Thermodynamic Stability of Mn(II) Complexes with Aminocarboxylate Ligands Analyzed Using Structural Descriptors

We present a quantitative analysis of the thermodynamic stabilities of Mn(II) complexes, defined by the equilibrium constants (log KMnL values) and the values of pMn obtained as −log[Mn]free for total metal and ligand concentrations of 1 and 10 μM, respectively. We used structural descriptors to analyze the contributions to complex stability of different structural motifs in a quantitative way. The experimental log KMnL and pMn values can be predicted to a good accuracy by adding the contributions of the different motifs present in the ligand structure. This allowed for the identification of features that provide larger contributions to complex stability, which will be very helpful for the design of efficient chelators for Mn(II) complexation. This issue is particularly important to develop Mn(II) complexes for medical applications, for instance, as magnetic resonance imaging (MRI) contrast agents. The analysis performed here also indicates that coordination number eight is more common for Mn(II) than is generally assumed, with the highest log KMnL values generally observed for hepta- and octadentate ligands. The X-ray crystal structure of [Mn2(DOTA)(H2O)2], in which eight-coordinate [Mn(DOTA)]2– units are bridged by six-coordinate exocyclic Mn(II) ions, is also reported.


■ INTRODUCTION
Magnetic resonance imaging (MRI) often uses contrastenhanced procedures to attain a more accurate diagnosis of different malignancies. 1−4 The contrast agents (CAs) that are currently used in clinics are complexes with the paramagnetic metal ion Gd(III), 5,6 which are very efficient relaxation agents of water proton nuclei in their vicinity. As a result, CAs shorten significantly the water longitudinal relaxation times, providing an enhanced signal of the tissues in which they are distributed, as fast T 1 relaxation allows for the accumulation of more signal intensity using short repetition times. 7 The efficacy of Gd(III) as a T 1 relaxation agent is related to the dipolar interaction between the nuclear and electron spins, which is particularly efficient due to the presence of seven unpaired electrons and the long electronic relaxation time. 8,9 While the use of Gd(III) CAs is regarded to be safe, a few cases of adverse effects have been reported. 10 Long-term accumulation of Gd(III) in patients that received multiple doses was also described, which stimulated the search for alternative CAs. 11 High-spin Mn(II) possesses five unpaired electrons that originate a symmetrical 6 S ground state term for the free ion. This leads to a slow electronic relaxation, making Mn(II) an efficient relaxation agent. 12 Thus, it is not surprising that Mn(II) complexes were considered as CA candidates with the advent of MRI in the 1970s and 1980s. 13,14 The Mn(II)-based CA [Mn(DPDP)] 4− (DPDP 6− = N,N′-dipyridoxylethylenediamine-N,N′-diacetate5,5′-bis(phosphate), L11, Chart 1) 15 was also introduced in clinical practice for liver imaging, 16,17 though its use has been discontinued due to poor sales. 18 Nevertheless, the problems associated with Gd(III) toxicity and deposition have provoked a renewed interest in Mn(II)based MRI contrast agents. 19 One of the main aims of the research in this field is to develop stable and inert complexes endowed with high relaxation efficiencies. 20 −29 In a recent paper, we proposed an empirical correlation to predict and rationalize the thermodynamic stabilities of Gd(III) complexes with polyaminopolycarboxylate ligands. 30 We showed that the thermodynamic stability constants and pGd values can be approximated to a good accuracy using structural descriptors. The contribution of each structural descriptor (ligand motif) to complex stability was obtained by a least-squares fitting procedure to stability data reported in the literature. The stability constants and pGd values were subsequently obtained by adding the contributions of each structural descriptor. We validated the predictive character of the model by determining the stability constants of a test set of complexes. The prediction of Mn(II) complex stability is of great interest to aid ligand design and reduce synthetic efforts.
Thus, we envisaged to extend to Mn(II) the methodology developed to predict Gd(III) complex stabilities.
This paper presents an overview of the stability constants of Mn(II) complexes reported in the literature, which are subsequently used to develop an empirical correlation To support our analysis, we also report here the X-ray structure of the Mn(II) complex of DOTA 4− , which displays eight-coordinate Mn(II) ions.

