# Evaluating Spin-Orbit Effects on the Thermochemistry of Proton-Coupled Electron Transfer

Daniel Delony, Arnd Fitterer, Martin Diefenbach, Florian Wätjen, Sandipan Maji, Serhiy Demeshko, Matthias Otte, Milan Orlita, Vera Krewald, Max Holthausen, et al.

► To cite this version:

Daniel Delony, Arnd Fitterer, Martin Diefenbach, Florian Wätjen, Sandipan Maji, et al. Evaluating Spin-Orbit Effects on the Thermochemistry of Proton-Coupled Electron Transfer. Inorganic Chemistry, 2025, 65 (1), pp.791-801. 10.1021/acs.inorgchem.5c05144. hal-05503266

HAL Id: hal-05503266

https://hal.science/hal-05503266v1

Submitted on 10 Feb 2026

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
<figure><img src="image_2.png" /></figure>

# Evaluating Spin-Orbit Effects on the Thermochemistry of Proton-Coupled Electron Transfer

Daniel Delony,⊥ Arnd Fitterer,⊥ Martin Diefenbach, Florian Wätjen, Sandipan Maji, Serhiy Demeshko, Matthias Otte, Milan Orlita, Vera Krewald, Max C. Holthausen,* and Sven Schneider*

<figure><img src="image_3.png" /></figure>

Cite This: *Inorg. Chem.* 2026, 65, 791–801

<figure><img src="image_4.png" /></figure>

Read Online

## ACCESS

<figure><img src="image_5.png" /></figure>

Metrics & More

<figure><img src="image_6.png" /></figure>

Article Recommendations

<figure><img src="image_7.png" /></figure>

Supporting Information

**ABSTRACT:** Many heavy transition metal compounds are active redox catalysts. Their redox potentials can be offset by differential spin-orbit coupling (SOC) effects in the case of strong perturbation of the ground-state energy of the oxidized or the reduced state. However, SOC effects are often considered negligible in the case of organometallic species, anticipating energetically well-separated, nondegenerate spin ground states for metal ions in strong ligand fields with low symmetry. We here report a rhenium(III) aminodiphosphine complex that undergoes proton-coupled electron transfer with a phenoxyl radical as a hydrogen abstractor. Experimental derivation of the PCET thermochemistry shows a deviation from coupled-cluster computations in the range of 6 kcal·mol⁻¹. The deviation can be attributed to a sizable SOC contribution by the amine precursor, which is largely quenched in the rhenium(IV) amido product. Our case study emphasizes potential pitfalls for coupled-cluster benchmarking of the reaction energetics of heavy d-block catalysts.

<figure><img src="image_8.png" /></figure>

## INTRODUCTION

Redox reactions are ubiquitous in biology, energy conversion, and chemical synthesis. Heavy metal catalysts often exhibit intriguing performance with prominent examples spanning commercial water electrolysis (Pt and IrO₂), W-catalyzed molecular N₂ electroreduction, or the recent emergence of bismuth catalysis.¹⁻³ In many—if not most—cases, quantum chemical methods are now routinely applied to elucidate the pertinent electronic structures and reaction mechanisms, which thus necessitate an accurate treatment of relativistic effects.⁴ For instance, Koch and coworkers demonstrated that the thermochemistry of methane activation by bare Pt ions in the gas phase is governed by scalar relativistic effects and spin-orbit coupling (SOC).⁵

Scalar relativistic effects are routinely accounted for in quantum chemistry by using relativistic effective core potentials.⁶ In contrast, the impact of SOC contributions on solution-phase thermochemistry has been examined much less extensively. As a rare reference study, Srnec et al. examined the redox potentials of heavy group 8 complexes by means of multireference computations with perturbational treatment of SOC.⁷,⁸ The authors reported sizable SOC contributions of up to Δ*E*<sub>SOC</sub> ≈ −390 mV (≈−9.0 kcal·mol<sup>−1</sup>) for compounds with idealized *O*<sub>h</sub> symmetry, such as [Os(H<sub>2</sub>O)<sub>6</sub>]<sup>3+/2+</sup>. These effects were attributed to SOC-induced splitting of the degenerate <sup>2</sup>T<sub>2g</sub>(Os<sup>III</sup>) spin ground state into spin-orbit states, whereas the nondegenerate <sup>1</sup>A<sub>1g</sub> state of the Os<sup>II</sup> ion is hardly affected by SOC. In contrast, much smaller SOC contributions were

computed for the [Ru(H<sub>2</sub>O)<sub>6</sub>]<sup>3+/2+</sup> redox couple (Δ*E*<sub>SOC</sub> ≈ −120 mV). Thus, differential SOC contributions of chemical relevance (>1–2 kcal·mol<sup>−1</sup>) can be expected in cases where only one of the two redox states exhibits a degenerate spin ground state.

Strong ligand fields with low symmetry, in turn, may sufficiently isolate the spin ground state and render SOC contributions to the redox potential chemically insignificant. Indeed, SOC effects on the thermochemistry of organometallic reactions are often negligible.⁹⁻¹² For example, we examined proton-coupled electron transfer (PCET) reactions of the hydroxo/oxo couple [Ir<sup>II</sup>(OH){N(CHCHP'Bu<sub>2</sub>)<sub>2</sub>}] and [Ir<sup>III</sup>(O){N(CHCHP'Bu<sub>2</sub>)<sub>2</sub>}] (Scheme 1A).¹³,¹⁴ The square-planar iridium compounds exhibit energetically well-separated <sup>2</sup>A and <sup>3</sup>A ground states, respectively, and therefore a negligible SOC contribution to the PCET thermochemistry. In contrast, the H atom transfer reaction in Scheme 1B appears to be driven by a sizable SOC effect arising from additive contributions of the Ir–H/Ir and the {Re<sup>IV</sup>(NBz)}/ {Re<sup>III</sup>(NHBz)} PCET couples (Δ*E*<sub>SOC</sub> = −8.7 kcal·mol<sup>−1</sup> and −5.8 kcal·mol<sup>−1</sup>, respectively).¹⁵ This computational result

Received: November 2, 2025

Revised: December 7, 2025

Accepted: December 11, 2025

Published: December 22, 2025

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>
**Scheme 1. Examples for Low (A) and High (B) SOC Contributions to PCET Thermochemistry Reported by Our Group<sup>13,15</sup>**

<figure><img src="image_11.png" /></figure>

is somewhat surprising given the low symmetry of the Re complex. The transient nature of the starting states, however, prevented experimental validation. We therefore set out to conduct a benchmarking study with a related system of low molecular symmetry ($C_S$) that undergoes clean H atom transfer with a suitable acceptor, such as the 2,4,6-tris-tert-butylphenoxyl radical (Mes\*O; Scheme 2). Charge-neutral PCET was also chosen<sup>16,17</sup> because its driving force is less sensitive to solvation than that of pure ET reactions, allowing a more robust computational treatment.

**Scheme 2. PCET Reaction Examined in this Study**

<figure><img src="image_12.png" /></figure>

The goal of this case study is to quantify SOC effects on the reaction thermochemistry by comparing isothermal titration calorimetry (ITC) data to high-level quantum-chemical results. For the full molecular systems, we employed DLPNO-CCSD(T₁) theory as the most rigorous method feasible at this scale. Refined energies were obtained through an ONIOM single-point extrapolation incorporating explicitly correlated CCSD(T\*)-F12 results for the truncated Re(PNP) core and unsubstituted phenol. These calculations, denoted CCONIOM in the following text, include only spin-free relativistic effects via an effective core potential for Re. SOC contributions are not captured in this treatment but were evaluated independently using multiconfigurational CASSCF/NEVPT2/QDPT theory.

In the following, we first assess the ground-state electronic structures of PCET couples **1a** and **2a** as a computational benchmark. We then compare the experimentally and quantum-chemically derived PCET driving forces to isolate and quantify the SOC contribution to the reaction thermochemistry.

## ■ RESULTS AND DISCUSSION

**Spectroscopic Characterization of the Precursors.** We recently reported the synthesis of the rhenium(III) complexes $[ReX_3(^{H}PNP)]$ (X = Cl (**1a**), Br (**1b**); $^{H}PNP = HN$(CH₂CH₂PPr₂)₂; Scheme 2) as precursors for reductive N₂ splitting.<sup>18,19</sup> The paramagnetically shifted ($\delta_{31P}$ = -1526 (**1a**), 1488 (**1b**) ppm) yet sharp NMR signals are typical for high-spin rhenium(III) due to rapid electronic relaxation.<sup>20,21</sup> The

chemical shifts exhibit little temperature dependence except for the N-H protons, presumably due to hydrogen bonding with the solvent. All others approximately scale linearly with temperature ($\delta \propto T$, Figure S12), as was previously reported for ReIII complexes.<sup>22-24</sup> While Curie behavior of the isotropic shielding ($\delta \propto T^{-1}$) is expected for S = 1/2 systems,<sup>25</sup> higher inverse order temperature dependence can arise for higher spin states with large axial zero-field splitting (D) and g-anisotropy.<sup>26</sup> The small and linear temperature dependence observed for **1a/b** supports a thermally isolated ($\Delta E \gg k_B T$), nonmagnetic ground state with excited state admixture in the magnetic field that leads to second-order (Van Vleck) paramagnetism.

