Tuning the Kinetic Inertness of Bi³⁺ Complexes: The Impact of Donor Atoms on Diaza-18-crown-6 Ligands as Chelators for ²¹³Bi Targeted Alpha Therapy

Abstract

The radionuclide ²¹³Bi can be applied for targeted α therapy (TAT), a type of nuclear medicine that harnesses α particles to eradicate cancer cells. To use this radionuclide for this application, a bifunctional chelator (BFC) is needed to attach it to a biological targeting vector that can deliver it selectively to cancer cells. Here, we investigated six macrocyclic ligands as potential BFCs, fully characterizing the Bi³⁺ complexes by NMR spectroscopy, mass spectrometry, and elemental analysis. Solid-state structures of three complexes revealed distorted coordination geometries about the Bi³⁺ center arising from the stereochemically active 6s² lone pair. The kinetic properties of the Bi³⁺ complexes were assessed by challenging them with a 1000-fold excess of the chelating agent diethylenetriaminepentaacetic acid (DTPA). The most kinetically inert complexes contained the most basic pendent donors. Density functional theory (DFT) and quantum theory of atoms in molecules (QTAIM) calculations were employed to investigate this trend, suggesting that the kinetic inertness is not correlated with the extent of the 6s² lone pair stereochemical activity, but with the extent of covalency between pendent donors. Lastly, radiolabeling studies of ²¹³Bi (30–210 kBq) with three of the most promising ligands showed rapid formation of the radiolabeled complexes at room temperature within 8 min for ligand concentrations as low as 10⁻⁷ M, corresponding to radiochemical yields of > 80% thereby demonstrating the promise of this ligand class for use in ²¹³Bi TAT.

Graphical Abstract

A series of 18-membered macrocyclic ligands is investigated for Bi³⁺ chelation. These ligands show promising affinity for this main group ion and are demonstrated to effectively radiolabel its therapeutic radioisotope, ²¹³Bi.

Introduction

Targeted α therapy (TAT) is a promising approach for the treatment of cancer that employs an α-emitting radionuclide to deliver highly localized internal radiation to malignant cells.^1–4 The high linear energy transfer and short penetration range in biological tissue of α particles make them well suited for internal radiotherapy because it ensures that the radiation is confined to a minimal area, thus limiting off-target damage.⁵ Directing these radionuclides to malignant tissue, however, requires attachment to an appropriate biological targeting agent, such as an antibody or peptide, that can selectively bind receptors overexpressed in cancer cells (Figure 1). A key component of these radiopharmaceutical agents is the bifunctional chelator (BFC) that covalently links the α-emitting radionuclide to the targeting vector.⁶ An effective BFC for radiopharmaceutical applications will form a thermodynamically stable and kinetically inert complex with the radiometal of interest within biological environments. In the context of TAT, finding a suitable BFC is hindered by the difficulty in forming stable complexes with appropriate α-emitters, which are generally isotopes of large metal ions near the bottom of the periodic table.⁷ The small charge density of these large α-emitters weakens the M–L interactions that stabilize their resulting coordination complexes, requiring ligand design separate from conventional methods for smaller metal ions and limiting progress towards the utilization of TAT.

Figure 1.

Schematic of TAT, demonstrating the role of the BFC in bridging the radiometal to the biological targeting vector.

The first and currently only FDA-approved α-emitting therapeutic agent, Xofigo^®, is widely employed for the management of bone metastases within castration-resistant prostate cancer patients. This drug, administered as the uncomplexed salt [²²³Ra]RaCl_2,^8,9 capitalizes on the bone-mimetic properties of the free Ra²⁺ ion to localize to bone metastases.¹⁰ Although there has been some limited success in developing chelating agents for Ra²⁺ that would enable its use for treating other cancer types,^11–15 the majority of TAT constructs under preclinical investigation are focused on other radionuclides. Among the most promising candidates for this application are ²²⁵Ac and its daughter ²¹³Bi. For example, clinical studies on a prostate-specific membrane antigen (PSMA)-targeting ²²⁵Ac construct showed it to eliminate nearly all metastatic lesions in castration-resistant prostate cancer patients.¹⁶ Despite the promising therapeutic properties of this radionuclide, there remain some concerns regarding the ability to produce it on a large enough scale with sufficiently high radionuclidic purity to sustain clinical applications.¹⁷ The use of the daughter of ²²⁵Ac, ²¹³Bi, may be advantageous in these regards as this radionuclide can conveniently be isolated from ²²⁵Ac/²¹³Bi generators with high purity.^18–21 Furthermore, the shorter half-life of ²¹³Bi (t_1/2 = 45.6 min) may be favorable for some applications that involve a fast-clearing biological targeting vector and is also beneficial with respect to minimizing the redistribution of toxic daughter nuclides due to the alpha recoil effect. These promising features of ²¹³Bi have led to several clinical trials using this radionuclide for cancer treatment.^22–26

To date, there have been numerous efforts to develop an ideal BFC for ²¹³Bi,^27–47 with varying degrees of success. Two widespread ligand design strategies for ²¹³Bi chelation focus on derivatives of the macrocyclic ligand 1,4,7,10-tetraazacyclodecane-1,4,7,10-tetraacetic acid (DOTA) and the analogue of diethylenetriaminepentaacetic acid (DTPA) with a rigidified backbone (CHX-DTPA) (Chart 1).^{24,26,28,48,49} These types of ligands form ²¹³Bi complexes with good in vivo stability and high molar activities. However, macrocyclic ligands based on DOTA typically require elevated temperatures for efficient radiolabeling.⁵⁰ Furthermore, acyclic chelators, like DTPA and CHX-DTPA, tend to form less inert complexes in vivo. It should be noted, however, that CHX-DTPA shows much greater inertness compared to DTPA, a feature that has facilitated its use for in vivo studies.^{22,26,48,51–55}

Chart 1.

