Ground state of a spin-crossover molecule calculated by diffusion Monte Carlo

Spin-crossover molecules have recently emerged as a family of compounds potentially useful for implementing molecular spintronics devices. The calculations of the electronic properties of such molecules is a formidable theoretical challenge, as one has to describe the spin ground state of a transition metal as the ligand field changes. The problem is dominated by the interplay between strong electron correlation at the transition-metal site and charge delocalization over the ligands, and thus it fits into a class of problems where density functional theory may be inadequate. Furthermore, the crossover activity is extremely sensitive to environmental conditions, which are difficult to fully characterize. Here we discuss the phase transition of a prototypical spin-crossover molecule as obtained with diffusion Monte Carlo simulations. We demonstrate that the ground state changes depending on whether the molecule is in the gas or in the solid phase. As our calculation provides a solid benchmark for the theory, we then assess the performances of density functional theory. We find that the low-spin state is always overstabilized, not only by the (semi-)local functionals, but even by the most commonly used hybrids (such as B3LYP and PBE0). We then propose that reliable results can be obtained by using hybrid functionals containing about $50\%$ of exact exchange.

Figure 1

The cationic unit [FeL${}_2$]${}^{2+}$ (L $=$ 2,6-dypirazol-1-yl-4-hydroxymethylpyridine) used in the DMC calculations. Color code: C: yellow; O: red (small sphere); Fe: red (large sphere); N: gray; H: blue.

Figure 2

Potential-energy surface of the HS and LS state of a SC molecule. The collective coordinate $r$ represents all of the nuclear coordinates of the molecule and interpolates between the LS and the HS geometries. The adiabatic energy gap $\Delta E^{\mathrm{adia}}$ and the vertical energy gaps $\Delta E_{\mathrm{LS}}^{\mathrm{vert}}=\Delta E^{\mathrm{vert}}\left(r_{\mathrm{LS}}\right)$ and $\Delta E_{\mathrm{HS}}^{\mathrm{vert}}=\Delta E^{\mathrm{vert}}\left(r_{\mathrm{HS}}\right)$ are also indicated.