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Density Functional Theory Study on the Complexation of NOTA as a Bifunctional Chelator with Radiometal Ions F. Y. Adeowo, B. Honarparvar,* and A. A. Skelton* School of Health Sciences, Discipline of Pharmacy, University of KwaZulu-Natal, Durban 4001, South Africa S Supporting Information *

ABSTRACT: 1,4,7-Triazacyclononane-1,4,7-triacetic acid (NOTA) is a key bifunctional chelator utilized for the complexation of metal ions in radiopharmaceutical applications; the ability of these chelators depends on the strength of their binding with ions. The focus of the present work is to evaluate the complexation of Cu2+, Ga3+, Sc3+, and In3+ radiometal ions with NOTA using density functional theory (B3LYP functional) and 6311+G(2d,2p)/DGDZVP basis sets. The significant role of ion−water interactions in the chelation interaction energies in solution reflects the competition between ion−water and NOTA−ion interaction in the chelation process. There is reasonable agreement between experimental and theoretical binding constants, geometries, and 1H NMR chemical shifts. Chelation interaction energies, Gibbs free energies, and entropies in solution show that the NOTA−Ga3+ and NOTA−Cu2+ are the most and least stable complexes, respectively. The natural atomic charges and second order perturbation analysis reveal charge transfer between NOTA and radiometal ions. The theoretical 1H NMR chemical shifts of NOTA are in good agreement with experiment; these values are influenced by the presence of the ions, which have a deshielding effect on the protons of NOTA. Global scalar properties such as EHOMO/ELUMO, ΔELUMO−HOMO, and chemical hardness/softness confirm that the NOTA−Cu2+ complex, which has a singly occupied molecular orbital, has the lowest ΔELUMO−HOMO value, the least chemical hardness, and the highest chemical softness. The significant variation of the hardness and ΔELUMO−HOMO values of the complexes can be attributed to the different positions of the metal ions on the periodic table. This study affirms that, among the radiometal ions, Ga3+ can be used to effectively radiolabel NOTA chelator for radiopharmaceutical usage as it binds most stably with NOTA.

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3.2 days).7−9 Before these isotopes can be used for a particular biological application, there is need to seclude the “free” radiometal ions from aqueous solution using chelators (ligands) to prevent the transchelation and hydrolysis processes.6 Chelators are a crucial component of radiopharmaceutical procedures that are used to form a tight, stable coordination complex by binding the radiometal ion firmly together so that it can be properly connected to a preferred molecular target in vivo.6 Chelators that are commonly used to produce radiopharmaceuticals are bifunctional chelators (BFCs). As the name implies, BFCs are chelators that consist of one functional group covalently conjugated to a targeting vector (e.g., peptides or antibodies) and a chelating unit, which connects the radioisotope to form a complex.6,10,11 A plethora of studies has been performed on diverse chelators combined with different radiometal ions for purposes of comparison or identifying a gold standard chelator for a particular radiometal. Deri et al.12 confirms that the use of 89Zr with 3,4,3-(Li-1,2,-HOPO) is a superior replacement to desferrioxamine (DFO) because 89Zr-HOPO is completely

INTRODUCTION For more than 30 years, nuclear imaging modalities have transformed the field of analytical medicine, particularly cardiology, neurology, and oncology.1,2 Early detection of disease, convenient deployment of therapies, and easy access of the efficacy of a particular therapy3 justify the reason for the increase in the use of chelators in molecular imaging. Molecular imaging adequately allows visualizing, characterization, and evaluation of not only the molecular and cellular entities of the human body system but also the whole organs in the body using some distinct imaging probes without interfering with biological functions.4 Radiometals (e.g., 64Cu, 89Zr, 68Ga, 86Y, and 99mTc) are used with imaging devices to provide labeling of biologically important macromolecules such as proteins, peptides, and antibodies, which are responsible for diagnosis or treatment of various diseases.5 Furthermore, the existence of biological targeting agents with a different range of half-lives necessitates the need to produce new radionuclides with halflives that match their biological properties.6,7 For example, agents that can stay for a long period of time in vivo can be labeled with gallium-68 (68Ga: t1/2 = 68 min) or technetium99m (99Tc: t1/2 = 6 h), while vectors that demand longer amounts of time to reach their target can be labeled with copper-64 (64Cu: t1/2 = 12.7 h), yttrium-86 (86Y: t1/2 = 14.7 h), indium-111 (111In: t1/2 = 2.8 days), or zirconium-89 (89Zr: t1/2 = © XXXX American Chemical Society