■ RESULTS AND DISCUSSION
Coordination Numbers in Mn(II) Complexes. The analysis described in this work assumes that the thermodynamic stability of Mn(II) complexes can be predicted by adding the contributions of the different donor groups present in the ligand structure. However, the number of donor groups that contribute to complex stability is limited by the coordination number of the metal ion. Once the coordination sphere is saturated, the incorporation of additional donor groups into the ligand scaffold is not expected to contribute to an increased stability. The metal ion in Mn(II) complexes with polyaminopolycarboxylate ligands generally displays coordination numbers 6 or 7. Depending on the denticity of the ligand, water molecules present in the first coordination sphere may complete the metal coordination environment. Heptacoordinated metal complexes are relatively rare within the first-row transition-metal series but are more abundant for Mn(II) than for any other metal ion within the series. 31,32 Typical sevencoordinate Mn(II) complexes are those with EDTA 4− (L4, Chart 1) and its derivatives, 33 in which a coordinated water molecule completes the metal coordination sphere. 34−37 A remarkable example of this class is H 3 PyC3A (L10, Chart 1), which forms a very stable Mn(II) complex that generates excellent MRI contrast. 38,39 Seven coordination is also favored by 15-membered macrocyclic ligands containing five donor atoms, which generally provide pentagonal bipyramidal coordination in which the equatorial positions are occupied by the donor atoms of the macrocyclic unit. 40,41 The Mn(II) complex with the triethyl ester derivative of the 12-membered macrocycle H 3 PCTA (L37, Chart 2) was also found to be seven-coordinated in the solid state. 42 However, complexes with 1,4,7-triazacyclononane derivatives such as H 3 NOTA and related ligands generally form six-coordinate complexes in solution. 43−45 Eight-coordinate Mn(II) complexes are rare. 46,47 Eightcoordinate bispidine derivatives providing exceptionally high thermodynamic stabilities (log K MnL > 24) have been reported recently. 48 Remarkable examples in the context of MRI contrast agents are the cyclen derivatives [Mn(DOTAM)] 2+ (DOTAM = L36, Chart 2) and the analogue containing four 2-pyridyl pendants, which were both found to exhibit eightcoordinate metal ions in the solid state. 49,50 However, it is not clear whether eight coordination is favored for these complexes by the presence of charge-neutral pendant arms. The chargeneutral [Mn(cis-DO2A)] complex (see L32, Chart 2) was found to display seven-coordinate Mn(II) ions in solution, thanks to the presence of a coordinated water molecule. 51 A seven-coordinate structure was also observed in the solid state. 52 The incorporation of a third acetic acid pendant into the cyclen structure to give H 3 DO3A (L25, Chart 2) yields a seven-coordinate Mn(II) complex, as demonstrated by relaxometric studies. 51 The coordination number of the metal ion in [Mn(DOTA)] 2− (see L35, Chart 2) was never ascertained, though the small zero field splitting evidenced by electron paramagnetic resonance (EPR) measurements is compatible with a rigid and symmetrical coordination environment. 53 56 The coordinated water molecules are involved in hydrogen bonds with oxygen atoms of the carboxylate groups.
The macrocyclic fragment in each of the [Mn(DOTA)] 2− entities is disordered into two positions, which correspond to the two square [3333] conformations 57 of cyclen that are usually denoted as (δδδδ) and (λλλλ). 58 Interestingly, the position of the pendant arms is not disordered, adopting either a Δ or a Λ conformation for each [Mn(DOTA)] 2− entity. 59 As a result, the two disordered macrocyclic units generate the Δ(λλλλ) and Δ(δδδδ) isomers, which provide square   76 and H 4 EGTA. 75 (4) Ligands related to the latter three classes in which some donor groups are absent. 76 A more exhaustive list of ligands and their protonation and stability constants is provided in Table S1 (Supporting Information).
A second ligand family comprises tripodal ligands, in which the different donor groups, up to three, are appended on an amine nitrogen atom. This family includes H 3 NTA 77 (L7) and derivatives in which acetic acid groups are replaced by different donors like picolinic acid (i.e. H 3 DPAAA, L13), 21 sulphonamide (i.e. H 3 DPASAm, L12) 78 or methylphosphonic acid 79 groups. Table 2 presents the stability constants reported for Mn(II) complexes of selected nonmacrocyclic ligands.
