Metal–Ligand Interactions in Scandium Complexes with Radiopharmaceutical Applications

Abstract

The radioisotopes of scandium (⁴³Sc, ⁴⁴Sc, and ⁴⁷Sc) are potential candidates for use in imaging and therapy both separately and as elementally matched pairs for radiotheranostics. In the present study the bonding interactions of Sc³⁺ with 18 hepta- to decadentate ligands are compared using density functional theory (DFT) calculations. The bonding analysis is based on the natural bond orbital (NBO) model. The main contributions to the bonding were assessed using natural energy decomposition analysis (NEDA). Most of the ligands have anionic character (charges from 2– to 8−); thus the electrical term determines the major differences in the interaction energies. However, interesting features were found in the covalent contributions manifested by the ligand → Sc³⁺ charge transfer (CT) interactions. Significant differences could be observed in the energetic contributions of the N and O donors to the total CT.

Short abstract

Density functional theory calculations in conjunction with energy decomposition analysis were used to uncover the bonding characteristics of Sc³⁺ complexes. The analysis confirmed the comparable stabilities of complexes with hepta- and octadentate ligands. The primary ligand donors are anionic oxygen and aromatic nitrogen atoms.

Introduction

Scandium radioisotopes (⁴³Sc, ⁴⁴Sc, and ⁴⁷Sc) are important candidates for use in imaging and radioimmunotherapy. Their main advantages are emitted low- or middle-energy β-particles and conveniently short half-lives.

⁴⁴Sc produces middle-energy β⁺ radiation with a high branching ratio (E_β⁺av = 632 keV, 94%) and a physical half-life of t_1/2 = 3.97 h.¹ This large t_1/2 compared with those of the most common β⁺ emitters, ¹⁸F (1.83 h) and ⁶⁸Ga (1.13 h), facilitates acquiring positron emission tomography (PET) images at later time points than with the latter conventional isotopes. The advantages are a higher image quality,² convenient investigation of pharmacokinetics of slower-circulating bioconjugates, and cost-effective centralized production and regional distribution of the isotope.

⁴⁷Sc is a high branching β^– emitter (E_β ^–av = 162 keV, 100%) with a significant half-life (t_1/2 = 3.35 d).¹ This low-energy radiation is appropriate for treatment of small tumors as well as cancer metastasis,³ making ⁴⁷Sc a promising competitor of the clinically established ¹⁷⁷Lu radionuclide (E_β^–av = 134 keV, t_1/2 = 6.65 d).¹ In addition, the emitted γ-rays (E_γ = 159 keV, I_γ = 68%) have an ideal energy for single photon emission computed tomography (SPECT) imaging.³

The above Sc isotopes are perfectly suitable for radiotheranostics, in which method the same molecular targeting vectors are labeled partly with a diagnostic, partly with a therapeutic radionuclide.^4,5 Currently, the pair of ⁶⁸Ga and ¹⁷⁷Lu is used in clinics for PET imaging and therapy.^6,7 However, the two elements have different coordination chemistries⁸ leading to somewhat different in vivo kinetics and receptor binding affinity, thus decreasing the therapeutic efficiency.⁹ From this point of view, the ideal solution would be the combination of different radioisotopes of the same chemical element like the matched pair ⁴⁴Sc and ⁴⁷Sc.

Additional useful Sc radioisotopes include ⁴³Sc (t_1/2 = 3.89 h, E_β ⁺av = 476 keV, 88%),¹ which is free from high-energy γ emission and therefore can be suitable for PET imaging.¹⁰ Last, the ^44mSc isotope (t_1/2 = 58.6 h), an isomeric state of ⁴⁴Sc, has been suggested as a potential in vivo ⁴⁴Sc generator allowing longer pharmacokinetic studies.¹¹

Currently, the primary chelating ligand for Sc³⁺ is 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetate (DOTA).¹² Disadvantages of this ligand are, however, its high affinity to other metal ions¹³ and the slow radiolabeling kinetics. There is a high demand for more suitable ligands which could increase the efficiency of Sc radiotheranostics.

In the present work the structural and bonding properties of Sc³⁺ with various cyclic and acyclic chelating ligands are studied in the isolated molecules using DFT calculations. The small ionic radius of Sc³⁺ may imply preferred interaction with small ligands with coordination numbers (CNs) of <8. However, a comparison of available stability constants of Sc³⁺ with octadentate and smaller hexadentate ligands proved the preference for octacoordination.^14,15 On the other hand, heptacoordination can be reasonably stable.¹⁶ Therefore, in the present study the bonding characteristics with selected potentially octa- or heptadentate ligands are assessed. They contain various donor groups with the main donor atoms including neutral N and O and anionic (mostly carboxylate) O. The metal–ligand interactions are analyzed using the natural bond orbital (NBO) model.¹⁷⁻¹⁹

Ligands

The cyclen-based ligands presented in Figure 1 compose an important group of chelators in radiopharmaceutics. The 12-membered ring of cyclen (1,4,7,10-tetraazacyclododecane) forms a semirigid basis of the ligand cavity with (generally four) pendant arms filling the conformational space around the captured metal ions. The cyclen ring itself can establish tetradentate coordination with its four N donor atoms.

Figure 1.