This electronic structure picture from NMR is confirmed by magnetic measurements in the solid state (Figures 1a and S13). The room-temperature magnetic moments of **1a/b** ($\mu_{eff}^{298K}$ = 1.60 $\mu_B$) are significantly smaller than the S = 1 spin-only values and are in the typical range for octahedral ReIII complexes. Temperature-independent magnetic susceptibility (TIP; $\chi_M/cm^3 \cdot mol^{-1}$ = 1063 × 10⁻⁶ (**1a**), 1083 × 10⁻⁶ (**1b**) is observed over the full range and is typical for octahedral 5d⁴ complexes (ReIII, OsIV).<sup>21,27-30</sup>

The electronic absorption spectra show dominating charge-transfer bands around 25,000 cm⁻¹ (**1a**: $\epsilon$ = 1.2 × 10³ M⁻¹cm⁻¹; Figure 1b). In addition, several weak NIR bands ($\epsilon$ < 50 M⁻¹cm⁻¹) were found, which extend all the way to the mid-IR (3510 (**1a**) and 3462 (**1b**) cm⁻¹), next to the sharper C-H (~2900 cm⁻¹) and N-H (~3200 cm⁻¹) vibrational transitions (Figure 1c).<sup>31</sup> Ligand-field bands in the IR range were previously reported for mer-ReIII$X_3L_3$ trisphosphine complexes.<sup>32,33</sup> For **1a**, this assignment was confirmed by magnetic IR spectroscopy, exploiting the magnetic field dependence of states with $|M_j| > 0$. The feature at ~3500 cm⁻¹ exhibits a rising intensity in the normalized transmission plots ($T_B/T_0$), confirming its origin from an electronic transition.

We previously reported that the rhenium(IV) amido complex $[Re^{IV}Cl_3(PNP)]$ (**2a**) results from PCET of **1a** with Mes\*O as a hydrogen atom acceptor (Scheme 2).<sup>18</sup> In analogy, the bromo complex **2b** is obtained from **1b** and Mes\*O in 63% isolated yield. The room-temperature magnetic moments of **2a** and **2b** ($\mu_{eff}^{298K}$ = 1.86 $\mu_B$ and 1.84 $\mu_B$, respectively) are larger than those of the parent **1a/b** and relatively close to the spin-only value for a doublet ground state (1.73 $\mu_B$). Accordingly, the temperature-dependent magnetic data (Figures 1a and S14) could be fitted for low-spin (S = 1/2) ground states ($g_{av}$ = 1.94 (**2a**), 2.00 (**2b**) with pronounced, yet much smaller TIP ($\chi_M/cm^3 \cdot mol^{-1}$ = 275 × 10⁻⁶ (**2a**), 870 × 10⁻⁶ (**2b**) compared to **1a/b**. This finding suggests a smaller perturbation of the spin ground state by SOC. Spectroscopic characterization also showed electronic transitions in the mid-IR range at significantly lower energy (1967 (**2a**) and 1861 (**2b**) cm⁻¹).

**Electronic Structure Calculations.** CCONIOM calculations on **1a** establish an electronic triplet ground state with a sizable adiabatic gap to the lowest singlet state ($\Delta E_{S-T}$ = 4.2 kcal·mol⁻¹). State-averaged CASSCF(14,10)/NEVPT2 calculations uncover an accidental near-degeneracy of the two lowest lying d orbitals, $d_{xy}$ and $d_{yz}$, which together host 3 electrons. Consequently, the multireference picture produces the two lowest triplet states that are separated by merely 124 cm⁻¹, each dominated by linear combinations of the
<figure><img src="image_13.png" /><figcaption>**Figure 1.** Magnetic and spectroscopic data. (a) SQUID magnetometry data of **1a** (left) and **2a** (right) at 0.5 T: experimental data (black circles), simulation data (red/blue lines with simulation parameters), and *ab initio* data (orange/turquoise lines). (b) UV-vis/NIR spectra of **1a** (left) and **2a** (right): experimental data in THF (black) and *ab initio* computed data (yellow, Gaussian line broadening set to fwhm = 1500 cm⁻¹, *y*-values scaled by 0.2). (c) Expansion of the IR spectrum of **1a** (top) and field-dependent IR spectra (bottom) at 4.2 K is shown as transmission spectra at applied field (*T*<sub>B</sub>) divided by the zero-field spectrum (*T*<sub>0</sub>).</figcaption></figure>

($d_{xy}$)$^2$(d$_{yz}$)$^1$(d$_{xz}$)$^1$ and (d$_{xy}$)$^1$(d$_{yz}$)$^2$(d$_{xz}$)$^1$ configurations (see *Supporting Information* for further detail).

The accidental quasi-degeneracy of the two lowest triplet states represents a “quasi-³E” spin ground state, even in a low symmetry field. Thus, sizable SOC effects are to be expected.⁷ The ground state can be derived from the parent Re<sup>III</sup> in an octahedral ligand field (O<sub>h</sub>). Its ³T<sub>1g</sub> spin ground state is expected to split by large SOC (z<sub>Re(III)</sub> = -2500 cm<sup>-1</sup>) to give an isolated J = 0 spin-orbit ground state.³⁴ The higher spin-orbit levels are further split in lower symmetry. For example, tetragonal distortion (C<sub>4</sub>) gives rise to six microstates that originate in ³E (e<sup>3</sup>b<sup>1</sup>) and ³A (b<sup>2</sup>e<sup>2</sup>) orbital states, respectively.³⁰ In the case of **1a** (C<sub>s</sub>), SOC effects evaluated by CASSCF(14,10)/NEVPT2/QDPT result in a large splitting of the multireference eigenstates (Figure 2). The spin-orbit ground state is composed of the two lowest triplet states and is strongly stabilized with respect to the NEVPT2 states (ΔE<sub>SOC</sub> = -3424 cm<sup>-1</sup> = -9.8 kcal·mol<sup>-1</sup>; Table S17). The influence of ligand field distortions on ΔE<sub>SOC</sub> was probed by

symmetrically displacing the axial halide ligands of **1a** and **2a** by ±0.05 Å along the Re–Cl bonds. ΔE<sub>SOC</sub> varies only marginally for **1a** and slightly more for **2a** (Table S21). However, the magnitude of ΔΔE<sub>SOC</sub> remains within a rather narrow range (4.2–6.7 kcal·mol<sup>-1</sup>), indicating that the spin-state near-degeneracy is lifted predominantly by SOC rather than by Jahn–Teller distortion.

CC<sup>ONIOM</sup> calculations on the rhenium(IV) complex **2a** establish a metal-centered doublet ground state that lies well below the quartet state (ΔE<sub>D–Q</sub> = -8.3 kcal·mol<sup>-1</sup>). This stabilization arises from strong π-donation by the amido ligand, reflected in the pronounced shortening of the Re–N bond compared to that in **1a** (Δd<sub>PBE0</sub> = 0.28 Å; Δd<sub>exp</sub> = 0.26 Å).¹⁸ Consequently, the d<sub>xz</sub> orbital is increased in energy, thereby strongly favoring a low-spin configuration. CASSCF(15,11)/NEVPT2 calculations corroborate a doublet ground state dominated by the (d<sub>xy</sub>)<sup>2</sup>(d<sub>yz</sub>)<sup>1</sup> configuration (82%). The first excited doublet state lies considerably higher in energy, at 1511 cm<sup>-1</sup> (Figure 2).³⁵ QDPT evaluation of SOC-induced state
<figure><img src="image_14.png" /><figcaption>**Figure 2.** CASSCF/NEVPT2/QDPT state correlation diagram for the lowest-lying states of **1a** (left) and **2a** (right). Spin-orbit coupling (SOC) stabilization energies are indicated with blue bars, and electronic excitations with significant oscillator strength are indicated with green arrows. The larger SOC-induced splitting of the almost degenerate triplet ground state of **1a** affords additional stabilization relative to the less SOC-stabilized doublet ground state of **2a**, thereby offsetting the driving force for the PCET process.</figcaption></figure>

mixing reveals a ground-state stabilization of $\Delta E_{SOC} = -1264 \text{ cm}^{-1}$ ($-3.6 \text{ kcal} \cdot \text{mol}^{-1}$), which is notably smaller than for **1a**.

The CASSCF/NEVPT2/QDPT computations reproduce the experimental magnetic and spectroscopic data for **1a** and **2a** reasonably well (Figure 1 and Table 1). Notably, the

<table><caption>**Table 1.** Spectroscopic and Magnetic Data of **1a** and **2a**: Comparison of Experimental and CASSCF/NEVPT2/QDPT Computed Data</caption><thead><tr><th rowspan="2"></th><th colspan="2">1a</th><th colspan="2">2a</th></tr><tr><th>Experiment<sup>a</sup></th><th>QDPT<sup>b</sup></th><th>Experiment<sup>a</sup></th><th>QDPT<sup>b</sup></th></tr></thead><tbody><tr><td>μ<sub>eff,RT</sub> (μ<sub>B</sub>)</td><td>1.60</td><td>1.52</td><td>1.86</td><td>1.84</td></tr><tr><td rowspan="2">UV/vis (cm<sup>-1</sup>)</td><td>24876 (1238)</td><td>26808</td><td>30030 (4446)</td><td>33136</td></tr><tr><td>19120 (31)</td><td>20825</td><td>19231 (934)</td><td>21391</td></tr><tr><td rowspan="3">NIR (cm<sup>-1</sup>)</td><td>9336 (9)</td><td>10790</td><td rowspan="3">5861 (30)</td><td rowspan="3">6651</td></tr><tr><td>6418 (7)</td><td>7700</td></tr><tr><td>5627 (22)</td><td>5063</td></tr><tr><td>IR (cm<sup>-1</sup>)</td><td>3510 (n.d.)</td><td>3592</td><td>1967 (n.d.)</td><td>2422</td></tr></tbody></table>

<sup>a</sup>ε in M<sup>-1</sup> cm<sup>-1</sup> in parentheses. <sup>b</sup>Selected transitions with significant f<sub>osc</sub>.

quantum chemical analysis suggests that the experimental IR feature at 3510 cm<sup>-1</sup> provides, albeit fortuitously, a measure of $\Delta E_{SOC}$ for **1a**, which we can directly relate to the computed value of 3592 cm<sup>-1</sup> (2% deviation).