Received: February 1, 2017 Revised: July 20, 2017 Published: July 24, 2017 A

DOI: 10.1021/acs.jpca.7b01017 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

radiometal ions for all complexes. It is notable that for the open shell Cu2+ ion, unrestricted DFT (UB3LYP) calculations were performed. Interaction energies (ENOTA−ion ) between NOTA and the int different metal ions were calculated using the following equation:26

emptied from the body without any sign of demetalation. Research by Mate et al. asserts that radiolabeling chelators NOPO and NOPA (1,4,7-triazacyclononane-7-acetic-1,4-bismethylenephosphinic acid) with 68Ga exhibits a better labeling efficiency at room temperature and 95 °C compared to that of NO2AP (1,4,7-triazacyclononane-4,7-diacetic-1-[methylene(2carboxyethl]phosphinic) acid.13 Darpan and co-workers discovered that the macrocyclic bifunctional chelator that incorporates propylene cross-bridges is capable of forming a strong complex with Cu.14 A recent review on some features and current development in using antibodies to target radionuclides for tumor imaging and therapy was published by Kraeber-Bodere et al.15 The chelator under investigation in the present study is 1,4,7triazacyclononane-1,4,7-triacetic acid (NOTA). NOTA, a hexadentate chelator, is one of the most extensively investigated macrocyclic BFCs, utilized for the complexation of a large number of bi- and trivalent metal ions.16 NOTA chelator has the geometry of the N3O3 coordination sphere and consists of three carboxylic (−COOH) functional arms (Figure 1).

NOTA − ion E int = E NOTA − ion − E NOTA − E ion

(1)

It is worth pointing out that in aqueous solution, the ion will be hydrated with a cluster of water molecules, and upon NOTA chelation, the water molecules must be removed to give the opportunity for NOTA−ion interaction. The chelation reaction in solution can, therefore, be defined as [ion(H 2O)6 ]n + + NOTA → [ion(NOTA)]n + + 6H 2O (2)

where n is the charge of the ion, and six water molecules are coordinated to the ion in octahedral conformation. 6H 2O − ion E int = E6H 2O − ion − E ion + E6H2O

(3)

Due to the competitive NOTA−ion and water−ion interactions, the chelation interaction energy includes the following components and is defined as NOTA − ion + 6H 2O NOTA − ion 6H 2O − ion E int = E int − E int

(4)

Thermodynamic properties (Gibbs free energy and entropy) were derived by the aforementioned equations. The vibrational, translational, and rotational contributions to entropy were calculated using normal-mode frequency analysis.27 The second-order Fock matrix was presented to assess the donor−acceptor interaction in the system.28,29 A clearer picture of the electron delocalization between NOTA and the ions in the complexes, that is, the donor and acceptor orbitals, with the highest stabilization energy in term of E2 from the second order theory was investigated.30 The second order perturbation energy E2 of the occupied NBO (i) of an electron donor, which interacts with unoccupied NBO (j) of the electron acceptor, is defined by the expression:

Figure 1. NOTA; coordination number = 6, N3O3.

All of the aforementioned studies are experimental, and investigation into the literature reveals that there have been few or no theoretical investigations to evaluate the complexation of NOTA with radiometal ions. We recently reported density functional theory (DFT) studies of NOTA complexation with alkali metal ions;17 it was concluded that there is a significant level of interaction between NOTA and alkali metal ions. In 2014, Price and Orvig6 investigated the matching of chelators to several radiometal ions (Cu2+, Ga3+, Sc3+, and In3+) with a range of different experimentally determined binding constants. To provide deep insight into the binding affinities of these ions with NOTA, at the molecular level, the focus of the present study is on evaluating the complexation of NOTA with selected radiometal ions (Cu2+, Ga3+, Sc3+, and In3+) using DFT. It should be noted that Cu2+ and Sc3+ are both transition metals, whereas In3+ and Ga3+ are group III metals. The aim of this study is to investigate the chelation process of NOTA with radiometal ions in solution. In this context, we analyzed the key factors such as ion−water and NOTA−ion interactions and charge transfer between NOTA and radiometal ions, which contribute to complexation at the molecular level. A further objective was to ascertain whether or not there exists competition between radiometal and alkali metal ions found in the body upon complexation with NOTA.

2

E =

qiF(i , j)2 εj − εi

(5)

The energy values of the highest occupied molecular orbital (EHOMO) and the lowest unoccupied molecular orbital (ELUMO) of all the complexes were calculated. Several other electronic properties such as ionization potential (IP), electronic affinities (EA), hardness (η), and softness (S) were calculated. The vertical ionization potential (IP) is defined as the difference in energy between the neutral (En) and cationic (Ec) species at the equilibrium geometry of the neutral molecule:31 IP = Ec − En

(6)

The vertical EA is defined as the difference in energy between En and anionic species (Ea) at the equilibrium geometry of the neutral molecule:

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COMPUTATIONAL DETAILS The Gaussian 09 program18,19 was used to perform all quantum chemical calculations. The Becke, 3-parameter, Lee−Yang−Parr (B3LYP)20,21 hybrid exchange correlation functional was used.22−25 The 6-311+G(2d,2p)22 basis set was used for NOTA, and the DGDZVP basis set was applied for the

EA = En − Ea

(7)

The term neutral is actually the standard charge state, for instance, the charge state for Cu2+ is +2, and therefore the cationic and anionic species have +3 and +1 charges, respectively. B


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The Journal of Physical Chemistry A The DFT-based structural features (chemical hardness, η, and softness, S) were obtained using the following equations:32,33

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η=

(IP − EA) 2

(8)