Cyclen-based ligands probed with Sc³⁺ in the present study. H₃PSMA′ and H₃DOTATATE′ are truncated models of the very large original ligands.

The most known ligand from the cyclen-based group is H₄DOTA (1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid). Due to its good performance for metal ions, it achieved the title of “gold standard” for a number of trivalent radioisotopes, including ¹¹¹In, ¹⁷⁷Lu, ^86/90Y, ²¹³Bi, ²²⁵Ac, and ^44/47Sc.¹² The crystal structure of the Sc complex as well as the thermodynamic stability in solution (log K = 30.79) was reported by Pniok et al.²⁰ The ligand is generally applied in alkaline aqueous solutions; thus the complexes formed between DOTA^4– and trivalent metal ions have a charge of 1–. In the complexes generally octacoordination is established through the cyclen N and carboxylate O donors. However, due to the small size of the pendant arms the metals are not fully surrounded, thus allowing coordination of an additional small ligand at the partly open side between the COO^– groups of the complex. In aqueous solutions this is generally a H₂O molecule;^21,22 its role in complexation of the Sc³⁺ ion is probed here too.

Three extended H₄DOTA derivatives are included in the present study in order to estimate the effect of popular linker moieties (which link the complex with the targeting vector) on the bonding properties. These linkers are substituents in the outer sphere of the tetraazacyclododecane ring in order to avoid direct interference with metal binding. We probed the p-SCN-Bn (4-isothiocyanatophenyl) methyl substituent²³ in position 2 as well as truncated H₃PSMA and H₃DOTATATE ligands, in which one COOH group of H₄DOTA is replaced by (CO)NH–CH₂–C₆H₁₁ and (CO)NH–CH(−CH₂–C₆H₅)–(CO)NH–CH₃ groups, respectively (cf. Figure 1). Note that the kinetic and thermodynamic stabilities of these latter complexes were found to be slightly lower than those of the H₄DOTA ones, but still sufficiently high for in vivo application.

Neutral ligands are represented in this study by 1,4,7,10-tetrakis(3-pyridazylmethyl)-1,4,7,10-tetraazacyclododecane (L^pyd). The N donors of the pendant arms facilitate octadentate coordination to the metal ion, whereas the large size of the arms can shield the metal and sterically hinder a coordination of additional small molecules (e.g., H₂O). This ligand was shown recently to be effective for the borderline Lewis acid Bi³⁺,²⁴ and it would be of interest to see how the bonding occurs in detail with the harder Lewis acid Sc³⁺.

The H₂MeDO2PA (6,6′-((4,10-dimethyl-1,4,7,10-tetraazacyclododecane-1,7-diyl) bis(methylene))dipicolinic acid) ligand has only two pendant arms, but it achieves octacoordination by the pyridine N and carboxylate O donors of the picolinic acid arms. This ligand was found to be superior to H₄DOTA in complexing Bi³⁺;^25,26 thus it would be interesting to see the relation in the case of Sc³⁺.

The H₄DOTPA (1,4,7,10-tetraazacyclododecane-1,4,7,10-tetrapropionic acid) molecule contains pendant arms elongated by a methylene group, and in this way it has a larger flexibility with respect to H₄DOTA. This larger flexibility seemed to be a slight advantage for bonding with the Bi³⁺ and Ac³⁺ ions as compared to H₄DOTA.²³

In the H₈DOTMP ligand (((1,4,7,10-tetraazacyclododecane-1,4,7,10-tetrayl)tetrakis(methylene))tetraphosphonic acid) the carboxylate oxygen donors of H₄DOTA are replaced by phosphonate ones. This chelator has been considered for a bone-seeking agent with various radioisotopes (¹¹¹In, ¹⁶⁶Ho, ¹⁵³Sm, ¹⁷⁷Lu, ²¹²Bi).²⁷⁻²⁹ In this study both the form with the fully deprotonated (charge 8−) and that with the half-deprotonated (charge 4−) tetraphosphonic acid were probed. The two forms facilitate a comparison of the coordination interactions in strong and moderately alkaline environments.

Figure 2 presents some additional cyclic ligands probed in the present study. From them H₄AAZTA (1,4-bis(carboxymethyl)-6-(bis(carboxymethyl))-amino-6-methylperhydro-1,4-diazepine) already has a history with Sc³⁺, forming highly stable complexes (log K = 27.7).¹⁶ This heptadentate ligand coordinates by four carboxylate O and three tertiary amine N donors. The backbone is flexible enough for room-temperature radiolabeling, while the semirigid cyclic moiety results in inertness comparable to DOTA.

Figure 2.

Other applied cyclic ligands. From H₂bispa² two heptadentate ligands (L², L³) were derived by modification of the top picolinic acid moiety; see text.

H₂macropa (N,N′-bis((6-carboxy-2-pyridil)methyl)-4,13-diaza-18-crown-6) is a recently introduced competitor for H₄DOTA for actinides and lanthanides.³⁰⁻³² This decadentate ligand can efficiently capture metal ions with the N and O donors in the crown and picolinate arms. Though H₂macropa was reported to prefer larger-size metals,³⁰ a comparative bonding analysis of its complex with Sc³⁺ can be of interest.

