Kinetic and High-Pressure Mechanistic Investigation of the Aqua Substitution in the Trans-Aquaoxotetracyano Complexes of Re(V) and Tc(V): Some Implications for Nuclear Medicine

A kinetic study of the aqua substitution in the [TcO(OH2)(CN)4]− complex by different thiourea ligands (TU = thiourea, NMTU = N-methyl thiourea, NNDMTU = N, N′-dimethylthiourea) yielded second-order formation rate constants (25°C) as follows [NNDMTU, NMTU, TU, respectively]: kf = 11.5 ± 0.1, 11.38 ± 0.04, and 7.4 ± 0.1 M−1s−1, with activation parameters: Δ H#kf : 55 ± 2, 42 ± 3, 35 ± 5 kJ mol−1; ΔS#kf : − 40 ± 8, − 84 ± 11, − 110 ± 17 J K−1mol−1. A subsequent high-pressure investigation of the aqua substitution in the [ReO(OH2)(CN)4]− and [TcO(OH2)(CN)4]− complexes by selected entering ligands yielded ΔV#kf values as follows: Re(V): −1.7 ± 0.3(NCS−), −22.1 ± 0.9 (TU) and for Tc(V): −3.5 ± 0.3(NCS−), −14 ± 1 (NNDMTU), and −6.0 ± 0.5 (TU) cm3mol −1, respectively. These results point to an interchange associative mechanism for the negative NCS− as entering group but even a pure associative mechanism for the neutral thiourea ligands.

With the ongoing development of new Tc and Re agents, it is essential that their basic coordination chemistry is understood. Nonradioactive rhenium is widely utilized to imitate technetium chemistry on a macroscale and has been extensively pursued for the past two decades or more, describing changes in coordination modes. We reported structural effects induced by different Re-cores while maintaining an equatorial ligand set, utilizing two dmpe ligands, while varying the axial core, to investigate the impact this change induces on the solid-state structure of the coordinated polyhedron and on the bidentate tertiary phosphine ligand, dmpe [26]. Similarly, the effect of different conformers/isomers and energies associated therewith has been described [27]. More recent extensive work by Alberto showed that the fac-[(CO) 3 M(H 2 O) 3 ] + {M = Re(I), Tc(I)} core provides excellent access to numbers of model radiopharmaceuticals [28][29][30][31][32][33][34][35].
The "lanthanide contraction" results in similar physical characteristics for analogous Re and Tc complexes (i.e., size or lipophilicity) [1,6]. Thus, when rhenium is used as the nonradioactive surrogate for the development of Tc chemistry because it is nonradioactive, their similar physical characteristics make it very difficult for biological systems to distinguish between analogous Tc and Re [6] complexes based on properties such as size, shape, and charge. However, firstly, they differ significantly in their redox properties, which can result in different in vivo handling of analogous complexes. Rhenium complexes are more stable in higheroxidation states and thus are more difficult to reduce (by ca. 200 mV) than their Tc analogs [36]. Thus, Re is more readily reoxidized to perrhenate (ReO 4 − ) than Tc is to pertechnetate (TcO 4 − ) in vivo, and perrhenate requires the use of stronger reducing agents for the synthesis of Re radiopharmaceuticals.
A second difference is the larger ligand field splitting for Re complexes, which results in slower-ligand substitution onto Re than Tc. We have previously investigated different aspects of the trans-dioxo complexes, with the general structure of trans-[MO 2 (L 4 )] n− , M = Mo(IV), W(IV), Tc(V), Re(V), Os(VI), and related systems, evaluating structural and reactivity correlations for a range of ligands L. It was shown that a twelve-order of magnitude in reactivity in these systems exists, ranging from the very rapid proton exchange, to the slower hydroxo and aqua substitution and the extremely slow-equatorial ligand substitution [37][38][39][40][41].
Subsequent kinetic studies on the [ReO(OH 2 )(TU) 4 ] 3+ complex, showed that the trans-substitution reactions of the aqua ligand most likely proceed via an interchange dissociative mechanism (I d ) [42]. This outlined a discrepancy in the proposed mechanism for trans-substitution reactions on the [ReO(OH 2 )(CN) 4 ) − complex as concluded earlier in the literature [43,44] 4 ] − complex, no tendency of limiting kinetics was observed.