**PCET Thermochemistry: Experimental Determination.** The electronic structure characterization indicates a sizable differential SOC contribution to hydrogen abstraction from **1** of around $\Delta E_{SOC} = -6.2 \text{ kcal} \cdot \text{mol}^{-1}$ (Scheme 2). This magnitude can be relevant for chemical reactivity and is well beyond the error margins of solution-phase thermochemical methods. For benchmarking, two independent approaches were pursued to derive the reaction energetics with the

reference hydrogen acceptor Mes\*O (Scheme 2; $BDFE_{O-H}(Mes\*OH) = 74.4 \text{ kcal} \cdot \text{mol}^{-1}$ in THF).¹⁷

On one hand, the N-H bond dissociation free energy of **1** ($BDFE_{N-H}$) can be derived via Bordwell's equation (eq 1), which refers to a Hess cycle (“square scheme”) that breaks down the formal driving force for N-H dissociation into electron and proton transfer contributions ($E^0$, pK<sub>a</sub>), as well as the solvent-dependent free energy of the hydrogen atom ($C_G$).¹⁶

$$BDFE = 23.06 \cdot E^0 + 1.37 \cdot pK_a + C_G \quad (1)$$

From there, the free reaction energy for H-transfer to Mes\*O ($\Delta_G^0$) is easily calculated for comparison with computations. On the other hand, the selective reaction of **1** with Mes\*O directly enables thermochemical analysis by isothermal titration calorimetry (ITC).¹³,³⁶,³⁷ Note that ITC offers reaction enthalpies ($\Delta_r H^0$), thus eliminating the computational uncertainties that are associated with estimating the reaction entropy.

The Re<sup>III</sup> amine complexes **1a/b** exhibit reversible 1e<sup>-</sup> oxidations in the cyclic voltammogram (THF) at $E^0 = -0.29$ (1a) and 0.22 (1b) ± 0.01 V.³⁸ The small anodic shift for the exchange of chloride with bromide ($\Delta E^0 = 0.07$ V) is in line with Lever's electrochemical ligand parameters (3·ΔE<sub>L</sub> = 0.06 V)³⁹ and is much less pronounced than for the five-coordinate Re<sup>III</sup> dihalide amido complexes [$ReX_2\{N(CH_2CH_2PtBu_2)_2\}$] (X = Cl, Br, I).⁴⁰ The rhenium(IV) reaction products, [$ReX_3\{H^+PNP\}]^+$ (X = Cl (3a), Br (3b)), were prepared by chemical oxidation of **1a/b** with AgBAr<sup>F</sup><sub>24</sub> (1a; BAr<sup>F</sup><sub>24</sub><sup>-</sup> = B{C<sub>6</sub>H<sub>3</sub>(3,5-CF<sub>3</sub>)<sub>2</sub>}<sub>4</sub><sup>-</sup>) and [FeCp<sub>2</sub>]BAr<sup>F</sup><sub>24</sub> (1b), respectively, in yields around 75%. **3a/b** were fully characterized including crystallography (see Supporting Information). pK<sub>a</sub>(N-H) determination of **3a/b** in THF was carried out by ITC titration with pyridine (3a) and lutidine (3b) as reference bases, respectively. Clean formation of the amide complexes **2a/b** was confirmed spectroscopically by NMR. Using the reported pK<sub>a</sub> values of pyridine (5.5) and lutidine (7.2) in THF,⁴¹ fitting of the thermogram gave pK<sub>a</sub> values of 5.3 ± 0.1 (3a) and 6.3 ± 0.1 (3b), respectively. From this data, eq 1 gives $BDFE_{N-H}$ values of 60.5 ± 2.4 (1a) and 63.5 ± 2.4 (1b) kcal·mol<sup>-1</sup> (Scheme 3), using the free energy of the hydrogen atom in THF recommended by Mayer and coworkers ($C_G = 59.9 \text{ kcal} \cdot \text{mol}^{-1}$).¹⁷ Thus, free reaction energies for PCET with

<figure><img src="image_15.png" /><figcaption>**Scheme 3.** PCET Square Scheme of **1a/b** in THF</figcaption></figure>
Mes\*O (Scheme 2) in THF of $\Delta_r G^0 = -13.9 \pm 2.6$ (1a) and $-10.9 \pm 2.6$ (1b) kcal·mol⁻¹ are derived.

In the alternative approach, ITC titration with Mes\*O was carried out in the less polar solvent dichloromethane, further reducing the propensity for hydrogen bonding with the solvent. In addition, titration in THF led to significant tailing and baseline shifts in the thermograms, indicating an underlying slower side reaction. Synthetic examination of 1a confirmed partial overoxidation by Mes\*O in THF due to dehydrogenation of the pincer backbone to give the Re¹¹³Imine complex [ReCl₃{N(CHCl₂PiPr₂)(CH₂Cl₂PiPr₂)}] as a side product.¹⁸ Unfortunately, tailing of the thermogram trace was also observed for the titration of 1b in dichloromethane. ITC results for 1b were therefore discarded. Titration of 1a in CH₂Cl₂ revealed a reaction enthalpy of $\Delta_r H^0 = -12.2 \pm 0.1$ kcal·mol⁻¹ (Scheme 4). The exothermic character of the reaction prevented meaningful fitting of the thermogram for the derivation of $\Delta_r G^0$.

<figure><img src="image_16.png" /><figcaption>**Scheme 4.** Calorimetric Titration Experiment for the PCET Reaction of 1a with Mes\*O in Dichloromethane</figcaption></figure>

Notably, the experimental values of $\Delta_r G^0$ in THF and $\Delta_r H^0$ in dichloromethane obtained from the two approaches for 1a are identical within error. This observation is in line with findings from Mayer et al. that (a) entropic contributions to the hydrogen transfer thermochemistry nearly cancel in the absence of major spin changes that affect the vibrational entropy and (b) BD(F)Es generally exhibit low solvent dependence.<sup>17,42,43</sup>

**PCET Thermochemistry: Quantum-Chemical Evaluation.** Based on a H-truncated model system, we performed a series of benchmark calculations to establish the accuracy that can be expected from our computational approach. Comparison of extrapolated CCSD(T\*-)-F12/CBS(DT) results obtained with HF, PBE0, and BP86 reference wave functions for spin-state splittings in 1a\*model and 2a\*model, the PCET reaction energy $\Delta E_r$, and the homolytic dissociation energies $\Delta E_{N-H}$ (1a\*model) and $\Delta E_{O-H}$ (phenol) show an overall agreement within 0.8 kcal·mol⁻¹ (cf. Table S9). None of the usual coupled-cluster diagnostics indicated any alarming problem; thus, the use of KS reference wave functions provides no obvious advantage. We therefore chose the HF-based CCSD(T\*-)-F12/CBS(DT) data as a reference for further comparison and for use within the ONIOM extrapolation discussed further below. Against this data, DLPNO-CCSD(T₁)/CBS(DT)/CPS(S6) results show non-negligible deviations between 0.7 and 2.1 kcal·mol⁻¹ for the spin-state splittings and the O-H dissociation energies, while the reaction energy benefits from error compensation. Notably, neither improvement of the extrapolated basis sets, nor of the PNO thresholds, nor the use of KS reference wave functions leads to consistently better agreement with the CCSD(T\*-)-F12/CBS(DT) reference data (Table S9). For improved results,

we thus chose the ONIOM approach, which we tested favorably for spin-state splittings (cf. Section S6.3 in the Supporting Information).

After inclusion of thermochemical contributions from the DFT Hessian analyses to the CCONIOM results, we obtain a reaction enthalpy of $\Delta H_r = -18.4$ kcal·mol⁻¹ and upon inclusion of SOC effects, $\Delta H_{r\,SOC} = -12.2$ kcal·mol⁻¹, matching perfectly the experimental value ($-12.2 \pm 0.1$ kcal·mol⁻¹). With $\Delta H_r = -18.0$ kcal·mol⁻¹ and $\Delta H_{r\,SOC} = -11.8$ kcal·mol⁻¹, the DLPNO-CCSD(T₁)/CBS(DT)/CPS(S6) results also show pleasing agreement, demonstrating consistency of the chosen computational protocols. Our results illustrate the chemical significance of the SOC effect ($\Delta\Delta E_{r\,SOC} = -6.2$ kcal·mol⁻¹), which contributes 51% to the overall PCET driving force.

