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

Abstract

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.