S=

1 2η

(9)

of water molecules with the ions, which compete with NOTA− ion interaction in the chelation process. In other words, according to the data in Table 2, the attraction of water for the ions is almost as strong as the attraction of NOTA for the ions, which led to more physically realistic CIE that vacuum, ENOTA−ion values. Overall, the observed trend in CIE, ENOTA−ion , int int 6H2O−ion values follow the order NOTA−Ga3+ > NOTA− and Eint In3+ > NOTA−Sc3+ > NOTA−Cu2+. The order of the interaction energies can be rationalized when we consider the different features of the ion. Ga3+ is in the same group as In3+ (group III) but is a smaller ion and therefore should have a stronger interaction. This is in agreement with results of our previous work, where it was found that the interaction strength of alkali metal ions increased up the group of the periodic table.17 The difference in interaction energy between Sc3+ and Cu2+, both transition metals, is related to their charge, Sc3+ being +3 has a stronger interaction than that of Cu2+ with a +2 charge. The reported BSSE values, in parentheses, for each ion− water complexes are lower than those of NOTA−ion complexes, and the difference between NOTA−ion and ion− water reveals that the BSSE will not significantly affect the chelation interaction. The long-range and dispersion interactions were taken into account by performing the geometry optimization of the complexes using the ωb97XD functional, and the ENOTA−ion int interaction energies are also reported in Table 2S. The values obtained by B3LYP and differences between ENOTA−ion int the ωB97XD functional could be due to different factors contributing to complexation because dispersion should have a less significant effect on the reported, large interaction energies in Table 1. It is notable that the interaction energies obtained with both B3LYP and ωb97XD functionals corresponds to the same trend. Thus, the results obtained with B3LYP are qualitatively similar. Thermodynamic Properties. To gain insight into the favorability of NOTA−ion complexation, the analysis of the chelation Gibbs free energies (ΔGNOTA−ion+6H2O), entropies 2O ), and its individual contributions (transla(ΔSNOTA−ion+6H tot tional, rotational, and vibrational), are discussed (Table 2). The ΔGNOTA−ion+6H2O values for the complexes follow the order; NOTA−Ga3+ > NOTA−In3+ > NOTA−Sc3+ > NOTA− Cu2+, matching the trend of the interaction energy values. The 2O are all positive except for NOTA−Cu2+, which ΔSNOTA−ion+6H tot could be attributed to the fact that just for Cu2+ complexes, the entropy loss for NOTA−ion is more evident than that of the ion−water contribution. For the other metal ions, particularly for Sc3+, the entropy loss for ion−water contribution is more significant than that in NOTA−ion. It seems that, among the entropic contributions, the vibrational entropy 2O ) is the driving parameter that controls the (ΔSNOTA−ion+6H vib 2O ). It can be also observed that total entropies (ΔSNOTA−ion+6H tot in the chelation process in solution, the role of ion−water 6H O−ion contribution is significant; in particular, the ΔSvib 2 value for 3+ Sc is considerably more negative than those the other ion 2O complexes, yielding a more positive ΔSNOTA−ion+6H . vib Comparison of Experimental and Theoretical Binding Constants. The theoretical and experimental Gibbs free NOTA−ion+6H 2O energies (ΔGtheo and ΔGexp) of the selected 6,7 complexes are related to the experimental binding constants (log Kexp) using Van’t Hoff equation (ΔG = −RT ln K). Experimental ΔGexp and theoretical binding constants (log Ktheo) were calculated at the standard temperature (298 K) and

RESULTS AND DISCUSSION For clearer data interpretation, the classification of atoms in the NOTA−radiometal ion complexes was made based on the position, connectivity of the atoms, and different functional groups, which dictates their different chemical environments (Figure 2).

Figure 2. Conformation of the NOTA−radiometal ion complexes. The dotted lines in the diagrams indicate intermolecular distances between radiometal ions and heteroatoms that are in close proximity. HIN, CIN, and N are hydrogen, carbon, and nitrogen atoms in the ring, respectively. HCA are hydrogen atoms attached to the arm. C(COOH) and H(COOH) are carbon and hydrogen atoms in the functional group, respectively. OH represents hydroxyl oxygen atoms, and OC represents carbonyl oxygen atoms.

Chelation Interaction Energies in Solution. The 2O chelation interaction energies in solution (ENOTA−ion+6H ) int and their corresponding components and basis set superposition errors (BSSE) provide insight into the binding of NOTA with the radiometal ions (Table 1). To understand the factors that influence the chelation interaction energy (CIE), analysis of its components, ENOTA−ion int 2O−ion and E6H , is required. It can be noticed that the reported int values for ENOTA−ion in the absence of water molecules (eq 1) int are considerably more negative and unrealistic compared to the 2O−ion CIE values. The E6H values reflect the crucial interaction int Table 1. Chelation Interaction Energies in Solution 2O (ENOTA−ion+6H ) and Their Corresponding Components int Defined in Eqs 1−4 and the Energies of the Complexesa NOTA−ion+6H2O

complex NOTA−Cu2+ NOTA−Sc3+ NOTA−In3+ NOTA−Ga3+ a

ENOTA−ion int kcal mol−1 −398.22 −626.86 −643.17 −798.13

(11.13) (21.25) (14.83) (8.19)