Ligands discussed in this work.

A common feature of both DOTA and CHX-DTPA, as well as the many other chelators that have been explored for ²¹³Bi, is their thermodynamic preference for small over large metal ions. Residing far down in the periodic table, Bi³⁺ has an ionic radius (0.96–0.99 Å for coordination number of six)^56,57 that is significantly larger than those of other +3 radiometals that have been chelated with these ligands. As such, we reasoned that investigating chelators with a reverse size-selectivity, a preference for large over small ions, would be a promising direction for the development of new BFCs for this radionuclide. In this context, ligands containing the 18-membered diaza-18-crown-6 macrocycle display this reverse size-selective property for metal ions.^58–66 Previously we have shown that macropa (Chart 1) forms remarkably stable complexes with large medicinally relevant radiometals like ^132/135La, ²²³Ra, and ²²⁵Ac.^11,67,68 We have further shown that altering the pendent donor arms and macrocyclic core rigidity changes the resulting selectivity for different metal ions.^59,60,69 Based on the reverse size-selectivity properties and tunability of this system, we sought to explore this class of ligands (Chart 1) for chelating Bi³⁺ for potential applications in TAT.

Results and Discussion.

Ligand synthesis and characterization.

The ligands investigated, macropa, CHX-macropa, macropaquin, macroquin-SO₃, macrophosphi, and macrophospho (Chart 1), feature varied macrocycle rigidity and pendent donor basicity, enabling us to investigate the roles of these variables on Bi³⁺ coordination. All of these ligands, except for macrophospho, have been previously reported and were synthesized following established procedures.^58,59,69 Macrophospho, which bears two pyridyl-2-phosphonic acid pendent arms, was synthesized following an approach that was used to obtain macrophosphi (Scheme 1).⁶⁹

Scheme 1.

Synthesis of macrophospho

The synthesis of the pendent donor arm intermediate 3 commenced from 2-(chloromethyl)pyridine-1-oxide (2), which could be prepared on a multigram scale in high yield by treating 2-chloromethylpyridine with meta-chloroperoxybenzoic acid (mCPBA).⁷⁰ Subsequently, the resulting pyridine-N-oxide 2 was activated towards an Arbuzov-type reaction^71,72 with ethyl chloroformate, and then treated in the same pot with triethyl phosphite to install the phosphonate ethyl ester. Compound 3 was isolated in 50–60% yield after sequential purification by both vacuum distillation and flash column chromatography. The alkylation of diaza-18-crown-6 with 3 in acetonitrile at reflux proceeded smoothly, resulting in the formation of 4 as a yellow oil. Compound 4, which was carried forward in the synthesis without additional purification, was hydrolyzed with 6 M HCl to remove the ethyl ester groups. The resulting product was purified by reverse-phase preparative high-performance liquid chromatography (HPLC), and then repeatedly dissolved in 6 M HCl and concentrated to dryness under vacuum to afford macrophospho as the hydrochloride salt. This ligand was fully characterized by ¹H, ¹³C{¹H}, and ³¹P{¹H} NMR spectroscopy, analytical HPLC, high-resolution mass spectrometry (HRMS), and elemental analysis (Figures S1–S6).

The protonation constants for macrophospho were determined via potentiometric titration, and are collected in Table 1, along with those for other diaza-18-crown-6-based ligands. The four most basic protonation constants of macrophospho most likely correspond to the tertiary amine nitrogens and one phosphonate oxygen on each pendent arm. We assign the two most basic protonation constants (log K 8.68 and 7.82) to tertiary amine nitrogens based on comparison to the analogous protonation constants for ligands such as macropa and macrophosphi, which also range from 7–8 (Table 1). A sixth protonation constant, which would belong to the last oxygen atom group, was too acidic to be measured via our potentiometric titration setup. The protonation constants of the phosphonates are lower than those of the other pendent donors, consistent with the higher acidity of this functional group. In particular, the comparison between macrophosphi and macrophospo show the that the most acidic protonation constant of the latter ligand is almost half a log unit lower. The greater acidity of phosphonates compared to phosphinates has been previously found in other ligand systems.⁷³

Table 1.

Protonation Constants for Investigated Ligands Determined via pH Potentiometry (25 °C and I = 0.1 M KCl)

	macropa2−a	macropaquin2−b	macroquin-SO34−b	CHX-macropa2−c	macrophosphi2−d	macrophospho2−
log Ka1	7.41	10.33	9.34	7.77	8.13	8.68(1)
log Ka2	6.85	7.15	9.43	6.95	6.77	7.82(1)
log Ka3	3.32	6.97	6.75	3.17	1.97	6.37(1)
log Ka4	2.36	3.24	6.62	2.51		5.68(1)
log Ka5	1.69					1.50(6)

^aReference 58,

^bReference 59,

^cReference 60,

^dReference 69

Bi³⁺ Complex Synthesis and Characterization.

