azide. We attribute this difference to ion-dipole interactions between free ${\text{N}}_3^{-}$ and solvent molecules being much weaker than the Cu-N bond, and thus the reorientation of free ${\text{N}}_3^{-}$ has a smaller energy barrier to overcome requiring less time to sample the possible orientations within the restricted space.

3.3. Two-dimensional Infrared (2DIR) Spectroscopy

After examining the ligand effects on the population and orientational relaxation dynamics of the copper-bound azide, we next turn to two-dimensional infrared (2DIR) spectroscopy to investigate the dynamic fluctuations of the local environment at the small molecule binding site with the goal of understanding how the structural variation of ligands impacts these dynamics.

Figure 7 displays the 2DIR spectra of the three copper complexes and free ${\text{N}}_3^{-}$ at t₂ = 0.5 ps (top) and 7 ps (bottom). Similar to the pump probe spectra, the positive peaks on the diagonal arise from the 0 → 1 transitions, while the off-diagonal negative peaks arise from the 1 → 2 transitions. As can be seen from the spectra in Figure 7, at t₂ = 0.5 ps the peaks are elongated along the diagonal indicating that these peaks are inhomogeneously broadened. As the t₂ time increases the spectral line shape evolves to become more symmetric as the azide group samples more configurations within its local environment. Comparing the 2DIR spectral lineshape at t₂ = 7 ps, differences are observed among the 1^PR3 series where the degree of elongation increases with increasing number of phenyl groups. This indicates that the different local environment configurations have not been fully sampled by the copper-bound azide group with bulkier ligands by 7 ps. Various analysis procedures have been developed to quantify the time evolution of 2DIR spectral lineshapes and extract timescales associated with spectral diffusion.^61,62 In this work, we use the center line slope (CLS) method.^42,43 The analysis procedure is described in Section 2.4.2.

Figure 7.

Normalized 2DIR spectra of 1^PMe3, 1^PMe2Ph, 1^PMePh2, and free ${\text{N}}_3^{-}$ dissolved in THF are displayed. The spectra are plotted with the same intensity scale as shown by the colorbar on the right. The spectra on the top row correspond to t₂ = 500 fs and those on the bottom row to t₂ = 7 ps. The dotted lines superposed on the spectra denote the diagonal where ω₁= ω₃.

Figure 8 displays the CLS decay of the copper complexes and free ${\text{N}}_3^{-}$ in THF obtained from the 2DIR spectra. Again, the data presented here focus on the data points obtained after 0.5 ps to avoid the influence from coherent artifacts and pulse overlap. The CLS decay can be fit well with a biexponential function, and the fitting parameters are reported in Table 3. Comparing the parameters for the three copper complexes, we find that the time constants for the fast decay components are indistinguishable within experimental error, and those of the slow components show a modest increasing trend as the number of phenyl groups is increased, though with some overlap among the error bars. The relative contributions from the slow decay components (A₂⁄(A₁ + A₂)) exhibit a greater change, increasing from 0.31 for 1^PMe3 to 0.49 for 1^PMe2Ph and further to 0.72 for 1^PMePh2. The CLS decay time constants of free ${\text{N}}_3^{-}$ are comparable to those of copper complexes and its slow component contribution is 0.38, lying between those of 1^PMe3 and 1PMe2Ph.

Figure 8.

Center line slope (CLS) of 1^PMe3 (red circle), 1^PMe2Ph (green star), 1^PMePh2 (blue triangle) and free ${\text{N}}_3^{-}$ anion (yellow diamond) in THF. Solid curves are biexponential fits to the data.

Table 3.

Optimized biexponential fitting parameters of the center line slope extracted from the 2DIR spectra. The CLS was fit with the following function $\text{CLS}(\text{t})={\text{A}}_1\exp \left(-\frac{\text{t}}{{\text{t}}_{1,\text{CLS}}}\right)+{\text{A}}_2\exp \left(-\frac{\text{t}}{{\text{t}}_{2,\text{CLS}}}\right)$. The error bars represent 95% confidence interval.

	A1	t1,CLS (ps)	A2	t2,CLS (ps)
1PMe3	0.38 ± 0.02	0.7 ± 0.1	0.17 ± 0.01	16 ± 3
1PMe2Ph	0.34 ± 0.04	0.7 ± 0.1	0.33 ± 0.02	20 ± 4
1PMePh2	0.19 ± 0.03	0.6 ± 0.1	0.48 ± 0.01	21 ± 1
Free ${\text{N}}_3^{-}$	0.40 ± 0.01	1.0 ± 0.1	0.25 ± 0.01	17 ± 2

The CLS reports on the frequency fluctuation dynamics since it is proportional to the normalized FFCF.⁴² In order to extract the FFCF parameters as described in Equation 10, we adopt the method developed by Fayer et al.⁴² Briefly, the FFCF time constants are directly equal to those of the CLS decays; Δ₂ is calculated from A₁, A₂, and the FWHM of FTIR spectra; T₂ and Δ₁ are obtained by fitting the experimental FTIR spectra. A detailed description of this process is given in Section 8 of the SI. The FFCF decay parameters are summarized in Table 4.

