V 3 : Structure and vibrations from density functional theory, Franck–Condon factors, and the pulsed-field ionization zero-electron-kinetic energy spectrum

Density functional calculations of neutral and cationic vanadium trimers are presented. The all-electron calculations employed a gradient-corrected exchange-correlation functional and a newly developed vanadium basis set optimized for gradient-corrected density functional calculations. For both neutral and charged systems, different isomers were studied in order to determine the lowest energy structures. A vibrational analysis was performed in order to characterize these isomers. We found an equilateral triangle ${}^2{\mathrm{A}}_1^{\prime }$ ground state for ${\mathrm{V}}_3$ and an equilateral triangle ${}^3{\mathrm{A}}_2^{\prime }$ ground state for ${\mathrm{V}}_3^{+}.$ The experimental pulsed-field ionization zero-electron-kinetic energy spectrum was simulated by calculating multidimensional Franck–Condon factors, using the geometries and harmonic frequencies of the calculated minima of ${\mathrm{V}}_3$ and ${\mathrm{V}}_3^{+}.$ The excellent agreement between the experimental and theoretical spectra allows the unequivocal determination of the ground state structure of ${\mathrm{V}}_3.$ This work provides a final answer to the controversy in the literature about the ground state structure of ${\mathrm{V}}_3$ and yields deeper insight into the electronic structure of the neutral and cationic systems.