Pyridine and phosphonate containing ligands for stable lanthanide complexation. An experimental and theoretical study to assess the solution structure

Article abstract of DOI:10.1039/b611544f

We report an experimental and theoretical study of the stability and solution structure of lanthanide complexes with two novel ligands containing pyridine units and phosphonate pendant arms on either ethane-1,2-diamine (L ²) or cyclohexane-1,2-diamine (L³) backbones. Potentiometric studies have been carried out to determine the protonation constants of the ligands and the stability constants of the complexes with Gd^III and the endogenous metal ions Zn^II and Cu ^II. While the stability constant of the GdL² complex is too high to be determined by direct pH-potentiometric titrations, the cyclohexyl derivative GdL³ has a lower and assessable stability (logK _{GdL 3} = 17.62). Due to the presence of the phosphonate groups, various protonated species can be detected up to pH ≈ 8 for both ligands and all metal ions studied. The molecular clusters [Ln(L)(H₂O)] ^3-·19H₂O (Ln = La, Nd, Ho or Lu; L = L² or L³) were characterized by theoretical calculations at the HF level. Our calculations provide two minimum energy geometries where the ligand adopts different conformations: twist-wrap (tw), in which the ligand wraps around the metal ion by twisting the pyridyl units relative to each other, and twist-fold (tf), where the slight twisting of the pyridyl units is accompanied by an overall folding of the two pyridine units towards one of the phosphonate groups. The relative free energies of the tw and tf conformations of [Ln(L)(H₂O)]^3- (L = L², L³) complexes calculated in aqueous solution (C-PCM) by using the B3LYP model indicate that the tw form is the most stable one along the whole lanthanide series for the complexes of L³, while for those of L² only the Gd^III complex is more stable in the tf conformation by ca. 0.5 kcal mol^-1. ¹H NMR studies of the Eu^III complex of L³ show the initial formation of the tf complex in aqueous solution, which slowly converts to the thermodynamically stable tw form. The structures calculated for the Nd^III complexes are in reasonably good agreement with the experimental solution structures, as demonstrated by Nd ^III-induced relaxation rate enhancement effects in the ¹H NMR spectra. This journal is The Royal Society of Chemistry.

Full text of DOI:10.1039/b611544f

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PAPER
www.rsc.org/dalton | Dalton Transactions
Pyridine and phosphonate containing ligands for stable lanthanide
complexation. An experimental and theoretical study to assess the
solution structure†
a
b
a ´
b,c
a
Marta Mato-Iglesias, Edina Balogh, Carlos Platas-Iglesias,* Eva T o´ th, Andr e´ s de Blas* and
a
Teresa Rodr ´ı guez Blas
Received 9th August 2006, Accepted 29th September 2006
First published as an Advance Article on the web 13th October 2006
DOI: 10.1039/b611544f
We report an experimental and theoretical study of the stability and solution structure of lanthanide
complexes with two novel ligands containing pyridine units and phosphonate pendant arms on either
2
3
ethane-1,2-diamine (L ) or cyclohexane-1,2-diamine (L ) backbones. Potentiometric studies have been
carried out to determine the protonation constants of the ligands and the stability constants of the
III
II
II
complexes with Gd and the endogenous metal ions Zn and Cu . While the stability constant of the
2
GdL complex is too high to be determined by direct pH-potentiometric titrations, the cyclohexyl
3
derivative GdL has a lower and assessable stability (log KGdL3 = 17.62). Due to the presence of the
phosphonate groups, various protonated species can be detected up to pH ≈ 8 for both ligands and all
3
−
2
metal ions studied. The molecular clusters [Ln(L)(H
2
O)] ·19H
2
O (Ln = La, Nd, Ho or Lu; L = L or
3
L ) were characterized by theoretical calculations at the HF level. Our calculations provide two
minimum energy geometries where the ligand adopts different conformations: twist-wrap (tw), in which
the ligand wraps around the metal ion by twisting the pyridyl units relative to each other, and twist-fold
(
tf ), where the slight twisting of the pyridyl units is accompanied by an overall folding of the two
pyridine units towards one of the phosphonate groups. The relative free energies of the tw and tf
3
−
2
3
conformations of [Ln(L)(H
2
O)] (L = L , L ) complexes calculated in aqueous solution (C-PCM) by
using the B3LYP model indicate that the tw form is the most stable one along the whole lanthanide
series for the complexes of L , while for those of L only the Gd complex is more stable in the tf
conformation by ca. 0.5 kcal mol . H NMR studies of the Eu complex of L show the initial
formation of the tf complex in aqueous solution, which slowly converts to the thermodynamically
stable tw form. The structures calculated for the Nd complexes are in reasonably good agreement with
3
2
III
−
1
1
III
3
III
III
the experimental solution structures, as demonstrated by Nd -induced relaxation rate enhancement
1
effects in the H NMR spectra.
Introduction
technique is related to the successful use of paramagnetic agents,
mainly Gd complexes, which enhance the intrinsic contrast of
III
Coordination chemistry of lanthanide complexes in aqueous
solution has been the subject of intense research efforts over
the past ten years. In particular, lanthanide complexes with
poly(aminocarboxylate) ligands present considerable interest due
to their application as contrast agents for magnetic reso-
the magnetic resonance images by preferentially influencing the
relaxation efficiency of the water proton nuclei in the target tissue.
1
III
These complexes contain at least one Gd -bound water molecule
that rapidly exchanges with the bulk water of the body, which
imparts an efficient mechanism for the longitudinal and transverse
2,3
nance imaging (MRI), or responsive luminescent lanthanide
relaxation (T
1
and T ) enhancement of water protons. Contrast
2
4
complexes. Within the last decade, MRI has become one of the
agents must be stable enough to avoid the in vivo release of toxic
most powerful tools for medical diagnosis. The development of this
III
free Gd . The ligands used must also show a good selectivity for
III
Gd over other metal ions present in body fluids such as the most
a
II
Departamento de Qu ´ı mica Fundamental, Universidade da Coru n˜ a, Alejan-
abundant Zn .
5
dro de la Sota 1, 15008 A, Coru n˜ a, Spain. E-mail: cplatas@udc.es
In a recent work, we reported a new receptor containing
pyridine units and carboxylate pendants (H
b
Laboratoire de Chimie Inorganique et Bioinorganique, Ecole Polytechnique
1
4
L , Scheme 1), which
F e´ d e´ rale de Lausanne, BCH, CH-1015, Lausanne, Switzerland
III
forms relatively stable complexes with Ln ions in aqueous
c
Centre de Biophysique Mol e´ culaire, CNRS, rue Charles-Sadron, 45071
6
III
solution. In these complexes, the Ln ion is nine-coordinate,
where a water molecule completes the metal ion coordination
sphere. This induces a relaxivity in solutions of the complex at the
imaging fields comparable to those reported for standard contrast
Orl e´ ans, Cedex 2, France
†
Electronic supplementary information (ESI) available: Optimized Carte-
sian coordinates ( A˚ ) of the [Ln(L)(H
O)] ·19H O (Ln = La, Nd, Gd,
2 3
3
−
2
3−
2
2
3
Ho or Lu; L = L or L ) and [Lu(L)] ·20H
2
O (L = L or L ) systems;
3
−
3−
hydrogen bonding data for [Gd(L)(H
2
O)] ·19H
2
O and [Lu(L)] ·20H
2
O
−
4−
2
3
1
III
agents such as [Gd(DOTA)(H O)] (DOTA = 1,4,7,10-tetraaza-
(
L = L or L ) systems; Fig. S1: H NMR spectrum of the Eu complex
2
2
2−
of L . See DOI: 10.1039/b611544f
cyclododecane-1,4,7,10-tetraacetate) and [Gd(DTPA)(H O)]
2
5
404 | Dalton Trans., 2006, 5404–5415
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1
experiments. Longitudinal H relaxation times T
1
were measured
11
III
by the inversion–recovery pulse sequence. Samples of the Ln
complexes for NMR measurements were prepared by dissolving
equimolar amounts of the ligand and hydrated Ln(NO
followed by adjustment of the pD with ND OD and DCl (Aldrich)
solutions in D O. The pH of the solutions was measured at room
3
)
3
in D
2
O,
4
2
temperature with a calibrated microcombination probe purchased
from Aldrich Chemical Co. The pH values were corrected for the
12
deuterium isotope effect using the relationship pH = pD − 0.4.