Table 4.

FFCF parameters determined from fitting the CLS decay curves and FTIR spectra.

	Γ2 (cm−1)c	T2 (ps)b	Δ1 (cm−1)b	τ1 (ps)a	Δ2 (cm−1)a	τ2 (ps)a
1PMe3	4.7 ± 0.6	2.3 ± 0.3	3.7 ± 0.4	0.7 ± 0.1	2.5 ± 0.1	16 ± 3
1PMe2Ph	4.3 ± 1.0	2.4 ± 0.5	4.2 ± 0.7	0.7 ± 0.1	3.9 ± 0.1	20 ± 4
1PMePh2	4.8 ± 1.4	2.2 ± 0.7	3.3 ± 1.5	0.6 ± 0.1	5.2 ± 0.1	21 ± 1
Free ${\text{N}}_3^{-}$	3.8 ± 1.2	2.8 ± 0.8	4.0 ± 0.7	1.0 ± 0.1	2.9 ± 0.1	17 ± 2

^aThe errors of τ₁, τ₂, Δ₂ are propagated from those in Table 3.

^bThe errors of T₂ and Δ₁ are estimated for the fitting of FTIR spectra with 95% confidence interval.

^cThe error of Γ₂ is propagated from that of T₂. The details of error estimation are included in Section 9 of SI.

Examining Table 4, the variation of frequency fluctuation dynamics among the copper complexes is mostly manifested in the longer timescale decay component, as the homogeneous linewidths as well as the amplitudes and time constants of the fast decay components cannot be distinguished among the copper complexes. The time constant of the slow decay component, τ₂, of 1^PMePh2 is larger than that of 1^PMe3, indicating that an increase in the steric bulk of the ligands leads to a slight decrease in the time constant associated with the local environment fluctuations of the copper-bound azide, though it is important to note that the error bars overlap among the three copper complexes. The main difference among the three copper complexes lies in the amplitude of the slow decay component, Δ₂, which increases from 2.5 cm⁻¹ for 1^PMe3 to 3.9 cm⁻¹ for 1^PMe2Ph and further to 5.2 cm⁻¹ for 1^PMePh2, suggesting that the local environment surrounding the bound azide group has increasing complexity with the addition of phenyl groups. Δ₂ of free ${\text{N}}_3^{-}$ (2.9 cm⁻¹) falls between those of 1^PMe3 and 1^PMe2Ph. As discussed in Section 3.1, the FWHM of FTIR spectra also exhibits an increasing trend in the order of 1^PMe3 < free ${\text{N}}_3^{-}$ < 1^PMe2Ph < 1^PMePh2, consistent with that of Δ₂. This indicates that the difference in the linear spectral broadening results from the increase of the inhomogeneous frequency distribution sampled on the ~20 ps timescale.

The spectral diffusion dynamics of the copper-bound azide can arise from an intermolecular (solvent dynamics) or an intramolecular (molecular structural dynamics) origin. Previous studies have shown that the frequency fluctuations of IR reporters, including azide, embedded in the protein scaffold are associated with the ultrafast reorganization of the protein structure.^59,60 For smaller coordination complexes, evidence for the intramolecular origin of the vibrational frequency fluctuations has also been found.^23,67,83 In the recently-published work in which the ^R3P₃tren-ligated copper complexes were introduced,³³ DFT calculations predicted that the PR₃ groups of the ligands impart local electrostatic fields at the small molecule binding sites of the complexes, with maxima in oriented electrostatic fields arising at ~ 2.2 Å from the copper atom. We note that this distance spatially overlaps with the binding nitrogen of the azide groups in 1^PR3. This observation would suggest that the copper-bound azide group is impacted by the presence of local electrostatic fields emanating from the phosphinimine ligands in the secondary coordination spheres of 1^PR3. Electrostatic field fluctuations can modulate the vibrational frequencies of azide and thus result in the experimentally observed spectral diffusion. The aforementioned increase of Δ₂ with more phenyl groups may therefore arise from a broader distribution of local electrostatic fields introduced by the phenyl substituents, which corresponds to the intramolecular origin of spectral diffusion.