6H O−ion

Eint 2 kcal mol−1 −384.59 −594.00 −598.32 −737.46

(8.39) (18.96) (12.68) (8.33)

Eint

(CIE) kcal mol−1 −13.63 −32.86 −44.85 −60.67

The numbers in parentheses denote the BSSE energies (EBSSE). C


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Table 2. Thermodynamic Properties for Chelation, Including Gibbs Free Energies, Entropies, and Entropic Contributions (Translational, Rotational, and Vibrational) for NOTA−Ion+6H2O, NOTA−Ion, and Ion−Water Complexes complexes NOTA−ion+6H2O

NOTA−ion

ion−water

NOTA−Cu2+ NOTA−Sc3+ NOTA−In3+ NOTA−Ga3+ NOTA−Cu2+ NOTA−Sc3+ NOTA−In3+ NOTA−Ga3+ NOTA−Cu2+ NOTA−Sc3+ NOTA−In3+ NOTA−Ga3+

ΔGcomplex kcal mol−1

ΔScomplex tot cal mol−1 K−1

ΔScomplex rot cal mol−1 K−1

ΔScomplex trans cal mol−1 K−1

ΔScomplex vib cal mol−1 K−1

−17.21 −39.89 −48.82 −63.35 −384.24 −623.91 −630.07 −781.45 −367.03 −584.03 −581.25 −718.09

−6.66 20.91 5.36 6.25 −39.95 −40.32 −36.93 −47.58 −33.30 −61.23 −42.29 −53.83

0.02 0.21 0.28 −0.05 0.02 0.21 0.28 −0.05 0.00 0.00 0.00 0.00

−0.81 −0.63 −1.20 −3.81 −37.78 −36.92 −39.17 −37.99 −36.97 −36.30 −37.97 −34.19

−5.87 21.33 6.29 10.12 −2.20 −3.60 1.97 −9.52 3.67 −24.93 −4.32 −19.64

molar gas constant R (1.987 × 10−3 kcal K−1 mol−1). The experimental and theoretical values of both the Gibbs free energies and binding constants are reported in Table 3. Table 3. Experimental and Theoretical Chelation Gibbs Free Energies and Binding Constant Values NOTA−ion+6H O

complexes NOTA−Cu2+ NOTA−Sc3+ NOTA−In3+ NOTA−Ga3+

2 ΔGtheo (kcal mol−1)

−17.21 −39.89 −48.83 −63.35

ΔGexp (kcal mol−1)

log Kexp

log Ktheo

−12.78 −9.75 −15.51 −18.35

21.65 16.57 26.28 31.04

29.06 67.36 82.46 107.00

It should be noted that, although the theoretical Gibbs free energies are significantly more negative than the experimental ΔG values and the theoretical binding constant values are significantly greater that the experimental binding constants, both the experimental and theoretical values follow the same trend. Comparison of Experimental and Theoretical Geometries. To further validate the theoretically optimized structures of NOTA−radiometal ion complexes with experimentally observed conformations, the geometries of the complexes were compared with experiment.6,7 This analysis is helpful to assess the validity of our theoretical models and further understand the electronic factors that may contribute to the possible conformations. The geometry of NOTA−Cu2+ was reported as distorted trigonal prism,34,35 and NOTA−Ga3+, NOTA−Sc3+, and NOTA−In3+ complexes were observed as distorted octahedral.36−42 Figure 3 shows the distorted trigonal prism geometry for NOTA−Cu2+ and NOTA−Ga3+ (experimental, Cuexp, Gaexp; theoretical, Cutheo, Gatheo). It can be noticed from Figure 3 that the geometry of Cutheo is close to the experimentally observed distorted trigonal prism; however, it could be argued that there is a certain degree of distorted octahedral character that caused some deviation from the experiment. This observation is supported by the appearance of two different categories of N−Cu2+ distance as well as two different categories of O−Cu2+; these different categories can be referred to as axial (Nax and Oax) and equatorial (Neq and Oeq), as reported in Table 4. The dotted lines in Figure 3 show the short-range interactions from Cu2+ and Ga3+ to axial nitrogen and oxygen atoms, while solid lines

Figure 3. Distorted octahedral geometry of NOTA−Cu2+ and NOTA−Ga3+ complexes. Cuexp and Gaexp, respectively, show experimental X-ray structures. 7 Cu theo and Ga theo show the theoretically optimized structures, respectively.