Scheme 1
Potentiometry
5
−
ꢀ
ꢀꢀ
ꢀꢀ
(
DTPA = diethylenetriamine-N,N,N ,N ,N -pentaacetate). In
2
previous papers, we have reported two new ligands (H
6
L and
The stock solution of GdCl
slight excess of concentrated HCl in double distilled water. The ex-
cess of aqueous HCl solution was removed by evaporation. Stock
solutions of Zn and Cu were prepared from ZnCl
salts in double distilled water. The concentration of the solutions
was determined by complexometric titration with a standardized
3
was made by dissolving Gd
2
O in a
3
3
H
6
L , Scheme 1) designed for stable complexation of lanthanide
7,8
III
ions. The corresponding Gd complexes present an extremely
high water exchange rate of the inner sphere water molecule, an
important parameter to be optimized for the design of new, more
effective, MRI contrast agents. In the present work we report an
experimental and theoretical study of the complexation properties
II
II
2
and CuSO
4
Na
2
H
2
EDTA solution (H
4
edta = ethylenediaminetetraacetic acid)
2
3
II III
of ligands H
ions. Ligand H
6
L and H
6
L towards lanthanide and some divalent
L maintains the same basic structure as H
using xylenol orange as indicator (Zn , Gd ) or by gravimetry
2
1
II
6
4
L ,
(Cu ). Ligand stock solutions were prepared in double distilled
but the acetate pendants have been replaced by phosphonic acid
water using KOH to increase the pH up to 4 in order to avoid
precipitation. The exact ligand concentrations were determined
3
pendant arms, while ligand H
6
L contains the same structural
2
backbone as H
6
L with the ethyl bridge being substituted by a more
by adding excess of GdCl
back the metal excess with standardized Na
Ligand protonation constants and stability constants with Zn ,
3
to the ligand solution and titrating
rigid cyclohexyl moiety. This structural modification has been
shown to have an important effect on the water exchange rate of
2
H
2
EDTA.
II
8
II
III
the inner sphere water molecule. In this work, the corresponding
Cu and Gd were determined by pH-potentiometric titration
1
13
◦
lanthanide complexes were characterized by H and C NMR
techniques in D O solution. Thermodynamic stability constants
at 25 C in 0.1 M KCl. The samples (2 or 3 ml) were stirred
while a constant N flow was bubbled through the solutions. The
2
2
III
of the Gd complexes of these ligands have been determined by pH
potentiometry. Stability studies on the complexes of these ligands
titrations were carried out adding standardized KOH solution
with a Methrom Dosimat 665 automatic burette. A combined
glass electrode (C14/02-SC, reference electrode Ag/AgCl in 3 M
KCl, Moeller Scientific Glass Instruments, Switzerland) and a
II
II
with some endogenously available metal ions, such as Cu and Zn
are also reported. In addition, the complexes were characterized
by ab initio calculations carried out at the HF level. These
calculations were performed on molecular clusters with formula
+
Metrohm 692 pH/ion-meter were used to measure pH. The H
concentration was obtained from the measured pH values using
3
−
3−
2
3
13
[
Ln(L)(H
2
O)] ·19H
2
O and [Ln(L)] ·20H
2
O (L = L , L ). Cal-
the correction method proposed by Irving et al. The protonation
culations on molecular clusters have the advantage of providing
useful direct information about the second sphere solvation shell,
which has been shown to enhance the relaxivity of Gd chelates
and stability constants were calculated from parallel titrations with
14
the program PSEQUAD. The errors given correspond to one
standard deviation.
III
9,10
bearing phosphonate groups.
The structures established by
these calculations were compared with the structural information
Computational methods
obtained in solution from paramagnetic NMR measurements
III
3−
(
Nd -induced relaxation rate enhancement effects).
Full geometry optimizations of the [Ln(L)(H
2
−
O)] ·19H
2
O (Ln =
3
La, Nd, Eu, Gd, Ho or Lu) and [Lu(L)] ·20H O (Ln = Lu)
2
2 3
systems were performed in vacuo at the RHF level (L = L or L ).
Experimental
For these calculations the effective core potential (ECP) of Dolg
15
2
3
8
et al. and the related [5s4p3d]-GTO valence basis set were used
for the lanthanides, while the 3-21G* basis set was used for the
ligand atoms. The stationary points found on the potential energy
surfaces as a result of the geometry optimizations have been tested
to represent energy minima rather than saddle points via frequency
analysis.
Ligands H
6
L and H
6
L were prepared as described previously.
The nitrate salts, Ln(NO
and were used without further purification. D
was obtained from Merck (99.9% D).
3
)
3
·nH
2
O, were from Alfa Laboratories,
2
O for NMR studies
NMR measurements
The relative free energies of the twist-wrap (tw) and twist-fold
(tf ) conformations of [Ln(L)(H
in aqueous solution at the DFT (B3LYP functional) level, by
using the 6-311G** basis set for the ligand atoms. In these
calculations second-sphere water molecules were excluded, and
solvent effects were included by using the polarizable continuum
1
13
31
3−
H, C and P NMR spectra were run on Bruker AC200 F or
Bruker Avance 300 spectrometers. Chemical shifts are reported
in d values. For measurements in D O, tert-butyl alcohol was
used as an internal standard with the methyl signal calibrated
2
O)] complexes were calculated
16
2
1
13
at d = 1.2 ( H) and 31.2 ppm ( C). Spectral assignments were
17
based in part on two-dimensional COSY, HMQC and HMBC
model (PCM). In particular, we used the C-PCM variant that,
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Dalton Trans., 2006, 5404–5415 | 5405

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+
employing conductor rather than dielectric boundary conditions,
allows a more robust implementation. The solute cavity is built as
an envelope of spheres centered on atoms or atomic groups with
appropriate radii. Each sphere is subdivided in 60 initial tesserae in
pentakisdodecahedral patterns. For the lanthanides the previously
K
MH L = [MH
i
L]/[MHi−1L][H ]; i = 1, 2, 3
(3)
i
1
2
3
In comparison with L , the L and L ligands have higher
protonation constants for the first and second protonation steps,
which occur on the amine nitrogen atoms. Thus, replacement of
the acetate pendants of L by methylphosphonate groups leads to
an important increase in the basicity of the two amine nitrogen
atoms. The first protonation constant of L and L is very similar
to that reported for ethylenediaminediphosphonic acid (EDDP,
18
6
parametrized radius was used. Final free energies include both
electrostatic and non-electrostatic contributions.
