Systematic theoretical investigation of the zero-field splitting in Gd(III) complexes: Wave function and density functional approaches

Effect of hydration equilibria on the relaxometric properties of Gd(III) complexes: new insights into old systems

We present a detailed relaxometric and computational investigation of three Gd(III) complexes that exist in solution as an equilibrium of two species with a different number of coordinated water molecules: [Gd(H2O)q]3+ (q = 8, 9), [Gd(EDTA)(H2O)q]- and [Gd(CDTA)(H2O)q]- (q = 2, 3). 1H nuclear magnetic relaxation dispersion (NMRD) data were recorded from aqueous solutions of these complexes using a wide Larmor frequency range (0.01-500 MHz). These data were complemented with 17O transverse relaxation rates and chemical shifts recorded at different temperatures. The simultaneous fit of the NMRD and 17O NMR data was guided by computational studies performed at the DFT and CASSCF/NEVPT2 levels, which provided information on Gd⋯H distances, 17O hyperfine coupling constants and the zero-field splitting (ZFS) energy, which affects electronic relaxation. The hydration equilibrium did not have a very important effect in the fits of the experimental data for [Gd(H2O)q]3+ and [Gd(CDTA)(H2O)q]-, as the hydration equilibrium is largely shifted to the species with the lowest hydration number (q = 8 and 2, respectively). The quality of the analysis improves however considerably for [Gd(EDTA)(H2O)q]- upon considering the effect of the hydration equilibrium. As a result, this study provides for the first time an analysis of the relaxation properties of this important model system, as well as accurate parameters for [Gd(H2O)q]3+ and [Gd(CDTA)(H2O)q]-.

Computational design of magnetic molecules and their environment using quantum chemistry, machine learning and multiscale simulations

Having served as a playground for fundamental studies on the physics of d and f electrons for almost a century, magnetic molecules are now becoming increasingly important for technological applications, such as magnetic resonance, data storage, spintronics and quantum information. All of these applications require the preservation and control of spins in time, an ability hampered by the interaction with the environment, namely with other spins, conduction electrons, molecular vibrations and electromagnetic fields. Thus, the design of a novel magnetic molecule with tailored properties is a formidable task, which does not only concern its electronic structures but also calls for a deep understanding of the interaction among all the degrees of freedom at play. This Review describes how state-of-the-art ab initio computational methods, combined with data-driven approaches to materials modelling, can be integrated into a fully multiscale strategy capable of defining design rules for magnetic molecules.

Rigid versions of PDTA4- incorporating a 1,3-diaminocyclobutyl spacer for Mn2+ complexation: stability, water exchange dynamics and relaxivity

Rigid derivatives of the acyclic ligand PDTA4- (H₄PDTA = propylenediamine-N,N,N',N'-tetraacetic acid) were prepared by functionalization of a 1,3-diaminocyclobutyl spacer. The new ligands contain either four acetate groups attached to the central scaffold (H4L1) or incorporate pyridyl (H2L2) or propylamide (H2L3) units replacing two of the carboxylate groups. The ligand protonation constants and the stability constants of their Mn²⁺ complexes were determined using potentiometric and spectrophotometric titrations. The stability of the [Mn(L1)]^2- complex was found to be significantly higher than that of the flexible [Mn(PDTA)]^2- derivative (log K_MnL = 10.78 and 10.01, respectively). A detailed study of the ¹H Nuclear Magnetic Relaxation Dispersion (NMRD) profiles and ¹⁷O NMR measurements evidence that the [Mn(L1)]^2- and [Mn(L2)] complexes display a hydration equilibrium in solution involving a seven-coordinate species with an inner-sphere water molecule and a six-coordinate species that lacks a coordinated water molecule. As a result the ¹H relaxivities of these complexes are somewhat lower than that of [Mn(EDTA)]^2- and related systems. The introduction of propylamide groups in [Mn(L3)] shifts the hydration equilibrium to the seven-coordinate species, which results in a ¹H relaxivity (r_1p = 3.7 mM^-1 s^-1 at 22 MHz and 25 °C) exceeding that of [Mn(EDTA)]^2- (r_1p = 3.3 mM^-1 s^-1 at 22 MHz and 25 °C). The parameters that control the relaxivities in this family of complexes were determined by simultaneous fitting of the experimental ¹H NMRD and ¹⁷O NMR data (transverse relaxation rates and chemical shifts), with the aid of computational studies performed at the DFT and CASSCF/NEVPT2 levels. These studies provide detailed insight of the parameters that control the efficiency of these relaxation agents at the molecular level.