depict the short-range interactions from Cu2+ and Ga3+ to equatorial nitrogen and oxygen atoms. It can be noted that the experimental Neq−Cu2+ and Oeq− Cu2+ distances are longer than that of Nax−Cu2+ and Oax−Cu2+, yet the experimental distances of Neq−Ga3+ and Nax−Ga3+ and the experimental distances of Oeq−Ga3+ and Oax−Ga3+ are comparable. This observation could be attributed to the presence of the Jahn−Teller effect, which occurs for Cu2+ complexes with d9 electronic configuration rather than Ga3+, which is a main group element in the periodic table. As for the theoretical short-range distances for DOTA−Cu2+, there are also differences between Neq−Cu2+ and Nax−Cu2+ and between Oeq−Cu2+ and Oax−Cu2+, implying a Jahn−Teller effect. Because the Nax−Cu2+ and Oax−Cu2+ distances are greater than Neq−Cu2+ and Oeq−Cu2+ distances, respectively, the Jahn−Teller effect is reversed compared with experiment. In accordance with experiment, the distances of Neq−Ga3+ and Nax−Ga3+ are also comparable, indicating an absence of the Jahn−Teller effect for Ga3+, which is a main group element. Overall, for both NOTA−Cu2+ and NOTA−Ga3+ complexes, N−ion distances are longer than OC−ion distances. As for DOTA−Sc3+ and DOTA−In3+, which are experimentally shown to be in distorted trigonal prism geometry, it can also be observed that N−ion distances are longer than OC−ion distances. This indicates that, with all ions, the strength of D


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Table 4. Interatomic Distances between Radiometal Ions (Cu2+, Ga3+, Sc3+, and In3+) and NOTA Heteroatoms in the Optimized Structure at B3LYP/6-311G+(2d, 2p) and DGDZVP Basis Setsa Neq−ion

Nax−ion

Oeq−ion

Oax−ion

2.09 [2.16] (2.08)

2.31 [2.04] (2.30)

2.06 [2.18] (2.07)

2.29 [2.00] (2.30)

2.12 [2.10] (2.10)

2.11 [2.10] (2.10)

2.00 [1.94] (2.01)

2.02 [1.94] (2.01)

complex 2+

DOTA−Cu DOTA−Sc3+ DOTA−In3+ DOTA−Ga3+

N−ion 2.16 2.34 2.33 2.11

(2.15) (2.36) (2.31) (2.10)

OC−ion 2.13 2.09 2.18 2.01

(2.15) (2.15) (2.19) (2.01)

a

Parentheses indicate the distances between heteroatoms and radiometal ions in complexes in water. Brackets indicate experimental values. OC and N are presented in Figure 2. Heteroatom−ion distances ≤3 Å were considered as the short-range interatomic distances for the selected complexes.

interaction between the OC atom is greater than that of N atom. To evaluate the dispersion effect on the geometric parameters, the interatomic distances using ωB97XD functional are reported in Table 3S. It can be observed that the average distances between the heteroatoms are shorter for ωB97XD than with B3LYP; this could be due to the inclusion of dispersion contributions in ωB97XD within the selected complexes. Natural Bond Orbital (NBO) Analysis. Charge transfer within the chelator−ion complexes is of importance because it influences the interaction of radiometal ions with NOTA. Charge transfer can be investigated using NBO analysis through monitoring the atom charges, change of atom charges upon complexation, and second-order perturbation theory.43 Natural atomic charge estimation plays a role in the application of quantum mechanical calculations for molecular systems because atomic charge affects the electronic structure, dipole moment, and other properties of the molecule.28 Charge distribution within the NOTA complexes and from NOTA to the radiometal ions is reported in Table 5. The atoms in all the complexes were categorized into groups (Figure 2), and the average natural atomic charges are reported. The NBO analysis shows that for all the complexes, there are considerable changes in charges for the cations after complexation with radiometal ions. The complexes, with initial charge of +2 for Cu2+ and +3 for Sc3+, In3+, and Ga3+, before complexation become less electron deficient after complexation. The charges of Cu2+, Sc3+, In3+, and Ga3+ after complexation are

1.02, 1.93, 2.05, and 1.89, respectively. The observed charge reduction, particularly for In3+ and Ga3+, which are in the same group of the periodic table, could be a key factor in the stronger interaction energies observed in Table 1. Furthermore, for all complexes, N, OC, CIN, and CA are more negatively charged in the complexed NOTA than in the free NOTA. Conversely, HIN, HCA, CCOOH, and HCOOH are more positively charged in the complexed NOTA than in the free NOTA. This is an indication that there was electron density transfer from NOTA to the radiometal ions upon complexation (Table 5); this will be addressed in more detail using secondorder perturbation theory in the next section. Second Perturbation Stabilization Energies. The second-order Fock matrix was presented to evaluate the donor−acceptor interactions in the system.28,44 The larger the stabilization energy (E2), the greater the charge transfer between electron donors and electron acceptors.45−47 The second-order perturbation theory analysis for all the complexes shows the charge transfer within NOTA−ion complexes (Table 6). The observed depletion of natural atomic charges (NAC) charges of the ions (Table 5) should be attributed to charge transfer from NOTA to the ions. This was observed for all NOTA−ion complexes where the highest stabilization energy values for electron transfer from NOTA to ions are from the Table 6. Second-Order Perturbation Energies, E2 (kcal/ mol), Corresponding to the Most Important Charge Transfer Interaction (Donor → Acceptor) within NOTA− Radiometal Ion Complexes Obtained by the B3LYP/6311+G(2d,2p) Level of Theory