1
19
The NMR shielding tensors (GIAO method) of the
3
−
2
3
2
3
[
La(L)(H
2
O)] (L = L or L ) systems were calculated in aqueous
solution at the B3LYP functional level by using the ECP of Stevens
20,21
et al.
and the 6-311G** basis set for the ligand atoms. For
log K
1
= 10.29), while the second protonation constant is higher
2
3
24
chemical shift calculation purposes, NMR shielding tensors of
tetramethylsilane (TMS) were calculated at the same computa-
tional level. All HF and DFT calculations were performed by using
in L and L than in EDDP (log K
2
= 7.85). The third and fourth
2
3
protonation steps of L and L correspond to partial protonation
of the phosphonate groups, which occur at slightly higher pH
22
24
the Gaussian 98 (Revision A.11.3) and Gaussian 03 (Revision
than in EDDP (log K
3
= 5.40, log K
4
= 4.35). The last two
23
C.1) program packages.
protonation steps probably correspond to the protonation of the
6
pyridylcarboxylate groups.
2
3
Potentiometric titrations of the L and L ligands have been
carried out in the presence of equimolar Gd in order to determine
Results and discussion
III
the stability constants of the metal complexes. The analysis of the
Ligand protonation constants and stability constants of the metal
complexes
2
titration curve for GdL shows that already at the beginning of the
III
titration (pH ∼2), there is no free Gd , all metal being in the form
2
3
The protonation constants of ligands L and L as well as the
of the diprotonated complex. Therefore, we could not calculate
the stability constant for this complex; only an estimation of
stability constants of their metal complexes formed with different
III
II
II
log KGdL2
> 20 can be made. Both mono- and diprotonated forms
metals (Gd , Zn and Cu ) were determined by potentiometric
titration; the constants and standard deviations are given in
III
of the Gd complex have been detected over the pH range studied.
These protonation steps are expected to occur on the phosphonate
groups. Partial protonation of phosphonate groups in solution has
1
Table 1. Table 1 also lists the protonation constants of L and
III
the stability constant of its Gd complex reported by Mazzanti
6
III
25,26
et al. The ligand protonation constants are defined as in eqn
been observed previously for Ln complexes with both cyclic
9
2
(
1), and the stability constants of the metal chelates and the
and acyclic ligands. The species distribution diagram for the GdL
system (Fig. 1) shows the presence of monoprotonated complex in
solution at pH < 8, while the second protonation of the complex
occurs at pH < 7.
protonation constants of the complexes are expressed in eqn (2)
and (3), respectively.
+
3
K
i
= [H
i
L]/[Hi−1L][H ]
(1)
(2)
The species distribution curves obtained for GdL (Fig. 1)
indicate dissociation of the complex at low pH, which allowed
us to determine the stability constant for this complex. This result
K
ML = [ML]/[M][L]
III
3
points to a lower stability of the Gd complex of L in comparison
2
to that of L . Thus, increasing the rigidity of the ligand lowers
the stability of the corresponding Gd complex. The stability
Table 1 Protonation constants of the ligands and stability constants of
III
◦
their metal complexes (25 C; I = 0.1 M KCl)
constant obtained (log KGdL3 = 17.62, Table 1) is approximately 2
1
6
1
a
2
3
log units higher than that of GdL , and similar to that reported
L
L
L
27
for GdEDTA (log KGdL = 17.37).
Cu and Zn complexes are found to be highly stable with
log K
log K
log K
log K
log K
log K
1
2
3
4
5
6
8.5
5.2
3.5
2.9
10.21(2)
8.84(3)
6.59(4)
5.16(4)
3.94(4)
1.4(1)
10.03(3)
9.69(2)
5.88(4)
5.08(4)
4.39(4)
3.20(4)
II
II
2
3
both L and L ; a quantitative assessment by direct potentiometry
3
III
was only possible for CuL (Table 1). As for the Gd analogues,
protonated complexes are present in all systems in an extended
pH range.
III
b
Non-toxicity is primordial for in vivo application of Gd (or
log KGdL
15.1
17.62(8)
6.61(7)
5.41(8)
log KGdHL
6.01(3)
5.00(5)
other metal) complexes as MRI contrast agents. It is evident
log KGdH2
log KGdH3
log KZnL
L
that competitive equilibria cannot solely explain the in vivo
L
4.86(4)
III
b
b
behavior of Gd complexes. The excretion of low molecular
III
weight Gd chelates from the body is very rapid (t1/2 = 1.6 h
log KZnHL
6.94(7)
6.60(4)
6.84(1)
6.01(1)
5.13(2)
18.17(8)
7.7(1)
2
−
log KZnH2
log KZnH3
log KCuL
L
for Gd(DTPA) ), whereas the dissociation and transmetallation
L
III
of the Gd complexes can be relatively slow. Therefore, the system
b
28–30
is far from equilibrium, and kinetic factors must be considered
log KCuHL
log KCuH2
7.08(7)
6.77(5)
L
7.03(5)
A detailed kinetic investigation was beyond the scope of this study.
However, we know that the present complexes protonate readily
and the protonated species are expected to have modest kinetic
stability with respect to proton mediated decomplexation, as it
a
b
From ref. 6. The complex is too stable to determine the stability constant
by direct titration.
5
406 | Dalton Trans., 2006, 5404–5415
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2
3
Fig. 1 Species distribution of the GdL (top) and GdL (bottom) systems,
1
III
III
◦
: 1 Gd : L; [Gd ] = 1 mM, l = 0.1 M (KCl), T = 25 C.
was recently shown for DTPA analogues with a phosphonic acid
31
pendant arm.
1
III
2
3
Fig. 2 H NMR spectra of the La complexes of L (top) and L (bottom)
NMR spectra
recorded in D
2
O solutions (30 mM, pH = 7.6, 298 K).
1
31
13
III
2
The H, P and C NMR spectra of the La complexes of L
3
and L were obtained in D
2
O solution at pH = 7.6. At this pH the
and between ortho-coupled pyridyl protons. A full assignment
1
13
major species in solution is expected to be the fully deprotonated
form [Ln(L)(H
of the H and C NMR spectra was achieved with the aid of
2D heteronuclear HMQC and HMBC experiments. The HMBC
spectra show a signal relating H5 with one of the aliphatic carbon
nuclei of the ligand backbone, which was therefore assigned to C7.
The signals corresponding to protons H8 could be easily identified
3
−
2
n
O) ] , as demonstrated by our potentiometric
measurements (see above). The proton spectra (Fig. 2) consist
2
3
of 9 (L ) and 12 (L ) signals corresponding to the different proton
magnetic environments of the ligand molecule (see Scheme 1 for
labelling scheme). This points to an effective C
the complexes in solution that is confirmed by the C spectra,
which show nine NMR peaks for the 18 carbon nuclei of L and
2
2
symmetry of
due to the presence of important JH–P couplings (ca. 6 Hz, Table 2).
