# Applying advanced quantum mechanical techniques to describe d-orbital excitations in highly correlated systems

# Applying advanced quantum mechanical techniques to describe d-orbital excitations in highly correlated systems

Promotor(en):**20SPEC02**/ Spectroscopy**V. Van Speybroeck**/## Probleemstelling:

Metal-organic frameworks (MOFs) are a new class of porous materials built up out of metal-based units connected by organic linkers. These materials have unique properties and are very promising for numerous applications. However, the MOF formation process, nucleating from isolated transition metal complexes to porous crystals, is not well understood. Spectroscopic techniques are an indispensable tool when we want to understand this complicated process: when various building blocks form larger units, the observed spectroscopic signals change and may thus be used to follow the nucleation in-situ. Recently, UV-Vis spectroscopy was employed to provide unprecedented insight as it sheds light on the electronic transitions and is widely used to characterize the structure of the material in which the transition takes place.

However, the experimentally observed spectra are often hard to interpret and it is complicated to relate observed signals to molecular structures of the involved complexes. To this end, computational methods are more and more used to determine the electronic structure of ground- and excited states and to computationally predict and interpret the UV-Vis spectra.

An example of such an important spectroscopic fingerprint to follow in situ the nucleation of MOFs that contain transition metals is the splitting of the d-orbitals of this transition metal when it coordinates to ligands. However, computationally characterizing the complicated electronic structure of these states is highly challenging. As these correlated states cannot be written as a single Slaterdeterminant, they are prone to static electron correlation. High-level wave-function based ab initio methods beyond Hartree-Fock, such as complete active space self-consistent field (CASSCF) and multi-reference configuration interaction (MRCI), are therefore needed. Furthermore, depending on the electron distribution among the d-orbitals, the system can be in a high or low spin state. It is still an open question which quantum mechanical techniques are capable of calculating the relative stability of these spin systems accurately and current insight into the performance of these methods on transition metal complexes is still lacking.

The calculation of excited state properties poses even more challenges. Transition energies and probabilities can, just like the ground-state properties, be calculated by wave-function based methods. However, applying these techniques to those complexes is not straightforward and computationally very expensive. Therefore, one often relies on another many-body technique which is computationally much more attractive, namely time-dependent density-functional theory (TD-DFT). This technique relies on the one-dimensional density instead of the much more complicated high-dimensional wave function. This is nowadays recognized as a powerful and reliable methodology to reproduce excited-state properties for a wide range of molecular systems. However, determining excited state properties of transition metal complexes is not trivial with TD-DFT due to their complex electronic structure. Therefore, a more thorough investigation on this matter is highly requested.

## Doelstelling:

The objective of this thesis is to accurately describe both ground- and excited states of a series of d2–d8 hexaaqua coordinated transition metal complexes [M(H2O)6]n+ with M a 3d transition metal ion (V2+/3+, Cr2+/3+, Mn2+/3+, Fe2+/3+, Co2+/3+, Ni2+/3+). These systems are highly interesting as they are the building blocks for materials like MOFs. Moreover, they exhibit orbital occupation schemes ranging from 2 to 8 d-electrons. To this end, both DFT and wave-function based methods will be used.

A first goal is to perform an extended theoretical study to make the thesis student familiar with the different concepts of wave-function based quantum mechanical methods such as CASSCF and MRCI. A good review on these accurate ab initio theoretical tools is given in Ref. [1]. One of the authors, F. Neese, is also a main developer of the ORCA program package, one of the prominent codes in the field of advanced ab initio electronic structure methods. With these techniques, you will be able to study the relative stability among different spin configurations and gain new insights into the characteristics related to the number of d-electrons.

The second goal of the thesis is to systematically investigate the advantages and drawbacks of TD-DFT in the study of the d–d transition energies and probabilities. The CMM has ample expertise with this technique and the concepts of it are explained thoroughly in literature, for example in Ref. [2]. Adequate experimental data are available and can be used to assess the accuracy of TD-DFT. As these transition metal complexes are highly symmetric (see figure), the semi-empirical symmetry-based ligand field theory (LFT) seems a natural approach to interpret the extremely diverse excitation spectra. While LFT also allows one to qualitatively determine the splitting pattern of the d-orbitals (see figure), it fails for some high-spin complexes.

Within this thesis, we will also investigate the influence of reduced symmetry on the predicted UV-Vis spectra by considering complexes in which the symmetry is systematically reduced, and compare TD-DFT to higher-level wave-function based methods. To this end, some of the water ligands in [M(H2O)6]2+/3+ will be replaced by ammonia or methanol resulting in transition metal complexes with lower symmetry. This aspect is highly relevant for experiments as this symmetry reduction naturally takes place in the nucleation of transition metal complexes in the formation of MOFs, but it has never been investigated before.

A thesis student choosing this topic should be interested in the fundamental quantum mechanical description of small molecular complexes and eager to apply various theoretical techniques to interesting complexes for which experimental data are available. The student will be actively coached to get acquainted as soon as possible with all necessary techniques to perform the suggested research successfully. The topic further builds on concepts such as many body techniques and spectroscopy which were taught within the course Atomic and Molecular Physics.

- Study programmeMaster of Science in Engineering Physics [EMPHYS], Master of Science in Physics and Astronomy [CMFYST]KeywordsSpectroscopy, time-dependent density-functional theory, Quantum mechanics, transition metal complexes, symmetryReferences
1. F. Neese et al., ’Advanced aspects of ab initio theoretical optical spectroscopy of transition metal complexes: Multiplets, spin-orbit coupling and resonance Raman intensities.’, Coord. Chem. Rev. 251, 288-327 (2007)

2. M.E. Casida and M. Huix-Rotllant, ‘Progress in Time-Dependent Density-Functional Theory’, Annu. Rev. Phys. Chem. 63, 287-323 (2012).

3. F. Vlahović et al., ‘Assessment of TD-DFT and LF-DFT for study of d-d transitions in first row transition metal hexaaqua complexes’, J. Chem. Phys. 142, 214111 (2015).