A Wave Function Theory and Density Functional Theory Investigation of Ground and Excited States of HfSi

In this work, the reaction between Hf and Si atoms was explored using high-level ab initio multireference configuration interaction (MRCI), coupled-cluster wave function methods, and density functional theory (DFT), in conjugation with large correlation-consistent basis sets. A comprehensive set of potential energy curves (PECs), spin-orbit curves, permanent dipole moment (PDM) curves, transition dipole moment (TDM) curves, chemical bonding patterns, spectroscopic parameters, and energy-related properties were determined. The two most stable electronic states of HfSi (1³Π and 1¹Σ⁺) exhibit 1σ²2σ²3σ¹1π³ and 1σ²2σ²1π⁴ electron configurations, respectively, with approximate charge localization of Hf^+0.50Si^-0.50. Both coupled-cluster and MRCI built on state-specific complete active space self-consistent field (CASSCF) wave functions predicted the 1¹Σ⁺ state to be slightly more stable than the 1³Π state. The spin-orbit ground state of HfSi is an Ω = 0⁺ state composed of 52% of 1³Π and 41% 1¹Σ⁺ character. Considering a few low-lying states, the rovibrational line spectrum of HfSi was investigated at 700 and 3000 K, and the spin-orbit effects were found to be significant. The dissociation energy (D₀) of HfSi, estimated by accounting for higher-order electron correlation effects, complete basis set corrections, and spin-orbit effects, [CBS-C-CCSD(T)+δT(Q)+SO], is 2.855 eV, in good agreement with the experimental value. The bond energies and electron populations of the isovalent HfX (X = C, Ge, Sn, Pb) were also investigated, showing a decrease in bond energy from X = C to X = Pb. A strong linear relationship between bond energy and ionicity was observed across the series. Finally, the performance of 16 exchange-correlation functionals, spanning three rungs of Jacob's ladder of density functional approximations (DFAs), was assessed against the coupled-cluster results.