To evaluate the Bi³⁺ coordination chemistry of these ligands, we synthesized the complexes by adding Bi(NO₃)₃·5H₂O to an aqueous solution of the ligand. After 30 min of stirring at room temperature, the pH of the resulting white suspension was adjusted from ≈1.5 to 4 with 2 M KOH, and then heated at 90 °C overnight. The Bi³⁺ complexes were isolated from this reaction mixture after filtration through a 0.20 μm nylon membrane and purification by reverse-phase HPLC. Notably, the mobile phase of this purification step employed 0.1% trifluoroacetic acid (TFA), highlighting the high stabilities of the complexes under acidic conditions. All six Bi³⁺ complexes were characterized by multinuclear NMR spectroscopy, HRMS, and elemental analysis (Figures S7–S41). HRMS for all complexes revealed the presence of the characteristic m/z molecular ion peak for the [M]⁺ species, and elemental analysis was consistent with the overall empirical formulae of these structures. Quantitative ¹H and ¹⁹F NMR spectroscopy was used as a further verification of the average number of TFA molecules per complex. Elemental analysis and quantitative NMR methods revealed non-integer quantities of TFA molecules for some of the ligands, reflecting them to be potentially isolated as a mixture of different protonation states. The mass of TFA present in these samples was taken into consideration for subsequent studies that required precise molecular weights of these ligands.

The ¹H and ¹³C{¹H} NMR spectra of the complexes were acquired in D₂O or DMSO-d₆ to characterize their solution properties. Coordination to the Bi³⁺ ion is confirmed by the presence of diastereotopic splitting of the methylene protons on the pendent arms and protons on the macrocyclic core. For [Bi(macropa)]⁺, [Bi(macrophospho)]⁺, [Bi(macrophosphi)]⁺, and [Bi(macroquin-SO₃)]⁻, these NMR spectra indicate that the complexes attain C₂ symmetry in solution, as reflected by the chemical equivalencies of the pendent donor groups. By contrast, [Bi(CHX-macropa)]⁺ and [Bi(macropaquin)]⁺ reveal asymmetric NMR spectra with discrete aromatic resonances corresponding to chemically distinct pendent donor groups (Figure 2). Distinct resonances are also observed for their associated methylenic linker protons. The lack of symmetry of these complexes suggests that the solution-state structure of all complexes involves conformations with both pendent arms on the same side of the macrocycle, similar to the solid-state structures for the Ln³⁺ and Ba²⁺ complexes.^59,67 Such a conformation has C₂ symmetry only when the pendent arms are identical, whereas different pendent arms results in a complex bearing C₁ symmetry, consistent with the NMR data.

Figure 2.

¹H NMR spectra (500 MHz, 298 K, D₂O) of [Bi(macropa)]⁺ (top) and [Bi(CHX-macropa)]⁺ (bottom), demonstrating C₂ or C₁ symmetry, respectively. The diagnostic aliphatic resonances marked by asterisks for each corresponds to the similarly marked methylene arm linker protons.

Additionally, the NMR spectra of [Bi(macrophosphi)]⁺ at room temperature show two species. The room temperature ³¹P{¹H} NMR spectrum of this complex displayed three resonances in a 1:1:2 ratio (Figure 3). Upon heating this solution to 120 °C in DMSO-d₆, the peaks coalesce to a single resonance at 26.47 ppm. This 1:1:2 ratio shows three separate environments for four phosphorus atoms, consistent with the presence of a symmetric and asymmetric diastereomer of the complex with different pendent arm conformations. At elevated temperature, the interconversion of the diastereomers is rapid, resulting in coalescence of the peaks in the NMR spectra. Similarly, the ¹³C{¹H} NMR spectrum of this complex displays three doublets for the phosphinate methyl group at room temperature that coalesce into a single doublet upon heating to 120 °C, and the aromatic region of ¹H NMR spectrum also converges to a clean single-set of resonances at this temperature. These data corroborate our prior observations on the La³⁺ complex of this ligand.⁶⁹ Upon metal coordination, the phosphorus atoms become chiral, and thus two diastereomeric forms of the complex are possible. At higher temperatures, racemization occurs at a fast rate, giving rise to an averaged NMR spectrum.

Figure 3.

¹H (left, 500 MHz), ¹³C{¹H} (middle, 126 MHz), and ³¹P{¹H} (right, 202 MHz) NMR spectra of [Bi(macrophosphi)]⁺ in DMSO-d₆ at 298 K (top) and 393.2 K (bottom).