Table 5. NAC of Atoms in Optimized Structure of NOTA Complex with Radio Metals and NOTA before Complexation at B3LYP/6-311G+(2d,2p) and DGDZVP Basis Setsa

atoms groups ions N (3) OH (3) OC (3) CIN (6) HIN (12) CA (3) HCA (6) CCOOH (3) HCOOH (3)

average of all atoms in group NOTA− Cu2+ 1.02 −0.62 −0.56 −0.62 −0.19 0.22 −0.28 0.25 0.85 0.52

average of all atoms in group NOTA− Sc3+

average of all atoms in group NOTA− In3+

average of all atoms in group NOTA− Ga3+

1.93

2.05

1.89

−0.653 −0.56 −0.72 −0.19 0.24 −0.27 0.27 0.89 0.56

−0.645 −0.57 −0.71 −0.20 0.22 −0.29 0.27 0.87 0.54

−0.654 −0.56 −0.70 −0.19 0.24 −0.28 0.28 0.88 0.54

complex NOTA−Cu2+

NOTA−Sc3+

free NOTA not applicable −0.57 −0.71 −0.61 −0.18 0.19 −0.26 0.22 0.81 0.49

NOTA−In3+

NOTA−Ga3+

NOTA−Cu2+ NOTA−Sc3+ NOTA−In3+ NOTA−Ga3+ NOTA

a

The numbers in parentheses represent the number of atoms within the specific group shown in Figure 2. E

donor

acceptor

from NOTA to ions LP(N) LP*(Cu2+) LP(O) LP*(Cu2+) σ(N−C) LP*(Cu2+) LP(N) LP*(Sc3+) LP(O) LP*(Sc3+) σ(N−C) LP*(Sc3+) LP(N) LP*(In3+) LP(O) LP*(In3+) σ(N−C) LP*(In3+) LP(N) LP*(Ga3+) LP(O) LP*(Ga3+) σ(N−C) LP*(Ga3+) within NOTA LP(O) σ*(C−O) LP(O) σ*(C−O) LP(O) σ*(C−O) LP(O) σ*(C−O) LP(O) σ*(C−O)

E2 (kcal/mol) 11.50 10.11 12.84 31.90 11.68 13.38 40.02 13.26 16.32 76.65 24.23 8.49 31.87 57.02 56.38 57.03 43.46


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(δ) are given in Table 7 for a set of NOTA− radiometal ion complexes.

lone pair (LP) of the nitrogen atom of NOTA to the LP* of the radiometal ions; this follows the order NOTA−Ga3+ > NOTA−In3+ > NOTA−Sc3+ > NOTA−Cu2+, which matches that of the interaction energy values (Table 1). There are charge transfers from LP orbitals of OC atoms to LP* of the ions, but these are less evident than the transfer from the LP of nitrogen atoms. It is noticed that the presence of different ions within the complexes can affect the charge transfer within NOTA. The highest E2 values within NOTA are electron donations from LP orbitals in OH to the antibonding acceptor σ*(C−OC). The stabilization energy follows the order NOTA−Ga3+ ≈ NOTA− Sc3+ ≈ NOTA−In3+ > NOTA−Cu2+; this is related to the contribution of charge for +3 charge ions compared to that of the divalent Cu2+ ion. The result of the second perturbation theory emphasizes the fact that electron transfer from OC and N atoms of NOTA to the radiometal ions in the complexes is prevalent. A similar observation was made from the our previous works, where we evaluated the interaction between diazacrown and the sodium cation26 and the interaction between NOTA and alkali metal ions.17 We can now provide a description of charge transfer (the highest stabilization energy values) that occurs from the NOTA molecule to the cations, and this is represented in Figure 4, where arrows point the path of charge transfer.

Table 7. 1H NMR Chemical Shifts of NOTA−Ga3+ and NOTA−In3+ Complexes in Vacuum and Water Mediaa proton G1 G2 G3 G4 G5 G6

δtheo Ga3+ (ppm) 9.54 [9.29] NAC = 0.54 4.54 [4.57] NAC = 0.28 4.05 [3.90] NAC = 0.26 3.47 [3.67] NAC = 0.25 3.62 [3.68] NAC = 0.24 3.03 [3.20] NAC = 0.23

δexp Ga3+ (ppm) not reported

δtheo In3+ (ppm)

9.46 [9.09] NAC = 0.54 3.88 4.514 [4.511] Δvac = −0.66 NAC = 0.27 3.23 3.99 [3.80] Δvac = −0.82 NAC = 0.25 not reported 3.65 [3.60] NAC = 0.25 3.51 3.64 [3.67] Δvac = −0.11 NAC = 0.25 not reported 2.92 [3.18] NAC = 0.22

δexp In3+ (ppm) not reported 3.70 Δvac = 0.81 3.07 Δvac = 0.92 not reported 3.24 Δvac = −0.4 not reported

δExp are experimental results.48 Δvac indicates the difference between the experimental and theoretical chemical shift in vacuum.