The class of macrocyclic ligands that have been more extensively investigated for Mn(II) complexation is certainly the family of tetraazamacrocycles (Chart 2), more commonly cyclen (1,4,7,10-tetraazacyclododecane), 80−82 cyclam (1,4,8,11-tetraazacyclotetradecane), 83,84 or pyclen (3,6,9,15tetraazabicyclo[9.3.1]pentadeca-1(15),11,13-triene) 26,85,86 functionalized with different pendant arms, typically acetic acid, primary or N-substituted acetamides, methylphosphonic, methylphosphinic, or picolinic acid groups, among others. Some of these macrocycles incorporate ether oxygen atoms into the macrocyclic structure replacing some of the amine N atoms. 87 Alternatively, macrocyclic ligands derived from 1,4,7triazacyclononane (TACN) functionalized with different pendant arms, and often with mixed N/O donor sets in the macrocyclic scaffold, can be used as ligands for Mn(II) (i.e. L43, Chart 3). 88−90 The structurally related 15-membered macrocyclic ligands containing mixed N/O donor sets form rather stable complexes as well (i.e. L47−L50, Chart 3). 40,41 Macrocyclic ligands of this family incorporating acetic acid pendant arms were also investigated for Mn(II) complexation. 91 Finally, the stability of Mn(II) complexes with a few mesocyclic ligands derived from AAZTA was also explored (i.e. L44−L46, Chart 3). 92 The thermodynamic stability of Mn(II) complexes depends on several factors, as illustrated in Figure 2. Stability constants generally increase with increasing ligand denticity, as would be expected. The highest log K MnL values are observed for complexes with hepta-and particularly octadentate ligands. This suggests that several Mn(II) complexes display coordination number eight in solution, as, for instance, the bispidines reported recently by Comba 48 and some cyclen derivatives such as [Mn(DOTA)] 2− . In the latter case, stability constants of log K MnL = 20.2 and 19.9 were determined using ionic strengths of 0.1 M Me 4 N(NO 3 ) 93 and Me 4 NCl, 52 while that reported for [Mn(DO3A)] − in 0.1 M Me 4 NCl is slightly lower (log K MnL = 19.4). 52 The log K MnL values determined for a given ligand denticity spread over several orders of magnitude, highlighting the critical effect of ligand topology and the nature of the donor groups incorporated into the ligand scaffold. The data shown in Figure 2 also evidence that macrocyclic ligands derived from the 12-membered macrocycles pyclen, and particularly cyclen, tend to form Mn(II) complexes with higher stabilities than other ligand classes, with the exception of the bispidine ligands described recently, 48 which form extraordinary stable Mn(II) complexes. Taken together, the stability constants reported for Mn(II) complexes span more than 20 orders of magnitude, from log K MnL values of ca. 1−3 for simple bidentate ligands (i.e. picolinic acid) 94 to log K MnL ∼ 24 for the mentioned bispidine complexes.
Structural Descriptors. The descriptors used to predict the thermodynamic stability of Mn(II) complexes are essentially those used previously for Gd(III) 30 and are listed in Table 3. Linear polyaminopolycarboxylate ligands are described by the corresponding number of amine N atoms, denoted as N, and the number of acetic acid groups C. For instance, H 4 EDTA is described as nN = 2 + nC = 4, where n indicates the number of groups of a given class. In the case of macrocyclic ligands, the macrocyclic unit as a whole, including Distance between the metal ion and the plane defined by the four N atoms of the macrocycle (N 4 ). b Twist angle of the O 4 and N 4 planes.   Table 3.

