Comparison of Crystal Field Dependent and Independent Methods to Analyse Lanthanide Induced NMR Shifts in Axially Symmetric Complexes. Part II: Systems with a C4 Symmetry Axis

Analysis of the LIS data for several series of Ln3+ complexes of C4 symmetry in terms of structural changes, crystal-field effects and/or variation of hyperfine constants along the lanthanide series was undertaken using a combination of the two-nuclei and three-nuclei techniques together with the classical onenucleus technique. Isostructurality of whole series of complexes, with changes of the Fi, and B02 parameters, was clearly defined for the complexes of L by the combination of the two first methods. Small changes, involving the three Fi, Gi and B02 parameters, are observed for the series of complexes of L-L4, using the three data plotting methods. Some of the plots according to the two- and three-nuclei methods are accidentally linear, without necessarily implying isostructurality of the complexes, as they involve parameters, which may be insensitive to any small structural changes occurring in these systems. These parameter variations could result from a magnification, by the present graphical analysis, of the breaks expected from the gradual structural changes along the series due to the lanthanide contraction. The α and β parameters of the three-nuclei method are not diagnostic of the type of structures the complexes have in solution, due to their very indirect dependence on the geometric factors.


INTRODUCTION
The binding of a ligand to a paramagnetic trivalent lanthanide metal ion, Ln>, generally results in large hyperfine NMR shifts (LIS) as well as nuclear relaxation enhancements (LIR) at the ligand nuclei, which have made them ideal structural probes of supramolecular complexes and proteins/1/, while Gd > complexes have found very useful biomedical applications as contrast agents for Magnetic Resonance Imaging/2/. In particular, the LIS have magnitudes and signs depending critically on both the nature of the Ln 3+ ion and the location of the nucleus relative to the metal center, making them very sensitive to structural changes/1,3,4/. para In fact, the observed LIS values, 60. induced by a paramagnetic Ln > ion j upon the NMR signal of a nucleus i, resulting from the coupling of the electronic magnetic moment of j with the nuclear magnetic moment of i, has two contributions/1 c,5-9/, a through-bond Fermi contact (6) and a through-space dipolar or pseudo-contact shift ( 60 d. ), which in an axially symmetric complex (with at least a C3 or C4 symmetry axis) can be written as/10/: para c d 60. 6. + 6 0. F <Si + C./ B G (1) where F is proportional to the hyperfine coupling constant A of nucleus i, <Sr/is the spin expectation value for the paramagnetic n Q is Bleaney's factor, a magnetic constant measuring at a given temperature the second-order magnetic axial anisotropy of the paramagnetic lanthanide j (scaled to -100 for Dy), B is the axial second-order crystal field parameter of the complex, and G is the axial geometric factor of nucleus i, [G (3COS20i-1)/r], where r and 0 are the axial polar coordinates of nucleus in the principal axis (z-axis) of the magnetic susceptibility tensor of the complex, with the Ln 3+ ion at the origin. Because only the dipolar term contains the geometric information of interest about the lantanide complex, any quantitative structural analysis requires a reliable separation of the observed shift into the contact and dipolar terms. An empirical separation method has been proposed/11/, based on measurement of LIS data for a series of lanthanide complexes. This one-nucleus technique uses plots based on rearrangement of eq. (1) into two linear forms (eqs. The LIS separation is then achieved at a fixed temperature with the following assumptions" (1) the and Q parameters tabulated for the Ln > free ions/5,7,12/are a valid approximation for all complexes; (2) the ("arlos f: G. C Geraldes et aL Bionhorganic C'hem&tty and Applications hyperfine coupling constants (A, and hence the F terms) for each nucleus, and the crystal field parameter, 2 , are invariant along the lanthanide series. Often plots of the observed LIS data according to eqs.
(2) and (3) are linear along the lanthanide series. Then, F and (B2 G) can be determined by linear regression and the above assumptions are proven to be valid, in particular that the complexes are isostructural and the crystal field coefficient is invariant along the Ln 3+ series. However, breaks frequently found in such plots near the middle of the Ln series (Gd-Dy)/lc/have in some cases been ascribed to a gradual change of the G factors associated with the lanthanide contraction/13/, an effect which is amplified for the heavier lanthanides because of their large C./ values /6/. However, in other cases such breaks have been assigned to variations of F and/or Be along the Ln series/14,17/. para ,para Combination of eq. (1) for the paramagnetic shifts (_0. and "kj ) of two nuclei and k, in the same complex, leads to the removal of the crystal field parameter B in eq. (4)/14,18/: where Rk G/Gk, which can be used to investigate the isostructurality of complexes along the lanthanide series. In fact, since eq. (4) does not depend on the crystal field parameter, any deviation from linearity found ,6 'para/<S.>! vs..para/<Sz,> j along the Ln series can be safely ascribed to structural changes on plots of -0 affecting R, and thus G and Gk/18-20/.
