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.

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 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.