Bispidine-based ligands showed high complex stability, inertness, and fast complexation kinetics^33,34 and can simply be conjugated to peptides and antibodies.³⁵⁻³⁷ Another advantage of this ligand family is the easy variation of O- and/or N-donor sets on the rigid bispidine scaffold producing CN = 4–8.^33,34,38,39 The recently introduced octadentate H₂bispa² (6,6′-((9- hydroxy-1,5-bis(methoxycarbonyl)-2,4-di(pyridin-2-yl)-3,7-diazabicyclo[3.3.1]nonane-3,7-diyl) bis(methylene))dipicolinic acid) provided excellent performances with medically relevant metal ions In³⁺, Bi³⁺, Lu³⁺, and La³⁺ including fast complex formation under ambient conditions.^33,40 Two other picolinate-/acetate-based heptadentate bispa-type ligands⁴⁰ are also included in the present study in order to check whether they might be more suitable for the small Sc³⁺ ion. They are derived from H₂bispa² by removing the COOH group from the top picolinic acid (see Figure 2) and by replacing this top picolinic acid with a COOH group, denoted as HL² and H₂L³, respectively.

Acyclic chelators are kinetically somewhat less stable than macrocyclic ones (like H₄DOTA), but they have the advantage that the formation of their complexes at room temperature is much faster. In the present study five octadentate acyclic chelators (Figure 3) were probed. Three of them have been reported for fast complex formation with Sc³⁺ and very high labeling yields.⁴¹

Figure 3.

Acyclic ligands probed with Sc³⁺ in the present study.

H₄EGTA (ethylene glycol-bis(2-aminoethyl ether)-N,N,N′,N′-tetraacetic acid, also known as egtazic acid) showed very good complexation properties to Sc³⁺, outperforming several acyclic ligands, and thus was suggested to be a suitable precursor for Sc radiopharmaceuticals.⁴¹ The strong complexes are formed by binding via the four carboxylic and two ether O atoms, completing the coordination by two tertiary amine N’s.

H₄BAPTA (6-dentate 1,2-bis(o-aminophenoxy)ethane-N,N,N′,N′-tetraacetic acid) is compatible with H₄EGTA for the binding of Ca²⁺ ions⁴² but for Sc³⁺ showed a worse performance than its parent H₄EGTA.⁴¹ Surely, the structure of H₄BAPTA is less flexible due to substitution of two ethylene moieties by benzyl rings. The present bonding analysis can elucidate the details behind the weaker complexation.

H₅DTPA (1,1,4,7,7-diethylenetriaminepentaacetic acid) belongs to the most efficient acyclic chelators¹² due primarily to the five carboxylate O donors and efficient encapsulation of metal ions. The coordination sphere is completed by three tertiary amine N’s (cf. Figure 3). This ligand has been found to exert great affinity for Sc³⁺ (log K = 27.43)²⁰ and was suggested to be a suitable precursor for Sc radiopharmaceuticals.⁴¹ The observed dissociation aptitude in solution was alleviated in its more preorganized (semirigid) derivative, CHX-A″-H₅DTPA (2-aminoethyl-trans-[S,S]-cyclohexane-1,2-diamine-N,N,N′,N″,N″-pentaacetic acid) while maintaining rapid labeling kinetics. The latter ligand is now widely used with radioimmunoconjugates.^12,43

3,4,3-LI(1,2-HOPO), N,N′-1,4-butanediylbis(N-(3-(((1,6-dihydro-1-hydroxy-6-oxo-2-pyridinyl)carbonyl)amino)propyl)-1,6-dihydro-1-hydroxy-6-oxo-2-pyridinecarboxamide (denoted as HOPO below), has demonstrated strong affinity for hard metal 3+ and 4+ ions^44,45 including Sc³⁺,⁴⁶ with log K_ScL = 25.16.⁴⁷ Advantages of this ligand include strong bonding with the hard O-donating hydroxypyridinone groups, complex formations at lower pH than H₄DOTA, and fast binding kinetics.

In the discussion below the abbreviations of the deprotonated ligands are used according to the complexing anionic forms (DOTA, etc.).

Results and Discussion

Structural Characteristics

The octacoordinated Sc³⁺ ion has a relatively small effective ionic radius: 0.870 Å.⁴⁸ It is smaller by 0.256 Å than Pr³⁺ (1.126 Å⁴⁸), where the switch of the DOTA conformers in complexes of the lanthanide (Ln) row occurs. Trivalent ions with ionic radii larger than that of Pr³⁺ are known to prefer the twisted square antiprismatic (TSAP) conformer of DOTA, whereas the smaller lanthanides favor the square antiprismatic (SAP) one.^8,49−51 These two conformers are presented in Figure 4. The SAP structure has slightly smaller cavity and thus can form stronger interactions with the smaller ions. It should be noted that in the crystal of K[Sc(DOTA)](H₆DOTA)Cl₂·4H₂O the TSAP conformer has been identified, which may be stabilized by the interaction of the four COO^– groups with K⁺ linking the H₆(DOTA)Cl₂ moiety to Sc(DOTA)⁻.²⁰

Figure 4.

Two conformers of the Sc(DOTA)⁻ complex omitting hydrogen atoms for clarity. Moieties toward the back are gradually faded.

