Application of Gradient-Corrected Density Functional Theory to the Structures and Thermochemistries of $\mbox{ScF}_3$, $\mbox{TiF}_4$, $\mbox{VF}_5$, and $\mbox{CrF}_6$

Density functional theory(DFT) and Hartree-Fock(HF) calculations are reported for the family of transition metal fluorides $\mbox{ScF}_3$, $\mbox{TiF}_4$, $\mbox{VF}_5$, and $\mbox{CrF}_6$. Both HF and the local-density-aproximation (LDA) yield excellent agreement with experimental bond lengths, while the B-LYP gradient-corrected density functional gives bond lengths $0.04-0.05$ Å too long. An investigation of various combinations of exchange and correlation functionals shows that, for this series, the origin of this behavior lies in the Becke exchange functional. Much improved bond distances are found using the hybrid HF/DFT functional advocated by Becke. This approximation also leads to much improved thermochemistries. The LDA overestimates average bond energies in this series by $30-40$ kcal/mol, whereas the B-LYP functional overbinds by only $\sim8-12$ kcal/mol, and the hybrid HF/DFT method overbinds by only $\sim 2$ kcal/mol. The hybrid method predicts the octahedral isomer of $\mbox{CrF}_6$ to be more stable than the trigonal prismatic form by $14$ kcal/mol. Comparison of theoretical vibrational frequencies with experiment supports the assignment of an octahedral geometry.

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