The solid state structures of [Bi(macropa)]⁺, [Bi(macrophospho)]⁺, and [Bi(macrophosphi)]⁺ were determined by X-ray diffraction (Figure 4). In contrast to their symmetric NMR spectra, these structures reveal an anisotropic coordination environment about the Bi³⁺ center. This difference between solid- and solution-state structures is most likely a consequence of stereochemical non-rigidity of the complex, which leads to time-averaged NMR spectra. The crystal structure of [Bi(macrophosphi)]⁺ exhibits disorder about the methyl group and oxygen atom of one of the pendent phosphinate donors, reflecting the different diastereomers that were observed by NMR spectroscopy. Interatomic distances between the Bi³⁺ atom and ligand donor atoms are given in Table 2. In contrast to previously reported Lu³⁺, La³⁺, and Ba²⁺ crystal structures of ligands of this type, the Bi³⁺ center does not equally interact with all donors of the macrocycle. Two of the Bi–macrocycle donor interactions (Bi–N3 and Bi–O3) are significantly shorter than those between the other 4 donor atoms (N1, O2, O4). Across the three complexes, the Bi–N3 distances span values of 2.668, 2.666, and 2.659 Å, and the Bi–O3 separations are 2.7541, 2.740, and 2.669 Å for [Bi(macropa)]⁺, [Bi(macrophospho)]⁺, and [Bi(macrophosphi)]⁺, respectively. The other macrocycle donor atom–Bi distances for all three complexes are greater than 2.85 Å, suggesting that only weak interactions are present. By contrast, the Bi–pendent donor atom distances are substantially shorter. The pyridyl nitrogen–Bi (Bi–N2 and Bi–N4) distances are less than 2.57 Å in all three complexes, potentially reflecting a much stronger interaction than those with the nitrogen atoms of the macrocycle. Furthermore, the Bi–O (Bi–O5 and Bi–O6) distances within all three complexes are between 2.2 and 2.3 Å, signifying a particularly strong interaction. For comparison, the Bi–O distances for the carboxylate donors within [Bi(DTPA)]²⁻ and [Bi(DOTA)]⁻ are longer at the 2.3–2.5 Å range.^74,75 Although a definitive coordination number is difficult to obtain, we propose that these structures can be best described as six-coordinate with the Bi centers displaying distorted pentagonal pyramidal geometries. Thus, the coordination environment consists of the two short Bi–macrocycle interactions, between N3 and O3, and the four Bi–pendent donor atom interactions. The pentagonal pyramidal geometry would originate from the presence of the 6s² stereochemically active lone pair, which following VSEPR theory considerations, would be predicted to occupy the axial position of an ideal pentagonal bipyramid. Because a well-known impact of the stereochemically active lone pair is to shorten interatomic distances on the side opposite to it,⁷⁶ it is informative to compare the Bi–O6 and Bi–O5 separations within the three complexes. The distances between Bi and O6, the donor atom that occupies the axial position of the pentagonal pyramid, are 2.2316, 2.212, and 2.216 Å for [Bi(macropa)]⁺, [Bi(macrophospho)]⁺, and [Bi(macrophosphi)]⁺, respectively, whereas the Bi–O5 distances are somewhat longer at 2.2577, 2.232. and 2.254 Å. These data therefore support our proposed pentagonal pyramidal geometry and the directionality of the stereochemically active 6s² lone pair.

Figure 4.

X-ray crystal structures of [Bi(macropa)](NO₃)·dioxane (top left), [Bi(macrophospho)](TFA)·H₂O (top middle), and [Bi(macrophosphi)](TFA)·H₂O (top right) complexes. Ellipsoids are drawn at the 50% probability level. Hydrogen atoms, counteranions, and solvent molecules are excluded for clarity. The six donor atoms that comprise the pentagonal pyramidal coordination sphere of the Bi³⁺ are shown below each structure.

Table 2.

Interatomic Distances (Å) Involving Bi^a

Bond	[Bi(macropa)]+	[Bi(macrophospho)]+	[Bi(macrophosphi)]+
Bi–O1	2.987(2)	2.960(3)	2.909(2)
Bi–O2	2.895(2)	2.934(4)	2.868(2)
Bi–O3	2.7541(17)	2.740(4)	2.669(2)
Bi–O4	3.048(2)	3.259(4)	3.257(3)
Bi–O5	2.2577(16)	2.232(3)	2.254(2)
Bi–O6	2.2316(17)	2.212(3)	2.216(2)
Bi–N1	2.930(3)	2.992(5)	3.014(4)
Bi–N2	2.4419(19)	2.538(4)	2.566(3)
Bi–N3	2.688(2)	2.666(4)	2.659(3)
Bi–N4	2.413(2)	2.434(4)	2.442(3)

^aAtoms are labeled as shown in Figure 4. The values in the parentheses are one standard deviation of the last significant figure(s).

The SHAPE program⁷⁷ was further used to validate our assignment of the coordination polyhedra of the Bi³⁺ center for these three complexes (Table S2). Among the various ideal six-coordinate polyhedra, two geometries better matched to the experimental coordination geometries from substantially smaller continuous shape measures (CSMs). These CSMs, a quantitative measure of the match of an experimental coordination geometry to an idealized polyhedron, range from 1–4 for the Johnson pentagonal pyramid and the pentagonal pyramid. The CSMs for all other ideal polyhedra are significantly larger, on the order of 20–30, indicating that they describe the experimental geometries much more poorly. Notably, [Bi(macropa)]⁺, [Bi(macrophospho)]⁺, and [Bi(macrophosphi)]⁺ have immediate coordination spheres that match the Johnson pentagonal pyramid slightly better than the pentagonal pyramid. The difference between these two geometries is the ratio of the distance of the axial vertex to the equatorial plane to the distance between two equatorial vertices, with the Johnson pentagonal pyramid having a smaller ratio. This closer match to the Johnson pentagonal pyramid is most likely due to a combination of the O6–Bi–L_equatorial angles being less than 90° as well as the aforementioned shortened Bi–O6 bond length. Both such effects, the shortened axial bond length and contracted bond angles, support our proposal that the stereochemically active lone pair resides opposite to the axial oxygen atom.