Inorganic Chemistry
pubs.acs.org/IC Article + 4C. Bispidine derivatives were excluded from the analysis presented below due to the scarce thermodynamic data reported for this family of complexes. The different donor groups incorporated into linear or macrocyclic structures are associated with the following descriptors: methylphosphonic acid (Pho), methylphosphinic acid (Phosphi), hydroxyethyl (HE), 2-methypyridine (Py), primary acetamide (A NH2 ), secondary acetamide (A NHR ), tertiary acetamide (A NR2 ), 2-propionic acid or α-substituted acetic acid (C α ), 2-methylpicolinic acid (Pic), and ethylsulphonamide (Sulph). The stability constants reported for 2methylphenol derivatives appear to be very sensitive to the nature of the substituent at position 4. Indeed, the stability constants of derivatives containing the electron withdrawing −NO 2 substituent (i.e. L18, Chart 1) are lower than those of unsubstituted derivatives (L17), which in turn are lower than the stability of derivatives containing an electron-donating −OMe substituent (L19, see stability constants in Table 2). 95 We thus used three structural descriptors for 2-methylphenol groups, denoted as Phe, PheNO2, and PheOMe. Similarly, the use of different descriptors for primary (A NH2 ), secondary (A NHR ), and tertiary (A NR2 ) acetamides is justified by the stability constants of complexes with ligands such as L30, L31, 96,97 and pyclen derivatives with amide groups, 81 which indicate that complex stability increases upon increasing the number of alkyl substituents. Ligands containing α-substituted acetic acid arms generally provide Mn(II) complexes with slightly lower stability than the parent derivatives (i.e. L45 and L46), 92 and thus we used two different descriptors to consider the effect of α-substitution.
The comparison of the stability constants reported for H 4 EDTA derivatives bearing different spacers evidences that this structural modification has an important impact on the thermodynamic stability constants. The incorporation of a cyclohexyl ring (i.e. H 4 CDTA, L14) results in increased stability, while all remaining modifications result in lower log K MnL values than for the parent complex. We note that the use of 1,2-cyclobutyl or cis-1,3-cyclobutyl spacers yields complexes with very similar stabilities. 73,74 Thus, these structural modifications, consisting in replacing an ethyl group such as that in H 4 EDTA by a cyclobutyl ring, are described by the same structural descriptor SCybu. Similarly, the complexes of cis-and trans-H 4 CDTA give also very similar values of log K MnL , 98 and thus these structural modifications are described by a single structural descriptor SCyhx. Additionally, the same descriptor was used to account for the incorporation of a piperidine ring into the ligand scaffold (see L9, Chart 1). 99 Similarly, the incorporation of a phenyl ring (i.e. H 4 PhDTA, L16) and a propyl chain (i.e. H 4 PDTA, L3) are denoted as SPh and Spropyl, respectively. The same descriptors are employed to account for the introduction of phenyl or propyl groups into macrocyclic units, for instance, the propyl chains in H 4 TRITA (L23) and H 4 TETA (L24). 93 A rather common structural modification introduced to macrocyclic systems consists in replacing amine N atoms by ether oxygen atoms (L21, 81 L22, 87 L40, 88 L41, 88 L50 40 ) or  40 These structural modifications are considered by structural descriptors SOe and SPy. Some nonmacrocyclic ligands also incorporate these structural motifs, for instance, H 4 OBETA (L2) 75,100 and H 4 PyDTA (L8). 76 The log K MnL values of C-alkylated linear and macrocyclic complexes, such as meso-H 4 DIMEDTA (L6) 70 and L48, 101 are slightly higher than the parent nonsubstituted derivatives. Thus, this alteration was considered with an additional descriptor (SCalk).
Prediction of Stability Constants and Conditional Stability. The structural descriptors presented in the previous section were used to estimate the log K MnL values of Mn(II) complexes using the following expression In this expression, n i is the number of structural descriptors of type i, while Δlog K i represents the contribution to the stability constant of this donor group. The second term accounts for the different structural modifications present in the ligand structure, where n j is the number modifications of a given type and Δlog K j its contribution to complex stability. For the complexes with acyclic ligands, A MnL was set to zero.
Similarly, we used a similar expression to analyze complex stabilities at pH 7.4 using pMn values (eq 2), which are defined here as −log[Mn] free for a total Mn(II) concentration of 1 μM and a total ligand concentration of [L] tot = 10 μM.  The values of pMn allow for a comparison of the stabilities of complexes with different ligands at physiological pH, which depend not only on log K MnL values but also on ligand basicity as well. In principle, one could define pMn using different conditions, for instance, taking equimolar concentrations of ligand and metal ions. We have chosen here the conditions proposed by Raymond, 115 which imply using a 10-fold ligand excess. This results in higher pMn values, increasing the number of ligands that provide a pMn value >6, as pMn = 6 corresponds to a fully dissociated system. Figure 2 shows that the pMn values vary in the range of ca. 6−21, and tend to increase with ligand denticity. Bidentate and tridentate ligands generally provide pMn values of 6 for the definition used here, and thus these ligands were excluded in Figure 2c.
