## Theoretical characterization of electronic and magnetic properties of lanthanide single molecule magnets

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##### Author

Calvello, Simone##### Date

2017##### Affiliation

School of Chemistry##### Metadata

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PhD thesis##### Access Status

**Open Access**

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© 2017 Dr. Simone Calvello

##### Abstract

Lanthanide Single Molecule Magnets (SMMs) are a class of metal complexes, behaving like tiny ferromagnets in spite of negligible intermolecular interactions, thus becoming the focus of intensive investigation for the study of single-molecule memory units, due to their much smaller size and to better chemical control over their synthesis. The highest blocking temperature reported in literature is of 60K for a di-cyclopentadienyl complex of Dy, only 17K lower than the boiling temperature of liquid N2. The design of SMMs able to display hysteresis of their magnetization under liquid N2 refrigeration would be a major scientific breakthrough, as molecular memories based on this effect would become commercially viable, thus sparking a huge interest in this field. In this Thesis, the development of an efficient ab initio software for the calculation of magnetic properties of lanthanide complexes, offering a tool to interpret experimental magnetic data and thus also to screen molecules with favorable electronic structure properties to display high blocking temperature SMM behavior, is presented.
Ab initio calculations are a very useful tool for investigating the magnetic properties of SMM candidates, thus requiring the development of efficient algorithms for performing these calculations. In the currently most used algorithm, called Complete Active Space Self-Consistent Field / Restricted Active Space State Interaction with Spin-Orbit coupling (CASSCF / RASSI-SO), which has been used to study many properties of lanthanide complexes such as the energy and angular momentum decomposition of crystal field states and the orientation and magnitude of their magnetic anisotropy, the wave functions of a manifold of spin states arising from excitations of 4f electrons within the ligand field space are optimized and subsequently used to represent the Spin-Orbit Coupling (SOC) operator. While this approach has proved very useful and sufficiently accurate to describe ground-state magnetic properties and a few low-energy crystal field excitations relevant to describe slow magnetic relaxation in these systems, the approach requires separate CASSCF orbital optmizations for different spin states, which makes the method scale unfavourably, especially for ions like Dy or Tb where several spin manifolds can be mixed by strong spin-orbit coupling.
Assuming that, in lanthanide complexes, the 4f-like valence orbitals are not changing significantly when optimized for different spin states, and based on the fact that the total spin is not a good quantum number because of the strong spin-orbit coupling, I contributed here to develop an alternative computational strategy, in which a Configurational- Averaged Hartree-Fock (CAHF) calculation is first performed by variationally optimizing the set of 4f orbitals that minimizes the average energy of the entire manifold of ligand field states, irrespective of their spin, followed by a Complete Active Space Configuration Interaction with Spin-Orbit (CASCI-SO) calculation in which both the electronic CI and the SOC Hamiltonian are built in the complete spin states basis generated from the common set of CAHF-optimized orthogonal 4f orbitals, thereby overcoming one of the computational limitations of the CASSCF / RASSI-SO approach. CAHF / CASCI-SO is predicted to be a more efficient algorithm, albeit conceptually different, than CASSCF / RASSI-SO and, in order to both test its performance and provide a platform for its application to the magnetic characterization of lanthanide complexes, it has been implemented in an efficient ab initio software, named Computational Emulator of Rare Earth Systems (CERES), whose structure is presented and discussed. CERES implements an efficient direct HF procedure, coupled with efficient integral calculation and screening and a robust mixed first-second order convergence algorithm based on, respectively, Direct Inversion in the Iterative Subspace (DIIS) and Quasi-Newton (QN) methods. CERES also features some new algorithms, tailor-suited to lanthanide complexes, such as an efficient initial CAHF guess based on the Superposition of Atomic Densities (SOAD) method, where partial charges can be added so as to improve the guess, and an efficient method, based on Population Analysis (PA) for single orbitals during the configurational-averaged SCF cycle, in which the wave function is transformed at every CAHF iteration so as to present an active space with the highest 4f character possible.
