Relativity as a Synthesis Design Principle: A Comparative Study of [3 + 2] Cycloaddition of Technetium(VII) and Rhenium(VII) Trioxo Complexes with Olefins

The difference in [3 + 2] cycloaddition reactivity between fac-[MO3(tacn)]+ (M = Re, 99Tc; tacn = 1,4,7-triazacyclononane) complexes has been reexamined with a selection of unsaturated substrates including sodium 4-vinylbenzenesulfonate, norbornene, 2-butyne, and 2-methyl-3-butyn-2-ol (2MByOH). None of the substrates was found to react with the Re cation in water at room temperature, whereas the 99Tc reagent cleanly yielded the [3 + 2] cycloadducts. Interestingly, a bis-adduct was obtained as the sole product for 2MByOH, reflecting the high reactivity of a 99TcO-enediolato monoadduct. On the basis of scalar relativistic and nonrelativistic density functional theory calculations of the reaction pathways, the dramatic difference in reactivity between the two metals has now been substantially attributed to differences in relativistic effects, which are much larger for the 5d metal. Furthermore, scalar-relativistic ΔG values were found to decrease along the series propene > norbornene > 2-butyne > dimethylketene, indicating major variations in the thermodynamic driving force as a function of the unsaturated substrate. The suggestion is made that scalar-relativistic effects, consisting of greater destabilization of the valence electrons of the 5d elements compared with those of the 4d elements, be viewed as a new design principle for novel 99mTc/Re radiopharmaceuticals, as well as more generally in heavy-element coordination chemistry.


■ INTRODUCTION
Technetium-99m, a metastable nuclear isomer of technetium-99, is the most commonly used radioisotope in medicine, and the demand for 99m Tc radiopharmaceuticals with novel biodistribution properties is considerable. 1−4 A common early step toward the development of these products involves model chemistries with 99 Tc and Re. Although the two elements are chemically very similar, they exhibit quantitative differences in reactivity, reflecting the somewhat greater stability (and lower reduction potentials) of the higher oxidation states of Re. In a seminal finding, Pearlstein and Davison in the 1980s showed that fac-[ 99 Tc VII O 3 ] + complexes undergo [3 + 2] cycloadditions with olefins to yield 99 Tc V O diolate derivatives. 5 The analogous Re V O-diolate species, in contrast, were found to be unstable, undergoing the opposite reaction when thermalized. We built on this finding to develop fac-[ 99m Tc VII O 3 ] + complexes as aqueous-phase labeling agents for olefins. 6−8 The factors underlying the difference in reactivity between the two group 7 elements, however, have remained obscure. Physicochemical measurements at the Tromsø laboratory on analogous pairs of 4d and 5d metallocorroles, 9−11 including those involving Mo 12 /W, 13 99 Tc V O 14 /Re V O, 15 Ru VI N 16 /Os VI N, 17 and Ag/Au, 18,19 suggested that relativistic effects might partly explain the difference in cycloaddition reactivity between 99m/99 Tc and Re. 20 Unfortunately, little is known about the importance of relativistic effects for transition-metal reactivity. 21−23 For most of the 20th century, relativistic effects were not considered important for chemistry. Indeed, in 1929, Paul Dirac asserted that the only imperfections remaining in quantum mechanics "give rise to difficulties only when high-speed particles are involved, and are therefore of no importance in the consideration of atomic and molecular structure and ordinary chemical reactions in which it is, indeed, usually sufficiently accurate if one neglects relativity variation of mass and velocity and assumes only Coulomb forces between the various electrons and atomic nuclei." 24 This view started changing only in the 1970s. 25,26 Today the importance of relativistic effects is well recognized for the static properties of sixth-and seventh-period elements. 27 Relativity thus accounts for such well-known effects as the liquid state of Hg 28 and the yellow color of elemental Au 29 and Cs as well as a host of less wellknown effects in heavy-element chemistry. 30−33 ■ RESULTS AND DISCUSSION Synthetic and Reactivity Studies. With the above as the backdrop, we chose to perform a comparative study of fac-[MO 3 (tacn)] + (M = Re, 99 Tc; tacn = 1,4,7-triazacyclononane) complexes with respect to their [3 + 2] cycloaddition reactivity with a selection of unsaturated substrates including sodium 4vinylbenzenesulfonate, norbornene, 2-butyne, and 2-methyl-3butyn-2-ol (2MByOH; Scheme 1). Because we already knew from our recent work that fac-[ 99 TcO 3 (tacn)] + reacts with a broad range of olefins to yield 99 TcO-diolate products, we focused here particularly on complexes of the type fac-[ReO 3 (tacn)]X (X = Cl, BPh 4 ). 