## ■ CONCLUSIONS

This combined experimental and computational benchmark study demonstrates a sizable SOC offset to the PCET thermochemistry of our heavy d-block model complex by more than 6 kcal·mol⁻¹. The large differential relativistic effect on the PCET thermochemistry can be ascribed to the accidental near-degeneracy of the two lowest spin configurations of amine complex 1a, which is lifted by SOC. In turn, the rhenium(IV) PCET product 2a exhibits an energetically isolated spin ground state due to the strong π-donation of the amido ligand. The spin-orbit ligand field transitions of 1a and 2a in the IR spectrum can serve as spectroscopic indicators and reliable benchmark data for computational treatment. ONIOM-based coupled-cluster and DLPNO-CC approaches in combination with CASSCF/NEVPT2/QDPT theory were calorimetrically validated as reliable protocols for computational treatment with high accuracy. Notably, despite the low molecular symmetry of 1a and 2a (C₈), the SOC contribution to PCET is remarkably close to that predicted by Srnec et al. for the redox potentials of O₂ symmetric 5d complexes ($\Delta E_{r\,SOC} \approx -390$ mV = $-9.0$ kcal·mol⁻¹).⁷ Our study, thus, emphasizes that chemically significant SOC effects on the thermochemistry of heavy metal ions can be preserved in strong ligand fields with low symmetry and need to be considered for accurate computational treatment of redox reactions.

## ■ EXPERIMENTAL SECTION

**Experimental Procedures.** All experiments were carried out using standard Schlenk or glovebox techniques under an argon atmosphere. Solvents were dried by passing them through columns packed with activated alumina. In addition, THF, benzene, toluene, and pentane were dried over Na/K alloy, distilled by trap-to-trap transfer *in vacuo*, and degassed by three freeze-pump-thaw cycles. 2,4,6-Tris(tert-butyl)-phenoxyl radical (Mes\*O), [ReCl₃(HPNP)] (1a), and [ReBr₃(HPNP)] (1b) were synthesized according to published procedures.<sup>18,19,44 AgBrF<sub>24</sub> and [FeCp<sub>2</sub>]BrF<sub>24</sub> were purchased from Merck and used without further purification.

Magneto FIR experiments were conducted in the transmission configuration, using the Faraday geometry, where the Poynting vector is parallel to the static magnetic field (P||B₀). 1a was ground in a mortar with eicosane in an approximate ratio of 1:8 and then pressed into pellets. These pellets were placed in a superconducting magnet and kept at T = 4.2 K in exchange helium. Then, THz/infrared radiation from a globar was analyzed by a Vertex 80 V FTIR spectrometer, delivered
using light-pipe optics to the pellet, and detected by a composite bolometer placed just beneath the pellet. Test spectra were recorded, and the pellets were diluted until the strongest absorptions in the 10–100 cm⁻¹ region were between 1 and 5% transmittance. Variable-field spectra between 0 and 16 T were then recorded at the optimal pellet concentration. Background corrections were applied by recording blank reference spectra at the same magnetic fields and taking the ratio of the sample to the reference spectrum at each field. In variable-field maps, the background-corrected transmission spectra were plotted in the form of relative magneto transmission using a differential averaging method developed for emphasizing the field-induced spectral features. The treatment was carried out using the custom-made tool FieldOptic.⁴⁵ All other IR spectra were recorded with a Bruker Alpha Platinum ATR-IR spectrometer. UV/vis NIR measurements and NMR spectra were measured with a Bruker Avance III HD 400 spectrometer.

Isothermal titration calorimetry was performed with a TA Instruments NanoITC calorimeter equipped with a 24K gold cell with a sample volume of 1 mL, operated in overfill mode, and controlled by the ITCRun software version 3.4.6.0. The obtained data were evaluated by the implemented Nano-Analyze software.

Temperature-dependent magnetic susceptibility measurements were carried out with a Quantum Design MPMS-XL-5 SQUID magnetometer equipped with a 5 T magnet in the range from 295 to 2.0 K at a magnetic field of 0.5 T. The freshly isolated crystalline samples were contained in a PTFE bucket and fixed in a nonmagnetic sample holder. Each raw data file for the measured magnetic moment was corrected for the diamagnetic contribution of the PTFE bucket according to $M_{dia}(bucket) = \chi_g \cdot m \cdot H$, with an experimentally obtained gram susceptibility of the PTFE bucket. The molar susceptibility data were corrected for the diamagnetic contribution according to $\chi_M^{dia}(sample) = -0.5 M \times 10^{-6} \text{ cm}^3 \cdot \text{mol}^{-1}$.⁴⁶ Paramagnetic impurities (PI) with $S = 1/2$ were included according to $\chi_{calc} = (1 - \text{PI}) \chi + \text{PI} \cdot \chi_{mono}$. Experimental $\chi_M T$ vs $T$ data were modeled with the julX program.⁴⁷ The following Hamiltonian was used for fitting the experimental data:

$$ \hat{H} = g\mu_B\vec{B}\vec{S} + D(\vec{S}_z^2 - 1/3S(S+1)) \quad (2) $$

**Syntheses.** [ReCl₃(PNP)](d₁-1). [ReCl₃(PH₃NP)](1) (6.0 mg, 10.0 µmol, 1.0 equiv) is suspended in a DCM/D₂O mixture (0.4 mL/0.1 mL) and stirred overnight. Afterward, the solvent is removed in vacuo, and the spectroscopically clean product [ReCl₃(PH₃NP)](1-d) is measured in CD₂Cl₂. The NMR spectra show signals largely identical to those of 1. The signal corresponding to the NH proton is largely gone (~2% remaining), and the signals at $\delta_{1H} = -5.10$ and $-10.44$ ppm exhibit different coupling patterns. ²H NMR (46.1 MHz, CD₂Cl₂, 25 °C): $\delta$ (ppm) = 152.6 (s, ND). $\text{IR}$ (cm⁻¹) = 3506 (br, electronic absorption), 2363 ($\nu_{ND}$).

[ReBr₃(PNP)](2b). A solution of Mes*O (14.4 mg, 55.2 µmol, 1.1 equiv) in benzene is slowly added to a suspension of 1b (30.0 mg, 50.2 µmol, 1.0 equiv) in benzene. Stirring for 1 h at room temperature results in a deep red solution. The solvent is removed in vacuo, and the crude product is washed with pentane four times. Extraction with benzene and evaporation of the solvent give the product as a purple solid in 63% yield. ¹H NMR(C₆D₆): $\delta$ (ppm) = 21.06 (br, 2H), 18.53 (12H), 16.22 (12H), -2.41 (br, 3H). Anal. Calc. for C₁₆H₃₆Br₃NP₂Re

(729.94): C 26.31, H 4.97, N 1.92; Found: C 26.20, H 4.74, N 1.89. LIFDI: m/z (%) = 729.9 (100)

[ReCl₃(PNP)]BrArF²⁴ (3a). To a suspension of 1a (50.0 mg, 86.6 µmol, 1.00 equiv) in PhCl (10 mL), a solution of AgBrArF²⁴ (79.4 µmol, 0.95 equiv) in PhCl (10 mL) is added dropwise. The solution is filtered, and the residue is extracted with a small amount of PhCl. Pentane (20 mL) is added to the solution to precipitate the product. The solution is filtered, and the residue is washed with a small amount of pentane and extracted with a small amount of DCM (~1 mL). Gas-phase layering with pentane yields the product as deep red crystals suitable for single-crystal analysis (53.3 mg, 63.6 µmol, 76%). ¹H NMR (DCM-d₂): $\delta$ (ppm) = 34.3 (2H), 31.7 (6H), 31.1 (6H), 31.0 (6H), 27.0 (6H), 11.7 (2H), -4.6 (2H), -11.0 (2H), -80.4 (2H), -104.9 (2H), N-H not found. Anal. Calc. for C₄₈H₄₉ClCl₃F₂₄NP₂Re: C 39.46, H 3.38, N 0.96; Found: C 40.02, H 3.33, N 0.93. ATR-IR: $\nu$(N-H) = 3212 cm⁻¹.

[ReBr₃(PNP)]BrArF²⁴ (3b). To a solution of 1b (30.0 mg, 41.0 µmol, 1.0 equiv) in DCM (5 mL), a solution of [FeCp₂]BrArF²⁴ (41.3 mg, 39.4 µmol, 0.96 equiv) in DCM (5 mL) is added dropwise. After 15 min of stirring, the solvent is removed under vacuum. The residue is washed with pentane (5 × 2 mL) and extracted with ether. Removal of the solvent yields the product as a reddish-purple solid (48.4 mg, 30.3 µmol, 74%). Slow evaporation in a pentane solution gave needle-shaped crystals suitable for XRD. ¹H NMR (THF-d₈): $\delta$ (ppm) = 71.1 (N-H), 39.1 (6H), 35.9 (14H), 34.4 (6H), 16.1 (2H), 7.3 (2H), -13.4 (2H), -79.6 (2H), -89.0 (2H). Anal. Calc. for C₄₈H₄₉BrBr₃F₂₄NP₂Re: C 36.16, H 3.10, N 0.88; Found: C 36.67, H 3.30, N 0.91

## COMPUTATIONAL METHODS

**DFT Calculations.** Using the Gaussian 16 program,⁴⁸ geometry optimizations on the full molecular models were performed employing the PBE0 hybrid density functional⁴⁹ in combination with the D3 dispersion correction⁵⁰ with Becke-Johnson damping⁵¹ and the def2-TZVP orbital basis set,⁵² including a quasi-relativistic 60-electron pseudopotential for rhenium.⁵³ Zero-point vibrational energies, thermal and entropy contributions to obtain enthalpies, and Gibbs free energies were obtained from Hessian analyses as implemented in Gaussian 16.