A least-squares fit of 168 log K MnL values reported in the literature to eq 1 provided the contribution to the complex stability of the different structural descriptors, which were used as fitting parameters. The results of the analysis are provided in Table 4. The agreement between the experimental log K MnL values and those predicted by eq 1 is very good, as shown in Figure 2. The linear fit of the data provides a slope very close to 1 [0.997 (5)], as would be expected, with a Pearson's correlation coefficient of 0.9978. The mean deviation of the calculated data with respect to the experimental values is only 0.63. The agreement between the experimental and calculated data is remarkable, as the mean deviation is comparable to the differences in stability constants reported for the same system by independent groups, often using different ionic strengths. For instance, log K MnL values differing by more than 1.3 and 0.7 log K units were reported for H 5 DTPA (L1) 108 and H 4 EGTA. 71,75 Similar differences in stability constants were observed for macrocyclic ligands when using different ionic strengths. 80 Furthermore, the structural descriptors presented above predict identical log K MnL values for regioisomeric ligands such as cis-H 2 PC2A (L38) and trans-H 2 PC2A (L39), which were found to differ by ∼1.5 log K units. 86 Thus, it is obvious that the stability constants of a given complex are affected not only by the nature of the donor groups present in the ligand scaffold but also by the arrangement of these donor groups in the ligand structure.
The analysis of the log K MnL values using eq 1 allows us to infer the coordination number of the metal ion in certain complexes, for which the assignment of a given coordination number is ambiguous. For instance, a log K MnL value of 17.12 is calculated for H 5 DTPA (L1) assuming octadentate binding of the ligand to the Mn(II) ion (3N + 5C). However, the value calculated for a seven-coordinate complex (3N + 4C) of 14.47 is in much better agreement with the experimental values of 15.50 102 and 14.54. 71 Thus, this complex is very likely heptacoordinated in aqueous solution, as observed in the solid state for bis(amide) derivatives of H 5 DTPA. 109 A similar situation is observed for H 4 TETA (L24), for which the log K MnL value estimated assuming eight coordination (14.71), differs considerably from the experimental value of log K MnL = 11.27. 93 A considerably better agreement is observed by assuming the formation of a heptacoordinated complex ( Table  2). Most likely the propyl chains present in the ligand structure introduce some steric hindrance around the metal ion, favoring a lower coordination number in comparison with H 4 DOTA, as observed for the corresponding Gd(III) complexes. 110 The presence of bulky methylphosphonic acid groups in H 6 DO3P (L26) and H 8 DOTP (L34) appears to favor the formation of six-coordinate complexes in solution (Table 2). 81 The empirical expression obtained here may be useful to aid experimental stability constant determination, as the predicted log K MnL value can help anticipate the pH range in which complex dissociation is expected to occur. Furthermore, eq 1 can be used to identify stability constant values that are likely to be incorrect. For instance, a stability constant of log K MnL = 14.29 was reported for a pentadentate ligand containing a piperazine ring functionalized with a picolinic acid and an acetic acid function. 25 The stability constant predicted with eq 1 using 2N + 1C + 1Pic + 1SCyhx is 11.07. The very large discrepancy between the experimental and calculated values suggests that the experimental stability constant may be incorrect and should be taken with some caution.
The pMn values obtained from 141 complexes were fitted to eq 2 following the same strategy used for stability constants. The number of data points used in this analysis is lower than for log K MnL , as ligands with pMn ∼ 6 had to be excluded from the analysis, and for a few systems, ligand protonation constants were not reported together with stability constants. The agreement between the experimental and calculated pMn data is reasonably good (Figure 2), though not as good as for log K MnL values. The linear fit of the data gives a slope of 0.993(7) and a Pearson's correlation coefficient of 0.9967. The mean deviation of calculated versus experimental data amounts  Table 3.

