Geometric and electronic structures of FeBn−/0/+ clusters (n = 1–3): insights from advanced computational methods

Abstract

Context

Boron-doped iron clusters are extensively studied for their potential in materials science. Despite several quantum calculations with DFT and MRCI methods, a comprehensive understanding of the geometric and electronic structures of small FeB_n^−/0/+ clusters (n = 1–3) is still lacking. This work provides new insights into ground and low-lying excited states, detachment energies, and ionization energies of these clusters using DFT and multireference CASPT2, RASPT2, and DMRG-CASPT2 computational methods. Key findings reveal ³Σ⁻, ⁴Σ⁻, and ³Σ⁻ as ground states for FeB^−/0/+, and cyclic-FeB₂^−/0/+ isomers (⁴B₂, ³B₂, ⁴B₁) as the most stable for FeB₂^−/0/+ clusters. For FeB₃ clusters, anionic species have a tetrahedral geometry, while neutral and cationic species favor rhombic structures. Detachment energies of the anionic ground states increase progressively from FeB⁻ to cyclic-FeB₂⁻, and further to the tetrahedral-FeB₃⁻ isomer, which correlates with the number of boron atoms bonded to the iron atom. The vibrational progression in transitions within tetrahedral-FeB₃^−/0 is more prominent than in FeB^−/0 clusters and cyclic-FeB₂^−/0 isomers. The ionization energies of neutral ground states rise from FeB clusters to rhombic-FeB₃ and cyclic-FeB₂ isomers.

Methods

The geometry optimization and vibrational frequency calculations for the electronic states of FeB₂^−/0/+ and FeB₃^−/0/+ clusters were conducted using density functional theory (DFT) with the BP86 and MN15 functionals and the def2-QZVP basis set, implemented in ORCA 5.0. Franck–Condon factor simulations were performed using the ezSpectra suite, based on DFT-derived geometries and vibrational normal modes. Multireference RASPT2 and CASPT2 calculations utilized OpenMolcas, while DMRG-CASPT2 calculations employed ChemPS2 interfaced to OpenMolcas. The aug-cc-pwCVQZ-DK basis set was applied to iron, and aug-cc-pVQZ-DK to boron. The 1 s, 2 s, and 2p orbitals of iron and the 1 s orbital of boron were frozen in the second-order perturbation calculations. IPEA and imaginary shift parameters were set to 0.25 and 0.10, respectively. To achieve high accuracy, the DMRG-CASPT2 active spaces were expanded to 22 orbitals for FeB^−/0/+ and FeB₂^−/0/+, and 23 orbitals for FeB₃^−/0/+.