**DLPNO-CCSD(T₁) Calculations.** Based on DFT-optimized geometries, local coupled-cluster single-point energies were computed with the ORCA 6.0.1 program,⁵⁴⁻⁵⁶ using the domain-based local-pair natural orbital (DLPNO) approach⁵⁷,⁵⁸ with improved iterative triples,⁵⁹ DLPNO-CCSD(T₁). Very tight SCF settings and tight PNO default settings were applied without full LMP2 guess to ensure consistency for closed-shell and open-shell calculations. Following Altun et al.,⁶⁰ two-point extrapolation to the complete pair natural orbital space (CPS) limit was performed using the Schwenke-style relation⁶¹

$$ E^{\infty} = E^{X} + F(E^{Y} - E^{X}) \quad (3) $$

where $Y = X + 1$ and, in the CPS extrapolation context, $E^X$ and $E^Y$ are the correlation energies obtained with the corresponding $T_{\text{CutPNO}}$ thresholds $10^{-X}$ and $10^{-Y}$ and $F = 1.5$ for both CPS(S6) and CPS(67) extrapolations. The same ansatz was used for two-point extrapolations to the complete basis set (CBS) limit separately for the reference energy and the correlation energy, employing the def2-SVP ($X = 2$), def2-
TZVPP (X = 3), and def2-QZVPP (X = 4) basis sets (the cardinal numbers are referred to below as D, T, and Q).⁵² For extrapolation of the reference energy, an exponential functional form of the type

$$E^X = E^{\text{CBS}} + A \cdot e^{\alpha \sqrt{X}} \quad (4)$$

was assumed as originally proposed by Karton and Martin.⁶² This results in the following expression for the two-point CBS extrapolated energy,⁶⁰

$$E_{\text{ref}}^{\text{CBS}} = \frac{e^{\alpha \sqrt{Y}} \cdot E_{\text{ref}}^{Y} - e^{\alpha \sqrt{X}} \cdot E_{\text{ref}}^{X}}{e^{\alpha \sqrt{Y}} - e^{\alpha \sqrt{X}}} \quad (5)$$

or, equivalently, in eq 3 with a factor F of

$$F_{\text{ref}} = \frac{e^{\alpha \sqrt{Y}}}{e^{\alpha \sqrt{Y}} - e^{\alpha \sqrt{X}}} \quad (6)$$

Use of exponents α optimized by Neese and Valeev⁶³ for the Ahlrichs basis set family results in $F_{\text{ref}}^{\text{DT}} = 1.038203$ and $F_{\text{ref}}^{\text{TQ}} = 1.137739$. For CBS extrapolation of the correlation energy, we used the functional expression proposed by Truhlar⁶⁴

$$E^X = E^{\text{CBS}} + B \cdot X^\beta \quad (7)$$

which leads to a two-point CBS extrapolation energy

$$E_{\text{corr}}^{\text{CBS}} = \frac{X^{\beta} \cdot E_{\text{corr}}^{X} - Y^{\beta} \cdot E_{\text{corr}}^{Y}}{X^{\beta} - Y^{\beta}} \quad (8)$$

This is equivalent to eq 3 with

$$F_{\text{corr}} = \frac{Y^{\beta}}{Y^{\beta} - X^{\beta}} \quad (9)$$

and, with optimized exponents β,⁶³ $F_{\text{corr}}^{\text{DT}} = 1.607468$ and $F_{\text{corr}}^{\text{TQ}} = 1.740740$. DLPNO-CCSD(T₁)/CBS(DT)/CPS(56) extrapolated calculations were feasible for the full molecular systems, while extrapolated CBS(TQ)/CPS(67) results were obtained for truncated molecular models. Detailed benchmark results against CBS extrapolated CCSD(T*)-F12 data are provided as Supporting Information. In a recent study, Aoalsteinsson and Bjørnsson⁶⁵ observed unsatisfactory performance of reference energy CBS extrapolation schemes for DLPNO-CCSD calculations using KS-DFT reference wave functions. They tentatively related this finding to the nonself-consistent nature of the HF reference energies evaluated on KS wave functions and therefore used the reference energy obtained with the larger basis set instead. We note in this context, that the current DLPNO-CCSD implementation in ORCA routinely applies a QRO transformation⁵⁸ for all unrestricted reference orbitals prior to the coupled-cluster calculation. Thus, QRO-transformed reference energies for open-shell cases are generally nonself-consistent whenever UHF or UKS reference orbitals are used (cf. Table S10). While this might raise some concern as to the generalizability of CBS extrapolation schemes for DLPNO-CCSD reference energies, we find no significant differences in pertinent test calculations (Table S11).

**CCSD(T*)-F12b Calculations.** For benchmarking and ONIOM calculations (cf. below) on truncated smaller molecular models, explicitly correlated coupled-cluster CCSD(T*)-F12b⁶⁶ single-point energy calculations with the cc-

pV{D,T}Z-F12⁶⁷ (aug-cc-pV{D,T}Z-PP for Re)⁶⁸ basis sets were performed with MOLPRO 2024.⁶⁹⁻⁷¹ Perturbative triples contributions improved toward the complete basis set limit via F12-scaling⁷² and denoted as (T*), were obtained by employing the scale factor $E_{\text{corr}}(\text{MP2-F12})/E_{\text{corr}}(\text{MP2})$. The corresponding triple-ζ auxiliary fit basis sets were used, i.e., the JKfit set⁷³ for the Fock and exchange integrals, the MP2fit⁷⁴ set for density fitting, and the OptRI set⁷⁵,⁷⁶ for nonmetal atoms along with the triple-ζ JKfit set for Re for the construction of the complementary auxiliary basis set (CABS). For open-shell cases, we used the ROHF/UCCSD(T*)-F12b implementation in MOLPRO ("rhf; uccsd(t)-f12").⁷⁷ Following Hill et al.,⁷⁸ CCSD and (T*) correlation energy contributions were extrapolated separately to the complete basis set limit employing eq 3 with $F_{\text{CCSD}}^{\text{DT}} = 1.387834$ and $F_{(T*)}^{\text{DT}} = 1.529817$.

Because CASSCF/NEVPT2/QDPT calculations indicated pronounced near-degeneracy effects in the electronic structure of 1a (see above), we performed additional CCSD(T*) calculations employing PBE0 and BP86 reference wave functions.⁷⁹ However, only minor differences in relative energies result, and in none of the calculations the usual diagnostics (J₁, t₁, and t₂ amplitudes) signaled alarm, indicating that the QDPT near-degeneracy is accidental in nature. In this context, we noted an inconsistency with the default settings in the CCSD(T*)-F12b implementation in MOLPRO, at least up to version 2024.2: For closed-shell cases, the use of density fitting in the MP2-based evaluation of the CABS contributions is switched off if KS references are used, whereas the unrestricted coupled-cluster code does use density fitting in this case. This led to substantial inconsistencies of up to 5 kcal·mol⁻¹ in computed ROKS-UCCSD(T*)-F12 results, originating in the CABS correction to the reference energy. For consistent results, we thus used the ROKS/UCCSD(T*)-F12 algorithm of the open-shell coupled-cluster program also for closed-shell calculations. Problems with (T) contributions in closed-shell KS-CCSD(T) calculations with MOLPRO have been previously reported by Radón et al., which led the authors to use the open-shell coupled cluster program also for closed-shell cases.⁸⁶

**ONIOM Calculations.** Improved relative energies for the full molecular systems were obtained by using a two-layer ONIOM approach. In this extrapolation scheme, a smaller model system containing the electronically demanding regions is separated from the full molecular system (the "real" system), which is too large for treatment at a sufficiently high level (HL) of theory. Based on a description of the real system employing a low-level (LL) method, a mechanical embedding scheme is used to extrapolate the high-level description of the model system to the entire molecule:⁸¹

$$E_{\text{real}}^{\text{HL}} \approx E^{\text{ONIOM(HL:LL)}} = E_{\text{real}}^{\text{LL}} - E_{\text{model}}^{\text{LL}} + E_{\text{model}}^{\text{HL}} \quad (10)$$

The truncated model systems were constructed by replacing the ¹Pr groups of the pincer ligands of 1a and 2a, and the ¹Bu groups of Mes*O and Mes*OH by hydrogen atoms placed along the cleaved P–C and C–C bonds. Constrained geometry optimizations were then performed by relaxing only the newly formed P–H and C–H bond lengths, while all pertinent bond angles and torsion angles, as well as the coordinates of all other atoms, were kept fixed. In the present study, we used DLPNO-CCSD(T₁)/CBS(DT)/CPS(56) as the low-level method for the real system and CCSD(T*)-
F12b/CBS(DT) as the high-level method for the H-truncated model systems. Above, this level of theory is abbreviated as CC$^{ONIOM}$.