Inorganic Chemistry
pubs.acs.org/IC Article to 0.66 pMn units. We note that the Δlog K i,j and ΔpMn i,j contributions characterizing some structural descriptors were obtained with rather large standard deviations (Table 4). This situation is generally associated with structural motifs that have been seldom incorporated into ligand structures (low Σn i,j values in Table 4).

Analysis of the Structural Descriptors.
The contributions of the different structural descriptors to log K MnL and pMn provide valuable information that can be used for ligand design. Figure 3 shows the contributions of the different motifs to log K MnL and pMn. The group with the highest contribution to log K MnL is the picolinic acid moiety (Pic), which is characterized by a Δlog K i value of 4.65. The latter value is significantly higher than the sum of the contributions of an acetic acid (C) and a pyridyl group (Py), which amounts to 4.16. Thus, picolinate units are particularly well suited for stable Mn(II) complexation. Other groups characterized by large Δlog K i contributions are methylphosphonic acid (Pho), ethylsulphonamide (Sulph), and 2-methylphenol groups, either unsubstituted at position 4 (Phe) or bearing a methoxy substituent (PheOMe). However, the high basicity of these groups results in a very significant decrease in their contribution to pMn compared with log K MnL . In other words, these groups provide a large contribution to the stability constant, but they are also prone to protonation at pH 7.4, which has a very negative impact on the stability of the complex close to physiological pH. Indeed, very high protonation constants were determined for Mn(II) complexes containing methylphosphonate, 82 ethylsulphonamide, 78 and phenolate groups, 95 with log K MnL typically >5.5. This effect is particularly dramatic for PheOMe, which is characterized by Δlog K i = 2.82 and ΔpMn i = −0.62. The lower basicity of the phenol group functionalized with a −NO 2 substituent at position 4 results however in very similar Δlog K i and ΔpMn i values. The high basicity of amine N atoms (N) also justifies the fact that Δlog K i > ΔpMn i .
The low basicity of acetate groups (C) results in very similar Δlog K i and ΔpMn i contributions. The introduction of α-alkyl groups (C α ) has a very minor impact in terms of Δlog K i , but decreases slightly ΔpMn i , likely because of an enhanced basicity associated with the electron-donating effect of the alkyl substituent. Picolinate groups are known to decrease the overall ligand basicity compared with similar ligands containing acetate groups, explaining that Δlog K i < ΔpMn i in the latter case. 111 Donor groups with low basicities are generally characterized by Δlog K i < ΔpMn i , and thus are well suited to increase complex stability at physiological pH. As a result, donor groups such as 2-methylpyridine (Py) and tertiary (A NR2 ) and secondary (A NHR ) acetamides provide contributions to ΔpMn i approaching that of carboxylates (C). The contribution of a picolinate group (4.98) is nearly identical to the sum of the contributions of acetate (2.64) and pyridine (2.29).
Concerning the effect of structural modifications, the incorporation of propyl groups (Spropyl), ether oxygen atoms (SOe), or cyclobutyl (SCybu) groups has a very negative impact on both log K and ΔpMn, as evidenced by their negative contributions. Replacing ethylene groups of the ligand backbone by phenyl groups has a negative impact in terms of log K, but results in a slight positive contribution to pMn. The incorporation of a pyridyl group into the ligand scaffold results in improved stability, with a particularly positive effect on pMn. This can be attributed to the lower basicity of pyridine with respect to amine N atoms. Examples of ligands that exploit this effect for stable Mn(II) complexation are H 4 PyDTA (L8) derivatives 76 and H 2 PC2A Figure 3. Comparison of the contributions of the different structural descriptors to log K MnL and pMn, obtained from the least-squares fit of the stability data to eqs 1 and 2. Structural descriptors detailed in Table 3.