Because theoretical <S..> and C./values for some of the lanthanide ions, in particular for Sm and Eu /5,7,21/, have anomalous temperature dependencies, there is a lack of reliable theoretical <Sz > and C values for either abnormally high or low temperatures. Thus, although these parameters are relatively independent from crystal field effects around room temperature, it is desirable to analyze LIS data and to test for isostructurality of series of lanthanide complexes without recourse to the use of both B of the complexes and the theoretical <S. and Ci flee-ion parameters. This can be achieved with the three-nuclei method/22/, based on eq. (5) for three different nuclei i, k, in the same lanthanide complex:  13, provided that the complexes are isostructural and the hyperfine coupling constants are invariant along the lanthanide series. As it is solely based on experimental LIS data, this method can be applied to any ligand for which the LIS data are available for at least three nuclei, over a very wide range of temperatures.
Complementary structural information on the complexes is provided by the experimental relative Ln-Hj distance values (raj), obtained from the paramagnetic contribution to the proton spin-lattice (Tl) and spin-spin The relative distances obtained by eq. (6) should be independent of the electronic spin relaxation time, rotational correlation time and magnetic moment of each individual complex. The combined use of the above two-nuclei and three-nuclei techniques together with the classical onenucleus technique, according to eqs.
(1)-(5), to study the LIS values for a series of lanthanide complexes, is particularly powerful in assigning eventual structural changes, crystal-field effects and/or variation of hyperfine constants along the lanthanide series/19,22-26/. A critical study of the results of this approach to the analysis of LIS data of a series Ln > complexes of three-fold symmetry (at least a C3 axis) in terms of structural changes, crystal-field effects and/or variation of hyperfine constants along the lanthanide series, has recently been undertaken/26,27/. We now extend this analysis to the LIS data available for complexes of four-fold symmetry (at least a C4 axis) of linear an macrocyclic ligands in different stoichiometries, solvents and temperatures (see Fig. 1).
-s,N o -s / \o---  O,O'-diethyl dithiophosphate)/28/. The observed NMR data fit an effectively axial symmetric coordination model in which the lanthanide ion is chelated by four SzPRzmolecules in a bidentate fashion (through the two sulfur atoms). These data were analysed using the usual two-nuclei crystal field independent method/18/ through plots based on a simplified version of eq. (4), where is the P nucleus and k are the CHz and CH protons and assuming no contact contribution to the LIS values of these protons. In this case, as F 0, the plots give directly as intercepts the values of the hyperfine coupling constant to the P nucleus, F,, and as slopes the g.eometric ratios R, G,/Gk. The breaks observed in such plots at the middle of the lanthanide series for all the compounds studied were assigned to structural (R, values) and P coupling constant (F,) changes along the lanthanide series, although no differences in solid state structures of the complexes along the series have been detected/18,28,32/. Large decreases of F, and R, values were observed from the first to the second group of Ln ions, indicating a substantial decrease of the contact and dipolar shifts of the P nucleus, consistent with a change of the coordination .polyhedron in solution from a dodecahedral to a square antiprismatic structure. We have confirmed the conclusions of these early studies by plotting the LIS data of the [Ln(SzP(OEt)2)4] complexes at 299 K and 233 K using eqs. (2) and (3)/26/. Indeed, breaks in those plots were seen at Tb, reflecting variations of the F and BGi terms ( Because another early analysis of the same P and H LIS data using a different crystal field independent method has concluded that the [Ln(SzP(OEt)2)]" complexes are isostructural along the Ln series/14/, we proceeded to analyse the same data on the basis of the full eq. (4)/26/. The corresponding plots for CH and k CHz indeed give a single straight line identical at both temperatures, indicating that either there is no structural change, or if it occurs it is not reflected in the proton G and F parameters, eg. Gc/Gc# is constant ( Fig. 2A). However, similar plots with P and k CH or CH, identical to the ones discussed above using the simplified version of eq. (4), give clear breaks at Tb, confirming that the F and G parameters of the P nucleus change abruptly at Tb (Fig. 2B). There is generally a good agreement of experimental and calculated R and (F Fk R) parameters (Table 1) (Table 1). This is not surprising because the temperature-dependent parameters, B, <S and Q., are all absent from eq. (5). The experimental e and [ parameters are in satisfactory agreement with those calculated from F and G values obtained by the other methods (Table 1). However, plots according to eq. (5) with other combinations, such as for P, CH and k CH2, show