**CASSCF/NEVPT2/QDPT Calculations.** Spin-orbit eigenstates for 1a/2a were calculated with the ORCA 6.0.1 program$^{54–56}$ from state-averaged complete active space computations corrected for dynamic correlation by *n*-electron valence state perturbation theory (CASSCF/NEVPT2) calculations,$^{82–84}$ followed by a quasi-degenerate perturbation theory (QDPT) treatment via a full spin-orbit mean field (SOMF) operator.$^{85}$ CASSCF wave functions were optimized employing the ZORA approximation$^{86–89}$ along with the ZORA-def2-TZVP$^{90}$ basis sets (SARC-ZORA-TZVPP for Re). The RIJK algorithm for fitting the Coulomb and exchange integrals was used in conjunction with the def2/JK auxiliary basis sets (AutoAux for Re).$^{91}$ The active space comprises the 5d orbitals of the complexes and the most important interactions of the ligand with the metal center. For 1a, the three occupied p-orbitals of the equatorial chlorine atom and two occupied pincer-ligand/axial chlorine orbitals were considered, which leads to a CAS(14,10) expansion. For 2a, the N–Re π-bonding interaction was additionally considered, giving rise to a CAS(15,11) expansion. The CAS expansions were state-averaged over 5 quintet, 45 triplet, and 50 singlet roots arising from the formal d⁴ configuration of the rhenium(III) ion (1a) and over 10 quartet and 40 doublet roots for the formal d³ configuration of the rhenium(IV) ion (2a), respectively.$^{92}$

## ASSOCIATED CONTENT

### Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.inorgchem.5c05144.

Spectroscopic, magnetic, electrochemical, crystallographic, calorimetric, and computational data (PDF)

XYZ coordinates of computed structures (TXT)

### Accession Codes

Deposition Numbers 2498886–2498887 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via the joint Cambridge Crystallographic Data Centre (CCDC) and Fachinformationszentrum Karlsruhe Access Structures service.

## AUTHOR INFORMATION

### Corresponding Authors

Sven Schneider – Universität Göttingen, Institut für Anorganische Chemie, Göttingen 37077, Germany;

● orcid.org/0000-0002-8432-7830;

Email: sven.schneider@chemie.uni-goettingen.de

Max C. Holthausen – Goethe-Universität Frankfurt, Institut für Anorganische Und Analytische Chemie, Frankfurt Am Main 60438, Germany;

● orcid.org/0000-0001-7283-8329; Email: max.holthausen@chemie.uni-frankfurt.de

### Authors

Daniel Delony – Universität Göttingen, Institut für Anorganische Chemie, Göttingen 37077, Germany

Arnd Fitterer – Goethe-Universität Frankfurt, Institut für Anorganische Und Analytische Chemie, Frankfurt Am Main 60438, Germany

Martin Diefenbach – TU Darmstadt, Department of Chemistry, Quantum Chemistry, Darmstadt 64287, Germany; ● orcid.org/0000-0002-8581-6193

Florian Wätjen – Universität Göttingen, Institut für Anorganische Chemie, Göttingen 37077, Germany

Sandipan Maji – Universität Göttingen, Institut für Anorganische Chemie, Göttingen 37077, Germany

Serhiy Demeshko – Universität Göttingen, Institut für Anorganische Chemie, Göttingen 37077, Germany

Matthias Otte – Universität Göttingen, Institut für Anorganische Chemie, Göttingen 37077, Germany;

● orcid.org/0000-0001-6858-4960

Milan Orlita – Laboratoire National des Champs Magnetiques Intenses, Grenoble 38042, France; Institute of Physics, Charles University, Prague 121 16, Czech Republic;

● orcid.org/0000-0002-9633-507X

Vera Krewald – TU Darmstadt, Department of Chemistry, Quantum Chemistry, Darmstadt 64287, Germany;

● orcid.org/0000-0002-4749-4357

Complete contact information is available at: https://pubs.acs.org/10.1021/acs.inorgchem.5c05144

### Author Contributions

¹D.D. and A.F. contributed equally to this work. All authors have given approval to the final version of the manuscript.

### Notes

The authors declare no competing financial interest.

## ACKNOWLEDGMENTS

This work was funded by the Deutsche Forschungsgemeinschaft (DFG) through the grants 389479699/RTG2455 and 510228793/SFB1633 (TP A02, TP A04, TP B05). Computing resources on the high-performance computer “Goethe-HLR” and excellent service were provided by the NHR Center NHR Süd West. This center is jointly supported by the Federal Ministry of Education and Research and the state governments participating in the NHR (www.nhr-verein.de/unsere-partner). The authors thank Dr. Christian Würtele for assistance with single-crystal X-ray crystallography. The Grenoble group acknowledges the support of LNCMI-CNRS, a member of the European Magnetic Field Laboratory (EMFL), and thanks Jan Wyzula and Ivan Mohelsky for their support.

## REFERENCES

(1) Wang, C. R.; Stansberry, J. M.; Mukundan, R.; Chang, H.-M. J.; Kulkarni, D.; Park, A. M.; Plymill, A. B.; Firas, N. M.; Liu, C. P.; Lang, J. T.; Lee, J. K.; Tolouei, N. E.; Morimoto, Y.; Wang, C. H.; Zhu, G.; Brouwer, J.; Atanassov, P.; Capuano, C. B.; Mittelsteadt, C.; Peng, X.; Zenyuk, I. V. Proton Exchange Membrane (PEM) Water Electrolysis: Cell-Level Considerations for Gigawatt-Scale Deployment. *Chem. Rev.* **2025**, *125*, 1257–1302.

(2) Garrido-Barros, P.; Derosa, J.; Chalkley, M. J.; Peters, J. C. Tandem electrocatalytic N₂ fixation via proton-coupled electron transfer. *Nature* **2022**, *609*, 71–77.

(3) Mato, M.; Cornella, J. Bismuth in Radical Chemistry and Catalysis. *Angew. Chem., Int. Ed.* **2024**, *63*, No. e202315046.

(4) Autschbach, J. Perspective: Relativistic effects. *J. Chem. Phys.* **2012**, *136*, 150902.

(5) Heinemann, C.; Schwarz, H.; Koch, W.; Dyall, K. G. Relativistic effects in the cationic platinum carbene PtCH⁺₂. *J. Chem. Phys.* **1996**, *104*, 4642–4652.

(6) Fleig, T. Relativistic String-Based Electron Correlation Methods; Springer: Dordrecht, Heidelberg, London, NY, 2010. DOI: .
(7) Srnec, M.; Chalupsky, J.; Fojta, M.; Zendlova, L.; Havran, L.; Hocek, M.; Kyvala, M.; Rulisek, L. Effect of Spin-Orbit Coupling on Reduction Potentials of Octahedral Ruthenium(II/III) and Osmium-(II/III) Complexes. *J. Am. Chem. Soc.* **2008**, *130*, 10947-10954.

(8) Bím, D.; Rulisek, L.; Srnec, M. Accurate Prediction of One-Electron Reduction Potentials in Aqueous Solution by Variable-Temperature H-Atom Addition/Abstraction Methodology. *J. Phys. Chem. Lett.* **2016**, *7*, 7-13.

(9) Siegbahn, P. E. M.; Svensson, M.; Crabtree, R. H. A Theoretical Study of Mercury Photosensitized Reactions. *J. Am. Chem. Soc.* **1995**, *117*, 6758-6765.

(10) Carroll, J. J.; Weisshaar, J. C.; Siegbahn, P. E. M.; Wittborn, C. A. M.; Blomberg, M. R. A. An Experimental and Theoretical Study of the Gas Phase Reactions between Small Linear Alkanes and the Platinum and Iridium Atoms. *J. Phys. Chem.* **1995**, *99*, 14388-14396.

(11) Chen, K.; Zhang, G.; Chen, H.; Yao, J.; Danovich, D.; Shaik, S. Spin-Orbit Coupling and Outer-Core Correlation Effects in Ir- and Pt-Catalyzed C-H Activation. *J. Chem. Theory Comput.* **2012**, *8*, 1641-1645.

(12) Jerabek, P.; Vondung, L.; Schwerdtfeger, P. Tipping the Balance between Ligand and Metal Protonation due to Relativistic Effects: Unusually High Proton Affinity in Gold(I) Pincer Complexes. *Chem.-Eur. J.* **2018**, *24*, 6047-6051.

(13) Delony, D.; Kinauer, M.; Diefenbach, M.; Demeshko, S.; Würtele, C.; Holthausen, M. C.; Schneider, S. A Terminal Iridium Oxo Complex with a Triplet Ground State. *Angew. Chem., Int. Ed.* **2019**, *58*, 10971-10974.

(14) Tepaske, M. A.; Fitterer, A.; Verplancke, H.; Delony, D.; Neben, M. C.; de Bruin, B.; Holthausen, M. C.; Schneider, S. C-H Bond Activation by Iridium(III) and Iridium(IV)Oxo Complexes. *Angew. Chem., Int. Ed.* **2024**, *63*, No. e202316729.

(15) Oelschlegel, K.; Heinz, M.; Maji, S.; Naumann, R.; Höhle, Y. F. S.; Alizadeh, N.; Finger, M.; Otte, M.; Heinze, K.; Holthausen, M. C.; Schneider, S. Photocatalytic Hydrogenation of an N₂-Derived ReV Imido Complex. *JACS Au* **2025**, *5* (10), 4706-4713.

(16) Warren, J. J.; Tronic, T. A.; Mayer, J. M. Thermochemistry of Proton-Coupled Electron Transfer Reagents and its Implications. *Chem. Rev.* **2010**, *110*, 6961-7001.

(17) Agarwal, R. G.; Coste, S. C.; Groff, B. D.; Heuer, A. M.; Noh, H.; Parada, G. A.; Wise, C. F.; Nichols, E. M.; Warren, J. J.; Mayer, J. M. Free Energies of Proton-Coupled Electron Transfer Reagents and Their Applications. *Chem. Rev.* **2022**, *122*, 1-49.