Understanding the Effect of the Electron Spin Relaxation on the Relaxivities of Mn(II) Complexes with Triazacyclononane Derivatives

Investigating the relaxation of water ¹H nuclei induced by paramagnetic Mn(II) complexes is important to understand the mechanisms that control the efficiency of contrast agents used in diagnostic magnetic resonance imaging (MRI). Herein, a series of potentially hexadentate triazacyclononane (TACN) derivatives containing different pendant arms were designed to explore the relaxation of the electron spin in the corresponding Mn(II) complexes by using a combination of ¹H NMR relaxometry and theoretical calculations. These ligands include 1,4,7-triazacyclononane-1,4,7-triacetic acid (H₃NOTA) and three derivatives in which an acetate group is replaced by sulfonamide (H₃NO2ASAm), amide (H₂NO2AM), or pyridyl (H₂NO2APy) pendants. The analogue of H₃NOTA containing three propionate pendant arms (H₃NOTPrA) was also investigated. The X-ray structure of the derivative containing two acetate groups and a sulfonamide pendant arm [Mn(NO2ASAm)]^- evidenced six-coordination of the ligand to the metal ion, with the coordination polyhedron being close to a trigonal prism. The relaxivities of all complexes at 20 MHz and 25 °C (1.1-1.3 mM^-1 s^-1) are typical of systems that lack water molecules coordinated to the metal ion. The nuclear magnetic relaxation profiles evidence significant differences in the relaxivities of the complexes at low fields (<1 MHz), which are associated with different spin relaxation rates. The zero field splitting (ZFS) parameters calculated by using DFT and CASSCF methods show that electronic relaxation is relatively insensitive to the nature of the donor atoms. However, the twist angle of the two tripodal faces that delineate the coordination polyhedron, defined by the N atoms of the TACN unit (lower face) and the donor atoms of the pendant arms (upper face), has an important effect in the ZFS parameters. A twist angle close to the ideal value for an octahedral coordination (60°), such as that in [Mn(NOTPrA)]^-, leads to a small ZFS energy, whereas this value increases as the coordination polyhedron approaches to a trigonal prism.

Mn2+ Complexes Containing Sulfonamide Groups with pH-Responsive Relaxivity

We present two ligands containing a N-ethyl-4-(trifluoromethyl)benzenesulfonamide group attached to either a 6,6'-(azanediylbis(methylene))dipicolinic acid unit (H₃DPASAm) or a 2,2'-(1,4,7-triazonane-1,4-diyl)diacetic acid macrocyclic platform (H₃NO2ASAm). These ligands were designed to provide a pH-dependent relaxivity response upon complexation with Mn²⁺ in aqueous solution. The protonation constants of the ligands and the stability constants of the Mn²⁺ complexes were determined using potentiometric titrations complemented by spectrophotometric experiments. The deprotonations of the sulfonamide groups of the ligands are characterized by protonation constants of log K_i^H = 10.36 and 10.59 for DPASAm^3- and HNO2ASAm^2-, respectively. These values decrease dramatically to log K_i^H = 6.43 and 5.42 in the presence of Mn²⁺, because of the coordination of the negatively charged sulfonamide groups to the metal ion. The higher log K_i^H value in [Mn(DPASAm)]^- is related to the formation of a seven-coordinate complex, while the metal ion in [Mn(NO2ASAm)]^- is six-coordinated. The X-ray crystal structure of Na[Mn(DPASAm)(H₂O)]·2H₂O confirms the formation of a seven-coordinate complex, where the coordination environment is fulfilled by the donor atoms of the two picolinate groups, the amine N atom, the N atom of the sulfonamide group, and a coordinated water molecule. The lower conditional stability of the [Mn(NO2ASAm)]^- complex and the lower protonation constant of the sulfonamide group results in complex dissociation at relatively high pH (<7.0). However, protonation of the sulfonamide group in [Mn(DPASAm)]^- falls into the physiologically relevant pH window and causes a significant increase in relaxivity from r_1p = 3.8 mM^-1 s^-1 at pH 9.0 to r_1p = 8.9 mM^-1 s^-1 at pH 4.0 (10 MHz, 25 °C).