We have previously correlated different in vivo reactivities with in vitro behaviour [41] and attempted to link certain sites with biodistribution and bioactivity, but was, and still is, unable to do more detailed comparisons. Thus, since detailed mechanistic studies and data on substitution processes are fairly limited, it prompted us to reinvestigate the type of mechanism obeyed for the [ReO(OH 2 )(CN) 4 ] − complex when reacted with different entering ligands and extending it to the Tc V complex, by specifically utilizing advanced high-pressure kinetics. This high-pressure study of the [MO(OH 2 )(CN) 4 ] − complex (M = Re and Tc), with different entering ligands, is therefore reported here.

MATERIAL AND METHODS
All reagents and chemicals were of analytical reagent grade, and double-distilled water was used in all experiments. All pH measurements were done with an Orion 701 pH meter and a combined glass/calomel electrode using standard buffer solutions and standardized hydrochloric acid solutions for calibration. The ionic strength was constant (μ = 1 M) in all the experiments, maintained with NaNO 3 as noncoordinating electrolyte. In all calculations, pH = −log [H + ]. Na 3 [ReO 2 (CN) 4 ] and Na 3 [TcO 2 (CN) 4 ] were prepared as previously described [37]. Caution: Technetium-99, although a low-energetic radio-active β-emitter (230 KeV, t 1/2 = 2.1 × 10 5 y), should always be handled with care and under approved conditions.
Kinetic measurements were done on modified Durrum-Gibson Model D110 and Applied Photophysics SX.18 MV (control experiments; coupled with a J&M Tidas-16 diode array) stopped flow spectrophotometers equipped with constant temperature syringe and cell holder systems (accurate within 0.1 • C). These were coupled to a personal computer or Acorn Risc workstation capable of performing least-squares analyses on the absorption values versus time data obtained from the kinetic runs. The SCIENTIST [45] program was used to fit the data to selected functions. High-pressure studies were done on a GBC 916 spectrophotometer in a high-pressure vessel with pill box cells of path length ≈15 mm or in a stopped flow high-pressure vessel [46]. All kinetic runs were performed under pseudo-first-order conditions with the ligand in large excess. The solid lines in the figures represent computer least-squares fits of data, while the experimentally determined values are given as points. The [MO(L)(CN) 4 ] n+ complexes from the reactions between [MO(OH 2 )(CN) 4 ] − and different entering ligands were characterised as previously described [43,44].

RESULTS AND DISCUSSION
It was previously shown that the complete reaction scheme governing the substitution reactions on the protonated forms of the trans-[MO 2  The pK a1 value (of the [TcO(OH 2 )(CN) 4 ] − complex, Scheme 1) was previously determined from the reaction between [TcO(OH 2 )(CN) 4 ] − and NCS − ions as 2.90(5) by Roodt et al. [44]. To further verify this by another ligand system, an independent kinetic pK a determination was carried out for the reaction between [TcO(OH 2 )(CN) 4 ] − and NNDMTU and is illustrated in Figure 1. NNDMTU was selected since these reactions showed the largest absorbance changes.
The general expression for the observed pseudo-firstorder rate constant { [L] [M]} shown in (1), as obtained previously, describes the acid-base behaviour of the trans-[MO(OH 2 )(CN) 4 ] n− complexes, where k f and k r represent the forward and reverse rate constants, that is, the anation/ligation and acid hydrolysis, respectively.
(1)  The data in Figure 1 was fitted to (1), and a pK a1 value as reported in Table 1 was obtained. The acid dissociation constant thus determined from the reaction between [TcO(OH 2 )(CN) 4 ] − and NNDMTU {2.99 ± 0.19} is in good agreement with the pK a value reported for the reaction between the metal complex and NCS − ions (2.90 ± 0.05) [44].