Protons H7 and H8 yield two multiplets, consisting of the AB part
of a ABX spectrum (X is the P nucleus). Although the specific
1
3
2
31
3
1
1 signals for the 22 carbon nuclei of L in the corresponding
CH proton assignments H9ax/H9eq, H8a/H8bandH7ax/H7eq,
2
1
3
complexes. The C NMR spectra show two doublets for the
were not possible on the basis of the 2D NMR spectra, they
were carried out using the stereochemically dependent proton shift
effects, resulting from the polarization of the C–H bonds by the
electric field effect caused by the cation charge. This results in a
deshielding effect of the H9eq, H7eq and H8b protons, which are
2
3
phosphonate carbon atoms C8 ( JC8–P ∼140 Hz) and C7 ( JC7–P ∼16
III
Hz). Similar coupling constants have been observed for other La
3
2
31
33
complexes with ligands containing phosphonate groups. The
NMR spectra recorded at 298 K show a single peak at ca. 17 ppm,
again in agreement with an effective C symmetry of the complexes
in solution. The assignments of the proton signals (Table 2)
were aided with standard 2D homonuclear COSY experiments,
P
III
2
pointing away from the La ion.
1
III
The H NMR spectra of the diamagnetic Lu complexes
recorded at 298 K are more complex than those of the cor-
III
which gave strong cross-peaks between the geminal CH
2
-protons
responding La analogues. Although this complexity prevented
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1
III
2
3
Table 2 H shifts (ppm) for the Ln complexes of L and L in 30 mM D
2
O solutions at pH 7.6
IIIa
III
III
III
La
Ce
Nd
Eu
2
b
3 c
2
3
2
3
2
3
L
L
L
L
L
L
L
L
H3
H4
H5
H7ax
H7eq
H8a
H8b
H9ax
H9eq
H10
7.96
7.99
7.57
3.61
4.76
2.49
2.63
2.57
3.86
7.96
7.96
7.56
3.91
4.51
2.43
2.87
3.69
10.72
9.94
8.75
7.08
1.46
−12.70
−5.19
−3.51
−2.66
10.49
9.70
8.40
8.50
1.37
−2.27
−6.75
1.20
9.61
9.42
8.67
2.51
5.05
10.24
9.82
9.00
2.97
1.20
−8.35
−0.66
−4.98
6.44
6.60
6.44
6.15
6.50
6.44
9.63
2.36
10.95
1.29
15.77
6.91
−1.22
16.13
3.33
11.63
−0.11
−5.11
1.68
−4.26
1.30
1.55
2.24
1.2
0.44
−0.52
−1.40
−1.65
−2.58
−1.95
−1.18
0.41
7.86
8.04
4.70
3.55
ꢀ
H10
H11
H11
ꢀ
1.82
a
b 2
2
2
2
Assignment supported by 2D H,H COSY, HMQC, and HMBC experiments at 298 K.
J
J
9ax,9eq = 9.4 Hz; J9eq,9ax = 10.6 Hz; J7eq,7ax = 14.6 Hz; J7ax,7eq
=
=
2
2
3
3
c 2
2
2
2
1
1
4.6 Hz; J8b,8a = 14.8 Hz; J8a,8b = 14.8 Hz; J5,4 = 7.3 Hz; J3,4 = 7.3 Hz; JH8–P = 5.8 Hz.
7eq,7ax = 14.4 Hz; J7ax,7eq = 14.4 Hz; J8b,8a = 14.9 Hz; J8a,8b
3
3
5.5 Hz; J5,4 = 6.4 Hz; J3,4 = 6.4 Hz; JH8–P = 6.6 Hz; JH7–P = 3.9 Hz.
the assignment of the spectra, they suggest the presence of two
species in solution with a C symmetry. These results point to
1
an increasing rigidity of the complexes in aqueous solutions on
III
decreasing the ionic radius of the Ln ion, as previously observed
III
34
2
for other Ln complexes. In the case of the complex of L the
3
1
P NMR spectrum recorded at 298 K indicates the presence of an
equilibrium between two species with an effective C symmetry. It
1
shows a pair of signals of equal intensity at 21.5 and 18.5 ppm and
a second pair of less intense signals at 22.4 and 13.7 ppm.
1
III
III
III
H NMR spectra of the paramagnetic Ce , Nd and Eu
2
3
complexes of L and L were obtained in D
and were assigned by comparison to the spectra of L complexes
2
O solution at pH = 7.4,
1
and with the aid of line-width analysis and COSY spectra,
which gave cross-peaks between the geminal CH
between ortho pyridyl protons. The spectra of the L complexes
2
protons and
2
show relatively sharp peaks, and they point to an effective C
2
symmetryofthecomplexesinsolution(Table2, Fig. S1, ESI†). The
3
complexes of L behave differently in solution: the spectra indicate
the formation of two distinct complex species whose concentration
changes with time. The spectra acquired immediately after mixing
stoichiometric amounts of the ligand and Ln show a single
1
III
3
Fig. 3 H NMR spectra of the Eu complex of L recorded in D
2
O
III
solution (30 mM, pH = 7.6, 298 K) immediately after the preparation
complex species in solution with C
1
symmetry, which converts
◦
of the complex and after heating the solution at 60 C for 24 h. HOD
slowly to a thermodynamically stable species with an effective C
2
t
and BuOH signals are denoted with an asterisk. The assignment of the
spectrum recorded at t = 24 h is given in Table 2.
1
symmetry. This behavior is illustrated in Fig. 3 with the H NMR
III
3
spectra of the Eu complex of L recorded immediately after the
◦
preparation of the complex and after heating the solution at 60 C
Ab initio calculations: molecular geometries
for 24 h. Our ab initio calculations discussed below provide two
3
2
3−
different minimum energy conformations for the L complexes:
The [Ln(L )(H
2
O)] systems (Ln = La, Nd, Gd, Ho or Lu)
twist-wrap (tw), in which the ligand wraps around the metal ion
by twisting the pyridyl units relative to each other, and twist-fold
were investigated by means of ab initio calculations at the HF/3-
21G* level. In the case of Gd complexes, the long electronic
III
(
tf ), where the slight twisting of the pyridyl units is accompanied
relaxation time of the metal ion prevents any observation of NMR
spectra, and for this reason their solution structures and properties
have to be deduced from the NMR spectra of other lanthanide
complexes. Theoretical calculations provide direct information on
gadolinium systems as well as on those dynamic processes that
are usually too fast to be observed on the NMR time scale, such
as the water exchange process. As there is not a good all-electron
basis set for lanthanides, the effective core potential (ECP) of
Dolg et al. and the related [5s4p3d]-GTO valence basis set was
by an overall folding of the two pyridine units towards one of
the phosphonate groups. Due to this folding, the tw form shows
a molecular geometry that is closer to a C
tf conformation. Thus, we assign the thermodynamically stable
form showing C symmetry to the tw isomer, while the kinetic
complex is attributed to the tf conformation. It should be noted
that the two conformations of the Gd complex are characterized
by identical proton relaxivities.
2
symmetry than the
2
III
5
408 | Dalton Trans., 2006, 5404–5415
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1
5
n
applied in these calculations. This ECP includes 46 + 4f electrons
in the core, leaving the outermost 11 electrons to be treated
explicitly, and it has been demonstrated to provide reliable results
18
for the lanthanide aqua-ions, several lanthanide complexes with
35,36
37
polyaminocarboxylate ligands
and lanthanide dipicolinates.