large breaks, thus confirming the structural and coupling constants change/26/. The reason why the first plot is not sensitive to the structural change is that [3 0 implies that Fcm/Fcm Gc#/G,m and tlese ratios do not change along the series. This example illustrates how both the two nuclei and three nuclei methods.may accidentally not reflect structural and/or F changes for some of the combinations of nuclei used in the plots. Thus, it is very important to analyse all the possible combinations. X-ray crystal structures have been determined for a series of [Ln(DOTA)(HzO)] chelates, which define nine-coordinated capped square antiprismatic (CSAP) (M) or inverted capped square antiprismatic structures (m). The acetate arms of the DOTA ligand are arranged in a propeller-like fashion above the basal plane containing one of the square faces of the coordination polyhedron, made up of the four ring N donor atoms which encompass the Ln 3+ ion, defining with their four O donor atoms the other square face in a parallel plane above it, thereby generating a C4 symmetry axis in these complexes. The O atom of the inner-sphere water molecule occupies a capping position. The twist angle between these two square faces can be positive or negative, leading to the two possible isomers, M and m, in which the macrocyclic rings have the same conformation and the difference between them is in the layout of the pendant arms. The X-ray structures of the [Ln(DOTA)(H20)]" complexes with Ln Eu, Gd, Y and Lu are CSAP (M), with twist angles of ca 39 /33-38/, whereas the La complex adopts an inverted CSAP structure (m) with twist angle of ca -22/39/.
The solution structures of these complexes have been intensively studied by NMR. In fact, the H and 3C LIS values of the [Ln(DOTA)]" (Ln La-Lu, except Pm and Gd) complexes have been reported in D20 at pH 7 and different temperatures /40-46/. The H and C NMR spectra exhibit two sets of resonances corresponding to the presence of two slowly interconverting coordination isomers, one set of resonances having constantly larger frequency shifts than the other group. The isomer displaying larger shifts was assigned to a nine-coordinate CSAP structure M, while the isomer displaying smaller shifts is either a ninecoordinate inverted CSAP m (from La to Ho), or an eight-coordinate inverted SAP m' structure with no I'ohtme I. No. I. 2003 Comparison oj'C.rystal Field Dependent and Independent Methods to Anal.vse Lanthanide Induced NMR Shift in Axially Table 1 Calculated values for F, Bo G and R (linear correlation coefficient) values, according to eq. (2), comparison of R and (F-RkFk) parameters calculated directly according to eq. (4), and c and 13 parameters calculated directly according to eq. (5), with those obtained from the above F and B G terms, for Hand 3P-nuclei in the [Ln(S2P(OEt)2)4] complexes in CD2C12 (adapted from/26,28/) ("Not determined. independent elements of chirality defined by the pendant arm C-C3-N-C and ring N-C-Cz-N torsion angles, leading to four possible stereoisomers, which constitute two diastereoisomers each with enantiomeric pairs which are not distinguishable by NMR spectroscopy in solution. The numbering scheme adopted for the hydrogen and carbon atoms is shown in Fig. 3, which schematically represents part of the structure of the complexes in one of the enantiomeric forms of the M isomer, where H denotes the pro-R and H6 the pro-S pendant arm methylene proton/20/. (m'), limiting any definite conclusion in these eases. However, with the available data, breaks between light and heavy Ln were observed in most of those plots (Fig. 4), as reported previously/44/, reflecting variations of the F and BGi parameters. In general, the M isomer shows less significant breaks than m/re'. b) 50 8 ,ara C .

Bioninorganic Chemistry and Applications
The LIS data were also plotted according to eq. (4), eliminating the effect of any changes of Bo (Fig. 5A) /20/. These plots again often show breaks at Eu/Tb, reflecting changes of Fi and Rik, and the Rk and (Fj-RjkF) parameters of the two groups (Ce-Eu and Tb-Yb) were evaluated. These breaks are much less significant than for the one-nucleus plots, not only due to the absence of Bo in the later plots, but also due to the presence of geometric term ratios Rik, which may be significantly less affected by small ,.para Various plots using eq. (5) were also obtained for this system/26/. For the 3C shifts of the M isomer, some of the plots give good linear correlations along the Ln series, eg. for Ca or Ca, C and k C2 (Fig.  5B). Other plots of this type give again a single line along the Ln series, such as for C2, C and k Ca, but other combinations give more or less pronounced breaks, such as for Ca, C and k C3, and for (. 'arlos t' G. (..: Geraldes el ai. Bioninorganic Chemistr), and Applications C or C3, l C and k C4/26/. This is in agreement with the changes of F and G parameters at the middle of the Ln series detected by the one-and two nuclei methods, and again illustrates the possibility that some of the plots according to eq. (5) may accidentally be linear without implying isostructurality of the complexes.
