Search for the ground-state electronic configurations of correlated organometallic metallocenes from constraint density functional theory

The ground-state electronic configurations of the correlated organometallic metallocenes, $M{\mathrm{Cp}}₂,\phantom{\rule{0.28em}{0ex}}M=\mathrm{V}$, Cr, Mn, Fe, Co, and Ni, are investigated using constraint density functional theory combined with nonempirical ${U}_{\mathrm{eff}}$ parameters determined from linear-response theory. The relative stability of the various $d$-orbital electronic configurations of these organometallic molecules is found to be sensitive to the amount of correlation. Using nonempirical values of ${U}_{\mathrm{eff}}$, the calculated electronic configurations are in agreement with the experiments: ${}⁴{A}_2g,\phantom{\rule{0.28em}{0ex}}{}³{E}_2g,\phantom{\rule{0.28em}{0ex}}{}⁶{A}_1g,\phantom{\rule{0.28em}{0ex}}{}¹{A}_1g,\phantom{\rule{0.28em}{0ex}}{}²{E}_1g$, and ${}³{A}_2g$ for the ${\mathrm{VCp}}₂,\phantom{\rule{0.28em}{0ex}}{\mathrm{CrCp}}₂,\phantom{\rule{0.28em}{0ex}}{\mathrm{MnCp}}₂,\phantom{\rule{0.28em}{0ex}}{\mathrm{FeCp}}₂,\phantom{\rule{0.28em}{0ex}}{\mathrm{CoCp}}₂$, and ${\mathrm{NiCp}}₂$, respectively.