34 We verified that the Re complexes do not react with olefins and alkynes, as indeed was expected from Pearlstein and Davison's original observations. 6 Because alkynes had not been examined as substrates until now, we chose to examine the interaction of the water-stable complex fac-[ 99 TcO 3 (tacn)]Cl 8 with the water-soluble propargylic alcohol 2MByOH. After the addition of 2 equiv of the propargylic alcohol to an aqueous solution of fac-  35 Given that two symmetry-nonequivalent addition modes are conceivable for the second equiv of fac-[ 99 TcO 3 (tacn)] + , 1 H a n d 1  O 2 (tacn)} 2 (2MByOH)]Cl 2 understandably indicated the formation of two diastereomers in a 2:1 ratio (Scheme 3). 36 Slow evaporation of an aqueous solution of the product in the presence of excess KBr led to crystallization of the major diastereomer of [{ 99 Tc V (O)O 2 (tacn)} 2 (2MByOH)]Br 2 (isomer 1 in Scheme 3). Single-crystal X-ray diffraction analysis (Table 1 and Figure 1) revealed an intramolecular N4−H···O7 hydrogen bond, which, along with less overall steric crowding, appears to be responsible for the formation of isomer 1 as the major product. In contrast to the [3 + 2] cycloadducts of fac-[ 99 TcO 3 (tacn)] + with alkenes, slow decomposition of isomer 1 of the bisadduct (formation of ([TcO 4 ] − ) was observed over days.
Theoretical Modeling. Relativistic and nonrelativistic density functional theory (DFT) calculations (typically with large all-electron STO-TZ2P basis sets; see Experimental Section for details) were used to investigate the [3 + 2] cycloaddition of the cationic complexes [MO 3 (tacn)] + (M = Tc, Re) with four different olefins, namely, propene, dimethylketene, 2-butyne, and norbornene, in acetonitrile (MeCN) as a solvent ( Table 2). Relativity was taken into account either via effective core potentials (ECPs) or with a scalar-relativistic treatment with the zeroth-order regular approximation (ZORA). Two-component spin−orbit relativistic calculations were undertaken in a few cases as random checks on the quality of the ECP and scalar-relativistic results; the latter results were indeed found to be adequate, with minimal differences relative to the spin−orbit calculations. The data in Table 1 led to the following conclusions.
Relativistic calculations indicate dramatically lower (in an algebraic sense) reaction free energies (ΔG) and free energies of activation (ΔG ⧧ ) for Tc than for Re, consistent with the experimentally observed difference in reactivity between the two metals. These translate to substantially "earlier" transition states for Tc than for Re; in other bonds, key bonds affected by the reaction are rather similar in length to the starting materials for the Tc reactions compared with the Re reactions ( Figure  2). In sharp contrast, nonrelativistic calculations (B3LYP nrel and PBE0 nrel in Table 2) indicate similar ΔG and ΔG ⧧ values for the two metals. The fact that these generalizations hold regardless of the exchange-correlation functional and the organic substrate indicates that the difference in reactivity between the two metals is largely a relativistic effect.
The above interpretation is supported by computations of the adiabatic electron affinities ( .20 eV, respectively, which translates to a difference of just over 300 meV between the two metals. These results prove that the difference in the EAs or reduction potentials between the Tc(VII) and Re(VII) species is substantially ascribable to the relativistic destabilization of the Re 5d orbitals relative to the Tc 4d orbitals. Much the same considerations should apply to the cycloaddition reaction of interest in this study because it also involves a reduction, albeit a two-electron one, of the M(VII) centers.
Another key observation from Table 2 is that the ΔG values, which decrease along the series propene > norbornene > 2butyne > dimethylketene, reflect dramatic variations in the thermodynamic driving force as a function of the olefinic substrate. In fact, for propene, all of the relativistic methods yield positive ΔG values, consistent with the experimental observation that simple, unstrained olefins do not react with cationic [Re VII O 3 ] + reagents at room temperature. 37 Interestingly, much smaller variations are observed among the ΔG ⧧ values for the four substrates. Again, for Re, the calculations generally indicate the highest ΔG ⧧ value for propene and lower values for dimethylketene and norbornene.