In the case of the 3C shifts of the m isomer, the data available (Ln Pr, Nd, Eu) gives linear plots within the first half of the Ln series (see Table 2). lots according to eq. (5) for the H LIS data of the M and m isomers, eg. for H3, H and H6, H and k Ha support these conclusions, showing two linear parts with breaks in the middle of the series (Fig. 5C). Table 2 compares the c and 13 values calculated for the two isomers, clearly showing that M has significantly larger values than m/m'/26/. The structural change occurring at Ho for the inverted SA' isomer, from m to m', involving loss of one hydration water molecule, is not reflected in any break at Ho in the plots obtained. These H LIS data were originally analysed using the one-nucleus method, through plots according to eqs. (2) and (3), which showed breaks at Eu/Tb, reflecting variations of the F and BgGi parameters, while the data for Tm significantly deviated from the linear correlation defined by the (Tb-Yb) group. The calculated BgG differed by 30% for the two Ln subgroups, while the F differed by 600%/51/. The H LIS data were also analysed by comparing the experimental dipolar shit, s, which are equal to the z-axis magnetic anisotropy C./BGi., with those calculated from the G values defined by MM2-calculated structures of these complexes.
The optimal calculated structure was of the M type, and the results further suggested a significant difference in G values between the light and heavy complexes. However, the derived . B2oGi values for the series of [Ln(DOTEA)] 3+ complexes did not follow the trend of constants, which was interpreted as due to a change of the B parameter along the Ln series, with the largest value for Tm/51/. However this analysis, which led to an M-type solution structure of these complexes, is in conflict with the solution structure analysis of the other tertiary tetraamide complex [Eu(DOTTA)]3+, with a m/M isomer ratio of 2/50/.
We reanalyzed these H LIS data, as well as the 3C LIS data (R Pr, Nd, Eu, excluding Sm) for the [Ln(DOTEA)] 3+ complexes, through plots according to eqs. (2) and (3) /20/ and using the H5 and H6 assignments of Fig. 3, leading to some reassignments of the original data/51/. Again breaks were observed at Eu/Tb in most of those plots, reflecting variations of F and BG /20/. The data were also plotted according to eq. (4) (Fig.6A)  confirmed that this complex lacks an inner-sphere water molecule /16/. The highly charged anionic [Ln(DOTP)]" complexes have four protonation steps over the pH 3-10 range, leading to significantly pH dependent LI.S values/54/. Thus, besides pH 10, the LIS values at pH 7 and 3 were also analyzed/20/. These four protonations correspond to the four residual negative charges localized on the phosphonate oxygen atoms, which are directed away from the Ln coordination site, while the fifth charge, which is averaged over the four bound oxygens in the coordination cage, is not titrated in this pH range.
The H, aC and aP LIS data (pH 10) were initially analysed through the one-nucleus technique. Shift data plots according to eqs. (2) and (3)/53/showed breaks at Eu/Tb, reflecting variations of F and BGg.
Systematic deviations were again .observed for Tm and Yb from the linear correlations defined by the other ions within the second half of the series. The H LIS data were also analysed by considering B02 constant and comparing the experimental G values and Ln-H distance ratios obtained from T relaxation data, with the corresponding values derived from MMX-calculated structures of these complexes, giving an optimal fit for an M'-type structure, in disagreement with the crystal structure/53/.
Because these contradictory structural results might originate from the assignments of the methylene protons of the pendant arms, in a recent reinvestigation, the H and H6 protons were reassigned to be in agreement with the convention of Fig 3, and the H and C LIS data available for the [Ln(DOTPHn)] (4) complexes at pH 10, 7 and 3 were reanalyzed/20/. Plots according to eqs.
(2) and (3) again showed breaks at Yb, due to F and BgGi changes/20/. Plots according to eq. (4) again show smaller (Hs, H6 << H4, C3 < H2, Ha, C2, P) but significant breaks at Tb, indicating changes of F and R at Eu/Tb/20/. An earlier analysis of the H, 13C and aP LIS data for the [Ln(DOTP)]" complexes within the second half of the series (Ln Tb-Yb) /16/ using Reuben's crystal-field parameter independent method/14/gave evidence that these complexes are isostructural (G and F constant). It also showed that the deviations in the plots according to eqs.