Compared to all-electron basis sets, ECPs account to some extent
for relativistic effects, which are believed to become important for
the elements from the fourth row of the periodic table.
2
3−
The in vacuo geometry optimization of the [Gd(L )(H
2
O)]
system provides a minimum energy conformation very similar
1
− 5
to that found for [Gd(L )(H
2
O)] , in which the phosphonate
pendant arms are alternatively situated above and below the planes
III
of the pyridyl units. In this structure the distance between the Gd
ion and the oxygen atom of the water molecule is large (Gd–O
w
=
˚
2
.803 A), and this water molecule is hydrogen bonded to one of the
phosphonate pendants. Thus, we have tried geometry optimiza-
2
3−
tions of the [Gd(L )(H
2
O)] system including the surrounding
solvent effects by using the C-PCM model. Unfortunately, because
38,39
of the optimizationconvergence difficultybythe C-PCMmodel
these studies were unsuccessful. An alternative to the use of a
continuum model of solvation such as C-PCM is to perform
cluster calculations that explicitly include a second hydration
38,40
shell.
These calculations have the advantage that minima and
transition states can be optimized and characterized in order to
study reactions. Moreover, cluster calculations may also provide
useful direct information about the second sphere solvation shell,
III
which has been shown to enhance the relaxivity of Gd chelates
Fig. 4 Molecular geometries of the twist-wrap (tw) and twist-fold (tf )
bearing phosphonate groups. The major disadvantage of cluster
calculations is that adding extra solvent molecules to the first
solvation sphere increases the computational cost. Moreover, the
more atoms are included in the system, the larger the number of
degrees of freedom and the higher the number of minimum energy
2
3−
isomers of [Gd(L )(H
2
O)] complexes obtained from cluster calculations
2
3−
on the [Gd(L )(H
2
O)] ·19H
2
O system. Uncoordinated water molecules
have been removed for better visualization.
3
−
2
3
III
structures. For the [Gd(L)(H
2
O)] complexes (L = L , L ) we
Optimized Cartesian coordinates obtained for the different Ln
have explicitly included 19 H O molecules in the second hydration
2
systems presented in this work are given in the ESI.† Calculated
III
shell. Our calculations provide two different minimum energy ge-
ometries where the ligand adopts different conformations (Fig. 4):
twist-wrap (tw), in which the ligand wraps around the metal ion
by twisting the pyridyl units relative to each other, and twist-fold
geometrical parameters (bond distances and angles) of the Ln
coordination spheres of these systems are listed in Table 3.
3
−
Attempts to model the [Ln(L)] complexes (Ln = La, Nd, Gd
or Ho) were unsuccessful, since a water molecule systematically
entered the metal coordination sphere during the optimization
(
tf ), where the slight twisting of the pyridyl units is accompanied
by an overall folding of the two pyridine units towards one of the
phosphonate groups. The tf conformation shows a smaller Npy
III
process. However, the smaller ionic radius of Lu allowed us
3
−
3−
–
to model both the [Lu(L)] and [Lu(L)(H O)] complexes
2
Gd–Npy angle than the tw one (Npy = pyridine nitrogen atom).
Both minimum energy structures are true energy minima because
the vibrational frequency analyses give no imaginary frequencies.
Calculated geometrical parameters (bond distances and angles)
in tw conformation. A comparison of the bond distances of
III
3−
the Lu coordination sphere in the [Lu(L)(H
2
O)] ·19H
2
O and
3
−
[Lu(L)] ·20H
2
O molecular clusters reveals that the depletion
of the coordinated water molecule results in a considerable
III
III
of the Gd coordination spheres of these systems are listed in
shortening of the Lu –L bond distances (Table 3).
˚
Table 3. The calculated Gd–O
w
distances (2.515–2.543 A) are in
The relative free energies of the twist-wrap (tw) and twist-fold
3
−
2
3
excellent agreement with that normally assumed in the analysis
of O NMR longitudinal relaxation data (2.50 A). For the L
complex, our calculations provide minimum energy conformations
with the cyclohexyl unit in chair conformation.
In order to obtain information about the solution structures
(tf ) conformations of [Ln(L)(H
2
O)] (L = L , L ) complexes were
1
7
3
˚
calculated in aqueous solution by using the B3LYP model and the
6-311G** basis set for the ligand atoms. In these calculations sec-
ond sphere water molecules were excluded, and solvent effects were
included by using the polarizable continuum model (C-PCM). It
III
of this series of Ln complexes, we also performed geometry
has been demonstrated that this computational approach provides
3
−
−
optimizations of the molecular clusters [Ln(L)(H
(
2
O)] ·19H
2
O
relative energies of the two isomers of [Ln(DOTA)(H
2
O)] in close
36
Ln = La, Nd, Ho or Lu) at the HF/3-21G* level. Moreover,
agreement to the experimental ones. Relative free energies were
sol
sol
sol
since the complexes appear to exist in aqueous solution as a
calculated as DG = G (tf ) − G (tw), and therefore a positive
relative energy indicates that the tw conformation is more stable
than the tf one. According to our results (Fig. 5), the relative
energy of the tf conformation decreases along the first half of
8
mixture of two hydration isomers with q = 0 and q = 1, we
3
−
also studied the [Lu(L)] ·20H
2
O systems. Frequency calculations
show that all calculated structures correspond to energy minima.