It is therefore evident that if the reaction between [TcO(OH 2 )(CN) 4 ] − and the different entering ligands (TU, NMTU, NNDMTU) is investigated at a pH value of 0.6 [pK a1 > 2.9, see Table 1], the trans-oxo aqua species of the metal complex is more than 99% present in solution. At these high-acidic conditions where K a1 [H + ], (1) simplifies to the well-known simple expression in (2), assuming negligible reverse or concurrent reactions (k r ca. 0). The k obsd versus [L] data obtained from these runs was fitted to (2), and values for k f and k r were consequently obtained (Table 1): The ligand concentration and temperature dependence study for each of the different thiourea entering ligands (TU, NMTU, and NNDMTU) were therefore completed for the [TcO(OH 2 )(CN) 4 ] − , with the data for NMTU as entering ligand shown in Figure 2. These k f versus temperature data sets were used in the Eyring equation [43] to calculate the activation parameters governing the k f step ( Table 1). The intercepts (k r ) in all these runs were zero within standard deviations, thus confirming a large K f value (K f = k f /k r ) for each of the different nucleophiles.
The activation entropies (Table 1) for all the reactions studied suggest increased order in the transition state, indicative of association being important.
Following similar arguments used by Grundler et al. [35], and by our group [47], different pathways for the substitution process were therefore considered.  4 ] − and the different thiourea entering ligands; μ = 1.0 M (NaNO 3 ), pH = 0.6. (a) L.S. fits to (2); (b) since small-negative intercepts were obtained in some cases, the value was fixed (= 0.00). The standard deviations reported are those from the first fits; (c) L.S. fits to (1).

Parameter
T  (11) -−110 (17) ΔH Firstly, for an associative mechanism (Scheme 1, A, k 1 and k 2 pathway), the rate of the reaction is given by [M]}, by assuming a fast k 2 step (Scheme 1), 5 {with k 2 = k 1 k 2 /(k −1 + k 2 )}, and defining the pseudo-first-order rate constant, is obtained: It is clear that (5) and (6) are similar and both adequately describe the experimental results {associative mechanism (5): k f = k 2 and k r = k −2 ; interchange mechanism (6): k f = k 4 K 3 and k r = k −4 and K 3 = k 3 /k −3 }, and both simplify to (1) and (2), respectively. The pressure dependence for the substitution process as studied here, at different pressures a and b, is given by [47] ln k a /k b = −ΔV # expt. P a − P b /RT.
Since the contribution by the reverse step is negligible in all cases in this study as concluded above, this implies that ΔV # expt. ≈ ΔV # k f . The data obtained for the trans-[TcO (OH 2 )(CN) 4 ] − are shown in Figure 3, where (7) was utilized to obtain ΔV # expt. , and the results are reported in Table 1. In order to compare the type of mechanism obeyed for trans-aqua substitution in the [ReO(OH 2 )(CN) 4 ] − complex, a high pressure study with NCS − ions and TU was also performed. Since the reaction between [ReO(OH 2 )(CN) 4 ] − and L (L = NCS − and TU) shows equilibrium constants of 87 ± 7 and 7.0 ± 0.4 M −1 , respectively [48,49], similar arguments to the Tc(V) as mentioned above could be used to determine the activation volume, ΔV # expt. , for which the values are reported in Table 2.
We previously concluded that with regard to the mechanism, due to the large distortion (metal displaced out of the plane formed by the four cis ligands bonded to the metal, away from the trans-oxo) observed for the [MO(L)(CN) 4 ] n− complexes of Mo IV , W IV , Re V , and Tc V , a dissociative activation would be favoured during trans-aqua substitution reactions [44,47]. A positive volume of activation (+10.6 ± 0.5 cm 3 /mol) was observed for the reaction between the corresponding isostructural [WO(OH 2 )(CN) 4 ] 2− complex and N 3 − , forming an important basis of the mechanistic assignment.
However, the current high-pressure study on the [ReO(OH 2 )(CN) 4  reactions (Table 2), ranging from slightly negative for the anionic NCS − as entering ligand, to substantially negative for the neutral thiourea ligands. This yields important evidence, along with the large negative ΔS # values, that an associative (A) mechanism or an associative interchange (I a ) mechanism is operative for the activation step during these trans-aqua substitution reactions on the M(V) metals. In principle, this is actually quite acceptable, since the [MO(OH 2 )(CN) 4 ] n− complexes of Mo IV , W IV , Re V and Tc V are all classic 16 electron species. Clearly, the M(IV) metal centres are softer than the corresponding Re V and Tc V , allowing easier dissociation of the aqua ligand in the rate determining step. This is confirmed by the solid state structures of the [MO(NCS)(CN) 4 ] 2− complexes, wherein both of the NCS − ligands where nitrogen bound. [43,44].
