Okayama University  Faculty of Science  Department of Physics  RIIS  Harald O. Jeschke

The study of metalorganic complexes has proven an innovative line of interdisciplinary research between physics and chemistry. In the process of the research, it turned out that in many metalorganic systems with interesting properties, a careful preparation of structures is a prerequisite before any further DFT analysis is possible. Therefore, the main methodological focus of this activity has been the development of a procedure that makes these materials accessible to precise electronic structure calculations; the approach can be characterized as structural design procedure for metalorganic materials. The usefulness of this development for future studies will become clear in the following description.

a) Design of the magnetic properties of a Cu²⁺ coordination polymer

A first study addressed the question whether the magnetic properties, namely the size of the interactions and the dimensionality of the underlying Hamiltonian, can be designed in the computer. This idea is based on the fact that synthetic chemistry is able to introduce small structural modifications which are significant for the magnetic interactions but do not change the basic crystal structure. Thus, the design of a material would proceed by introducing feasible substitutions or ligands to form a hypothetical structure which could then be recommended for synthesis if the analysis proved promising. This is a task of significant complexity because metalorganic materials have large unit cells containing many atoms, and the precise description of the transition metal centers translate to high demands on the precision of the DFT calculations. Therefore, achieving our aim required assembly of various force field and DFT methods, each of which had a precise purpose in the procedure: The design stage in which a hypothetical structure is constructed employs a force field because only this computationally light weight approach allows a global optimization, i.e. the search for the space group and lattice parameters of the new compound. The second, equilibration stage is performed with ab initio molecular dynamics; in this way, a local optimization (relaxation of the fractional coordinates) of the structures leads to the precise DFT equilibrium structure and is the prerequisite for the subsequent analysis: On the one hand, rough structures out of the force field relaxation often cause convergence problems in methods like FPLAPW and LMTO, and on the other, magnetic interaction pathways are very susceptible to even small changes in bond lengths and angles, and thus the analysis would be meaningless if it is not conducted on precise equilibrium structures. The third, analysis stage then involves calculation of the band structures and extraction of the underlying Hamiltonian by NMTO downfolding and by calculation of total energy differences between different spin configurations. The material that was chosen for testing the outlined approach is a coordination polymer containing Cu²⁺ centers and forms an antiferromagnetically coupled S = 1/2 Heisenberg chain. The crystal structure of this recently synthesized material [1] has been resolved by X-ray diffraction, and the exchange coupling of J = 20K was determined from the measured susceptibility. It turned out that it is possible to significantly vary the band width of the low energy bands close to the Fermi level and thus modify the exchange interaction strength between minus 90% and plus 25% via side chains to the polymer backbone or ligands. The modifications also proved suitable to change the dimensionality from purely one-dimensional towards more two- or even three-dimensional. The results of this study are published in Refs. [JSV+07,SJR+07].

b) Spin dimer system C₃₆H₄₈Cu₂F₆N₈O₁₂S₂ (TK91)

In the recently synthesized material TK91, two Cu²⁺ ions have been bridged via hydroquinone linkers [2]. The resulting Cu²⁺ dimers are arranged in the crystal in staggered chains. In a magnetic field, this spin dimer system exhibits an exotic magnetic state (probably a Kosterlitz-Thouless condensation of magnetic excitations). With the help of NMTO downfolding, we find that besides the dominant coupling in the Cu²⁺ dimer, there are, out of a large number of possible interaction pathways, only two further important interactions between Cu²⁺ centers. This allows the elucidation of the connectivity of the underlying model Hamiltonian which corresponds to a 2D network. Quantum Monte Carlo calculations with the model obtained in this way yields excellent agreement with the measured data. A publication is in preparation. The method of designing metalorganic materials with certain magnetic properties developed and tested on the Cu²⁺ polymer will become important when it is applied to materials that show important effects like TK91. Here, tuning of the material can yield insight into complex many body effects.

c) Microscopic investigation of a spin crossover coordination complex

In a second study, we have employed the method outlined under a) for the study of the microscopic origins of spin crossover. Spin crossover is an important phenomenon in which transition metal ions can be changed from a low spin to a high spin state by a change in temperature or pressure. This phenomenon has up to now been described by phenomenological models that assumed the mechanism of spin crossover to be elastic in origin; the purpose of the present investigation was to make progress towards a microscopic understanding of the phenomenon. Spin crossover is especially interesting in low dimensional systems because this makes the effect cooperative, leading to a large hysteresis in the transition temperatures.

An important family of spin crossover polymers are Fe²⁺ triazole systems. The difficulty for a microscopic study is the fact that these polymers form only nanocrystalline powders and thus their structure cannot be resolved with certainty. Besides, even candidates for the crystal structure contain so many atoms in the unit cell that the computational effort would be prohibitive. Therefore our study proceeds in two steps: in a first step, we use force field global optimization to construct a simplified model system that contains the crucial Fe²⁺ triazole backbone but has simplified counterions and side chains. In the second step, based on the fact that the spin state of iron depends on the bond lengths in the FeN₆ octahedron, we construct a series of structures with different sizes of the FeN₆ octahedron and relax them first with force field, then with Car Parrinello molecular dynamics methods. The structures obtained in this way show the transition from low spin to high spin in a straight forward way in spin resolved DFT. Furthermore, with the help of NMTO downfolding as well as total energy differences we can determine the strength of the magnetic exchange between Fe²⁺ centers in the polymer. We find that this exchange interaction is significant, making magnetic interactions equally important as elastic interactions for explaining the cooperative effect of the large hysteresis between high spin and low spin states. This study is published in Refs. [JSV+07,JSR+07].