@Article{JPhysChemA_111_9145,
author = {M. Atanasov and P. Comba and C.A. Daul and A. Hauser},
title = {{DFT-Based Studies on the Jahn-Teller Effect in 3d Hexacyanometalates with Orbitally Degenerate Ground States}},
journal= {J. Phys. Chem. A},
ISSN = {1089-5639},
volume= {111},
number= {37},
pages = {9145-9163},
url = {http://pubs.acs.org/cgi-bin/abstract.cgi/jpcafh/2007/111/i37/abs/jp0731912.html},
eprint= {http://www.unige.ch/sciences/chifi/publis/refs_pdf/ref00900.pdf},
doi= {10.1021/jp0731912},
abstract = {{The topology of the ground-state potential energy surface of M(CN)$_6$ with orbitally degenerate $^2$T$_{2g}$ (M = Ti$^{III}$ (t$_{2g}^{1}$), Fe$^{III}$ and Mn$^{II}$ (both low-spin t$_{2g}^{5}$)) and $^{3}$T$_{1g}$ ground states (M = V$^{III}$ (t$_{2g}^{2}$), Mn$^{III}$ and Cr$^{II}$ (both low-spin t$_{2g}^{4}$)) has been studied with linear and quadratic Jahn-Teller coupling models in the five-dimensional space of the $\epsilon_{g}$ and $\tau_{2g}$ octahedral vibrations (T$_{g}$â($\epsilon_{g}$+$\tau_{2g}$) Jahn-Teller coupling problem (T$_{g}$ = $^{2}$T$_{2g}$, $^{3}$T$_{1g}$)). A procedure is proposed to give access to all vibronic coupling parameters from geometry optimization with density functional theory (DFT) and the energies of a restricted number of Slater determinants, derived from electron replacements within the t$_{2g}^{1,5}$ or t$_{2g}^{2,4}$ ground-state electronic configurations. The results show that coupling to the $\tau_{2g}$ bending mode is dominant and leads to a stabilization of {\em D}$_{3}${\em $_{d}$} structures (absolute minima on the ground-state potential energy surface) for all complexes considered, except for [Ti(CN)$_{6}$]$^{3-}$, where the minimum is of {\em D}$_{4}${\em $_{h}$} symmetry. The Jahn-Teller stabilization energies for the {\em D}$_{3}${\em $_{d}$} minima are found to increase in the order of increasing CN-M $\pi$ back-donation (Ti$^{III}$ < V$^{III}$ < Mn$^{III}$ < Fe$^{III}$ < Mn$^{II}$ < Cr$^{II}$). With the angular overlap model and bonding parameters derived from angular distortions, which correspond to the stable {\em D}$_{3}${\em $_{d}$} minima, the effect of configuration interaction and spin-orbit coupling on the ground-state potential energy surface is explored. This approach is used to correlate Jahn-Teller distortion parameters with structures from X-ray diffraction data. Jahn-Teller coupling to trigonal modes is also used to reinterpret the anisotropy of magnetic susceptibilities and g tensors of [Fe(CN)$_{6}$]$^{3-}$, and the $^{3}$T$_{1g}$ ground-state splitting of [Mn(CN)$_{6}$]$^{3-}$, deduced from near-IR spectra. The implications of the pseudo Jahn-Teller coupling due to t$_{2g}$-e$_{g}$ orbital mixing via the trigonal modes ($\tau_{2g}$) and the effect of the dynamic Jahn-Teller coupling on the magnetic susceptibilities and g tensors of [Fe(CN)$_{6}$]$^{3-}$ are also addressed.}},
year = {2007}
}