The above calculations are far from perfect. While the ΔG values are moderately consistent across different functionals (for the relativistic calculations), the ΔG ⧧ values exhibit much wider variations. Of the different functionals examined, PBE-D2 ECP appears to yield the lowest, and probably most realistic, ΔG ⧧ values, which has also been observed in a DFT study of Ir-catalyzed reactions. 38 Overall, our results underscore the need for substantial additional benchmarking of different functionals vis-a-vis transition-metal-mediated redox reactions, especially for 4d and 5d elements.

■ CONCLUSION
In earlier studies of metalloporphyrin-type compounds, 9−11 we concluded that the difference in redox potential between        Synthetic and Reactivity Studies. Caution! 99 Tc is a weak β emitter. All experiments were performed in laboratories approved for working with low-level radioactive materials.
[ 99 TcO 3 (tacn)]Cl was prepared as previously reported. 40 Doubledistilled water (dd-water) was used throughout. All chemicals were of reagent-grade quality or higher and were obtained from commercial suppliers.

Reactions of [ReO 3 (tacn)](BPh 4 ) in MeCN with Alkenes and
Alkynes. To a solution of [ReO 3 (tacn)](BPh 4 ) (36 mg, 0.05 mmol) in MeCN (3.0 mL) was added the olefin or alkyne of interest (0.5 mmol), and the reaction mixture was stirred for 2 h at room temperature, followed by UPLC−MS analysis. If no reaction was observed, the temperature was raised to 85°C for 2 h, and the reaction mixture was again analyzed by UPLC−MS. We found no evidence for the formation of a [3 + 2] cycloadduct for either norbornene or 2-butyne.
Reactions of [ReO 3 (tacn)]Cl in Water with Alkenes and Alkynes. To a solution of [ReO 3 (tacn)]Cl (18 mg, 0.05 mmol) dissolved in ddwater (2.0 mL) was added a water-soluble olefin or alkyne (0.5 mmol), and the reaction mixture was stirred for 2 h at room temperature, followed by UPLC−MS analysis. If no reaction was observed, the temperature was raised to 85°C for 2 h, and the reaction mixture was again analyzed by UPLC−MS. We found no evidence for the formation of a [3 + 2]  X-ray Structure Analysis. Crystallographic data were collected at 183(2) K with Mo Kα radiation (λ = 0.7107 Å) monochromatized with graphite on an Oxford Diffraction Xcalibur system with a Ruby detector. Suitable crystals were covered with oil (Infineum V8512, formerly known as Paratone N), mounted atop a glass fiber, and immediately transferred to the diffractometer. The CrysAlisPro 43 program suite was used for data collection, semiempirical absorption correction, and data analysis. The structure was solved with direct methods using SIR97 44 and refined by full-matrix least-squares methods on F 2 with SHELXL-2018 45 using the Olex2 GUI. 46 The refinement was done with anisotropic thermal parameters for all non-H atoms, unless otherwise indicated. The positions of the H atoms were calculated using the "riding atom" option in SHELXL-2018. More details on data collection and structure calculations are given in Table 1 and in the crystallographic information file.
Computational Methods. The majority of DFT calculations (including full geometry optimizations in the presence of a solvent) were carried out with the ADF 2018 program system. 47 Relativistic effects were taken into account with the ZORA 48 method, applied both as a scalar correction and with spin−orbit coupling at the twocomponent level. A parallel set of calculations were carried out with the same basis set but with a nonrelativistic Hamiltonian. Specially optimized all-electron ZORA STO-TZ2P basis sets were used throughout. A variety of exchange-correlation functionals were tested, including OLYP, 49,50 B3LYP, 51,52 PBE0, 53,54 and OPBE0. 55 The potential influence of dispersion corrections was examined, and, in general, they did not make a significant difference. Our results therefore generally refer to the pristine functionals. Zero-point energy and thermal corrections (vibrational, rotational, and translational) were made to the electronic energies in the calculation of the where U is the gas-phase thermodynamic energy, E el the total electronic energy, and E nuc the nuclear internal energy (sum of the vibrational, rotational, and translational energies and the zero-point energy correction); R is the ideal gas constant, T the temperature, and S the entropy. S was calculated from the temperature-dependent partition function in ADF at 298.15 K. Solvent effects were taken into account with COSMO (conductor-like screening model), 56−58 as implemented 59 in ADF. The type of cavity used is Esurf, 60