Evaluation of the Kinetic Properties of Bi³⁺ Complexes.

To effectively use BFCs in nuclear medicine, they need to form kinetically inert complexes. To probe the kinetic inertness of each of the six Bi³⁺ complexes, we challenged them with a 1000-fold excess of the high-affinity chelator DTPA in an aqueous solution buffered at pH 7.4 with 3-(N-morpholino)propanesulfonic acid (MOPS). Based on the large thermodynamic affinity and significant excess of DTPA, these conditions should favor transchelation of the Bi³⁺ ion from our macrocyclic ligands to DTPA. The kinetics of this process were monitored by UV-visible spectroscopy (Figures S42–S47), allowing for the pseudo first-order half-life of this transchelation to be obtained. After spectral changes were no longer observed, the solution was analyzed by HPLC, revealing the presence of either only free ligand or the starting complex.

The half-lives measured under these conditions are collected in Table 3. Apparent from these data, the rate of transchelation varies significantly depending on the macrocyclic ligand. The most labile complexes are [Bi(macrophospho)]⁺ and [Bi(macrophosphi)]⁺, with dissociation half-lives of <10 and 1 min, respectively. The picolinate-bearing complexes [Bi(CHX-macropa)]⁺ and [Bi(macropa)]⁺ exhibit similar kinetic lability; both ligands possess half-lives near 40 min. The introduction of an 8-hydroxyquinolinate arm in the [Bi(macropaquin)]⁺ complex increased the half-life to 14 h, marking a significant enhancement of kinetic inertness. Remarkably, [Bi(macroquin-SO₃)]⁻, which contains two 8-hydroxyquinolinate-based pendent arms, does not show any spectral changes over a 21-d time period, demonstrating excellent kinetic inertness.

Table 3.

Half-Lives of Bi³⁺ Complexes in the Presence of 1000× Excess DTPA at pH 7.4.

Complex	Half-life
[Bi(macrophosphi)]+	< 1 min
[Bi(macrophopho)]+	8.9 ± 1.7 min
[Bi(CHX-macropa)]+	40.4 ± 4.3 min
[Bi(macropa)]+	46.6 ± 0.9 min
[Bi(macropaquin)]+	14.3 ± 1.4 h
[Bi(macroquin-SO3)]−	> 21 d

In comparing [Bi(CHX-macropa)]⁺ and [Bi(macropa)]⁺, which exhibit nearly identical decomplexation half-lives, the rigidity of the macrocycle does not significantly influence the complex inertness towards the DTPA challenges. By contrast, more significant inertness manifests with increasing pendent donor basicity. Macrophospho and macrophosphi, which possess the least basic pendent arms (oxygen donor pK_a values of < 2), form the most labile complexes with Bi³⁺, whereas the ligands with the significantly more basic quinolinate donors, macropaquin and macroquin-SO₃ (oxygen donor pK_a values of 9–10), demonstrate the highest levels of kinetic inertness. Macropa and CHX-macropa, bearing carboxylate oxygen donors (pK_a values of 2–3), show intermediate levels of kinetic inertness. The efficacy of macropaquin and macroquin-SO₃ for stabilizing Bi³⁺ in this DTPA challenge contrasts our observations with other large labile metal ions. For example, macroquin-SO₃ was previously found to be the poorest candidate for retaining Ba²⁺ under similar challenge conditions, whereas macropa was the most effective.⁵⁹ Furthermore, the La³⁺ complex of macropa is kinetically inert for over 20 d when treated with DTPA under similar conditions.⁶⁷ Considering that Bi³⁺ and La³⁺ have similar ionic radii, the relative lability of the [Bi(macropa)]⁺ complex is surprising and points to additional factors that are required to stabilize this main group ion.

Computational Studies.