This journal is © The Royal Society of Chemistry 2006
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O)]3−·19H
O (L = L , L ) complexes at the HF/3-21G* level
2
3
a
Table 3 Values of the main geometrical parameters of calculated structures for [Ln(L)(H
2
2
L2
L3
La
tw (q = 1)
tf (q = 1)
tw (q = 0)
tw (q = 1)
tf (q = 1)
tw (q = 0)
La–Nam(1)
La–Nam(2)
La–Npy(1)
La–Npy(2)
La–OCOO(1)
La–OCOO(2)
3.061
2.962
2.861
2.741
2.513
2.487
2.441
2.408
2.657
2.941
2.918
2.757
2.731
2.500
2.527
2.436
2.426
2.637
3.071
3.075
2.807
2.722
2.525
2.491
2.408
2.424
2.652
2.904
2.958
2.752
2.730
2.606
2.519
2.437
2.437
2.634
La–OPO (1)
3
La–OPO (2)
3
La–Ow
Npy–La–Npy
159.923
146.181
153.431
151.109
158.776
146.441
154.233
152.520
OPO –La–OPO3
3
Nd
Nd–Nam(1)
Nd–Nam(2)
Nd–Npy(1)
Nd–Npy(2)
Nd–OCOO(1)
Nd–OCOO(2)
3.081
2.965
2.830
2.698
2.464
2.427
2.381
2.350
2.604
2.923
2.899
2.709
2.696
2.548
2.462
2.382
2.371
2.590
3.097
3.095
2.771
2.682
2.474
2.427
2.347
2.363
2.601
2.897
2.977
2.698
2.680
2.559
2.460
2.379
2.371
2.576
Nd–OPO (1)
3
Nd–OPO (2)
3
Nd–Ow
Npy–Nd–Npy
159.219
146.532
153.485
151.193
158.171
145.996
152.595
151.377
OPO –Nd–OPO3
3
Gd
Gd–Nam(1)
Gd–Nam(2)
Gd–Npy(1)
Gd–Npy(2)
Gd–OCOO(1)
Gd–OCOO(2)
3.134
2.991
2.805
2.656
2.406
2.360
2.314
2.287
2.543
2.920
2.893
2.665
2.642
2.502
2.392
2.321
2.309
2.518
3.158
3.155
2.738
2.647
2.412
2.356
2.280
2.295
2.538
2.881
2.944
2.660
2.644
2.521
2.386
2.319
2.318
2.515
Gd–OPO (1)
3
Gd–OPO (2)
3
Gd–Ow
Npy–Gd–Npy
157.715
146.352
153.229
150.847
156.286
144.709
152.957
151.737
OPO –Gd–OPO3
3
Ho
Ho–Nam(1)
Ho–Nam(2)
Ho–Npy(1)
Ho–Npy(2)
Ho–OCOO(1)
Ho–OCOO(2)
3.196
3.027
2.793
2.632
2.363
2.312
2.241
2.268
2.506
2.928
2.909
2.637
2.618
2.468
2.346
2.267
2.278
2.467
3.232
3.217
2.721
2.629
2.367
2.306
2.232
2.249
2.497
2.902
2.975
2.631
2.621
2.485
2.339
2.272
2.272
2.462
Ho–OPO (1)
3
Ho–OPO (2)
3
Ho–Ow
Npy–Ho–Npy
156.140
145.709
152.711
149.804
154.378
143.138
152.324
150.160
OPO –Ho–OPO3
3
Lu
Lu–Nam(1)
Lu–Nam(2)
Lu–Npy(1)
Lu–Npy(2)
Lu–OCOO(1)
Lu–OCOO(2)
3.283
3.098
2.785
2.610
2.308
2.253
2.212
2.188
2.454
2.957
2.938
2.613
2.593
2.425
2.290
2.225
2.218
2.419
3.121
2.895
2.710
2.570
2.274
2.226
2.190
2.143
3.327
3.307
2.704
2.612
2.310
2.245
2.193
2.177
2.444
2.973
3.038
2.602
2.593
2.426
2.282
2.215
2.214
2.414
3.136
2.960
2.665
2.588
2.272
2.220
2.181
2.138
Lu–OPO (1)
3
Lu–OPO (2)
3
Lu–Ow
Npy–Lu–Npy
153.533
144.112
151.757
148.752
160.842
163.346
151.463
140.719
151.163
148.151
160.351
162.891
OPO –Lu–OPO3
3
a
˚
◦
Distances (A), angles ( ). Nam = amine nitrogen atoms; Npy = pyridyl nitrogen atoms; OCOO = carboxylate oxygen atoms; OPO3 = phosphonate oxygen
atoms; O
w
= water oxygen atom.
5
410 | Dalton Trans., 2006, 5404–5415
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III
decrease along the lanthanide series, as usually observed for Ln
34
complexes. The destabilization of the tw conformation along
the first half of the lanthanide series can be attributed to the
III
weakening of the interaction between the Ln ion and the amine
nitrogen atoms, since the Ln–Nam distances clearly increase along
the lanthanide series (Fig. 5). A similar enlargement of Ln–N bond
distances has been previously observed for lanthanide complexes
with crown ethers, which has been attributed to a better size match
III
41
between the ligand cavity and the lightest Ln ions. On the
contrary, the Ln–Nam distances decrease along the first half of the
III
lanthanide series for the tf form, reaching a minimum with Gd ,
and then increasing for the heaviest lanthanide ions. According
to the variation of the Ln–Nam bond distances for the tw and tf
conformations one expects a maximum stabilization of the tf form
for the middle of the lanthanide series.
Second-sphere hydration shell
Recent studies have demonstrated that due to their charge
and important structure ordering effect, phosphonate groups
have a tendency to induce a second hydration sphere around
9,10
the metal complexes.
By remaining in the proximity of the
III
paramagnetic Gd center for a non-negligible time, these second
sphere water molecules may represent a significant contribution
to the overall proton relaxivity of MRI contrast agents. The
analysis of the NMRD profiles of phosphonic acid derivatives
of diethylenetriamine suggested the presence of two second sphere
water molecules contributing to the overall proton relaxivity.
The ab initio calculations presented here provide useful direct
information about the second sphere solvation shell. The calcula-
Fig. 5 Top: In aqueous solution (C–PCM) relative free energies of the tf
sol
sol
sol
3−
2
3
isomer (DG = G (tf ) − G (tw)) for [Ln(L)(H O)] (L = L , L ) complexes.
2
Bottom: Calculated values of the bond distance between the lanthanide
9
ion and the amine nitrogen atoms (Ln–Nam) in the tw and tf isomers of
2
3−
[
2
Ln(L )(H O)] complexes.
3
−
tions on molecular clusters [Gd(L)(H
2
O)] ·19H
2
O indicate that
most of the second sphere water molecules are hydrogen bonded
to the highly charged phosphonate groups. The distances between
the Gd ion and the oxygen and hydrogen atoms of second sphere
the lanthanide series, reaches a minimum with Gd, and then
III
increases for the heaviest lanthanides. The tw form is the most
3
stable along the whole lanthanide series for the L complexes,
water molecules hydrogen bonded to the phosphonate groups
are given in Table S1 (ESI†). Our calculations indicate that at
least six or seven water molecules are hydrogen-bonded to each
phosphonate group. For the complexes in tw conformation only
2
III
while for those of L only the Gd complex is more stable in
−
1
3
the tf conformation by ca. 0.5 kcal mol . The L complexes
present higher relative energies of the tw conformation than the
L complexes. The reason is probably the higher flexibility of L ,
which allows the folding of the pyridine units relative to each
other without increasing importantly the strain of the ligand in
the complexes. It is noteworthy that the tf conformation has
been observed by H NMR for EuL . As discussed above, this
conformation slowly converts to the thermodynamically stable tw
form.
2
2
three second sphere water molecules are in close proximity of
III
˚
the Gd ion with Gd–O distances of 4.1–4.2 A, whereas the
other second-sphere water molecules are relatively distant (Gd–
˚
O distances above 5.4 A). Among the three water molecules close
1
3
III
to the Gd ion two are hydrogen bonded to the phosphonate
group situated close to the inner sphere water molecule (Fig. 4),
while the third one is interacting with the second (more sterically
crowded) phosphonate group. A similar situation occurs for the
3
3−
For the [Ln(L )(H
2
O)] complexes a third minimum energy
3
−
geometry has been obtained, in which the cyclohexyl unit adopts
twist-boat conformation. The calculated geometries are given
in the ESI.† Calculated relative free energies indicate that the
conformational change from chair to twist-boat (tb) provokes an
[Lu(L)] systems, which show two second sphere water molecules
III
in the close proximity of the Lu ion with Lu–O distances of 3.9–
˚
4.0 A, and a third water molecule showing an intermediate Lu–O
˚
distance (ca. 4.6 A). The remaining second sphere water molecules
sol
sol
sol
1
17
important destabilization of the system: DG = G (tb) − G (tw)
=
are relatively far from the lanthanide ion. Since both H and
longitudinal relaxation rates depend on 1/r , where r represents
the distance between the observed nucleus and the Gd ion,
O
−
1
6
1
0.93 (Nd), 4.85 (Gd) and 6.87 kcal mol (Lu). According to
III
42
these values, the twist-boat form is less stable than the tw and tf
conformations described above.
only water molecules relatively close to the paramagnetic centre
are expected to provide a substantial second sphere contribution.