In agreement with expectations, in the present B3LYP/6-31G** calculations the SAP conformer of ScDOTA proved to be more stable by 15.2 kJ/mol than the TSAP conformer. A similar stability relation was computed for the DOTA-p-NCS-Bn, DOTATATE′, and PSMA′ ligands. In contrast, the other cyclen-based ligands with larger pendant arms, DOTPA, DOTMP, and L^pyd, preferred the TSAP conformer by 15–50 kJ/mol at the B3LYP/6-31G** level.

Another ligand with significant conformational varieties is macropa, from which the Δ(λδλ)(λδλ) and Δ(δλδ)(δλδ) conformers, denoted by LDL and DLD, respectively, were probed with Sc³⁺ in the present study. For Ln, the LDL form was found to form the most stable complexes with smaller Ln³⁺ (Lu³⁺),³⁰ whereas DLD prefers larger ions (e.g., La³⁺, Ac³⁺).^30,52 In agreement with the above trend, the Sc(macropa_LDL)⁺ complex was computed at the B3LYP/6-31G** level to be more stable by 15.9 kJ/mol than the Sc(macropa_DLD)⁺ conformer. The distortion of the C₂ symmetry to C₁ in the macropa_DLD complex is likely the consequence of the lesser ability of this macropa conformer to efficiently encapsulate Sc³⁺.

Some of the probed ligands are known to allow the coordination of an additional small ligand, like H₂O. This is due to insufficient encapsulation of the metal ion, leaving a site with considerable free space in the coordination sphere of the metal. The optimized structures of the present Sc³⁺ complexes were thoroughly inspected from this point of view. The conclusion of this visual inspection is that small ligands can easily coordinate to the significant free site of the cyclen-type and AAZTA complexes, whereas the other ligands encapsulate Sc³⁺ more tightly, leaving not enough space for attack by a small ligand. The effect of a H₂O ligand at the ninth coordination site on the bonding properties was assessed in the Sc(DOTA_SAP)⁻ complex; similar effects can be expected for the other related complexes too.

Table 1 compiles the symmetries of the optimized structures. The well-known C₄ symmetry of DOTA complexes^{8,23,49−51,53,54} is preserved in the derivatives with L^pyd, DOTPA, and DOTMP. Similarly to literature data on Bi³⁺ complexes, optimized structures with C₂ symmetry were obtained for the MeDO2PA, macropa_LDL, and BAPTA complexes with Sc³⁺.²³ In contrast, the C₂ symmetry reported for Ln(macropa_DLD)⁺ complexes^30,52 was destroyed with the smaller Sc³⁺ ion.

Table 1. Selected Structural Characteristics^a.

complex	CN	symmetry	Sc–Oav	Sc–Nav
DOTATSAP	8	C4	2.099 (4)	2.655 (4)
DOTASAP	8	C4	2.099 (4)	2.617 (4)
DOTASAP + H2O	9	C2	2.157 (5)	2.740 (4)
DOTA-p-NCS-Bn	8	C1	2.097 (4)	2.631 (4)
PSMA′	8	C1	2.122 (4)	2.587 (4)
DOTATATE′	8	C1	2.122 (4)	2.573 (4)
Lpyd	8	C4	–	2.422 (8)
MeDO2PA	8	C2	2.053 (2)	2.455 (6)
DOTPA	8	C4	2.069 (4)	2.747 (4)
DOTMP	8	C4	2.097 (4)	2.661 (4)
DOTMP″	8	C4	2.059 (4)	3.244 (4)
AAZTA	7	C1	2.091 (4)	2.468 (3)
macropaLDL	10	C2	2.339 (6)	2.730 (4)
bispa2	8	C1	2.048 (2)	2.483 (6)
L3	7	C1	2.006 (2)	2.382 (5)
L2	7	C1	1.985 (1)	2.347 (6)
EGTA	8	C1	2.230 (6)	2.474 (2)
BAPTAb	8	C2	2.016 (6)	2.687 (2)
DTPA	8	C1	2.165 (5)	2.599 (3)
CHX-A″-DTPA	8	C1	2.161 (5)	2.597 (3)
HOPO	8	C1	2.231 (8)	–

^aThe Sc³⁺ complexes are denoted by the ligand names given in the first column. The PSMA′ and DOTATATE′ notations mean the truncated ligands to 73 and 77 atoms, respectively; DOTMP and DOTMP″ mean the DOTMP^4– and DOTMP^8– ligands, respectively. The average Sc–O and Sc–N bond distances are given in angstroms. The number of coordinating O and N atoms are given in parentheses.

^bTwo Sc–O distances around 3.4 Å in the Sc(BAPTA)⁻ complex are too large for a significant interaction. They were excluded from the average data in order to reflect the very strong character of the relevant Sc–O interactions.

The average Sc–O and Sc–N distances are given in Table 1, whereas the individual bond distances are compiled in Figure 5. The values depicted in Figure 5 as well as the Cartesian coordinates of the optimized structures are given in the Supporting Information. We can distinguish O donors with formal negative charge (carboxylate in most ligands and deprotonated hydroxypyridinone in HOPO, denoted as O^–) and formally neutral (ether O in macropa, EGTA, BAPTA; C=O in PSMA′, DOTATATE′, and HOPO; denoted as O). The formally neutral N donors can be separated as aliphatic (in cyclen and macropa rings, denoted as N_cyc) or aromatic (in the picolinate and pyridine/piperidine groups, denoted as N_ar).