The origin of the differing kinetic properties of these complexes was investigated using density functional theory (DFT) calculations at the TPSSh level of theory.⁷⁸ The Bi³⁺ atom was treated with the large core relativistic effective core potential (ECP60MDF)⁷⁹ and related basis set, and the ligand atoms were described using the triple zeta valence potential (TZVP) basis set.⁸⁰ We selected this computational approach based on previous studies that have demonstrated that this functional and effective core potential combination yield good results for Bi³⁺ complexes.^39,46 Upon optimization, all six geometries converged to local minima with significant structural distortions about the central Bi³⁺ ion due to the presence of the stereochemically active lone pair. Notably, the DFT-optimized structures of [Bi(macropa)]⁺, [Bi(macrophospho)]⁺, and [Bi(macrophosphi)]⁺ compare favorably to those determined experimentally by X-ray crystallography with root-mean square differences (RMSDs) between these structures of 0.144, 0.218, and 0.233 Å, respectively. As discussed above, the Bi³⁺ complex of macropa is significantly less inert than those of macropaquin and macroquin-SO₃, which is in contrast to that of the highly inert La³⁺ complex of macropa. We hypothesized that the stereochemical activity of the 6s² lone pair in the Bi³⁺ complexes, a feature that is not present within the La³⁺ complex, may affect their relative kinetic labilities. The degree of stereochemical activity of the Bi³⁺ lone pair is a result of mixing between the 6s and 6p orbitals, which perturbs the spherical distribution of the 6s shell.⁸¹ The degree of 6p mixing was analyzed using a Natural Bond Orbital (NBO) analysis, which has proven useful for calculations dealing with stereochemical activity of the lone pair in Bi³⁺ and Pb²⁺ complexes.^{46,63,76,82–84} Each complex contains 1–2% 6p character, which agrees well with previous calculations on similar complexes (Table 4).^46,84 Contour plots of the electron density of the molecular orbitals (MOs) containing significant (15–20%) Bi 6s² contribution show that the lone pair extends away from the Bi³⁺ nucleus and towards the macrocyclic core (Figure 5). Contrary to our hypothesis, however, there is not a distinctive trend between the degree of 6p contribution and the kinetic lability of the Bi³⁺ complex (Table 3). This result suggests that the stereochemical activity of the lone pair is not the sole source of the differing kinetic labilities of these macrocyclic chelators with Bi.

Table 4.

NBO Analysis of the Bi³⁺ Lone Pair for [Bi(L)]^+/− Complexes

Complex
[Bi(macrophosphi)]+	s(98.79%) p(1.20%)
[Bi(macrophospho)]+	s(98.74%) p(1.26%)
[Bi(CHX-macropa)]+	s(98.14%) p(1.85%)
[Bi(macropa)]+	s(98.10%) p(1.89%)
[Bi(macropaquin)]+	s(98.05%) p(1.95%)
[Bi(macroquin-SO3)]−	s(98.19%) p(1.80%)

Figure 5.

Contour plots of the electron density (e⁻ Å⁻³) for the MOs containing significant Bi 6s² contribution on the plane defined by the Bi³⁺ ion and the oxygen donor atoms of the pendent arms. (A) [Bi(macrophosphi)]⁺ HOMO, (B) [Bi(macrophospho)]⁺ HOMO, (C) [Bi(macropa)]⁺ HOMO, (D) [Bi(CHX-macropa)]⁺ HOMO, (E) [Bi(macropaquin)]⁺ HOMO–1, (F) [Bi(macroquin-SO₃)]⁻ HOMO–2. Values indicate maximum (blue) and minimum (red) electron density isovalues.

To further investigate the origin of the differing complex kinetic properties, we employed Bader’s quantum theory of atoms in molecules (QTAIM) analysis.⁸⁵ This technique probes the topology of the electron density of complexes and has been used with great success to understand bonding in metal complexes.^86,87 Within the QTAIM framework, the electron density, ρ(r), is divided into partitions represented by zero-flux surfaces, with the bond path between two atoms defined by the line of local maximum density. The intersection of the bond path and the zero-flux surface is defined as the bond critical point (BCP). Properties at the BCP, such as the electron density ρ(r), Laplacian of the electron density ∇²ρ(r), Lagrangian kinetic energy G(r), potential energy V(r), total energy density H(r), and delocalization index δ, describe the nature of the chemical interaction between two atoms. In the case of heavy elements, such as Bi, the ∇²ρ(r) may not properly describe the nature of metal-ligand bonding interactions.^88,89 To avoid this issue, the energy density parameters V(r), G(r), and H(r), the ratio of potential and kinetic energies |V|/G, and the normalized total energy density H/ρ are commonly used to interpret the nature of bonding interactions in heavy metal complexes.^90–95

Complete QTAIM results are compiled in Tables 5 and S3–S8. In agreement with our X-ray crystallographic and NBO analysis, the interactions of the Bi³⁺ center with the crown ether oxygen (O1–O4) and amine nitrogen (N1 and N3) atoms of the diaza-18-crown-6 core are almost purely ionic nature, as evidenced by the values of H(r) ≥ 0 and |V|/G < 1 (Table S3–S8). The interatomic interactions between the Bi center and the donor atoms of the pendent arms (O5, O6, N2, and N4) are more covalent, with values of H(r) < 0 and |V|/G > 1. The degree of covalency in these bonds can be analyzed by comparing the magnitude of the normalized energy density (H/ρ). Increased covalent character is reflected by more negative values of this parameter.^91,92,96,97 As seen in Table 5, the covalency of the Bi–O and Bi–N bonds increases with the ligand basicity and agrees well with the trend in experimental kinetic properties of the chelators. A similar trend is observed for δ, which is an integral property that can be considered as a measure of covalent bond order.^81,98

Table 5.