a

To compare our theoretical results with experiment, we performed the 1H NMR calculations in vacuum (Table 7). This comparison is particularly informative, as it has been shown that the hydrogen atoms are a source of electron density for charge transfer from NOTA to ions, which should be the driving force for chemical shift changes. In most cases, the theoretical chemical shift values follows a decreasing order (NOTA−Ga3+ > NOTA−In3+) down group III of the periodic table. The decreasing effect is due to the ions having a deshielding effect on the protons of the NOTA that are in close proximity. The decrease in the δ values is consistent with the decrease in the electron withdrawing effect of the ions, which causes a decline in the NAC values down the group. It is observed that the theoretical δ values are in reasonable agreement with the experiment (differences are less than 1 ppm), which confirms the suitability of the applied DFT functional and basis set. Furthermore, there is no significant difference between the 1H NMR in the vacuum and the water. The protons in the complexes were characterized (G1−G6) based on the different theoretical δ values (Figure 5). This

Figure 4. Description of electron transfers shown in NBO analysis. The curved arrows (a, b, c, c′, and d) depict the direction of charge transfer. a: LP (O) → σ* (CO), b: LP (O) → LP* (ion), c: σ (C− H) ring → σ (N−C), c′: σ (C−H) arm → σ (N−C), d: LP (N) → LP* (ion).

There is electron movement from OH to the carbonyl bond followed by the direct transfer of electron from the NOTA oxygen atoms to the metal ions in the complexes and also electron from CA, followed by a direct transfer from nitrogen atoms to the metal ions in the complexes. Analysis of 1H NMR Chemical Shifts. To gain a better understanding of the chemical environment of different fragments involved in the NOTA complexed with radiometal ions, the 1H NMR spectra in vacuum and water media were studied and compared with the experimentally measured 1H NMR chemical shifts for the NOTA−Ga3+ and NOTA−In3+ complexes.48 Experimental and theoretical 1H chemical shifts

Figure 5. NOTA−radiometal ion complex based on the intensity of the different chemical shifts. G indicates the different groups of hydrogen. Hydrogen atoms with the same color code belong to the same chemical environment.

classification highlighted the fact that each group operates in different chemical environments, which could be identified in the experiment. This motivated a measurement of the theoretical chemical shifts for all proton groups. For both Ga3+ and In3+ complexes, carboxyl protons (G1) are identified as the protons with the highest chemical shift F


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trivalent ions (Ga3+, Sc3+, and In3+), the less negative EA, the smaller IE and chemical hardness were obtained for Cu2+. The DFT-based parameters revealed a chemically soft nature of NOTA compared to that of the ions, and consequently, the complexation of NOTA with the ions should have a considerable effect which depends on the specific ion in question. Indeed, in all cases, there is a significant increase in chemical hardness upon complexation. It is evident that the IP and hardness values of all trivalent complexes are similar and higher than the divalent NOTA− Cu2+ complex. Moreover, NOTA−Ga3+ complex has EA and hardness values slightly more negative than those of the NOTA−In3+ complex; this could be attributed to the smaller ionic radius of Ga3+ than of In3+. The changes in EA, IP, softness, and hardness provide trends in complex stability that are related to the trends in interaction energies and thermodynamic properties (Tables 1 and 2). Implication of the Results. In the article by Price and Orvig, 6 matching of chelators to radiometal ions for radiopharmaceuticals was discussed and assessed in terms of experimentally measured binding constants. It was also noticed that, apart from the structural stability of chelator−ion complexes, ion−water contributions should also be considered for assessing the chelation strength, which can influence the radiolabeling efficiency.6 The present study revealed a significant level of intermolecular interactions between radiometal ions and NOTA as well as the ions and solvation water clusters, which were compared with the reported binding constants. The electronic structure properties such as interaction energies, frontier molecular orbitals, 1H NMR chemical shifts, chemical hardness, ionization potential, and electron affinity values and stabilization energies, which indicate the charge transfer between NOTA and ions, offer an explanation for the chelation affinities within the selected complexes. The present study shows that the DFT-based electronic structure calculations can be applied to rank the ions toward finding the optimal match between ions and a specific chelator. According to the experimentally reported binding constants and obtained quantum chemical parameters calculated for NOTA−radiometal ion complexes, it is observed that, among the radiometal ions under investigation, Ga3+ is an optimal match for NOTA chelator for radiopharmaceuticals. Following our previous study on the complexation of NOTA with alkali metal ions,17 it can be stated that in vivo alkali metal ions might constitute insignificant competition and less interference with radiometal ions (Cu2+, Ga3+, Sc3+, and In3+). In light of the above explanation, it is assumed that this study is helpful to rationalize the relative chelation affinities of similar systems with unknown experimental binding constants.

