Towards an accurate and computationally-efficient modelling of Fe(ii)-based spin crossover materials

Abstract

The DFT + U methodology is regarded as one of the most-promising strategies to treat the solid state of molecular materials, as it may provide good energetic accuracy at a moderate computational cost. However, a careful parametrization of the U-term is mandatory since the results may be dramatically affected by the selected value. Herein, we benchmarked the Hubbard-like U-term for seven Fe(ii)N6-based pseudo-octahedral spin crossover (SCO) compounds, using as a reference an estimation of the electronic enthalpy difference (ΔHelec) extracted from experimental data (T1/2, ΔS and ΔH). The parametrized U-value obtained for each of those seven compounds ranges from 2.37 eV to 2.97 eV, with an average value of U = 2.65 eV. Interestingly, we have found that this average value can be taken as a good starting point since it leads to an unprecedented mean absolute error (MAE) of only 4.3 kJ mol(-1) in the evaluation of ΔHelec for the studied compounds. Moreover, by comparing our results on the solid state and the gas phase of the materials, we quantify the influence of the intermolecular interactions on the relative stability of the HS and LS states, with an average effect of ca. 5 kJ mol(-1), whose sign cannot be generalized. Overall, the findings reported in this manuscript pave the way for future studies devoted to understand the crystalline phase of SCO compounds, or the adsorption of individual molecules on organic or metallic surfaces, in which the rational incorporation of the U-term within DFT + U yields the required energetic accuracy that is dramatically missing when using bare-DFT functionals.

Cooperativity of Spin Crossover Complexes: Combining Periodic Density Functional Calculations and Monte Carlo Simulations

“…It is assumed here that the cutoff of 50 Ry for the plane waves that has been used in ref. [12] is too low in energy so that precision changes coming along with changes of the cell size during cell optimization produced artefacts [23]. The present calculations with a cutoff of 75 Ry instead have reproduced well the degeneracy of equivalent configurations.…”

“…The proper choice of the Hubbard parameter U is obviously connected to the choice of the density functional. For calculations employing gradient corrected functionals values of about 2.5 eV are normally chosen for U [19,21,23] whereas larger U values were reported for LDA calculations [12,22]. It is known that electron correlation is less well accounted for by local density functionals than by gradient corrected ones, and, therefore, LDA methods need a larger U in order to localize the strongly correlated iron 3d electrons.…”

“…1) has been chosen as a complex that is most suitable to test the methods described above. It certainly is one of the most intensively studied SCO complex and also one of the very few that have been studied by periodic DFT calculations [12,[19][20][21][22][23][24]. High precision crystal structures are available for the HS and LS phases at different temperatures down to 15 K [25,26].…”

Periodic Density Functional Calculations in Order to Assess the Cooperativity of the Spin Transition in Fe(phen)2(NCS)2

“…Wavefunction based methods have the advantage that in principle any order of accuracy can be reached. However, since the spin crossover is the result of a delicate balance of different contributions to the electronic energy, reasonably accurate results for ∆E HL can only be reached with sophisticated post-HF methods, which can currently only be applied to systems with a few atoms [12]. For this reason practically all electronic structure calculations on realistic SCO systems have been performed with methods utilizing density functional theory (DFT), either with pure density functionals or with hybrid functionals which include some amount of HF exchange like B3LYP* [13].…”

Disclosing the Ligand- and Solvent-Induced Changes on the Spin Transition and Optical Properties of Fe(II)-Indazolylpyridine Complexes

“…However, some advances have been made in the field and, especially, in the application of DFT + U to calculate the adiabatic energy difference between the LS and HS phases of SCO compounds in their unit cells, thus, accounting for all the crystal packing effects and weak interactions [22]. This is a promising strategy that paves the way for the close collaboration of experimentalists and theoreticians in the quest for SCO compounds presenting a wide hysteresis loop that encompasses room temperature.…”