The efficiency of CAHF / CASCI-SO, as implemented in our in-house ab initio code CERES, has then been tested by comparing timings and accuracy for the calculation of the resulting magnetic properties of a set of lanthanide complexes using CERES with those of the well-known software MOLCAS, which features an efficient implementation of the CASSCF/RASSI-SO method. The results show that the CAHF/CASCI-SO strategy, despite being a conceptually different method, is significantly more efficient than CASSCF / RASSI-SO, while not leading to any systematic loss of accuracy. The effectiveness of the PA method is also tested, with the resulting data showing that the PA method introduces big improvements in both reliability and efficiency of the calculation.
Moreover, I have carried out further work on the theoretical modelling of the electronic structure of strongly anisotropic open-shell molecules, such as lanthanide complexes, in the context of the optimization of chiral paramagnetic systems which are suitable candidates to achieve direct chiral discrimination in Nuclear Magnetic Resonance (NMR) spectroscopy. In this Thesis, in fact, the generalization of direct chiral discrimination theory in NMR spectroscopy for open-shell molecules is also presented. Chirality plays a fundamental role in biological processes, therefore the development of new experimental techniques which are capable to directly discriminate between the two enantiomers of a chiral molecule is a very active research field. Among the experimental techniques available for performing direct chiral discrimination, that is discrimination achieved within an achiral environment by probing molecular observables that have different values for the two enantiomers of a chiral molecule (typically same magnitude but opposite sign, i.e. they are odd under spacial inversion), NMR spectroscopy would be an ideal choice because of its non-invasive character, of its high measurement speed and of its sensitivity to tiny details of the electronic and geometric structure of the molecule. Due to the even character under space inversion of the shielding tensor and of the spin-spin coupling tensor, however, two enantiomers will not be distinguishable in a typical NMR experimental set up.
Recently, Buckingham and Fischer predicted that, in a pulsed NMR experiment, the external magnetic field and the rotating nuclear magnetic moments generate a macrocopic rotating chiral electric polarization which can be detected as an AC-voltage between the plates of a capacitor. In a subsequent publication, Buckingham described a second contribution to the chiral NMR experiment arising from the rotation of the permanent electric dipole of the molecule under the torque generated by the external magnetic field and the rotating nuclear moment. Although this contribution has been predicted to be stronger, computational tests on a wide range of closed-shell molecules predicted this effect to be too small to be detectable at room temperature.
By applying third-order perturbation theory to the electronic free energy, following the approach proposed by Soncini and Van den Heuvel for the NMR chemical shifts in paramagnetic molecules, based on Feynman free-energy perturbation theory, the chiral effect described by Buckingham has been generalized to molecules with an arbitrary electronic structure. The new property, named generalized shielding polarizability tensor, features additional contributions with respect to Buckingham’s theory, which are non- zero only in open-shell molecules. One of these new temperature-dependent contributions describes a combined orientational mechanism, whereby the external magnetic field partially orients the paramagnetic molecules along their magnetic anisotropy axis, while the combined effect of the external field and of the perpendicular rotating nuclear magnetic dipole coupled to the dipolar field generated by the paramagnetic ion at the NMR-probed nuclear site exerts a torque on the molecular permanent electric dipole, thus inducing a rotation of the latter, resulting in a rotating macroscopic electric polarization which is predicted to be detectable at room temperature in some lanthanide complexes.
Since the new predicted mechanism is particularly relevant for strongly anisotropic molecules, such as lanthanide SMMs, two sets of calculations of this property for a range of Dy SMMs have been performed. In the first study, Thermally Isolated Ground State (TIGS) approximation is employed by assuming only the ground state energy level is thermally populated at room temperature so as to estimate the magnitude of the novel physical mechanism. Results show that, for all complexes, room temperature detectability is indeed achievable, predicting that direct chiral discrimination via NMR spectroscopy is possible. In the second study, excited states are also included so as to estimate the relative magnitude of the three physical mechanisms. Results show that our proposed physical mechanism is indeed the most relevant component for strongly anisotropic molecules, with the presence of thermally populated excited states not hindering room temperature detectability.

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