Benchmarking Periodic Density Functional Theory Calculations for Spin-State Energies in Spin-Crossover Systems

Spin energetics is one of the biggest challenges associated with energy calculations for electronic structure methods. The energy differences of the spin states in spin-crossover compounds are very small, making them one of the most difficult systems to calculate. Few methods provide accurate results for calculating these energy differences. In addition, studies have usually focused on calculating energetics of single molecules, while spin-crossover properties are usually experimentally studied in the solid phase. In this paper, we have used periodic boundary conditions employing methods based on density functional theory to calculate the high- and low-spin energy differences for a test case of 20 extended systems. Compounds with different metals and ligands have been selected, and the results indicate that a semiquantitative description of the energy differences can be obtained with the combination of geometry optimization using the PBE functional including many-body dispersion approach and the use of meta-GGA functionals, such as r2SCAN but especially KTBM24, for the energy calculation. Other hybrid functionals, such as TPSSh, give generally good results, but the calculation of the exact exchange with periodic boundary conditions involves a huge increase in computer time and computational resources. It makes the proposed nonhybrid functional approach (KTBM24//PBE+MB) a great advantage for the study of periodic systems.

Effect of Exocyclic Substituents and π-System Length on the Electronic Structure of Chichibabin Diradical(oid)s

The ground state (GS) of Chichibabin's polycyclic hydrocarbons (CPHs) can be singlet [open- or closed-shell (OSS or CS)] or triplet (T), depending on the elongation of the π-system and the exocyclic substituents. CPHs with either a small singlet-triplet energy gap (ΔE ST) or even a triplet GS have potential applications in optoelectronics. To analyze the effect of the size and exocyclic substituents on the nature of the GS of CPHs, we have selected a number of them with different substituents in the exocyclic carbon atoms and different ring chain lengths. The OPBE/cc-pVTZ level of theory was used for the optimization of the systems. The aromaticity of the resulting electronic structures was evaluated with HOMA, NICS, FLU, PDI, Iring, and MCI aromaticity indices. Our results show that the shortest π-systems (one or two rings) have a singlet GS. However, systems with three to five rings favor OSS GSs. Electron-withdrawing groups (EWGs) and aromatic substituents in the exocyclic carbons tend to stabilize the OSS and T states, whereas electron-donating groups slightly destabilize them. For CS, OSS, and T states, aromaticity measures indicate a gain of aromaticity of the 6-membered rings of the CPHs with the increase in their size and when CPHs incorporate EWGs or aromatic substituents. In general, the CPHs analyzed present small singlet-triplet energy gaps, and in particular, the ones containing EWGs or aromatic substituents present the smallest singlet-triplet energy gaps.

Spinning around in Transition-Metal Chemistry

The great diversity and richness of transition metal chemistry, such as the features of an open d-shell, opened a way to numerous areas of scientific research and technological applications. Depending on the nature of the metal and its environment, there are often several energetically accessible spin states, and the progress in accurate theoretical treatment of this complicated phenomenon is presented in this Account. The spin state energetics of a transition metal complex can be predicted theoretically on the basis of density functional theory (DFT) or wave function based methodology, where DFT has advantages since it can be applied routinely to medium-to-large-sized molecules and spin-state consistent density functionals are now available. Additional factors such as the effect of the basis set, thermochemical contributions, solvation, relativity, and dispersion, have been investigated by many researchers, but challenges in unambiguous assignment of spin states still remain. The first DFT studies showed intrinsic spin-state preferences of hybrid functionals for high spin and early generalized gradient approximation functionals for low spin. Progress in the development of density functional approximations (DFAs) then led to a class of specially designed DFAs, such as OPBE, SSB-D, and S12g, and brought a very intriguing and fascinating observation that the spin states of transition metals and the S_N2 barriers of organic molecules are somehow intimately linked. Among the many noteworthy results that emerged from the search for the appropriate description of the complicated spin state preferences in transition metals, we mainly focused on the examination of the connection between the spin state and the structures or coordination modes of the transition metal complexes. Changes in spin states normally lead only to changes in the metal-ligand bond lengths, but to the best of our knowledge, the dapsox ligand showed the first example of a transition-metal complex where a change in spin state leads also to changes in the coordination, switching between pentagonal-bipyramidal and capped-octahedron. Moreover, we have summarized the results of the thorough study that corrected the experimental assignment of the nature of the recently synthesized Sc³⁺ adduct of [Fe^IV(O)(TMC)]²⁺ (TMC = 1,4,8,11-tetramethylcyclam) and firmly established that the Sc³⁺-capped iron-oxygen complex corresponds to high-spin Fe^III. Last, but not least, we have provided deeper insight and rationalization of the observation that unlike in metalloenzymes, where the Fe^IV-oxo is usually observed with high spin, biomimetic Fe^IV-oxo complexes typically have a intermediate spin state. Energy decomposition analyses on the trigonal-bypiramidal (TBP) and octahedral model systems with ammonia ligands have revealed that the interaction energy of the prepared metal ion in the intermediate spin state is much smaller for the TBP structure. This sheds light on the origin of the intermediate spin state of the biomimetic TBP Fe^IV-oxo complexes.

Predicting the spin state of paramagnetic iron complexes by DFT calculation of proton NMR spectra

Many transition-metal complexes easily change their spin state S in response to external perturbations (spin crossover). Determining such states and their dynamics can play a central role in the understanding of useful properties such as molecular magnetism or catalytic behavior, but is often far from straightforward. In this work we demonstrate that, at a moderate computational cost, density functional calculations can predict the correct ground spin state of Fe(ii) and Fe(iii) complexes and can then be used to determine the (1)H NMR spectra of all spin states. Since the spectral features are remarkably different according to the spin state, calculated (1)H NMR resonances can be used to infer the correct spin state, along with supporting the structure elucidation of numerous paramagnetic complexes.

Charge transport properties of spin crossover systems

The study of spin crossover compounds by means of theoretical or experimental approaches has provided interesting results in recent decades. The main feature of such compounds is the change in the spin state induced by many different external stimuli, i.e. temperature, light, pressure, solvent coordination and the electric field. Spin crossover systems are potentially more useful than other magnetic molecules because their switching behaviour can occur closer to room temperature, and they are thus candidates for use in spintronic devices. Here, I review the state of the art in quantum chemical approaches to the study of such systems and discuss experiments that have focused on transport properties in single-molecule, nano-objects or thin-film spin crossover systems.