Selected QTAIM Metrics for Bi–Donor Interactions with the Ligand Pendent Arms in [Bi(L)]^+/− Complexes. The Corresponding Units are ρ (e⁻ Å⁻³), H/ρ (kJ/mol per e⁻), |V|/G (unitless), and δ (unitless)

Complex	ρ(r)		H/ρ		|V|/G		δ
	Bi–O6a	Bi–O5	Bi–O6	Bi–O5	Bi–O6	Bi–O5	Bi–O6	Bi–O5
[Bi(macrophosphi)]+	0.0790	0.0816	−481.7647	−500.7658	1.1599	1.1648	0.9476	0.9708
[Bi(macrophospho)]+	0.0718	0.0881	−432.9824	−540.2123	1.1495	1.1707	0.8771	0.9977
[Bi(CHX-macropa)]+	0.0786	0.0776	−502.2058	−498.0826	1.1729	1.1724	0.9626	0.9523
[Bi(macropa)]+	0.0778	0.0792	−498.4372	−506.3900	1.1724	1.1737	0.9526	0.9690
[Bi(macropaquin)]+	0.0790	0.0797	−503.1691	−524.1951	1.1726	1.1820	0.9715	0.9831
[Bi(macroquinSO3)]−	0.0872	0.0872	−579.2422	−579.2698	1.2008	1.2008	1.0345	1.0345
Complex	ρ(r)		H/ρ		|V|/G		δ
	Bi–N2	Bi–N4	Bi–N2	Bi–N4	Bi–N2	Bi–N4	Bi–N2	Bi–N4
[Bi(macrophosphi)]+	0.0507	0.0416	−350.5292	−261.7623	1.1785	1.1398	0.6846	0.6054
[Bi(macrophospho)]+	0.0476	0.0444	−321.6876	−291.0008	1.1654	1.1527	0.6499	0.6323
[Bi(CHX-macropa)]+	0.0155	0.0322	234.3138	−206.1312	0.8699	1.1323	0.2722	0.4715
[Bi(macropa)]+	0.0566	0.0512	−401.4145	−353.3262	1.1957	1.1766	0.7238	0.6839
[Bi(macropaquin)]+	0.0152	0.0263	301.8964	−86.6741	0.8457	1.0523	0.2916	0.4341
[Bi(macroquinSO3)]−	0.0581	0.0581	−407.7068	−407.6882	1.2066	1.2066	0.7213	0.7213

^aAtom numbering scheme is shown in Figure S48.

A recent study has shown that topological analysis of QTAIM parameters along the length of the bond path, rather than just at the BCP, provides useful information into the nature of the bonding interactions in complexes containing heavy main-group elements.⁹⁹ As such, we evaluated ρ and ∇²ρ(r) across the entire length of the Bi–O bonds in [Bi(macrophosphi)]⁺ and [Bi(macroquin-SO₃)]⁻. To account for differing interatomic distances and facilitate comparison of the complexes, the interatomic distances were normalized to one-unit length. The plot of ρ(r) reveals a clear minimum between the atoms, indicating the location of the BCP for the Bi–O interaction (Figure 6a). For both complexes, the BCP is shifted away from the midpoint of the bond path and towards the oxygen atom, which highlights the different electronegativities of the elements and the polarized nature of this interaction. The BCP is less shifted from the midpoint of the Bi and O atoms for [Bi(macroquin-SO₃)]⁻ compared to [Bi(macrophosphi)]⁺, which suggests that the distribution of ρ(r) across the bond is slightly more symmetric and the interaction is more covalent in nature. This result agrees with the analysis of the energy density parameters at the BCP (Table 5). In the plot of ∇²ρ(r), the single local minimum along the bond path is located near the oxygen atom (Figure 6b), a feature that is observed in other systems with interactions between second-period elements and third- and fourth-period elements.^99–104 It has been shown that the decrease in the magnitude of this local minimum can be attributed to a decrease in bond order.⁹⁹ As expected, the local minimum for [Bi(macroquin-SO₃)]⁻ is considerably more negative than for [Bi(macroposphi)]⁺, suggesting that the interaction between Bi and the O donor atoms of the quinoline pendent arms is more covalent in nature than those of the picolinate donors. Taken together, these results suggest that the enhanced kinetic inertness of [Bi(macroquin-SO₃)]⁻ compared to the other chelators described here may stem from the increased covalency between the metal center and the donor atoms of the pendent arms.

Figure 6.

Evaluation of (a) ρ and (b) ∇²ρ along the normalized Bi–O bond paths of [Bi(macrophosphi)]⁺ and [Bi(macroquin-SO₃)]⁻. Dashed vertical lines represent the location of the BCP.

Radiolabeling Studies.

