Exploring the Coexistence of Spin States in [Fe-(tpy-ph)$_2$]$^{2+}$ Complexes on Au(111) using ab initio calculations

Abstract: In this work, we systematically study the electronic structure and stability of spin states of the [Fe-(tpy-ph)$_2$]$^{2+}$ molecule in both gas phase and on a Au(111) substrate using density functional theory +U (DFT+U) calculations. We find that the stability of the Fe$^{2+}$ ion's spin states is significantly influenced by the Hubbard U parameter. In the gas phase, the low-spin (LS, S=0) state is found to be energetically favorable for U(Fe) $\leq$ 3 eV, whereas the high-spin (HS, S=2) state is stabilized for U(Fe) > 3 eV. Interaction with the Au(111) substrate is found to elevate the critical U for the spin-state transition to 3.5 eV. Additionally, we perform L-edge X-ray absorption spectroscopy (XAS) calculations based on time-dependent DFT (TD-DFT) for both HS and LS states. The calculated XAS suggests that the HS state more closely aligns with the experimental observations, indicating the potential coexistence of the HS state as the initial state during the X-ray excitation process. These findings enrich our understanding of spin-state dynamics in [Fe-(tpy-ph)$_2$]$^{2+}$.