Thus, it appears reasonable to assume three second sphere water
The variation of the relative energies of the two isomers of
and L complexes along the lanthanide series appears to
2
3
L
1
7
be related, at least in part, to the bond distances of the metal
coordination environment. Most of the calculated bond distances
between the lanthanide and the coordinated donor atoms (Table 3)
molecules in the analysis of the relaxivity and O NMRD data
III
2
3 8
of the Gd complexes with L and L . In contrast to the tw
conformation in the tf form all three closely situated second sphere
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3
water molecules are hydrogen-bonded to one of the phosphonate
groups, for steric reasons.
(Dd) for the tw and tf complexes of L obtained at the B3LYP/6-
311G** level, where it is possible to appreciate larger deviations
from the experimental values for most carbon nuclei of the tf form
than for the same nuclei in the tw one. An analogous analysis of the
1
3
C NMR shielding constants
2
scaled theoretical shifts calculated for the complex of L leads to
similar conclusions. These results therefore confirm that the La
complexes of L and L are present in solution in tw conformation,
in agreement with the relative free energies of the two isomers
discussed above.
III
It has been demonstrated that quantum-mechanical GIAO cal-
1
3
2
3
culations of C NMR chemical shifts can be used as a tool
43
for structure validation of coordination compounds, including
3
6,44
13
lanthanide complexes.
of the tw and tf forms of the [La(L)(H
complexes were calculated on the in vacuo optimized structures
Thus, the C NMR shielding constants
3
−
2
3
2
O)] (L = L , L )
3
−
III
of [La(L)(H
2
O)] ·19H
2
O by using the GIAO method. Due to
Nd -Induced relaxation rate enhancement effects
the importance of including electronic correlation effects the
calculations of the NMR shielding constants were performed at
the B3LYP/6-311G** level, by using the 46 core electron ECP by
Information on the solution structure of the complexes was
obtained from Nd -induced relaxation rate enhancements of the
H nuclei of ligands L and L . Among the lighter Ln ions (Ln =
Ce → Eu), Nd has the longest electron relaxation times,
and therefore this cation is very suitable for obtaining structural
III
1
2
3
III
20
Stevens et al. In these calculations solvent effects (water) were
III
46,47
1
3
included by using the C-PCM model. The calculated C NMR
shifts are compared with the experimental values in Table 4. We
notice a systematic deviation to lower fields of the calculated values
with respect to the experimental ones. Thus, in order to asses
the agreement between the experimental and calculated C NMR
spectra, we have plotted the experimental C chemical shift values
vs. the corresponding GIAO calculated C chemical shifts for the
tw and tf isomers. These plots give straight lines whose slopes and
intercepts are given in Table 4. The correlation plots obtained for
48
III
information of lanthanide complexes in solution. The Nd -
1
induced H NMR relaxation enhancements for both ligands
◦
1
3
were measured at 7.05 T and 25 C (Table 5). In order to
1
3
correct for diamagnetic contributions, the relaxation rates for the
corresponding La complex were subtracted from the measured
values of the Nd complex (see Table 5).
Since the outer-sphere contribution (1/T1os) becomes signif-
III
1
3
III
3
icant only for remote nuclei, this contribution was neglected.
the complexes of L are shown in Fig. 6. In general, the linear
III
−13
The electron relaxation for Nd is very fast (T1e ≈ 10
s)
correlation of these plots is better for the tw than for the tf form in
2
3
2
and, consequently, the contact contribution to the paramagnetic
relaxation is negligible. Two contributions are of importance: the
both L and L complexes, as indicated by the R values obtained
from the linear least squares fit. This implies that the tf form is a
less probable structure of the complexes in solution. To confirm
this we have calculated scaled theoretical chemical shift values
“
classical” dipolar relaxation and the Curie relaxation. Eqn (5) can
be derived from a simplified Solomon–Bloembergen equation
and from the equation for the Curie relaxation (assuming extreme
49
45
i
(d ,esc) obtained as:
50,51
narrowing):
d
i
,
esc = (d
i
,
calc − A)/B
(4)



ꢁ
ꢂ
ꢁ
ꢂ
where d
i
,
calc are the GIAO calculated chemical shifts, and A and
2
2
ꢀ
ꢀ
1
2
2
0
4
4
1
l0
l0 c H l b
1
2
2
1
2
B are the intercept and slope obtained from the linear correlation
plots of the same compound. Fig. 6 shows a plot of differences
between experimental and scaled theoretical C NMR shift values
4
l c b t1e + 6
=
s
R
3
5
2
6
T
1
4p
4p
(3kT)
r
1
3
(5)
13
III
2
3
13
Table 4 Experimental C shifts (ppm) for the La complexes of L and L in 30 mM D
chemical shift values for the tw and tf conformations (see Scheme 1 for labelling)
2
O solutions at pH 7.6 and calculated (GIAO method) C NMR
2
3
L
L
d
i,exptl
d
i,calc(tw)
d
i,calc(tf )
d
i,exptl
d
i,calc(tw)
d
i,calc(tf )
1
2
3
4
5
6
7
8
9
0
1
175.1
153.1
124.9
141.4
127.6
159.4
62.5
178.2
156.9
127.6
143.8
130.2
167.6
67.5
179.1
157.8
127.4
144.2
129.8
168.4
69.3
175.0
152.7
124.8
141.5
128.2
159.6
58.0
52.6
63.2
24.8
26.3
178.2
157.1
127.7
143.7
131.0
168.5
62.7
55.0
66.2
28.8
31.7
179.2
157.9
127.3
144.0
130.3
169.1
64.3
57.1
64.2
27.1
25.0
57.2
55.4
59.4
58.7
63.0
59.8
1
1
2
a
R
A
B
0.9992
0.998
0.9994
0.9990
a
2.6 ± 1.9
5.4 ± 2.2
3.7 ± 1.3
1.1 ± 1.7
a
1.01 ± 0.01
0.99 ± 0.02
1.00 ± 0.01
1.02 ± 0.02
a
13
Intercept, slope and correlation coefficient obtained by linear fitting of calculated vs. experimental C NMR chemical shift plots (see text).
5
412 | Dalton Trans., 2006, 5404–5415
This journal is © The Royal Society of Chemistry 2006

View Article Online
−
1
III
Table 5 Relaxation rates (s ) determined for 40 mM solutions of Ln
◦
complexes in D
2
1
O (300 MHz, 25 C, pH = 7.6) and Nd · · · H distances ( A˚ )
calculated from H NMR relaxation data
Nd · · · H
Nd · · · H
b
c
1
/T1(Nd)
1/T1(La)
(Calc.)
(Exptl.)