Figure 5.

Distributions of Sc–O and Sc–N distances in the studied complexes. For the notation of ligands, see footnote a of Table 1. The red and blue lines indicate the average Sc–O and Sc–N values, respectively.

The primary Sc–O distances are around 2.1 Å, whereas those of the Sc–N_ar and Sc–N_cyc are around 2.3 and 2.6 Å, respectively (cf. Figure 5). Note that the two Sc–O distances around 3.4 Å in the Sc(BAPTA)⁻ complex are too large for a significant interaction; therefore they were excluded from the average data.

The data indicate generally stronger interactions with the O donors than with N, which is reasoned by the anionic character of most O donors in the complexes. The relatively large Sc–O_av values in the macropa and EGTA complexes can be attributed to the neutral ether O’s in these ligands, which form very weak interactions with Sc³⁺. The carbonyl oxygens in the HOPO ligand establish intermediate interactions due partly to their better donor abilities with respect to ether O and to their more flexible position in the ligand. Moreover, in HOPO the C=O groups have Sc–O distances comparable to those of the anionic N–O groups implying similar interaction strengths of the two types of O donors.

From the two types of Sc–N interactions, the ones with N_ar have generally shorter distances (see Figure 5). As the Sc–N interactions are generally weaker than the Sc–O ones, the latter ones play the major role in the structure of the complexes. Consequently, the bond distances of the weaker Sc–N interactions show a larger variation in Figure 5.

The H₂O ligand at the ninth coordination site slightly increases the Sc–N_cyc distance with respect to that in the parent Sc(DOTA)⁻ complex as it pulls Sc³⁺ slightly closer to the ninth coordination site.

The effects of pendant arms on the Sc–N_cyc interaction can be analyzed in the first half of Figure 5 (from DOTA to DOTMP). This effect on the Sc–N_cyc bond distances is generally small. A striking exception can be observed in the Sc(DOTMP)^5– molecule, where the Sc³⁺ ion is pulled significantly away from the cyclen moiety by the strong electrostatic interactions with the PO₃^2– groups. The Sc–N distance of 3.244 Å suggests marginal interaction with N; thus this complex can rather be referred to as tetracoordinated Sc³⁺. (This marginal Sc–N interaction is reflected also in the CT data, vide infra.) In contrast, the Sc–N distances in the tetraprotonated Sc(DOTMP)⁻ are in the range of those in the complexes with DOTA and other DOTA derivatives. A small but significant increase in the Sc–N_cyc distance can be observed also in Sc(DOTPA)⁻, where the pendant arm increased by a CH₂ group results in an increased cavity affecting primarily the positions of the O donors.

Comparison of the Sc–ligand bond distances in the complexes with DOTA_SAP and DOTA_TSAP can provide a clue to the stability relations. The Sc–O distances are the same whereas the Sc–N distances are shorter by 0.04 Å in the Sc(DOTA_SAP)⁻ complex (cf. Table 1 and Figure 5). This refers to comparable Sc–O interactions in the two conformers and indicates that the larger stability of the Sc(DOTA_SAP)⁻ complex is enforced by its stronger Sc–N interactions. The latter feature is facilitated by the smaller cavity of the SAP structure.

The effect of water solvent on the Sc–donor distances was investigated on selected complexes using the polarizable continuum model (PCM).^55,56 A figure comparing the average Sc–N and Sc–O distances of the isolated and solvated structures is given in the Supporting Information (Figure S1). The general effect of the water solvent is a slight increase of the Sc–O distances and a minor decrease of the Sc–N ones. The longest Sc–N bonds (with average distances above 2.6 Å) shortened more significantly. The polar solvent changes the polarization of the carboxylate groups and thus reduces the attraction toward Sc³⁺. This gives the possibility to the N donors for a strengthened interaction with Sc³⁺.

Natural Energy Decomposition Analysis (NEDA)

Briefly, NEDA^57,58 is an energy partitioning procedure for molecular interactions applicable for self-consistent field (SCF) wave functions and DFT charge densities. The total interaction energy (ΔE_int) between the appropriately selected fragments consists of electrical interaction (EL), charge transfer (CT), and core repulsion (CORE) contributions:

The electrical term, EL = ES + POL + SE, consists of classical electrostatic (ES) and polarization interactions (POL + SE), where SE is the linear response self-energy (energy penalty) of polarization. CT is evaluated as the difference between the energies of the total and localized charge densities. The CORE contribution, CORE = XC + DEF – SE, results from intermolecular exchange–correlation interactions (XC) and deformation (DEF), the latter being the energy difference of the perturbed and relaxed monomer densities.

Metal–DOTA interactions have previously been analyzed in several studies.^{8,24,54,59−63} The main results from the present NEDA study on the isolated complexes are compiled in Table 2. The reported efficient bonding of the DOTA ligand to Sc³⁺ is reflected in the high interaction energy of the Sc(DOTA)⁻ complex in the present set. The other complexes in the present set with 4– charged free ligands have either the same or lower computed interaction energies.

