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.