Inorganic Chemistry
pubs.acs.org/IC Article derivatives L38 and L39. 86 Cyclohexyl rings have also a beneficial impact on complex stability when replacing ethyl groups of polyaminopolycarboxylate ligands, an effect exploited in the well-known H 3 PyC3A ligand (L10), which affords a stable Mn(II) complex with appealing properties as an MRI contrast agent. 38,39 The terms describing the contributions of macrocyclic and mesocyclic platforms indicate that 15-membered macrocycles provide the largest contribution to both complex stability and pMn, followed by 12-membered macrocycles, TACN and AAZTA derivatives. The same trend is observed for both log K and ΔpMn values. However, one has to consider that these structural motifs contain a different number of donor groups, and thus impose some limitations to the number of additional donor atoms that can be incorporated into the Mn(II) coordination sphere. 15-Membered macrocycles generally favor seven-coordinate complexes, where two additional donor atoms coordinate to the metal ion from different sides of the macrocyclic mean plane. As a result, only one additional donor atom can be incorporated into the ligand scaffold if an inner-sphere water molecule should be present. The TACN unit contains three donor atoms, but Mn(II) complexes based on this platform do not exceed coordination number six, which greatly limits the stability that can be achieved ( Figure 2). Thus, 12-membered macrocycles appear to be the best choice among those analyzed here, as they combine rather large A MnL and A pMn contributions and coordination numbers of seven or even eight in the case of cyclen derivatives, as demonstrated here for [Mn(DOTA)] 2− . Figure 4 provides a comparison of the contributions of the different structural descriptors to Mn(II) and Gd(III) 30 complex stabilities. The Δlog K values of most structural descriptors fall close to the line of identity, indicating that they contribute to a similar extent to Gd(III) and Mn(II) complex stability. However, Gd(III) complexes with high denticity ligands (8−10) are often characterized by higher stability constants than the Mn(II) analogues, due to the higher coordination numbers that the former achieve. 9-Membered and 15-membered macrocyclic units appear to be better suited for Mn(II) than Gd(III) complexation, while 12-membered macrocycles provide similar contributions to the stabilities of complexes with the two metal ions. Hydroxyethylmethyl and phosphinic acid arms are not adequate for stable Mn(II) complexation. On the contrary, phenyl and propyl spacers are more detrimental to Gd(III) complex stability compared with Mn(II). In the case of Spropyl term, this is related to the strong preference of large metal ions to form five-membered chelate rings. 112

■ CONCLUSIONS
The reemergence of Mn(II) complexes as MRI contrast agents has stimulated a great amount of work to determine their thermodynamic stabilities. 48,86,95 Compared to Gd(III)-based MRI contrast agents, the stability constants of Mn(II) complexes are typically lower. High-spin Mn(II) has no ligand field stabilization energy (LFSE), is generally kinetically labile, and forms less stable complexes than biologically important divalent cations like Fe(II), Zn(II), and Cu(II). Thus, for in vivo applications, it is critical to achieve as high a stability as possible to minimize the risk of Mn(II) dissociation in the body. This is also true for emerging applications involving Mn-52 PET imaging. 113,114 Concurrently, Mn-based MRI contrast agents require the presence of an inner-sphere water ligand to increase the relaxivity of the complex, and leaving a coordination site vacant for water access may result in lower stability. Finally, the large size of the Mn(II) ion and lack of LFSE results in coordination numbers of 6, 7, and 8 for complexes in aqueous solution, and coordination number is difficult to predict a priori.
Here, we utilized the large body of published stability constant data to establish quantitative structure−stability correlations to predict stability constants, employing the methodology we initially applied to Gd(III). The empirical relations presented here are remarkably accurate despite known differences in experimental stability constants arising from the use of different ionic media and ionic strengths. An interesting result from this study was the prediction of the denticity of the coordinated ligand when multidentate ligands are used, e.g., [Mn(DOTA)] 2− has eight-coordinate Mn(II) (confirmed by X-ray crystallography), while the predicted stability constant for [Mn(DTPA)] 3− is consistent with sevencoordinate Mn(II). Our approach also serves to identify published stability constant data that may be incorrect. For the development of novel Mn(II) complexes, this method allows the prediction of stability constants and the ability to rule out the synthesis of likely inferior complexes. Finally, the quantification of different structural parameters like donor atom or chelate ring type allows the design of new complexes that might have optimal stability.
Having now applied this methodology to Gd(III) and Mn(II) complexes, it is apparent that this work can be extended to other metal ions for which exist a large body of stability constant data. A limitation of this work is that the method requires stability constant data for specific donors or ligand archetypes. As such, it does not anticipate novel chelators like bispidines. 27   The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.