pH-Dependent Hydration Change in a Gd-Based MRI Contrast Agent with a Phosphonated Ligand

The heptadentate ligand L was shown to form an extremely stable Gd complex at neutral pH with a pGd value of 18.4 at pH 7.4. The X-ray crystal structures of the complexes formed with Gd and Tb displayed two very different coordination behaviors being, respectively, octa- and nonacoordinated. The relaxometric properties of the Gd complex were studied by field-dependent relaxivity measurements at various temperatures and by ¹⁷ O NMR spectroscopy. The pH-dependence of the longitudinal relaxivity profile indicated large changes around neutral pH leading to a very large value of 10.1 mm^-1 ⋅s^-1 (60 MHz, 298 K) at pH 4.7. The changes were attributed to an increase of the hydration number from one water molecule in basic conditions to two at acidic pH. A similar trend was observed for the luminescence of the Eu complex, confirming the change in hydration state. DOSY experiments were performed on the Lu analogue, pointing to the absence of dimers in solution in the considered pH range. A breathing mode of the complex was postulated, which was further supported by ¹ H and ³¹ P NMR spectroscopy of the Yb complex at varying pH and was finally modeled by DFT calculations.

A pentadentate member of the picolinate family for Mn(ii) complexation and an amphiphilic derivative

We report a pentadentate ligand containing a 2,2'-azanediyldiacetic acid moiety functionalized with a picolinate group at the nitrogen atom (H3paada), as well as a lipophylic derivative functionalized with a dodecyloxy group at position 4 of the pyridyl ring (H3C12Opaada). The protonation constants of the paada3- ligand and the stability constant of the Mn(ii) complex were determined using a combination of potentiometric and spectrophotometric titrations (25 °C, 0.15 M NaCl). A detailed relaxometric characterisation was accomplished by recording 1H Nuclear Magnetic Relaxation Dispersion (NMRD) profiles and 17O chemical shifts and relaxation rates. These studies provide detailed information on the microscopic parameters that control their efficiency as relaxation agents in vitro. For the sake of completeness and to facilitate comparison, we also characterised the related [Mn(nta)]- complex (nta = nitrilotriacetate). Both the [Mn(paada)]- and [Mn(nta)]- complexes turned out to contain two inner-sphere water molecules in aqueous solution. The exchange rate of these coordinated water molecules was slower in [Mn(paada)]- (k298ex = 90 × 107 s-1) than in [Mn(nta)]- (k298ex = 280 × 107 s-1). The complexes were also characterised using both DFT (TPSSh/def2-TZVP) and ab initio CAS(5,5) calculations. The lipophylic [Mn(C12Opaada)]- complex forms micelles in solution characterised by a critical micellar concentration (cmc) of 0.31 ± 0.01 mM. This complex also forms a rather strong adduct with Bovine Serum Albumin (BSA) with an association constant of 5.5 × 104 M-1 at 25 °C. The enthalpy and entropy changes obtained for the formation of the adduct indicate that the binding event is driven by hydrophobic interactions.