2
3
2
3
2
3
2
3
L
L
L
L
L
L
L
L
H3
H4
H5
9.221
4.384
8.454
8.718 0.683 0.524 5.600 5.572 5.89 5.63
4.337 0.756 0.524 6.562 6.529 6.79 6.26
8.326 0.914 1.294 5.799 5.762 6.02 5.75
H7ax
H7eq
H8a
H8b
H9ax
H9eq
H10
95.111 a75.896 3.650 6.976 3.997 3.989 3.97 4a .02
27.054
4.0
5.786 4.764 4.766 4.99
a
a
102.135
3.630 4.086 3.946 3.868 3.92
29.619 28.490 3.057 5.814 4.727 4.744 4.88 4.81
86.08
66.05
3.481 3.519 4.015 4.137 4a .04 4.08
a
4.552 4.823
14.95
13.038
8.423
6.798
7.196
a6.954
5.634
5.767
6.641
7.471
5.67
a5.87
ꢀ
H10
H11
H11
ꢀ
5.519
7.06
a
b
III
Not obtained. Nd · · · H distances obtained from ab initio calculations
c
III
1
(
tw conformations). Nd · · · H distances obtained from experimental H
NMR relaxation data.
−
55
6
−1
2
slopes k = (3.57 ± 0.09) × 10 m s (L ) and k = (2.88 ± 0.07) ×
m s (L ). The slope obtained from this plot represents the
term between the brackets in eqn (5). Using the s obtained from
H NMR relaxation data at a concentration of 40 mM (s
−
55
6
−1
3
10
R
2
R
=
8
−13
2
1
52 ps) we obtain T1e = 2.69 × 10 s for the L complex, a value
substantially longer than the one determined by Alsaadi et al. for
−
13
52
the aqua ion (T1e = 1.15 × 10 s). The experimental values of k
III
were used to obtain experimental Nd · · · H distances in solution
from relaxation data by using eqn (5). In general, the experimental
distances are in satisfactory agreement with those obtained from
the theoretical calculations (Table 5), thereby confirming that the
computational approach provides a reliable description of the
solution structures.
Fig. 6 Top: data points and fitting straight lines of calculated vs.
13
experimental C NMR chemical shifts at the B3LYP/6-311G** level for
3
3−
2
the tw and tf structures of [La(L )(H O)] complexes in aqueous solution.
The plot relative to tf has been displaced by 30 ppm along the ordinate
Conclusions
axis for better visualization. Bottom: Differences between experimental
13
and scaled theoretical C NMR chemical shifts (B3LYP/6-311G** level)
2
3
The octadentate ligands L and L form thermodynamically stable
3
3−
2
for the tw and tf isomers of [La(L )(H O)] .
III
Gd complexes in aqueous solution, and thus can be considered
as new basic structural frameworks for the design of novel MRI
contrast agents. Our results show an improved stability of the
Gd complexes in aqueous solution when the acetate arms of L
where the first term between the square brackets represents the
classical” dipolar contribution, and the second term describes
the Curie relaxation. Here, l /4p is the magnetic permeability in a
vacuum, l is the effective magnetic moment of the lanthanide ion,
is the gyromagnetic ratio of the nucleus under study, b is the
III
1
“
0
are replaced by phosphonate pendants. NMR studies in solution
2
3
III
indicate octadentate binding of L and L to the Ln ions.
Quantum mechanical calculations performed at the HF level
provide two minimum energy geometries of the complexes where
the ligand adopts different conformations: twist-wrap (tw), in
which the ligand wraps around the metal ion by twisting the
pyridyl units relative to each other, and twist-fold (tf ), where the
slight twisting of the pyridyl units is accompanied by an overall
folding of the two pyridine units towards one of the phosphonate
groups. The tw form is the most stable one along the whole
c
I
Bohr magneton, T1e is the electron spin relaxation time, r is the
1
distance between the H nucleus in question and the lanthanide
ion, H
T is the temperature, and s
the complex. The contribution of the Curie spin mechanism to
0
is the magnetic field strength, k is the Boltzmann constant,
R
is the rotational tumbling time of
the total relaxation becomes significant for larger molecules (s
R
increases), particularly at higher fields.
3
2
At constant temperature and B
the determination of relative r values in the complexes without the
need to estimate T1e and s , which would be needed to calculate
absolute distances. Plots of 1/T
0
, application of eqn (5) allows
lanthanide series for the complexes of L , while for those of L
III
only the Gd complex is more stable in the tf conformation by ca.
−
1
R
0.5 kcal mol . Our results indicate that the relative energy of the
tf conformation decreases along the first half of the lanthanide
series, reaches a minimum with Gd, then increases for the heaviest
6
1
vs. 1/r , where r stands for the
Nd · · · H distances obtained from the ab initio optimized structures
2
1
3
give straight lines (R > 0.996) passing through the origin with
lanthanides. H NMR studies of EuL show the initial formation
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Dalton Trans., 2006, 5404–5415 | 5413

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of the tf complex in aqueous solution, which slowly converts to
the thermodynamically stable tw form. The calculated structures
19 R. Ditchfield, Mol. Phys., 1974, 27, 789.
2
0 W. J. Stevens, M. Krauss, H. Basch and P. G. Jaisen, Can. J. Chem.,
992, 70, 612.
1 T. R. Cundari and W. Stevens, J. Chem. Phys., 1993, 98, 5555.
1
III
for the Nd complexes are in reasonably good agreement with
2
III
the experimental solution structures, as demonstrated by Nd -
22 M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A.
Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery, Jr., R. E.
Stratmann, J. C. Burant, S. Dapprich, J. M. Millam, A. D. Daniels,
K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V. Barone, M.
Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford,
J. Ochterski, G. A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma,
P. Salvador, J. J. Dannenberg, D. K. Malick, A. D. Rabuck, K.
Raghavachari, J. B. Foresman, J. Cioslowski, J. V. Ortiz, A. G. Baboul,
B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.
Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham,
C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. G.
Johnson, W. Chen, M. W. Wong, J. L. Andres, C. Gonzalez, M. Head-
Gordon, E. S. Replogle and J. A. Pople, GAUSSIAN 98 (Revision
A.11), Gaussian, Inc., Pittsburgh, PA, 2001.
1
induced relaxation rate enhancement effects in the H NMR
spectra. The computational approach presented in this work, in
combination with experimental information obtained by NMR
spectroscopy, represents a powerful tool to obtain structural
information of lanthanide complexes in solution.
Acknowledgements
M. M.-I, C. P.-I., A. de B. and T. R-B. thank Ministerio de
Ciencia y Tecnolog ´ı a and FEDER (BQU2001-0796), Xunta de
Galicia (PGIDIT02PXI10301PN) and Universidade da Coru n˜ a
2
3 M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb,
J. R. Cheeseman, J. A. Montgomery, Jr., T. Vreven, K. N. Kudin, J. C.
Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci,
M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M.
Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T.
Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E.
Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo,
R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi,
C. Pomelli, J. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P.
Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D.
Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K.
Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S.
Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz,
I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y.
Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. G. Johnson,
W. Chen, M. W. Wong, C. Gonzalez and J. A. Pople, GAUSSIAN 03
´
for financial support. E. T. and E. B. thank the Swiss National
Science Foundation and the Swiss State Secretariat for Education
and Research (SER) for financial support. This research was
performed in the framework of the EU COST Action D18
“
Lanthanide Chemistry for Diagnosis and Therapy”, and the
European-founded EMIL program (LSCH-2004-503569); their
support and sponsorship is also kindly acknowledged. The authors
are indebted to Centro de Supercomputaci o´ n of Galicia (CESGA)
for providing the computer facilities.
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