The for Re V and Tc V , respectively. These are considered too small negative values to support a pure associative activation, although electrostriction between the negatively charged complex and entering NCS − ligand might affect the total value of ΔV # expt. . For an I a mechanism, the volume of activation can be expressed as the sum of the individual contributions for each step in Scheme 1 (8), where k f = k 4 K 3 and ΔV K3 = reaction volume for the equilibrium reaction defined by K 3 : The k 4 step is associated with a simultaneous bond breaking/formation process, and therefore ΔV # k4 is expected to be slightly negative in an interchange associative process. Furthermore, ΔV K3 can be expressed in terms of its individual components (9): Since ΔV # k−3 is expected to be positive (associated with bond breaking), and ΔV # k3 in turn is slightly negative, ΔV K3 is expected to be either small positive or slightly negative. It is thus clear from (9), that depending on the relative magnitude of the volume change associated with K 3 and k 4 , that either an I d or I a mechanism is possible. However, since an overall negative tendency for ΔV # expt. was obtained, an associative interchange mechanism is considered more likely for the NCS − reaction, since there should be significant electrostriction between the NCS − and [M] − species. For the neutral thiourea ligands, an even larger-negative activation volume is observed, and a pure associative mode of activation could well be operative.  Table 2]. A comprehensive explanation of this rate difference is not yet possible. It is, however, known that the Tc V centre can more readily accept electron density than does the Re V [50,51] and to some extend favour, in spite of the negative charge on the NCS − as entering ligand, association with the Tc V centre. This is, however, not manifested in the activation volumes. The rate constants of the thiourea ligands are more comparable, showing a great deal of consistency for both metal centres, although a slight dependence on steric bulk/electron density of the TU ligands is apparent, but cannot currently be convincingly explained, see below. Secondly, since it is known that methyl substituents on a ligand can increase the pK a value and therefore the electron donating ability thereof (see examples in Table 3 [52]), it is expected in an associative mechanism that the methyl substituted thiourea will react slightly faster than TU, as was concluded from this work on the Re V system.
Thirdly, the [MO(OH 2 )(CN) 4 ] n− compounds of Tc V and Re V react both according to an associative mechanism or partly associative, while the Mo IV and W IV compounds react via a dissociative mechanism. From this, it is clear that the work done on the Mo IV and W IV centres, although all isostructural d 2 species, cannot be applied directly to the Tc V and Re V centres, as assumed previously [13]. It also implies that the higher-oxidation state of the Tc V and Re V centres favour the more associative activation, while the Mo IV and W IV could favour a dissociative activation mode.
However, even more detailed high-pressure studies, to enable construction of complete volume profiles, are required in future.
These results, along with the fact that the Tc(V) centre is much more reactive than the Re(V), is of particular relevance to nuclear medicine. In the preparation of 99m Tc radiopharmaceuticals or in the labelling of antibodies with 99m Tc, "transfer" ligands are often used to stabilize the required oxidation state, and then the actual labelling is accomplished by simple ligand substitution onto the "transfer complex" [53]. From this work, the best way of optimizing labelling conditions would be to use a S-donor transfer ligand instead of a C-or N-donor transfer ligand so that the exchange process would be dissociative in nature. This would imply that the transfer ligand, rather than the concentration of the antibody or chelating moiety attached to the antibody, would influence the reaction rate and yield a much "cleaner" reaction mixture (concentration of unlabeled antibody in solution would be low). Furthermore, the greater reactivity of Tc compared to Re must be taken into account when developing therapeutic radio-rhenium analogues to known diagnostic 99m Tc radiopharmaceuticals. For example, more drastic conditions are required in the preparation of 186 Re diphosphonates (for bone imaging) than in the preparation of 99m Tc diphosphonates [54]. These differences in reactivities between Tc V and Re V centres needs to be taken into account before procedures that are available for certain technetium complexes are applied to the preparation of the rhenium analogues.