Ab initio paramagnetic NMR shifts via point-dipole approximation in a large magnetic-anisotropy Co(ii) complex

Transition metal complexes can possess a large magnetic susceptibility anisotropy, facilitating applications such as paramagnetic tags or shift agents in nuclear magnetic resonance (NMR) spectroscopy. Due to its g-shift and zero-field splitting (ZFS) we demonstrate on a Co(ii) clathrochelate with an aliphatic 16-carbon chain, a modern approach for ab initio calculation of paramagnetic susceptibility. Due to its large anisotropy, large linear dimension but relatively low number of atoms, the chosen complex is especially well-suited for testing the long-range point-dipole approximation (PDA) for the pseudocontact shifts (PCSs) of paramagnetic NMR. A static structure of the complex is used to compare the limiting long-distance PDA with full first-principles quantum-mechanical calculation. A non-symmetric formula for the magnetic susceptibility tensor is necessary to be consistent with the latter. Comparison with experimental shifts is performed by conformational averaging over the chain dynamics using Monte Carlo simulation. We observe satisfactory accuracy from the rudimentary simulation and, more importantly, demonstrate the fast applicability of the ab initio PDA.

Interplay of spin-dependent delocalization and magnetic anisotropy in the ground and excited states of [Gd2@C78]- and [Gd2@C80]. J Chem Phys 2017;147:124305. [PMID: 28964020 DOI: 10.1063/1.5004183]

The magnetic properties and electronic structure of the ground and excited states of two recently characterized endohedral metallo-fullerenes, [Gd₂@C₇₈]^- (1) and [Gd₂@C₈₀]^- (2), have been studied by theoretical methods. The systems can be considered as [Gd₂]⁵⁺ dimers encapsulated in a fullerene cage with the fifteen unpaired electrons ferromagnetically coupled into an S = 15/2 high-spin configuration in the ground state. The microscopic mechanisms governing the Gd-Gd interactions leading to the ferromagnetic ground state are examined by a combination of density functional and ab initio calculations and the full energy spectrum of the ground and lowest excited states is constructed by means of ab initio model Hamiltonians. The ground state is characterized by strong electron delocalization bordering on a σ type one-electron covalent bond and minor zero-field splitting (ZFS) that is successfully described as a second order spin-orbit coupling effect. We have shown that the observed ferromagnetic interaction originates from Hund's rule coupling and not from the conventional double exchange mechanism. The calculated ZFS parameters of 1 and 2 in their optimized geometries are in qualitative agreement with experimental EPR results. The higher excited states display less electron delocalization, but at the same time they possess unquenched first-order angular momentum. This leads to strong spin-orbit coupling and highly anisotropic energy spectrum. The analysis of the excited states presented here constitutes the first detailed study of the effects of spin-dependent delocalization in the presence of first order orbital angular momentum and the obtained results can be applied to other mixed valence lanthanide systems.

Transient versus Static Electron Spin Relaxation in Mn(2+) Complexes Relevant as MRI Contrast Agents

The zero-field splitting (ZFS) parameters of the [Mn(EDTA)(H2O)](2-)·2H2O and [Mn(MeNO2A)(H2O)]·2H2O systems were estimated by using DFT and ab initio CASSCF/NEVPT2 calculations (EDTA = 2,2',2″,2‴-(ethane-1,2-diylbis(azanetriyl))tetraacetate; MeNO2A = 2,2'-(7-methyl-1,4,7-triazonane-1,4-diyl)diacetate). Subsequent molecular dynamics calculations performed within the atom-centered density matrix propagation (ADMP) approach provided access to the transient and static ZFS parameters, as well as to the correlation time of the transient ZFS. The calculated ZFS parameters present a reasonable agreement with the experimental values obtained from the analysis of (1)H relaxation data. The correlation times calculated for the two systems investigated turned out to be very short (τc ∼ 0.02-0.05 ps), which shows that the transient ZFS is modulated by molecular vibrations. On the contrary, the static ZFS is modulated by the rotation of the complexes in solution, which for the small complexes investigated here is characterized by rotational correlation times of τR ∼ 35-60 ps. As a result, electron spin relaxation in small Mn(2+) complexes is dominated by the static ZFS.