As a final validation on the value of these chelators for ²¹³Bi TAT, we carried out radiolabeling studies using macropa, macropaquin, and macroquin-SO₃, which formed comparatively more inert Bi³⁺ complexes than the other ligands. These ligands, in concentrations ranging from 10⁻⁷ to 10⁻⁴ M, were mixed with [²¹³Bi]BiI₄⁻/[²¹³Bi]BiI₅²⁻ (30 kBq–210 kBq), freshly eluted from a ²²⁵Ac/²¹³Bi generator, in pH 5.5 2-(N-morpholino)ethanesulfonic acid (MES) buffer. As radiolabeling progressed at room temperature for 18-membered macrocycles or 95 °C for DOTA, aliquots were removed and analyzed by radio-TLC to assess the radiochemical yields (RCYs) after 8 min for 18-membered macrocycles or 5.5 min for DOTA. The resulting concentration-dependent RCYs for each ligand are collected in Table 6 and Figure 7. Notably, despite the radiolabeling reactions being performed at room temperature for the 18-membered macrocycles, the RCYs obtained are greater than those for DOTA, which required heating at 95 °C for all concentrations. At the highest ligand concentration (10⁻⁴ M), macropa, macropaquin, and DOTA quantitatively radiolabel ²¹³Bi, whereas macroquin-SO₃ achieved a 91% RCY under these conditions. For all four ligands, RCYs of approximately 90% are maintained upon decreasing the ligand concentration by two order of magnitude to 10⁻⁶ M. At ligand concentrations of 10⁻⁷ M, significant differences in the RCYs are observed across the four chelators. DOTA and macropaquin perform the poorest at this concentration, reaching RCYs of approximately 12 and 15%, respectively. Macroquin-SO₃ achieves a moderate 40% RCY at this concentration, whereas macropa maintains a RCY of approximately 80%, affirming its superior radiolabeling capabilities. Notably, all three of these macrocyclic ligands outperform DOTA, indicating that they may be more favorable for use in ²¹³Bi TAT.

Table 6.

Average RCYs (%) of [²¹³Bi]Bi-Complexes at 95 °C for DOTA after 5.5 min and Room Temperature for other Ligands after 8 min

Ligand Concentration	macropa	macropaquin	macroquin-SO3	DOTA (95 °C)
10−4 M	>99	>99	91 ± 1	>99
10−5 M	98 ± 1	>99	91 ± 1	94 ± 3
10−6 M	97 ± 2	93 ± 2	87 ± 2	91 ± 1
10−7 M	84 ± 17	15 ± 6	42 ± 4	12 ± 12
10−8M	4 ± 1

Figure 7.

RCYs for each ligand vs. concentration. Concentration-dependent radiolabeling studies were performed by the addition of [²¹³Bi]BiI₄⁻/[²¹³Bi]BiI₅²⁻ (30 kBq–210 kBq) to a solution containing ligands in MES buffer (0.5 M, pH 5.5–6). All radiolabeling studies were carried out within 5 min post-elution of the ²²⁵Ac/²¹³Bi generator. Macropa, macropaquin, and macroquin-SO₃ were incubated at room temperature for 8 min, whereas DOTA was incubated at 95 °C for 5.5 min.

A comparison of the radiolabeling properties of these ligands can also be discerned from the decay-corrected molar activities (Table 7). At the lowest ligand concentrations required to achieve > 80% RCY, molar activities of 8.69, 1.49, and 1.82 MBq/nmol were obtained for the radiolabeled complexes of macropa, macropaquin, and macroquin-SO₃, respectively. These values are significantly larger than the molar activity of 0.284 MBq/mol that was achieved with DOTA under elevated temperatures. In particular, the 30-fold greater molar activity of macropa in comparison to DOTA, which was accomplished at room temperature, highlights the effective ²¹³Bi-radiolabeling properties of these 18-membered macrocycles.

Table 7.

Molar Activities (MBq/nmol) of [²¹³Bi]Bi-Complexes at the Lowest Ligand Concentrations Required to Attain > 80% RCY

Ligand	Molar Activity (MBq/nmol)
macropa	8.69
macropaquin	1.49
macroquin-SO3	1.82
DOTA	0.284

Conclusions

In conclusion, a set of six macrocyclic ligands were evaluated for their potential as Bi³⁺ chelators in TAT. These ligands, all containing the 18-membered diaza-18-crown-6 macrocyclic core, differed based on their pendent donors, as well as macrocycle rigidity. The evaluation of the kinetic properties of the Bi³⁺ complexes revealed that macrocycle rigidity had little influence on their inertness, in contrast to pendent donor basicity, which played a large role. Specifically, more basic donors, like the quinolinate groups found in macroquin-SO₃, gave rise to more kinetically inert complexes, whereas the least basic phosphinate and phosphonate groups yielded labile complexes. To understand the origins of this effect, the complexes were fully characterized by solid-state and solution methods. Although the solid-state X-ray crystal structures showed profound structural distortion arising from the stereochemically active 6s² lone pair of the Bi³⁺ ion, NMR studies indicate that an averaged symmetric complex is obtained in solution. Furthermore, DFT calculations verified that the extent of the stereochemical activity of this lone pair, as measured by the corresponding %p character, had little ramifications on the overall inertness of the complexes. By contrast, these computational studies predicted that an increase in covalency contributed to the enhanced inertness of the macroquin-SO₃ complex over those of the other ligands. Despite the excellent kinetic inertness of the [Bi(macroquin-SO₃)]⁻ complex, radiolabeling of this ligand with ²¹³Bi was relatively inefficient compared to macropa. Given the short half-life of ²¹³Bi, the faster radiolabeling and higher molar activities afforded by macropa may be more favorable for applications in TAT.

In summary, this study has shown that the diaza-18-crown-6 scaffold is highly promising for use in Bi³⁺ chelation, displaying several advantages, such as vast tunability and rapid complex formation, over the conventional cyclen-based chelators. The tunability of this class of ligands via changing the basicity of the pendent donor groups can be valuable for accessing new highly promising BFCs for ²¹³Bi TAT. Future work will assess the suitability of the ligands in this study for this application.