(2) and (3) is otten observed in the (Tb-Yb) half series, in particular for Tm and Yb, reflect large changes of Bg, with the largest value for Tm and the smallest for Yb/16/. Fig. 7A shows the 3P/3C LIS data plotted according to eq. (5) for P, l C and k C2, where all data points (n=l 1) fall on a straight line. The aC LIS data of C3 when plotted in the same way (i P, C and k Cz ) also show a good linear relationship/26/. The c and 13 values obtained directly from these plots agree quite reasonably with those calculated from the F and B{ G parameters obtained from eq (2)/26/. However, like for the complexes of DOTA and DOTEA, plots using other nuclear combinations give more or less pronounced breaks, such as for Ca, C and k C3, and for C2 or C3, C and k C4. This is again in agreement with the detected changes of F and G parameters at Eu/Tb, and illustrates the appearance of accidentally linear plots according to eq. (5).  It is worth noting that comparison of the c and 13 values, obtained from plots of the H LIS for the CH2 protons in the pendant arms of the three complexes according to eq. (5), for H5 and H6, with H1 and k H4 (Table 2) However, the data analysis available does not prove isostructurality in solution.
Thus, we studied the same data using the two-nuclei crystal-field independent technique, eliminating the effect of any B02 changes, and a plot according to eq. (4) (i H2 and k H) gives a single straight line along the lanthanide series (Fig. 8B) (2) and (3)) often seen for many systems. The resulting large statistical errors in Fi and B Gi values obtained by the method often preclude any reliable quantitative study of the structural and bonding properties of the respective lanthanide complexes. In particular, the B G term obtained cannot be used for detecting structural G changes because it is affected by any variation of the crystal-field parameter Bo 2 along the lanthanide series /lc/. The two-nuclei technique (eq. (4)) /18,19/, independent of Bo 2 is a reliable method to study the isostructurality of a series of lanthanide complexes. The linearity of the corresponding experimental plots is a proof of isostructurality of the complexes, due to the constancy of their slopes Rk=(G/Gk) and intercepts (F-FkR,), and therefore of the geometric terms G and hyperfine coupling constants F. The combined use of the one-and two-nuclei techniques allows us to conclude if the changes of B02 G reflected by breaks of plots using the first method result from changes of B02 G or both/20/. The three nuclei shift ratio method (eq (5))/22/has some advantages in the analysis of the isostructurality of lanthanide complexes, as it is based exclusively on the experimental shift data, requiring no knowledge of B, <S or C values, and thus can be applied to the shift data measured at any temperature, as long as the data are available for at least three nuclei within a given ligand. However, the cz and 13 values of the plots obtained are complicated functions of F and G ratios rather than of their values, which may reduce or magnify in some cases the effects of Ln 3+ contraction on F and G parameters. It also cannot provide quantitative values for F and G.
The combined use of the three methods gives new insights for the solution structural study of a series of lanthanide complexes on the basis of the measured LIS values, as shown by a recent critical analysis of the LIS data for several series of Ln 3+ complexes of C3 symmetry in terms of structural changes, crystal-field effects and/or variation of hyperfine constants along the lanthanide series/26,27/. In the present study, this approach was extended to a series of linear and macrocyclic Ln 3+ complexes of C4 symmetry, at different temperatures, solvents and pH values. None of the systems studied showed constancy of the three F, G and B02 parameters for the whole series of lanthanide complexes, but isostructurality was proven, with change of F and Bo 2 for the complexes of L ([Ln(PHT)2]') using the one-and two-nuclei methods. Sudden variations of the F, G and B( parameters at Eu/Tb were observed for the series of complexes of all the other ligands studied, L-L4. Breaks in plots according to the two-nuclei method were generally smaller than for the onenucleus method, as the geometric term ratios R,=(G/G,) tend to be less sensitive than the geometric terms Gi to the structural changes that may occur. For some particular combinations of nuclei, the plots according to eqs. (4) and (5) are accidentally linear, without necessarily implying isostructurality of the complexes, as they involve parameters insensitive to the structural changes which may occur. This illustrates the need to analyse as many plots as possible, as conclusions based on a small number of plots may be wrong. The changes involving the three F, G and B( parameters were interpreted as reflecting small distortions of Bioninorganic Chemistry and Applications changes of the parameters could also result from a magnification, by the present graphical analysis, of the breaks expected from the gradual structural changes along the series due to the lanthanide contraction/13/. The structural change occurring for the [Ln(DOTA)] isomer with an inverted SAP structure, from m to m' at Ho, involving loss of one hydration water molecule, is not reflected in any break at Ho in the plots obtained.
The various and [3 parameters, obtained from plots according to the three-nuclei method for the tetraazamacrocyclic complexes, were found not to be diagnostic of their structure being either M/M' or m/m'. They do not reflect such structural differences, due to their very indirect dependence on the relevant geometric terms.