(18) Schendzielorz, F.; Finger, M.; Abbenseth, J.; Würtele, C.; Krewald, V.; Schneider, S. Metal-Ligand Cooperative Synthesis of Benzonitrile by Electrochemical Reduction and Photolytic Splitting of Dinitrogen. *Angew. Chem., Int. Ed.* **2019**, *131*, 840-844.

(19) Fritz, M.; Rupp, S.; Kiene, C. I.; Kisan, S.; Telser, J.; Würtele, C.; Krewald, V.; Schneider, S. Photoelectrochemical Conversion of Dinitrogen to Benzonitrile: Selectivity Control by Electrophile- versus Proton-Coupled Electron Transfer. *Angew. Chem., Int. Ed.* **2022**, *61* (35), No. e202205922.

(20) Bertini, I.; Luchinat, C. Relaxation. *Coord. Chem. Rev.* **1996**, *150*, 77-110.

(21) Oulette, E. T.; Estrada, J. I. A.; Lussier, D. J.; Chakarawet, K.; Lohrey, T. D.; Karon, L.; Bergman, R. G.; Arnold, J. Spectroscopic, Magnetic, and Computational Investigations on a Series of Rhenium-(III) Cyclopentadienide β-diketiminate Halide and Pseudohalide Complexes. *Organometallics* **2022**, *41*, 3128-3137.

(22) Chatt, J.; Leigh, G. J.; Mingos, D. M. P. Configurations of some complexes of rhenium, ruthenium, osmium, rhodium, iridium, and platinum halides with mono(tertiary phosphines) and mono(tertiary arsines). *J. Chem. Soc. A* **1969**, 1674-1680.

(23) Randall, E. W.; Shaw, D. Nuclear magnetic resonance spectra of d⁴-cornplexes of rheniurn(iii) and osmium(iv) with phosphine and arsine ligands. *J. Chem. Soc. A* **1969**, 2867-2872.

(24) Mitsopoulou, C. A.; Mahiea, N.; Motevalli, M.; Randall, E. W. Second-order paramagnetic rhenium(III) complexes: solid-state structure and assignment of the carbon-13 magnetic resonance spectra in solution. *J. Chem. Soc., Dalton Trans.* **1996**, 4563-4566.

(25) Bertini, I.; Luchinat, C. The hyperfine shift. *Coord. Chem. Rev.* **1996**, *150*, 29-75.

(26) Martin, B.; Autschbach, J. Temperature dependence of contact and dipolar NMR chemical shifts in paramagnetic molecules. *J. Chem. Phys.* **2015**, *142*, 054108.

(27) Gunz, B. H. P.; Leigh, G. J. Magnetic Susceptibilities of Some Rhenium(iii) and Osmium(iv) Halide Complexes; Preparation of Some New d4 Complexes. *J. Chem. Soc. A* **1971**, 2229-2233.

(28) Figgis, B. N.; Lewis, J. The Magnetic Properties of Transition Metal Complexes. *Prog. Inorg. Chem.* **1964**, *6*, 37-239.

(29) Uzelmeier, C. E.; Bartley, S. L.; Fourmigué, M.; Rogers, R.; Grandinetti, G.; Dunbar, K. R. Reaction of Octachlorodirhenate with a Redox-Active Tetrathiafulvalene Phosphine Ligand: Spectroscopic, Magnetic, and Structural Characterization of the Unusual Para-magnetic Salt [ReCl2(o-P2)2][Re2Cl6(o-P2)] (o-P2 = o-{P(C6H5)-2}2(CH3)2TTF). *Inorg. Chem.* **1998**, *37*, 6706-6713.

(30) Palion-Gazda, J.; Gryca, I.; Machura, B.; Lloret, F.; Julve, M. Synthesis, crystal structure and magnetic properties of the complex [ReCl 3 (tppz)]. *MeCN. RSC Adv.* **2015**, *5*, 101616-101622.

(31) The assignment of the N-H stretching mode was confirmed by deuterium labelling.

(32) Cariati, F.; Sgamellotti, A.; Morazzoni, F.; Valenti, V. Electronic spectra and magnetic properties of some rhenium(IV) and rhenium-(III) complexes. *Inorg. Chim. Acta* **1971**, *5*, 531-535.

(33) Hay-Motherwell, R. S.; Wilkinson, G.; Hussain-Bates, B.; Hursthouse, M. B. Synthesis and X-ray crystal structure of oxotrimesityliridium(V). *Polyhedron* **1993**, *12*, 2009-2012.

(34) Earnshaw, A.; Figgis, B. N.; Lewis, J.; Peacock, R. D. The magnetic properties of some d⁴-complexes. *J. Chem. Soc.* **1961**, 3132-3138.

(35) The CASSCF treatment of 2a reflects the active space of 1a with one additional orbital to accommodate the N-Re π-Interaction in the amide complexes.

(36) Abbenseth, J.; Delony, D.; Neben, M. C.; Würtele, C.; de Bruin, B.; Schneider, S. Interconversion of Phosphinyl Radical and Phosphinidene Complexes by Proton Coupled Electron Transfer. *Angew. Chem., Int. Ed.* **2019**, *58*, 6338-6341.

(37) Connor, G. P.; Delony, D.; Weber, J. E.; Mercado, B. Q.; Curley, J. B.; Schneider, S.; Mayer, J. M.; Holland, P. L. Facile conversion of ammonia to a nitride in a rhenium system that cleaves dinitrogen. *Chem. Sci.* **2022**, *13*, 4010-4018.

(38) Careful reevaluation of the electrochemical properties of 1a/b gave slightly different half-wave potentials to those previously reported for 1a (-0.24 V; ref. 18) and 1b (-0.20 V; ref. 19).

(39) Lever, A. B. P. Electrochemical Parametrization of Metal Complex Redox Potentials, Using the Ruthenium(III)/Ruthenium-(II) Couple To Generate a Ligand Electrochemical Series. *Inorg. Chem.* **1990**, *29*, 1271-1285.

(40) van Alten, R. S.; Wieser, P. A.; Finger, M.; Abbenseth, J.; Demeshko, S.; Würtele, C.; Siewert, I.; Schneider, S. Halide Effects in Reductive Splitting of Dinitrogen with Rhenium Pincer Complexes. *Inorg. Chem.* **2022**, *61*, 11581-11591.

(41) Tshepelevitsh, S.; Kütt, A.; Lökov, M.; Kaljurand, I.; Saame, J.; Heering, A.; Plieger, P. G.; Vianello, R.; Leito, I. On the Basicity of Organic Bases in Different Media. *Eur. J. Org. Chem.* **2019**, 2019, 6735-6748.

(42) Mader, E. A.; Manner, V. W.; Markle, T. F.; Wu, A.; Franz, J. A.; Mayer, J. M. Trends in Ground-State Entropies for Transition Metal Based Hydrogen Atom Transfer Reactions. *J. Am. Chem. Soc.* **2009**, *131*, 4335-4345.

(43) Wise, C. F.; Agarwal, R. G.; Mayer, J. M. Determining Proton-Coupled Standard Potentials and X-H Bond Dissociation Free Energies in Nonaqueous Solvents Using Open-Circuit Potential Measurements. *J. Am. Chem. Soc.* **2020**, *142*, 10681-10691.

(44) Manner, V. W.; Markle, T. F.; Freudenthal, J. H.; Roth, J. P.; Mayer, J. M. The first crystal structure of a monomeric phenoxyl radical: 2, 4, 6-tri-tert-butylphenoxy radical. *Chem. Commun.* **2008**, 246, 256-258.
(45) LeMardele, FieldOptic, FieldOptic https://github.com/LeMardele/FieldOptic. 2024.

(46) Kahn, O. *Molecular Magnetism*; VCH Publishers Inc.: New York, 1993.

(47) Bill, E.; *JulX*, *Program for Simulation of Molecular Magnetic Data. Max-Planck Institute For Chemical Energy Conversion*; JulX: Mülheim, Ruhr, 2008.

(48) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H., et al. *Gaussian 16, Revision B.01.*; Gaussian, Inc.: Wallingford CT, 2016.

(49) Adamo, C.; Barone, V. Toward reliable density functional methods without adjustable parameters: The PBE0 model. *J. Chem. Phys.* **1999**, *110*, 6158–6170.

(50) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate *ab initio* parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. *J. Chem. Phys.* **2010**, *132*, 154104.

(51) Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the damping function in dispersion corrected density functional theory. *J. Comput. Chem.* **2011**, *32*, 1456–1465.

(52) Weigend, F.; Ahlrichs, R. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. *Phys. Chem. Chem. Phys.* **2005**, *7*, 3297–3305.

(53) Andrae, D.; Häußermann, U.; Dolg, M.; Stoll, H.; Preuß, H. Energy-adjusted *ab initio* pseudopotentials for the second and third row transition elements. *Theor. Chim. Acta* **1990**, *77*, 123–141.

(54) Neese, F. The ORCA program system. *WIREs Comput. Mol. Sci.* **2012**, *2*, 73–78.

(55) Neese, F.; Wennmohs, F.; Becker, U.; Riplinger, C. The ORCA quantum chemistry program package. *J. Chem. Phys.* **2020**, *152*, 224108.