Table 2. Selected Results from the NEDA Analysis^a of the Isolated Sc Complexes.

complexb	qcc	ΔEINT	ΔEEL	ΔECT	ΔECORE	%ΔEELd
DOTATSAP	1–	–7093	–6947	–2033	1887	77.4
DOTASAP	1–	–7109	–6969	–2070	1929	77.1
DOTASAP + H2Oe	1–	–6440	–6496	–1934	1990	77.1
DOTA-p-NCS-Bn	1–	–6936	–6699	–2060	1823	76.5
PSMA′	0	–6159	–6041	–2092	1974	74.3
DOTATATE′	0	–6141	–6017	–2089	1966	74.2
Lpyd	3+	–3364	–3085	–1753	1474	63.8
MeDO2PA	1+	–5207	–5088	–2081	1963	71.0
DOTPA	1–	–7080	–6974	–1931	1825	78.3
DOTMP	1–	–6839	–6705	–2014	1881	76.9
DOTMP″	5–	–10481	–10452	–1675	1646	86.2
AAZTA	1–	–7084	–6986	–2163	2066	76.4
macropaLDL	1+	–5213	–4993	–1950	1729	71.9
bispa2	1+	–5211	–5099	–2026	1914	71.6
L3	1+	–5154	–5120	–2106	2072	70.9
L2	2+	–4238	–4165	–1969	1896	67.9
EGTA	1–	–7149	–7011	–2247	2108	75.7
BAPTA	1–	–6952	–7050	–2051	2149	77.5
DTPA	2–	–8075	–7872	–2110	1907	78.9
CHX-A″-DTPA	2–	–8044	–7844	–2120	1920	78.7
HOPO	1–	–6933	–6628	–2438	2134	73.1

^aEnergy data (kJ/mol) according to ΔE_INT = ΔE_EL + ΔE_CT + ΔE_CORE. ΔE_INT means the total interaction energy between the two fragments Sc³⁺ and ligand consisting of electrical interaction (EL), charge transfer (CT), and core repulsion (CORE) contributions.

^bThe Sc³⁺ complexes are denoted by the ligand names given in the first column. The PSMA′ and DOTATATE′ notations mean the truncated ligands to 73 and 77 atoms, respectively; DOTMP and DOTMP″ mean the DOTMP^4– and DOTMP^8– ligands, respectively.

^cCharges of the isolated complex molecules.

^d%ΔE_EL = 100·ΔE_EL/(ΔE_EL + ΔE_CT).

^eNEDA results of the two-fragment model Sc(H₂O)³⁺ + DOTA^4–.

The trends in the total interaction energies of the complexes (ΔE_INT), the electrical contributions (ΔE_EL), and formal charges of the free ligands are graphically demonstrated in Figure 6. The total interaction energies between the Sc³⁺ and the ligand fragments vary between −3000 and −11 000 kJ/mol. The trend is primarily determined by the electrical term (EL) due to approximate cancellation of the attractive charge transfer (CT) and repulsive CORE contributions having similar values but opposite signs. The EL contribution is obviously strongly related to the charges of the free ligands: it is the largest with the highly negative DOTMP^8– and the smallest with the neutral L^pyd. This latter significant computed value (−3400 kJ/mol), in spite of the neutral net charge of L^pyd, originates mainly from the interaction of Sc³⁺ with the negatively polarized N atoms. The roughly linear relation of ΔE_INT and free ligand charges is well reflected by the gradual increase of ΔE_int from neutral L^pyd < MeDO2PA^2–, mac^2– < DOTA^4– derivatives < DTPA^5– < DOTMP^8– (cf. Figure 6). On the other hand, the markedly different ligand charges do not considerably influence the CT and CORE contributions, as they vary only within 200 kJ/mol (cf. Table 2).

Figure 6.

Total interaction energies (ΔE_INT) and electrical contributions (ΔE_EL) of the complexes from the NEDA analysis compared with the formal charges (q_L) of the free ligands. For the notation of ligands, see footnote a of Table 1.

The ratio of the attractive EL and CT interactions is also strongly related to the charges of the free ligands. The dominant (around 70%) EL interactions have a larger ratio in the complexes with highly negative ligands than in those with less negative ones at the cost of CT (cf. Table 2).

Figure 6 provides also a graphical overview on the minor differences of the various derivatives. Attachment of H₂O, like any additional coordination at the ninth coordination site, decreases slightly the interaction energy of the DOTA complex. In both the two-fragment (Sc(H₂O)³⁺ + DOTA^4–) and three-fragment (Sc³⁺ + DOTA^4– + H₂O) models, ΔE_INT is smaller than the related Sc³⁺ + DOTA^4– interaction energy in the Sc(DOTA)⁻ complex. This result is in line with the endothermic dissociation to Sc(DOTA)⁻ + H₂O from the present B3LYP/6-31G** calculations including a correction for BSSE as well as with literature X-ray diffraction results on K[Sc(DOTA)](H₆DOTA)Cl₂·4H₂O lacking any ninth-coordinated ligand.²⁰

The interaction of Sc³⁺ with DOTA is weakened also by the substituents p-NCS-Bn, PSMA′, and DOTATATE′. From these latter substituents, the p-NCS-Bn one is the most favorable for the complex. It is attached to a cyclen carbon atom and thus leaves all the O and N donors in operation. The slight effect may mainly be attributed to steric interactions. In contrast, the PSMA′ and DOTATATE′ fragments substitute one carboxyl group of DOTA by an amide moiety: accordingly, the strong interaction of Sc³⁺ with the anionic carboxyl O is replaced by a significantly weaker one with a polarized C=O bond of the amide group. As a consequence, ΔE_INT is decreased by ca. 14%.

