The prime objectives of contrast agents in Magnetic Resonance Imaging (MRI) is to accelerate the relaxation rate of the solvent water protons in the surrounding tissue. Paramagnetic relaxation originates from dipole-dipole interactions between the nuclear spins and the fluctuating magnetic field induced by unpaired electrons. Currently Gadolinium(III) chelates are the most widely used contrast agents in MRI, and therefore it is incumbent to extend the fundamental theoretical understanding of parameters that drive the relaxation mechanism in these complexes. In compounds such as Gadolinium(III) complexes with total electron spins higher than 1 (in this case S=7/2) the Zero-Field Splitting (ZFS) plays a significant role in influencing the electron spin dynamics and nuclear spin dynamics. For this purpose, the current research delves into an understanding of the relaxation process, focusing on ZFS in various complexes of interest, using multi-scale modelling by combining quantum, semi-quantum and newtonian methods.

We compare and contrast Density Function Theory (DFT) with multi-configurational quantum chemical calculation and find that DFT is highly functional dependent and unreliable in accurately reproducing experimental data for the static ZFS. It was found that long-range corrected functionals (in particular LC-BLYP) perform significantly better as compared to other functionals in predicting the magnitude of the static ZFS. We study hydrated Gd(III) and Eu(II) systems to compare and contrast these isoelectronic complexes (both contain 7 unpaired electrons in their valence shell) and through ab-initio molecular dynamics (AIMD) sampling followed by multi-reference quantum chemical calculations, it was established that inclusion of the first shell has a dominant influence (over 90%) on the ZFS. We also studied the complex [Gd(III)(HPDO3A)(H2O)], which is of clinical relevance as a contrast agent for MRI, through post-Hartree-Fock and DFT calculations by utilizing configurations derived from AIMD trajectories. From the fluctuations in the ZFS tensor, we extract a correlation time of the transient ZFS which is on the sub-picosecond time scale, showing a faster decay than experimental data.

The zero-field splitting (ZFS) of the ground state octet in aqueous Eu(II) and Gd(III) solutions was investigated through multi-configurational quantum chemical calculations and ab initio molecular dynamics (AIMD) simulations. Investigation of the ZFS of the lanthanide ions is essential to understand the electron spin dynamics and nuclear spin relaxation around paramagnetic ions and consequently the mechanisms underlying applications like magnetic resonance imaging. We found by comparing clusters at identical geometries but different metallic centres that there is not a simple relationship for their ZFS, in spite of the complexes being isoelectronic-each containing 7 unpaired f electrons. Through sampling it was established that inclusion of the first hydration shell has a dominant (over 90 %) influence on the ZFS. Extended sampling of aqueous Gd(III) showed that the 2nd order spin Hamiltonian formalism is valid and that the rhombic ZFS component is decisive.

In this work, we present ab initio calculations of the zero-field splitting (ZFS) of a gadolinium complex [Gd(m)(HPDO3A)(H2O)] sampled from an ab initio molecular dynamics (AIMD) simulation. We perform both post-Hartree-Fock (complete active space self-consistent field-CASSCF) and density functional theory (DFT) calculations of the ZFS and compare and contrast the methods with experimental data. Two different density functional approximations (TPSS and LC-BLYP) were investigated. The magnitude of the ZFS from the CASSCF calculations is in good agreement with experiment, whereas the DFT results in varying degrees overestimate the magnitude of the ZFS for both functionals and exhibit a strong functional dependence. It was found in the sampling over the AIMD trajectory that the fluctuations in the transient ZFS tensor derived from DFT are not correlated with those of CASSCF nor does the magnitude of the ZFS from CASSCF and DFT correlate. From the fluctuations in the ZFS tensor, we extract a correlation time of the transient ZFS which is on the sub-picosecond time scale, showing a faster decay than experimental estimates.

The zero-field splitting (ZFS) of the electronic ground state in paramagnetic ions is a sensitive probe of the variations in the electronic and molecular structure with an impact on fields ranging from fundamental physical chemistry to medical applications. A detailed analysis of the ZFS in a series of symmetric Gd(III) complexes is presented in order to establish the applicability and accuracy of computational methods using multiconfigurational complete-active-space self-consistent field wave functions and of density functional theory calculations. The various computational schemes are then applied to larger complexes Gd(III)DOTA(H2O)(-), Gd(III)DTPA(H2O)(2-), and Gd(III)(H2O)(8)(3+) in order to analyze how the theoretical results compare to experimentally derived parameters. In contrast to approximations based on density functional theory, the multiconfigurational methods produce results for the ZFS of Gd(III) complexes on the correct order of magnitude.

The prime objectives of contrast agents in Magnetic Resonance Imaging(MRI) is to accelerate the relaxation rate of the solvent water protons in the surrounding tissue. Paramagnetic relaxation originates from dipole-dipole interactions between the nuclear spins and the fluctuating magnetic field induced by unpaired electrons. Currently Gadolinium(III) chelates are the most widely used contrast agents in MRI, and therefore it is incumbent to extend the fundamental theoretical understanding of parameters that drive the relaxation mechanism in these complexes.

Traditionally the Solomon-Bloembergen-Morgan equations have been utilized to describe relaxation times in terms, primarily of the Zeeman interaction, which is the splitting of degenerate energy levels due to an applied magnetic field. However, in compounds such as Gadolinium(III) complexes with total electron spins higher than 1 (in this case S=7/2) other interactions such as the Zero-Field Splitting(ZFS) play a significant role. ZFS is the splitting of degenerate energy levels in the absence of an external magnetic field. For this purpose, the current research delves into an understanding of the relaxation process, focusing on ZFS in various complexes of interest, using quantum chemical methods as well as molecular dynamic simulations.