values and correspondingly the most positive atomic charges, followed by the proton of the methylene group (−CH2−) within the pendant arms (G2); this ranking of chemical shift values is in agreement with experimental results. The G3−G6 are protons in the ring with the same functional group but different chemical environments. It is observed that the protons in G3 have chemical shift values higher than those of the other protons in the ring because G3 protons are located facing each other. Another factor that dictates the chemical shift is the chemical environment of protons in relation to other atoms within NOTA. This is demonstrated by the fact that the ranking for the free NOTA is exactly the same as that for the complexed NOTA (Table 1S). G2, G3, and G6 become less deshielded upon complexation, while G1, G4, and G5 become more deshielded; this is in contrast to the natural atomic charge of all groups (G1−G6), which are more positive upon complexation, suggesting two different chemical environments that affect chelation. First, the inductive effect, through charge transfer from σ(C−H) ring to the σ(N−C), as illustrated in Figure 4, could be responsible for the observed trend in natural atomic charges. Second, short-range coupling could probably affect the chemical shift values. It is noted that our observations regarding 1H NMR results for NOTA−radiometal ion complexes agree with those of our recent study where we evaluated the 1H NMR on NOTA−alkali metal ions.17 Conceptual DFT-Based Properties. Various chemical reactivity descriptors have been proposed for understanding different facets of pharmacological sciences, including drug design and possible eco-toxicological attributes of drug molecules.49 Density functional theory can be used to calculate global reactivity descriptors such as chemical potential, electronegativity, hardness, softness, and electrophilicity index.50 Ionization potential describes the capability of an atom or molecule to donate electrons, while electron affinity describes the capability of an atom or molecule to attract electrons. Chemical hardness describes the resistance to modification in electron distribution and is correlated with the stability of the chemical system. The inverse of the hardness is expressed as the global softness and correlated with the reactivity of the chemical system. The calculated DFT-based quantities such as electron affinity (EA), ionization potential (IP), chemical hardness (η) and softness (S) for the complexes are presented in Table 8. For the free ions, the more negative EA, the greater IE and chemical hardness were observed for Ga3+ than In3+ with a larger ionic radius. As for divalent Cu2+ compared with the Table 8. DFT-Based Quantities for Radiometal Ion (Cu2+, Ga3+, Sc3+, and In3+) Complexes with NOTA Calculated at the B3LYP/6-311+G(2d,2p) Level of Theory system

EA (eV)

IP (eV)

η (eV)

S (eV)

Cu2+ Sc3+ In3+ Ga3+ NOTA NOTA−Cu2+ NOTA−Sc3+ NOTA−In3+ NOTA−Ga3+

−21.06 −25.73 −27.75 −31.45 0.60 −8.81 −10.74 −9.82 −10.17

45.46 76.22 59.38 68.76 7.11 15.73 20.28 20.13 20.51

33.26 50.97 43.56 50.11 3.26 12.27 15.51 14.98 15.34

0.015 0.01 0.011 0.010 0.15 0.04 0.032 0.033 0.033

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CONCLUSIONS DFT using B3LYP functional and 6-311G+(2d,2p)/DGDZVP basis sets was utilized to investigate interactions that occur in the complexation process of NOTA with radiometal ions (Cu2+, Ga3+, Sc3+, and In3+). Our study reveals that NOTA−Ga3+ is more stable than the other complexes (NOTA−Cu2+, NOTA−Sc3+, and NOTA− In3+) resulting in more negative chelation interaction energies in solution, the close proximity of the heteroatoms after geometry optimization, and higher electron charge transfer from NOTA to the ions. Generally speaking, chelator−ion and ion−water interactions are governed by the atomic charges and G


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atomic radii of the selected radiometal ions, which are the principal factors contributing to the chelation stability. There is a reasonable consistency between experimental and theoretical binding constants, structural geometries, and 1H NMR chemical shifts. In other words, the observed order of interaction energies is consistent with the experimental ranking in terms of the measured binding constants. A comparable trend was also observed between theoretical 1H NMR chemical shifts of different proton categories of NOTA with experiment. The δ values and therefore the deshielding effect of the ions on the protons of NOTA is related to natural atomic charge exchange within the complexes. Lastly, there is satisfactory agreement between experimental and theoretical geometries of DOTA−Cu2+ and DOTA−Ga3+ complexes, which adopt distorted octahedral conformations. The equatorial N−Cu2+ short-range distances differ with axial N−Cu2+ distances, reflecting the Jahn−Teller effect for Cu2+ complexes with d9 electronic configuration rather than Ga3+. Overall, the chelation interaction energies in solution, shortrange interatomic distances, NBO and chemical shifts, and DFT-based reactivity-related properties revealed a significant level of interaction between NOTA and radiometal ions. The findings of our study are informative for understanding the factors that contribute to complex stabilities.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b01017. 1 H NMR chemical shifts (δ) and NAC of NOTA in vacuum and the interaction energies/interatomic distances within NOTA−radiometal ion complexes using the ωB97XD functional (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]; Tel.: +27 31 2608520. *E-mail: [email protected]; Tel.: +27 31 2608482. ORCID

A. A. Skelton: 0000-0003-0155-8287 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by a grant from College of Health Sciences (CHS) at UKZN in South Africa. We are also grateful for the helpful support of CHPC (www.chpc.ac.za) and UKZN HPC cluster for providing computational resources.

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REFERENCES

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