The interaction energy of the DOTA complex is preserved upon increasing the pendant arms by CH₂ groups in Sc(DOTPA)⁻. The lengthening/weakening of the Sc–N bonds noted in the previous section seems to be efficiently compensated by the shortening/strengthening of the Sc–O bonds. In contrast, the slightly longer Sc–N bonds (with preserved Sc–O bond distances) result in a slight decrease of ΔE_INT for the Sc(DOTMP)⁻ complex.

Essentially the same ΔE_INT as that with DOTA was computed for the heptadentate AAZTA complex, supporting the experimental observation¹⁶ and confirming that octacoordination is not a strict requirement for strong metal–ligand interaction in the case of Sc³⁺.

From the acyclic ligands, a ΔE_INT comparable to that of Sc(DOTA)⁻ is achieved with EGTA, whereas slightly smaller ones are achieved with the BAPTA and HOPO ligands. Thus, the shorter carboxylate O–Sc distances upon benzyl substitution in Sc(BAPTA)⁻ are not enough to increase ΔE_INT with respect to Sc(EGTA)⁻ as they insufficiently compensate the considerable weakening of the Sc–N and ether O–Sc interactions (see these longer bonds in Figure 5) in the former complex.

There seems to be no gain for the Sc–ligand interaction with introducing a cyclohexyl group in the DTPA^5– ligand either. The decreased flexibility of the ligand in CHX-A″-DTPA^5– decreased the scattering of the Sc–O and Sc–N distances (cf. Figure 5) and decreased slightly ΔE_INT with respect to that of Sc(DTPA)^2–.

The complexes with free ligand charges of 2– (MeDO2PA, macropa, bispa², L³) have very close ΔE_INT’s. The marginally smaller value of L³ further supports the potential of acyclic heptadentate ligands for complexing Sc³⁺.

Charge Transfer Interactions

Figure 7 compares the energy contribution of CT interactions from the NEDA analysis with the total transferred amount of electrons to Sc³⁺ and natural populations of the acceptor Sc 4s and Sc 3d orbitals from NBO analysis. There is a reasonably good correlation between the CT energies and transferred electrons. As is known for transition metals, the main electron acceptors are the d orbitals, hence 3d for Sc³⁺, which thus determines the trend for the totally transferred electrons. The population of the 4s orbitals is ca. 25% of those of 3d with small nonsystematic variations.

Figure 7.

Compilation of the energy contributions of CT interactions in the complexes (ΔE_CT) from the NEDA analyses, the total transferred amount of electrons to Sc³⁺ (∑CT), and natural populations of the acceptor Sc 4s and Sc 3d orbitals from NBO analysis. For the notation of ligands, see footnote a of Table 1.

The CT interactions were analyzed in more detail using the second-order perturbation theory approach in the frame of the NBO model. This approach can give the energy contributions of CT between each relevant natural bond orbital and thus facilitates a separation of different types of donors. The contributions of these various donor types in the Sc complexes are summarized in Figure 8.

Figure 8.

Energetics of CT interactions in the complexes from second-order perturbation theory analysis of the Fock matrix in NBO basis: variation of the total CT energy (ΔE_CT) and % contributions from the four type of donors: anionic O (O^–), neutral O, aliphatic N (N_cyc), and aromatic N (N_ar). The data of Sc(DOTA)(H₂O)⁻ refer to the three-fragment model: Sc³⁺ + DOTA^4– + H₂O. For the notation of ligands, see footnote a of Table 1.

The curve of the total CT energy from second-order perturbation theory analysis agrees qualitatively with the one from the NEDA analysis (cf. Figures 6 and 7). There are only minor quantitative differences due to the different model theories.

Figure 8 demonstrates the CT predominance of carboxylic O donors in the studied Sc complexes. The lower (%) energetic contribution in the complexes with MeDO2PA, macropa, bispa², L², and L³ is in agreement with the small number (one or two) of COO^– groups in these ligands. Yet, their cumulative contribution is in most cases higher than that of the (in larger number available) N donors. Interestingly, in the HOPO complex the formally neutral C=O and the formally anionic N–O^– donors of the hydroxypyridinone group have nearly identical CT energies. This can be explained by the considerable delocalization of the negative charge in the (O=C—N—O)⁻ moiety (cf. Figure 3) leading to a highly polarized C=O group while at the same time preserving its carbonyl character with a bond distance of 1.26 Å. In contrast, the formally neutral C=O (PSMA′, DOTATATE′) and ring O donors in the other ligands (macropa, EGTA, BAPTA) have low-energy CT contributions.

According to the expectations, the H₂O ligand in Sc(DOTA)(H₂O)⁻ has a weak (9.6%) CT to Sc³⁺. Yet, this interaction is considerably stronger than a single Sc–N one (3.95%, summed up to 15.8% of the four N’s). The data in Figure 8 confirm the weakening of both the Sc–O and Sc–N interactions upon H₂O coordination with respect to the Sc(DOTA)⁻ parent complex.