(56) Neese, F. Software Update: The ORCA Program System—Version 6.0. *WIREs Comput. Mol. Sci.* **2025**, *15*, No. e70019.

(57) Riplinger, C.; Neese, F. An efficient and near linear scaling pair natural orbital based local coupled cluster method. *J. Chem. Phys.* **2013**, *138*, 034106.

(58) Saitow, M.; Becker, U.; Riplinger, C.; Valeev, E. F.; Neese, F. A new near-linear scaling, efficient and accurate, open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory. *J. Chem. Phys.* **2017**, *146*, 164105.

(59) Guo, Y.; Riplinger, C.; Becker, U.; Liakos, D. G.; Minenkov, Y.; Cavallo, L.; Neese, F. Communication: An improved linear scaling perturbative triples correction for the domain based local pair-natural orbital based singles and doubles coupled cluster method [DLPNO-CCSD(T)]. *J. Chem. Phys.* **2018**, *148*, 011101.

(60) Altun, A.; Neese, F.; Bistoni, G. Extrapolation to the Limit of a Complete Pair Natural Orbital Space in Local Coupled-Cluster Calculations. *J. Chem. Theory Comput.* **2020**, *16*, 6142–6149.

(61) Schwenke, D. W. The extrapolation of one-electron basis sets in electronic structure calculations: How it should work and how it can be made to work. *J. Chem. Phys.* **2005**, *122*, 014107.

(62) Karton, A.; Martin, J. M. L. Comment on: "Estimating the Hartree-Fock limit from finite basis set calculations" [Jensen F (2005) Theor Chem Acc 113: 267]. *Theor. Chem. Acc.* **2006**, *115*, 330–333.

(63) Neese, F.; Valeev, E. F. Revisiting the Atomic Natural Orbital Approach for Basis Sets: Robust Systematic Basis Sets for Explicitly Correlated and Conventional Correlated ab initio Methods? *J. Chem. Theory Comput.* **2011**, *7*, 33–43.

(64) Truhlar, D. G. Basis set extrapolation. *Chem. Phys. Lett.* **1998**, *294*, 45–48.

(65) Adalsteinsson, H. M.; Bjornsson, R. Ionization energies of metallorenes: a coupled cluster study of cobaltocene. *Phys. Chem. Chem. Phys.* **2023**, *25*, 4570–4587.

(66) Adler, T. B.; Knizia, G.; Werner, H.-J. A simple and efficient CCSD(T)-F12 approximation. *J. Chem. Phys.* **2007**, *127*, 221106.

(67) Peterson, K. A.; Adler, T. B.; Werner, H.-J. Systematically convergent basis sets for explicitly correlated wavefunctions: The atoms H, He, B-Ne, and Al-Ar. *J. Chem. Phys.* **2008**, *128*, 084102.

(68) Figgen, D.; Peterson, K. A.; Dolg, M.; Stoll, H. Energy-consistent pseudopotentials and correlation consistent basis sets for the 5d elements Hf-Pt. *J. Chem. Phys.* **2009**, *130*, 164108.

(69) Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M. Molpro: a general-purpose quantum chemistry program package. *Wiley Interdiscip. Rev. Comput. Mol. Sci.* **2012**, *2*, 242–253.

(70) Werner, H.-J.; Knowles, P. J.; Manby, F. R.; Black, J. A.; Doll, K.; Heßelmann, A.; Kats, D.; Köhn, A.; Korona, T.; Kreplin, D. A.; et al. The Molpro quantum chemistry package. *J. Chem. Phys.* **2020**, *152*, 144107.

(71) Werner, H.-J.; Knowles, P. J. MOLPRO, Version 2024, a package of *ab initio* programs. Molpro, 2025.

(72) Knizia, G.; Adler, T. B.; Werner, H.-J. Simplified CCSD(T)-F12 methods: Theory and benchmarks. *J. Chem. Phys.* **2009**, *130*, 054104.

(73) Weigend, F. Hartree-Fock exchange fitting basis sets for H to Rn. *J. Comput. Chem.* **2008**, *29*, 167–175.

(74) Hill, J. G. Auxiliary basis sets for density fitting second-order Møller-Plesset perturbation theory: correlation consistent basis sets for the 5d elements Hf-Pt. *J. Chem. Phys.* **2011**, *135*, 044105.

(75) Yousaf, K. E.; Peterson, K. A. Optimized auxiliary basis sets for explicitly correlated Methods. *J. Chem. Phys.* **2008**, *129*, 184108.

(76) Kritikou, S.; Hill, J. G. Auxiliary Basis Sets for Density Fitting in Explicitly Correlated Calculations: The Atoms H-Ar. *J. Chem. Theory Comput.* **2015**, *11*, 5269–5276.

(77) Watts, J. D.; Gauss, J.; Bartlett, R. J. Coupled-cluster methods with noniterative triple excitations for restricted open-shell Hartree-Fock and other general single determinant reference functions. *Energies and analytical gradients*. *J. Chem. Phys.* **1993**, *98*, 8718–8733.

(78) Hill, J. G.; Peterson, K. A.; Knizia, G.; Werner, H.-J. Extrapolating MP2 and CCSD explicitly correlated correlation energies to the complete basis set limit with first and second row correlation consistent basis sets. *J. Chem. Phys.* **2009**, *131*, 194105.

(79) Verplancke, H.; Diefenbach, M.; Lienert, J. N.; Ugandi, M.; Kitsaras, M.-P.; Roemelt, M.; Stopkowicz, S.; Holthausen, M. C. Another Torture Track for Quantum Chemistry: Reinvestigation of the Benzaldehyde Amidation by Nitrogen-Atom Transfer from Platinum(II) and Palladium(II) Metallonitrenes. *Isr. J. Chem.* **2023**, *63*, No. e202300060.

(80) Radón, M.; Drabik, G.; Hodorowicz, M.; Szklarzewicz, J. Performance of quantum chemistry methods for a benchmark set of spin-state energetics derived from experimental data of 17 transition metal complexes (SSE17). *Chem. Sci.* **2024**, *15*, 20189–20204.

(81) Chung, L. W.; Sameera, W. M. C.; Ramozzi, R.; Page, A. J.; Hatanaka, M.; Petrova, G. P.; Harris, T. V.; Li, X.; Ke, Z.; Liu, F.; Li, H.-B.; Ding, L.; Morokuma, K. The ONIOM Method and Its Applications. *Chem. Rev.* **2015**, *115*, 5678–5796.

(82) Angeli, C.; Cimiraglia, R.; Evangelisti, S.; Leininger, T.; Malrieu, J. P. Introduction of *n*-electron valence states for multi-reference perturbation theory. *J. Chem. Phys.* **2001**, *114*, 10252–10264.

(83) Angeli, C.; Cimiraglia, R.; Malrieu, J. P. *n*-electron valence state perturbation theory: a fast implementation of the strongly contracted variant. *Chem. Phys. Lett.* **2001**, *350*, 297–305.

(84) Angeli, C.; Cimiraglia, R.; Malrieu, J. P. *n*-electron valence state perturbation theory: A spinless formulation and an efficient implementation of the strongly contracted and of the partially contracted variants. *J. Chem. Phys.* **2002**, *117*, 9138–9153.

(85) Heß, B. A.; Marian, C. M.; Wahlgren, U.; Gropen, O. A mean-field spin-orbit method applicable to correlated wavefunctions. *Chem. Phys. Lett.* **1996**, *251*, 365–371.

(86) Van Lenthe, E.; Baerends, E. J.; Snijders, J. G. Relativistic regular two-component Hamiltonians. *J. Chem. Phys.* **1993**, *99*, 4597–4610.
(87) Van Lenthe, E.; Baerends, E. J.; Snijders, J. G. Relativistic total energy using regular approximations. *J. Chem. Phys.* **1994**, *101*, 9783–9792.

(88) Van Lenthe, E.; Snijders, J. G.; Baerends, E. J. The zero-order regular approximation for relativistic effects: The effect of spin-orbit coupling in closed shell molecules. *J. Chem. Phys.* **1996**, *105*, 6505–6516.

(89) Van Wüllen, C. Molecular density functional calculations in the regular relativistic approximation: Method, application to coinage metal diatomics, hydrides, fluorides and chlorides, and comparison with first-order relativistic calculations. *J. Chem. Phys.* **1998**, *109*, 392–399.

(90) Pantazis, D. A.; Chen, X. Y.; Landis, C. R.; Neese, F. All-Electron Scalar Relativistic Basis Sets for Third-Row Transition Metal Atoms. *J. Chem. Theory Comput.* **2008**, *4*, 908–919.

(91) Weigend, F. A fully direct RI-HF algorithm: Implementation, optimized auxiliary basis sets, demonstration of accuracy and efficiency. *Phys. Chem. Chem. Phys.* **2002**, *4*, 4285–4291.

(92) Singh, S. K.; Eng, J.; Atanasov, M.; Neese, F. Covalency and chemical bonding in transition metal complexes: An ab initio based ligand field perspective. *Coord. Chem. Rev.* **2017**, *344*, 2–25.

<figure><img src="image_17.png" /></figure>

CAS BIOFINDER DISCOVERY PLATFORM™

ELIMINATE DATA
SILOS. FIND
WHAT YOU
NEED, WHEN
YOU NEED IT.

A single platform for relevant,
high-quality biological and
toxicology research

Streamline your R&D

CAS
A division of the
American Chemical Society

<figure><img src="image_18.png" /></figure>