DFT-Based Studies on the Jahn−Teller Effect in 3d Hexacyanometalates with Orbitally Degenerate Ground States

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 g and τ 2g octahedral vibrations (T g X( g +τ 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 τ 2g bending mode is dominant and leads to a stabilization of D 3d 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 D 4h symmetry. The Jahn-Teller stabilization energies for the D 3d minima are found to increase in the order of increasing CN-M π 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 D 3d 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 (τ 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.

Density functional theory study of the Jahn-Teller effect in cobaltocene

“…These alternative para meters are connected to the set of parameters discussed in previous sections using the following relations [2]: (11) (12) (13) In this paper, we use DFT, today the method of choice in theoretical coordination chemistry. DFT is a single-determinant method.…”

“…Additionally, conventional single-determinant DFT has been extended to handle multiplet problem [9,10]. Application of multideterminental DFT to the JT systems has been developed in our group [11] and used with success [11][12][13].…”

DFT study of the Jahn–Teller effect in Cu(II) chelate complexes

“…Several studies [13,18,19] 3+ isomers LDA and the generalized gradient approximation (GGA) with Becke exchange [21] and Perdew correlation [22] (BP86) and in the form given by Perdew-Wang (PW91) [23,24] have been compared. All electron Triple-zeta Slater-type orbital (STO) plus one polarization function (TZP) basis set have been used for all atoms.…”

Density Functional Theory Study of the Multimode Jahn-Teller Effect – Ground State Distortion of Benzene Cation

“…KS-DFT in its present implementations is not able to derive correct energies in the case of orbital degeneracy [3,9,10]. On the other hand, multideterminental-DFT approach, developed by Daul et al [11,12], can be successfully applied for detailed analysis of the JT active molecules [10][11][12][13][14][15][16][17][18][19][20]. This method gives the JT parameters, Fig.…”