CT from N donors is generally low (around 20%) except when the ligand contains aromatic N in pyridazine or picoline groups (L^pyd, macropa, bispa², and derivatives). In the Sc(DOTMP)^5– complex the above-mentioned extraordinary move of Sc³⁺ toward the PO₃^2– groups results in marginal N → Sc CT interaction (altogether 6.2% by the four N’s). The similarly weak (6.7%) N → Sc charge donation in the Sc(BAPTA)⁻ complex in spite of the reasonable Sc–N proximity is mainly due to the delocalization of the N lone pairs with the benzene rings in this ligand.

Conclusions

In the present DFT study the bonding interactions of the pharmaceutically important Sc³⁺ ion with 18 hepta- to decadentate ligands in isolated complex molecules have been assessed. The theoretical analysis was based on natural energy decomposition analysis and second-order perturbation energies of the Fock matrix from the NBO model. The latter results facilitated a differentiation between the various O and N donors for the CT interactions.

The most stable complexes in terms of interaction energies were formed with octa- and heptadentate ligands. With appropriate donors no significant difference was found between the two coordination forms. In contrast, decadentate coordination (with macropa) had no advantage in complex formation. The steric effects originating from the small size of Sc³⁺ and the weak coordination efficiency of ether O donors appeared in several longer Sc–donor distances in this complex.

The computed total interaction energies are differentiated in magnitude of a few thousand kilojoules per mole by the charges of the free ligands from 0 to 8–. In contrast, the covalent charge transfer interactions vary within a few hundred kilojoules per mole only. In agreement with the expectations, in all the complexes (even with the neutral L^pyd ligand) the electrical term has the major contribution amounting to 64–86% of the total interaction energy.

More detailed information was obtained on the CT interactions, where both the number of electrons transferred to the acceptor Sc atomic orbitals (3d, 4s) and the energetic contribution of the various O and N donors could be assessed. ΔE_CT follows qualitatively the trend in the amount of electrons transferred to Sc³⁺, in particular to the 3d orbitals. The 4s orbitals received ca. 20% of the donated electrons and show marginal variations in the complexes.

The energetic analysis of the CT interactions revealed the overwhelming preference of the carboxylate O donors. From N’s, those incorporated in aromatic rings are more efficient donors in spite of their smaller (less negative) natural charges compared to the cyclen N’s.

Computational Details

The computations were carried out with the Gaussian 09 suite of programs⁶⁴ using the B3LYP exchange–correlation functional^65,66 in conjunction with the 6-31G** basis set.⁶⁷⁻⁷² The B3LYP functional was extended with the D3 version of Grimme’s dispersion correction applying the original D3 damping function.⁷³ The SuperFine grid, containing 175 radial shells and 974 angular points (175,974) per shell for H, C, O and N and 250,974 for P, S, and Sc, was applied for integration accuracy. For visualization and construction of some initial geometries, GaussView 5 software⁷⁴ was applied.

The initial structures for geometry optimizations were taken from the following literature data: complexes with DOTA, L^pyd, MeDO2PA, DOTPA, and DOTMP from computed structures of analogous Bi complexes;²³ from computed structures of Lu(macropa)⁺,⁵² In(bispa²)⁺,⁷⁵ In(L³)⁺ and In(L²)²⁺;⁷⁶ from the crystal structures of NaGd(AAZTA),⁷⁷ H₂Bi(DTPA) and H₂Bi(CHX-A″-DTPA),⁷⁸ KSc(HOPO);⁴⁶ manually generated from the crystal structures of Cd complexes with methoxy-tetrakisquinoline analogues of EGTA and BAPTA.⁷⁹ The applied fragments of the large PSMA and DOTATATE ligands were generated manually starting from the computed Sc(DOTA)⁻ geometries. In addition to geometry optimizations of the isolated complexes, optimizations in aqueous solution using the polarizable continuum model (PCM)^55,56 were also performed.

The natural atomic charges, valence orbital populations, and second-order perturbation energies were evaluated on the basis of the natural bond orbital model¹⁷ on the isolated complexes. The metal–ligand interactions were further explored with natural energy decomposition analysis^57,58 using the NBO 5.9 code⁸⁰ incorporated in Firefly software.⁸¹ This software is partially based on the GAMESS (US)⁸² source code. The choice of the B3LYP/6-31G** level of theory for this study was primarily determined by the limited availability of exchange–correlation functionals in the Firefly software. A comparison of the computed and available experimental solid-state^20,22 Sc–O and Sc–N bond distances of Sc(DOTA), Sc(DTPA), and Sc(HOPO) complexes is provided in Table S4 together with a brief discussion in the Supporting Information.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.inorgchem.3c02211.

• Average Sc–N and Sc–O distances in isolated and solvated structures of selected complexes; tables with data presented in Figures 4, 6, and 7 and comparing experimental and computed Sc–O and Sc–N bond distances; Cartesian coordinates of relevant optimized structures (PDF)

Author Contributions

All the calculations, analyses, and manuscript preparation have been carried out by A.K.

The calculations have been carried out using resources provided by the affiliation of the author (JRC Karlsruhe). No external funding was received.

The author declares no competing financial interest.