In addition to intramolecular contributions to the spectral diffusion, intermolecular contributions also need to be considered. The molecular structures displayed in Figure 6 show that the copper-bound azide group is not completely shielded by the peripheral phosphine ligands. Thus, it is likely that interactions exist between the solvent molecules and the bound azide group. Furthermore, the frequency correlation time constants of the bound azide are similar to those of the free azide anion. For the longer timescale component, τ₂ of 1^PMe3 and 1^PMe2Ph cannot be differentiated from that of free ${\text{N}}_3^{-}$ within the error range, and τ₂ of 1^PMePh2 is slightly larger than that of free ${\text{N}}_3^{-}$. In previous work it was shown that the spectral diffusion of a monoazide iron complex is much slower than that of the free azide anion,⁶⁷ and the difference in time constants was used to differentiate the intramolecular structural dynamics and solvent reorganization. In the current work, the similarities among the spectral diffusion time constants indicate that solvent dynamics may also play a role in the spectral diffusion processes of the bound azide group. In addition to the intra- and intermolecular contributions, the reorientation of the vibrational probe can also induce changes in the local environment and thus the vibrational frequencies.^84–86 Future work will use molecular dynamics simulations and polarization dependent 2DIR spectroscopy to gain further insight into the underlying mechanisms of the experimentally observed spectral diffusion dynamics.

To summarize our findings from the pump-probe and 2DIR measurements, we find that the additional phenyl groups act to spatially confine the reorientation of azide, while also creating more distinct configurations in the local electrostatic environment sensed by the azide group. Previous work has suggested that the dynamics of reactants and their local environments can create conformations that can facilitate the formation or stabilization of transition states for reactions.^20,87,88 For the copper complexes studied here, the increase in the number of phenyl groups in the supporting ligands introduces additional configurations in the local electrostatic environment, which could potentially be favorable for reactivity. However, the increase in the number of phenyl groups also leads to an increase in the steric bulk of the phosphine ligands, quantified by the cone semiangle parameters from the anisotropy measurements. The increase in steric bulk can prohibit a small molecule from binding to the copper center, which could have a negative impact on reactivity. The reactivity of the current series of copper complexes is still under investigation, and further studies are needed to disentangle the interplay among the different factors.

4. CONCLUDING REMARKS

This work provides a dynamical perspective for examining the structure-function relationship of a series of copper based complexes with varied ligand structures. These copper complexes are structural and electronic analogues of the well-characterized η¹-cupric superoxide complex [(TMG₃tren)CuO₂]⁺,^30–32 which models an important intermediate in a number of biological and synthetic catalytic systems. We investigated the influence of ligand structural variation on the ultrafast equilibrium dynamics of the series of copper complexes using polarization-dependent mid-IR pump probe and 2DIR spectroscopies. An azide group was bound to the copper atom to serve as a vibrational probe of the small molecule binding site. Measurements were also conducted on the free ${\text{N}}_3^{-}$ anion that served as a control.

Vibrational population relaxation and orientational relaxation dynamics of the bound and free azide were measured through pump probe experiments. Compared to free ${\text{N}}_3^{-}$ the population relaxation of the copper-bound azide was faster. We attribute the population relaxation of the bound azide group to intramolecular vibrational energy dissipation. No appreciable difference among the relaxation rates was observed across the three copper complexes indicating that the coupling between the azide group and other intramolecular vibrational modes was not affected by the substituents on the phosphine ligands. The orientational relaxation dynamics were obtained by applying a wobbling-in-a-cone analysis to the anisotropy decay. The spatial restriction of the orientational motion of azide was quantified by the cone semiangle parameters. The cone semiangle associated with the restricted diffusion showed a decreasing trend with increasing phenyl group content, indicating a greater spatial restriction resulted from the steric hinderance of the bulky phenyl groups.

2DIR spectroscopy was used to investigate how changes in the supporting ligand structure affect the ultrafast fluctuations of the local environment in the spatial region where small molecules bind to the metal center. The change in 2D spectral line shape was analyzed with the center line slope (CLS) method and the frequency frequency correlation function (FFCF) was obtained by fitting the CLS decay curve and experimental FTIR spectra. The FFCF has two components, a fast sub-picosecond component and a slower ~20 ps component. The frequency fluctuation range of the slow component increases with more phenyl groups, which suggests that the additional phenyl groups act to create more distinct configurations in the local electrostatic environment surrounding the copper-bound azide group. Future work will further investigate the intra- and intermolecular contributions to the spectral diffusion through molecular dynamics simulations.

To summarize, this work characterizes the effects of ligand structural variation on the relaxation pathways and ultrafast dynamics at the substrate-binding metal center on picosecond timescales. The pump probe and 2DIR measurements combined show that the addition of bulky phenyl groups impacts the local environment sensed by the azide group, making it sterically more “crowded” and electrostatically more inhomogeneous. These changes could impact small molecule binding reactivity in different ways. The reactivity of the Cu^I complexes, for which the 1^PR3 series serve as a model, is still under investigation, and further studies are needed to disentangle the interplay among the various factors that can dictate reactivity, including the redox potential. Though the reactivity is still being investigated, this work provides a detailed characterization of the ultrafast dynamics of 1^PR3, which will help to facilitate a better understanding of the structure-function relationship in the current series of Cu^I complexes, and copper-based catalysts in general.